Safety Prediction Methodology and Analysis Tool for Freeways and Interchanges (2021)

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523 APPENDIX D: PROPOSED HSM RAMPS CHAPTER CHAPTER 19—PREDICTIVE METHOD FOR RAMPS TABLE OF CONTENTS List of Figures ................................................................................................................................ 525 List of Tables .................................................................................................................................. 527 19.1. Introduction ........................................................................................................................... 531 19.2. Overview of the Predictive Method ....................................................................................... 531 19.3. Ramps—Definitions and Predictive Models .......................................................................... 532 19.3.1. Definition of Ramp Site Types ........................................................................................ 533 19.3.2. Predictive Model for Ramp Segments ............................................................................ 537 19.3.3. Predictive Model for Ramp Terminals ............................................................................ 539 19.4. Predictive Method for Ramps and Ramp Terminals ............................................................. 541 19.4.1. Step-by-Step Description of the Predictive Method ........................................................ 541 19.4.2. Data Needed to Apply the Predictive Method ................................................................ 549 19.5. Ramp Segments and Ramp Terminals ................................................................................. 559 19.5.1. Definition of Ramp Segment and Ramp Terminal .......................................................... 559 19.5.2 Segmentation Process .................................................................................................... 560 19.5.3. Crash Assignment to Sites ............................................................................................. 561 19.6. Safety Performance Functions .............................................................................................. 561 19.6.1. Safety Performance Functions for Ramp Segments ...................................................... 562 19.6.2. Safety Performance Functions for Ramp Terminals ...................................................... 570 19.7. Crash Modification Factors ................................................................................................... 583 19.7.1. Crash Modification Factors for Ramp Segments ............................................................ 584 19.7.2. Crash Modification Factors for Ramp Terminals ............................................................ 593 19.7.3. Supplemental Calculations to Apply Crash Modification Factors ................................... 606 19.8. Severity Distribution Functions ............................................................................................. 612

524 19.8.1. Severity Distribution Functions for Ramp Segments ...................................................... 613 19.8.2. Severity Distribution Functions for Ramp Terminals ...................................................... 614 19.9. Calibration of the SPFs and SDFs to Local Conditions ........................................................ 616 19.10. Interim Predictive Method for All-Way Stop Control ............................................................ 617 19.11. Limitations of Predictive Method ......................................................................................... 618 19.12. Application of Predictive Method ......................................................................................... 619 19.13. Summary ............................................................................................................................. 619 19.14. Sample Problems ................................................................................................................ 620 19.14.1. Sample Problem 1 ....................................................................................................... 620 19.14.2. Sample Problem 2 ........................................................................................................ 631 19.14.3. Sample Problem 3 ........................................................................................................ 641 19.14.4. Sample Problem 4 ........................................................................................................ 654 19.14.5. Sample Problem 5 ........................................................................................................ 665 19.14.6. Sample Problem 6 ........................................................................................................ 674 19.15. References .......................................................................................................................... 683 Appendix 19A—Worksheets for Predictive Method for Ramps ..................................................... 684

525 List of Figures Figure 19-1. Ramp Terminal Configurations .................................................................................. 533 Figure 19-2. The HSM Predictive Method ...................................................................................... 542 Figure 19-3. Number-of-Lanes Determination for Ramp Segments .............................................. 550 Figure 19-4. Starting Location on Ramps and C-D Roads ............................................................ 552 Figure 19-5. Barrier Variables ........................................................................................................ 553 Figure 19-6. Speed-Change Lane Location on Ramps and C-D Roads ........................................ 553 Figure 19-7. C-D Road Weaving Section Length ........................................................................... 554 Figure 19-8. Illustrative Ramp Terminals ....................................................................................... 555 Figure 19-9. Exit Ramp Skew Angle .............................................................................................. 556 Figure 19-10. Illustrative Ramp Segments and Ramp Terminals .................................................. 560 Figure 19-11. Graphical Form of the SPFs for Multiple-Vehicle Crashes on Entrance Ramp Segments ....................................................................................................................................... 564 Figure 19-12. Graphical Form of the SPFs for Multiple-Vehicle Crashes on Exit Ramp Segments565 Figure 19-13. Graphical Form of the SPFs for Single-Vehicle Crashes on Entrance Ramp Segments ....................................................................................................................................... 568 Figure 19-14. Graphical Form of the SPFs for Single-Vehicle Crashes on Exit Ramp Segments . 568 Figure 19-15. Graphical Form of the SPF for Crashes at Signalized Ramp Terminals–Three-Leg Terminal at Two-Quadrant Parclo A or B (A2, B2) ......................................................................... 575 Figure 19-16. Graphical Form of the SPF for Crashes at Signalized Ramp Terminals–Three-Leg Terminal with Diagonal Exit Ramp or Four-Leg Terminal at Four-Quadrant Parclo A (D3ex, A4) . 575 Figure 19-17. Graphical Form of the SPF for Crashes at Signalized Ramp Terminals–Three-Leg Terminal with Diagonal Entrance Ramp or Four-Leg Terminal at Four-Quadrant Parclo B (D3en, B4) ................................................................................................................................................. 576 Figure 19-18. Graphical Form of the SPF for Crashes at Signalized Ramp Terminals–Four-Leg Terminal with Diagonal Ramps (D4) .............................................................................................. 576 Figure 19-19. Graphical Form of the SPF Crashes at One-Way Stop-Controlled Ramp Terminals–Three-Leg Terminal at Two-Quadrant Parclo A or B (A2, B2) ..................................... 580

526 Figure 19-20. Graphical Form of the SPF Crashes at One-Way Stop-Controlled Ramp Terminals–Three-Leg Terminal with Diagonal Exit Ramp or Four-Leg Terminal at Four-Quadrant Parclo A (D3ex, A4) ....................................................................................................................... 580 Figure 19-21. Graphical Form of the SPF Crashes at One-Way Stop-Controlled Ramp Terminals–Three-Leg Terminal with Diagonal Entrance Ramp or Four-Leg Terminal at Four- Quadrant Parclo B (D3en, B4) ....................................................................................................... 581 Figure 19-22. Graphical Form of the SPF Crashes at One-Way Stop-Controlled Ramp Terminals–Four-Leg Terminal with Diagonal Ramps (D4) ............................................................. 581 Figure 19-23. Effective Number of Lanes for Various Exit Ramp Configurations .......................... 595 Figure 19-24. Starting Location for Ramp and C-D Road Combinations ....................................... 607

527 LIST OF TABLES Table 19-1. Urban Ramp and Collector-Distributor Road Segment SPFs ..................................... 535 Table 19-2. Urban Crossroad Ramp Terminal SPFs for Three-Leg Terminals with a Diagonal Exit Ramp ...................................................................................................................................... 536 Table 19-3. Ramp Safety Performance Functions ......................................................................... 562 Table 19-4. Applicable AADT Volume Ranges for Ramp SPFs ..................................................... 563 Table 19-5. SPF Coefficients for Multiple-Vehicle Crashes on Ramp Segments .......................... 564 Table 19-6. Default Distribution of Multiple-Vehicle Crashes by Crash Type for Ramp and C-D Road Segments ............................................................................................................................. 565 Table 19-7. SPF Coefficients for Multiple-Vehicle Crashes on C-D Road Segments .................... 566 Table 19-8. SPF Coefficients for Single-Vehicle Crashes on Ramp Segments ............................. 567 Table 19-9. Default Distribution of Single-Vehicle Crashes by Crash Type for Ramp and C-D Road Segments ............................................................................................................................. 569 Table 19-10. SPF Coefficients for Single-Vehicle Crashes on C-D Road Segments .................... 570 Table 19-11. Applicable AADT Volume Ranges for Crossroad Ramp Terminal SPFs .................. 571 Table 19-12. SPF Coefficients for Crashes at Signalized Ramp Terminals–Three-Leg Terminal at Two-Quadrant Parclo A or B (A2, B2) ........................................................................................ 573 Table 19-13. SPF Coefficients for Crashes at Signalized Ramp Terminals–Three-Leg Terminal with Diagonal Exit Ramp or Four-Leg Terminal at Four-Quadrant Parclo A (D3ex, A4) ................ 573 Table 19-14. SPF Coefficients for Crashes at Signalized Ramp Terminals–Three-Leg Terminal with Diagonal Entrance Ramp or Four-Leg Terminal at Four-Quadrant Parclo B (D3en, B4) ....... 574 Table 19-15. SPF Coefficients for Crashes at Signalized Ramp Terminals–Four-Leg Terminal with Diagonal Ramps (D4) ............................................................................................................. 574 Table 19-16. Default Distribution of Signal-Controlled Ramp Terminal Crashes by Crash Type ... 577 Table 19-17. SPF Coefficients for Crashes at One-Way Stop-Controlled Ramp Terminals– Three-Leg Terminal at Two-Quadrant Parclo A or B (A2, B2) ....................................................... 578 Table 19-18. SPF Coefficients for Crashes at One-Way Stop-Controlled Ramp Terminals– Three-Leg Terminal with Diagonal Exit Ramp or Four-Leg Terminal at Four-Quadrant Parclo A (D3ex, A4) ...................................................................................................................................... 579

528 Table 19-19. SPF Coefficients for Crashes at One-Way Stop-Controlled Ramp Terminals– Three-Leg Terminal with Diagonal Entrance Ramp or Four-Leg Terminal at Four-Quadrant Parclo B (D3en, B4) ....................................................................................................................... 579 Table 19-20. SPF Coefficients for Crashes at One-Way Stop-Controlled Ramp Terminals–Four- Leg Terminal with Diagonal Ramps (D4) ....................................................................................... 579 Table 19-21. Default Distribution of One-Way Stop-Controlled Ramp Terminal Crashes by Crash Type .................................................................................................................................... 582 Table 19-22. Ramp Segment Crash Modification Factors and their Corresponding SPFs ............ 583 Table 19-23. Crossroad Ramp Terminal Crash Modification Factors and their Corresponding SPFs .............................................................................................................................................. 584 Table 19-24. Coefficients for Horizontal Curve CMF–Ramp and C-D Road Segments ................. 585 Table 19-25. Coefficients for Lane Width CMF–Ramp and C-D Road Segments ......................... 586 Table 19-26. Coefficients for Right Shoulder Width CMF–Ramp and C-D Road Segments ......... 587 Table 19-27. Coefficients for Left Shoulder Width CMF–Ramp and C-D Road Segments ............ 588 Table 19-28. Coefficients for Right Side Barrier CMF–Ramp and C-D Road Segments ............... 589 Table 19-29. Coefficients for Left Side Barrier CMF–Ramp and C-D Road Segments ................. 590 Table 19-30. Coefficients for Lane Add or Drop CMF–Ramp and C-D Road Segments ............... 591 Table 19-31. Coefficients for Weaving Section CMF–C-D Road Segments .................................. 593 Table 19-32. Coefficients for Exit Ramp Capacity CMF–Crossroad Ramp Terminals................... 594 Table 19-33. Coefficients for Crossroad Left-Turn Lane CMF–Crossroad Ramp Terminals ......... 596 Table 19-34. Coefficients for Crossroad Right-Turn Lane CMF–Crossroad Ramp Terminals ....... 598 Table 19-35. Coefficients for Access Point Frequency CMF–Crossroad Ramp Terminals ........... 599 Table 19-36. Coefficients for Segment Length CMF–Crossroad Ramp Terminals ........................ 600 Table 19-37. Coefficients for Median Width CMF–Crossroad Ramp Terminals ............................ 601 Table 19-38. Coefficients for Protected Left-Turn Operation CMF–Crossroad Ramp Terminals .. 603 Table 19-39. Coefficients for Channelized Right Turn on Crossroad CMF–Crossroad Ramp Terminals ....................................................................................................................................... 603 Table 19-40. Coefficients for Channelized Right Turn on Exit Ramp CMF–Crossroad Ramp Terminals ....................................................................................................................................... 604 Table 19-41. Coefficients for Non-Ramp Public Street Leg CMF–Crossroad Ramp Terminals .... 605

529 Table 19-42. Input Data for Ramp Curve Speed Prediction .......................................................... 608 Table 19-43. SDF Coefficients for Ramp Segments ...................................................................... 614 Table 19-44. SDF Coefficients for Crossroad Ramp Terminals ..................................................... 616 Table 19-45. Default Distribution of All-Way Stop-Controlled Ramp Terminal Crashes by Crash Type ............................................................................................................................................... 618 Table 19-46. List of Sample Problems .......................................................................................... 620 Table 19-47. Ramp Segment Worksheet (1 of 4)—Sample Problem 1 ......................................... 628 Table 19-48. Ramp Segment Worksheet (2 of 4)—Sample Problem 1 ......................................... 629 Table 19-49. Ramp Segment Worksheet (3 of 4)—Sample Problem 1 ......................................... 630 Table 19-50. Ramp Segment Worksheet (4 of 4)—Sample Problem 1 ......................................... 631 Table 19-51. Ramp Segment Worksheet (1 of 4)—Sample Problem 2 ......................................... 638 Table 19-52. Ramp Segment Worksheet (2 of 4)—Sample Problem 2 ......................................... 639 Table 19-53. Ramp Segment Worksheet (3 of 4)—Sample Problem 2 ......................................... 640 Table 19-54. Ramp Segment Worksheet (4 of 4)—Sample Problem 2 ......................................... 641 Table 19-55. Ramp Segment Worksheet (1 of 4)—Sample Problem 3 ......................................... 650 Table 19-56. Ramp Segment Worksheet (2 of 4)—Sample Problem 3 ......................................... 651 Table 19-57. Ramp Segment Worksheet (3 of 4)—Sample Problem 3 ......................................... 652 Table 19-58. Ramp Segment Worksheet (4 of 4)—Sample Problem 3 ......................................... 653 Table 19-59. Ramp Barrier Worksheet—Sample Problem 3 ......................................................... 654 Table 19-60. Ramp Terminal Worksheet (1 of 4)—Sample Problem 4.......................................... 662 Table 19-61. Ramp Terminal Worksheet (2 of 4)—Sample Problem 4.......................................... 663 Table 19-62. Ramp Terminal Worksheet (3 of 4)—Sample Problem 4.......................................... 664 Table 19-63. Ramp Terminal Worksheet (4 of 4)—Sample Problem 4.......................................... 665 Table 19-64. Ramp Terminal Worksheet (1 of 4)—Sample Problem 5.......................................... 671 Table 19-65. Ramp Terminal Worksheet (2 of 4)—Sample Problem 5.......................................... 672 Table 19-66. Ramp Terminal Worksheet (3 of 4)—Sample Problem 5.......................................... 673 Table 19-67. Ramp Terminal Worksheet (4 of 4)—Sample Problem 5.......................................... 674

530 Table 19-68. Ramp Terminal Worksheet (1 of 4)—Sample Problem 6.......................................... 680 Table 19-69. Ramp Terminal Worksheet (2 of 4)—Sample Problem 6.......................................... 681 Table 19-70. Ramp Terminal Worksheet (3 of 4)—Sample Problem 6.......................................... 682 Table 19-71. Ramp Terminal Worksheet (4 of 4)—Sample Problem 6.......................................... 683

531 Chapter 19—Predictive Method for Ramps 19.1. INTRODUCTION This chapter presents the predictive method for ramps, as used to connect two or more roadways at an interchange. The method is also applicable to collector-distributor (C-D) roadways that connect with ramps and one or more roadways at an interchange. A general introduction to the Highway Safety Manual (HSM) predictive method is provided in Part C—Introduction and Applications Guidance. The predictive methodology for ramps provides a structured methodology to estimate the expected average crash frequency (in total, or by crash type or severity) for a ramp with known characteristics. Crashes involving vehicles of all types are included in the estimate. The predictive method can be applied to an existing ramp, a design alternative for an existing ramp, a new ramp, or for alternative traffic volume projections. An estimate can be made of expected average crash frequency for a prior time period (i.e., what did or would have occurred) or a future time period (i.e., what is expected to occur). The development of the predictive method in this chapter is documented by Bonneson et al. (1). This chapter presents the following information about the predictive method for ramps:  A concise overview of the predictive method.  The definitions of the site types addressed by the predictive method.  A step-by-step description of the predictive method.  Details for dividing a ramp into individual evaluation sites.  Safety performance functions (SPFs) for ramps.  Crash modification factors (CMFs) for ramps.  Severity distribution functions (SDFs) for ramps.  Limitations of the predictive method.  Sample problems illustrating the application of the predictive method. 19.2. OVERVIEW OF THE PREDICTIVE METHOD The predictive method provides an 18-step procedure to estimate the expected average crash frequency (in total, or by crash type or severity) for an entire ramp or C-D road. The gore point of the speed-change lane is used to define the beginning (or ending) point of a ramp or C-D road. The predictive method is used to evaluate an entire ramp, C-D road, or site. A site is a ramp segment, a C- D road segment, or crossroad ramp terminal. A crossroad ramp terminal is a controlled terminal between a ramp and a crossroad. A crossroad speed-change lane (i.e., an uncontrolled terminal between a ramp and a crossroad) is not addressed by the method. The predictive method is applicable to ramps or C-D roads in the vicinity of an interchange. The interchange may connect a freeway and a crossroad (service interchange) or two freeways (system interchange). The method is applicable to ramps and C-D roads that are one-way roadways.

532 The predictive method is used to estimate the expected number of crashes for an individual site. This estimate can be summed for all sites to compute the expected number of crashes for the entire ramp or C- D road. The estimate represents a given time period of interest (in years) during which the geometric design and traffic control features are unchanged and traffic volumes are known or forecasted. The expected average crash frequency is obtained by dividing the expected number of crashes by the number of years during the time period of interest. The estimate is obtained by combining the prediction from the predictive model with observed crash data using the empirical Bayes (EB) Method. The predictive models used in this chapter are described in detail in Section 19.3. The variables that comprise the predictive models include a series of subscripts to describe precisely the conditions to which they apply. These subscripts are described in detail in later sections of this chapter. For this section, it is sufficient to use “place-holder” subscripts such as w, x, y, z, and m. The subscript w is a place-holder for specific site-type subscripts that define the equation’s application (e.g., it is replaced with “rps” when needed to indicate that the equation applies to a ramp segment). Similarly, x is a place-holder for segment cross-section or intersection control-type subscripts, y is a place-holder for crash-type subscripts, z is a place holder for crash severity, and m is a place-holder for a specific geometric design or traffic control feature. The predictive models used in this chapter to determine the predicted average crash frequency are of the general form shown in Equation 19-1. ( ) z,y,x,wz,y,x,w,mz,y,x,w,z,y,x,w,z,y,x,w,spfz,y,x,w,p CCMFCMFCMFNN ×××××= 21 Where: Np, w, x, y, z = predicted average crash frequency for a specific year for site type w, cross section or control type x, crash type y, and severity z (crashes/yr); Nspf, w, x, y, z = predicted average crash frequency determined for base conditions of the SPF developed for site type w, cross section or control type x, crash type y, and severity z (crashes/yr); CMFm, w, x, y, z = crash modification factors specific to site type w, cross section or control type x, crash type y, and severity z for specific geometric design and traffic control feature m; and Cw, x y, z = calibration factor to adjust SPF for local conditions for site type w, cross section or control type x, crash type y, and severity z. The predictive models provide estimates of the predicted average crash frequency in total, or by crash type or severity. A default distribution of crash type is included in the predictive method. It is used with the predictive models to quantify the crash frequency for each of several crash types. The models predict fatal-and-injury crash frequency and property-damage-only crash frequency. A severity distribution function is available to further quantify the crash frequency by the following severity levels: fatal, incapacitating injury, non-incapacitating injury, and possible injury. 19.3. RAMPS—DEFINITIONS AND PREDICTIVE MODELS This section provides the definitions of the site types discussed in this chapter. It also describes the predictive models for each of the site types. Equation 19-1

533 19.3.1. Definition of Ramp Site Types The predictive method in this chapter applies to the following site types: entrance ramp segment with one or two lanes, exit ramp segment with one or two lanes, C-D road segment with one or two lanes, and crossroad ramp terminal. Connector ramp segments are represented using one of these site types. There are many different configurations of crossroad ramp terminal used at interchanges. For this reason, the definition of “site type” is broadened when applied to crossroad ramp terminals to be specific to each configuration. The more common configurations are identified in Figure 19-1. a. Three-Leg Ramp Terminal With Diagonal Exit or Entrance Ramp (D3ex and D3en) b. Four-Leg Ramp Terminal With Diagonal Ramps (D4) c. Four-Leg Ramp Terminal at Four-Quadrant Parclo A (A4) Figure 19-1. Ramp Terminal Configurations Crossroad Fr ee w ay Exit Ramp Type: D3ex Type: D3en Entrance Ramp Crossroad Fr ee w ay Type: D4 Type: D4 Exit Ramp Exit Ramp Entrance Ramp Entrance Ramp Crossroad Fr ee w ay Exit Ramp Entrance Ramp Entrance Ramp Entrance Ramp Exit Ramp Entrance Ramp Type: A4 Type: A4

534 Crossroad Fr ee w ay Exit Ramp Entrance Ramp Entrance Ramp Exit Ramp Exit Ramp Exit RampType: B4 Type: B4 d. Four-Leg Ramp Terminal at Four-Quadrant Parclo B (B4) e. Three-Leg Ramp Terminal at Two-Quadrant Parclo A (A2) f. Three-Leg Ramp Terminal at Two-Quadrant Parclo B (B2) Figure 19-1. Ramp Terminal Configurations continued Differences among the terminals shown Figure 19-1 reflect the number of ramp legs, number of left-turn movements, and location of crossroad left-turn storage (i.e., inside or outside of the interchange). Although not shown, control type (i.e., signalized or stop controlled) is also an important factor in characterizing a crossroad ramp terminal. Crossroad Fr ee w ay Exit Ramp Entrance Ramp Exit Ramp Entrance Ramp Type: A2 Type: A2 Crossroad Fr ee w ay Exit Ramp Exit Ramp Entrance Ramp Entrance Ramp Type: B2 Type: B2

535 Classifying an area as urban, suburban, or rural is subject to the roadway characteristics, surrounding population, and surrounding land uses, and is at the analyst’s discretion. In the HSM, the definition of “urban” and “rural” areas is based on Federal Highway Administration (FHWA) guidelines which classify “urban” areas as places inside urban boundaries where the population is greater than 5,000 persons. “Rural” areas are defined as places outside urban areas where the population is less than 5,000 persons. The HSM uses the term “suburban” to refer to outlying portions of an urban area; the predictive method does not distinguish between urban and suburban portions of a developed area. Table 19-1 identifies the urban ramp and C-D road segment configurations for which SPFs have been developed. A second set of SPFs have been developed for rural ramps and C-D road segments with one lane (they are not shown in the table, but use the same nomenclature). The SPFs are used to estimate the predicted average crash frequency by crash type and crash severity. These estimates are added to yield the total predicted average crash frequency for an individual site. Table 19-1. Urban Ramp and Collector-Distributor Road Segment SPFs Site Type (w) Cross Section (x) Crash Type (y) Crash Severity (z) SPF Ramp segments (rps) One-lane entrance ramp (1EN) Multiple vehicle (mv) Fatal and injury (fi) Nspf, rps, 1EN, mv, fi Property damage only (pdo) Nspf, rps, 1EN, mv, pdo Single vehicle (sv) Fatal and injury (fi) Nspf, rps, 1EN, sv, fi Property damage only (pdo) Nspf, rps, 1EN, sv, pdo Two-lane entrance ramp (2EN) Multiple vehicle (mv) Fatal and injury (fi) Nspf, rps, 2EN, mv, fi Property damage only (pdo) Nspf, rps, 2EN, mv, pdo Single vehicle (sv) Fatal and injury (fi) Nspf, rps, 2EN, sv, fi Property damage only (pdo) Nspf, rps, 2EN, sv, pdo One-lane exit ramp (1EX) Multiple vehicle (mv) Fatal and injury (fi) Nspf, rps, 1EX, mv, fi Property damage only (pdo) Nspf, rps, 1EX, mv, pdo Single vehicle (sv) Fatal and injury (fi) Nspf, rps, 1EX, sv, fi Property damage only (pdo) Nspf, rps, 1EX, sv, pdo Two-lane exit ramp (2EX) Multiple vehicle (mv) Fatal and injury (fi) Nspf, rps, 2EX, mv, fi Property damage only (pdo) Nspf, rps, 2EX, mv, pdo Single vehicle (sv) Fatal and injury (fi) Nspf, rps, 2EX, sv, fi Property damage only (pdo) Nspf, rps, 2EX, sv, pdo C-D road segments (cds) One-lane C-D road (1) Multiple vehicle (mv) Fatal and injury (fi) Nspf, cds, 1, mv, fi Property damage only (pdo) Nspf, cds, 1, mv, pdo Single vehicle (sv) Fatal and injury (fi) Nspf, cds, 1, sv, fi Property damage only (pdo) Nspf, cds, 1, sv, pdo Two-lane C-D road (2) Multiple vehicle (mv) Fatal and injury (fi) Nspf, cds, 2, mv, fi Property damage only (pdo) Nspf, cds, 2, mv, pdo Single vehicle (sv) Fatal and injury (fi) Nspf, cds, 2, sv, fi Property damage only (pdo) Nspf, cds, 2, sv, pdo The ramp segment and C-D road segment are defined as follows:  One-lane segment—a length of roadway consisting of one through lane with a continuous cross section providing one direction of travel.

536  Two-lane segment— a length of roadway consisting of two through lanes with a continuous cross section providing one direction of travel. Table 19-2 identifies the urban crossroad ramp terminal configurations for which SPFs have been developed for three-leg terminals with a diagonal exit ramp. A second set of SPFs have been developed for rural three-leg terminals with either stop control, or signal control and two, three, or four lanes on the crossroad (they are not shown in the table, but use the same nomenclature).The SPFs are used to estimate the predicted average crash frequency by crash severity. These estimates are added to yield the total predicted average crash frequency for an individual site. Table 19-2. Urban Crossroad Ramp Terminal SPFs for Three-Leg Terminals with a Diagonal Exit Ramp Site Type (w) Cross Section and Control Type (x) Crash Type (y) Crash Severity (z) SPF Three-leg terminals with diagonal exit ramp (D3ex), One-way stop control; 2, 3, or 4 lane crossroad (ST) All types (at) Fatal and injury (fi) Nspf, w, ST, at, fi Property damage only (pdo) Nspf, w, ST, at, pdo Signal control, 2-lane crossroad (SG2) All types (at) Fatal and injury (fi) Nspf, w, SG2, at, fi Property damage only (pdo) Nspf, w, SG2, at, pdo Signal control, 3-lane crossroad (SG3) All types (at) Fatal and injury (fi) Nspf, w, SG3, at, fi Property damage only (pdo) Nspf, w, SG3, at, pdo Signal control, 4-lane crossroad (SG4) All types (at) Fatal and injury (fi) Nspf, w, SG4, at, fi Property damage only (pdo) Nspf, w, SG4, at, pdo Signal control, 5-lane crossroad (SG5) All types (at) Fatal and injury (fi) Nspf, w, SG5, at, fi Property damage only (pdo) Nspf, w, SG5, at, pdo Signal control, 6-lane crossroad (SG6) All types (at) Fatal and injury (fi) Nspf, w, SG6, at, fi Property damage only (pdo) Nspf, w, SG6, at, pdo One set of urban SPFs (and one set of rural SPFs) for the configurations shown in Table 19-2 have also been developed for each of the following six site types (they also use the same nomenclature shown in the table).  Three-leg terminals with diagonal entrance ramp (D3en),  Four-leg terminals with diagonal ramps (D4),  Four-leg terminals at four-quadrant parclo A (A4),  Four-leg terminals at four-quadrant parclo B (B4),

537  Three-leg terminals at two-quadrant parclo A (A2),  Three-leg terminals at two-quadrant parclo B (B2). For the purposes of evaluation, a crossroad ramp terminal’s “site type” is defined in terms of its configuration. The terminal configurations addressed in the predictive method are shown in Figure 19-1. These terminals are further categorized by crossroad cross section and the type of traffic control used at the terminal. Stop-controlled terminals have a stop sign on the ramp approach to the intersection, and no stop or yield sign on the crossroad approaches. Signal-controlled terminals have traffic signals on the ramp and crossroad approaches. 19.3.2. Predictive Model for Ramp Segments In general, a predictive model is used to compute the predicted average crash frequency for a site. It combines with the SPF, CMFs, and a calibration factor. The predicted quantity can describe crash frequency in total, or by crash type or severity. This section describes the predictive model for ramp and C-D road segments. The next section describes the predictive model for crossroad ramp terminals. The predictive model for ramp and C-D road segments is used to estimate the predicted average crash frequency of segment crashes (i.e., the estimate does not include ramp-terminal-related crashes). Segment crashes include crashes that occur in the segment and either (a) away from the crossroad ramp terminal or (b) within the limits of the crossroad ramp terminal but not related to the terminal. That is, the predictive model estimate includes crashes that would occur regardless of whether the crossroad ramp terminal is present. The predictive model for entrance ramps (and connector ramps at service interchanges that serve motorists traveling from the crossroad to the freeway) is presented in Equation 19-2. This equation consists of four terms, where each of Equation 19-3 to Equation 19-6 correspond to one term. pdosvnENrpsppdomvnENrpspfisvnENrpspfimvnENrpspasatnENrpsp NNNNN ,,,,,,,,,,,,,,,,,,,, +++= ( ) ( )fiatacrpsmfiatacrps fimvacrpsmfimvacrpsfimvnENrpsspffimvENrpsfimvnENrpsp CMFCMF CMFCMFNCN ,,,,,,,,1 ,,,,,,,,1,,,,,,,,,,, ××× ××××=   ( ) ( )fiatacrpsmfiatacrps fisvacrpsmfisvacrpsfisvnENrpsspffisvENrpsfisvnENrpsp CMFCMF CMFCMFNCN ,,,,,,,,1 ,,,,,,,,1,,,,,,,,,,, ××× ××××=   ( ) ( )pdoatacrpsmpdoatacrps pdomvacrpsmpdomvacrpspdomvnENrpsspfpdomvENrpspdomvnENrpsp CMFCMF CMFCMFNCN ,,,,,,,,1 ,,,,,,,,1,,,,,,,,,,, ××× ××××=   ( ) ( )pdoatacrpsmpdoatacrps pdosvacrpsmpdosvacrpspdosvnENrpsspfpdosvENrpspdosvnENrpsp CMFCMF CMFCMFNCN ,,,,,,,,1 ,,,,,,,,1,,,,,,,,,,, ××× ××××=   Where: Np, rps, nEN, y, z = predicted average crash frequency of an entrance ramp segment with n lanes, crash type y (y = sv: single vehicle, mv: multiple vehicle, at: all types), and severity z (z = fi: fatal and injury, pdo: property damage only, as: all severities) (crashes/yr); Equation 19-2 Equation 19-3 Equation 19-4 Equation 19-5 Equation 19-6

538 Nspf, rps, nEN, y, z = predicted average crash frequency of an entrance ramp segment with base conditions, n lanes, crash type y (y = sv: single vehicle, mv: multiple vehicle, at: all types), and severity z (z = fi: fatal and injury, pdo: property damage only) (crashes/yr); CMFm, rps, ac, y, z = crash modification factor for a ramp segment with any cross section ac, feature m, crash type y (y = sv: single vehicle, mv: multiple vehicle, at: all types), and severity z (z = fi: fatal and injury, pdo: property damage only); and Crps, EN, y, z = calibration factor for entrance ramp segments with any lanes, crash type y (y = sv: single vehicle, mv: multiple vehicle, at: all types), and severity z (z = fi: fatal and injury, pdo: property damage only). The predictive model for exit ramps (and connector ramps at service interchanges that serve motorists traveling from the freeway to the crossroad) is identical to that for entrance ramps except that the subscript “EX” is substituted for “EN” in Equation 19-2 to Equation 19-6. Equation 19-2 shows that entrance ramp segment crash frequency is estimated as the sum of four components: fatal-and-injury multiple-vehicle crash frequency, fatal-and-injury single-vehicle crash frequency, property-damage-only multiple-vehicle crash frequency, and property-damage-only single- vehicle crash frequency. Different CMFs are used in Equation 19-3 to Equation 19-6. The first terms in parentheses in each equation recognizes that the influence of some features is unique to each crash type. In contrast, the second term in parentheses in these equations recognizes that some features have a similar influence on all crash types. All CMFs are unique to crash severity. Equation 19-3 and Equation 19-4 are used to estimate the fatal-and-injury crash frequency. Equation 19-5 and Equation 19-6 are used to estimate the property-damage-only crash frequency. The predictive model for C-D roads (and connector ramps at system interchanges) is presented in Equation 19-7. This equation consists of four terms, where each of Equation 19-8 to Equation 19-11 correspond to one term. pdosvncdsppdomvncdspfisvncdspfimvncdspasatncdsp NNNNN ,,,,,,,,,,,,,,,,,,,, +++= ( ) ( )fiataccdsmfiataccds fimvaccdsmfimvaccdsfimvncdsspffimvaccdsfimvncdsp CMFCMF CMFCMFNCN ,,,,,,,,1 ,,,,,,,,1,,,,,,,,,,, ××× ××××=   ( ) ( )fiatacrpsmfiatacrps fisvaccdsmfisvaccdsfisvncdsspffisvaccdsfisvncdsp CMFCMF CMFCMFNCN ,,,,,,,,1 ,,,,,,,,1,,,,,,,,,,, ××× ××××=   ( ) ( )pdoataccdsmpdoataccds pdomvaccdsmpdomvaccdspdomvncdsspfpdomvaccdspdomvncdsp CMFCMF CMFCMFNCN ,,,,,,,,1 ,,,,,,,,1,,,,,,,,,,, ××× ××××=   ( ) ( )pdoataccdsmpdoataccds pdosvaccdsmpdosvaccdspdosvncdsspfpdosvaccdspdosvncdsp CMFCMF CMFCMFNCN ,,,,,,,,1 ,,,,,,,,1,,,,,,,,,,, ××× ××××=   Equation 19-7 Equation 19-8 Equation 19-9 Equation 19-10 Equation 19-11

539 Where: Np, cds, n, y, z = predicted average crash frequency of a C-D road segment with n lanes, crash type y (y = sv: single vehicle, mv: multiple vehicle, at: all types), and severity z (z = fi: fatal and injury, pdo: property damage only, as: all severities) (crashes/yr); Nspf, cds, n, y, z = predicted average crash frequency of a C-D road segment with base conditions, n lanes, crash type y (y = sv: single vehicle, mv: multiple vehicle, at: all types), and severity z (z = fi: fatal and injury, pdo: property damage only) (crashes/yr); CMFm, cds, ac, y, z = crash modification factor for a C-D road segment with any cross section ac, feature m, crash type y (y = sv: single vehicle, mv: multiple vehicle, at: all types), and severity z (z = fi: fatal and injury, pdo: property damage only); and Ccds, ac, y, z = calibration factor for C-D road segments with any cross section ac, crash type y (y = sv: single vehicle, mv: multiple vehicle, at: all types), and severity z (z = fi: fatal and injury, pdo: property damage only). The interpretation of these equations is similar to that described previously for ramp entrance segments. The SPFs for ramp and C-D road segments are presented in Section 19.6.1. The associated CMFs are presented in Section 19.7.1. Similarly, the associated SDFs are presented in Section 19.8.1. A procedure for establishing the value of the calibration factor is described in Section B.1 of Appendix B to Part C. 19.3.3. Predictive Model for Ramp Terminals The predictive model for crossroad ramp terminals is used to compute the predicted average crash frequency for a crossroad ramp terminal. Terminal-related crashes include (a) all crashes that occur within the limits of the intersection (i.e., at-intersection crashes) and (b) crashes that occur on the ramp or crossroad legs and are attributed to the presence of an intersection (i.e., intersection-related crashes). The predictive model for one-way stop-controlled crossroad ramp terminals is presented in Equation 19- 12. This equation consists of two terms, where each of Equation 19-13 and Equation 19-14 correspond to one term. pdoatSTwpfiatSTwpasatSTwp NNN ,,,,,,,,,,,, += ( )fiatSTaSmfiatSTaSfiatSTwspffiatSTaSfiatSTwp CMFCMFNCN ,,,,,,,,1,,,,,,,,,,, ××××=  ( )pdoatSTaSmpdoatSTaSpdoatSTwspfpdoatSTaSpdoatSTwp CMFCMFNCN ,,,,,,,,1,,,,,,,,,,, ××××=  Where: Np, w, ST, at, z = predicted average crash frequency of a stop-controlled crossroad ramp terminal of site type w (w = D3ex, D3en, D4, A4, B4, A2, B2), all crash types at, and severity z (z = fi: fatal and injury, pdo: property damage only, as: all severities) (crashes/yr); Nspf, w, ST, at, z = predicted average crash frequency of a one-way stop-controlled crossroad ramp terminal of site type w (w = D3ex, D3en, D4, A4, B4, A2, B2) with base conditions, all crash types at, and severity z (z = fi: fatal and injury, pdo: property damage only) (crashes/yr); Equation 19-12 Equation 19-13 Equation 19-14

540 CMFm, aS, ST, at, z = crash modification factor for a stop-controlled crossroad ramp terminal (any site type aS) with feature m, all crash types at, and severity z (z = fi: fatal and injury, pdo: property damage only); and CaS, ST, at, z = calibration factor for a stop-controlled crossroad ramp terminal (any site type aS) with all crash types at and severity z (z = fi: fatal and injury, pdo: property damage only). The seven site types (i.e., D3ex, D3en, D4, A4, B4, A2, B2) are shown in Figure 19-1. Equation 19-12 shows that crossroad ramp terminal crash frequency is estimated as the sum of two components: predicted average fatal-and-injury crash frequency and predicted average property-damage- only crash frequency. Different CMFs are used in Equation 19-13 and Equation 19-14. The term in parentheses in each equation recognizes that the influence of some features is unique to the type of control used at the terminal. All CMFs are unique to crash severity. The predictive model for signal-controlled crossroad ramp terminals is presented in Equation 19-15. This equation consists of two terms, where each of Equation 19-16 and Equation 19-17 correspond to one term. pdoatSGnwpfiatSGnwpasatSGnwp NNN ,,,,,,,,,,,, += ( )fiatSGnaSmfiatSGnaSfiatSGnwspffiatSGaSfiatSGnwp CMFCMFNCN ,,,,,,,,1,,,,,,,,,,, ××××=  ( )pdoatSGnaSmpdoatSGnaSpdoatSGnwspfpdoatSGaSpdoatSGnwp CMFCMFNCN ,,,,,,,,1,,,,,,,,,,, ××××=  Where: Np, w, SGn, at, z = predicted average crash frequency of a signal-controlled crossroad ramp terminal of site type w (w = D3ex, D3en, D4, A4, B4, A2, B2) with n crossroad lanes, all crash types at, and severity z (z = fi: fatal and injury, pdo: property damage only, as: all severities) (crashes/yr); Nspf, w, SGn, at, z = predicted average crash frequency of a signal-controlled crossroad ramp terminal of site type w (w = D3ex, D3en, D4, A4, B4, A2, B2) with base conditions, n crossroad lanes, all crash types at, and severity z (z = fi: fatal and injury, pdo: property damage only) (crashes/yr); CMFm, aS, SGn, at, z = crash modification factor for a signal-controlled crossroad ramp terminal (any site type aS) on a crossroad with n lanes, feature m, all crash types at, and severity z (z = fi: fatal and injury, pdo: property damage only); and CaS, SG, at, z = calibration factor for a signal-controlled crossroad ramp terminal (any site type aS) with all crash types at and severity z (z = fi: fatal and injury, pdo: property damage only). The SPFs for crossroad ramp terminals are presented in Section 19.6.2. The associated CMFs are presented in Section 19.7.2. Similarly, the associated SDFs are presented in Section 19.8.2. A procedure for establishing the value of the calibration factor is described in Section B.1 of Appendix B to Part C. Equation 19-15 Equation 19-16 Equation 19-17

541 19.4. PREDICTIVE METHOD FOR RAMPS AND RAMP TERMINALS This section describes the predictive method for ramps, C-D roads, and ramp terminals. It consists of two sections. The first section provides a step-by-step description of the predictive method. The second section describes the geometric design features, traffic control features, and traffic volume data needed to apply the predictive method. 19.4.1. Step-by-Step Description of the Predictive Method The predictive method for ramps is shown in Figure 19-2. Applying the predictive method yields an estimate of the expected average crash frequency (in total, or by crash type or severity) for an entire ramp or C-D road. The predictive models described in this chapter are applied in Steps 9, 10, and 11 of the predictive method. The information needed to apply each step is provided in this section.

542 Define roadway limits and facility type. Define the period of study. Determine AADT and availability of crash data for every year in the period of interest. Determine geometric conditions. Divide ramp or C-D road into individual segments and crossroad ramp terminals Assign observed crashes to individual sites (if applicable). Select a segment or crossroad ramp terminal. Select first or next year of the evaluation period. Select and apply SPF. Apply CMFs. Apply a calibration factor. Is there another year? Apply site-specific EB method (if applicable) and apply SDF. Sum all sites and years. Apply project-level EB method (if applicable). Compare and evaluate results. Is there another site? Is there an alternative design, treatment, or forecast AADT to be evaluated? YES YES YES Step 1 Step 2 Step 3 Step 4 Step 5 Step 6 Step 7 Step 8 Step 9 Step 10 Step 11 Step 12 Step 13 Step 14 Step 15 Step 16 Step 17 Step 18 NO NO NO Figure 19-2. The HSM Predictive Method

543 There are 18 steps in the predictive method. In some situations certain steps will not be needed because data are not available or the step is not applicable to the situation at hand. In other situations, steps may be repeated if an estimate is desired for several sites or for a period of several years. In addition, the predictive method can be repeated as necessary to undertake crash estimation for each alternative design, traffic volume scenario, or proposed treatment option (within the same time period to allow for comparison). The following discussion explains the details of each step of the method as applied to ramps. Step 1—Define the limits of the project. A project can be all of the ramps and C-D roads in the vicinity of an interchange, an entire ramp, an entire C-D road, or an individual site. A site is a crossroad ramp terminal, a homogeneous ramp segment, or a homogeneous C-D road segment. A site is further categorized by its cross section or control type. A description of the specific site types is provided in Section 19.3.1. The project limits are defined in this step. They will depend on the purpose of the study. The study may be limited to one specific site, or to a group of contiguous sites. Alternatively, the limits can be expanded to include all of the ramps, C-D roads, and crossroad ramp terminals in the vicinity of an interchange. For comparative analysis of design alternatives, the project limits should be the same for all alternatives. The analyst should identify (or establish) a reference line for each ramp and C-D road. This line is defined as the right edge of traveled way in the direction of travel. All lengths along the roadway are determined using this line. The location of the reference line is shown in subsequent figures (e.g., Figure 19-4). Locations along this line are specified using a linear referencing system, and are identified using the label “ramp-mile X,” where the number for X has units of miles (e.g., ramp-mile 1.4). Step 2—Define the period of interest. The study period is defined as the consecutive years for which an estimate of the expected average crash frequency is desired. The crash period is defined as the consecutive years for which observed crash data are available. The evaluation period is defined as the combined set of years represented by the study period and crash period. Every year in the evaluation period is evaluated using the predictive method. All periods are measured in years. If the EB Method is not used, then the study period is the same as the evaluation period. The EB Method is discussed in more detail in Step 3. If the EB Method is used and the crash period is not fully included in the study period, then the predictive models need to be applied to the study years plus each year of the crash period not represented in the study period. In this situation, the evaluation period includes the study period and any additional years represented by the crash data but not in the study period. For example, let the study period be defined as the years 2010, 2011, and 2012. If crash data are available for 2008, 2009, and 2010, then the evaluation period is 2008, 2009, 2010, 2011, and 2012. The study period can represent either a past time period or a future time period. Whether the predictive method is used for a past or future period depends upon the purpose of the study. The study period may be:  A past period for:  An existing ramp or C-D road. If observed crash data are available, the study period is the period of time for which the observed crash data are available and for which (during that period) the site geometric design features, traffic control features, and traffic volumes are known.

