Proposed Guidelines for Fixed Objects in the Roadside Design Guide (2022)

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73 Chapter 7. Modified RAP Model for Predicting Crashes Involving Collisions with Trees and Utility Poles This chapter presents a modified RAP model for predicting fatalities and injuries in ROR crashes involving collisions with roadside trees and utility poles. This modified model is based on the RAP model for ROR crashes presented in Appendix A, modified as discussed in Chapter 6. Thus, this chapter differs from Appendix A in that the model in this chapter has been adapted for application specifically to roadside trees and utility poles. The modified RAP model addresses the likelihood and severity of crashes involving collisions with roadside trees and utility poles on paved