544  An existing ramp or C-D road for which alternative geometric design or traffic control features are proposed (for near-term conditions) and site traffic volumes are known.  A future period for:  An existing ramp or C-D road for a future period where forecast traffic volumes are available.  An existing ramp or C-D road for which alternative geometric design or traffic control features are proposed and forecast traffic volumes are available.  A new ramp or C-D road that does not currently exist but is proposed for construction and for which forecast traffic volumes are available. Step 3—For the study period, determine the availability of AADT volumes and, for an existing project, the availability of observed crash data (to determine whether the EB Method is applicable). Traffic volume data are acquired in this step. Also, a decision is made whether the EB Method will be applied. If it will be applied, then it must also be decided whether the site-specific or project-level EB Method will be applied. If the EB Method will be applied, then the observed crash data are also acquired in this step. Determining Traffic Volumes The SPFs used in Step 9 (and some CMFs in Step 10) include annual average daily traffic (AADT) volume as a variable. For a past period, the AADT volume may be determined by using automated recorder data, or estimated by a sample survey. For a future period, the AADT volume may be a forecast estimate based on appropriate land use planning and traffic volume forecasting models. The AADT volume of the ramp is needed for each ramp segment. The AADT volume of the C-D road is needed for the evaluation of each C-D road segment. For each crossroad ramp terminal, one AADT value is needed for each intersecting leg. Thus, for a four- leg ramp terminal, the following values are needed: AADT volume of the crossroad leg “inside” the interchange, AADT volume of the crossroad leg “outside” of the interchange, AADT volume of the exit ramp, and AADT volume of the entrance ramp. The inside crossroad leg is the leg that is on the side of the ramp terminal nearest to the freeway. The outside crossroad leg is on the other side of the ramp terminal. The AADT volumes are needed for each year of the evaluation period. The AADT volume for a given year represents an annual average daily 24-hour traffic volume. The ramp and C-D road segment AADT volume is a one-way volume. The crossroad segment AADT volume is a two-way volume (i.e., total of both travel directions). In many cases, it is expected that AADT data will not be available for all years of the evaluation period. In that case, an estimate of AADT volume for each missing year is interpolated or extrapolated, as appropriate. If there is not an established procedure for doing this, the following rules may be applied within the predictive method to estimate the AADT volumes for years in which no data are available. If these rules are applied, the fact that some AADT volumes are estimated should be documented with the analysis results.  If AADT volume is available for only a single year, that same volume is assumed to apply to all years of the evaluation period.

545  If two or more years of AADT data are available, the AADT volumes for intervening years are computed by interpolation.  The AADT volumes for years before the first year for which data are available are assumed to be equal to the AADT volume for that first year.  The AADT volumes for years after the last year for which data are available are assumed to be equal to the AADT volume for that last year. Determining Availability of Observed Crash Data Where an existing site (or an alternative condition for an existing site) is being considered, the EB Method can be used to obtain a more reliable estimate of the expected average crash frequency. The EB Method is applicable when crash data are available for the entire project, or for its individual sites. Crash data may be obtained directly from the jurisdiction’s crash report system. At least two years of crash data are desirable to apply the EB Method. The EB Method (and criteria to determine whether the EB Method is applicable) is presented in Section B.2 in Appendix B to Part C. The EB Method can be applied at the site-specific level or at the project level. At the site-specific level, crash data are assigned to specific sites in Step 6. The site-specific EB Method is applied in Step 13. At the project level, crash data are assigned to a group of sites (typically because they cannot be assigned to individual sites). The project-level EB Method is applied in Step 15. In general, the best results will be obtained if the site-specific EB Method is used. Guidance to determine whether the site-specific or project-level EB Method is applicable is presented in Section B.2.2 in Appendix B to Part C. Step 4—Determine geometric design features, traffic control features, and site characteristics for all sites in the project limits. A range of data is needed to apply a predictive model. These data are used in the SPFs and CMFs to estimate the predicted average crash frequency for the selected site and year. These data represent the geometric design features, traffic control features, and traffic demand characteristics that have been found to have some relationship to safety. These data are needed for each site in the project limits. They are needed for the study period and, if applicable, the crash period. The specific data, and means by which they are measured or obtained, is described in Section 19.4.2. Step 5—Divide the roadway into sites. Using the information from Step 1 and Step 4, the ramp or C-D road is divided into individual sites, consisting of individual homogeneous segments and ramp terminals. The procedure for dividing the ramp or C-D road into individual segments is provided in Section 19.5. Step 6—Assign observed crashes to the individual sites (if applicable). Step 6 applies if it was determined in Step 3 that the site-specific EB Method is applicable. If the site- specific EB Method is not applicable, then proceed to Step 7. In this step, the observed crash data are assigned to the individual sites using the criteria outlined in the next paragraph. Specific criteria for assigning crashes to individual sites are presented in Section B.2.3 in Appendix B to Part C. Step 7—Select the first or next individual site in the project limits. If there are no more sites to be evaluated, proceed to Step 15. Steps 7 through 14 are repeated for each site within the project limits identified in Step 1.

546 Any site can be selected for evaluation because each site is considered to be independent of the other sites. However, good practice is to select the sites in an orderly manner, such as in the order of their physical occurrence in the direction of travel. Step 8—For the selected site, select the first or next year in the period of interest. If there are no more years to be evaluated for that site, proceed to Step 13. Steps 8 through 12 are repeated for each year in the evaluation period for the selected site. The individual years of the evaluation period are analyzed one year at a time because the SPFs and some CMFs are dependent on AADT volume, which may change from year to year. Step 9—For the selected site, determine and apply the appropriate SPF. The SPF determines the predicted average crash frequency for a site whose features match the SPF’s base conditions. The SPFs (and their base conditions) are described in Section 19.6. Determine the appropriate SPF for the selected site based on its site type and cross section (or traffic control). This SPF is then used to compute the crash frequency for the selected year using the AADT volume for that year, as determined in Step 3. Step 10—Multiply the result obtained in Step 9 by the appropriate CMFs. Collectively, the CMFs are used in the predictive model to adjust the SPF estimate from Step 9 such that the resulting predicted average crash frequency accurately reflects the geometric design and traffic control features of the selected site. The available CMFs are described in Section 19.7. All CMFs presented in this chapter have the same base conditions as the SPFs in this chapter. Only the CMFs presented in Section 19.7 may be used as part of the predictive method described in this chapter. For the selected site, determine the appropriate CMFs for the site type, geometric design features, and traffic control features present. The CMF’s designation by crash type and severity must match that of the SPF with which it is used (unless indicated otherwise in the CMF description). The CMFs for the selected site are calculated using (a) the AADT volume determined in Step 3 for the selected year and (b) the geometric design and traffic control features determined in Step 4. Multiply the result from Step 9 by the appropriate CMFs. Step 11—Multiply the result obtained in Step 10 by the appropriate calibration factor. The SPFs and CMFs in this chapter have each been developed with data from specific jurisdictions and time periods. Calibration to local conditions will account for any differences between these conditions and those present at the selected sites. A calibration factor is applied to each SPF in the predictive method. Detailed guidance for the development of calibration factors is included in Section B.1 of Appendix B to Part C. Multiply the result from Step 10 by the calibration factor to obtain the predicted average crash frequency. Step 12—If there is another year to be evaluated in the evaluation period for the selected site, return to Step 8. Otherwise, proceed to Step 13. This step creates a loop from Step 8 through Step 12 that is repeated for each year of the evaluation period for the selected site.

547 Step 13—Apply site-specific EB Method (if applicable) and apply SDFs. The site-specific EB Method combines the predicted average crash frequency computed in Step 11 with the observed crash frequency of the selected site. It produces a more statistically reliable estimate of the site’s expected average crash frequency. The procedure for applying the site-specific EB Method is provided in Section B.2.4 of Appendix B to Part C. The decision to apply the site-specific EB Method was determined in Step 3. If the EB Method is not used, then the estimate of expected average crash frequency for each year of the study period is limited to the predicted average crash frequency for that year, as computed in Step 11. If the EB Method is used, then the expected average crash frequency is equal to the estimate obtained from the EB Method. An estimate is obtained for each year of the crash period (i.e., the period for which the observed crash data are available). The individual years of the crash period are analyzed one year at a time because the SPFs and some CMFs are dependent on AADT volume, which may change from year to year. Apply the site-specific EB Method to a future time period, if appropriate. Section B.2.6 in Appendix B to Part C provides a procedure for converting the estimates from the EB Method to any years in the study period that are not represented in the crash period (e.g., future years). This approach gives consideration to any differences in traffic volume, geometry, or traffic control between the study period and the crash period. This procedure yields the expected average crash frequency for each year of the study period. Apply the severity distribution functions (SDFs), if desired. The SDFs can be used to compute the expected average crash frequency for each of the following severity levels: fatal, incapacitating injury, non-incapacitating injury, and possible injury. Each SDF includes variables that describe the geometric design and traffic control features of a site. In this manner, the computed distribution gives consideration to the features present at the selected site. The SDFs are described in Section 19.8. They can benefit from being updated based on local data as part of the calibration process. Detailed guidance for the development of the SDF calibration factor is included in Section B.1.4 of Appendix B to Part C. Apply the crash type distribution, if desired. Each predictive model includes a default distribution of crash type. This distribution can be used to compute the expected average crash frequency for each of ten crash types (e.g., head-on, fixed object). The distribution is presented in Section 19.6. It can benefit from being updated based on local data as part of the calibration process. Step 14—If there is another site to be evaluated, return to Step 7; otherwise, proceed to Step 15. This step creates a loop from Step 7 through Step 14 that is repeated for each site of interest. Step 15—Apply the project-level EB Method (if applicable) and apply SDFs. The activities undertaken during this step are the same as undertaken for Step 13 but they occur at the project level (i.e., entire ramp, entire C-D road, or interchange). They are based on estimating the project- level predicted average crash frequency. This crash frequency is computed for each year during the crash period. It is computed as the sum of the predicted average crash frequency for all sites (as computed in Step 11). The project-level EB Method combines the project-level predicted average crash frequency with the observed crash frequency for all sites within the project limits. It produces a more statistically reliable

548 estimate of the project-level expected average crash frequency. The procedure for applying the project- level EB Method is provided in B.2.5 of Appendix B to Part C. The decision to apply the project-level EB Method was determined in Step 3. If this method is not used, then the project-level expected average crash frequency for each year of the study period is limited to the project-level predicted average crash frequency for that year, as computed in Step 11. If the EB Method is used, then the project-level expected average crash frequency is equal to the estimate obtained from the EB Method. An estimate is obtained for each year of the crash period (i.e., the period for which the observed crash data are available). The individual years of the crash period are analyzed one year at a time because the SPFs and some CMFs are dependent on AADT volume, which may change from year to year. Apply the project-level EB Method to a future time period, if appropriate. Follow the same guidance as provided in Step 13 using the estimate from the project-level EB Method. Apply the severity distribution functions, if desired. Follow the same guidance as provided in Step 13 using the estimate from the project-level EB Method. Apply the crash type distribution, if desired. Follow the same guidance as provided in Step 13 using the estimate from the project-level EB Method. Step 16—Sum all sites and years in the study to estimate total crash frequency. One outcome of the predictive method is the total expected average crash frequency. The term “total” indicates that the estimate includes all crash types and severities. It is computed from an estimate of the total expected number of crashes, which represents the sum of the total expected average crash frequency for each site and for each year in the study period. The total expected number of crashes during the study period is calculated using Equation 19-18:   = ===         ++= sn j sitesall i jasataciwe sitesall i jasatacicdse sitesall i jasatacirpseasatacaSe NNNN 1 1 ,,,),(, 1 ,,,),(, 1 ,,,),(, * ,,,, Where: N*e, aS, ac, at, as = total expected number of crashes for all sites aS and all years in the study period (includes all cross sections and control types ac, all crash types at, and all severities as) (crashes); Ne, rps(i), ac, at, as, j = expected average crash frequency of ramp segment i for year j (includes all cross sections ac, all crash types at, and all severities as) (crashes/yr); Ne, cds(i), ac, at, as, j = expected average crash frequency of C-D road segment i for year j (includes all cross sections ac, all crash types at, and all severities as) (crashes/yr); Ne, w(i), ac, at, as, j = expected average crash frequency of crossroad ramp terminal i of site type w(i) (w = D3ex, D3en, D4, A4, B4, A2, B2) for year j (includes all control types ac, all crash types at, and all severities as) (crashes/yr); and ns = number of years in the study period (yr). Equation 19-18

549 Equation 19-18 is used to compute the total expected number of crashes estimated to occur in the project limits during the study period. The summation of crashes for each terminal type, cross section, control type, crash type, and severity for each site and year is not shown in mathematic terms (but it is implied by the subscripts w, ac, at, and as, respectively). Equation 19-19 is used to estimate the overall expected average crash frequency within the project limits during the study period. s asatacaSe asatacaSe n N N * ,,,, ,,,, = Where: Ne, aS, ac, at, as = overall expected average crash frequency for all sites aS and all years in the study period (includes all cross sections and control types ac, all crash types at, and all severities as) (crashes/yr). Step 17—Determine if there is an alternative design, treatment, or forecast AADT to be evaluated. Steps 3 through 17 are repeated as appropriate for the same project limits but for alternative conditions, treatments, periods of interest, or forecast AADT volumes. Step 18—Evaluate and compare results. The predictive method is used to provide a statistically reliable estimate of the expected average crash frequency (in total, or by crash type and severity) for the specified project limits, study period, geometric design and traffic control features, and known or estimated AADT volume. 19.4.2. Data Needed to Apply the Predictive Method The input data needed for the predictive models are identified in this section. These data represent the geometric design features, traffic control features, and traffic demand characteristics that have been found to have some relationship to safety. They are identified by bullet in this section, and are listed in Table B- 2 of Appendix B to Part C. The input data are needed for each site in the project limits. Criteria for defining site boundaries are described in Section 19.5. The data are described in two subsections. The first subsection describes input data for ramp and C-D road segments. The second subsection describes input data for crossroad ramp terminals. Features of Ramp and C-D Road Segments The input data needed for ramp and C-D road segments is described in this subsection. There are several data identified in this section that describe a length along the roadway (e.g., segment length, curve length, weaving section length, etc.). All of these lengths are measured along the reference line, which is the right edge of traveled way in the direction of travel. Points that do not lie on the reference line must be projected onto the reference line (along a perpendicular line if the alignment is straight, or along a radial line if the alignment is curved) to facilitate length determination. These dimensions can be obtained from field measurements, a plan set, or aerial photographs.  Number of through lanes. The total number of through lanes in the segment. Rural ramp segments are limited to one lane. Urban ramp segments are limited to two lanes. A segment with a lane-add (or lane- drop) taper is considered to have the same number of through lanes as the roadway just downstream of Equation 19-19

550 the lane-add (or lane-drop) taper. If the segment ends at a ramp terminal, then the number of through lanes is not based on the lane assignment, or lane markings, at the terminal. Do not include any high-occupancy vehicle (HOV) bypass lanes. Do not include any auxiliary lanes that are associated with a C-D road weaving section, unless the weaving section length exceeds 0.30 mi (1,600 ft). If this length is exceeded, then the auxiliary lane is counted as a through lane that starts as a lane-add ramp entrance and ends as a lane-drop ramp exit. Do not include any auxiliary lanes that are developed as a turn bay (for queued vehicle storage) at the crossroad ramp terminal. Do not include the speed-change lane that is associated with a second ramp that merges with (or diverges from) the subject ramp, unless its length exceeds 0.19 mi (1,000 ft). If this length is exceeded, then the speed-change lane is counted as a through lane that starts as a lane-add ramp entrance and ends as a lane drop by taper (or starts as a lane add by taper and ends as a lane-drop ramp exit). This guidance is illustrated in Figure 19-3 using a portion of an exit ramp. The portion is shown to end at the crossroad ramp terminal. It consists of three segments. The first segment ends at the lane add section and has one lane. The second segment ends at the start of the bay taper and has two lanes. The third segment ends at the crossroad. Four lanes are shown at the downstream end of this segment, but two of the lanes are in turn bays and are not included in the determination of the number of through lanes for the segment. Thus, this segment is considered to have two lanes (= 4 – 2) for this application. Segment 1 (1 lane) Segment 2 (2 lanes) Segment 3 (2 lanes) Figure 19-3. Number-of-Lanes Determination for Ramp Segments  Length of ramp or C-D road segment.  Average traffic speed on the freeway during off-peak periods of the typical day. This speed is used to compute the speed for each curve (if any) that is present on the ramp. If better information is not available, then this speed can be estimated as the freeway’s maximum speed limit.  Type of traffic control used at the crossroad ramp terminal to regulate intersecting traffic (none, yield, stop, signal). The term “None” is appropriate if the ramp intersects the crossroad as a speed-change lane or as a lane added (or lane dropped).  Presence of a horizontal curve prior to (or in) the subject segment. Curves located prior to the segment influence the speed on the subject segment. For each curve located prior to (or in) the segment, the following data are needed:  Length of curve. Curve length is measured along the reference line from the point where the tangent ends and the curve begins (i.e., the PC) to the point where the curve ends and the tangent begins (PT).

551 If the curve has spiral transitions, then measure from the “effective” PC point to the “effective” PT point. The effective PC point is located midway between the TS and SC, where the TS is the point of change from tangent to spiral and the SC is the point of change from spiral to circular curve. The effective PT is located midway between the CS and ST. If the curve is continued from a curve on an intersecting alignment, then consider only the curve length on the subject alignment. For example, if the subject ramp diverges from another ramp and the curvature from the originating ramp continues into the subject ramp, then the curve on the subject ramp is considered to start at the beginning of the subject ramp (i.e., at the gore point).  Radius of curve. The radius is defined by the right edge of traveled way. If the curve has spiral transitions, then use the radius of the central circular portion of the curve.  Length of curve in segment. The length of the curve within the boundaries of the segment. This length cannot exceed the segment length or the curve length.  Ramp-mile of beginning of curve in direction of travel. This value equals the distance from ramp- mile 0.0 to the point where the tangent ends and the curve begins. Ramp-mile locations are measured along the right edge of the ramp traveled way in the direction of travel (in the absence of tapers and speed-change lanes, this edge coincides with the right edge of traveled way). These locations are established for this application, and may or may not coincide with the mileposts (or stations) established for the ramp’s design. The gore point will often be used to define ramp-mile 0.0 for a ramp or C-D road. The gore point is located where the pair of solid white pavement edge markings that separate the ramp from the intersecting roadway are 2.0 ft apart. If the markings do not extend to a point where they are 2.0 ft apart, then the gore point is found by extrapolating both markings until the extrapolated portion is 2.0 ft apart. This point is shown in the top part of Figure 19-4. For exit ramps and C-D roads that diverge from the freeway (and entrance ramps that diverge from the crossroad using a speed-change lane), ramp-mile 0.0 is located where the gore point projects onto the ramp reference line. The ramp reference line is defined as the right edge of the ramp traveled way. For entrance ramps that intersect the crossroad, ramp-mile 0.0 is located where the ramp reference line intersects with the near edge of traveled way of the crossroad. This point is shown in the bottom part of Figure 19-4. If two or more ramps merge such that there is a choice of two or more points at which ramp-mile 0.0 could be established for curves downstream of the merge point, then establish ramp-mile 0.0 for these curves on the ramp with the highest volume. If the subject curve is preceded by a spiral transition, then measure to the “effective” curve beginning point. This point is located midway between the TS and SC, where the TS is the point of change from tangent to spiral and the SC is the point of change from spiral to circular curve.

552 Gore point 2 ft Ramp-mile 0.0 Ramp-mile 0.0 Exit Ramp, C-D Road, Entrance Ramp with Speed-Change Lane Entrance Ramp with Intersection Measure lane and shoulder widths in areas with constant cross section. Measure along a line such as line A or line B. If necessary, move the line off the subject segment to the nearest point with constant cross section. A BThis barrier is on the ramp. This barrier is on the freew ay. This barrier is on the freew ay and ramp. Reference line Reference line Figure 19-4. Starting Location on Ramps and C-D Roads  Widths of lanes, right shoulder, and left shoulder. These elements represent an average for the segment. These widths should be measured where the cross section is constant, such as along line A or B shown in Figure 19-4. They should not be measured where one or more edges are discontinuous or tapered. If a width varies along the segment (but not enough to justify beginning a new segment), then compute the length-weighted average width. Rules for defining segment boundaries are provided in Section 19.5.2.  Lane width. This width is computed as an average for all through lanes.  Shoulder width. This width represents only the paved width.  Length of (and offset to) the right-side barrier and the left-side barrier. Measured separately for each short piece of barrier and for barrier that continues for the length of the segment (and beyond). Each piece is represented once for a site. Barrier length is measured along the reference line. Offset is measured from the nearest edge of traveled way to the barrier face. Figure 19-5 illustrates these measurements for a barrier element protecting a sign support on the right side of a ramp with right shoulder width Wrs. The barrier element has a portion of its length that is parallel to the ramp and a portion of its length that is tapered away from the ramp. To evaluate this element, separate it into two pieces, as shown in Figure 19-5. Each piece is represented by its average offset Woff, r, i and length Lrb, i. Barrier pieces with the same offset can be combined by adding their length and using their common offset. A barrier is associated with a ramp if its offset from the near edge of traveled way is 30 ft or less. Barrier adjacent to the freeway but also within 30 ft of the ramp traveled way should also be associated with the ramp. The determination of whether a barrier is adjacent to a freeway speed-change lane or a ramp is based on the gore point, as shown in Figure 19-4.

553 Traveled way Right shoulder Left shoulder Wof f ,r,2 Lrb,2Lrb,1 Wof f ,r,1Wrs Reference line Figure 19-5. Barrier Variables  Presence of an entrance speed-change lane (due to a second merging ramp). If a speed-change lane is present, then the length of the speed-change lane in the segment is needed. Guidance for measuring this length is provided in the following list. Speed-change lane length in the segment is measured between the segment’s begin and end points. It cannot exceed the length of the segment, regardless of the length of the speed-change lane. It cannot exceed the length of the speed-change lane. Speed-change lane length is measured along the edge of the subject ramp traveled way from the gore point to the taper point. The gore point is located where the pair of solid white pavement edge markings that separate the subject ramp from the intersecting ramp are 2.0 ft apart. If the markings do not extend to a point where they are 2.0 ft apart, then the gore point is found by extrapolating both markings until the extrapolated portion is 2.0 ft apart. This point is shown in Figure 19-6. The taper point is located where the outside edge marking of the intersecting ramp intersects the subject ramp’s outside edge marking. It marks the point where the taper ends (or begins). It is shown in Figure 19-6. Taper point Exit Ramp with Taper Design Entrance Ramp with Parallel Design Ramp Exit Length Ramp Entrance Length * * * Point where marked gore is 2 ft wide (gore point) Taper point Figure 19-6. Speed-Change Lane Location on Ramps and C-D Roads  Presence of an exit speed-change lane (due to a second diverging ramp). If a speed-change lane is present, then the length of the speed-change lane in the segment is needed. Guidance for measuring this length is the same as for entrance speed-change lanes.

554  Lane added to the ramp or C-D road (not as a result of a second merging ramp). If a lane is added, then the length of the taper in the segment is needed. Guidance for measuring this length is provided in the following list:  Length of taper in the segment. This length is measured between the segment’s begin and end points. This length cannot exceed the length of the segment. This length cannot exceed the taper length.  Taper length. This length is measured along the edge of the ramp traveled way from the point where the traveled way width first begins changing to the point where this width first stops changing. Traveled way width is measured between the solid white pavement edge lines.  Lane dropped from the ramp or C-D road (not as a result of a second diverging ramp). If a lane is dropped, then the length of the taper in the segment is needed. Guidance for measuring this length is the same as for the lane add case.  Presence of a weaving section on a C-D road segment. If the segment is partially or wholly within a weaving section then the following data are needed:  Weaving section length. This length is measured along the edge of the C-D road traveled way from the gore point of the ramp entrance to the gore point of the next ramp exit, as shown in Figure 19-7. The gore point is located where the pair of solid white pavement edge markings that separate the ramp from the C-D road are 2.0 ft apart. If the markings do not extend to a point where they are 2.0 ft apart, then the gore point is found by extrapolating both markings until the extrapolated portion is 2.0 ft apart. If the measured gore-to-gore distance exceeds 0.30 mi (1,600 ft), then a weaving section is not considered to exist. Rather, the entrance ramp is a “lane add” and the exit ramp is a “lane drop.”  Length of weaving section located in the segment, between the segment’s begin and end points. This length cannot exceed the length of the segment. This length cannot exceed the length of the weaving section.  Segment AADT volume. Lwev = w eaving section length 2' 2' Lwev Figure 19-7. C-D Road Weaving Section Length Features of Crossroad Ramp Terminals The input data that describe a crossroad ramp terminal are described in this subsection. The phrase “crossroad ramp terminal” refers to a controlled terminal between the ramp and crossroad. This type of terminal is addressed by the predictive method. A terminal where the ramp merges with (or diverges from) the crossroad as a speed-change lane is not addressed by the predictive method. Figure 19-8a and Figure 19-8b illustrate these two terminal types.

555 a. Four-Leg Intersection and Three-Leg Intersection b. Speed-Change Lane c. Two Three-Leg Intersections and a Speed-Change Lane Figure 19-8. Illustrative Ramp Terminals If the crossroad intersects two ramps that are relatively near one another, there may be some question as to whether the two ramps are part of one intersection or two separate intersections (for the purpose of applying the predictive method). The following guidance is offered to help with this decision; however, some engineering judgment may also be required. If the centerlines of the two ramps are offset by 75 ft or less, and they are configured to function as one intersection, then both ramps are considered to be part of the same intersection. This point is illustrated in Figure 19-8a for the left-side ramp and the right-side ramp at an interchange. Two intersections are shown in this figure. If the two ramps are offset by more than 250 ft, then each ramp terminal is considered to form a separate intersection. This point is illustrated in Figure 19-8c for the left-side ramps at a four-quadrant parclo B interchange. Two intersections are shown in this figure. Occasionally, the ramp offset is between 75 and 250 ft. In this situation, engineering judgment is required to determine whether the two ramps function as one or two intersections. Factors considered in making Crossroad Left-Side Ramp Right-Side Ramp Intersection center ≤ 75 ft≤ 75 ft Crossroad Left-Side Ramp 2 (entrance ramp) > 250 ft Left-Side Ramp 1 (exit ramp) Left-Side Ramp 3 (exit ramp) Speed-Change Lane Crossroad Exit Ramp

556 this determination will include the intersection control, traffic volume level, traffic movements being served (see Figure 19-1), channelization, average queue length, and pavement markings. Higher volume conditions often dictate that the two ramps are controlled as one signalized intersection. Ramp offsets in this range are typically avoided for new designs. A description of the following geometric design and traffic control features is needed to use the CMFs associated with the predictive model for crossroad ramp terminals:  Ramp terminal configuration, as described in Figure 19-1.  Ramp terminal control type (signal, one-way stop control, all-way stop control). The predictive models are calibrated to address signal control and one-way stop control, where the ramp is stop controlled. An interim predictive model is provided in Section 19.10 for all-way stop control.  Presence of a non-ramp public street leg at the terminal (signal control). This situation occurs occasionally. When it does, the public street leg is opposite from one ramp, and the other ramp either does not exist or is located at some distance from the subject ramp terminal such that it is not part of the terminal. This information is needed only for signalized terminals.  Exit ramp skew angle (one-way stop control). Skew angle equals 90 minus the intersection angle (in degrees). These angles are shown in Figure 19-9. The intersection angle is the acute angle between the crossroad centerline and a line along the center of an imaginary vehicle stopped at the end of the ramp (i.e., where it joins the crossroad). The vehicle is centered in the traveled way and behind the stop line. If vehicles can exit the ramp as left- or right-turn movements, then use a left-turning vehicle as the vehicle of reference. This information is needed only for terminals with one-way stop control. At a B4 terminal configuration, the skew angle represents that for the diagonal exit ramp (not the loop exit ramp). Reference angles to a left-turn vehicle at the stop line. Skew angle Crossroad Intersection angle Intersection angle Skew angle If a left-turn movement is not served by the ramp, then reference angles to a right-turn vehicle at the stop line. Inside approach Outside approach Inside approachOutside approach Figure 19-9. Exit Ramp Skew Angle  Distance to the next public street intersection on the outside crossroad leg. This data element represents the distance between the subject ramp terminal and the nearest public street intersection located in a direction away from the freeway (measured along the crossroad from subject terminal center to intersection center).

557  Distance to the adjacent ramp terminal. This data element represents the distance between the subject ramp terminal and the adjacent ramp terminal (measured along the crossroad from terminal center to terminal center). If there is no adjacent ramp terminal, then use the distance to the next public street intersection (located on the crossroad in the direction opposite to the intersection described in the previous bullet).  Presence of protected left-turn operation (signal control). This information is needed for each crossroad left-turn movement that exists at the terminal. An affirmative response is indicated if the left-turn operates as protected only. If it operates as permissive or protected-permissive, then the response is negative. This information is needed only for signalized terminals.  Exit ramp right-turn control type. This information is needed only for the exit ramp (at terminals with an exit ramp). It is focused on the right-turn movement, which may have a different control type than the left-turn movement. Control types considered include: free flow, merge, yield, stop, and signal (where free-flow and merge operation are recognized to represent “no control”). The free-flow type is associated with an accepting (or auxiliary) lane on the crossroad for the right-turn movement. The merge type is associated with a speed-change lane for the right-turn movement.  Crossroad median width. This width is measured along a line perpendicular to the centerline of the crossroad in the vicinity of the intersection. If no median exists, then a width of 0.0 ft is used in the predictive model. If a raised curb is present, then the width is measured from face-of-curb to face-of- curb. If a raised curb is not present, then the width is measured between the near edge of traveled way for the two opposing travel directions. If a left-turn bay is present, then the median width includes the width of the left-turn bay. It is measured from the lane line delineating the bay to the face-of-curb adjacent to (or the near edge of traveled way for) the opposing travel direction. If the median width is different on the two crossroad legs, then use an average of the two widths.  Number of through lanes on the inside crossroad approach. Number of lanes (shared or exclusive) serving through traffic on the crossroad approach that is nearest to the freeway (i.e., the inside approach), as shown in Figure 19-9. This variable includes only lanes that continue through the intersection. Count the lanes along the crosswalk (or the logical location of the crosswalk if it is not marked).  Number of through lanes on the outside crossroad approach. Number of lanes (shared or exclusive) serving through traffic on the crossroad approach that is more distant from the freeway (i.e., the outside approach), as shown in Figure 19-9. This variable includes only lanes that continue through the intersection. Count the lanes along the crosswalk (or the logical location of the crosswalk if it is not marked).  Number of lanes on the exit ramp leg at the terminal. Lanes can serve any movement (left, right, or through). If right-turn channelization is provided, then count the lanes at the last point where all exiting movements are joined (i.e., count at the channelization gore point). All lanes counted must be fully developed for 100 ft or more before they intersect the crossroad. If a lane’s development length is less than 100 ft, then it is not counted as a lane for this application. The lane (or lanes) associated with the loop exit ramp at a B4 terminal configuration are not included in this count.  Presence of right-turn channelization on the inside crossroad approach (signal control). This channelization creates a turning roadway that serves right-turn vehicles. It is separated from the intersection by a triangular channelizing island (delineated by markings or raised curb). The gore point at the upstream end of the island must be within 200 ft of the downstream stop line for right-turn channelization to be considered “present.” If this distance exceeds 200 ft, then the right-turn movement is served by a ramp roadway that is separate from the intersection (i.e., it should be evaluated as a

558 ramp). The right-turn movement can be free-flow, stop, or yield controlled. This information is needed only for signalized terminals.  Presence of right-turn channelization on the outside crossroad approach (signal control). The guidance provided in the previous bullet also applies to this variable. It is needed only for signalized terminals.  Presence of right-turn channelization on the exit ramp approach (signal control). The guidance provided in the previous bullet also applies to this variable. It is needed only for signalized terminals. The presence of right-turn channelization on the loop exit ramp at a B4 terminal configuration is not considered when determining this input data.  Presence of a left-turn lane (or bay) on the inside crossroad approach. The lane (or bay) can have one or two lanes. A lane (or bay) is considered to be present when it (a) is for the exclusive use of a turn movement, (b) extends 100 ft or more back from the stop line, and (c) ends at the intersection stop line.  Presence of a left-turn lane (or bay) on the outside crossroad approach. The guidance provided in the previous bullet also applies to this variable.  Width of left-turn lane (or bay) on the inside crossroad approach. This variable represents the total width of all lanes that exclusively serve turning vehicles on the subject approach. It is measured from the near edge of traveled way of the adjacent through lane to the near lane marking (or curb face) that delineates the median.  Width of left-turn lane (or bay) on the outside crossroad approach. The guidance provided in the previous bullet also applies to this variable.  Presence of a right-turn lane (or bay) on the inside crossroad approach. The lane (or bay) can have one or two lanes. A lane (or bay) is considered to be present when it (a) is for the exclusive use of a turn movement, (b) extends 100 ft or more back from the stop line, and (c) satisfies one of the following rules. If the bay or turn lane does not have island channelization at the intersection, then it must end at the intersection stop line. If the bay or turn lane has island channelization at the intersection, then the bay or turn lane must have (a) stop, yield, or signal control at its downstream end, and (b) an exit gore point that is within 200 ft of the intersection.  Presence of a right-turn lane (or bay) on the outside crossroad approach. The guidance provided in the previous bullet also applies to this variable.  Number of driveways on the outside crossroad leg (signal control). This number represents the count of unsignalized driveways on the outside crossroad leg and within 250 ft of the ramp terminal. The count is taken on both sides of the leg (i.e., it is a two-way total). The count should only include “active” driveways (i.e., those driveways with an average daily volume of 10 veh/day or more). This information is needed only for signalized terminals.  Number of public street approaches on the outside crossroad leg. This number represents the count of unsignalized public street approaches on the outside crossroad leg and within 250 ft of the ramp terminal. The count is taken on both sides of the leg (i.e., it is a two-way total). If a public street approach is present at the terminal, then it is not counted for this entry. Rather, it is identified as being

559 present using the “Presence of a non-ramp public street leg at the terminal” data that was discussed previously.  AADT volume for the inside crossroad leg, AADT volume for the outside crossroad leg, AADT volume for each ramp leg. The inside crossroad leg is the leg that is on the side of the ramp terminal nearest to the freeway. The outside crossroad leg is on the other side of the ramp terminal. The AADT of the loop ramp at a terminal with a either an A4 or B4 configuration is not needed (or used in the calculations). 19.5. RAMP SEGMENTS AND RAMP TERMINALS This section consists of three subsections. The first subsection defines ramp segments, C-D road segments, and crossroad ramp terminals. The second subsection provides guidelines for segmenting the ramp or C-D road. The assignment of crashes to sites is discussed in the last subsection. 19.5.1. Definition of Ramp Segment and Ramp Terminal When using the predictive method, the ramps and C-D roads within the defined project limits are divided into individual sites. A site is a homogeneous ramp segment, a homogeneous C-D road segment, or a crossroad ramp terminal. Four ramps and one C-D road are shown in Figure 19-10. This figure represents one side of an interchange. Each ramp is shown to consist of one segment. The C-D road is divided into five segments. The ramp segments are labeled Ren1, Ren2, Rex3, and Rex4. The C-D road segments are labeled CD1 to CD5. Two of the C-D road segments include a speed-change lane with a ramp. A third C-D road segment includes two speed-change lanes associated with the two loop ramps. The C-D road is not shown to have a weaving section; however, the predictive models can address C-D roads with or without a weaving section. One crossroad ramp terminal is shown in Figure 19-10. It is labeled In, and is noted to have an influence area that extends 250 ft in each direction along the crossroad and ramps. The terminal has four legs–two crossroad legs and two ramp legs. Given the presence of the loop ramps, it is likely that this terminal serves only right-turn maneuvers to and from the crossroad.

560 PLAN VIEW COMPONENT PARTS Collector-Distributor Road Crossroad Ramp Terminal Seg. length = Lcd Type: diagonal, 4-leg 250-ft influence area (note: segment includes ramp speed-change lane) Interchange Ramp Interchange Ramp Type: entrance ramp Type: exit ramp Seg. length = Lr1 Seg. length = Lr3 (note: ramp can be comprised of several segments) (note: ramp can be comprised of several segments) Interchange Ramp Interchange Ramp Type: entrance ramp Type: exit ramp Seg. length = Lr2 Seg. length = Lr4 (note: ramp can be comprised of several segments) (note: ramp can be comprised of several segments) Ren1 Rex3 In In Lr3Lr1 Ren1 Rex3 CD2 CD3CD1 Rex4 Ren2 Ren2 Rex4 CD Len Lex C ro ss ro ad (freeway not shown) CD4 CD5 Lcd3Lcd2Lcd1 Lcd4 Lcd5 Figure 19-10. Illustrative Ramp Segments and Ramp Terminals 19.5.2 Segmentation Process The segmentation process produces a set of segments of varying length, each of which is homogeneous with respect to characteristics such as traffic volume, key geometric design features, and traffic control features. A new homogeneous ramp or C-D road segment begins where there is a change in at least one of the following characteristics of the roadway:  Number of through lanes. Begin segment at the gore point if the lane is added or dropped at a ramp or C-D road. Begin segment at the upstream start of taper if the lane is added or dropped by taper. Guidance in this regard is described in the text accompanying Figure 19-3.  Lane width. Measure the lane width at successive points along the roadway. Compute an average lane width for each point and round this average to the nearest 0.5 ft. Begin a new segment if the rounded value for the current point changes from that of the previous point (e.g., from 12.5 to 13.0 ft).  Right shoulder width. Measure the right shoulder width at successive points along the roadway. Round the measured shoulder width at each point to the nearest 1.0 ft. Begin a new segment if the rounded value for the current point changes from that of the previous point (e.g., from 4 to 5 ft).  Left shoulder width. Measure the left shoulder width at successive points along the roadway. Round the measured shoulder width at each point to the nearest 1.0 ft. Begin a new segment if the rounded value for the current point changes from that of the previous point (e.g., from 4 to 3 ft).

561  Merging ramp or C-D road presence. Begin segment at the gore point.  Diverging ramp or C-D road presence. Begin segment at the gore point. The presence of a horizontal curve does not necessarily define ramp or C-D road segment boundaries. This approach represents a difference with the process described in Chaper 10, where a curve does define segment boundaries. When a segment begins or ends at a crossroad ramp terminal, the length of the segment is measured from the near edge of the crossroad traveled way (shown as ramp-mile 0.0 in the lower half of Figure 19-4). When a segment begins or ends at a terminal formed by a merging or diverging ramp or C-D road, then the length of the segment is measured from the gore point, as shown in Figure 19-4. A ramp or C-D road segment can include no more than one ramp entrance (i.e., merge with a second ramp) and one ramp exit (i.e., diverge with a second ramp). Guidance regarding the location of the lane and shoulder width measurement points is provided in Figure 19-4. Each width represents an average for the segment. The rounded lane and shoulder width values are used solely to determine segment boundaries. Once these boundaries are determined, the unrounded values for the segment are then used for all subsequent calculations in the predictive method. 19.5.3. Crash Assignment to Sites Observed crash counts are assigned to the individual sites to apply the site-specific EB Method. Any crashes that occur on a ramp or C-D road are classified as either intersection-related or segment-related crashes. The intersection-related crashes are assigned to the corresponding crossroad ramp terminal. The predictive model for crossroad ramp terminals estimates the frequency of these crashes. The segment- related crashes are assigned to the corresponding ramp or C-D road segment. The ramp segment predictive model estimates the frequency of these crashes. The procedure for assignment of crashes to individual sites is presented in Section B.2.3 in Appendix B to Part C. Speed-change lanes can occur at locations where ramp segments and C-D road segments connect, or where two ramp segments connect. For the predictive method, these speed-change lanes are considered to be part of the ramp or C-D road segment. Crashes occurring in these speed-change lanes are assigned to the segment. 19.6. SAFETY PERFORMANCE FUNCTIONS When using the predictive method, the appropriate safety performance functions (SPFs) are used to estimate the predicted average crash frequency of a site with base conditions. Each SPF was developed as a regression model using observed crash data for a set of similar sites as the dependent variable. The SPFs, like all regression models, estimate the value of the dependent variable as a function of a set of independent variables. The independent variables for the ramp and C-D road segment SPFs include the segment AADT volume, segment length, and area type (i.e., rural or urban). The independent variables for the crossroad ramp terminal SPFs include the AADT volume of the intersection legs and area type. The SPFs in this chapter are summarized in Table 19-3. A detailed discussion of SPFs and their use in the HSM is presented in Section 3.5.2 of Chapter 3, and in Section C.6.3 of Part C. Some transportation agencies may have performed statistically-sound studies to develop their own jurisdiction-specific SPFs. These SPFs may be substituted for the SPFs presented in this chapter. Criteria for the development of SPFs for use in the predictive method are addressed in the calibration procedure presented in Section B.1.2 in Appendix B to Part C.

562 Each SPF has an associated overdispersion parameter k. The overdispersion parameter provides an indication of the statistical reliability of the SPF. The closer the overdispersion parameter is to zero, the more statistically reliable the SPF. This parameter is used in the EB Method that is discussed in Section B.2 in Appendix B to Part C. Table 19-3. Ramp Safety Performance Functions Site Type (w) Cross Section and Control Type (x) Crash Type (y) SPF Equations Ramp segments (rps) Ramp entrance, n lanes (nEN) Multiple vehicle (mv) Equation 19-20 Single vehicle (sv) Equation 19-24 Ramp exit, n lanes (nEX) Multiple vehicle (mv) Equation 19-20 Single vehicle (sv) Equation 19-24 C-D road segments (cds) n lanes (n) Multiple vehicle (mv) Equation 19-22 Single vehicle (sv) Equation 19-26 Three-leg terminals with diagonal exit ramp (D3ex) One-way stop control (ST) All types (at) Equation 19-31 Signal control, n lanes (SGn) All types (at) Equation 19-28 Three-leg terminals with diagonal entrance ramp (D3en) One-way stop control (ST) All types (at) Equation 19-31 Signal control, n lanes (SGn) All types (at) Equation 19-28 Four-leg terminals with diagonal ramps (D4) One-way stop control (ST) All types (at) Equation 19-31 Signal control, n lanes (SGn) All types (at) Equation 19-28 Four-leg terminals at four- quadrant parclo A (A4) One-way stop control (ST) All types (at) Equation 19-31 Signal control, n lanes (SGn) All types (at) Equation 19-28 Four-leg terminals at four- quadrant parclo B (B4) One-way stop control (ST) All types (at) Equation 19-31 Signal control, n lanes (SGn) All types (at) Equation 19-28 Three-leg terminals at two- quadrant parclo A (A2) One-way stop control (ST) All types (at) Equation 19-31 Signal control, n lanes (SGn) All types (at) Equation 19-28 Three-leg terminals at two- quadrant parclo B (B2) One-way stop control (ST) All types (at) Equation 19-31 Signal control, n lanes (SGn) All types (at) Equation 19-28 19.6.1. Safety Performance Functions for Ramp Segments The SPFs for ramp and C-D road segments are presented in this section. Specifically, SPFs are provided for ramp and C-D road segments with 1 or 2 through lanes. The range of AADT volume for which these SPFs are applicable is shown in Table 19-4. Application of the SPFs to sites with AADT volumes substantially outside these ranges may not provide reliable results.

563 Table 19-4. Applicable AADT Volume Ranges for Ramp SPFs Area Type Cross Section (Through Lanes) (x) Applicable AADT Volume Range (veh/day) Rural 1 0 to 7,000 Urban 1 0 to 18,000 2 0 to 32,000 Other types of ramp and C-D road segments may be found at interchanges, but they are not addressed by the predictive model described in this chapter. Multiple-Vehicle Crashes on Ramp Segments The base conditions for the SPFs for multiple-vehicle crashes on ramp segments are presented in the following list. The variables are defined in Section 19.4.2.  Length of horizontal curve 0.0 mi (i.e., not present)  Lane width 14 ft  Right shoulder width (paved) 8 ft  Left shoulder width (paved) 4 ft  Length of right-side barrier 0.0 mi (i.e., not present)  Length of left-side barrier 0.0 mi (i.e., not present)  Length of lane add or drop 0.0 mi (i.e., not present)  Length of ramp speed-change lane 0.0 mi (i.e., not present) The SPFs for multiple-vehicle crashes on ramp segments is represented using the following equation. ( )][]ln[exp,,,, rrrzmvxrpsspf AADTcdAADTcbaLN ×+××+×= Where: Nspf, rps, x, mv, z = predicted average multiple-vehicle crash frequency of a ramp segment with base conditions, cross section x (x = nEN: n-lane entrance ramp, nEX: n-lane exit ramp), and severity z (z = fi: fatal and injury, pdo: property damage only) (crashes/yr); Lr = length of ramp segment (mi); AADTr = AADT volume of ramp segment (veh/day); a, b, d = regression coefficients; and c = AADT scale coefficient. Equation 19-20

564 The SPF coefficients and inverse dispersion parameter are provided in Table 19-5. The SPFs are illustrated in Figure 19-11 and Figure 19-12. Table 19-5. SPF Coefficients for Multiple-Vehicle Crashes on Ramp Segments Crash Severity (z) Area Type Cross Section (x) SPF Coefficient Inverse Dispersion Parameter Krps, x, mv, z (mi-1) a b c d Fatal and injury (fi) Rural One-lane entrance (1EN) -5.226 0.524 0.001 0.0699 14.6 One-lane exit (1EX) -6.692 0.524 0.001 0.0699 14.6 Urba n One-lane entrance (1EN) -3.505 0.524 0.001 0.0699 14.6 One-lane exit (1EX) -4.971 0.524 0.001 0.0699 14.6 Two-lane entrance (2EN) -3.023 0.524 0.001 0.0699 14.6 Two-lane exit (2EX) -4.489 0.524 0.001 0.0699 14.6 Property damage only (pdo) Rural One-lane entrance (1EN) -3.819 1.256 0.001 0.00 12.7 One-lane exit (1EX) -4.851 1.256 0.001 0.00 12.7 Urba n One-lane entrance (1EN) -3.819 1.256 0.001 0.00 12.7 One-lane exit (1EX) -4.851 1.256 0.001 0.00 12.7 Two-lane entrance (2EN) -2.983 1.256 0.001 0.00 12.7 Two-lane exit (2EX) -4.015 1.256 0.001 0.00 12.7 0.0 0.1 0.2 0.3 0.4 0.5 0 4 8 12 16 20 24 28 AADT (1000s of veh/day) PD O M ul tip le -V eh ic le C ra sh Fr eq ue nc y (c ra sh es /y r) 0.2 Mile Segment Length, No Barrier, No Curves 1 Lane 2 Lanes Rural & Urban Ramps C-D Road Entrance Ramp and C-D 0.00 0.05 0.10 0.15 0 4 8 12 16 20 24 28 AADT (1000s of veh/day) FI M ul tip le -V eh ic le C ra sh Fr eq ue nc y (c ra sh es /y r) 0.2 Mile Segment Length, No Barrier, No Curves 1 Lane 2 Lanes Rural Ramp Urban Ramp C-D Road Entrance Ramp and C-D a. Fatal-and-Injury Crash Frequency. b. Property-Damage-Only Crash Frequency. Figure 19-11. Graphical Form of the SPFs for Multiple-Vehicle Crashes on Entrance Ramp Segments

565 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0 4 8 12 16 20 24 28 AADT (1000s of veh/day) FI M ul tip le -V eh ic le C ra sh Fr eq ue nc y (c ra sh es /y r) 0.2 Mile Segment Length, No Barrier, No Curves 1 Lane 2 Lanes Rural Ramp Urban Ramp Exit Ramp 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0 4 8 12 16 20 24 28 AADT (1000s of veh/day) PD O M ul tip le -V eh ic le C ra sh Fr eq ue nc y (c ra sh es /y r) 0.2 Mile Segment Length, No Barrier, No Curves 1 Lane 2 Lanes Rural & Urban Ramps Exit Ramp a. Fatal-and-Injury Crash Frequency b. Property-Damage-Only Crash Frequency Figure 19-12. Graphical Form of the SPFs for Multiple-Vehicle Crashes on Exit Ramp Segments The value of the overdispersion parameter associated with the SPFs for ramp segments is determined as a function of the segment length. This value is computed using Equation 19-21. rzmvxrps zmvxrps LK k × = ,,, ,,, 1 Where: krps, x, mv, z = overdispersion parameter for ramp segments with cross section x, multiple-vehicle crashes mv, and severity z; and Krps, x, mv, z = inverse dispersion parameter for ramp segments with cross section x, multiple-vehicle crashes mv, and severity z (mi-1). The crash frequency obtained from Equation 19-20 can be multiplied by the proportions in Table 19-6 to estimate the predicted average multiple-vehicle crash frequency by crash type category. Table 19-6. Default Distribution of Multiple-Vehicle Crashes by Crash Type for Ramp and C-D Road Segments Area Type Crash Type Category Proportion of Crashes by Severity Fatal and Injury Property Damage Only Rural or urban Head-on 0.015 0.009 Right-angle 0.010 0.005 Rear-end 0.707 0.550 Sideswipe 0.129 0.335 Other multiple-vehicle crashes 0.139 0.101 Equation 19-21

566 Multiple-Vehicle Crashes on C-D Road Segments The base conditions for the SPFs for multiple-vehicle crashes on C-D road segments are the same as those for multiple-vehicle crashes on ramp segments, as described in the preceding subsection. One additional base condition for this SPF is that there is no weaving section present. The SPFs for multiple-vehicle crashes on C-D road segments is represented using the following equation. ( )][]ln[exp,,,, cccdzmvncdsspf AADTcdAADTcbaLN ×+××+×= Where: Nspf, cds, n, mv, z = predicted average multiple-vehicle crash frequency of a C-D road segment with base conditions, n lanes, and severity z (z = fi: fatal and injury, pdo: property damage only) (crashes/yr); Lcd = length of C-D road segment (mi); and AADTc = AADT volume of C-D road segment (veh/day). The SPF coefficients and inverse dispersion parameter are provided in Table 19-7. The SPFs are illustrated in Figure 19-11. Table 19-7. SPF Coefficients for Multiple-Vehicle Crashes on C-D Road Segments Crash Severity (z) Area Type Number of Through Lanes (n) SPF Coefficient Inverse Dispersion Parameter Kcds, x, mv, z (mi-1) a b c d Fatal and injury (fi) Rural 1 -4.718 0.524 0.001 0.0699 14.6 Urban 1 -2.997 0.524 0.001 0.0699 14.6 2 -2.515 0.524 0.001 0.0699 14.6 Property damage only (pdo) Rural 1 -3.311 1.256 0.001 0.00 12.7 Urban 1 -3.311 1.256 0.001 0.00 12.7 2 -2.475 1.256 0.001 0.00 12.7 The value of the overdispersion parameter associated with the SPFs for C-D road segments is determined as a function of the segment length. This value is computed using Equation 19-23. cdzmvxcds zmvxcds LK k × = ,,, ,,, 1 Where: kcds, x, mv, z = overdispersion parameter for C-D road segments with cross section x, multiple-vehicle crashes mv, and severity z; and Kcds, x, mv, z = inverse dispersion parameter for C-D road segments with cross section x, multiple- vehicle crashes mv, and severity z (mi-1). Equation 19-22 Equation 19-23

567 The crash frequency obtained from Equation 19-22 can be multiplied by the proportions in Table 19-6 to estimate the predicted average multiple-vehicle crash frequency by crash type category. Single-Vehicle Crashes on Ramp Segments With one exception, the base conditions for the SPFs for single-vehicle crashes on ramp segments are the same as those for multiple-vehicle crashes on ramp segments, as described in a preceding subsection. The “ramp speed-change lane presence” condition does not apply to the single-vehicle SPFs. The SPFs for single-vehicle crashes on ramp segments are represented with the following equation. ( )]ln[exp,,,, rrzsvxrpsspf AADTcbaLN ××+×= Where: Nspf, rps, x, sv, z = predicted average single-vehicle crash frequency of a ramp segment with base conditions, cross section x (x = nEN: n-lane entrance ramp, nEX: n-lane exit ramp), and severity z (z = fi: fatal and injury, pdo: property damage only) (crashes/yr). The SPF coefficients and inverse dispersion parameter are provided in Table 19-8. The SPFs are illustrated in Figure 19-13 and Figure 19-14. Table 19-8. SPF Coefficients for Single-Vehicle Crashes on Ramp Segments Crash Severity (z) Area Type Cross Section (x) SPF Coefficient Inverse Dispersion Parameter Krps, x, sv, z (mi-1) a b c Fatal and injury (fi) Rural One-lane entrance (1EN) -2.120 0.718 0.001 7.91 One-lane exit (1EX) -1.799 0.718 0.001 7.91 Urban One-lane entrance (1EN) -1.966 0.718 0.001 7.91 One-lane exit (1EX) -1.645 0.718 0.001 7.91 Two-lane entrance (2EN) -1.999 0.718 0.001 7.91 Two-lane exit (2EX) -1.678 0.718 0.001 7.91 Property damage only (pdo) Rural One-lane entrance (1EN) -1.946 0.689 0.001 9.77 One-lane exit (1EX) -1.739 0.689 0.001 9.77 Urban One-lane entrance (1EN) -1.715 0.689 0.001 9.77 One-lane exit (1EX) -1.508 0.689 0.001 9.77 Two-lane entrance (2EN) -1.400 0.689 0.001 9.77 Two-lane exit (2EX) -1.193 0.689 0.001 9.77 Equation 19-24

568 0.00 0.10 0.20 0.30 0.40 0 4 8 12 16 20 24 28 AADT (1000s veh/day) FI S in gl e- Ve hi cl e C ra sh Fr eq ue nc y (c ra sh es /y r) 1 Lane Rural Ramp Urban Ramp C-D Road 0.2 Mile Segment Length, No Barrier, No Curves 2 Lanes Entrance Ramp and C-D 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0 4 8 12 16 20 24 28 AADT (1000s veh/day) PD O S in gl e- Ve hi cl e C ra sh Fr eq ue nc y (c ra sh es /y r) 1 Lane Rural Ramp Urban Ramp C-D Road 0.2 Mile Segment Length, No Barrier, No Curves 2 Lanes Entrance Ramp and C-D 0.00 0.10 0.20 0.30 0.40 0 4 8 12 16 20 24 28 AADT (1000s veh/day) FI S in gl e- Ve hi cl e C ra sh Fr eq ue nc y (c ra sh es /y r) 1 Lane 1 Lane 2 Lanes Rural Ramp Urban Ramp 0.2 Mile Segment Length, No Barrier, No Curves Exit Ramp 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0 4 8 12 16 20 24 28 AADT (1000s veh/day) PD O S in gl e- Ve hi cl e C ra sh Fr eq ue nc y (c ra sh es /y r) 1 Lane 1 Lane 2 Lanes Rural Ramp Urban Ramp 0.2 Mile Segment Length, No Barrier, No Curves Exit Ramp a. Fatal-and-Injury Crash Frequency b. Property-Damage-Only Crash Frequency Figure 19-13. Graphical Form of the SPFs for Single-Vehicle Crashes on Entrance Ramp Segments a. Fatal-and-Injury Crash Frequency b. Property-Damage-Only Crash Frequency Figure 19-14. Graphical Form of the SPFs for Single-Vehicle Crashes on Exit Ramp Segments The value of the overdispersion parameter associated with the SPFs for ramp segments is determined as a function of the segment length. This value is computed using Equation 19-25. rzsvxrps zsvxrps LK k × = ,,, ,,, 1 Where: krps, x, sv, z = overdispersion parameter for ramp segments with cross section x, single-vehicle crashes mv, and severity z; and Krps, x, sv, z = inverse dispersion parameter for ramp segments with cross section x, single-vehicle crashes mv, and severity z (mi-1). The crash frequency obtained from Equation 19-24 can be multiplied by the proportions in Table 19-9 to estimate the predicted average single-vehicle crash frequency by crash type category. Equation 19-25

569 Table 19-9. Default Distribution of Single-Vehicle Crashes by Crash Type for Ramp and C-D Road Segments Area Type Crash Type Category Proportion of Crashes by Severity Fatal and Injury Property Damage Only Rural Crash with animal 0.012 0.022 Crash with fixed object 0.422 0.538 Crash with other object 0.000 0.011 Crash with parked vehicle 0.024 0.055 Other single-vehicle crashes 0.542 0.374 Urban Crash with animal 0.003 0.005 Crash with fixed object 0.718 0.834 Crash with other object 0.015 0.023 Crash with parked vehicle 0.012 0.012 Other single-vehicle crashes 0.252 0.126 Single-Vehicle Crashes on C-D Road Segments With one exception, the base conditions for the SPFs for single-vehicle crashes on C-D road segments are the same as those for multiple-vehicle crashes on ramp segments, as described in a preceding subsection. The “ramp speed-change lane presence” condition does not apply to the single-vehicle SPFs. One additional base condition for this SPF is that there is no weaving section present. The SPFs for single-vehicle crashes on C-D road segments are represented with the following equation. ( )]ln[exp,,,, ccdzsvncdsspf AADTcbaLN ××+×= Where: Nspf, cds, n, sv, z = predicted average single-vehicle crash frequency of a C-D road segment with base conditions, n lanes, and severity z (z = fi: fatal and injury, pdo: property damage only) (crashes/yr). The SPF coefficients and inverse dispersion parameter are provided in Table 19-10. The SPFs are illustrated in Figure 19-13. Equation 19-26

570 Table 19-10. SPF Coefficients for Single-Vehicle Crashes on C-D Road Segments Crash Severity (z) Area Type Number of Through Lanes (n) SPF Coefficient Inverse Dispersion Parameter Kcds, n, sv, z (mi-1) a b c Fatal and injury (fi) Rural 1 -3.002 0.718 0.001 7.91 Urban 1 -2.848 0.718 0.001 7.91 2 -2.881 0.718 0.001 7.91 Property damage only (pdo) Rural 1 -2.890 0.689 0.001 9.77 Urban 1 -2.659 0.689 0.001 9.77 2 -2.344 0.689 0.001 9.77 The value of the overdispersion parameter associated with the SPFs for C-D road segments is determined as a function of the segment length. This value is computed using Equation 19-27. cdzsvncds zsvncds LK k × = ,,, ,,, 1 Where: kcds, x, sv, z = overdispersion parameter for C-D road segments with cross section x, single-vehicle crashes mv, and severity z; and Kcds, x, sv, z = inverse dispersion parameter for C-D road segments with cross section x, single- vehicle crashes mv, and severity z (mi-1). The crash frequency obtained from Equation 19-26 can be multiplied by the proportions in Table 19-9 to estimate the predicted average single-vehicle crash frequency by crash type category. 19.6.2. Safety Performance Functions for Ramp Terminals The SPFs for crossroad ramp terminals are presented in this section. Specifically, SPFs are provided for crossroad ramp terminals with 2 to 6 crossroad through lanes (total of both travel directions). The range of AADT volume for which these SPFs are applicable is shown in Table 19-11. Application of the SPFs to sites with AADT volumes substantially outside these ranges may not provide reliable results. Other types of crossroad ramp terminal configurations may be found at interchanges, but they are not addressed by the predictive model described in this chapter. Equation 19-27

571 Table 19-11. Applicable AADT Volume Ranges for Crossroad Ramp Terminal SPFs Site Type (w) Control Type (x) Applicable AADT Volume Range (veh/day) Crossroad Total All Ramps Three-leg terminals with diagonal exit ramp (D3ex) Stop control (ST) 0 to 22,000 0 to 8,000 Signal control (SG) 0 to 34,000 0 to 16,000 Three-leg terminals with diagonal entrance ramp (D3en) Stop control (ST) 0 to 22,000 0 to 15,000 Signal control (SG) 0 to 29,000 0 to 21,000 Four-leg terminals with diagonal ramps (D4) Stop control (ST) 0 to 18,000 0 to 10,000 Signal control (SG) 0 to 47,000 0 to 31,000 Four-leg terminals at four- quadrant parclo A (A4) Stop control (ST) 0 to 21,000 0 to 12,000 Signal control (SG) 0 to 71,000 0 to 30,000 Four-leg terminals at four- quadrant parclo B (B4) Stop control (ST) 0 to 20,000 0 to 12,000 Signal control (SG) 0 to 45,000 0 to 29,000 Three-leg terminals at two- quadrant parclo A (A2) Stop control (ST) 0 to 17,000 0 to 12,000 Signal control (SG) 0 to 46,000 0 to 25,000 Three-leg terminals at two- quadrant parclo B (B2) Stop control (ST) 0 to 26,000 0 to 14,000 Signal control (SG) 0 to 44,000 0 to 22,000 Signal-Controlled Crossroad Ramp Terminals The base conditions for the signalized crossroad ramp terminal SPFs are presented in the following list. The variables are defined in Section 18.4.2.  Crossroad left-turn lane (or bay) Not present  Crossroad right-turn lane (or bay) Not present  Public street approach presence No public street approaches present  Driveway presence No driveways present  Distance to adjacent intersection No adjacent ramp or public street intersection within 6 mi  Median width (on crossroad) 12 ft  Protected left-turn phase Not present on either crossroad approach leg  Channelized right turn on crossroad Not present  Channelized right turn on exit ramp Not present

572  Non-ramp public street leg Not present The SPFs for crashes at signalized crossroad ramp terminals are presented using the following equation. ( )]ln[]ln[exp,,,, enexxrdzatSGnwspf AADTcAADTcdAADTcbaN ×+××+××+= with )(5.0 outinxrd AADTAADTAADT +×= Where: Nspf, w,SG n, at, z = predicted average crash frequency of a signal-controlled crossroad ramp terminal of site type w (w = D3ex, D3en, D4, A4, B4, A2, B2) with base conditions, n crossroad lanes, all crash types at, and severity z (z = fi: fatal and injury, pdo: property damage only) (crashes/yr); AADTxrd = AADT volume for the crossroad (veh/day); AADTin = AADT volume for the crossroad leg between ramps (veh/day); AADTout = AADT volume for the crossroad leg outside of interchange (veh/day); AADTex = AADT volume for the exit ramp (veh/day); and AADTen = AADT volume for the entrance ramp (veh/day). The SPF coefficients and inverse dispersion parameter are provided in Table 19-12 to Table 19-15. The SPFs are illustrated in Figure 19-15 to Figure 19-18. The AADT volume of the loop exit ramp at a B4 terminal configuration is not included in AADTex. Similarly, the AADT volume of the loop entrance ramp at an A4 configuration is not included in AADTen. The Exit ramp capacity CMF is combined with the SPF for fatal-and-injury crashes to create the trend lines shown in the figures for fatal-and-injury crashes. This CMF is a function of exit ramp volume, number of exit ramp lanes, and the traffic control for the exit ramp right turn. These variables in combination do not readily lend themselves to the specification of a representative base condition. For this reason, the CMF is combined with the SPF for the graphical presentation. The Exit ramp capacity CMF is described in Section 19.7.2 Equation 19-28 Equation 19-29

573 Table 19-12. SPF Coefficients for Crashes at Signalized Ramp Terminals–Three-Leg Terminal at Two-Quadrant Parclo A or B (A2, B2) Crash Severity (z) Area Type Number of Crossroad Through Lanes (n) SPF Coefficient Inverse Dispersion Parameter Kw, SGn, at, z a b c d Fatal and injury (fi) Rural or urban 2 -0.458 0.325 0.001 0.212 2.17 3 -0.298 0.325 0.001 0.212 2.17 4 -0.138 0.325 0.001 0.212 2.17 5 (urban only) 0.022 0.325 0.001 0.212 2.17 6 (urban only) 0.182 0.325 0.001 0.212 2.17 Property damage only (pdo) Rural or urban 2 -1.537 0.592 0.001 0.516 4.27 3 -1.449 0.592 0.001 0.516 4.27 4 -1.361 0.592 0.001 0.516 4.27 5 (urban only) -1.274 0.592 0.001 0.516 4.27 6 (urban only) -1.186 0.592 0.001 0.516 4.27 Table 19-13. SPF Coefficients for Crashes at Signalized Ramp Terminals–Three-Leg Terminal with Diagonal Exit Ramp or Four-Leg Terminal at Four-Quadrant Parclo A (D3ex, A4) Crash Severity (z) Area Type Number of Crossroad Through Lanes (n) SPF Coefficient Inverse Dispersion Parameter Kw, SGn, at, z a b c d Fatal and injury (fi) Rural or urban 2 -1.352 0.379 0.001 0.394 8.72 3 -1.192 0.379 0.001 0.394 8.72 4 -1.032 0.379 0.001 0.394 8.72 5 (urban only) -0.872 0.379 0.001 0.394 8.72 6 (urban only) -0.712 0.379 0.001 0.394 8.72 Property damage only (pdo) Rural or urban 2 -2.247 0.797 0.001 0.384 4.05 3 -2.159 0.797 0.001 0.384 4.05 4 -2.071 0.797 0.001 0.384 4.05 5 (urban only) -1.984 0.797 0.001 0.384 4.05 6 (urban only) -1.896 0.797 0.001 0.384 4.05

574 Table 19-14. SPF Coefficients for Crashes at Signalized Ramp Terminals–Three-Leg Terminal with Diagonal Entrance Ramp or Four-Leg Terminal at Four-Quadrant Parclo B (D3en, B4) Crash Severity (z) Area Type Number of Crossroad Through Lanes (n) SPF Coefficient Inverse Dispersion Parameter KSw, SGn, at, z a b c d Fatal and injury (fi) Rural or urban 2 -2.068 0.265 0.001 0.905 5.37 3 -1.908 0.265 0.001 0.905 5.37 4 -1.748 0.265 0.001 0.905 5.37 5 (urban only) -1.588 0.265 0.001 0.905 5.37 6 (urban only) -1.428 0.265 0.001 0.905 5.37 Property damage only (pdo) Rural or urban 2 -2.931 0.741 0.001 0.845 3.72 3 -2.843 0.741 0.001 0.845 3.72 4 -2.755 0.741 0.001 0.845 3.72 5 (urban only) -2.668 0.741 0.001 0.845 3.72 6 (urban only) -2.580 0.741 0.001 0.845 3.72 Table 19-15. SPF Coefficients for Crashes at Signalized Ramp Terminals–Four-Leg Terminal with Diagonal Ramps (D4) Crash Severity (z) Area Type Number of Crossroad Through Lanes (n) SPF Coefficient Inverse Dispersion Parameter Kw, SGn, at, z a b c d Fatal and injury (fi) Rural or urban 2 -2.655 1.191 0.001 0.131 11.5 3 -2.495 1.191 0.001 0.131 11.5 4 -2.335 1.191 0.001 0.131 11.5 5 (urban only) -2.175 1.191 0.001 0.131 11.5 6 (urban only) -2.015 1.191 0.001 0.131 11.5 Property damage only (pdo) Rural or urban 2 -2.248 0.879 0.001 0.545 7.21 3 -2.160 0.879 0.001 0.545 7.21 4 -2.072 0.879 0.001 0.545 7.21 5 (urban only) -1.985 0.879 0.001 0.545 7.21 6 (urban only) -1.897 0.879 0.001 0.545 7.21

575 0 5 10 15 20 0 10 20 30 40 50 60 Crossroad AADT (1000s of veh/day) Fl C ra sh F re qu en cy (c ra sh es /y r) Terminal Types: A2, B2 Ramp AADT = 0.32 x Crossroad AADT 6-lane crossroad, 2-lane exit ramp 4-lane crossroad, 1-lane exit ramp 2-lane crossroad, 1-lane exit ramp Exit ramp right turn: signal controlled All other CMFs = 1.00 0 5 10 15 20 25 30 0 10 20 30 40 50 60 Crossroad AADT (1000s of veh/day) PD O C ra sh F re qu en cy (c ra sh es /y r) Terminal Types: A2, B2 Ramp AADT = 0.32 x Crossroad AADT 6-lane crossroad, 2-lane exit ramp 4-lane crossroad, 1-lane exit ramp 2-lane crossroad, 1-lane exit ramp 0 5 10 15 20 0 10 20 30 40 50 60 Crossroad AADT (1000s of veh/day) Fl C ra sh F re qu en cy (c ra sh es /y r) Terminal Type: A4 D3 with exit ramp Ramp AADT = 0.32 x Crossroad AADT 6-lane crossroad, 2-lane exit ramp 4-lane crossroad, 1-lane exit ramp 2-lane crossroad, 1-lane exit ramp Exit ramp right turn: signal controlled All other CMFs = 1.00 0 5 10 15 20 25 30 0 10 20 30 40 50 60 Crossroad AADT (1000s of veh/day) PD O C ra sh F re qu en cy (c ra sh es /y r) Terminal Type: A4 D3 with exit ramp Ramp AADT = 0.32 x Crossroad AADT 6-lane crossroad, 2-lane exit ramp 4-lane crossroad, 1-lane exit ramp 2-lane crossroad, 1-lane exit ramp a. Fatal-and-Injury Crash Frequency b. Property-Damage-Only Crash Frequency Figure 19-15. Graphical Form of the SPF for Crashes at Signalized Ramp Terminals–Three-Leg Terminal at Two-Quadrant Parclo A or B (A2, B2) a. Fatal-and-Injury Crash Frequency b. Property-Damage-Only Crash Frequency Figure 19-16. Graphical Form of the SPF for Crashes at Signalized Ramp Terminals–Three-Leg Terminal with Diagonal Exit Ramp or Four-Leg Terminal at Four-Quadrant Parclo A (D3ex, A4)

576 0 5 10 15 20 0 10 20 30 40 50 60 Crossroad AADT (1000s of veh/day) Fl C ra sh F re qu en cy (c ra sh es /y r) Terminal Type: B4 D3 with entrance ramp Ramp AADT = 0.32 x Crossroad AADT 6-lane crossroad, 2-lane exit ramp 4-lane crossroad, 1-lane exit ramp 2-lane crossroad, 1-lane exit ramp Exit ramp right turn: signal controlled All other CMFs = 1.00 0 5 10 15 20 25 30 0 10 20 30 40 50 60 Crossroad AADT (1000s of veh/day) PD O C ra sh F re qu en cy (c ra sh es /y r) Terminal Type: B4 D3 with entrance ramp Ramp AADT = 0.32 x Crossroad AADT 6-lane crossroad, 2-lane exit ramp 4-lane crossroad, 1-lane exit ramp 2-lane crossroad, 1-lane exit ramp 0 5 10 15 20 0 10 20 30 40 50 60 Crossroad AADT (1000s of veh/day) Fl C ra sh F re qu en cy (c ra sh es /y r) Terminal Type: D4 Ramp AADT = 0.32 x Crossroad AADT 6-lane crossroad, 2-lane exit ramp 4-lane crossroad, 1-lane exit ramp 2-lane crossroad, 1-lane exit ramp Exit ramp right turn: signal controlled All other CMFs = 1.00 0 5 10 15 20 25 30 0 10 20 30 40 50 60 Crossroad AADT (1000s of veh/day) PD O C ra sh F re qu en cy (c ra sh es /y r) Terminal Type: D4 Ramp AADT = 0.32 x Crossroad AADT 6-lane crossroad, 2-lane exit ramp 4-lane crossroad, 1-lane exit ramp 2-lane crossroad, 1-lane exit ramp a. Fatal-and-Injury Crash Frequency b. Property-Damage-Only Crash Frequency Figure 19-17. Graphical Form of the SPF for Crashes at Signalized Ramp Terminals–Three-Leg Terminal with Diagonal Entrance Ramp or Four-Leg Terminal at Four-Quadrant Parclo B (D3en, B4) a. Fatal-and-Injury Crash Frequency b. Property-Damage-Only Crash Frequency Figure 19-18. Graphical Form of the SPF for Crashes at Signalized Ramp Terminals–Four-Leg Terminal with Diagonal Ramps (D4) The value of the overdispersion parameter associated with the SPFs for signalized crossroad ramp terminals is computed using Equation 19-30. zatSGnw zatSGnw K k ,,, ,,, 1= Where: kw, SGn,at, z = overdispersion parameter for signal-controlled site of type w, when n crossroad lanes, all crash types at, and severity z; and Equation 19-30

577 Kw, SGn, at, z = inverse dispersion parameter for signal-controlled site of type w, when n crossroad lanes, all crash types at, and severity z. The crash frequency obtained from Equation 19-28 can be multiplied by the proportions in Table 19-16 to estimate the predicted average signalized crossroad ramp terminal crash frequency by crash type or crash type category. Table 19-16. Default Distribution of Signal-Controlled Ramp Terminal Crashes by Crash Type Area Type Crash Type Crash Type Category Proportion of Crashes by Severity Fatal and Injury Property Damage Only Rural Multiple vehicle Head-on 0.000 0.006 Right-angle 0.333 0.187 Rear-end 0.552 0.466 Sideswipe 0.000 0.219 Other multiple-vehicle crash 0.014 0.013 Single vehicle Crash with animal 0.000 0.000 Crash with fixed object 0.043 0.077 Crash with other object 0.000 0.000 Crash with parked vehicle 0.000 0.013 Other single-vehicle crashes 0.058 0.019 Urban Multiple vehicle Head-on 0.011 0.007 Right-angle 0.260 0.220 Rear-end 0.625 0.543 Sideswipe 0.042 0.149 Other multiple-vehicle crash 0.009 0.020 Single vehicle Crash with animal 0.000 0.000 Crash with fixed object 0.033 0.050 Crash with other object 0.001 0.002 Crash with parked vehicle 0.001 0.002 Other single-vehicle crashes 0.018 0.007 One-Way Stop-Controlled Crossroad Ramp Terminals The predictive models described in this section are calibrated to address one-way stop control, where the ramp is stop controlled. An interim predictive model is provided in Section 19.10 for all-way stop control. The base conditions for the one-way stop-controlled crossroad ramp terminal SPFs are presented in the following list. The variables are defined in Section 18.4.2.

578  Crossroad left-turn lane (or bay) Not present  Crossroad right-turn lane (or bay) Not present  Public street approach presence No public street approaches present  Distance to adjacent intersection No adjacent ramp or public street intersection within 6 mi  Median width (on crossroad) 12 ft  Skew angle 0.0 degrees (i.e., no skew) The SPF for crashes at one-way stop-controlled ramp terminals is applied as follows: ( )]ln[]ln[exp,,,, enexxrdzatSTwspf AADTcAADTcdAADTcbaN ×+××+××+= Where: Nspf, w,ST, at, z = predicted average crash frequency of a one-way stop-controlled crossroad ramp terminal of site type w (w = D3ex, D3en, D4, A4, B4, A2, B2) with base conditions, all crash types at, and severity z (z = fi: fatal and injury, pdo: property damage only) (crashes/yr). The SPF coefficients and inverse dispersion parameter are provided in Table 19-17 to Table 19-20. The SPFs are illustrated in Figure 19-19 to Figure 19-22. The Exit ramp capacity CMF is combined with the SPF for fatal-and-injury crashes to create the trend lines shown in the figures for fatal-and-injury crashes. This CMF is a function of exit ramp volume, number of exit ramp lanes, and the traffic control for the exit ramp right turn. These variables in combination do not readily lend themselves to the specification of a representative base condition. For this reason, the CMF is combined with the SPF for the graphical presentation. The Exit ramp capacity CMF is described in Section 19.7.2. Table 19-17. SPF Coefficients for Crashes at One-Way Stop-Controlled Ramp Terminals–Three-Leg Terminal at Two-Quadrant Parclo A or B (A2, B2) Crash Severity (z) Area Type Number of Crossroad Through Lanes (n) SPF Coefficient Inverse Dispersion Parameter Kw, ST, at, z a b c d Fatal and injury (fi) Rural All lanes -2.363 0.260 0.001 0.947 3.40 Urban All lanes -2.687 0.260 0.001 0.947 3.40 Property damage only (pdo) Rural All lanes -3.055 0.773 0.001 0.878 5.49 Urban All lanes -3.055 0.773 0.001 0.878 5.49 Equation 19-31

579 Table 19-18. SPF Coefficients for Crashes at One-Way Stop-Controlled Ramp Terminals–Three-Leg Terminal with Diagonal Exit Ramp or Four-Leg Terminal at Four-Quadrant Parclo A (D3ex, A4) Crash Severity (z) Area Type Number of Crossroad Through Lanes (n) SPF Coefficient Inverse Dispersion Parameter Kw, ST, at, z a b c d Fatal and injury (fi) Rural All lanes -2.899 0.582 0.001 0.899 2.16 Urban All lanes -3.223 0.582 0.001 0.899 2.16 Property damage only (pdo) Rural All lanes -2.670 0.595 0.001 0.937 6.57 Urban All lanes -2.670 0.595 0.001 0.937 6.57 Table 19-19. SPF Coefficients for Crashes at One-Way Stop-Controlled Ramp Terminals–Three-Leg Terminal with Diagonal Entrance Ramp or Four-Leg Terminal at Four-Quadrant Parclo B (D3en, B4) Crash Severity (z) Area Type Number of Crossroad Through Lanes (n) SPF Coefficient Inverse Dispersion Parameter Kw, ST, at, z a b c d Fatal and injury (fi) Rural All lanes -2.817 0.709 0.001 0.730 0.92 Urban All lanes -3.141 0.709 0.001 0.730 0.92 Property damage only (pdo) Rural All lanes -2.358 0.885 0.001 0.350 3.90 Urban All lanes -2.358 0.885 0.001 0.350 3.90 Table 19-20. SPF Coefficients for Crashes at One-Way Stop-Controlled Ramp Terminals–Four-Leg Terminal with Diagonal Ramps (D4) Crash Severity (z) Area Type Number of Crossroad Through Lanes (n) SPF Coefficient Inverse Dispersion Parameter Kw, ST, at, z a b c d Fatal and injury (fi) Rural All lanes -2.740 1.00 8 0.001 0.177 2.58 Urban All lanes -3.064 1.00 8 0.001 0.177 2.58 Property damage only (pdo) Rural All lanes -2.432 0.84 5 0.001 0.476 4.27 Urban All lanes -2.432 0.84 5 0.001 0.476 4.27

580 0.0 0.4 0.8 1.2 1.6 2.0 0 5 10 15 20 25 Crossroad AADT (1000s of veh/day) Fl C ra sh F re qu en cy (c ra sh es /y r) Terminal Types: A2, B2 Ramp AADT = 0.32 x Crossroad AADT 4-lane crossroad, 2-lane exit ramp 2-lane crossroad, 1-lane exit ramp Urban area Exit ramp right turn: stop controlled All other CMFs = 1.00 0.0 1.0 2.0 3.0 4.0 0 5 10 15 20 25 Crossroad AADT (1000s of veh/day) PD O C ra sh F re qu en cy (c ra sh es /y r) Terminal Types: A2, B2 Ramp AADT = 0.32 x Crossroad AADT All lanes 0.0 0.4 0.8 1.2 1.6 2.0 0 5 10 15 20 25 Crossroad AADT (1000s of veh/day) Fl C ra sh F re qu en cy (c ra sh es /y r) 4-lane crossroad, 2-lane exit ramp 2-lane crossroad, 1-lane exit ramp Urban area Exit ramp right turn: stop controlled All other CMFs = 1.00 Terminal Type: A4 D3 with exit ramp Ramp AADT = 0.32 x Crossroad AADT 0.0 1.0 2.0 3.0 4.0 0 5 10 15 20 25 Crossroad AADT (1000s of veh/day) PD O C ra sh F re qu en cy (c ra sh es /y r) Terminal Type: A4 D3 with exit ramp Ramp AADT = 0.32 x Crossroad AADT a. Fatal-and-Injury Crash Frequency b. Property-Damage-Only Crash Frequency Figure 19-19. Graphical Form of the SPF Crashes at One-Way Stop-Controlled Ramp Terminals– Three-Leg Terminal at Two-Quadrant Parclo A or B (A2, B2) a. Fatal-and-Injury Crash Frequency b. Property-Damage-Only Crash Frequency Figure 19-20. Graphical Form of the SPF Crashes at One-Way Stop-Controlled Ramp Terminals– Three-Leg Terminal with Diagonal Exit Ramp or Four-Leg Terminal at Four-Quadrant Parclo A (D3ex, A4)

581 0.0 0.4 0.8 1.2 1.6 2.0 0 5 10 15 20 25 Crossroad AADT (1000s of veh/day) Fl C ra sh F re qu en cy (c ra sh es /y r) 4-lane crossroad, 2-lane exit ramp 2-lane crossroad, 1-lane exit ramp Urban area Exit ramp right turn: stop controlled All other CMFs = 1.00 Terminal Type: B4 D3 with entrance ramp Ramp AADT = 0.32 x Crossroad AADT 0.0 1.0 2.0 3.0 4.0 0 5 10 15 20 25 Crossroad AADT (1000s of veh/day) PD O C ra sh F re qu en cy (c ra sh es /y r) Terminal Type: B4 D3 with entrance ramp Ramp AADT = 0.32 x Crossroad AADT All lanes 0.0 0.4 0.8 1.2 1.6 2.0 0 5 10 15 20 25 Crossroad AADT (1000s of veh/day) Fl C ra sh F re qu en cy (c ra sh es /y r) Terminal Type: D4 Ramp AADT = 0.32 x Crossroad AADT 4-lane crossroad, 2-lane exit ramp 2-lane crossroad, 1-lane exit ramp Urban area Exit ramp right turn: stop controlled All other CMFs = 1.00 0.0 1.0 2.0 3.0 4.0 0 5 10 15 20 25 Crossroad AADT (1000s of veh/day) PD O C ra sh F re qu en cy (c ra sh es /y r) Terminal Type: D4 Ramp AADT = 0.32 x Crossroad AADT a. Fatal-and-Injury Crash Frequency b. Property-Damage-Only Crash Frequency Figure 19-21. Graphical Form of the SPF Crashes at One-Way Stop-Controlled Ramp Terminals– Three-Leg Terminal with Diagonal Entrance Ramp or Four-Leg Terminal at Four-Quadrant Parclo B (D3en, B4) a. Fatal-and-Injury Crash Frequency b. Property-Damage-Only Crash Frequency Figure 19-22. Graphical Form of the SPF Crashes at One-Way Stop-Controlled Ramp Terminals– Four-Leg Terminal with Diagonal Ramps (D4) The value of the overdispersion parameter associated with the SPFs for one-way stop-controlled crossroad ramp terminals is computed using Equation 19-32. zatSTw zatSTw K k ,,, ,,, 1= Where: kw, ST, at, z = overdispersion parameter for a stop-controlled site of type w, with n crossroad lanes, and all crash types at and severity z; and Kw, ST, at, z = inverse dispersion parameter for a stop-controlled site of type w, with n crossroad lanes, and all crash types at and severity z. Equation 19-32

582 The crash frequency obtained from Equation 19-31 can be multiplied by the proportions in Table 19-21 to estimate the predicted average stop-controlled crossroad ramp terminal crash frequency by crash type or crash type category. Table 19-21. Default Distribution of One-Way Stop-Controlled Ramp Terminal Crashes by Crash Type Area Type Crash Type Crash Type Category Proportion of Crashes by Severity Fatal and Injury Property Damage Only Rural Multiple vehicle Head-on 0.020 0.015 Right-angle 0.522 0.372 Rear-end 0.275 0.276 Sideswipe 0.020 0.107 Other multiple-vehicle crash 0.013 0.026 Single vehicle Crash with animal 0.000 0.000 Crash with fixed object 0.078 0.158 Crash with other object 0.000 0.005 Crash with parked vehicle 0.007 0.015 Other single-vehicle crashes 0.065 0.026 Urban Multiple vehicle Head-on 0.017 0.012 Right-angle 0.458 0.378 Rear-end 0.373 0.377 Sideswipe 0.025 0.079 Other multiple-vehicle crash 0.017 0.016 Single vehicle Crash with animal 0.000 0.000 Crash with fixed object 0.085 0.110 Crash with other object 0.000 0.000 Crash with parked vehicle 0.000 0.008 Other single-vehicle crashes 0.025 0.020

583 19.7. CRASH MODIFICATION FACTORS This section describes the CMFs applicable to the SPFs presented in Section 19.6. These CMFs were calibrated along with the SPFs. They are summarized in Table 19-22 and Table 19-23. Table 19-22. Ramp Segment Crash Modification Factors and their Corresponding SPFs Applicable SPF(s) CMF Variable CMF Description CMF Equations Ramp or C-D road segments CMF1, w, x, y, z Horizontal curve Equation 19-33 CMF2, w, x, y, fi Lane width Equation 19-34 CMF3, w, x, y, z Right shoulder width Equation 19-35 CMF4, w, x, y, z Left shoulder width Equation 19-36 CMF5, w, x, y, z Right side barrier Equation 19-37 CMF6, w, x, y, z Left side barrier Equation 19-38 CMF7, w, x, y, fi Lane add or drop Equation 19-39 Multiple-vehicle crashes on ramp or C-D Road segments CMF8, w, x, mv, fi Ramp speed-change lane Equation 19-40 C-D road segments CMF9, cds, ac, y, z Weaving section Equation 19-41 Note: Subscripts to the CMF variables use the following notation: • Site type w (w = rps: ramp segment, cds: C-D road segment), • Cross section x (x = n: n-lane C-D road, nEN: n-lane entrance ramp, nEX: n-lane exit ramp, ac: any cross section), • Crash type y (y = sv: single vehicle, mv: multiple vehicle, at: all types), and • Severity z (z = fi: fatal and injury, pdo: property damage only, as: all severities). Many of the CMFs in Table 19-22 and Table 19-23 are developed for specific site types, cross sections, crash types, or crash severities. This approach was undertaken to make the predictive model sensitive to the geometric design and traffic control features of specific sites with specific cross sections, in terms of their influence on specific crash types and severities. The subscripts for each CMF variable indicate the sites, cross sections, crash types, and severities to which each CMF is applicable. The subscript definitions are provided in the table footnote. In some cases, a CMF is applicable to several site types, cross sections, crash types, or severities. In these cases, the subscript retains the generic letter w, x, y, or z, as appropriate. The discussion of these CMFs in Section 19.7.1 or 19.7.2 identifies the specific site types, cross sections, crash types, or severities to which they apply. As indicated in Table 19-22, some of the CMFs apply to both ramp segments and C-D road segments. For some of the CMFs, supplemental calculations must be performed before the CMF value can be computed. For example, to apply the Right side barrier CMF, the proportion of the segment length having barrier on the right side and the length-weighted average barrier offset (as measured from the edge of the outside shoulder) must be computed. Procedures for supplemental calculations are described in Section 19.7.3.

584 Table 19-23. Crossroad Ramp Terminal Crash Modification Factors and their Corresponding SPFs Applicable SPF(s) CMF Variable CMF Description CMF Equations Signal-controlled or one-way stop-controlled ramp terminals CMF10, w, x, at, fi Exit ramp capacity Equation 19-42 CMF11, w, x, at, z Crossroad left-turn lane Equation 19-45 CMF12, w, x, at, z Crossroad right-turn lane Equation 19-48 CMF13, w, x, at, z Access point frequency Equation 19-49 CMF14, w, x, at, z Segment length Equation 19-50 CMF15, w, x, at, z Median width Equation 19-51 Signal-controlled crossroad ramp terminals CMF16, w, SGn, at, z Protected left-turn operation Equation 19-53 CMF17, w, SGn, at, z Channelized right turn on crossroad Equation 19-55 CMF18, w, SGn, at, z Channelized right turn on exit ramp Equation 19-56 CMF19, w, SGn, at, z Non-ramp public street leg Equation 19-57 One-way stop-controlled ramp terminals CMF20, w, ST, at, fi Skew angle Equation 19-58 Note: Subscripts to the CMF variables use the following notation: • Site type w (w = D3ex, D3en, D4, A4, B4, A2, B2), • Cross section x (x = ST: one-way stop control; SGn: signal control with n-lane crossroad; ac: any cross section), • Crash type y (y = sv: single vehicle, mv: multiple vehicle, at: all types), and • Severity z (z = fi: fatal and injury, pdo: property damage only, as: all severities). 19.7.1. Crash Modification Factors for Ramp Segments The CMFs for geometric design and traffic control features of freeway segments are presented in this section. CMF1, w, x, y, z—Horizontal Curve Four CMFs are used to describe the relationship between horizontal curve geometry and predicted crash frequency. The six fatal-and-injury SPFs to which they apply are identified in the following list:  SPF for fatal-and-injury multiple-vehicle crashes, n-lane entrance ramp (rps, nEN, mv, fi);  SPF for fatal-and-injury single-vehicle crashes, n-lane entrance ramp (rps, nEN, sv, fi);  SPF for fatal-and-injury multiple-vehicle crashes, n-lane exit ramp (rps, nEX, mv, fi);  SPF for fatal-and-injury single-vehicle crashes, n-lane exit ramp (rps, nEX, sv, fi);  SPF for fatal-and-injury multiple-vehicle crashes, n-lane C-D road (cds, n, mv, fi); and  SPF for fatal-and-injury single-vehicle crashes, n-lane C-D road (cds, n, sv, fi).

585 The six property-damage-only SPFs to which these CMFs apply are not shown in the previous list. However, the only difference is that the fi subscript (shown in parentheses in the previous list) is replaced by pdo. The base condition is an uncurved (i.e., tangent) segment. The CMFs are described using the following equation.               ×+=  = m i ic i ient zyxw PR v aCMF 1 , 2 , ,,,,1 2.32 000,10.1 Where: CMF1, w, x, y, z = crash modification factor for horizontal curvature on a site of type w, cross section x, crash type y, and severity z; vent, i = average entry speed for curve i (ft/s); Ri = radius of curve i (ft); Pc, i = proportion of segment length with curve i; and m = number of horizontal curves in the segment. The coefficient for Equation 19-33 is provided in Table 19-24. Equation 19-33 is derived to recognize that more than one curve may exist in a segment and that a curve may be located only partially in the segment (and partially on an adjacent segment). The variable Pc, i is computed as the ratio of the length of curve i in the segment to the length of the segment (i.e., Lr or Lcd). For example, consider a segment that is 0.5 mi long and a curve that is 0.2 mi long. If one-half of the curve is in the segment, then Pc, i = 0.20 (= 0.1/0.5). In fact, this proportion is the same regardless of the curve’s length (provided that it is 0.1 mi or longer and 0.1 mi of this curve is located in the segment). Table 19-24. Coefficients for Horizontal Curve CMF–Ramp and C-D Road Segments Cross Section (x) Crash Type (y) Crash Severity (z) CMF Variable CMF Coefficient (a) Any cross section (ac) Multiple vehicle (mv) Fatal and injury (fi) CMF1, w, ac, mv, fi 0.779 Property damage only (pdo) CMF1, w, ac, mv, pdo 0.545 Single vehicle (sv) Fatal and injury (fi) CMF1, w, ac, sv, fi 2.406 Property damage only (pdo) CMF1, w, ac, sv, pdo 3.136 Details regarding the measurement of radius and curve length are provided in Section 19.4. A procedure for estimating the average curve entry speed is provided in Section 19.7.3. The CMF is applicable to curves with a radius of 100 ft or larger. Equation 19-33

586 CMF2, w, x, y, fi—Lane Width Two CMFs are used to describe the relationship between average lane width and predicted crash frequency. The SPFs to which they apply are identified in the following list:  SPF for fatal-and-injury multiple-vehicle crashes, n-lane entrance ramp (rps, nEN, mv, fi);  SPF for fatal-and-injury single-vehicle crashes, n-lane entrance ramp (rps, nEN, sv, fi);  SPF for fatal-and-injury multiple-vehicle crashes, n-lane exit ramp (rps, nEX, mv, fi);  SPF for fatal-and-injury single-vehicle crashes, n-lane exit ramp (rps, nEX, sv, fi);  SPF for fatal-and-injury multiple-vehicle crashes, n-lane C-D road (cds, n, mv, fi); and  SPF for fatal-and-injury single-vehicle crashes, n-lane C-D road (cds, n, sv, fi). The base condition is a 14-ft lane width. The CMFs are described using the following equation. ( )]14[exp,,,,2 −×= lfiyxw WaCMF Where: CMF2, w, x, y, fi = crash modification factor for lane width on a site of type w, cross section x, crash type y, and fatal-and-injury crashes fi; and Wl = lane width (ft). The coefficient for Equation 19-34 is provided in Table 19-25. In fact, the coefficient value is the same for both crash types listed in the table, which indicates that the CMF value is the same for the corresponding SPFs. The CMF is applicable to lane widths in the range of 10 to 20 ft. Table 19-25. Coefficients for Lane Width CMF–Ramp and C-D Road Segments Cross Section (x) Crash Type (y) Crash Severity (z) CMF Variable CMF Coefficient (a) Any cross section (ac) Multiple vehicle (mv) Fatal and injury (fi) CMF2, w, ac, mv, fi -0.0458 Single vehicle (sv) Fatal and injury (fi) CMF2, w, ac, sv, fi -0.0458 CMF3, w, x, y, z—Right Shoulder Width Four CMFs are used to describe the relationship between average right shoulder width and predicted crash frequency. The six fatal-and-injury SPFs to which they apply are identified in the following list:  SPF for fatal-and-injury multiple-vehicle crashes, n-lane entrance ramp (rps, nEN, mv, fi);  SPF for fatal-and-injury single-vehicle crashes, n-lane entrance ramp (rps, nEN, sv, fi);  SPF for fatal-and-injury multiple-vehicle crashes, n-lane exit ramp (rps, nEX, mv, fi);  SPF for fatal-and-injury single-vehicle crashes, n-lane exit ramp (rps, nEX, sv, fi); Equation 19-34

587  SPF for fatal-and-injury multiple-vehicle crashes, n-lane C-D road (cds, n, mv, fi); and  SPF for fatal-and-injury single-vehicle crashes, n-lane C-D road (cds, n, sv, fi). The six property-damage-only SPFs to which these CMFs apply are not shown in the previous list. However, the only difference is that the fi subscript (shown in parentheses in the previous list) is replaced by pdo. The base condition is an 8-ft shoulder width. The CMFs are described using the following equation. ( )]8[exp,,,,3 −×= rszyxw WaCMF Where: CMF3, w, x, y, z = crash modification factor for the right shoulder width on a site of type w, cross section x, crash type y, and severity z; and Wrs = paved right shoulder width (ft). The coefficient for Equation 19-35 is provided in Table 19-26. For a given severity, the coefficient values are the same for both crash types listed in the table, which indicates that the CMF value is the same for the corresponding SPFs. The CMF is applicable to shoulder widths in the range of 2 to 12 ft. Table 19-26. Coefficients for Right Shoulder Width CMF–Ramp and C-D Road Segments Cross Section (x) Crash Type (y) Crash Severity (z) CMF Variable CMF Coefficient (a) Any cross section (ac) Multiple vehicle (mv) Fatal and injury (fi) CMF3, w, ac, mv, fi -0.0539 Property damage only (pdo) CMF3, w, ac, mv, pdo -0.0259 Single vehicle (sv) Fatal and injury (fi) CMF3, w, ac, sv, fi -0.0539 Property damage only (pdo) CMF3, w, ac, sv, pdo -0.0259 CMF4, w, x, y, z—Left Shoulder Width Four CMFs are used to describe the relationship between average left shoulder width and predicted crash frequency. The six fatal-and-injury SPFs to which they apply are identified in the following list:  SPF for fatal-and-injury multiple-vehicle crashes, n-lane entrance ramp (rps, nEN, mv, fi);  SPF for fatal-and-injury single-vehicle crashes, n-lane entrance ramp (rps, nEN, sv, fi);  SPF for fatal-and-injury multiple-vehicle crashes, n-lane exit ramp (rps, nEX, mv, fi);  SPF for fatal-and-injury single-vehicle crashes, n-lane exit ramp (rps, nEX, sv, fi);  SPF for fatal-and-injury multiple-vehicle crashes, n-lane C-D road (cds, n, mv, fi); and Equation 19-35

588  SPF for fatal-and-injury single-vehicle crashes, n-lane C-D road (cds, n, sv, fi). The six property-damage-only SPFs to which these CMFs apply are not shown in the previous list. However, the only difference is that the fi subscript (shown in parentheses in the previous list) is replaced by pdo. The base condition is a 4-ft shoulder width. The CMFs are described using the following equation. ( )]4[exp,,,,4 −×= lszyxw WaCMF Where: CMF4, w, x, y, z = crash modification factor for the left shoulder width on a site of type w, cross section x, crash type y, and severity z; and Wls = paved left shoulder width (ft). The coefficient for Equation 19-36 is provided in Table 19-27. For a given severity, the coefficient values are the same for both crash types listed in the table, which indicates that the CMF value is the same for the corresponding SPFs. The CMF is applicable to shoulder widths in the range of 2 to 10 ft. Table 19-27. Coefficients for Left Shoulder Width CMF–Ramp and C-D Road Segments Cross Section (x) Crash Type (y) Crash Severity (z) CMF Variable CMF Coefficient (a) Any cross section (ac) Multiple vehicle (mv) Fatal and injury (fi) CMF4, w, ac, mv, fi -0.0539 Property damage only (pdo) CMF4, w, ac, mv, pdo -0.0259 Single vehicle (sv) Fatal and injury (fi) CMF4, w, ac, sv, fi -0.0539 Property damage only (pdo) CMF4, w, ac, sv, pdo -0.0259 CMF5, w, x, y, z—Right Side Barrier Four CMFs are used to describe the relationship between right side barrier presence and predicted crash frequency. The six fatal-and-injury SPFs to which they apply are identified in the following list:  SPF for fatal-and-injury multiple-vehicle crashes, n-lane entrance ramp (rps, nEN, mv, fi);  SPF for fatal-and-injury single-vehicle crashes, n-lane entrance ramp (rps, nEN, sv, fi);  SPF for fatal-and-injury multiple-vehicle crashes, n-lane exit ramp (rps, nEX, mv, fi);  SPF for fatal-and-injury single-vehicle crashes, n-lane exit ramp (rps, nEX, sv, fi);  SPF for fatal-and-injury multiple-vehicle crashes, n-lane C-D road (cds, n, mv, fi); and  SPF for fatal-and-injury single-vehicle crashes, n-lane C-D road (cds, n, sv, fi). Equation 19-36

589 The six property-damage-only SPFs to which these CMFs apply are not shown in the previous list. However, the only difference is that the fi subscript (shown in parentheses in the previous list) is replaced by pdo. The base condition is no barrier present on the right side of the ramp. The CMFs are described using the following equation. ( )       ×+×−= rcb rbrbzyxw W aPPCMF exp0.10.1,,,,5 Where: CMF5, w, x, y, z = crash modification factor for right side barrier on a site of type w, cross section x, crash type y, and severity z; and Prb = proportion of segment length with a barrier present on the right side; and Wrcb = distance from edge of right shoulder to barrier face (ft). The coefficient for Equation 19-37 is provided in Table 19-28. For a given severity, the coefficient values are the same for both crash types listed in the table, which indicates that the CMF value is the same for the corresponding SPFs. Guidance for computing the variables Prb and Wrcb is provided in Section 19.7.3. The CMF is applicable to Wrcb values in the range of 0.75 to 25 ft. This CMF is applicable to cable barrier, concrete barrier, guardrail, and bridge rail. Table 19-28. Coefficients for Right Side Barrier CMF–Ramp and C-D Road Segments Cross Section (x) Crash Type (y) Crash Severity (z) CMF Variable CMF Coefficient (a) Any cross section (ac) Multiple vehicle (mv) Fatal and injury (fi) CMF5, w, ac, mv, fi 0.210 Property damage only (pdo) CMF5, w, ac, mv, pdo 0.193 Single vehicle (sv) Fatal and injury (fi) CMF5, w, ac, sv, fi 0.210 Property damage only (pdo) CMF5, w, ac, sv, pdo 0.193 CMF6, w, x, y, z—Left Side Barrier Four CMFs are used to describe the relationship between left side barrier presence and predicted crash frequency. The six fatal-and-injury SPFs to which they apply are identified in the following list:  SPF for fatal-and-injury multiple-vehicle crashes, n-lane entrance ramp (rps, nEN, mv, fi);  SPF for fatal-and-injury single-vehicle crashes, n-lane entrance ramp (rps, nEN, sv, fi);  SPF for fatal-and-injury multiple-vehicle crashes, n-lane exit ramp (rps, nEX, mv, fi);  SPF for fatal-and-injury single-vehicle crashes, n-lane exit ramp (rps, nEX, sv, fi);  SPF for fatal-and-injury multiple-vehicle crashes, n-lane C-D road (cds, n, mv, fi); and Equation 19-37

590  SPF for fatal-and-injury single-vehicle crashes, n-lane C-D road (cds, n, sv, fi). The six property-damage-only SPFs to which these CMFs apply are not shown in the previous list. However, the only difference is that the fi subscript (shown in parentheses in the previous list) is replaced by pdo. The base condition is no barrier present on the left side of the ramp. The CMFs are described using the following equation. ( )       ×+×−= lcb lblbzyxw W aPPCMF exp0.10.1,,,,6 Where: CMF6, w, x, y, z = crash modification factor for left side barrier on a site of type w, cross section x, crash type y, and severity z; and Plb = proportion of segment length with a barrier present on the left side; and Wlcb = distance from edge of left shoulder to barrier face (ft). The coefficient for Equation 19-38 is provided in Table 19-29. For a given severity, the coefficient values are the same for both crash types listed in the table, which indicates that the CMF value is the same for the corresponding SPFs. Guidance for computing the variables Plb and Wlcb is provided in Section 19.7.3. The CMF is applicable to Wlcb values in the range of 0.75 to 24 ft. This CMF is applicable to cable barrier, concrete barrier, guardrail, and bridge rail. Table 19-29. Coefficients for Left Side Barrier CMF–Ramp and C-D Road Segments Cross Section (x) Crash Type (y) Crash Severity (z) CMF Variable CMF Coefficient (a) Any cross section (ac) Multiple vehicle (mv) Fatal and injury (fi) CMF6, w, ac, mv, fi 0.210 Property damage only (pdo) CMF6, w, ac, mv, pdo 0.193 Single vehicle (sv) Fatal and injury (fi) CMF6, w, ac, sv, fi 0.210 Property damage only (pdo) CMF6, w, ac, sv, pdo 0.193 CMF7, w, x, y, fi—Lane Add or Drop Two CMFs are used to describe the relationship between a change in lanes and predicted crash frequency. The SPFs to which they apply are identified in the following list:  SPF for fatal-and-injury multiple-vehicle crashes, n-lane entrance ramp (rps, nEN, mv, fi);  SPF for fatal-and-injury single-vehicle crashes, n-lane entrance ramp (rps, nEN, sv, fi);  SPF for fatal-and-injury multiple-vehicle crashes, n-lane exit ramp (rps, nEX, mv, fi); Equation 19-38

591  SPF for fatal-and-injury single-vehicle crashes, n-lane exit ramp (rps, nEX, sv, fi);  SPF for fatal-and-injury multiple-vehicle crashes, n-lane C-D road (cds, n, mv, fi); and  SPF for fatal-and-injury single-vehicle crashes, n-lane C-D road (cds, n, sv, fi). The base condition is no lane change (i.e., no lanes added or dropped). The CMFs are described using the following equation. ( ) ( )][exp0.10.1,,,,7 dropaddtprtprfiyxw IIaPPCMF −××+×−= Where: CMF7, w, x, y, fi = crash modification factor for lane add or drop on a site of type w, cross section x, crash type y, and fatal-and-injury crashes fi; Ptpr = proportion of segment length adjacent to the taper associated with a lane add or drop; Iadd = lane add indicator variable (= 1.0 if one or more lanes are added, 0.0 otherwise); and Idrop = lane drop indicator variable (= 1.0 if one or more lanes are dropped, 0.0 otherwise). The coefficient for Equation 19-39 is provided in Table 19-30. In fact, the coefficient value is the same for both crash types listed in the table, which indicates that the CMF value is the same for the corresponding SPFs. The variable Ptpr is computed as the ratio of the length of the lane add (or drop) taper in the segment to the length of the segment. If the segment is wholly located in the taper, then this variable is equal to 1.0. Table 19-30. Coefficients for Lane Add or Drop CMF–Ramp and C-D Road Segments Cross Section (x) Crash Type (y) Crash Severity (z) CMF Variable CMF Coefficient (a) Any cross section (ac) Multiple vehicle (mv) Fatal and injury (fi) CMF7, w, ac, mv, fi -0.231 Single vehicle (sv) Fatal and injury (fi) CMF7, w, ac, sv, fi -0.231 This CMF is not used with the Weaving section CMF. If a C-D road segment is being evaluated, either the Lane add or drop CMF is used for the subject segment or the Weaving section CMF is used. If a lane add occurs as a result of a ramp-to-ramp merge, then a taper does not exist and this CMF is not used. Similarly, if a lane drop occurs as a result of a ramp-to-ramp diverge, then a taper does not exist and this CMF is not used. CMF8, w, x, mv, fi—Ramp Speed-Change Lane One CMF is used to describe the relationship between ramp speed-change lane presence and predicted crash frequency. The SPFs to which it applies are identified in the following list:  SPF for fatal-and-injury multiple-vehicle crashes, n-lane entrance ramp (rps, nEN, mv, fi);  SPF for fatal-and-injury multiple-vehicle crashes, n-lane exit ramp (rps, nEX, mv, fi); and Equation 19-39

592  SPF for fatal-and-injury multiple-vehicle crashes, n-lane C-D road (cds, n, mv, fi). The base condition is no ramp speed-change lane present. The CMF is described using the following equation. ( ) ( )310.0exp0.10.1,,,,8 ×+×−= −− exenexenfimvxw PPCMF Where: CMF8, w, x, mv, fi = crash modification factor for speed-change lane presence on a site of type w, cross section x, and with multiple-vehicle mv fatal-and-injury crashes fi; and Pen-ex = proportion of segment length that is adjacent to the speed-change lane for a connecting ramp. This CMF is used to evaluate a ramp or C-D road segment that is being joined by another ramp by way of a speed-change lane. The speed-change lane can be either an acceleration lane or a deceleration lane. This CMF is not used with the Weaving section CMF because the ramps in weaving section are joined by an auxiliary lane (i.e., they do not have a speed-change lane). The variable Pen-ex in Equation 19-40 is computed as the ratio of the length of the ramp speed-change lane in the segment to the length of the segment. If the segment is wholly located in the speed-change lane, then this variable is equal to 1.0. If this CMF is used with the Lane add or drop CMF, then the variable Pen-ex is equal to the variable Ptpr. CMF9, cds, ac, y, z—Weaving Section Two CMFs are used to describe the relationship between weaving section presence and predicted crash frequency. The four SPFs to which they apply are identified in the following list:  SPF for fatal-and-injury multiple-vehicle crashes, n-lane C-D road (cds, n, mv, fi);  SPF for property-damage-only multiple-vehicle crashes, n-lane C-D road (cds, n, mv, pdo);  SPF for fatal-and-injury single-vehicle crashes, n-lane C-D road (cds, n, sv, fi); and  SPF for property-damage-only single-vehicle crashes, n-lane C-D road (cds, n, sv, pdo). The base condition is no weaving section on the C-D road segment. The CMFs are described using the following equation. ( ) [ ]      ××+×+×−= wev c wevwevzyaccds L AADTcbaPPCMF lnexp0.10.1,,,,9 Where: CMF9, cds, ac, y, z = crash modification factor for weaving section presence on a C-D road segment with any cross section ac, crash type y, and severity z; AADTc = AADT volume of C-D road segment (veh/day); Equation 19-40 Equation 19-41

593 Pwev = proportion of segment length within a weaving section; and Lwev = weaving section length (may extend beyond segment boundaries) (mi). The coefficients for Equation 19-41 are provided in Table 19-31. The variable Pwev in Equation 19-41 is computed as the ratio of the length of the weaving section in the segment to the length of the segment. If the segment is wholly located in the weaving section, then this variable is equal to 1.0. Table 19-31. Coefficients for Weaving Section CMF–C-D Road Segments Cross Section (x) Crash Type (y) Crash Severity (z) CMF Variable CMF Coefficients a b c Any cross section (ac) All types (mv) Fatal and injury (fi) CMF9, cds, ac, mv, fi 0.191 -0.0715 0.001 Property damage only (pdo) CMF9, cds,ac, mv, pdo 0.187 -0.0580 0.001 All types (sv) Fatal and injury (fi) CMF9, cds, ac, sv, fi 0.191 -0.0715 0.001 Property damage only (pdo) CMF9, cds,ac, sv, pdo 0.187 -0.0580 0.001 This CMF is used to evaluate C-D road segments that have some or all of their length in a weaving section. This CMF is not used with the Ramp speed-change lane CMF or the Lane add or drop CMF. The variable for weaving section length Lwev in Equation 19-41 is intended to reflect the degree to which the weaving activity is concentrated along the C-D road. The CMF is applicable to weaving section lengths in the range from 0.05 to 0.30 mi. 19.7.2. Crash Modification Factors for Ramp Terminals The CMFs for geometric design and traffic control features of crossroad ramp terminals are presented in this section. CMF10, w, x, at, fi—Exit Ramp Capacity Excessively long queues on exit ramps are recognized as sometimes creating unsafe operating conditions. Crash risk tends to increase as the length of ramp available for deceleration to the back of queue is reduced due to long queues at the downstream ramp terminal. The Exit ramp capacity CMF is derived to capture this influence. Two CMFs are used to describe the relationship between exit ramp capacity and predicted crash frequency. The SPFs applicable to three-leg terminals with a diagonal exit ramp (D3ex) are identified in the following list:  SPF for fatal-and-injury crashes, three-legs with diagonal exit ramp, stop control, n lanes (D3ex, ST, at, fi); and  SPF for fatal-and-injury crashes, three-legs with diagonal exit ramp, signal control, n lanes (D3ex, SGn, at, fi). There are two more SPFs for each of six terminal configurations (i.e., site types) to which these CMFs apply. They are not shown in the previous list. However, the only difference is that the D3ex subscript (shown in parentheses in the previous list) is replaced by the other configuration subscripts (D3en, D4, A4, B4, A2, B2).

594 The CMFs are described using the following equation. ( )        ×××+×−= effex ex exexfiatxw n AADTcaPPCMF , ,,,,10 exp0.10.1 with, turnrightcontrolledyieldorstopsignal turnrightflowfreeormerge n n n ex ex effex − −    × +−× = ,,: : 5.0 0.1)0.1(5.0 , exenoutin ex ex AADTAADTAADTAADT AADTP +++ = Where: CMF10, w, x, at, fi = crash modification factor for exit ramp capacity at a site of type w, control type x, and all types at of fatal-and-injury crashes; Pex = proportion of total leg AADT on exit ramp leg; AADTen = AADT volume for the entrance ramp (veh/day); AADTex = AADT volume for the exit ramp (veh/day); AADTin = AADT volume for the crossroad leg between ramps (veh/day); AADTout = AADT volume for the crossroad leg outside of interchange (veh/day); nex, eff = effective number of lanes serving exit ramp traffic (lanes); and nex = number of lanes serving exit ramp traffic (lanes). The coefficients for Equation 19-42 are provided in Table 19-32. When computing Pex, the AADT volume of the loop exit ramp at a B4 terminal configuration is not included in AADTex. Similarly, the AADT volume of the loop entrance ramp at an A4 configuration is not included in AADTen. Table 19-32. Coefficients for Exit Ramp Capacity CMF–Crossroad Ramp Terminals Control Type (x) Crash Type (y) Crash Severity (z) CMF Variable CMF Coefficients a c One-way stop control (ST) All types (at) Fatal and injury (fi) CMF10, w, ST, at, fi 0.151 0.001 Signal control, n lanes (SGn) All types (at) Fatal and injury (fi) CMF10, w, SGn, at, fi 0.0668 0.001 The effective number of lanes is based on the number of lanes on the exit ramp at the terminal, and the type of control used for the exit ramp right-turn movement. The constant “0.5” in Equation 19-43 Equation 19-42 Equation 19-43 Equation 19-44

595 approximately represents the ratio of capacity for a signal, stop, or yield controlled lane to the capacity of a free-flow lane. Figure 19-23 illustrates the use of Equation 19-43 to calculate the effective number of lanes for various exit ramp configurations. This figure also indicates that all lanes counted need to be fully developed for 100 ft or more upstream from the point at which their respective movement intersects with the crossroad (as discussed in Section 19.4.2). Figure 19-23 shows eight exit ramps in plan view. The four ramps on the left side of the figure have two lanes serving exit ramp traffic. The four ramps on the right side of the figure have one lane serving exit ramp traffic (because the lane development is less than 100 ft). The two ramps at the bottom of the figure have merge or free-flow operation for the ramp right-turn movement. The other ramps have signal, stop, or yield control for the right-turn movement. The computed number of effective lanes is typically less than the actual lanes (i.e., nex, eff ≤ nex) due to the control used for the ramp movement. This CMF is applicable to stop-controlled terminals with one or two lanes serving exit ramp traffic. It is applicable to signal-controlled terminals with one, two, three, or four lanes serving exit ramp traffic. nex = 2, nex,ef f = 1 nex = 1, nex,ef f = 0.5 nex = 2, nex,ef f = 1 nex = 1, nex,ef f = 0.5 Lbay > 100 ft Lbay < 100 ft nex = 2, nex,ef f = 1 nex = 1, nex,ef f = 0.5 Lbay > 100 ft Lbay < 100 ft nex = 2, nex,ef f = 1.5 nex = 1, nex,ef f = 1 Lbay > 100 ft Lbay < 100 ft Figure 19-23. Effective Number of Lanes for Various Exit Ramp Configurations CMF11, w, x, at, z—Crossroad Left-Turn Lane Eight CMFs are used to describe the relationship between left-turn lane (or bay) presence and predicted crash frequency. The SPFs applicable to three-leg terminals with a diagonal exit ramp (D3ex) are identified in the following list:

596  SPF for fatal-and-injury crashes, three-legs with diagonal exit ramp, stop control, n lanes (D3ex, ST, at, fi);  SPF for property-damage-only crashes, three-legs with diagonal exit ramp, stop control, n lanes (D3ex, ST, at, pdo);  SPF for fatal-and-injury crashes, three-legs with diagonal exit ramp, signal control, n lanes (D3ex, SGn, at, fi); and  SPF for property-damage-only crashes, three-legs with diagonal exit ramp, signal control, n lanes (D3ex, SGn, at, pdo). There are four more SPFs for each of six terminal configurations (i.e., site types) to which these CMFs apply. They are not shown in the previous list. However, the only difference is that the D3ex subscript (shown in parentheses in the previous list) is replaced by the other configuration subscripts (D3en, D4, A4, B4, A2, B2). The base condition is no left-turn lane (or bay) present. The CMFs are described using the following equation. ( )[ ] ( )[ ] outltbayinltbay IoutoutIininzatxw aPPaPPCMF ,,,, 0.10.10.10.1,,,,11 ×+×−××+×−= with, exenoutin in in AADTAADTAADTAADT AADTP +++ = exenoutin out out AADTAADTAADTAADT AADTP +++ = Where: CMF11, w, x, at, z = crash modification factor for left-turn lane (or bay) presence at a site of type w, control type x, all crash types at, and severity z; Pin = proportion of total leg AADT on crossroad leg between ramps; Pout = proportion of total leg AADT on crossroad leg outside of interchange; and Ibay, lt, k = left-turn lane (or bay) indicator variable for crossroad leg k (k = in or out) (= 1.0 if left- turn lane [or bay] is present, 0.0 otherwise). The coefficient for Equation 19-45 is provided in Table 19-33. When computing Pin and Pout, the AADT volume of the loop exit ramp at a B4 terminal configuration is not included in AADTex. Similarly, the AADT volume of the loop entrance ramp at an A4 configuration is not included in AADTen. Table 19-33. Coefficients for Crossroad Left-Turn Lane CMF–Crossroad Ramp Terminals Control Type (x) Area Type Crash Type (y) Crash Severity (z) CMF Variable CMF Coefficient (a) One-way stop Rural All types (at) Fatal and injury (fi) CMF11, w, ST, at, fi 0.36 Equation 19-45 Equation 19-46 Equation 19-47

597 control (ST) Property damage only (pdo) CMF11, w, ST, at, pdo 0.55 Urban All types (at) Fatal and injury (fi) CMF11, w, ST, at, fi 0.59 Property damage only (pdo) CMF11, w, ST, at, pdo 0.58 Signal control, n lanes (SGn) Rural All types (at) Fatal and injury (fi) CMF11, w, SGn, at, fi 0.44 Property damage only (pdo) CMF11, w, SGn, at, pdo 0.66 Urban All types (at) Fatal and injury (fi) CMF11, w, SGn, at, fi 0.65 Property damage only (pdo) CMF11, w, SGn, at, pdo 0.68 This CMF is applicable to any crossroad approach that is either signalized or uncontrolled. It is not applicable to a stop-controlled approach. The CMF value is applicable to turn bays that have a design that is consistent with agency policy such that their length adequately provides for vehicle storage or deceleration, as appropriate. CMF12, w, x, at, z—Crossroad Right-Turn Lane Eight CMFs are used to describe the relationship between right-turn lane (or bay) presence and predicted crash frequency. The SPFs applicable to three-leg terminals with a diagonal exit ramp (D3ex) are identified in the following list:  SPF for fatal-and-injury crashes, three-legs with diagonal exit ramp, stop control, n lanes (D3ex, ST, at, fi);  SPF for property-damage-only crashes, three-legs with diagonal exit ramp, stop control, n lanes (D3ex, ST, at, pdo);  SPF for fatal-and-injury crashes, three-legs with diagonal exit ramp, signal control, n lanes (D3ex, SGn, at, fi); and  SPF for property-damage-only crashes, three-legs with diagonal exit ramp, signal control, n lanes (D3ex, SGn, at, pdo). There are four more SPFs for each of six terminal configurations (i.e., site types) to which these CMFs apply. They are not shown in the previous list. However, the only difference is that the D3ex subscript (shown in parentheses in the previous list) is replaced by the other configuration subscripts (D3en, D4, A4, B4, A2, B2). The base condition is no right-turn lane (or bay) present. The CMFs are described using the following equation. ( )[ ] ( )[ ] outrtbayinrtbay IoutoutIininzatxw aPPaPPCMF ,,,, 0.10.10.10.1,,,,12 ×+×−××+×−= Where: Equation 19-48

598 CMF12, w, x, at, z = crash modification factor for right-turn lane (or bay) presence at a site of type w, control type x, all crash types at, and severity z; and Ibay, rt, k = right-turn lane (or bay) indicator variable for crossroad leg k (k = in or out) (= 1.0 if right-turn lane [or bay] is present, 0.0 otherwise). The coefficient for Equation 19-48 is provided in Table 19-34. The variable Pin is computed using Equation 19-46. The variable Pout is computed using Equation 19-47. This CMF is applicable to any crossroad approach that is either signalized or uncontrolled. It is not applicable to a stop-controlled approach. The CMF value is applicable to turn bays that have a design that is consistent with agency policy such that their length adequately provides for vehicle storage or deceleration, as appropriate. Table 19-34. Coefficients for Crossroad Right-Turn Lane CMF–Crossroad Ramp Terminals Control Type (x) Area Type Crash Type (y) Crash Severity (z) CMF Variable CMF Coefficient (a) One-way stop control (ST) Rural All types (at) Fatal and injury (fi) CMF12, w, ST, at, fi 0.76 Property damage only (pdo) CMF12, w, ST, at, pdo 0.63 Urban All types (at) Fatal and injury (fi) CMF12, w, ST, at, fi 0.87 Property damage only (pdo) CMF12, w, ST, at, pdo 0.69 Signal control, n lanes (SGn) Rural All types (at) Fatal and injury (fi) CMF12, w, SGn, at, fi 0.59 Property damage only (pdo) CMF12, w, SGn, at, pdo 0.97 Urban All types (at) Fatal and injury (fi) CMF12, w, SGn, at, fi 0.76 Property damage only (pdo) CMF12, w, SGn, at, pdo 0.94 CMF13, w, x, at, z—Access Point Frequency Three CMFs are used to describe the relationship between unsignalized access point presence and predicted crash frequency. The SPFs applicable to three-leg terminals with a diagonal exit ramp (D3ex) are identified in the following list:  SPF for fatal-and-injury crashes, three-legs with diagonal exit ramp, stop control, n lanes (D3ex, ST, at, fi);  SPF for fatal-and-injury crashes, three-legs with diagonal exit ramp, signal control, n lanes (D3ex, SGn, at, fi); and  SPF for property-damage-only crashes, three-legs with diagonal exit ramp, signal control, n lanes (D3ex, SGn, at, pdo). There are three more SPFs for each of six terminal configurations (i.e., site types) to which these CMFs apply. They are not shown in the previous list. However, the only difference is that the D3ex subscript

599 (shown in parentheses in the previous list) is replaced by the other configuration subscripts (D3en, D4, A4, B4, A2, B2). The base condition is no unsignalized driveways and no unsignalized public street approaches present on the outside leg of the crossroad ramp terminal. The CMFs are described using the following equation. ( ) ( )psdwoutoutzatxw nbnaPPCMF ×+××+×−= exp0.10.1,,,,13 Where: CMF13, w, x, at, z = crash modification factor for access point frequency at a site of type w, control type x, all crash types at, and severity z; nps = number of unsignalized public street approaches to the crossroad leg outside of the interchange and within 250 ft of the ramp terminal; and ndw = number of unsignalized driveways on the crossroad leg outside of the interchange and within 250 ft of the ramp terminal. The coefficients for Equation 19-49 are provided in Table 19-35. The variable Pout is computed using Equation 19-47. This CMF applies to any ramp terminal with unsignalized driveways or unsignalized public street approaches on the crossroad leg that is outside of the interchange. Table 19-35. Coefficients for Access Point Frequency CMF–Crossroad Ramp Terminals Control Type (x) Crash Type (y) Crash Severity (z) CMF Variable CMF Coefficients a b One-way stop control (ST) All types (at) Fatal and injury (fi) CMF13, w, ST, at, fi 0.00 0.522 Signal control, n lanes (SGn) All types (at) Fatal and injury (fi) CMF13, w, SGn, at, fi 0.158 0.158 Property damage only (pdo) CMF13, w, SGn, at, pdo 0.203 0.203 This CMF is applicable when there are four or fewer driveways, and two or fewer unsignalized public street approaches, on the crossroad leg outside of the interchange. CMF14, w, x, at, z—Segment Length The distance between the subject ramp terminal and adjacent intersections (or terminals) along the crossroad is logically correlated with crossroad operating speed. This speed is likely to increase as distance increases, and an increase in speed may increase the risk of a crash. Three CMFs are used to describe the relationship between intersection spacing and predicted crash frequency. The SPFs applicable to three-leg terminals with a diagonal exit ramp (D3ex) are identified in the following list:  SPF for fatal-and-injury crashes, three-legs with diagonal exit ramp, stop control, n lanes (D3ex, ST, at, fi);  SPF for fatal-and-injury crashes, three-legs with diagonal exit ramp, signal control, n lanes (D3ex, SGn, at, fi); and Equation 19-49

600  SPF for property-damage-only crashes, three-legs with diagonal exit ramp, signal control, n lanes (D3ex, SGn, at, pdo). There are three more SPFs for each of six terminal configurations (i.e., site types) to which these CMFs apply. They are not shown in the previous list. However, the only difference is that the D3ex subscript (shown in parentheses in the previous list) is replaced by the other configuration subscripts (D3en, D4, A4, B4, A2, B2). The base condition is no adjacent ramp or public street intersection within 6 mi. The CMFs are described using the following equation.                 −+×= 333.00.10.1exp,,,,14 strrmp zatxw LL aCMF Where: CMF14, w, x, at, z = crash modification factor for segment length at a site of type w, control type x, all crash types at, and severity z; Lrmp = distance between subject ramp terminal and adjacent ramp terminal (measured along the crossroad from terminal center to terminal center) (mi); and Lstr = distance between subject ramp terminal and nearest public road intersection in a direction away from freeway (measured along the crossroad from terminal center to intersection center) (mi). The coefficient for Equation 19-50 is provided in Table 19-36. Table 19-36. Coefficients for Segment Length CMF–Crossroad Ramp Terminals Control Type (x) Crash Type (y) Crash Severity (z) CMF Variable CMF Coefficient (a) One-way stop control (ST) All types (at) Fatal and injury (fi) CMF14, w, ST, at, fi -0.0141 Signal control, n lanes (SGn) All types (at) Fatal and injury (fi) CMF14, w, SGn, at, fi -0.0185 Property damage only (pdo) CMF14, w, SGn, at, pdo -0.0186 This CMF describes the relationship between ramp terminal crash frequency and the distance to the adjacent ramp or nearest public street intersection. The adjacent ramp or intersection can be signalized or unsignalized. The CMF is applicable to distances of 0.02 mi or more. CMF15, w, x, at, z—Median Width Research indicates that median width at an intersection can influence crash frequency, provided that this width is 14 ft or more (2). At rural unsignalized intersections, an increase in median width is associated with a decrease in crash frequency. In contrast, at urban intersections (unsignalized and signalized), an increase in median width is associated with an increase in crash frequency. This latter trend is contrary to segment-based safety research that shows crash frequency decreases with an increase in median width. Conflict studies have confirmed a tendency for improper use of wide median areas within intersections Equation 19-50

601 that, when complicated by high traffic volume, results in an increased propensity for multiple-vehicle crashes (2). Three CMFs are used to describe the relationship between crossroad median width and predicted crash frequency. The SPFs applicable to three-leg terminals with a diagonal exit ramp (D3ex) are identified in the following list:  SPF for fatal-and-injury crashes, three-legs with diagonal exit ramp, stop control, n lanes (D3ex, ST, at, fi);  SPF for fatal-and-injury crashes, three-legs with diagonal exit ramp, signal control, n lanes (D3ex, SGn, at, fi); and  SPF for property-damage-only crashes, three-legs with diagonal exit ramp, signal control, n lanes (D3ex, SGn, at, pdo). There are three more SPFs for each of six terminal configurations (i.e., site types) to which these CMFs apply. They are not shown in the previous list. However, the only difference is that the D3ex subscript (shown in parentheses in the previous list) is replaced by the other configuration subscripts (D3en, D4, A4, B4, A2, B2). The base condition is a 12-ft median width. The CMFs are described using the following equation. ( ) ( )[ ] ( ) ( )[ ]outmeoutoutout inmeinininzatxw WAADTcbaPP WAADTcbaPPCMF , ,,,,,15 ][exp0.10.1 ][exp0.10.1 ×××+×+×−× ×××+×+×−= with, 0.0)12,max( ,, ≥−= kbmkme WWW Where: CMF15, w, x, at, z = crash modification factor for median width at a site of type w, control type x, all crash types at, and severity z; Wme, k = width of median adjacent to turn lane (or bay) for crossroad leg k (k = in or out) (ft); Wb, k = left-turn lane (or bay) width for crossroad leg k (k = in or out) (= 0.0 if no lane present on leg) (ft); and Wm = median width (ft). The coefficients for Equation 19-51 are provided in Table 19-37. The variable Pin is computed using Equation 19-46. The variable Pout is computed using Equation 19-47. Table 19-37. Coefficients for Median Width CMF–Crossroad Ramp Terminals Control Type (x) Crash Type (y) Crash Severity (z) CMF Variable CMF Coefficients a b c One-way stop control (ST) All types (at) Fatal and injury (fi) CMF15, w, ST, at, fi -0.0322 0.00354 0.001 Equation 19-51 Equation 19-52

602 Signal control, n lanes (SGn) All types (at) Fatal and injury (fi) CMF15, w, SGn, at, fi 0.0287 -0.00074 0.001 Property damage only (pdo) CMF15, w,SGn, at, pdo 0.0610 -0.00246 0.001 For signalized ramp terminals, the applicable values for AADTin and AADTout range from 14,000 to 60,000 veh/day. AADT volumes smaller than 14,000 should be set to 14,000 in Equation 19-51. For unsignalized ramp terminals, the applicable values for AADTin and AADTout range from 0 to 14,000 veh/day. AADT volumes larger than 14,000 should be set to 14,000 in Equation 19-51. The CMF is applicable to Wm values in the range of 0 to 50 ft. Similarly, it is applicable to Wb, k values in the range of 0 to 26 ft. CMF16, w, SGn, at, z—Protected Left-Turn Operation Two CMFs are used to describe the relationship between protected-only left-turn operation and predicted crash frequency. The SPFs applicable to three-leg terminals with a diagonal exit ramp (D3ex) are identified in the following list:  SPF for fatal-and-injury crashes, three-legs with diagonal exit ramp, signal control, n lanes (D3ex, SGn, at, fi); and  SPF for property-damage-only crashes, three-legs with diagonal exit ramp, signal control, n lanes (D3ex, SGn, at, pdo). There are two more SPFs for each of six terminal configurations (i.e., site types) to which these CMFs apply. They are not shown in the previous list. However, the only difference is that the D3ex subscript (shown in parentheses in the previous list) is replaced by the other configuration subscripts (D3en, D4, A4, B4, A2, B2). The base condition is permissive or protected-permissive left-turn operation (i.e., not protected-only operation). The CMFs are described using the following equation. ( ) ( )[ ] ( ) ( )[ ] outltp inltp I outoxrdxrd I inoxrdxrdzatSGnw naPP naPPCMF ,, ,, , ,,,,,16 exp0.10.1 exp0.10.1 ××+×−× ××+×−= with, exenoutin outin xrd AADTAADTAADTAADT AADTAADTP +++ += Where: CMF16, w, SGn, at, z = crash modification factor for protected left-turn operation at a signal-controlled site of type w, with n crossroad lanes, all crash types at, and severity z; no, k = number of through traffic lanes that oppose the left-turn movement on crossroad leg k (k = in or out) (lanes); Pxrd = proportion of total leg AADT on crossroad; and Equation 19-53 Equation 19-54

603 Ip, lt, k = protected left-turn operation indicator variable for crossroad leg k (k = in or out) (= 1.0 if protected operation exists, 0.0 otherwise). The coefficient for Equation 19-53 is provided in Table 19-38. When computing Pxrd, the AADT volume of the loop exit ramp at a B4 terminal configuration is not included in AADTex. Similarly, the AADT volume of the loop entrance ramp at an A4 configuration is not included in AADTen. Table 19-38. Coefficients for Protected Left-Turn Operation CMF–Crossroad Ramp Terminals Control Type (x) Crash Type (y) Crash Severity (z) CMF Variable CMF Coefficient (a) Signal control, n lanes (SGn) All types (at) Fatal and injury (fi) CMF16, w, SGn, at, fi -0.363 Property damage only (pdo) CMF16, w, SGn, at, pdo -0.223 The CMF is applicable to no, k values in the range of 1 to 3 lanes. CMF17, w, SGn, at, z—Channelized Right Turn on Crossroad Two CMFs are used to describe the relationship between crossroad right-turn channelization and predicted crash frequency. The SPFs applicable to three-leg terminals with a diagonal exit ramp (D3ex) are identified in the following list:  SPF for fatal-and-injury crashes, three-legs with diagonal exit ramp, signal control, n lanes (D3ex, SGn, at, fi); and  SPF for property-damage-only crashes, three-legs with diagonal exit ramp, signal control, n lanes (D3ex, SGn, at, pdo). There are two more SPFs for each of six terminal configurations (i.e., site types) to which these CMFs apply. They are not shown in the previous list. However, the only difference is that the D3ex subscript (shown in parentheses in the previous list) is replaced by the other configuration subscripts (D3en, D4, A4, B4, A2, B2). The base condition is no crossroad right-turn channelization. The CMFs are described using the following equation. ( ) ( )[ ] ( ) ( )[ ] outchinch IoutoutIininzatSGnw aPPaPPCMF ,, exp0.10.1exp0.10.1,,,,17 ×+×−××+×−= Where: CMF17, w, SGn, at, z = crash modification factor for crossroad right-turn channelization at a signal-controlled site of type w, with n crossroad lanes, all crash types at, and severity z; and Ich, k = right-turn channelization indicator variable for crossroad leg k (k = in or out) (= 1.0 if right-turn channelization exists, 0.0 otherwise). The coefficient for Equation 19-55 is provided in Table 19-39. The variable Pin is computed using Equation 19-46. The variable Pout is computed using Equation 19-47. Table 19-39. Coefficients for Channelized Right Turn on Crossroad CMF–Crossroad Ramp Terminals Equation 19-55

604 Control Type (x) Crash Type (y) Crash Severity (z) CMF Variable CMF Coefficient (a) Signal control, n lanes (SGn) All types (at) Fatal and injury (fi) CMF17, w, SGn, at, fi 0.466 Property damage only (pdo) CMF17, w, SGn, at, pdo 0.465 This CMF is applicable to any ramp terminal with right-turn channelization on one or both crossroad legs, where the associated right-turn movement is turning from the crossroad. This CMF can be applied to channelization associated with the loop entrance ramp of the A4 configuration. CMF18, w, SGn, at, z—Channelized Right Turn on Exit Ramp Two CMFs are used to describe the relationship between exit ramp right-turn channelization and predicted crash frequency. The SPFs applicable to three-leg terminals with a diagonal exit ramp (D3ex) are identified in the following list:  SPF for fatal-and-injury crashes, three-legs with diagonal exit ramp, signal control, n lanes (D3ex, SGn, at, fi); and  SPF for property-damage-only crashes, three-legs with diagonal exit ramp, signal control, n lanes (D3ex, SGn, at, pdo). There are two more SPFs for each of six terminal configurations (i.e., site types) to which these CMFs apply. They are not shown in the previous list. However, the only difference is that the D3ex subscript (shown in parentheses in the previous list) is replaced by the other configuration subscripts (D3en, D4, A4, B4, A2, B2). The base condition is no exit ramp right-turn channelization. The CMFs are described using the following equation. ( ) ( )[ ] exchIexexzatSGnw aPPCMF ,exp0.10.1,,,,18 ×+×−= Where: CMF18, w, SGn, at, z = crash modification factor for exit ramp right-turn channelization at a signal-controlled site of type w, with n crossroad lanes, all crash types at, and severity z; and Ich, ex = right-turn channelization indicator variable for exit ramp (= 1.0 if right-turn channelization exists, 0.0 otherwise). The coefficient for Equation 19-56 is provided in Table 19-40. The variable Pex is computed using Equation 19-44. Table 19-40. Coefficients for Channelized Right Turn on Exit Ramp CMF–Crossroad Ramp Terminals Control Type (x) Crash Type (y) Crash Severity (z) CMF Variable CMF Coefficient (a) Signal control, n lanes (SGn) All types (at) Fatal and injury (fi) CMF18, w, SGn, at, fi 0.992 Property damage only (pdo) CMF18, w, SGn, at, pdo 1.429 Equation 19-56

605 This CMF is applicable to any ramp terminal with an exit ramp that has left-turn and right-turn movements and right-turn channelization. This CMF is not applicable to the loop exit ramp of the B4 configuration. CMF19, w, SGn, at, z—Non-Ramp Public Street Leg Two CMFs are used to describe the relationship between public-street leg presence and predicted crash frequency. The SPFs applicable to three-leg terminals with a diagonal exit ramp (D3ex) are identified in the following list:  SPF for fatal-and-injury crashes, three-legs with diagonal exit ramp, signal control, n lanes (D3ex, SGn, at, fi); and  SPF for property-damage-only crashes, three-legs with diagonal exit ramp, signal control, n lanes (D3ex, SGn, at, pdo). There are two more SPFs for each of six terminal configurations (i.e., site types) to which these CMFs apply. They are not shown in the previous list. However, the only difference is that the D3ex subscript (shown in parentheses in the previous list) is replaced by the other configuration subscripts (D3en, D4, A4, B4, A2, B2). The base condition is no public-street leg present. The CMFs are described using the following equation. ( )pszatSGnw IaCMF ×= exp,,,,19 Where: CMF19, w, SGn, at, z = crash modification factor for non-ramp public street leg presence at a signal-controlled site of type w, with n crossroad lanes, all crash types at, and severity z; and Ips = non-ramp public street leg indicator variable (= 1.0 if leg is present, 0.0 otherwise). The coefficient for Equation 19-57 is provided in Table 19-41. The variable Pex is computed using Equation 19-44. This CMF is applicable to any ramp terminal that has a fourth leg that (a) is a public street serving two- way traffic and (b) intersects with the crossroad at the terminal. This situation occurs occasionally. When it does, the public street leg is opposite from one ramp and the other ramp either does not exist or is located at some distance from the subject ramp terminal such that it is not part of the terminal. Table 19-41. Coefficients for Non-Ramp Public Street Leg CMF–Crossroad Ramp Terminals Control Type (x) Crash Type (y) Crash Severity (z) CMF Variable CMF Coefficient (a) Signal control, n lanes (SGn) All types (at) Fatal and injury (fi) CMF19, w, SGn, at, fi 0.592 Property damage only (pdo) CMF19, w, SGn, at, pdo 0.520 Equation 19-57

606 CMF20, w, ST, at, fi—Skew Angle One CMF is used to describe the relationship between the exit ramp skew angle and predicted crash frequency. The SPFs applicable to three-leg terminals with a diagonal exit ramp (D3ex) are identified in the following list:  SPF for fatal-and-injury crashes, three-legs with diagonal exit ramp, stop control, n lanes (D3ex, ST, at, fi). There is one more SPF for each of six terminal configurations (i.e., site types) to which these CMFs apply. They are not shown in the previous list. However, the only difference is that the D3ex subscript (shown in parentheses in the previous list) is replaced by the other configuration subscripts (D3en, D4, A4, B4, A2, B2). The base condition is no skew in the intersecting alignments (i.e., a skew angle of 0.0 degrees). The CMFs are described using the following equation. ( ) ( )exskexexfiatSTw AADTIPPCMF ××××+×−= 001.0]sin[341.0exp0.10.1,,,,20 Where: CMF20, w, ST, at, fi = crash modification factor for skew angle at a stop-controlled site of type w, with n crossroad lanes, and all types at of fatal-and-injury crashes fi; and Isk = skew angle between exit ramp and crossroad (degrees). The variable Pex is computed using Equation 19-44. This CMF is applicable to any one-way stop-controlled ramp terminal with an exit ramp that has stop or yield control for the “reference” exit ramp movement. The reference movement is the left-turn movement for all terminal configurations except the B4 configuration. At a B4 ramp terminal, the reference movement is the right-turn movement on the diagonal exit ramp (not the loop exit ramp). This CMF is applicable to skew angles in the range of 0 to 70 degrees. 19.7.3. Supplemental Calculations to Apply Crash Modification Factors Some of the CMFs in Section 19.7.1 require the completion of supplemental calculations before they can be applied to the SPFs in Section 19.6. These CMFs are: Horizontal curve, Right side barrier, and Left side barrier. This section consists of two subsections. The first section describes the procedure for calculating the curve entry speed needed for the Horizontal curve CMF. The second section describes the procedure for calculating the barrier-related variables for the Right side Barrier CMF and the Left side Barrier CMF. Calculation of Curve Entry Speed This subsection describes a procedure for predicting the average curve entry speed for each curve on a ramp or C-D road. This procedure is developed for use with the Horizontal curve CMF, as described in Section 19.7.1. It is not intended to be used with other applications, or to predict vehicle speed at other points along a ramp or C-D road. The speed prediction procedure consists of a sequence of steps that lead to a prediction of average entry speed for each horizontal curve on the subject ramp or C-D road. Each curve is addressed by the procedure in the same sequence as they are encountered when traveling along the ramp or C-D road. In this manner, the speed for all previous curves encountered must be calculated first, before the speed on Equation 19-58

607 Ramp-mile 0.0 (both ramps) Ramp 1 Ramp 2 Ramp 3 Ramp 2 C-D road 1 Ramp-mile 0.0 (C-D road 1, Ramp 2, and Ramp 4) Ramp 4 Ramp 5 Ramp-mile 0.0 (Ramp 3) Ramp-mile 0.0 (Ramp 5) C-D road 1 has the highest volume so its ramp-mile 0.0 is used for the combined entrance ramp segments. Ramp 2 Ramp 1 Ramp-mile 0.0 (Ramp 1) Ramp-mile 0.0 (Ramp 2) Ramp 1 has the highest volume so its ramp-mile 0.0 is used for the combined entrance ramp segments. the subject curve can be calculated. The steps used will vary depending on whether the segment is part of an entrance ramp, exit ramp, connector ramp, or C-D road. The horizontal curves are located along the ramp or C-D road using a linear referencing system. For exit ramps, ramp-mile 0.0 is located at the gore point. For entrance ramps that intersect the crossroad, ramp- mile 0.0 is located at the point where the ramp reference line intersects with the near edge of traveled way of the crossroad. The location of ramp-mile 0.0 is shown in Figure 19-4 for simple situations. It is shown in Figure 19-24 for more complex ramp and C-D road combinations. When a specific entrance ramp or C- D road segment serves traffic from two or more sources combined, ramp-mile 0.0 for this segment should be that of the one ramp that is the source of the highest daily traffic volume. a. Exit Ramp b. Entrance Ramp c. Entrance and Exit Ramps with C-D Road Figure 19-24. Starting Location for Ramp and C-D Road Combinations

608 The input data needed for this procedure are identified in Table 19-42. The first three variables listed represent required input data. Default values are provided for the remaining variables. Table 19-42. Input Data for Ramp Curve Speed Prediction Variable Description Default Value Applicable Site Type Xi Ramp-mile of the point of change from tangent to curve (PC) for curve ia (mi) None All Ri Radius of curve ib (ft) None All Lc, i Length of horizontal curve i (mi) None All Vfrwy Average traffic speed on the freeway during off-peak periods of the typical day (mi/h) Estimate as equal to the speed limit All Vxroad Average speed at the point where the ramp connects to the crossroad (mi/h) 15 – ramps with stop-, yield-, or signal- controlled crossroad ramp terminals 30 – all other ramps at service interchanges Entrance ramp, exit ramp, connector ramp at service interchange Vcdroad Average speed on C-D road or connector ramp (measured at the mid-point of the C-D road or ramp) (mi/h) 40 C-D road, connector ramp at system interchange Notes: a If the curve is preceded by a spiral transition, then Xi is computed as equal to the average of the TS and SC ramp- mile locations, where TS is the point of change from tangent to spiral and SC is the point of change from spiral to curve. b If the curve has spiral transitions, then Ri is equal to the radius of the central circular portion of the curve. Entrance Ramp Procedure This procedure is applicable to entrance ramps and connector ramps at service interchanges that serve motorists traveling from the crossroad to the freeway. Step 1—Gather Input Data. The input data needed for this procedure are identified in Table 19-42. Step 2—Compute Limiting Curve Speed. The limiting curve speed is computed for each curve on the ramp using the following equation. ( ) 30.0max, 2.3224.3 ii Rv ××= where vmax, i is the limiting speed for curve i (ft/s). The analysis proceeds in the direction of travel. The first curve encountered is curve 1 (i =1). The value of vmax is computed for all curves prior to, and including, the curve of interest. The value obtained from Equation 19-59 represents an upper limit on the curve speed. The vehicle may reach this speed if the distance between curves is lengthy or the crossroad speed is high. Step 3—Calculate Curve 1 Entry Speed. The average entry speed at curve 1 is computed using the following equation. ( ) frwyxroadent VXVv ×≤××+×= 47.1280,5495]47.1[ 3/1131, Equation 19-59 Equation 19-60

609 where vent, 1 is the average entry speed for curve 1 (ft/s). The boundary condition on the right side of the equation indicates that the value computed cannot exceed the average freeway speed. Step 4—Calculate Curve 1 Exit Speed. The average exit speed at curve 1 is equal to the value obtained from the following equation. ( ) frwycentext VandvLvv ×≤≤××+= 47.1280,5495 1max,3/11,3 1,1, where vext, 1 is the average exit speed for curve 1 (ft/s). The boundary condition indicates that the value computed should not exceed the limiting curve speed or the average freeway speed. Step 5—Calculate Curve i Entry Speed. The average entry speed at curve 2 (and all subsequent curves) is computed using the following equation. ( ) frwyiciiiextient VLXXvv ×≤−−××+= −−− 47.1][280,5495 3/11,13 1,, where, vent, i equals the average entry speed for curve i (i = 2, 3, ...) (ft/s) and vext, i equals the average exit speed for curve i (ft/s). Step 6—Calculate Curve i Exit Speed. The average exit speed at curve 2 (and all subsequent curves) is computed using the following equation. ( ) frwyiicientiext VandvLvv ×≤≤××+= 47.1280,5495 max,3/1,3 ,, Step 7—Calculate Speed on Successive Curves. The entry and exit speeds for curve 3 and higher are computed by applying Steps 5 and 6 for each curve. Step 6 does not need to be applied for the last curve because only the entry speed is used in the safety evaluation. Exit Ramp Procedure This procedure is applicable to exit ramps and connector ramps at service interchanges that serve motorists traveling from the freeway to the crossroad. Step 1—Gather Input Data. The input data needed for this procedure are identified in Table 19-42. Step 2—Compute Limiting Curve Speed. This step is the same as Step 2 for the entrance ramp procedure. A lower curve speed than that obtained from Equation 19-59 is possible due to the deceleration that occurs as the driver transitions from the freeway speed to the crossroad speed. Step 3—Calculate Curve 1 Entry Speed. The average entry speed at curve 1 is computed using the following equation. xroadfrwyent VXVv ×≥××−×= 47.1280,5034.047.1 11, The boundary condition on the right side of the equation indicates that the value computed cannot be less than the average speed at the point where the ramp connects to the crossroad. Equation 19-61 Equation 19-62 Equation 19-63 Equation 19-64

610 Step 4—Calculate Curve 1 Exit Speed. This step is the same as Step 4 for the entrance ramp procedure. xroadcentext VandvLvv ×≥≤××−= 47.1280,5034.0 1max,1,1,1, The boundary condition indicates that the value computed should not exceed the limiting curve speed and should not be less than the average speed at the point where the ramp connects to the crossroad. Step 5—Calculate Curve i Entry Speed. The average entry speed at curve 2 (and all subsequent curves) is computed using the following equation. xroadiciiiextient VLXXvv ×≥−−××−= −−− 47.1)(280,5034.0 1,11,, Step 6—Calculate Curve i Exit Speed. The average exit speed at curve 2 (and all subsequent curves) is computed using the following equation. xroadiicientiext VandvLvv ×≥≤××−= 47.1280,5034.0 max,,,, Step 7—Calculate Speed on Successive Curves. This step is the same as Step 7 for the entrance ramp procedure. C-D Road Procedure This procedure is applicable to C-D roads and connector ramps at system interchanges. Step 1—Gather Input Data. The input data needed for this procedure are identified in Table 19-42. Step 2—Compute Limiting Curve Speed. This step is the same as Step 2 for the entrance ramp procedure. Step 3—Calculate Curve 1 Entry Speed. The average entry speed at curve 1 is computed using Equation 19-68 or Equation 19-69, depending on the following two conditions. If 1.47×Vfrwy ≤ vmax, 1 then: frwyent Vv ×= 47.11, If 1.47×Vfrwy > vmax, 1 then: cdroadfrwyent VXVv ×≥××−×= 47.1280,5034.047.1 11, The boundary condition for Equation 19-69 indicates that the value computed cannot be less than the average speed on the C-D road. Step 4—Calculate Curve 1 Exit Speed. The average exit speed at curve 1 is equal to the entrance speed, provided that it does not exceed the limiting curve speed. The following rule is used to make this determination. 1max,1,1, vvv entext ≤= Step 5—Calculate Curve i Entry Speed. The average entry speed at curve 2 (and all subsequent curves) is computed using Equation 19-71 or Equation 19-72, depending on the following conditions. Equation 19-65 Equation 19-66 Equation 19-67 Equation 19-68 Equation 19-69 Equation 19-70

611 If vext, i-1 ≤ vmax, i then: ( ) frwyiciiiextient VLXXvv ×≤−−××+= −−− 47.1][280,5495 3/11,13 1,, If vext, i-1 > vmax, i then: cdroadiciiiextient VLXXvv ×≥−−××−= −−− 47.1)(280,5034.0 1,11,, Step 6—Calculate Curve i Exit Speed. The average exit speed at curve 2 (and all subsequent curves) is computed using the following equation. iientiext vvv max,,, ≤= Step 7—Calculate Speed on Successive Curves. This step is the same as Step 7 for the entrance ramp procedure. Calculation of Barrier-Related Variables The two barrier CMFs include variables that describe the presence of barrier on the left or right side of the ramp or C-D road. These variables include barrier offset and length. Barrier offset represents a lateral distance measured from the near edge of the shoulder to the face of the barrier (i.e., it does not include the width of the shoulder). Barrier length represents the length of lane paralleled by a barrier; it is a total for both travel directions. For example, if the left side barrier extends for the length of the ramp segment, then the left side barrier length equals the segment length. Two key variables that are needed for the evaluation of barrier presence are the right side barrier offset distance Wrcb and the left side barrier offset distance Wlcb. As indicated in Equation 19-37 and Equation 19-38, this distance is included as a divisor in the exponential term. This relationship implies that the correlation between distance and crash frequency is an inverse one (i.e., crash frequency decreases with increasing distance to the barrier). When multiple sections of barrier exist along the segment, a length- weighted average of the reciprocal of the individual distances is needed to properly reflect this inverse relationship. The length used to weight the average is the barrier length. Additional key variables include the proportion of segment length with a barrier present on the right side Prb and the proportion of segment length with a barrier present on the left side Plb. Equations for calculating these proportions and the aforementioned distances are described in the following paragraphs. The length of segment L used in the following equations is equal to that of the ramp segment Lr or C-D road segment Lcd, as appropriate for the CMF to which the calculated value will be applied. The following equations should be used to estimate Wrcb and Prb.   − = rsiroff irb irb rcb WW L L W ,, , , L L P irbrb = , Equation 19-71 Equation 19-72 Equation 19-73 Equation 19-74 Equation 19-75

612 Where: Wrcb = distance from edge of right shoulder to barrier face (ft); Prb = proportion of segment length with a barrier present on the right side; L = length of segment (mi); Lrb, i = length of right side lane paralleled by barrier i (mi); Wrs = paved right shoulder width (ft); and Woff, r, i = horizontal clearance from the edge of the traveled way to the face of right side barrier i (ft). Any clearance distance (= Woff, r, i – Wrs) that is less than 0.75 ft should be set to 0.75 ft. The following equations should be used to estimate Wlcb and Plb.   − = lsiloff ilb ilb lcb WW L L W ,, , , L L P ilblb = , Where: Wlcb = distance from edge of left shoulder to barrier face (ft); Plb = proportion of segment length with a barrier present on the left side; L = length of segment (mi); Llb, i = length of left side lane paralleled by barrier i (mi); Wls = paved left shoulder width (ft); and Woff, l, i = horizontal clearance from the edge of the traveled way to the face of left side barrier i (ft). Any clearance distance (= Woff, l, i – Wls) that is less than 0.75 ft should be set to 0.75 ft. 19.8. SEVERITY DISTRIBUTION FUNCTIONS The severity distribution functions (SDFs) are presented in this section. They are used in the predictive model to estimate the expected average crash frequency for the following severity levels: fatal K, incapacitating injury A, non-incapacitating injury B, and possible injury C. Each SDF was developed as a regression model using observed crash data for a set of similar sites as the dependent variable. The SDF, like all regression models, estimates the value of the dependent variable as a function of a set of independent variables. The independent variables include various geometric features, traffic control features, and area type (i.e., rural or urban). Separate SDFs described in this section for ramp segments and crossroad ramp terminals. Equation 19-76 Equation 19-77

613 The general model form for the severity distribution prediction is shown in the following equation. jatacwfiyxweiyxwe PNN ,,,,,,,,,,, ×= Where: Ne, w, x, y, j = expected average crash frequency for site type w, cross section or control type x, crash type y, and severity level j ( j = K: fatal, A: incapacitating injury, B: non-incapacitating injury, C: possible injury) (crashes/yr); Ne, w, x, y, fi = expected average crash frequency for site type w, cross section or control type x, crash type y, and fatal-and-injury crashes fi (crashes/yr); and Pw, x, at, j = probability of the occurrence of severity level j ( j = K: fatal, A: incapacitating injury, B: non-incapacitating injury, C: possible injury) for all crash types at at site type w with cross section or control type x. There is one SDF associated with each probability level j in the predictive model. An SDF predicts the probability of occurrence of severity level j for a crash based on various geometric design and traffic control features at the subject site. Each SDF also contains a calibration factor that is used to calibrate it to local conditions. 19.8.1. Severity Distribution Functions for Ramp Segments The SDFs for ramp and C-D road segments are described by the following equations. ( ) ( ) ( ) ataccdsrpsAKK BAK cdsrpssdf AK Kataccdsrps P VV C VP ,,,| , ,,, expexp0.1 exp ++ + + + + × ++ = ( ) ( ) ( ) )0.1( expexp0.1 exp ,,,| , ,,, ataccdsrpsAKK BAK cdsrpssdf AK Aataccdsrps P VV C VP ++ + + + + −× ++ = ( ) ( ) ( )BAK cdsrpssdf B Bataccdsrps VV C VP expexp0.1 exp , ,,, ++ = + + + )(0.1,,, BAKCataccdsrps PPPP ++−=+ Where: Vj = systematic component of crash severity likelihood for severity level j; PK|K+A, rps+cds, ac, at = probability of a fatal K crash given that the crash has a severity of either fatal or incapacitating injury A on a ramp or C-D road segment based on all crash types at and any cross section ac; and Csdf, rps+cds = calibration factor to adjust SDF for local conditions for ramp and C-D road segments. Equation 19-78 Equation 19-79 Equation 19-80 Equation 19-81 Equation 19-82

614 The first term Equation 19-79 estimates the probability of a fatal or incapacitating injury crash. The second term (i.e., PK|K+A) is used to convert the estimate into the probability of a fatal crash. A value of 0.248 is used for PK|K+A based on an analysis of fatal and incapacitating injury crashes on ramps and C-D road segments. A model for estimating the systematic component of crash severity Vj for ramp and C-D road segments is described by the following equation. ( ) ( ) ( )exrruralrblbj IeIdncPPbaV ×+×+×+      +×+= 2 Where: Plb = proportion of segment length with a barrier present on the left side; Prb = proportion of segment length with a barrier present on the right side; n = number of through lanes in the segment (lanes); Irural = area type indicator variable (= 1.0 if area is rural, 0.0 if it is urban); Iexr = exit ramp indicator variable (= 1.0 if segment is an exit ramp, 0.0 otherwise); and a, b, c, d, e = regression coefficients. The SDF coefficients in Equation 19-83 are provided in Table 19-43. Guidance for computing the variables Plb and Prb is provided in Section 19.7.3. Table 19-43. SDF Coefficients for Ramp Segments Severity Level ( j) Variable SDF Coefficients a b c d e Fatal or incapacitating injury (K+A) VK+A -1.537 -0.481 -0.228 0.668 0.426 Non-incapacitating injury (B) VB 0.236 -0.431 -0.435 0.696 0.00 The SDF is applicable to rural ramps and C-D roads with one lane (i.e., n = 1), and to urban ramps and C- D roads with one or two lanes (i.e., n = 1 or 2). The sign of a coefficient in Table 19-43 indicates the change in the proportion of crashes associated with a change in the corresponding variable. For example, the negative coefficient associated with barrier presence indicates that the proportion of fatal K and incapacitating injury A crashes decreases with an increase in the proportion of barrier present in the segment. A similar trend is indicated for barrier presence on non-incapacitating injury B crashes. By inference, the proportion of possible injury C crashes increases with an increase in the proportion of barrier present. 19.8.2. Severity Distribution Functions for Ramp Terminals The SDFs for crossroad ramp terminals are described by the following equations. Equation 19-83

615 ( ) ( ) ( ) atxaSAKK BAK xaSsdf AK KatxaS P VV C V P ,,,| ,, ,,, expexp0.1 exp + + + × ++ = ( ) ( ) ( ) )0.1( expexp0.1 exp ,,,| ,, ,,, atxaSAKK BAK xaSsdf AK AatxaS P VV C V P + + + −× ++ = ( ) ( ) ( )BAK xaSsdf B BatxaS VV C V P expexp0.1 exp ,, ,,, ++ = + )(0.1,,, BAKCatxaS PPPP ++−= Where: Vj = systematic component of crash severity likelihood for severity level j; PK|K+A, aS, x, at = probability of a fatal K crash given that the crash has a severity of either fatal or incapacitating injury A for all ramp terminal sites aS based on all crash types at and control type x (x = ST: one-way stop control; SGn: signal control, n-lane crossroad); and Csdf, aS, x = calibration factor to adjust SDF for local conditions for all ramp terminal sites aS with control type x (x = ST: stop control, SGn: signal control, n-lane crossroad). The first term Equation 19-84 estimates the probability of a fatal or incapacitating injury crash. The second term (i.e., PK|K+A) is used to convert the estimate into the probability of a fatal crash. For signal- controlled ramp terminals, a value of 0.0385 is used for PK|K+A based on an analysis of fatal and incapacitating injury crashes at signalized ramp terminals. For one-way stop-controlled ramp terminals, a value of 0.160 is used for PK|K+A based on a similar analysis. A model for estimating the systematic component of crash severity Vj for crossroad ramp terminals is described by the following equation. ( ) ( ) ( ) ( )ruralpspsdwltpj IeIdnncIbaV ×+×++×+×+= ][, Where: Ip, lt = protected left-turn operation indicator variable for crossroad (= 1.0 if protected operation exists, 0.0 otherwise); ndw = number of unsignalized driveways on the crossroad leg outside of the interchange and within 250 ft of the ramp terminal; Equation 19-84 Equation 19-85 Equation 19-86 Equation 19-87 Equation 19-88

616 nps = number of unsignalized public street approaches to the crossroad leg outside of the interchange and within 250 ft of the ramp terminal; and Ips = non-ramp public street leg indicator variable (= 1.0 if leg is present, 0.0 otherwise). The SDF coefficients in Equation 19-88 are provided in Table 19-44. Table 19-44. SDF Coefficients for Crossroad Ramp Terminals Control Type (x) Severity Level ( j) Variable SDF Coefficients a b c d e One-way stop control (ST) Fatal or incapacitating inj. (K+A) VK+A -3.168 0.00 0.00 0.00 0.891 Non-incapacitating injury (B) VB -1.476 0.00 0.00 0.00 0.221 Signal control, n lanes (SGn) Fatal or incapacitating inj. (K+A) VK+A -3.257 -0.288 0.0991 1.171 0.619 Non-incapacitating injury (B) VB -1.511 -0.193 0.149 0.741 0.416 This SDF is applicable when there are four or fewer driveways, and two or fewer unsignalized public street approaches, on the crossroad leg outside of the interchange. The variable Ip, lt is equal to 1.0 if protected-only left-turn operation is provided on each crossroad leg with a left-turn movement. If permissive or protected-permissive operation is provided on either leg, then the variable equals 0.0. The variable Ips is equal to 1.0 if the ramp terminal has a fourth leg that (a) is a public street serving two- way traffic and (b) intersects with the crossroad at the terminal. This situation occurs occasionally. When it does, the public street leg is opposite from one ramp and the other ramp either does not exist or is located at some distance from the subject ramp terminal such that it is not part of the terminal. The sign of a coefficient in Table 19-44 indicates the change in the proportion of crashes associated with a change in the corresponding variable. For example, the negative coefficient associated with protected left-turn operation indicates that the proportion of fatal K and incapacitating injury A crashes decreases when protected-only left-turn operation is provided. A similar trend is indicated for protected-only left- turn operation on non-incapacitating injury B crashes. By inference, the proportion of possible injury C crashes increases when protected-only left-turn operation is provided. 19.9. CALIBRATION OF THE SPFS AND SDFS TO LOCAL CONDITIONS Crash frequencies, even for nominally similar ramp segments or ramp terminals, can vary widely from one jurisdiction to another. Geographic regions differ markedly in climate, animal population, driver populations, crash-reporting threshold, and crash-reporting practices. These variations may result in some jurisdictions experiencing a different number of traffic crashes on ramps than others. Calibration factors are included in the methodology to allow transportation agencies to adjust the SPFs and SDFs to match actual local conditions. The SPF calibration factors will have values greater than 1.0 for segments or terminals that, on average, experience more crashes than those used in the development of the SPFs. Similarly, the calibration factors for segments or terminals that experience fewer crashes on average than those used in the development of the SPFs will have values less than 1.0. The calibration procedures for SPFs are presented in Section B.1.1 of Appendix B to Part C.

617 The SDF calibration factors will have values greater than 1.0 for segments or terminals that, on average, experience more severe crashes than those used in the development of the SDFs. Similarly, the calibration factors for segments or terminals that experience fewer severe crashes on average than those used in the development of the SDFs will have values less than 1.0. The calibration procedures for SDFs are presented in Section B.1.4 of Appendix B to Part C. Default values are also provided for the crash type distributions used in the methodology. These values can also be replaced with locally derived values. The derivation of these values is addressed in Section B.1.3 of Appendix B to Part C. 19.10. INTERIM PREDICTIVE METHOD FOR ALL-WAY STOP CONTROL Sufficient research has not yet been conducted to form the basis for development of a predictive method for crossroad ramp terminals with all-way stop control. An interim method is presented in this section. It consists of the same steps as described previously in Section 19.4. The discussion below highlights the modifications to these steps when they are applied to an all-way stop-controlled ramp terminal. Steps 1 to 18―Evaluate the Crossroad Ramp Terminal as One-Way Stop Control. Apply the predictive method described in Section 19.4 to the subject crossroad ramp terminal. The subject crossroad ramp terminal has all-way stop control but it is evaluated using the predictive method for one-way stop control. Step 10―The following list identifies the CMFs that can be used in Step 10 of the predictive method to evaluate all-way stop-controlled ramp terminals.  Exit ramp capacity.  Access point frequency.  Segment length.  Median width. The Crossroad left-turn lane CMF, Crossroad right-turn lane CMF, and Skew angle CMF cannot be used to evaluate all-way stop-controlled ramp terminals. In addition, the All-way stop control CMF is used in Step 10 of the predictive method. This CMF has a value of 0.686 when applied to fatal-and-injury crashes. Research has not established a value for this CMF when applied to property-damage-only crashes, so the unadjusted estimate from the predictive method is considered to be equally applicable to all-way stop-controlled ramp terminals. Step 13―The crash-type distribution in Table 19-45 can be used in Step 13 of the predictive method, if desired, to compute the expected average crash frequency for each of ten crash types (e.g., head-on, fixed object).

618 Table 19-45. Default Distribution of All-Way Stop-Controlled Ramp Terminal Crashes by Crash Type Area Type Crash Type Crash Type Category Proportion of Crashes by Severity Fatal and Injury Property Damage Only Rural Multiple vehicle Head-on 0.000 0.000 Right-angle 0.500 0.375 Rear-end 0.500 0.405 Sideswipe 0.000 0.094 Other multiple-vehicle crash 0.000 0.000 Single vehicle Crash with animal 0.000 0.000 Crash with fixed object 0.000 0.063 Crash with other object 0.000 0.000 Crash with parked vehicle 0.000 0.000 Other single-vehicle crashes 0.000 0.063 Urban Multiple vehicle Head-on 0.000 0.000 Right-angle 0.182 0.333 Rear-end 0.727 0.500 Sideswipe 0.000 0.000 Other multiple-vehicle crash 0.000 0.000 Single vehicle Crash with animal 0.000 0.000 Crash with fixed object 0.000 0.167 Crash with other object 0.000 0.000 Crash with parked vehicle 0.000 0.000 Other single-vehicle crashes 0.091 0.000 19.11. LIMITATIONS OF PREDICTIVE METHOD The limitations of the predictive method which apply generally across all of the Part C chapters are discussed in Section C.14 of Part C. This section discusses limitations of the predictive models described this chapter. The predictive method described in this chapter does not account for the influence of the following conditions on ramp safety:  Ramp or C-D road segments in rural areas with 2 or more lanes.  Ramp or C-D road segments in urban areas with 3 or more lanes.

619  Ramps and C-D roads providing two-way travel.  Ramp metering.  A high-occupancy vehicle (HOV) bypass lane on a ramp or C-D road.  A frontage-road segment.  A frontage-road ramp terminal.  A frontage-road crossroad terminal.  A crossroad speed-change lane.  A crossroad ramp terminal with 3 or more left-turn lanes on a crossroad approach.  A crossroad ramp terminal where the crossroad provides one-way travel.  The crossroad ramp terminal formed by a single-point urban interchange or roundabout. The predictive method does not distinguish between barrier types (i.e., cable barrier, concrete barrier, guardrail, and bridge rail) in terms of their possible different influence on crash severity. 19.12. APPLICATION OF PREDICTIVE METHOD The predictive method presented in this chapter is applied to a ramp by following the 18 steps presented in Section 19.4. Worksheets are provided in Appendix 14A for applying calculations in the predictive method. All computations of crash frequencies within these worksheets are conducted with values expressed to three decimal places. This level of precision is needed only for consistency in computations. In the last stage of computations, rounding the final estimates of expected average crash frequency to one decimal place is appropriate. 19.13. SUMMARY The predictive method for ramps is applied by following the 18 steps of the predictive method presented in Section 19.4. It is used to estimate the expected average crash frequency for a series of contiguous sites, or a single individual site. If a ramp is being evaluated, then it is divided into a series of sites in Step 5 of the predictive method. Predictive models are applied in Steps 9, 10, and 11 of the method. Each predictive model consists of a safety performance function (SPF), crash modification factors (CMFs), a severity distribution function (SDF), and calibration factors. The SPF is selected in Step 9. It is used to estimate the predicted average crash frequency for a site with base conditions. CMFs are selected in Step 10. They are combined with the estimate from the SPF to produce the predicted average crash frequency. When observed crash data are available, the EB Method is applied in Step 13 or 15 of the predictive method to estimate the expected average crash frequency. The EB Method can be applied at the site- specific level in Step 13, or at the project level in Step 15. The choice of level will depend on (a) the required reliability of the estimate and (b) the accuracy with which each observed crash can be associated with an individual site. The EB Method is described in Section B.2 of Appendix B to Part C. Optionally, SDFs are selected in Step 13. They can be used to estimate the average crash frequency for one or more crash severity levels (i.e., fatal, incapacitating injury, non-incapacitating injury, or possible

620 injury crash). Optionally, the crash type distribution can be used in Step 13 to estimate the average crash frequency for one or more crash types (e.g., head-on, fixed object). The SPF should be calibrated to the specific state or geographic region in which the project is located. Calibration accounts for differences in state or regional crash frequencies, relative to the states and regions represented in the data used to define the predictive models described in this chapter. The process for determining calibration factors for the predictive models is described in Section B.1 of Appendix B to Part C. Section 19.14 presents several sample problems that detail the application of the predictive method. A series of worksheets are used to guide the method application and document the calculations. The use of these worksheets is illustrated in the sample problems. Appendix 19A contains blank worksheets that can be copied to document future method applications. 19.14. SAMPLE PROBLEMS In this section, six sample problems are presented using the predictive method steps for ramp facilities. Sample Problems 1 through 3 illustrate how to calculate the predicted average crash frequency for ramp segments. Sample Problems 4 through 6 illustrate how to calculate the predicted average crash frequency for ramp terminals. Table 19-46. List of Sample Problems Problem No. Description 1 Predicted average crash frequency for a one-lane exit ramp segment 2 Predicted average crash frequency for a two-lane C-D road segment 3 Predicted average crash frequency for a one-lane entrance ramp segment 4 Predicted average crash frequency for a D4 ramp terminal with signal control 5 Predicted average crash frequency for a A4 ramp terminal with one-way stop control 6 Predicted average crash frequency for a B2 ramp terminal with all-way stop control 19.14.1. Sample Problem 1 The Site/Facility A one-lane urban exit ramp segment. The Question What is the predicted average crash frequency of the ramp segment for a one-year period? The Facts The study year is 2011. The conditions present during this year are provided in the following list.  0.15-mi length  6,750 veh/day  65-mi/h average speed on freeway mainline

621  Signal control at crossroad ramp terminal  One off-segment horizontal curve  400-ft radius  0.025-mi length  Beginning at ramp-mile 0.07  One in-segment horizontal curve  400-ft radius  0.07-mi length, entirely in the segment  Beginning at ramp-mile 0.19  14-ft lane width  8-ft right shoulder width (paved)  4-ft left shoulder width (paved)  No lane adds or lane drops  No barrier on the right or left sides of the roadway  No ramp entrances or exits in the segment  No weaving section Assumptions  Crash type distributions used are the default values presented in Table 19-6 and Table 19-9.  The calibration factor is 1.00. Results Using the predictive method steps as outlined below, the predicted average fatal-and-injury crash frequency for the ramp segment in Sample Problem 1 is determined to be 0.2 crashes per year, and the predicted average property-damage-only crash frequency is determined to be 0.2 crashes per year (rounded to one decimal place). Steps Step 1 through 8 To determine the predicted average crash frequency of the ramp segment in Sample Problem 1, only Steps 9 through 13 are conducted. No other steps are necessary because only one ramp segment is analyzed for a one-year period and the EB Method is not applied.

622 Step 9 – For the selected site, determine and apply the appropriate SPF. For a one-lane urban exit ramp segment, SPF values for multiple-vehicle and single-vehicle crashes are determined. Multiple-Vehicle Crashes The SPF for multiple-vehicle fatal-and-injury crashes is calculated from Equation 19-20 and Table 19-5 as follows: [ ] [ ]( ) [ ] [ ]( ) arcrashes/ye005.0 750,6001.00699.0750,6001.0ln524.0971.4exp15.0 lnexp,,1,, = ×+××+−×= ×+××+×= rrrfimvEXrpsspf AADTcdAADTcbaLN Similarly, the SPF for multiple-vehicle property-damage-only crashes is calculated from Equation 19-20 and Table 19-5 to yield the following result: arcrashes/ye013.0,,1,, =pdomvEXrpsspfN Single-Vehicle Crashes The SPF for single-vehicle fatal-and-injury crashes is calculated from Equation 19-24 and Table 19-8 as follows: [ ]( ) [ ]( ) arcrashes/ye114.0 750,6001.0ln718.0645.1exp15.0 lnexp,,1,, = ××+−×= ××+×= rrfisvEXrpsspf AADTcbaLN Similarly, the SPF for single-vehicle property-damage-only crashes is calculated from Equation 19-24 and Table 19-8 to yield the following result: arcrashes/ye124.0,,1,, =pdosvEXrpsspfN Step 10 – Multiply the result obtained in Step 9 by the appropriate CMFs. Each CMF used in the calculation of the predicted average crash frequency of the ramp segment is calculated in this step. Horizontal Curve (CMF1, rps, 1EX, y, z ) The limited curve speed for the off-segment horizontal curve (curve 1) is computed using Equation 19-59 as follows: ( ) ( ) ft/s4.55 4002.3224.3 2.3224.3 30.0 30.0 11max, = ××= ××= Rv The in-segment horizontal curve (curve 2) has the same radius as curve 1. Hence, its limited speed vmax, 2 is also equal to 55.4 ft/s. The average entry speed at curve 1 is computed using Equation 19-64 and the default values in Table 19- 42 as follows:

623 ( ) ( ) ft/s0.83 1547.107.0280,5034.06547.1 47.1280,5034.047.1 11, = ×≥××−×= ×≥××−×= V XVv xroadfrwyent The average exit speed at curve 1 is computed using Equation 19-65 as follows: ( ) ( ) ft/s4.55 1547.14.55025.0280,5034.00.83 47.1280,5034.0 1max,1,1,1, = ×≥≤××−= ×≥≤××−= and V and v Lvv xroadcentext The average entry speed at curve 2 is computed using Equation 19-66 and the default values in Table 19- 42 as follows: ft/s3.38 1547.1)025.007.019.0(280,5034.04.55 47.1)(280,5034.0 1,11,, = ×≥−−××−= ×≥−−××−= −−− xroadiciiiextient VLXXvv CMF1, rps, 1EX, y, fi is calculated using Equation 19-33 as follows:         ×      ×+=  = m i ic i ient fiyEXrps PR v aCMF 1 , 2 , ,,1,,1 2.32 000,10.1 Only curve 2 is included in the summation term. Curve 1 is not in the segment, but its presence upstream of the segment affects vehicle speeds in curve 2. From Table 19-24, a = 0.779 for multiple-vehicle fatal- and-injury crashes. CMF1, rps, 1EX, mv, fi is calculated as follows: 104.1 15.0 07.0 400 3.38 2.32 000,1779.00.1 2 ,,1,,1 = ×     ×+=fimvEXrpsCMF Calculations using the other coefficients from Table 19-24 yield the following results: 320.1,,1,,1 =fisvEXrpsCMF 073.1,,1,,1 =pdomvEXrpsCMF 418.1,,1,,1 =pdosvEXrpsCMF Lane Width (CMF2, rps, 1EX, y, z ) The segment has 14-ft lanes, which is the base condition for the lane width CMF. Hence, CMF2, rps, 1EX, y, fi and CMF2, rps, 1EX, y, pdo are equal to 1.000. Right Shoulder Width (CMF3, rps, 1EX, y, z ) The segment has 8-ft right shoulders, which is the base condition for the right shoulder width CMF. Hence, CMF3, rps, 1EX, y, fi and CMF3, rps, 1EX, y, pdo are equal to 1.000.

624 Left Shoulder Width (CMF4, rps, 1EX, y, z ) The segment has 4-ft left shoulders, which is the base condition for the left shoulder width CMF. Hence, CMF4, rps, 1EX, y, fi and CMF4, rps, 1EX, y, pdo are equal to 1.000. Right Side Barrier (CMF5, rps, 1EX, y, z ) The segment does not have right side barrier. Hence, CMF5, rps, 1EX, y, fi and CMF5, rps, 1EX, y, pdo are equal to 1.000. Left Side Barrier (CMF6, rps, 1EX, y, z ) The segment does not have left side barrier. Hence, CMF6, rps, 1EX, y, fi and CMF6, rps, 1EX, y, pdo are equal to 1.000. Lane Add or Drop (CMF7, rps, 1EX, y, fi ) The segment does not have a lane add or a lane drop. Hence, CMF7, rps, 1EX, y, fi is equal to 1.000. Ramp Speed-Change Lane (CMF8, rps, 1EX, mv, fi ) The segment does not have a speed-change lane. Hence, CMF8, rps, 1EX, mv, fi is equal to 1.000. Multiple-Vehicle Crashes The CMFs are applied to the multiple-vehicle fatal-and-injury SPF as follows: ( ) ( ) arcrashes/ye005.0 104.1005.0 000.1000.1000.1000.1000.1000.1000.1104.1005.0 ,,1,,8,,1,,1,,1,,,,1,*, = ×= ××××××××= ×××= fimvEXrpsfimvEXrpsfimvEXrpsspffimvEXrpsp CMFCMFNN  The CMFs are applied to the multiple-vehicle property-damage-only SPF as follows: ( ) ( ) arcrashes/ye014.0 073.1013.0 000.1000.1000.1000.1000.1000.1000.1073.1013.0 ,,1,,8,,1,,1,,1,,,,1,*, = ×= ××××××××= ×××= pdomvEXrpspdomvEXrpspdomvEXrpsspfpdomvEXrpsp CMFCMFNN  Single-Vehicle Crashes The CMFs are applied to the single-vehicle fatal-and-injury SPF as follows: ( ) ( ) arcrashes/ye151.0 320.1114.0 000.1000.1000.1000.1000.1000.1000.1320.1114.0 ,,1,,8,,1,,1,,1,,,,1,*, = ×= ××××××××= ×××= fisvEXrpsfisvEXrpsfisvEXrpsspffisvEXrpsp CMFCMFNN  The CMFs are applied to the single-vehicle property-damage-only SPF as follows:

625 ( ) ( ) arcrashes/ye176.0 418.1124.0 000.1000.1000.1000.1000.1000.1000.1418.1124.0 ,,1,,8,,1,,1,,1,,,,1,*, = ×= ××××××××= ×××= pdosvEXrpspdosvEXrpspdosvEXrpsspfpdosvEXrpsp CMFCMFNN  Step 11 – Multiply the result obtained in Step 10 by the appropriate calibration factor. It is assumed that a calibration factor of 1.00 has been determined for local conditions. As a result, Np, rps, 1EX, y, z = Np*, rps, 1EX, y, z for both crash types y (y = mv: multiple-vehicle, sv: single-vehicle) and both crash severities z (z = fi: fatal-and-injury, pdo: property-damage-only). See Section B.1 of Appendix B to Part C for further discussion on calibration of the predicted models. Calculation of Predicted Average Crash Frequency The predicted average crash frequency is calculated using Equation 19-1 based on the results obtained in Steps 9 through 11 as follows. Fatal-and-injury crashes: arcrashes/ye156.0 151.0005.0 ,,1,,,,1,,,,1,, = += += fisvEXrpspfimvEXrpspfiatEXrpsp NNN Property-damage-only crashes: arcrashes/ye190.0 176.0014.0 ,,1,,,,1,,,,1,, = += += pdosvEXrpsppdomvEXrpsppdoatEXrpsp NNN Step 12—If there is another year to be evaluated in the evaluation period for the selected site, return to Step 8. Otherwise, proceed to Step 13. The study period is one year (2011), so steps 8 through 11 need not be repeated. Step 13—Apply site-specific EB Method (if applicable) and apply SDFs. This step consists of three optional sets of calculations—site-specific EB Method, severity distribution functions, and crash type distribution. Apply the site-specific EB Method to a future time period, if appropriate. The site-specific EB Method is not applied in this sample problem because crash data are not available. Apply the severity distribution functions (SDFs), if desired. To apply the SDFs, the systematic component of crash severity likelihood Vj is computed for each severity level j using Equation 19-83 as follows: ( ) ( ) ( )exrruralrblbj IeIdncPPbaV ×+×+×+      +×+= 2

626 The coefficients a, b, c, d, and e are obtained from Table 19-43 for each severity level j. The segment does not have barrier, so Plb and Prb are equal to 0.0. Vj is computed for fatal and incapacitating injury crashes as follows: ( ) ( ) ( ) 339.1 0.1426.00.0668.00.1228.0 2 0.00.0481.0537.1 −= ×+×+×−+      +×−+−=+ AKV Similar calculations using the coefficients from Table 19-43 for non-incapacitating injury crashes yield the following results: 199.0−=BV Using these computed VK+A and VB values, and assuming a calibration factor Csdf, rps+cds of 1.0, the probability of occurrence of a fatal crash is computed using Equation 19-79 as follows: ( ) ( ) ( ) ( ) ( ) ( ) 032.0 248.0 199.0exp339.1exp 0.1 0.1 339.1exp expexp0.1 exp ,,,| , ,,, = × −+−+ −= × ++ = ++ + + + + ataccdsrpsAKK BAK cdsrpssdf AK Kataccdsrps P VV C VP Similar calculations using Equation 19-80 and Equation 19-81 yield the following results: 096.0,,, =+ AataccdsrpsP 391.0,,, =+ BataccdsrpsP The probability of occurrence of a possible-injury crash is computed using Equation 19-82 as follows: 481.0 )391.0096.0032.0(0.1 )(0.1 ,,,,,,,,,,,, = ++−= ++−= ++++ BataccdsrpsAataccdsrpsKataccdsrpsCataccdsrps PPPP The probability of occurrence of a fatal crash is multiplied by the fatal-and-injury crash frequency obtained in Step 11 using Equation 19-78 as follows: arcrashes/ye005.0 032.0156.0 ,,,,,1,,,,1,, = ×= ×= + KataccdsrpsfiatEXrpseKatEXrpse PNN Similar calculations using Equation 19-78 and the probabilities of occurrences of the other crash severities yield the following results: arcrashes/ye015.0,,1,, =AatEXrpseN

627 arcrashes/ye061.0,,1,, =BatEXrpseN arcrashes/ye075.0,,1,, =CatEXrpseN Apply the crash type distribution, if desired. The crash type distributions are applied by multiplying the default crash type distribution proportions in Table 19-6 and Table 19-9 by the predicted average crash frequencies obtained in Step 11. Worksheets The step-by-step instructions are provided to illustrate the predictive method for calculating the predicted average crash frequency for a ramp segment. To apply the predictive method steps to multiple segments, a series of worksheets are provided for determining the predicted average crash frequency. The worksheets include:  Table 19-47. Ramp Segment Worksheet (1 of 4)—Sample Problem 1  Table 19-48. Ramp Segment Worksheet (2 of 4)—Sample Problem 1  Table 19-49. Ramp Segment Worksheet (3 of 4)—Sample Problem 1  Table 19-50. Ramp Segment Worksheet (4 of 4)—Sample Problem 1 Filled versions of these worksheets are provided below. Blank versions of worksheets used in the Sample Problems are provided in Appendix 19A. Table 19-47 is a summary of general information about the ramp segment, analysis, input data (i.e., “The Facts”), and assumptions for Sample Problem 1. The input data include area type, crash data, basic roadway data, and alignment data. Table 19-48 is a summary of general information about the ramp segment, analysis, input data (i.e., “The Facts”), and assumptions for Sample Problem 1. The input data include cross section data, roadside data, ramp access data, and traffic data. Table 19-49 is a tabulation of the CMF and SPF computations for Sample Problem 1. Table 19-50 is a tabulation of the crash severity and crash type distributions for Sample Problem 1.

628 Table 19-47. Ramp Segment Worksheet (1 of 4)—Sample Problem 1 General Information Location Information Analyst Roadway Agency or company Roadway section Date performed Study year Area type X Urban Rural Input Data Crash Data Crash Period Study Year Complete the study year column. Complete the crash period column if the EB Method is used. Crash data time period First year -- Last year -- Count of multiple-vehicle FI crashes N*o, w, n, mv, fi -- Count of single-vehicle FI crashes N*o, w, n, sv, fi -- Count of multiple-vehicle PDO crashes N*o, w, n, mv, pdo -- Count of single-vehicle PDO crashes N*o, w, n, sv, pdo -- Basic Roadway Data Number of through lanes n 1 Same value for crash period and study year. Segment length L (mi) -- 0.15 Average traffic speed on the freeway Vfrwy (mi/h) -- 65 Segment type Exit Choices: Entrance, Exit, C-D road, Connector Type of control at crossroad ramp terminal -- Signal Choices: Stop, Yield, Signal, None Alignment Data Horizontal Curve Data 1 Presence of horizontal curve 1 -- Off Seg. Choices: No, In segment, Off segment. Curve radius R1 (ft) -- 400 If “In segment” or “Off segment”, enter data for curve radius, length, and ramp-mile. Length of curve Lc1 (mi) -- 0.025 Length of curve in segment Lc1, seg (mi) -- -- Ramp-mile of beginning of curve in dir. of travel X1 (mi) -- 0.07 2 Presence of horizontal curve 2 -- In Seg. Choices: No, In segment, Off segment Curve radius R2 (ft) -- 400 If “In segment” or “Off segment”, enter data for curve radius, length, and ramp-mile. Length of curve Lc2 (mi) -- 0.07 Length of curve in segment Lc2, seg (mi) -- 0.07 Ramp-mile of beginning of curve in dir. of travel X2 (mi) -- 0.19 3 Presence of horizontal curve 3 -- No Choices: No, In segment, Off segment Curve radius R3 (ft) -- -- If “In segment” or “Off segment”, enter data for curve radius, length, and ramp-mile. Length of curve Lc3 (mi) -- -- Length of curve in segment Lc3, seg (mi) -- -- Ramp-mile of beginning of curve in dir. of travel X3 (mi) -- -- 4 Presence of horizontal curve 4 -- No Choices: No, In segment, Off segment Curve radius R4 (ft) -- -- If “In segment” or “Off segment”, enter data for curve radius, length, and ramp-mile. Length of curve Lc4 (mi) -- -- Length of curve in segment Lc4, seg (mi) -- -- Ramp-mile of beginning of curve in dir. of travel X4 (mi) -- --

629 Table 19-48. Ramp Segment Worksheet (2 of 4)—Sample Problem 1 Input Data Cross Section Data Crash Period Study Year Complete the study year column. Complete the crash period column if the EB Method is used. Lane width Wl (ft) -- 14 Right shoulder width Wrs (ft) -- 8 Left shoulder width Wls (ft) -- 4 Presence of lane add or lane drop -- No Choices: No, Lane add, Lane drop Length of taper in segment Ladd, seg or Ldrop, seg (mi) -- -- If “Lane add” or “Lane drop”, enter length. Roadside Data Presence of barrier on right side of roadway -- Y/N N Y/N If Yes, then use the ramp barrier worksheet. Presence of barrier on left side of roadway -- Y/N N Y/N If Yes, then use the ramp barrier worksheet. Ramp Access Data Ramp Entrance Ent. ramp Presence of speed-change lane in segment -- Y/N N Y/N If Yes, then enter data in the next row. Length of s-c lane in segment Len,seg (mi) -- -- Exit ramp Presence of speed-change lane in segment -- Y/N N Y/N If Yes, then enter data in the next row. Length of s-c lane in segment Lex,seg (mi) -- -- Weave Presence of a weaving section in segment -- Y/N -- Y/N If Yes, then enter data in the next two rows. Length of weaving section Lwev (mi) -- -- Length of weaving section in seg. Lwev, seg (mi) -- -- Traffic Data Segment AADT AADTr or AADTc (veh/day) -- 6,750

630 Table 19-49. Ramp Segment Worksheet (3 of 4)—Sample Problem 1 Crash Modification Factors Fatal and Injury Property Damage Only Complete the study year column. Complete the crash period column if the EB Method is used. Multiple Vehicle Single Vehicle Multiple Vehicle Single Vehicle Equation Crash Period Study Year Crash Period Study Year Crash Period Study Year Crash Period Study Year Horizontal curve CMF1, w, x, y, z 19-33 -- 1.104 -- 1.320 -- 1.073 -- 1.418 Lane width CMF2, w, x, y, fi 19-34 -- 1.000 -- 1.000 Right shoulder width CMF3, w, x, y, z 19-35 -- 1.000 -- 1.000 -- 1.000 -- 1.000 Left shoulder width CMF4, w, x, y, z 19-36 -- 1.000 -- 1.000 -- 1.000 -- 1.000 Right side barrier CMF5, w, x, y, z 19-37 -- 1.000 -- 1.000 -- 1.000 -- 1.000 Left side barrier CMF6, w, x, y, z 19-38 -- 1.000 -- 1.000 -- 1.000 -- 1.000 Lane add or drop CMF7, w, x, y, fi 19-39 -- 1.000 -- 1.000 Ramp speed-change lane CMF8, w, x, mv, fi 19-40 -- 1.000 Weaving section CMF9, cds, ac, y, z 19-41 -- 1.000 -- 1.000 -- 1.000 -- 1.000 Combined CMF (multiply all CMFs evaluated) -- 1.104 -- 1.320 -- 1.073 -- 1.418 Expected Average Crash Frequency a Fatal and Injury Property Damage Only Complete the study year column. Complete the crash period column if the site-specific EB Method is used. Multiple Vehicle Single Vehicle Multiple Vehicle Single Vehicle Crash Period Study Year Crash Period Study Year Crash Period Study Year Crash Period Study Year Calibration factor Cw, x, y, z 1.00 1.00 1.00 1.00 Overdispersion parameter kw, x, y, z -- -- -- -- Observed crash count N*o, w, x, y, z (cr) -- -- -- -- Reference year r -- -- -- -- Predicted average crash freq. for reference year Np, w, x, y, z, r (cr/yr) -- -- -- -- Predicted number of crashes for crash period (sum all years) N*p, w, x, y, z (cr) -- -- -- -- Equivalent years associated with crash count Cb, w, x, y, z, r (yr) -- -- -- -- Adjusted average crash freq. for ref. year given N*o, Na, w, x, y, z, r (cr/yr) -- -- -- -- Study year s 2011 2011 2011 2011 Predicted average crash freq. for study year Np, w, x, y, z, s (cr/yr) 0.005 0.151 0.014 0.175 Expected average crash freq. for study year Ne, w, x, y, z, s (cr/yr) 0.005 0.151 0.014 0.175 Expected average crash freq. for study year (all crash types) Ne, w, x, at, z, s (cr/yr) 0.156 0.189 Note: a If the EB Method is not used, then substitute the word “predicted” for the word “expected” and substitute the subscript “p” for the subscript “e”.

631 Table 19-50. Ramp Segment Worksheet (4 of 4)—Sample Problem 1 Expected Average Crash Frequency a Crash Severity Distribution K A B C Total FI PDO Total FI + PDO Proportion by injury level 0.032 0.096 0.391 0.481 1.000 Expected average crash freq. for study year (all crash types) Ne, w, x, at, z, s (cr/yr) 0.005 0.015 0.061 0.075 0.156 0.189 0.345 Crash Type Distribution Fatal and Injury Property Damage Only Total Crash Type Category Proportion Expected Average Crash Frequency for Study Year Ne, w, x, y, fi, s (cr/yr) Proportion Expected Average Crash Frequency for Study Year Ne, w, x, y, pdo, s (cr/yr) Expected Average Crash Frequency for Study Year Ne, w, x, y, as, s (cr/yr) Table Multiple-Vehicle Crashes 19-6 Head-on 0.015 0.000 0.009 0.000 0.000 Right-angle 0.010 0.000 0.005 0.000 0.000 Rear-end 0.707 0.003 0.550 0.008 0.011 Sideswipe 0.129 0.001 0.335 0.005 0.005 Other multiple-vehicle crashes 0.139 0.001 0.101 0.001 0.002 Total 1.000 0.005 1.000 0.014 0.019 Single-Vehicle Crashes 19-9 Crash with animal 0.003 0.000 0.005 0.001 0.001 Crash with fixed object 0.718 0.108 0.834 0.146 0.254 Crash with other object 0.015 0.002 0.023 0.004 0.006 Crash with parked vehicle 0.012 0.002 0.012 0.002 0.004 Other single-vehicle crashes 0.252 0.038 0.126 0.022 0.060 Total 1.000 0.151 1.000 0.175 0.326 Note: a If the EB Method is not used, then substitute the word “predicted” for the word “expected” and substitute the subscript “p” for the subscript “e”. 19.14.2. Sample Problem 2 The Site/Facility A two-lane urban C-D road segment. The Question What is the predicted average crash frequency of the C-D road segment for a one-year period? The Facts The study year is 2011. The conditions present during this year are provided in the following list.  0.08-mi length  5,500 veh/day

632  60-mi/h average speed on freeway mainline  One off-segment horizontal curve  1,100-ft radius  0.08-mi length  Beginning at ramp-mile 0.09  14-ft lane width  8-ft right shoulder width (paved)  4-ft left shoulder width (paved)  No lane adds or lane drops  No barrier on the right or left sides of the roadway  No ramp entrances or exits in the segment  0.08-mi weaving section along entire length of segment Assumptions  Crash type distributions used are the default values presented in Table 19-6 and Table 19-9.  The calibration factor is 1.00. Results Using the predictive method steps as outlined below, the predicted average fatal-and-injury crash frequency for the C-D road segment in Sample Problem 2 is determined to be 0.1 crashes per year, and the predicted average property-damage-only crash frequency is determined to be 0.2 crashes per year (rounded to one decimal place). Steps Step 1 through 8 To determine the predicted average crash frequency of the C-D road segment in Sample Problem 2, only Steps 9 through 13 are conducted. No other steps are necessary because only one C-D road segment is analyzed for a one-year period and the EB Method is not applied. Step 9 – For the selected site, determine and apply the appropriate SPF. For a two-lane urban C-D road segment, SPF values for multiple-vehicle and single-vehicle crashes are determined. Multiple-Vehicle Crashes The SPF for multiple-vehicle fatal-and-injury crashes is calculated from Equation 19-22 and Table 19-7 as follows:

633 [ ] [ ]( ) [ ] [ ]( ) arcrashes/ye023.0 500,5001.00699.0500,5001.0ln524.0515.2exp08.0 lnexp,,2,, = ×+××+−×= ×+××+×= cccdfimvcdsspf AADTcdAADTcbaLN Similarly, the SPF for multiple-vehicle property-damage-only crashes is calculated from Equation 19-22 and Table 19-7 to yield the following result: arcrashes/ye057.0,,2,, =pdomvcdsspfN Single-Vehicle Crashes The SPF for single-vehicle fatal-and-injury crashes is calculated from Equation 19-26 and Table 19-10 as follows: [ ]( ) [ ]( ) arcrashes/ye015.0 500,5001.0ln718.0881.2exp08.0 lnexp,,2,, = ××+−×= ××+×= ccdfisvcdsspf AADTcbaLN Similarly, the SPF for single-vehicle property-damage-only crashes is calculated from Equation 19-26 and Table 19-10 to yield the following result: arcrashes/ye025.0,,2,, =pdosvcdsspfN Step 10 – Multiply the result obtained in Step 9 by the appropriate CMFs. Each CMF used in the calculation of the predicted average crash frequency of the ramp segment is calculated in this step. Horizontal Curve (CMF1, cds, 2, y, z ) CMF1, cds, 2, y, z is calculated using Equation 19-33 as follows:         ×      ×+=  = m i ic i ient zycds PR v aCMF 1 , 2 , ,,2,,1 2.32 000,10.1 Only in-segment curves are included in the summation term. The C-D road has a curve upstream of the segment being analyzed, but there are no curves in the segment. Hence, CMF1, cds, 2, y, z is equal to 1.000. Lane Width (CMF2, cds, 2, y, z ) The segment has 14-ft lanes, which is the base condition for the lane width CMF. Hence, CMF2, cds, 2, y, fi and CMF2, cds, 2, y, pdo are equal to 1.000. Right Shoulder Width (CMF3, cds, 2, y, z ) The segment has 8-ft right shoulders, which is the base condition for the right shoulder width CMF. Hence, CMF3, cds, 2, y, fi and CMF3, cds, 2, y, pdo are equal to 1.000. Left Shoulder Width (CMF4, cds, 2, y, z ) The segment has 4-ft left shoulders, which is the base condition for the left shoulder width CMF. Hence, CMF4, cds, 2, y, fi and CMF4, cds, 2, y, pdo are equal to 1.000.

634 Right Side Barrier (CMF5, cds, 2, y, z ) The segment does not have right side barrier. Hence, CMF5, rps, 1EX, y, fi and CMF5, rps, 1EX, y, pdo are equal to 1.000. Left Side Barrier (CMF6, rps, 1EX, y, z ) The segment does not have left side barrier. Hence, CMF6, cds, 2, y, fi and CMF6, cds, 2, y, pdo are equal to 1.000. Lane Add or Drop (CMF7, cds, 2, y, fi ) The segment does not have a lane add or a lane drop. Hence, CMF7, rps, 1EX, y, fi is equal to 1.000. Ramp Speed-Change Lane (CMF8, cds, 2, mv, fi ) The segment does not have a speed-change lane. Hence, CMF8, cds, 2, mv, fi is equal to 1.000. Weaving Section (CMF9, cds, 2, at, z ) CMF9, cds, 2, at, z is calculated using Equation 19-41 as follows: ( ) [ ]      ××+ ×+×−= wev c wevwevzatcds L AADTcba PPCMF ln exp0.10.1,,2,,9 From Table 19-31, a = 0.191, b = -0.0715, and c = 0.001 for multiple-vehicle fatal-and-injury crashes. CMF9, cds, 2, at, z is calculated as follows: ( ) [ ] 372.2 08.0 500,5001.0ln0715.0191.0exp0.10.10.10.1,,2,,9 =       ××−×+×−=fiatcdsCMF Similar calculations using the property-damage-only coefficients from Table 19-31 yield the following results: 009.3,,2,,9 =pdoatcdsCMF Multiple-Vehicle Crashes The CMFs are applied to the multiple-vehicle fatal-and-injury SPF as follows: ( ) ( ) arcrashes/ye055.0 372.2023.0 372.2000.1000.1000.1000.1000.1000.1000.1000.1023.0 ,,2,,9,,2,,1,,2,,,,2,*, = ×= ×××××××××= ×××= fimvcdsfimvcdsfimvcdsspffimvcdsp CMFCMFNN  The CMFs are applied to the multiple-vehicle property-damage-only SPF as follows: ( ) ( ) arcrashes/ye172.0 009.3057.0 009.3000.1000.1000.1000.1000.1000.1000.1000.1057.0 ,,2,,9,,2,,1,,2,,,,2,*, = ×= ×××××××××= ×××= pdomvcdspdomvcdspdomvcdsspfpdomvcdsp CMFCMFNN 

635 Single-Vehicle Crashes The CMFs are applied to the single-vehicle fatal-and-injury SPF as follows: ( ) ( ) arcrashes/ye036.0 372.2015.0 372.2000.1000.1000.1000.1000.1000.1000.1015.0 ,,2,,9,,2,,7,,2,,1,,2,,,,2,*, = ×= ××××××××= ××××= fisvcdsfisvcdsfisvcdsfisvcdsspffisvcdsp CMFCMFCMFNN  The CMFs are applied to the single-vehicle property-damage-only SPF as follows: ( ) ( ) arcrashes/ye075.0 009.3025.0 009.3000.1000.1000.1000.1000.1000.1000.1025.0 ,,2,,9,,2,,7,,2,,1,,2,,,,2,*, = ×= ××××××××= ××××= pdosvcdspdosvcdspdosvcdspdosvcdsspfpdosvcdsp CMFCMFCMFNN  Step 11 – Multiply the result obtained in Step 10 by the appropriate calibration factor. It is assumed that a calibration factor of 1.00 has been determined for local conditions. As a result, Np, cds, 2, y, z = Np*, cds, 2, y, z for both crash types y (y = mv: multiple-vehicle, sv: single-vehicle) and both crash severities z (z = fi: fatal-and-injury, pdo: property-damage-only). See Section B.1 of Appendix B to Part C for further discussion on calibration of the predicted models. Calculation of Predicted Average Crash Frequency The predicted average crash frequency is calculated using Equation 19-1 based on the results obtained in Steps 9 through 11 as follows. Fatal-and-injury crashes: arcrashes/ye091.0 036.0055.0 ,,2,,,,2,,,,2,, = += += fisvcdspfimvcdspfiatcdsp NNN Property-damage-only crashes: arcrashes/ye247.0 075.0172.0 ,,2,,,,2,,,,2,, = += += pdosvcdsppdomvcdsppdoatcdsp NNN Step 12—If there is another year to be evaluated in the evaluation period for the selected site, return to Step 8. Otherwise, proceed to Step 13. The study period is one year (2011), so steps 8 through 11 need not be repeated. Step 13—Apply site-specific EB Method (if applicable) and apply SDFs. This step consists of three optional sets of calculations—site-specific EB Method, severity distribution functions, and crash type distribution.

636 Apply the site-specific EB Method to a future time period, if appropriate. The site-specific EB Method is not applied in this sample problem because crash data are not available. Apply the severity distribution functions (SDFs), if desired. To apply the SDFs, the systematic component of crash severity likelihood Vj is computed for each severity level j using Equation 19-83 as follows: ( ) ( ) ( )exrruralrblbj IeIdncPPbaV ×+×+×+      +×+= 2 The coefficients a, b, c, d, and e are obtained from Table 19-43 for each severity level j. The segment does not have barrier, so Plb and Prb are equal to 0.0. Vj is computed for fatal and incapacitating injury crashes as follows: ( ) ( ) ( ) 993.1 0.0426.00.0668.00.2228.0 2 0.00.0481.0537.1 −= ×+×+×−+      +×−+−=+ AKV Similar calculations using the coefficients from Table 19-43 for non-incapacitating injury crashes yield the following results: 634.0−=BV Using these computed VK+A and VB values, and assuming a calibration factor Csdf, rps+cds of 1.0, the probability of occurrence of a fatal crash is computed using Equation 19-79 as follows: ( ) ( ) ( ) ( ) ( ) ( ) 022.0 248.0 634.0exp993.1exp 0.1 0.1 993.1exp expexp0.1 exp ,,,| , ,,, = × −+−+ −= × ++ = ++ + + + + ataccdsrpsAKK BAK cdsrpssdf AK Kataccdsrps P VV C VP Similar calculations using Equation 19-80 and Equation 19-81 yield the following results: 065.0,,, =+ AataccdsrpsP 315.0,,, =+ BataccdsrpsP The probability of occurrence of a possible-injury crash is computed using Equation 19-82 as follows: 598.0 )315.0065.0022.0(0.1 )(0.1 ,,,,,,,,,,,, = ++−= ++−= ++++ BataccdsrpsAataccdsrpsKataccdsrpsCataccdsrps PPPP The probability of occurrence of a fatal crash is multiplied by the fatal-and-injury crash frequency obtained in Step 11 using Equation 19-78 as follows:

637 arcrashes/ye002.0 022.0091.0 ,,,,,2,,,,2,, = ×= ×= + KataccdsrpsfiatcdseKatcdse PNN Similar calculations using Equation 19-78 and the probabilities of occurrences of the other crash severities yield the following results: arcrashes/ye006.0,,2,, =AatcdseN arcrashes/ye029.0,,2,, =BatcdseN arcrashes/ye055.0,,2,, =CatcdseN Apply the crash type distribution, if desired. The crash type distributions are applied by multiplying the default crash type distribution proportions in Table 19-6 and Table 19-9 by the predicted average crash frequencies obtained in Step 11. Worksheets The step-by-step instructions are provided to illustrate the predictive method for calculating the predicted average crash frequency for a ramp segment. To apply the predictive method steps to multiple segments, a series of worksheets are provided for determining the predicted average crash frequency. The worksheets include:  Table 19-51. Ramp Segment Worksheet (1 of 4)—Sample Problem 2  Table 19-52. Ramp Segment Worksheet (2 of 4)—Sample Problem 2  Table 19-53. Ramp Segment Worksheet (3 of 4)—Sample Problem 2  Table 19-54. Ramp Segment Worksheet (4 of 4)—Sample Problem 2 Filled versions of these worksheets are provided below. Blank versions of worksheets used in the Sample Problems are provided in Appendix 19A. Table 19-51 is a summary of general information about the ramp segment, analysis, input data (i.e., “The Facts”), and assumptions for Sample Problem 2. The input data include area type, crash data, basic roadway data, and alignment data. Table 19-52 is a summary of general information about the ramp segment, analysis, input data (i.e., “The Facts”), and assumptions for Sample Problem 2. The input data include cross section data, roadside data, ramp access data, and traffic data. Table 19-53 is a tabulation of the CMF and SPF computations for Sample Problem 2. Table 19-54 is a tabulation of the crash severity and crash type distributions for Sample Problem 2.

638 Table 19-51. Ramp Segment Worksheet (1 of 4)—Sample Problem 2 General Information Location Information Analyst Roadway Agency or company Roadway section Date performed Study year Area type X Urban Rural Input Data Crash Data Crash Period Study Year Complete the study year column. Complete the crash period column if the EB Method is used. Crash data time period First year -- Last year -- Count of multiple-vehicle FI crashes N*o, w, n, mv, fi Count of single-vehicle FI crashes N*o, w, n, sv, fi Count of multiple-vehicle PDO crashes N*o, w, n, mv, pdo Count of single-vehicle PDO crashes N*o, w, n, sv, pdo Basic Roadway Data Number of through lanes n 2 Same value for crash period and study year. Segment length L (mi) 0.08 Average traffic speed on the freeway Vfrwy (mi/h) 60 Segment type C-D Road Choices: Entrance, Exit, C-D road, Connector Type of control at crossroad ramp terminal -- Choices: Stop, Yield, Signal, None Alignment Data Horizontal Curve Data 1 Presence of horizontal curve 1 Off Seg. Choices: No, In segment, Off segment. Curve radius R1 (ft) 1,100 If “In segment” or “Off segment”, enter data for curve radius, length, and ramp-mile. Length of curve Lc1 (mi) 0.08 Length of curve in segment Lc1, seg (mi) -- Ramp-mile of beginning of curve in dir. of travel X1 (mi) 0.09 2 Presence of horizontal curve 2 No Choices: No, In segment, Off segment Curve radius R2 (ft) -- If “In segment” or “Off segment”, enter data for curve radius, length, and ramp-mile. Length of curve Lc2 (mi) -- Length of curve in segment Lc2, seg (mi) -- Ramp-mile of beginning of curve in dir. of travel X2 (mi) -- 3 Presence of horizontal curve 3 No Choices: No, In segment, Off segment Curve radius R3 (ft) -- If “In segment” or “Off segment”, enter data for curve radius, length, and ramp-mile. Length of curve Lc3 (mi) -- Length of curve in segment Lc3, seg (mi) -- Ramp-mile of beginning of curve in dir. of travel X3 (mi) -- 4 Presence of horizontal curve 4 No Choices: No, In segment, Off segment Curve radius R4 (ft) -- If “In segment” or “Off segment”, enter data for curve radius, length, and ramp-mile. Length of curve Lc4 (mi) -- Length of curve in segment Lc4, seg (mi) -- Ramp-mile of beginning of curve in dir. of travel X4 (mi) --

639 Table 19-52. Ramp Segment Worksheet (2 of 4)—Sample Problem 2 Input Data Cross Section Data Crash Period Study Year Complete the study year column. Complete the crash period column if the EB Method is used. Lane width Wl (ft) -- 14 Right shoulder width Wrs (ft) -- 8 Left shoulder width Wls (ft) -- 4 Presence of lane add or lane drop -- No Choices: No, Lane add, Lane drop Length of taper in segment Ladd, seg or Ldrop, seg (mi) -- -- If “Lane add” or “Lane drop”, enter length. Roadside Data Presence of barrier on right side of roadway -- Y/N N Y/N If Yes, then use the ramp barrier worksheet. Presence of barrier on left side of roadway -- Y/N N Y/N If Yes, then use the ramp barrier worksheet. Ramp Access Data Ramp Entrance Ent. ramp Presence of speed-change lane in segment -- Y/N N Y/N If Yes, then enter data in the next row. Length of s-c lane in segment Len,seg (mi) -- -- Exit ramp Presence of speed-change lane in segment -- Y/N N Y/N If Yes, then enter data in the next row. Length of s-c lane in segment Lex,seg (mi) -- -- Weave Presence of a weaving section in segment -- Y/N Y Y/N If Yes, then enter data in the next two rows. Length of weaving section Lwev (mi) -- 0.08 Length of weaving section in seg. Lwev, seg (mi) -- 0.08 Traffic Data Segment AADT AADTr or AADTc (veh/day) -- 5,500

640 Table 19-53. Ramp Segment Worksheet (3 of 4)—Sample Problem 2 Crash Modification Factors Fatal and Injury Property Damage Only Complete the study year column. Complete the crash period column if the EB Method is used. Multiple Vehicle Single Vehicle Multiple Vehicle Single Vehicle Equation Crash Period Study Year Crash Period Study Year Crash Period Study Year Crash Period Study Year Horizontal curve CMF1, w, x, y, z 19-33 -- 1.000 -- 1.000 -- 1.000 -- 1.000 Lane width CMF2, w, x, y, fi 19-34 -- 1.000 -- 1.000 Right shoulder width CMF3, w, x, y, z 19-35 -- 1.000 -- 1.000 -- 1.000 -- 1.000 Left shoulder width CMF4, w, x, y, z 19-36 -- 1.000 -- 1.000 -- 1.000 -- 1.000 Right side barrier CMF5, w, x, y, z 19-37 -- 1.000 -- 1.000 -- 1.000 -- 1.000 Left side barrier CMF6, w, x, y, z 19-38 -- 1.000 -- 1.000 -- 1.000 -- 1.000 Lane add or drop CMF7, w, x, y, fi 19-39 -- 1.000 -- 1.000 Ramp speed-change lane CMF8, w, x, mv, fi 19-40 -- 1.000 Weaving section CMF9, cds, ac, y, z 19-41 -- 2.372 -- 2.372 -- 3.009 -- 3.009 Combined CMF (multiply all CMFs evaluated) -- 2.372 -- 2.372 -- 3.009 -- 3.009 Expected Average Crash Frequency a Fatal and Injury Property Damage Only Complete the study year column. Complete the crash period column if the site-specific EB Method is used. Multiple Vehicle Single Vehicle Multiple Vehicle Single Vehicle Crash Period Study Year Crash Period Study Year Crash Period Study Year Crash Period Study Year Calibration factor Cw, x, y, z 1.00 1.00 1.00 1.00 Overdispersion parameter kw, x, y, z -- -- -- -- Observed crash count N*o, w, x, y, z (cr) -- -- -- -- Reference year r -- -- -- -- Predicted average crash freq. for reference year Np, w, x, y, z, r (cr/yr) -- -- -- -- Predicted number of crashes for crash period (sum all years) N*p, w, x, y, z (cr) -- -- -- -- Equivalent years associated with crash count Cb, w, x, y, z, r (yr) -- -- -- -- Adjusted average crash freq. for ref. year given N*o, Na, w, x, y, z, r (cr/yr) -- -- -- -- Study year s 2011 2011 2011 2011 Predicted average crash freq. for study year Np, w, x, y, z, s (cr/yr) 0.055 0.036 0.172 0.075 Expected average crash freq. for study year Ne, w, x, y, z, s (cr/yr) 0.055 0.036 0.172 0.075 Expected average crash freq. for study year (all crash types) Ne, w, x, at, z, s (cr/yr) 0.091 0.247 Note: a If the EB Method is not used, then substitute the word “predicted” for the word “expected” and substitute the subscript “p” for the subscript “e”.

641 Table 19-54. Ramp Segment Worksheet (4 of 4)—Sample Problem 2 Expected Average Crash Frequency a Crash Severity Distribution K A B C Total FI PDO Total FI + PDO Proportion by injury level 0.022 0.065 0.315 0.598 1.000 Expected average crash freq. for study year (all crash types) Ne, w, x, at, z, s (cr/yr) 0.002 0.006 0.029 0.055 0.091 0.247 0.338 Crash Type Distribution Fatal and Injury Property Damage Only Total Crash Type Category Proportion Expected Average Crash Frequency for Study Year Ne, w, x, y, fi, s (cr/yr) Proportion Expected Average Crash Frequency for Study Year Ne, w, x, y, pdo, s (cr/yr) Expected Average Crash Frequency for Study Year Ne, w, x, y, as, s (cr/yr) Table Multiple-Vehicle Crashes 19-6 Head-on 0.015 0.001 0.009 0.002 0.002 Right-angle 0.010 0.001 0.005 0.001 0.001 Rear-end 0.707 0.039 0.550 0.095 0.134 Sideswipe 0.129 0.007 0.335 0.058 0.065 Other multiple-vehicle crashes 0.139 0.008 0.101 0.017 0.025 Total 1.000 0.055 1.000 0.172 0.227 Single-Vehicle Crashes 19-9 Crash with animal 0.003 0.000 0.005 0.000 0.000 Crash with fixed object 0.718 0.026 0.834 0.062 0.088 Crash with other object 0.015 0.001 0.023 0.002 0.002 Crash with parked vehicle 0.012 0.000 0.012 0.001 0.001 Other single-vehicle crashes 0.252 0.009 0.126 0.009 0.019 Total 1.000 0.036 1.000 0.075 0.111 Note: a If the EB Method is not used, then substitute the word “predicted” for the word “expected” and substitute the subscript “p” for the subscript “e”. 19.14.3. Sample Problem 3 The Site/Facility A one-lane urban entrance ramp segment. The Question What is the predicted average crash frequency of the ramp segment for a one-year period? The Facts The study year is 2011. The conditions present during this year are provided in the following list.  0.3-mi length  7,250 veh/day

642  65-mi/h average speed on freeway mainline  Yield control at crossroad ramp terminal  One in-segment horizontal curve  475-ft radius  0.08-mi length, entirely in the segment  Beginning at ramp-mile 0.07  14-ft lane width  8-ft right shoulder width (paved)  4-ft left shoulder width (paved)  No lane adds or lane drops  Barrier on both sides of the roadway  Right-side barrier length: 0.15 mi  Right-side barrier offset: 9 ft  Left-side barrier length: 0.15 mi  Left-side barrier offset: 5 ft  No ramp entrances or exits in the segment  No weaving section Assumptions  Crash type distributions used are the default values presented in Table 19-6 and Table 19-9.  The calibration factor is 1.00. Results Using the predictive method steps as outlined below, the predicted average fatal-and-injury crash frequency for the ramp segment in Sample Problem 3 is determined to be 0.3 crashes per year, and the predicted average property-damage-only crash frequency is determined to be 0.5 crashes per year (rounded to one decimal place). Steps Step 1 through 8 To determine the predicted average crash frequency of the ramp segment in Sample Problem 3, only Steps 9 through 13 are conducted. No other steps are necessary because only one ramp segment is analyzed for a one-year period and the EB Method is not applied.

643 Step 9 – For the selected site, determine and apply the appropriate SPF. For a one-lane urban exit ramp segment, SPF values for multiple-vehicle and single-vehicle crashes are determined. Multiple-Vehicle Crashes The SPF for multiple-vehicle fatal-and-injury crashes is calculated from Equation 19-20 and Table 19-5 as follows: [ ] [ ]( ) [ ] [ ]( ) arcrashes/ye042.0 250,7001.00699.0250,7001.0ln524.0505.3exp3.0 lnexp,,1,, = ×+××+−×= ×+××+×= rrrfimvENrpsspf AADTcdAADTcbaLN Similarly, the SPF for multiple-vehicle property-damage-only crashes is calculated from Equation 19-20 and Table 19-5 to yield the following result: arcrashes/ye079.0,,1,, =pdomvENrpsspfN Single-Vehicle Crashes The SPF for single-vehicle fatal-and-injury crashes is calculated from Equation 19-24 and Table 19-8 as follows: [ ]( ) [ ]( ) arcrashes/ye174.0 250,7001.0ln718.0966.1exp3.0 lnexp,,1,, = ××+−×= ××+×= rrfisvENrpsspf AADTcbaLN Similarly, the SPF for single-vehicle property-damage-only crashes is calculated from Equation 19-24 and Table 19-8 to yield the following result: arcrashes/ye211.0,,1,, =pdosvENrpsspfN Step 10 – Multiply the result obtained in Step 9 by the appropriate CMFs. Each CMF used in the calculation of the predicted average crash frequency of the ramp segment is calculated in this step. Horizontal Curve (CMF1, rps, 1EN, y, z ) The limited curve speed for the in-segment horizontal curve is computed using Equation 19-59 as follows: ( ) ( ) ft/s3.58 4752.3224.3 2.3224.3 30.0 30.0 11max, = ××= ××= Rv The average entry speed at the curve is computed using Equation 19-60 and the default values in Table 19-42 as follows:

644 [ ]( ) [ ]( ) ft/s9.57 6547.107.0280,54951547.1 47.1280,549547.1 3/13 3/1 1 3 1, = ×≤××+×= ×≤××+×= frwyxroadent VXVv The average exit speed at curve 1 is computed using Equation 19-61 as follows: ( ) ( ) ft/s3.58 6547.13.583.0280,54959.57 47.1280,5495 3/13 1max, 3/1 1, 3 1,1, = ×≤≤××+= ×≤≤××+= and V and vLvv frwycentext CMF1, rps, 1EN, y, fi is calculated using Equation 19-33 as follows:         ×      ×+=  = m i ic i ient fiyENrps PR v aCMF 1 , 2 , ,,1,,1 2.32 000,10.1 From Table 19-24, a = 0.779 for multiple-vehicle fatal-and-injury crashes and 2.406 for single-vehicle fatal-and-injury crashes. CMF1, rps, 1EN, mv, fi is calculated as follows: 096.1 3.0 08.0 475 9.57 2.32 000,1779.00.1 2 ,,1,,1 = ×     ×+=fimvENrpsCMF Calculations using the other coefficients from Table 19-24 yield the following results: 296.1,,1,,1 =fisvENrpsCMF 067.1,,1,,1 =pdomvENrpsCMF 385.1,,1,,1 =pdosvENrpsCMF Lane Width (CMF2, rps, 1EN, y, z ) The segment has 14-ft lanes, which is the base condition for the lane width CMF. Hence, CMF2, rps, 1EN, y, fi and CMF2, rps, 1EN, y, pdo are equal to 1.000. Right Shoulder Width (CMF3, rps, 1EN, y, z ) The segment has 8-ft right shoulders, which is the base condition for the right shoulder width CMF. Hence, CMF3, rps, 1EN, y, fi and CMF3, rps, 1EN, y, pdo are equal to 1.000. Left Shoulder Width (CMF4, rps, 1EN, y, z ) The segment has 4-ft left shoulders, which is the base condition for the left shoulder width CMF. Hence, CMF4, rps, 1EN, y, fi and CMF4, rps, 1EN, y, pdo are equal to 1.000. Right Side Barrier (CMF5, rps, 1EN, y, z ) CMF5, rps, 1EN, y, fi is calculated using Equation 19-37 as follows:

645 ( )       ×+×−= rcb brbrfiyENrps W aPPCMF exp0.10.1,,1,,5 The distance from the edge of the right shoulder to the barrier face Wrcb is computed using Equation 19-74 as follows: 0.1 89 15.0 15.0 ,, , , =       − = − =   rsiroff irb irb rcb WW L L W From Table 19-28, a = 0.210 for multiple-vehicle crashes. CMF5, rps, 1EN, y, fi is calculated as follows: 117.1 0.1 210.0exp 3.0 15.00.1 3.0 15.00.1,,1,,5 =      ×+×      −=fiyENrpsCMF Similar calculations using the property-damage-only coefficients from Table 19-28 yield the following results: 106.1,,1,,5 =pdoyENrpsCMF Left Side Barrier (CMF6, rps, 1EN, y, z ) CMF6, rps, 1EN, y, fi is calculated using Equation 19-38 as follows: ( )       ×+×−= lcb blblfiyENrps W aPPCMF exp0.10.1,,1,,6 The distance from the edge of the right shoulder to the barrier face Wrcb is computed using Equation 19-76 as follows: 0.1 45 15.0 15.0 ,, , , =       − = − =   lsiloff ilb ilb lcb WW L L W From Table 19-29, a = 0.210 for multiple-vehicle crashes. CMF6, rps, 1EN, y, fi is calculated as follows:

646 117.1 0.1 210.0exp 3.0 15.00.1 3.0 15.00.1,,1,,6 =      ×+×      −=fiyENrpsCMF Similar calculations using the property-damage-only coefficients from Table 19-29 yield the following results: 106.1,,1,,6 =pdoyENrpsCMF Lane Add or Drop (CMF7, rps, 1EN, y, fi ) The segment does not have a lane add or a lane drop. Hence, CMF7, rps, 1EN, y, fi is equal to 1.000. Ramp Speed-Change Lane (CMF8, rps, 1EN, mv, fi ) The segment does not have a speed-change lane. Hence, CMF8, rps, 1EN, mv, fi is equal to 1.000. Multiple-Vehicle Crashes The CMFs are applied to the multiple-vehicle fatal-and-injury SPF as follows: ( ) ( ) arcrashes/ye058.0 367.1042.0 000.1000.1117.1117.1000.1000.1000.1096.1042.0 ,,1,,8,,1,,1,,1,,,,1,*, = ×= ××××××××= ×××= fimvENrpsfimvENrpsfimvENrpsspffimvENrpsp CMFCMFNN  The CMFs are applied to the multiple-vehicle property-damage-only SPF as follows: ( ) ( ) arcrashes/ye104.0 305.1079.0 000.1000.1106.1106.1000.1000.1000.1067.1079.0 ,,1,,8,,1,,1,,1,,,,1,*, = ×= ××××××××= ×××= pdomvENrpspdomvENrpspdomvENrpsspfpdomvENrpsp CMFCMFNN  Single-Vehicle Crashes The CMFs are applied to the single-vehicle fatal-and-injury SPF as follows: ( ) ( ) arcrashes/ye281.0 617.1174.0 000.1000.1117.1117.1000.1000.1000.1296.1174.0 ,,1,,8,,1,,1,,1,,,,1,*, = ×= ××××××××= ×××= fisvENrpsfisvENrpsfisvENrpsspffisvENrpsp CMFCMFNN  The CMFs are applied to the single-vehicle property-damage-only SPF as follows: ( ) ( ) arcrashes/ye358.0 694.1211.0 000.1000.1106.1106.1000.1000.1000.1385.1211.0 ,,1,,8,,1,,1,,1,,,,1,*, = ×= ××××××××= ×××= pdosvENrpspdosvENrpspdosvENrpsspfpdosvENrpsp CMFCMFNN 

647 Step 11 – Multiply the result obtained in Step 10 by the appropriate calibration factor. It is assumed that a calibration factor of 1.00 has been determined for local conditions. As a result, Np, rps, 1EN, y, z = Np*, rps, 1EN, y, z for both crash types y (y = mv: multiple-vehicle, sv: single-vehicle) and both crash severities z (z = fi: fatal-and-injury, pdo: property-damage-only). See Section B.1 of Appendix B to Part C for further discussion on calibration of the predicted models. Calculation of Predicted Average Crash Frequency The predicted average crash frequency is calculated using Equation 19-1 based on the results obtained in Steps 9 through 11 as follows. Fatal-and-injury crashes: arcrashes/ye339.0 281.0058.0 ,,1,,,,1,,,,1,, = += += fisvENrpspfimvENrpspfiatENrpsp NNN Property-damage-only crashes: arcrashes/ye462.0 358.0104.0 ,,1,,,,1,,,,1,, = += += pdosvENrpsppdomvENrpsppdoatENrpsp NNN Step 12—If there is another year to be evaluated in the evaluation period for the selected site, return to Step 8. Otherwise, proceed to Step 13. The study period is one year (2011), so steps 8 through 11 need not be repeated. Step 13—Apply site-specific EB Method (if applicable) and apply SDFs. This step consists of three optional sets of calculations—site-specific EB Method, severity distribution functions, and crash type distribution. Apply the site-specific EB Method to a future time period, if appropriate. The site-specific EB Method is not applied in this sample problem because crash data are not available. Apply the severity distribution functions (SDFs), if desired. To apply the SDFs, the systematic component of crash severity likelihood Vj is computed for each severity level j using Equation 19-83 as follows: ( ) ( ) ( )exrruralrblbj IeIdncPPbaV ×+×+×+      +×+= 2 The coefficients a, b, c, d, and e are obtained from Table 19-43 for each severity level j. Vj is computed for fatal and incapacitating injury crashes as follows: ( ) ( ) ( ) 006.2 0.0426.00.0668.00.1228.0 2 5.05.0481.0537.1 −= ×+×+×−+      +×−+−=+ AKV

648 Similar calculations using the coefficients from Table 19-43 for non-incapacitating injury crashes yield the following results: 415.0−=BV Using these computed VK+A and VB values, and assuming a calibration factor Csdf, rps+cds of 1.0, the probability of occurrence of a fatal crash is computed using Equation 19-79 as follows: ( ) ( ) ( ) ( ) ( ) ( ) 018.0 248.0 415.0exp006.2exp 0.1 0.1 006.2exp expexp0.1 exp ,,,| , ,,, = × −+−+ −= × ++ = ++ + + + + ataccdsrpsAKK BAK cdsrpssdf AK Kataccdsrps P VV C VP Similar calculations using Equation 19-80 and Equation 19-81 yield the following results: 056.0,,, =+ AataccdsrpsP 369.0,,, =+ BataccdsrpsP The probability of occurrence of a possible-injury crash is computed using Equation 19-82 as follows: 557.0 )369.0056.0018.0(0.1 )(0.1 ,,,,,,,,,,,, = ++−= ++−= ++++ BataccdsrpsAataccdsrpsKataccdsrpsCataccdsrps PPPP The probability of occurrence of a fatal crash is multiplied by the fatal-and-injury crash frequency obtained in Step 11 using Equation 19-78 as follows: arcrashes/ye006.0 018.0339.0 ,,,,,1,,,,1,, = ×= ×= + KataccdsrpsfiatENrpseKatENrpse PNN Similar calculations using Equation 19-78 and the probabilities of occurrences of the other crash severities yield the following results: arcrashes/ye019.0,,1,, =AatENrpseN arcrashes/ye125.0,,1,, =BatENrpseN arcrashes/ye189.0,,1,, =CatENrpseN Apply the crash type distribution, if desired. The crash type distributions are applied by multiplying the default crash type distribution proportions in Table 19-6 and Table 19-9 by the predicted average crash frequencies obtained in Step 11.

649 Worksheets The step-by-step instructions are provided to illustrate the predictive method for calculating the predicted average crash frequency for a ramp segment. To apply the predictive method steps to multiple segments, a series of worksheets are provided for determining the predicted average crash frequency. The worksheets include:  Table 19-55. Ramp Segment Worksheet (1 of 4)—Sample Problem 3  Table 19-56. Ramp Segment Worksheet (2 of 4)—Sample Problem 3  Table 19-57. Ramp Segment Worksheet (3 of 4)—Sample Problem 3  Table 19-58. Ramp Segment Worksheet (4 of 4)—Sample Problem 3  Table 19-59. Ramp Barrier Worksheet—Sample Problem 3 Filled versions of these worksheets are provided below. Blank versions of worksheets used in the Sample Problems are provided in Appendix 19A. Table 19-55 is a summary of general information about the ramp segment, analysis, input data (i.e., “The Facts”), and assumptions for Sample Problem 3. The input data include area type, crash data, basic roadway data, and alignment data. Table 19-56 is a summary of general information about the ramp segment, analysis, input data (i.e., “The Facts”), and assumptions for Sample Problem 3. The input data include cross section data, roadside data, ramp access data, and traffic data. Table 19-57 is a tabulation of the CMF and SPF computations for Sample Problem 3. Table 19-58 is a tabulation of the crash severity and crash type distributions for Sample Problem 3. Table 19-59 is used to complete the barrier calculations for Sample Problem 3.

650 Table 19-55. Ramp Segment Worksheet (1 of 4)—Sample Problem 3 General Information Location Information Analyst Roadway Agency or company Roadway section Date performed Study year Area type X Urban Rural Input Data Crash Data Crash Period Study Year Complete the study year column. Complete the crash period column if the EB Method is used. Crash data time period First year -- Last year -- Count of multiple-vehicle FI crashes N*o, w, n, mv, fi -- Count of single-vehicle FI crashes N*o, w, n, sv, fi -- Count of multiple-vehicle PDO crashes N*o, w, n, mv, pdo -- Count of single-vehicle PDO crashes N*o, w, n, sv, pdo -- Basic Roadway Data Number of through lanes n 1 Same value for crash period and study year. Segment length L (mi) -- 0.3 Average traffic speed on the freeway Vfrwy (mi/h) -- 65 Segment type Entrance Choices: Entrance, Exit, C-D road, Connector Type of control at crossroad ramp terminal -- Yield Choices: Stop, Yield, Signal, None Alignment Data Horizontal Curve Data 1 Presence of horizontal curve 1 -- In Seg. Choices: No, In segment, Off segment. Curve radius R1 (ft) -- 475 If “In segment” or “Off segment”, enter data for curve radius, length, and ramp-mile. Length of curve Lc1 (mi) -- 0.08 Length of curve in segment Lc1, seg (mi) -- 0.08 Ramp-mile of beginning of curve in dir. of travel X1 (mi) -- 0.07 2 Presence of horizontal curve 2 -- No Choices: No, In segment, Off segment Curve radius R2 (ft) -- -- If “In segment” or “Off segment”, enter data for curve radius, length, and ramp-mile. Length of curve Lc2 (mi) -- -- Length of curve in segment Lc2, seg (mi) -- -- Ramp-mile of beginning of curve in dir. of travel X2 (mi) -- -- 3 Presence of horizontal curve 3 -- No Choices: No, In segment, Off segment Curve radius R3 (ft) -- -- If “In segment” or “Off segment”, enter data for curve radius, length, and ramp-mile. Length of curve Lc3 (mi) -- -- Length of curve in segment Lc3, seg (mi) -- -- Ramp-mile of beginning of curve in dir. of travel X3 (mi) -- -- 4 Presence of horizontal curve 4 -- No Choices: No, In segment, Off segment Curve radius R4 (ft) -- -- If “In segment” or “Off segment”, enter data for curve radius, length, and ramp-mile. Length of curve Lc4 (mi) -- -- Length of curve in segment Lc4, seg (mi) -- -- Ramp-mile of beginning of curve in dir. of travel X4 (mi) -- --

651 Table 19-56. Ramp Segment Worksheet (2 of 4)—Sample Problem 3 Input Data Cross Section Data Crash Period Study Year Complete the study year column. Complete the crash period column if the EB Method is used. Lane width Wl (ft) -- 14 Right shoulder width Wrs (ft) -- 8 Left shoulder width Wls (ft) -- 4 Presence of lane add or lane drop -- No Choices: No, Lane add, Lane drop Length of taper in segment Ladd, seg or Ldrop, seg (mi) -- -- If “Lane add” or “Lane drop”, enter length. Roadside Data Presence of barrier on right side of roadway -- Y/N Y Y/N If Yes, then use the ramp barrier worksheet. Presence of barrier on left side of roadway -- Y/N Y Y/N If Yes, then use the ramp barrier worksheet. Ramp Access Data Ramp Entrance Ent. ramp Presence of speed-change lane in segment -- Y/N N Y/N If Yes, then enter data in the next row. Length of s-c lane in segment Len,seg (mi) -- -- Exit ramp Presence of speed-change lane in segment -- Y/N N Y/N If Yes, then enter data in the next row. Length of s-c lane in segment Lex,seg (mi) -- -- Weave Presence of a weaving section in segment -- Y/N -- Y/N If Yes, then enter data in the next two rows. Length of weaving section Lwev (mi) -- -- Length of weaving section in seg. Lwev, seg (mi) -- -- Traffic Data Segment AADT AADTr or AADTc (veh/day) -- 7,250

652 Table 19-57. Ramp Segment Worksheet (3 of 4)—Sample Problem 3 Crash Modification Factors Fatal and Injury Property Damage Only Complete the study year column. Complete the crash period column if the EB Method is used. Multiple Vehicle Single Vehicle Multiple Vehicle Single Vehicle Equation Crash Period Study Year Crash Period Study Year Crash Period Study Year Crash Period Study Year Horizontal curve CMF1, w, x, y, z 19-33 -- 1.096 -- 1.296 -- 1.067 -- 1.385 Lane width CMF2, w, x, y, fi 19-34 -- 1.000 -- 1.000 Right shoulder width CMF3, w, x, y, z 19-35 -- 1.000 -- 1.000 -- 1.000 -- 1.000 Left shoulder width CMF4, w, x, y, z 19-36 -- 1.000 -- 1.000 -- 1.000 -- 1.000 Right side barrier CMF5, w, x, y, z 19-37 -- 1.117 -- 1.117 -- 1.106 -- 1.106 Left side barrier CMF6, w, x, y, z 19-38 -- 1.117 -- 1.117 -- 1.106 -- 1.106 Lane add or drop CMF7, w, x, y, fi 19-39 -- 1.000 -- 1.000 Ramp speed-change lane CMF8, w, x, mv, fi 19-40 -- 1.000 Weaving section CMF9, cds, ac, y, z 19-41 -- 1.000 -- 1.000 -- 1.000 -- 1.000 Combined CMF (multiply all CMFs evaluated) -- 1.367 -- 1.617 -- 1.305 -- 1.694 Expected Average Crash Frequency a Fatal and Injury Property Damage Only Complete the study year column. Complete the crash period column if the site-specific EB Method is used. Multiple Vehicle Single Vehicle Multiple Vehicle Single Vehicle Crash Period Study Year Crash Period Study Year Crash Period Study Year Crash Period Study Year Calibration factor Cw, x, y, z 1.00 1.00 1.00 1.00 Overdispersion parameter kw, x, y, z -- -- -- -- Observed crash count N*o, w, x, y, z (cr) -- -- -- -- Reference year r -- -- -- -- Predicted average crash freq. for reference year Np, w, x, y, z, r (cr/yr) -- -- -- -- Predicted number of crashes for crash period (sum all years) N*p, w, x, y, z (cr) -- -- -- -- Equivalent years associated with crash count Cb, w, x, y, z, r (yr) -- -- -- -- Adjusted average crash freq. for ref. year given N*o, Na, w, x, y, z, r (cr/yr) -- -- -- -- Study year s 2011 2011 2011 2011 Predicted average crash freq. for study year Np, w, x, y, z, s (cr/yr) 0.058 0.281 0.103 0.358 Expected average crash freq. for study year Ne, w, x, y, z, s (cr/yr) 0.058 0.281 0.103 0.358 Expected average crash freq. for study year (all crash types) Ne, w, x, at, z, s (cr/yr) 0.339 0.461 Note: a If the EB Method is not used, then substitute the word “predicted” for the word “expected” and substitute the subscript “p” for the subscript “e”.

653 Table 19-58. Ramp Segment Worksheet (4 of 4)—Sample Problem 3 Expected Average Crash Frequency a Crash Severity Distribution K A B C Total FI PDO Total FI + PDO Proportion by injury level 0.018 0.056 0.369 0.557 1.000 Expected average crash freq. for study year (all crash types) Ne, w, x, at, z, s (cr/yr) 0.006 0.019 0.125 0.189 0.339 0.462 0.801 Crash Type Distribution Fatal and Injury Property Damage Only Total Crash Type Category Proportion Expected Average Crash Frequency for Study Year Ne, w, x, y, fi, s (cr/yr) Proportion Expected Average Crash Frequency for Study Year Ne, w, x, y, pdo, s (cr/yr) Expected Average Crash Frequency for Study Year Ne, w, x, y, as, s (cr/yr) Table Multiple-Vehicle Crashes 19-6 Head-on 0.015 0.001 0.009 0.001 0.002 Right-angle 0.010 0.001 0.005 0.001 0.001 Rear-end 0.707 0.041 0.550 0.057 0.098 Sideswipe 0.129 0.007 0.335 0.035 0.042 Other multiple-vehicle crashes 0.139 0.008 0.101 0.011 0.019 Total 1.000 0.058 1.000 0.104 0.162 Single-Vehicle Crashes 19-9 Crash with animal 0.003 0.001 0.005 0.002 0.003 Crash with fixed object 0.718 0.202 0.834 0.299 0.501 Crash with other object 0.015 0.004 0.023 0.008 0.012 Crash with parked vehicle 0.012 0.003 0.012 0.004 0.008 Other single-vehicle crashes 0.252 0.071 0.126 0.045 0.116 Total 1.000 0.282 1.000 0.358 0.640 Note: a If the EB Method is not used, then substitute the word “predicted” for the word “expected” and substitute the subscript “p” for the subscript “e”.

654 Table 19-59. Ramp Barrier Worksheet—Sample Problem 3 Input Data Segment length L (mi) 0.3 Crash period X Study year Left shoulder width Wls (ft) 4 Right shoulder width Wrs (ft) 8 Individual Right Side Barrier Element Data Barrier Location Length Lrb, i (mi) Width from Edge of Traveled Way to Face of Right Side Barrier Woff , r, i (ft) Ratio Lrb,i/(Woff,r,i–Wrs) 1. Bridge 0.10 9 0.10 2. Sign support 0.05 9 0.05 3. 4. 5. 6. 7. Sum1 0.15 Sum2 0.15 Individual Left Side Barrier Element Data Barrier Location Length Llb, i (mi) Width from Edge of Traveled Way to Face of Left Side Barrier Woff , l, i (ft) Ratio Llb,i/(Woff, l, i– Wls) 1. Bridge 0.10 5 0.10 2. Sign support 0.05 5 0.05 3. 4. 5. 6. 7. Sum3 0.15 Sum4 0.15 Right Side Barrier Calculations Proportion of segment length with barrier in median Prb = Sum1/L 0.500 Width from edge of shoulder to barrier face Wrcb = Sum1 / Sum2 (ft) 1.000 Left Side Barrier Calculations Proportion of segment length with barrier in median Plb = Sum3/L 0.500 Width from edge of shoulder to barrier face Wlcb = Sum3 / Sum4 (ft) 1.000 19.14.4. Sample Problem 4 The Site/Facility A signalized diamond interchange ramp terminal on an urban arterial. The Question What is the predicted average crash frequency of the ramp terminal for a one-year period? The Facts The study year is 2011. The conditions present during this year are provided in the following list.

655  D4 configuration  No non-ramp public street leg present  1.0 mi to the next public street intersection on the outside crossroad leg  0.1 mi to the adjacent ramp terminal  Protected-permissive left-turn operational mode on the inside crossroad leg  12-ft left-turn bay present  Signal control for the exit ramp right-turn movement  12-ft crossroad median width  4 through lanes on the crossroad (2 on each approach)  3 lanes on the exit ramp approach (developed at a distance of 150 ft from the ramp terminal)  No right-turn channelization or bays  No driveways present  28,000 veh/day on the crossroad (same for both legs)  7,100 veh/day on the exit ramp leg  6,750 veh/day on the entrance ramp leg Assumptions  Crash type distributions used are the default values presented in Table 19-16.  The calibration factor is 1.00. Results Using the predictive method steps as outlined below, the predicted average fatal-and-injury crash frequency for the ramp terminal in Sample Problem 4 is determined to be 5.3 crashes per year, and the predicted average property-damage-only crash frequency is determined to be 7.1 crashes per year (rounded to one decimal place). Steps Step 1 through 8 To determine the predicted average crash frequency of the ramp terminal in Sample Problem 4, only Steps 9 through 13 are conducted. No other steps are necessary because only one ramp terminal is analyzed for a one-year period and the EB Method is not applied. Step 9 – For the selected site, determine and apply the appropriate SPF. For a ramp terminal, an SPF value for all crash types is determined. The SPF for fatal-and-injury crashes is calculated from Equation 19-28 and Table 19-15 as follows:

656 [ ] [ ]( ) [ ] [ ]( ) arcrashes/ye228.7 750,6001.0100,7001.0ln131.0000,28001.0ln191.1335.2exp lnlnexp,,4,4, = ×+××+××+−= ×+××+××+= enexxrdfiatSGDspf AADTcAADTcdAADTcbaN Similarly, the SPF for property-damage-only crashes is calculated from Equation 19-28 and Table 19-15 to yield the following result: arcrashes/ye869.9,,4,4, =pdoatSGDspfN Step 10 – Multiply the result obtained in Step 9 by the appropriate CMFs. Each CMF used in the calculation of the predicted average crash frequency of the ramp terminal is calculated in this step. Exit Ramp Capacity (CMF10, D4, SG4, at, fi ) CMF10, D4, SG4, at, fi is calculated from Equation 19-42 as follows: ( )        × ××+×−= effex ex exexfiatSGD n AADTc aPPCMF , ,,4,4,10 exp0.10.1 For a signalized exit-ramp right-turn movement, the effective number of lanes serving exit ramp traffic nex, eff is computed using the second portion of Equation 19-43 as follows: 5.1 35.0 5.0, = ×= ×= exeffex nn The proportion of total leg AADT on the exit ramp leg Pex is computed using Equation 19-44 as follows: 102.0 100,7750,6000,28000,28 100,7 = +++ = +++ = exenoutin ex ex AADTAADTAADTAADT AADTP From Table 19-32, a = 0.0668 and c = 0.001 for signal-controlled ramp terminals. CMF10, D4, SG4, at, fi is calculated as follows: ( ) 038.1 5.1 100,7001.00668.0exp102.00.1102.00.1,,4,4,10 =       ×××+×−=fiatSGDCMF Crossroad Left-Turn Lane (CMF11, D4, SG4, at, z ) CMF11, D4, SG4, at, fi is calculated from Equation 19-45 as follows: ( )[ ] ( )[ ] outltbayinltbay IoutoutIininfiatSGD aPPaPPCMF ,,,, 0.10.10.10.1,,4,4,11 ×+×−××+×−=

657 The proportion of total leg AADT on the crossroad leg between ramps Pin is computed using Equation 19- 46 as follows: 401.0 100,7750,6000,28000,28 000,28 = +++ = +++ = exenoutin in in AADTAADTAADTAADT AADTP The proportion of total leg AADT on the crossroad leg outside of the interchange Pout is computed using Equation 19-47 as follows: 401.0 100,7750,6000,28000,28 000,28 = +++ = +++ = exenoutin out out AADTAADTAADTAADT AADTP From Table 19-33, a = 0.65 for signal-controlled ramp terminals. CMF11, D4, SG4, at, fi is calculated as follows: ( )[ ] ( )[ ] 860.0 65.0401.00.1401.00.165.0401.00.1401.00.1 01,,4,4,11 = ×+×−××+×−=fiatSGDCMF Similar calculations using the property-damage-only coefficient from Table 19-33 yield the following results: 872.0,,4,4,11 =pdoatSGDCMF Crossroad Right-Turn Lane (CMF12, D4, SG4, at, z ) The ramp terminal does not have right-turn lanes or bays on the crossroad legs, which is the base condition for the crossroad right-turn lane CMF. Hence, CMF12, D4, SG4, at, fi and CMF12, D4, SG4, at, pdo are equal to 1.000. Access Point Frequency (CMF13, D4, SG4, at, z ) The ramp terminal has no unsignalized driveways or unsignalized public street approaches on the outside leg, which are the base conditions for the access point frequency CMF. Hence, CMF13, D4, SG4, at, fi and CMF13, D4, SG4, at, pdo are equal to 1.000. Segment Length (CMF14, D4, SG4, at, z ) CMF14, D4, SG4, at, fi is calculated from Equation 19-50 as follows:                 −+×= 333.00.10.1exp,,4,4,14 strrmp fiatSGD LL aCMF From Table 19-36, a = -0.0185 for fatal-and-injury crashes. CMF14, D4, SG4, at, fi is calculated as follows:

658 821.0 333.0 0.1 0.1 1.0 0.10185.0exp,,4,4,14 =           −+×−=fiatSGDCMF Similar calculations using the property-damage-only coefficient from Table 19-36 yield the following results: 820.0,,4,4,14 =pdoatSGDCMF Median Width (CMF15, D4, SG4, at, z ) The crossroad has a 12-ft median, which is the base condition for the median width CMF. Hence, CMF15, D4, SG4, at, fi and CMF15, D4, SG4, at, pdo are equal to 1.000. Protected Left-Turn Operation (CMF16, D4, SG4, at, z ) Protected-only left-turn operational mode is not used on the crossroad legs, which is the base condition for the protected left-turn operation CMF. Hence, CMF16, D4, SG4, at, fi and CMF16, D4, SG4, at, pdo are equal to 1.000. Channelized Right Turn on Crossroad (CMF17, D4, SG4, at, z ) Right-turn channelization is not used on the crossroad legs, which is the base condition for the channelized right turn on crossroad CMF. Hence, CMF17, D4, SG4, at, fi and CMF17, D4, SG4, at, pdo are equal to 1.000. Channelized Right Turn on Exit Ramp (CMF18, D4, SG4, at, z ) Right-turn channelization is not used on the exit-ramp leg, which is the base condition for the channelized right turn on exit ramp CMF. Hence, CMF18, D4, SG4, at, fi and CMF18, D4, SG4, at, pdo are equal to 1.000. Non-Ramp Public Street Leg (CMF19, D4, SG4, at, z ) A non-ramp public street leg is not present at the ramp terminal, which is the base condition for the non- ramp public street leg CMF. Hence, CMF19, D4, SG4, at, fi and CMF19, D4, SG4, at, pdo are equal to 1.000. Crashes The CMFs are applied to the fatal-and-injury SPF as follows: ( ) ( ) arcrashes/ye294.5 733.0228.7 000.1000.1000.1000.1000.1821.0000.1000.1860.0038.1228.7 ,,4,4,19,,4,4,10,,4,4,,,4,4*, = ×= ××××××××××= ×××= fiatSGDfiatSGDfiatSGDspffiatSGDp CMFCMFNN  The CMFs are applied to the property-damage-only SPF as follows: ( ) ( ) arcrashes/ye052.7 715.0869.9 000.1000.1000.1000.1000.1820.0000.1000.1872.0000.1869.9 ,,4,4,19,,4,4,10,,4,4,,,4,4*, = ×= ××××××××××= ×××= pdoatSGDpdoatSGDpdoatSGDspfpdoatSGDp CMFCMFNN 

659 Step 11 – Multiply the result obtained in Step 10 by the appropriate calibration factor. It is assumed that a calibration factor of 1.00 has been determined for local conditions. See Section B.1 of Appendix B to Part C for further discussion on calibration of the predicted models. Calculation of Predicted Average Crash Frequency The predicted average crash frequency is calculated using Equation 19-1 based on the results obtained in Steps 9 through 11 as follows. Fatal-and-injury crashes: arcrashes/ye294.5 00.1294.5 ,,4,4,,4,4*,,,4,4, = ×= ×= fiatSGDfiatSGDpfiatSGDp CNN Property-damage-only crashes: arcrashes/ye052.7 00.1052.7 ,,4,4,,4,4*,,,4,4, = ×= ×= pdoatSGDpdoatSGDppdoatSGDp CNN Step 12—If there is another year to be evaluated in the evaluation period for the selected site, return to Step 8. Otherwise, proceed to Step 13. The study period is one year (2011), so steps 8 through 11 need not be repeated. Step 13—Apply site-specific EB Method (if applicable) and apply SDFs. This step consists of three optional sets of calculations—site-specific EB Method, severity distribution functions, and crash type distribution. Apply the site-specific EB Method to a future time period, if appropriate. The site-specific EB Method is not applied in this sample problem because crash data are not available. Apply the severity distribution functions (SDFs), if desired. To apply the SDFs, the systematic component of crash severity likelihood Vj is computed for each severity level j using Equation 19-88 as follows: ( ) ( ) ( ) ( )ruralpspsdwltpj IeIdnncIbaV ×+×++×+×+= ][, The coefficients a, b, c, d, and e are obtained from Table 19-44 for each severity level j. Vj is computed for fatal and incapacitating injury crashes as follows: ( ) ( ) ( ) ( ) 257.3 0.0619.00.0171.1]0.00.0[0991.00.0288.0257.3 −= ×+×++×+×−+−=+ AKV Similar calculations using the coefficients from Table 19-44 for non-incapacitating injury crashes yield the following results: 511.1−=BV

660 Using these computed VK+A and VB values, and assuming a calibration factor Csdf, aS, x of 1.0, the probability of occurrence of a fatal crash is computed using Equation 19-84 as follows: ( ) ( ) ( ) ( ) ( ) ( ) 001.0 0385.0 511.1exp257.3exp 0.1 0.1 257.3exp expexp0.1 exp ,,,| ,, ,,, = × −+−+ −= × ++ = + + + atxaSAKK BAK xaSsdf AK KatSGaS P VV C VP Similar calculations using Equation 19-85 and Equation 19-86 yield the following results: 029.0,,, =AatSGaSP 175.0,,, =BatSGaSP The probability of occurrence of a possible-injury crash is computed using Equation 19-87 as follows: 794.0 )175.0029.0001.0(0.1 )(0.1 ,,,,,,,,,,,, = ++−= ++−= BatSGaSAatSGaSKatSGaSCatSGaS PPPP The probability of occurrence of a fatal crash is multiplied by the fatal-and-injury crash frequency obtained in Step 11 using Equation 19-78 as follows: arcrashes/ye006.0 001.0294.5 ,,,,,4,4,,,4,4, = ×= ×= KatSGaSfiatSGDeKatSGDe PNN Similar calculations using Equation 19-78 and the probabilities of occurrences of the other crash severities yield the following results: arcrashes/ye156.0,,,4, =AatSGDeN arcrashes/ye928.0,,,4, =BatSGDeN arcrashes/ye204.4,,,4, =CatSGDeN Apply the crash type distribution, if desired. The crash type distributions are applied by multiplying the default crash type distribution proportions in Table 19-16 by the predicted average crash frequencies obtained in Step 11. Worksheets The step-by-step instructions are provided to illustrate the predictive method for calculating the predicted average crash frequency for a ramp terminal. To apply the predictive method steps to multiple terminals, a

661 series of worksheets are provided for determining the predicted average crash frequency. The worksheets include:  Table 19-60. Ramp Terminal Worksheet (1 of 4)—Sample Problem 4  Table 19-61. Ramp Terminal Worksheet (2 of 4)—Sample Problem 4  Table 19-62. Ramp Terminal Worksheet (3 of 4)—Sample Problem 4  Table 19-63. Ramp Terminal Worksheet (4 of 4)—Sample Problem 4 Filled versions of these worksheets are provided below. Blank versions of worksheets used in the Sample Problems are provided in Appendix 19A. Table 19-60 is a summary of general information about the ramp terminal, analysis, input data (i.e., “The Facts”), and assumptions for Sample Problem 4. The input data include area type, crash data, basic intersection data, alignment data, traffic control data, and cross section data. Table 19-61 is a summary of general information about the ramp terminal, analysis, input data (i.e., “The Facts”), and assumptions for Sample Problem 4. The input data include cross section data, access data, and traffic data. Table 19-62 is a tabulation of the CMF and SPF computations for Sample Problem 4. Table 19-63 is a tabulation of the crash severity and crash type distributions for Sample Problem 4.

662 Table 19-60. Ramp Terminal Worksheet (1 of 4)—Sample Problem 4 General Information Location Information Analyst Roadway Agency or company Intersection Date performed Study year Area type X Urban Rural Input Data Crash Data Crash Period Study Year Complete the study year column. Complete the crash period column if the EB Method is used. Crash data time period First year -- Last year -- Count of FI crashes N*o, w, x, at, fi -- Count of PDO crashes N*o, w, x, at, pdo -- Basic Intersection Data Ramp terminal configuration D4 Choices: D3ex, D3en, D4, A4, B4, A2, B2 Same choice for crash period and study year. Ramp terminal traffic control type Signal Choices: Signal, One-way-stop, All-way stop Presence of a non-ramp public street leg Ips -- Y/N N Y/N Alignment Data Exit ramp skew angle Isk (degrees) -- -- Distance to the next public street intersection on the outside crossroad leg Lstr (mi) -- 1.0 Distance to the adjacent ramp terminal Lrmp (mi) -- 0.1 Traffic Control Left-Turn Operational Mode Crossroad Inside approach Prot.-only mode Ip, lt, in -- Y/N N Y/N Outside approach Prot.-only mode Ip, lt, out -- Y/N -- Y/N Right-Turn Control Type Ramp Exit ramp approach Right-turn control type -- Signal Choices: Signal, Stop, Yield, Merge, Free Cross Section Data Crossroad median width Wm (ft) -- 12 Number of Lanes Crossroad Inside approach Through lanes nth, in 2 Same choice for crash period and study year. Outside approach Through lanes nth, out 2 Same choice for crash period and study year. Ramp Exit ramp approach All lanes nex 3 Same choice for crash period and study year. Right-Turn Channelization Crossroad Inside approach Chan. present Ich, in -- Y/N -- Y/N Outside approach Chan. present Ich, out -- Y/N N Y/N Ramp Exit ramp approach Chan. present Ich, ex -- Y/N N Y/N

663 Table 19-61. Ramp Terminal Worksheet (2 of 4)—Sample Problem 4 Input Data Cross Section Data Crash Period Study Year Complete the study year column. Complete the crash period column if the EB Method is used. Left-Turn Lane or Bay Crossroad Inside approach Lane or bay present Ibay, lt, in -- Y/N Y Y/N If Yes, then enter data in the next row. Lane or bay width Wb, in (ft) -- 12 Outside approach Lane or bay present Ibay,lt,out -- Y/N N Y/N If Yes, then enter data in the next row. Lane or bay width Wb,out(ft) -- -- Right-Turn Lane or Bay Crossroad Inside approach Lane or bay present Ibay, rt, in -- Y/N -- Y/N Outside approach Lane or bay present Ibay,rt,out -- Y/N N Y/N Access Data Number of driveways on the outside crossroad leg ndw -- 0 Number of public street approaches on the outside crossroad leg nps -- -- Traffic Data Crossroad Inside leg AADTin (veh/day) -- 28,000 Outside leg AADTout (veh/day) -- 28,000 Ramp Exit ramp AADTex (veh/day) -- 7,100 Entrance ramp AADTen (veh/day) -- 6,750

664 Table 19-62. Ramp Terminal Worksheet (3 of 4)—Sample Problem 4 Crash Modification Factors Complete the study year column. Complete the crash period column if the EB Method is used. Fatal and Injury Property Damage Only Equation Crash Period Study Year Crash Period Study Year Signal Control Exit ramp capacity CMF10, w, SGn, at, fi 19-42 -- 1.038 Crossroad left-turn lane CMF11, w, SGn, at, z 19-45 -- 0.860 -- 0.872 Crossroad right-turn lane CMF12, w, SGn, at, z 19-48 -- 1.000 -- 1.000 Access point frequency CMF13, w, SGn, at, z 19-49 -- 1.000 -- 1.000 Segment length CMF14, w, SGn, at, z 19-50 -- 0.821 -- 0.820 Median width CMF15, w, SGn, at, z 19-51 -- 1.000 -- 1.000 Protected left-turn operation CMF16, w, SGn, at, z 19-53 -- 1.000 -- 1.000 Chan. right turn on crossroad CMF17, w, SGn, at, z 19-55 -- 1.000 -- 1.000 Chan. right turn on exit ramp CMF18, w, SGn, at, z 19-56 -- 1.000 -- 1.000 Non-ramp public street leg CMF19, w, SGn, at, z 19-57 -- 1.000 -- 1.000 Stop Control Exit ramp capacity CMF10, w, ST, at, fi 19-42 -- -- Crossroad left-turn lane CMF11, w, ST, at, z 19-45 -- -- -- -- Crossroad right-turn lane CMF12, w, ST, at, z 19-48 -- -- -- -- Access point frequency CMF13, w, ST, at, fi 19-49 -- -- Segment length CMF14, w, ST, at, fi 19-50 -- -- Median width CMF15, w, ST, at, fi 19-51 -- -- Skew angle CMF20, w, ST, at, fi 19-58 -- -- All-way stop-control (exclude CMF11, CMF12, CMF20) -- -- Combined CMF (multiply all CMFs evaluated) -- 0.733 -- 0.715 Expected Average Crash Frequency a Complete the study year column. Complete the crash period column if the site-specific EB Method is used. Fatal and Injury Property Damage Only Crash Period Study Year Crash Period Study Year Calibration factor CaS, x, at, z 1.00 1.00 Overdispersion parameter kw, x, at, z -- -- Observed crash count N*o, w, x, at, z (cr) -- -- Reference year r -- -- Predicted average crash freq. for reference year Np, w, x, at, z, r (cr/yr) -- -- Predicted number of crashes for crash period (sum all years) N*p, w, x, y, z (cr) -- -- Equivalent years associated with crash count Cb, w, x, at, z, r (yr) -- -- Adjusted average crash freq. for ref. year given N*o, Na, w, x, at, z, r (cr/yr) -- -- Study year s 2011 2011 Predicted average crash freq. for study year Np, w, x, at, z, s (cr/yr) 5.294 7.052 Expected average crash freq. for study year Ne, w, x, at, z, s (cr/yr) 5.294 7.052 Note: a If the EB Method is not used, then substitute “predicted” for “expected” and substitute the subscript “p” for the subscript “e”.

665 Table 19-63. Ramp Terminal Worksheet (4 of 4)—Sample Problem 4 Expected Average Crash Frequency Crash Severity Distribution K A B C Total FI PDO Total FI + PDO Proportion by injury level 0.001 0.029 0.175 0.794 1.000 Expected average crash freq. for study year Ne, w, x, at, z, s (cr/yr) 0.006 0.156 0.928 4.204 5.294 7.052 12.346 Crash Type Distribution Fatal and Injury Property Damage Only Total Crash Type Category Table 19-16, 19-21, or 19-45 Proportion Expected Average Crash Frequency for Study Year Ne, w, x, at, fi, s (cr/yr) Proportion Expected Average Crash Frequency for Study Year Ne, w, x, at, pdo, s (cr/yr) Expected Average Crash Frequency for Study Year Ne, w, x, at, as, s (cr/yr) Multiple-Vehicle Crashes Head-on 0.011 0.058 0.007 0.049 0.108 Right-angle 0.260 1.376 0.220 1.551 2.928 Rear-end 0.625 3.309 0.543 3.829 7.138 Sideswipe 0.042 0.222 0.149 1.051 1.273 Other multiple-vehicle crashes 0.009 0.048 0.020 0.141 0.189 Single-Vehicle Crashes Crash with animal 0.000 0.000 0.000 0.000 0.000 Crash with fixed object 0.033 0.175 0.050 0.353 0.527 Crash with other object 0.001 0.005 0.002 0.014 0.019 Crash with parked vehicle 0.001 0.005 0.002 0.014 0.019 Other single-vehicle crashes 0.018 0.095 0.007 0.049 0.145 Total 1.000 0.281 1.000 0.430 0.711 19.14.5. Sample Problem 5 The Site/Facility A one-way stop-controlled partial cloverleaf interchange ramp terminal on an urban arterial. The Question What is the predicted average crash frequency of the ramp terminal for a one-year period? The Facts The study year is 2011. The conditions present during this year are provided in the following list.  A4 configuration  1.0 mi to the next public street intersection on the outside crossroad leg  0.09 mi to the adjacent ramp terminal  0-degree skew angle on exit-ramp approach

666  Merge control for the exit ramp right-turn movement  12-ft crossroad median width  4 through lanes on the crossroad  2 lanes on the exit ramp approach (developed at a distance of 200 ft from the ramp terminal)  No right-turn channelization or bays  21,500 veh/day on the crossroad (same for both legs)  3,400 veh/day on the exit ramp leg  3,750 veh/day on the entrance ramp leg Assumptions  Crash type distributions used are the default values presented in Table 19-21.  The calibration factor is 1.00. Results Using the predictive method steps as outlined below, the predicted average fatal-and-injury crash frequency for the ramp terminal in Sample Problem 5 is determined to be 1.2 crashes per year, and the predicted average property-damage-only crash frequency is determined to be 2.7 crashes per year (rounded to one decimal place). Steps Step 1 through 8 To determine the predicted average crash frequency of the ramp terminal in Sample Problem 5, only Steps 9 through 13 are conducted. No other steps are necessary because only one ramp terminal is analyzed for a one-year period and the EB Method is not applied. Step 9 – For the selected site, determine and apply the appropriate SPF. For a ramp terminal, an SPF value for all crash types is determined. The SPF for fatal-and-injury crashes is calculated from Equation 19-31 and Table 19-18 as follows: [ ] [ ]( ) [ ] [ ]( ) arcrashes/ye392.1 750,3001.0400,3001.0ln899.0500,21001.0ln582.0223.3exp lnlnexp,,,4, = ×+××+××+−= ×+××+××+= enexxrdfiatSTAspf AADTcAADTcdAADTcbaN Similarly, the SPF for property-damage-only crashes is calculated from Equation 19-31 and Table 19-18 to yield the following result: arcrashes/ye715.2,,,4, =pdoatSTAspfN

667 Step 10 – Multiply the result obtained in Step 9 by the appropriate CMFs. Each CMF used in the calculation of the predicted average crash frequency of the ramp terminal is calculated in this step. Exit Ramp Capacity (CMF10, A4, ST, at, fi ) CMF10, A4, ST, at, fi is calculated from Equation 19-42 as follows: ( )        ×××+×−= effex ex exexfiatSTA n AADTcaPPCMF , ,,,4,10 exp0.10.1 For a merge-controlled exit-ramp right-turn movement, the effective number of lanes serving exit ramp traffic nex, eff is computed using the first portion of Equation 19-43 as follows: ( ) ( ) 5.1 0.10.125.0 0.10.15.0, = +−×= +−×= exeffex nn The proportion of total leg AADT on the exit ramp leg Pex is computed using Equation 19-44 as follows: 068.0 400,3750,3500,21500,21 400,3 = +++ = +++ = exenoutin ex ex AADTAADTAADTAADT AADTP From Table 19-32, a = 0.151 and c = 0.001 for one-way stop-controlled ramp terminals. CMF10, A4, ST, at, fi is calculated as follows: ( ) 028.1 5.1 400,3001.0151.0exp068.00.1068.00.1,,,4,10 =       ×××+×−=fiatSTACMF Crossroad Left-Turn Lane (CMF11, A4, ST, at, z ) The ramp terminal does not have left-turn lanes or bays on the crossroad legs, which is the base condition for the crossroad left-turn lane CMF. Hence, CMF11, A4, ST, at, fi and CMF11, A4, ST, at, pdo are equal to 1.000. Crossroad Right-Turn Lane (CMF12, A4, ST, at, z ) The ramp terminal does not have right-turn lanes or bays on the crossroad legs, which is the base condition for the crossroad right-turn lane CMF. Hence, CMF12, A4, ST, at, fi and CMF12, A4, ST, at, pdo are equal to 1.000. Access Point Frequency (CMF13, A4, ST, at, fi ) The ramp terminal has no unsignalized public street approaches on the outside leg, which is the base condition for the access point frequency CMF. Hence, CMF13, A4, ST, at, fi is equal to 1.000. Segment Length (CMF14, A4, ST, at, fi ) CMF14, A4, ST, at, fi is calculated from Equation 19-50 as follows:

668                 −+×= 333.00.10.1exp,,,4,14 strrmp fiatSTA LL aCMF From Table 19-36, a = -0.0141 for fatal-and-injury crashes. CMF14, A4, ST, at, fi is calculated as follows: 847.0 333.0 0.1 0.1 09.0 0.10141.0exp,,,4,14 =           −+×−=fiatSTACMF Median Width (CMF15, A4, ST, at, fi ) The crossroad has a 12-ft median, which is the base condition for the median width CMF. Hence, CMF15, A4, ST, at, fi is equal to 1.000. Skew Angle (CMF20, A4, ST, at, fi ) The ramp terminal has no skew, which is the base condition for the skew angle CMF. Hence, CMF20, A4, ST, at, fi is equal to 1.000. Crashes The CMFs are applied to the fatal-and-injury SPF as follows: ( ) ( ) arcrashes/ye212.1 871.0392.1 000.1000.1847.0000.1000.1000.1028.1392.1 ,,,4,20,,,4,15,,,4,10,,,4,,,,4*, = ×= ×××××××= ××××= fiatSTAfiatSTAfiatSTAfiatSTAspffiatSTAp CMFCMFCMFNN  The CMFs are applied to the property-damage-only SPF as follows: ( ) ( ) arcrashes/ye715.2 000.1715.2 000.1000.1715.2 ,,,4,12,,,4,11,,,4,,,,4*, = ×= ××= ××= pdoatSTApdoatSTApdoatSTAspfpdoatSTAp CMFCMFNN Step 11 – Multiply the result obtained in Step 10 by the appropriate calibration factor. It is assumed that a calibration factor of 1.00 has been determined for local conditions. See Section B.1 of Appendix B to Part C for further discussion on calibration of the predicted models. Calculation of Predicted Average Crash Frequency The predicted average crash frequency is calculated using Equation 19-1 based on the results obtained in Steps 9 through 11 as follows. Fatal-and-injury crashes: arcrashes/ye212.1 00.1212.1 ,,,4,,,4*,,,,4, = ×= ×= fiatSTAfiatSTApfiatSTAp CNN

669 Property-damage-only crashes: arcrashes/ye715.2 00.1715.2 ,,,4,,,4*,,,,4, = ×= ×= pdoatSTApdoatSTAppdoatSTAp CNN Step 12—If there is another year to be evaluated in the evaluation period for the selected site, return to Step 8. Otherwise, proceed to Step 13. The study period is one year (2011), so steps 8 through 11 need not be repeated. Step 13—Apply site-specific EB Method (if applicable) and apply SDFs. This step consists of three optional sets of calculations—site-specific EB Method, severity distribution functions, and crash type distribution. Apply the site-specific EB Method to a future time period, if appropriate. The site-specific EB Method is not applied in this sample problem because crash data are not available. Apply the severity distribution functions (SDFs), if desired. To apply the SDFs, the systematic component of crash severity likelihood Vj is computed for each severity level j using Equation 19-88 as follows: ( ) ( ) ( ) ( )ruralpspsdwltpj IeIdnncIbaV ×+×++×+×+= ][, The coefficients a, b, c, d, and e are obtained from Table 19-44 for each severity level j. Vj is computed for fatal and incapacitating injury crashes as follows: ( ) ( ) ( ) ( ) 168.3 0.0891.00.000.0]0.00.0[00.00.000.0168.3 −= ×+×++×+×+−=+ AKV Similar calculations using the coefficients from Table 19-44 for non-incapacitating injury crashes yield the following results: 476.1−=BV Using these computed VK+A and VB values, and assuming a calibration factor Csdf, aS, x of 1.0, the probability of occurrence of a fatal crash is computed using Equation 19-84 as follows: ( ) ( ) ( ) ( ) ( ) ( ) 005.0 160.0 476.1exp168.3exp 0.1 0.1 168.3exp expexp0.1 exp ,,,| ,, ,,, = × −+−+ −= × ++ = + + + atxaSAKK BAK xaSsdf AK KatSTaS P VV C VP Similar calculations using Equation 19-85 and Equation 19-86 yield the following results: 028.0,,, =AatSTaSP

670 180.0,,, =BatSTaSP The probability of occurrence of a possible-injury crash is computed using Equation 19-87 as follows: 787.0 )180.0028.0005.0(0.1 )(0.1 ,,,,,,,,,,,, = ++−= ++−= BatSTaSAatSTaSKatSTaSCatSTaS PPPP The probability of occurrence of a fatal crash is multiplied by the fatal-and-injury crash frequency obtained in Step 11 using Equation 19-78 as follows: arcrashes/ye006.0 005.0212.1 ,,,,,,4,,,,4, = ×= ×= KatSTaSfiatSTAeKatSTAe PNN Similar calculations using Equation 19-78 and the probabilities of occurrences of the other crash severities yield the following results: arcrashes/ye034.0,,,4, =AatSTAeN arcrashes/ye218.0,,,4, =BatSTAeN arcrashes/ye954.0,,,4, =CatSTAeN Apply the crash type distribution, if desired. The crash type distributions are applied by multiplying the default crash type distribution proportions in Table 19-21 by the predicted average crash frequencies obtained in Step 11. Worksheets The step-by-step instructions are provided to illustrate the predictive method for calculating the predicted average crash frequency for a ramp terminal. To apply the predictive method steps to multiple terminals, a series of worksheets are provided for determining the predicted average crash frequency. The worksheets include:  Table 19-64. Ramp Terminal Worksheet (1 of 4)—Sample Problem 5  Table 19-65. Ramp Terminal Worksheet (2 of 4)—Sample Problem 5  Table 19-66. Ramp Terminal Worksheet (3 of 4)—Sample Problem 5  Table 19-67. Ramp Terminal Worksheet (4 of 4)—Sample Problem 5 Filled versions of these worksheets are provided below. Blank versions of worksheets used in the Sample Problems are provided in Appendix 19A. Table 19-64 is a summary of general information about the ramp terminal, analysis, input data (i.e., “The Facts”), and assumptions for Sample Problem 5. The input data include area type, crash data, basic intersection data, alignment data, traffic control data, and cross section data.

671 Table 19-65 is a summary of general information about the ramp terminal, analysis, input data (i.e., “The Facts”), and assumptions for Sample Problem 5. The input data include cross section data, access data, and traffic data. Table 19-66 is a tabulation of the CMF and SPF computations for Sample Problem 5. Table 19-67 is a tabulation of the crash severity and crash type distributions for Sample Problem 5. Table 19-64. Ramp Terminal Worksheet (1 of 4)—Sample Problem 5 General Information Location Information Analyst Roadway Agency or company Intersection Date performed Study year Area type X Urban Rural Input Data Crash Data Crash Period Study Year Complete the study year column. Complete the crash period column if the EB Method is used. Crash data time period First year -- Last year -- Count of FI crashes N*o, w, x, at, fi -- Count of PDO crashes N*o, w, x, at, pdo -- Basic Intersection Data Ramp terminal configuration A4 Choices: D3ex, D3en, D4, A4, B4, A2, B2 Same choice for crash period and study year. Ramp terminal traffic control type One-way stop Choices: Signal, One-way-stop, All-way stop Presence of a non-ramp public street leg Ips -- Y/N -- Y/N Alignment Data Exit ramp skew angle Isk (degrees) -- 0 Distance to the next public street intersection on the outside crossroad leg Lstr (mi) -- 1.0 Distance to the adjacent ramp terminal Lrmp (mi) -- 0.09 Traffic Control Left-Turn Operational Mode Crossroad Inside approach Prot.-only mode Ip, lt, in -- Y/N -- Y/N Outside approach Prot.-only mode Ip, lt, out -- Y/N -- Y/N Right-Turn Control Type Ramp Exit ramp approach Right-turn control type -- Merge Choices: Signal, Stop, Yield, Merge, Free Cross Section Data Crossroad median width Wm (ft) -- 12 Number of Lanes Crossroad Inside approach Through lanes nth, in 2 Same choice for crash period and study year. Outside approach Through lanes nth, out 2 Same choice for crash period and study year. Ramp Exit ramp approach All lanes nex 2 Same choice for crash period and study year. Right-Turn Channelization Crossroad Inside approach Chan. present Ich, in -- Y/N -- Y/N Outside approach Chan. present Ich, out -- Y/N -- Y/N Ramp Exit ramp approach Chan. present Ich, ex -- Y/N -- Y/N

672 Table 19-65. Ramp Terminal Worksheet (2 of 4)—Sample Problem 5 Input Data Cross Section Data Crash Period Study Year Complete the study year column. Complete the crash period column if the EB Method is used. Left-Turn Lane or Bay Crossroad Inside approach Lane or bay present Ibay, lt, in -- Y/N -- Y/N If Yes, then enter data in the next row. Lane or bay width Wb, in (ft) -- -- Outside approach Lane or bay present Ibay,lt,out -- Y/N -- Y/N If Yes, then enter data in the next row. Lane or bay width Wb,out(ft) -- -- Right-Turn Lane or Bay Crossroad Inside approach Lane or bay present Ibay, rt, in -- Y/N N Y/N Outside approach Lane or bay present Ibay,rt,out -- Y/N N Y/N Access Data Number of driveways on the outside crossroad leg ndw -- -- Number of public street approaches on the outside crossroad leg nps -- -- Traffic Data Crossroad Inside leg AADTin (veh/day) -- 21,500 Outside leg AADTout (veh/day) -- 21,500 Ramp Exit ramp AADTex (veh/day) -- 3,400 Entrance ramp AADTen (veh/day) -- 3,750

673 Table 19-66. Ramp Terminal Worksheet (3 of 4)—Sample Problem 5 Crash Modification Factors Complete the study year column. Complete the crash period column if the EB Method is used. Fatal and Injury Property Damage Only Equation Crash Period Study Year Crash Period Study Year Signal Control Exit ramp capacity CMF10, w, SGn, at, fi 19-42 -- -- Crossroad left-turn lane CMF11, w, SGn, at, z 19-45 -- -- -- -- Crossroad right-turn lane CMF12, w, SGn, at, z 19-48 -- -- -- -- Access point frequency CMF13, w, SGn, at, z 19-49 -- -- -- -- Segment length CMF14, w, SGn, at, z 19-50 -- -- -- -- Median width CMF15, w, SGn, at, z 19-51 -- -- -- -- Protected left-turn operation CMF16, w, SGn, at, z 19-53 -- -- -- -- Chan. right turn on crossroad CMF17, w, SGn, at, z 19-55 -- -- -- -- Chan. right turn on exit ramp CMF18, w, SGn, at, z 19-56 -- -- -- -- Non-ramp public street leg CMF19, w, SGn, at, z 19-57 -- -- -- -- Stop Control Exit ramp capacity CMF10, w, ST, at, fi 19-42 -- 1.028 Crossroad left-turn lane CMF11, w, ST, at, z 19-45 -- 1.000 -- 1.000 Crossroad right-turn lane CMF12, w, ST, at, z 19-48 -- 1.000 -- 1.000 Access point frequency CMF13, w, ST, at, fi 19-49 -- 1.000 Segment length CMF14, w, ST, at, fi 19-50 -- 0.847 Median width CMF15, w, ST, at, fi 19-51 -- 1.000 Skew angle CMF20, w, ST, at, fi 19-58 -- 1.000 All-way stop-control (exclude CMF11, CMF12, CMF20) -- -- Combined CMF (multiply all CMFs evaluated) -- 0.871 -- 1.000 Expected Average Crash Frequency a Complete the study year column. Complete the crash period column if the site-specific EB Method is used. Fatal and Injury Property Damage Only Crash Period Study Year Crash Period Study Year Calibration factor CaS, x, at, z 1.00 1.00 Overdispersion parameter kw, x, at, z -- -- Observed crash count N*o, w, x, at, z (cr) -- -- Reference year r -- -- Predicted average crash freq. for reference year Np, w, x, at, z, r (cr/yr) -- -- Predicted number of crashes for crash period (sum all years) N*p, w, x, y, z (cr) -- -- Equivalent years associated with crash count Cb, w, x, at, z, r (yr) -- -- Adjusted average crash freq. for ref. year given N*o, Na, w, x, at, z, r (cr/yr) -- -- Study year s 2011 2011 Predicted average crash freq. for study year Np, w, x, at, z, s (cr/yr) 1.212 2.715 Expected average crash freq. for study year Ne, w, x, at, z, s (cr/yr) 1.212 2.715 Note: a If the EB Method is not used, then substitute “predicted” for “expected” and substitute the subscript “p” for the subscript “e”.

674 Table 19-67. Ramp Terminal Worksheet (4 of 4)—Sample Problem 5 Expected Average Crash Frequency Crash Severity Distribution K A B C Total FI PDO Total FI + PDO Proportion by injury level 0.005 0.028 0.180 0.787 1.000 Expected average crash freq. for study year Ne, w, x, at, z, s (cr/yr) 0.006 0.034 0.218 0.954 1.212 2.715 3.927 Crash Type Distribution Fatal and Injury Property Damage Only Total Crash Type Category Table 19-16, 19-21, or 19-45 Proportion Expected Average Crash Frequency for Study Year Ne, w, x, at, fi, s (cr/yr) Proportion Expected Average Crash Frequency for Study Year Ne, w, x, at, pdo, s (cr/yr) Expected Average Crash Frequency for Study Year Ne, w, x, at, as, s (cr/yr) Multiple-Vehicle Crashes Head-on 0.017 0.021 0.012 0.033 0.053 Right-angle 0.458 0.055 0.378 1.026 1.581 Rear-end 0.373 0.452 0.377 1.023 1.476 Sideswipe 0.025 0.030 0.079 0.214 0.245 Other multiple-vehicle crashes 0.017 0.021 0.016 0.043 0.064 Single-Vehicle Crashes Crash with animal 0.000 0.000 0.000 0.000 0.000 Crash with fixed object 0.085 0.103 0.110 0.299 0.402 Crash with other object 0.000 0.000 0.000 0.000 0.000 Crash with parked vehicle 0.000 0.000 0.008 0.022 0.022 Other single-vehicle crashes 0.025 0.030 0.020 0.054 0.085 Total 1.000 1.212 1.000 2.715 3.927 19.14.6. Sample Problem 6 The Site/Facility An all-way stop-controlled partial cloverleaf interchange ramp terminal on an urban arterial. The Question What is the predicted average crash frequency of the ramp terminal for a one-year period? The Facts The study year is 2011. The conditions present during this year are provided in the following list.  B2 configuration  1.0 mi to the next public street intersection on the outside crossroad leg  0.15 mi to the adjacent ramp terminal  Stop control for the exit ramp right-turn movement

675  12-ft crossroad median width  4 through lanes on the crossroad  2 lanes on the exit ramp approach (developed at a distance of 125 ft from the ramp terminal)  14,000 veh/day on the crossroad (same for both legs)  1,450 veh/day on the exit ramp leg  1,300 veh/day on the entrance ramp leg Assumptions  Crash type distributions used are the default values presented in Table 19-45.  The calibration factor is 1.00. Results Using the predictive method steps as outlined below, the predicted average fatal-and-injury crash frequency for the ramp terminal in Sample Problem 6 is determined to be 0.2 crashes per year, and the predicted average property-damage-only crash frequency is determined to be 0.9 crashes per year (rounded to one decimal place). As stated in the interim predictive method for all-way stop control in Section 19.10, the ramp terminal is evaluated as a one-way stop-controlled terminal, but with a smaller set of CMFs in Step 10. None of the CMFs apply to the property-damage-only SPF. Steps Step 1 through 8 To determine the predicted average crash frequency of the ramp terminal in Sample Problem 6, only Steps 9 through 13 are conducted. No other steps are necessary because only one ramp terminal is analyzed for a one-year period and the EB Method is not applied. Step 9 – For the selected site, determine and apply the appropriate SPF. For a ramp terminal, an SPF value for all crash types is determined. The SPF for fatal-and-injury crashes is calculated from Equation 19-31 and Table 19-17 as follows: [ ] [ ]( ) [ ] [ ]( ) arcrashes/ye352.0 300,1001.0450,1001.0ln947.0000,14001.0ln260.0687.2exp lnlnexp,,,2, = ×+××+××+−= ×+××+××+= enexxrdfiatSTBspf AADTcAADTcdAADTcbaN Similarly, the SPF for property-damage-only crashes is calculated from Equation 19-31 and Table 19-17 to yield the following result: arcrashes/ye881.0,,,2, =pdoatSTBspfN

676 Step 10 – Multiply the result obtained in Step 9 by the appropriate CMFs. Each CMF used in the calculation of the predicted average crash frequency of the ramp terminal is calculated in this step. Exit Ramp Capacity (CMF10, B2, ST, at, fi ) CMF10, B2, ST, at, fi is calculated from Equation 19-42 as follows: ( )        ×××+×−= effex ex exexfiatSTB n AADTcaPPCMF , ,,,2,10 exp0.10.1 For a stop-controlled exit-ramp right-turn movement, the effective number of lanes serving exit ramp traffic nex, eff is computed using the second portion of Equation 19-43 as follows: 0.1 25.0 5.0, = ×= ×= exeffex nn The proportion of total leg AADT on the exit ramp leg Pex is computed using Equation 19-44 as follows: 047.0 450,1300,1000,14000,14 450,1 = +++ = +++ = exenoutin ex ex AADTAADTAADTAADT AADTP From Table 19-32, a = 0.151 and c = 0.001 for one-way stop-controlled ramp terminals. CMF10, B2, ST, at, fi is calculated as follows: ( ) 012.1 0.1 450,1001.0151.0exp047.00.1047.00.1,,,2,10 =       ×××+×−=fiatSTBCMF Access Point Frequency (CMF13, B2, ST, at, fi ) The ramp terminal has no unsignalized public street approaches on the outside leg, which is the base condition for the access point frequency CMF. Hence, CMF13, B2, ST, at, fi is equal to 1.000. Segment Length (CMF14, B2, ST, at, fi ) CMF14, B2, ST, at, fi is calculated from Equation 19-50 as follows:                 −+×= 333.00.10.1exp,,,2,14 strrmp fiatSTB LL aCMF From Table 19-36, a = -0.0141 for fatal-and-injury crashes. CMF14, B2, ST, at, fi is calculated as follows:

677 902.0 333.0 0.1 0.1 15.0 0.10141.0exp,,,2,14 =           −+×−=fiatSTBCMF Median Width (CMF15, B2, ST, at, fi ) The crossroad has a 12-ft median, which is the base condition for the median width CMF. Hence, CMF15, B2, ST, at, fi is equal to 1.000. All-Way Stop Control (CMFawsc ) As stated in Section 19.10, the all-way stop control CMF, CMFawsc, is equal to 0.686. It applies to fatal- and-injury crashes only. Crashes The CMFs are applied to the fatal-and-injury SPF as follows: ( ) arcrashes/ye221.0 626.0352.0 686.0000.1902.0000.1012.1352.0 ,,,2,15,,,2,14 ,,,2,13,,,2,10 ,,,2,,,,2*, = ×= ×××××=         ×× ×× ×= awscfiatSTBfiatSTB fiatSTBfiatSTB fiatSTBspffiatSTBp CMFCMFCMF CMFCMF NN The CMFs are applied to the property-damage-only SPF as follows: arcrashes/ye881.0 ,,,2,,,,2*, = = pdoatSTBspfpdoatSTBp NN Step 11 – Multiply the result obtained in Step 10 by the appropriate calibration factor. It is assumed that a calibration factor of 1.00 has been determined for local conditions. See Section B.1 of Appendix B to Part C for further discussion on calibration of the predicted models. Calculation of Predicted Average Crash Frequency The predicted average crash frequency is calculated using Equation 19-1 based on the results obtained in Steps 9 through 11 as follows. Fatal-and-injury crashes: arcrashes/ye221.0 00.1221.0 ,,,2,,,2*,,,,2, = ×= ×= fiatSTBfiatSTBpfiatSTBp CNN Property-damage-only crashes: arcrashes/ye881.0 00.1881.0 ,,,2,,,2*,,,,2, = ×= ×= pdoatSTBpdoatSTBppdoatSTBp CNN

678 Step 12—If there is another year to be evaluated in the evaluation period for the selected site, return to Step 8. Otherwise, proceed to Step 13. The study period is one year (2011), so steps 8 through 11 need not be repeated. Step 13—Apply site-specific EB Method (if applicable) and apply SDFs. This step consists of three optional sets of calculations—site-specific EB Method, severity distribution functions, and crash type distribution. Apply the site-specific EB Method to a future time period, if appropriate. The site-specific EB Method is not applied in this sample problem because crash data are not available. Apply the severity distribution functions (SDFs), if desired. To apply the SDFs, the systematic component of crash severity likelihood Vj is computed for each severity level j using Equation 19-88 as follows: ( ) ( ) ( ) ( )ruralpspsdwltpj IeIdnncIbaV ×+×++×+×+= ][, The coefficients a, b, c, d, and e are obtained from Table 19-44 for each severity level j. Vj is computed for fatal and incapacitating injury crashes as follows: ( ) ( ) ( ) ( ) 168.3 0.0891.00.000.0]0.00.0[00.00.000.0168.3 −= ×+×++×+×+−=+ AKV Similar calculations using the coefficients from Table 19-44 for non-incapacitating injury crashes yield the following results: 476.1−=BV Using these computed VK+A and VB values, and assuming a calibration factor Csdf, aS, x of 1.0, the probability of occurrence of a fatal crash is computed using Equation 19-84 as follows: ( ) ( ) ( ) ( ) ( ) ( ) 005.0 160.0 476.1exp168.3exp 0.1 0.1 168.3exp expexp0.1 exp ,,,| ,, ,,, = × −+−+ −= × ++ = + + + atxaSAKK BAK xaSsdf AK KatSTaS P VV C VP Similar calculations using Equation 19-85 and Equation 19-86 yield the following results: 028.0,,, =AatSTaSP 180.0,,, =BatSTaSP The probability of occurrence of a possible-injury crash is computed using Equation 19-87 as follows:

679 787.0 )180.0028.0005.0(0.1 )(0.1 ,,,,,,,,,,,, = ++−= ++−= BatSTaSAatSTaSKatSTaSCatSTaS PPPP The probability of occurrence of a fatal crash is multiplied by the fatal-and-injury crash frequency obtained in Step 11 using Equation 19-78 as follows: arcrashes/ye001.0 005.0221.0 ,,,,,,2,,,,2, = ×= ×= KatSTaSfiatSTBeKatSTBe PNN Similar calculations using Equation 19-78 and the probabilities of occurrences of the other crash severities yield the following results: arcrashes/ye006.0,,,2, =AatSTBeN arcrashes/ye040.0,,,2, =BatSTBeN arcrashes/ye174.0,,,2, =CatSTBeN Apply the crash type distribution, if desired. The crash type distributions are applied by multiplying the default crash type distribution proportions in Table 19-45 by the predicted average crash frequencies obtained in Step 11. Worksheets The step-by-step instructions are provided to illustrate the predictive method for calculating the predicted average crash frequency for a ramp terminal. To apply the predictive method steps to multiple terminals, a series of worksheets are provided for determining the predicted average crash frequency. The worksheets include:  Table 19-68. Ramp Terminal Worksheet (1 of 4)—Sample Problem 6  Table 19-69. Ramp Terminal Worksheet (2 of 4)—Sample Problem 6  Table 19-70. Ramp Terminal Worksheet (3 of 4)—Sample Problem 6  Table 19-71. Ramp Terminal Worksheet (4 of 4)—Sample Problem 6 Filled versions of these worksheets are provided below. Blank versions of worksheets used in the Sample Problems are provided in Appendix 19A. Table 19-68 is a summary of general information about the ramp terminal, analysis, input data (i.e., “The Facts”), and assumptions for Sample Problem 6. The input data include area type, crash data, basic intersection data, alignment data, traffic control data, and cross section data. Table 19-69 is a summary of general information about the ramp terminal, analysis, input data (i.e., “The Facts”), and assumptions for Sample Problem 6. The input data include cross section data, access data, and traffic data.

680 Table 19-70 is a tabulation of the CMF and SPF computations for Sample Problem 6. Table 19-71 is a tabulation of the crash severity and crash type distributions for Sample Problem 6. Table 19-68. Ramp Terminal Worksheet (1 of 4)—Sample Problem 6 General Information Location Information Analyst Roadway Agency or company Intersection Date performed Study year Area type X Urban Rural Input Data Crash Data Crash Period Study Year Complete the study year column. Complete the crash period column if the EB Method is used. Crash data time period First year Last year Count of FI crashes N*o, w, x, at, fi Count of PDO crashes N*o, w, x, at, pdo Basic Intersection Data Ramp terminal configuration B2 Choices: D3ex, D3en, D4, A4, B4, A2, B2 Same choice for crash period and study year. Ramp terminal traffic control type All-way stop Choices: Signal, One-way-stop, All-way stop Presence of a non-ramp public street leg Ips Y/N -- Y/N Alignment Data Exit ramp skew angle Isk (degrees) -- Distance to the next public street intersection on the outside crossroad leg Lstr (mi) 1.0 Distance to the adjacent ramp terminal Lrmp (mi) 0.15 Traffic Control Left-Turn Operational Mode Crossroad Inside approach Prot.-only mode Ip, lt, in Y/N -- Y/N Outside approach Prot.-only mode Ip, lt, out Y/N -- Y/N Right-Turn Control Type Ramp Exit ramp approach Right-turn control type Stop Choices: Signal, Stop, Yield, Merge, Free Cross Section Data Crossroad median width Wm (ft) 12 Number of Lanes Crossroad Inside approach Through lanes nth, in 2 Same choice for crash period and study year. Outside approach Through lanes nth, out 2 Same choice for crash period and study year. Ramp Exit ramp approach All lanes nex 2 Same choice for crash period and study year. Right-Turn Channelization Crossroad Inside approach Chan. present Ich, in Y/N -- Y/N Outside approach Chan. present Ich, out Y/N -- Y/N Ramp Exit ramp approach Chan. present Ich, ex Y/N -- Y/N

681 Table 19-69. Ramp Terminal Worksheet (2 of 4)—Sample Problem 6 Input Data Cross Section Data Crash Period Study Year Complete the study year column. Complete the crash period column if the EB Method is used. Left-Turn Lane or Bay Crossroad Inside approach Lane or bay present Ibay, lt, in Y/N -- Y/N If Yes, then enter data in the next row. Lane or bay width Wb, in (ft) -- Outside approach Lane or bay present Ibay,lt,out Y/N -- Y/N If Yes, then enter data in the next row. Lane or bay width Wb,out(ft) -- Right-Turn Lane or Bay Crossroad Inside approach Lane or bay present Ibay, rt, in Y/N -- Y/N Outside approach Lane or bay present Ibay,rt,out Y/N -- Y/N Access Data Number of driveways on the outside crossroad leg ndw -- Number of public street approaches on the outside crossroad leg nps -- Traffic Data Crossroad Inside leg AADTin (veh/day) 14,000 Outside leg AADTout (veh/day) 14,000 Ramp Exit ramp AADTex (veh/day) 1,450 Entrance ramp AADTen (veh/day) 1,300

682 Table 19-70. Ramp Terminal Worksheet (3 of 4)—Sample Problem 6 Crash Modification Factors Complete the study year column. Complete the crash period column if the EB Method is used. Fatal and Injury Property Damage Only Equation Crash Period Study Year Crash Period Study Year Signal Control Exit ramp capacity CMF10, w, SGn, at, fi 19-42 -- -- Crossroad left-turn lane CMF11, w, SGn, at, z 19-45 -- -- -- -- Crossroad right-turn lane CMF12, w, SGn, at, z 19-48 -- -- -- -- Access point frequency CMF13, w, SGn, at, z 19-49 -- -- -- -- Segment length CMF14, w, SGn, at, z 19-50 -- -- -- -- Median width CMF15, w, SGn, at, z 19-51 -- -- -- -- Protected left-turn operation CMF16, w, SGn, at, z 19-53 -- -- -- -- Chan. right turn on crossroad CMF17, w, SGn, at, z 19-55 -- -- -- -- Chan. right turn on exit ramp CMF18, w, SGn, at, z 19-56 -- -- -- -- Non-ramp public street leg CMF19, w, SGn, at, z 19-57 -- -- -- -- Stop Control Exit ramp capacity CMF10, w, ST, at, fi 19-42 -- 1.012 Crossroad left-turn lane CMF11, w, ST, at, z 19-45 -- -- -- -- Crossroad right-turn lane CMF12, w, ST, at, z 19-48 -- -- -- -- Access point frequency CMF13, w, ST, at, fi 19-49 -- 1.000 Segment length CMF14, w, ST, at, fi 19-50 -- 0.902 Median width CMF15, w, ST, at, fi 19-51 -- 1.000 Skew angle CMF20, w, ST, at, fi 19-58 -- -- All-way stop-control (exclude CMF11, CMF12, CMF20) -- 0.686 Combined CMF (multiply all CMFs evaluated) -- 0.626 -- 1.000 Expected Average Crash Frequency a Complete the study year column. Complete the crash period column if the site-specific EB Method is used. Fatal and Injury Property Damage Only Crash Period Study Year Crash Period Study Year Calibration factor CaS, x, at, z 1.00 1.00 Overdispersion parameter kw, x, at, z -- -- Observed crash count N*o, w, x, at, z (cr) -- -- Reference year r -- -- Predicted average crash freq. for reference year Np, w, x, at, z, r (cr/yr) -- -- Predicted number of crashes for crash period (sum all years) N*p, w, x, y, z (cr) -- -- Equivalent years associated with crash count Cb, w, x, at, z, r (yr) -- -- Adjusted average crash freq. for ref. year given N*o, Na, w, x, at, z, r (cr/yr) -- -- Study year s 2011 2011 Predicted average crash freq. for study year Np, w, x, at, z, s (cr/yr) 0.221 0.881 Expected average crash freq. for study year Ne, w, x, at, z, s (cr/yr) 0.221 0.881 Note: a If the EB Method is not used, then substitute “predicted” for “expected” and substitute the subscript “p” for the subscript “e”.

683 Table 19-71. Ramp Terminal Worksheet (4 of 4)—Sample Problem 6 Expected Average Crash Frequency Crash Severity Distribution K A B C Total FI PDO Total FI + PDO Proportion by injury level 0.005 0.028 0.180 0.787 1.000 Expected average crash freq. for study year Ne, w, x, at, z, s (cr/yr) 0.001 0.006 0.040 0.174 0.221 0.881 1.102 Crash Type Distribution Fatal and Injury Property Damage Only Total Crash Type Category Table 19-16, 19-21, or 19-45 Proportion Expected Average Crash Frequency for Study Year Ne, w, x, at, fi, s (cr/yr) Proportion Expected Average Crash Frequency for Study Year Ne, w, x, at, pdo, s (cr/yr) Expected Average Crash Frequency for Study Year Ne, w, x, at, as, s (cr/yr) Multiple-Vehicle Crashes Head-on 0.017 0.000 0.012 0.000 0.000 Right-angle 0.458 0.040 0.378 0.293 0.333 Rear-end 0.373 0.160 0.377 0.440 0.601 Sideswipe 0.025 0.000 0.079 0.000 0.000 Other multiple-vehicle crashes 0.017 0.000 0.016 0.000 0.000 Single-Vehicle Crashes Crash with animal 0.000 0.000 0.000 0.000 0.000 Crash with fixed object 0.085 0.000 0.110 0.147 0.147 Crash with other object 0.000 0.000 0.000 0.000 0.000 Crash with parked vehicle 0.000 0.000 0.008 0.000 0.000 Other single-vehicle crashes 0.025 0.020 0.020 0.000 0.020 Total 1.000 0.221 1.000 0.881 1.102 19.15. REFERENCES (1) Bonneson, J., S. Geedipally, M. Pratt, and D. Lord. Safety Prediction Methodology and Analysis Tool for Freeways and Interchanges. Final Report. NCHRP Project 17-45. Texas Transportation Institute, College Station, Texas, 2012. http://apps.trb.org/cmsfeed/TRBNetProjectDisplay.asp?ProjectID=2512 (2) Harwood, D. W., M. T. Pietrucha, M. D. Wooldridge, R. E. Brydia, and K. Fitzpatrick. NCHRP Report 375: Median Intersection Design. National Cooperative Highway Research Association, Transportation Research Board, Washington, D.C., 1995.

684 APPENDIX 19A—WORKSHEETS FOR PREDICTIVE METHOD FOR RAMPS Ramp Segment Worksheet (1 of 4) General Information Location Information Analyst Roadway Agency or company Roadway section Date performed Study year Area type Urban Rural Input Data Crash Data Crash Period Study Year Complete the study year column. Complete the crash period column if the EB Method is used. Crash data time period First year Last year Count of multiple-vehicle FI crashes N*o, w, n, mv, fi Count of single-vehicle FI crashes N*o, w, n, sv, fi Count of multiple-vehicle PDO crashes N*o, w, n, mv, pdo Count of single-vehicle PDO crashes N*o, w, n, sv, pdo Basic Roadway Data Number of through lanes n Same value for crash period and study year. Segment length L (mi) Average traffic speed on the freeway Vfrwy (mi/h) Segment type Choices: Entrance, Exit, C-D road, Connector Type of control at crossroad ramp terminal Choices: Stop, Yield, Signal, None Alignment Data Horizontal Curve Data 1 Presence of horizontal curve 1 Choices: No, In segment, Off segment. Curve radius R1 (ft) If “In segment” or “Off segment”, enter data for curve radius, length, and ramp-mile. Length of curve Lc1 (mi) Length of curve in segment Lc1, seg (mi) Ramp-mile of beginning of curve in dir. of travel X1 (mi) 2 Presence of horizontal curve 2 Choices: No, In segment, Off segment Curve radius R2 (ft) If “In segment” or “Off segment”, enter data for curve radius, length, and ramp-mile. Length of curve Lc2 (mi) Length of curve in segment Lc2, seg (mi) Ramp-mile of beginning of curve in dir. of travel X2 (mi) 3 Presence of horizontal curve 3 Choices: No, In segment, Off segment Curve radius R3 (ft) If “In segment” or “Off segment”, enter data for curve radius, length, and ramp-mile. Length of curve Lc3 (mi) Length of curve in segment Lc3, seg (mi) Ramp-mile of beginning of curve in dir. of travel X3 (mi) 4 Presence of horizontal curve 4 Choices: No, In segment, Off segment Curve radius R4 (ft) If “In segment” or “Off segment”, enter data for curve radius, length, and ramp-mile. Length of curve Lc4 (mi) Length of curve in segment Lc4, seg (mi) Ramp-mile of beginning of curve in dir. of travel X4 (mi)

685 Ramp Segment Worksheet (2 of 4) Input Data Cross Section Data Crash Period Study Year Complete the study year column. Complete the crash period column if the EB Method is used. Lane width Wl (ft) Right shoulder width Wrs (ft) Left shoulder width Wls (ft) Presence of lane add or lane drop Choices: No, Lane add, Lane drop Length of taper in segment Ladd, seg or Ldrop, seg (mi) If “Lane add” or “Lane drop”, enter length. Roadside Data Presence of barrier on right side of roadway Y/N Y/N If Yes, then use the ramp barrier worksheet. Presence of barrier on left side of roadway Y/N Y/N If Yes, then use the ramp barrier worksheet. Ramp Access Data Ramp Entrance Ent. ramp Presence of speed-change lane in segment Y/N Y/N If Yes, then enter data in the next row. Length of s-c lane in segment Len,seg (mi) Exit ramp Presence of speed-change lane in segment Y/N Y/N If Yes, then enter data in the next row. Length of s-c lane in segment Lex,seg (mi) Weave Presence of a weaving section in segment Y/N Y/N If Yes, then enter data in the next two rows. Length of weaving section Lwev (mi) Length of weaving section in seg. Lwev, seg (mi) Traffic Data Segment AADT AADTr or AADTc (veh/day)

686 Ramp Segment Worksheet (3 of 4) Crash Modification Factors Fatal and Injury Property Damage Only Complete the study year column. Complete the crash period column if the EB Method is used. Multiple Vehicle Single Vehicle Multiple Vehicle Single Vehicle Equation Crash Period Study Year Crash Period Study Year Crash Period Study Year Crash Period Study Year Horizontal curve CMF1, w, x, y, z 14-33 Lane width CMF2, w, x, y, fi 14-34 Right shoulder width CMF3, w, x, y, z 14-35 Left shoulder width CMF4, w, x, y, z 14-36 Right side barrier CMF5, w, x, y, z 14-37 Left side barrier CMF6, w, x, y, z 14-38 Lane add or drop CMF7, w, x, y, fi 14-39 Ramp speed-change lane CMF8, w, x, mv, fi 14-40 Weaving section CMF9, cds, ac, y, z 14-41 Combined CMF (multiply all CMFs evaluated) Expected Average Crash Frequency a Fatal and Injury Property Damage Only Complete the study year column. Complete the crash period column if the site-specific EB Method is used. Multiple Vehicle Single Vehicle Multiple Vehicle Single Vehicle Crash Period Study Year Crash Period Study Year Crash Period Study Year Crash Period Study Year Calibration factor Cw, x, y, z Overdispersion parameter kw, x, y, z Observed crash count N*o, w, x, y, z (cr) Reference year r Predicted average crash freq. for reference year Np, w, x, y, z, r (cr/yr) Predicted number of crashes for crash period (sum all years) N*p, w, x, y, z (cr) Equivalent years associated with crash count Cb, w, x, y, z, r (yr) Adjusted average crash freq. for ref. year given N*o, Na, w, x, y, z, r (cr/yr) Study year s Predicted average crash freq. for study year Np, w, x, y, z, s (cr/yr) Expected average crash freq. for study year Ne, w, x, y, z, s (cr/yr) Expected average crash freq. for study year (all crash types) Ne, w, x, at, z, s (cr/yr) Note: a If the EB Method is not used, then substitute the word “predicted” for the word “expected” and substitute the subscript “p” for the subscript “e”.

687 Ramp Segment Worksheet (4 of 4) Expected Average Crash Frequency a Crash Severity Distribution K A B C Total FI PDO Total FI + PDO Proportion by injury level 1.000 Expected average crash freq. for study year (all crash types) Ne, w, x, at, z, s (cr/yr) Crash Type Distribution Fatal and Injury Property Damage Only Total Crash Type Category Proportion Expected Average Crash Frequency for Study Year Ne, w, x, y, fi, s (cr/yr) Proportion Expected Average Crash Frequency for Study Year Ne, w, x, y, pdo, s (cr/yr) Expected Average Crash Frequency for Study Year Ne, w, x, y, as, s (cr/yr) Table Multiple-Vehicle Crashes 14-6 Head-on Right-angle Rear-end Sideswipe Other multiple-vehicle crashes Total 1.000 1.000 Single-Vehicle Crashes 14-9 Crash with animal Crash with fixed object Crash with other object Crash with parked vehicle Other single-vehicle crashes Total 1.000 1.000 Note: a If the EB Method is not used, then substitute the word “predicted” for the word “expected” and substitute the subscript “p” for the subscript “e”.

688 Ramp Barrier Worksheet Input Data Segment length L (mi) Crash period Study year Left shoulder width Wls (ft) Right shoulder width Wrs (ft) Individual Right Side Barrier Element Data Barrier Location Length Lrb, i (mi) Width from Edge of Traveled Way to Face of Right Side Barrier Woff , r, i (ft) Ratio Lrb,i/(Woff,r,i–Wrs) 1. 2. 3. 4. 5. 6. 7. Sum1 Sum2 Individual Left Side Barrier Element Data Barrier Location Length Llb, i (mi) Width from Edge of Traveled Way to Face of Left Side Barrier Woff , l, i (ft) Ratio Llb,i/(Woff, l, i– Wls) 1. 2. 3. 4. 5. 6. 7. Sum3 Sum4 Right Side Barrier Calculations Proportion of segment length with barrier in median Prb = Sum1/L Width from edge of shoulder to barrier face Wrcb = Sum1 / Sum2 (ft) Left Side Barrier Calculations Proportion of segment length with barrier in median Plb = Sum3/L Width from edge of shoulder to barrier face Wlcb = Sum3 / Sum4 (ft)

689 Ramp Terminal Worksheet (1 of 4) General Information Location Information Analyst Roadway Agency or company Intersection Date performed Study year Area type Urban Rural Input Data Crash Data Crash Period Study Year Complete the study year column. Complete the crash period column if the EB Method is used. Crash data time period First year Last year Count of FI crashes N*o, w, x, at, fi Count of PDO crashes N*o, w, x, at, pdo Basic Intersection Data Ramp terminal configuration Choices: D3ex, D3en, D4, A4, B4, A2, B2 Same choice for crash period and study year. Ramp terminal traffic control mode Choices: Signal, One-way-stop, All-way stop Presence of a non-ramp public street leg Ips Y/N Y/N Alignment Data Exit ramp skew angle Isk (degrees) Distance to the next public street intersection on the outside crossroad leg Lstr (mi) Distance to the adjacent ramp terminal Lrmp (mi) Traffic Control Left-Turn Operational Mode Crossroad Inside approach Prot.-only mode Ip, lt, in Y/N Y/N Outside approach Prot.-only mode Ip, lt, out Y/N Y/N Right-Turn Control Mode Ramp Exit ramp approach Right-turn control mode Choices: Signal, Stop, Yield, Merge, Free Cross Section Data Crossroad median width Wm (ft) Number of Lanes Crossroad Inside approach Through lanes nth, in Same choice for crash period and study year. Outside approach Through lanes nth, out Same choice for crash period and study year. Ramp Exit ramp approach All lanes nex Same choice for crash period and study year. Right-Turn Channelization Crossroad Inside approach Chan. present Ich, in Y/N Y/N Outside approach Chan. present Ich, out Y/N Y/N Ramp Exit ramp approach Chan. present Ich, ex Y/N Y/N

690 Ramp Terminal Worksheet (2 of 4) Input Data Cross Section Data Crash Period Study Year Complete the study year column. Complete the crash period column if the EB Method is used. Left-Turn Lane or Bay Crossroad Inside approach Lane or bay present Ibay, lt, in Y/N Y/N If Yes, then enter data in the next row. Lane or bay width Wb, in (ft) Outside approach Lane or bay present Ibay,lt,out Y/N Y/N If Yes, then enter data in the next row. Lane or bay width Wb,out(ft) Right-Turn Lane or Bay Crossroad Inside approach Lane or bay present Ibay, rt, in Y/N Y/N Outside approach Lane or bay present Ibay,rt,out Y/N Y/N Access Data Number of driveways on the outside crossroad leg ndw Number of public street approaches on the outside crossroad leg nps Traffic Data Crossroad Inside leg AADTin (veh/day) Outside leg AADTout (veh/day) Ramp Exit ramp AADTex (veh/day) Entrance ramp AADTen (veh/day)

691 Ramp Terminal Worksheet (3 of 4) Crash Modification Factors Complete the study year column. Complete the crash period column if the EB Method is used. Fatal and Injury Property Damage Only Equation Crash Period Study Year Crash Period Study Year Signal Control Exit ramp capacity CMF10, w, SGn, at, fi 14-42 Crossroad left-turn lane CMF11, w, SGn, at, z 14-45 Crossroad right-turn lane CMF12, w, SGn, at, z 14-48 Access point frequency CMF13, w, SGn, at, z 14-49 Segment length CMF14, w, SGn, at, z 14-50 Median width CMF15, w, SGn, at, z 14-51 Protected left-turn operation CMF16, w, SGn, at, z 14-53 Chan. right turn on crossroad CMF17, w, SGn, at, z 14-55 Chan. right turn on exit ramp CMF18, w, SGn, at, z 14-56 Non-ramp public street leg CMF19, w, SGn, at, z 14-57 Stop Control Exit ramp capacity CMF10, w, ST, at, fi 14-42 Crossroad left-turn lane CMF11, w, ST, at, z 14-45 Crossroad right-turn lane CMF12, w, ST, at, z 14-48 Access point frequency CMF13, w, ST, at, fi 14-49 Segment length CMF14, w, ST, at, fi 14-50 Median width CMF15, w, ST, at, fi 14-51 Skew angle CMF20, w, ST, at, fi 14-58 All-way stop-control (exclude CMF11, CMF12, CMF20) Combined CMF (multiply all CMFs evaluated) Expected Average Crash Frequency a Complete the study year column. Complete the crash period column if the site-specific EB Method is used. Fatal and Injury Property Damage Only Crash Period Study Year Crash Period Study Year Calibration factor CaS, x, at, z Overdispersion parameter kw, x, at, z Observed crash count N*o, w, x, at, z (cr) Reference year r Predicted average crash freq. for reference year Np, w, x, at, z, r (cr/yr) Predicted number of crashes for crash period (sum all years) N*p, w, x, y, z (cr) Equivalent years associated with crash count Cb, w, x, at, z, r (yr) Adjusted average crash freq. for ref. year given N*o, Na, w, x, at, z, r (cr/yr) Study year s Predicted average crash freq. for study year Np, w, x, at, z, s (cr/yr) Expected average crash freq. for study year Ne, w, x, at, z, s (cr/yr) Note: a If the EB Method is not used, then substitute the word “predicted” for the word “expected” and substitute the subscript “p” for the subscript “e”.

692 Ramp Terminal Worksheet (4 of 4) Expected Average Crash Frequency a Crash Severity Distribution K A B C Total FI PDO Total FI + PDO Proportion by injury level 1.000 Expected average crash freq. for study year Ne, w, x, at, z, s (cr/yr) Crash Type Distribution Fatal and Injury Property Damage Only Total Crash Type Category Table 14-16, 14-21, or 14-45 Proportion Expected Average Crash Frequency for Study Year Ne, w, x, at, fi, s (cr/yr) Proportion Expected Average Crash Frequency for Study Year Ne, w, x, at, pdo, s (cr/yr) Expected Average Crash Frequency for Study Year Ne, w, x, at, as, s (cr/yr) Multiple-Vehicle Crashes Head-on Right-angle Rear-end Sideswipe Other multiple-vehicle crashes Single-Vehicle Crashes Crash with animal Crash with fixed object Crash with other object Crash with parked vehicle Other single-vehicle crashes Total 1.000 1.000 Note: a If the EB Method is not used, then substitute the word “predicted” for the word “expected” and substitute the subscript “p” for the subscript “e”.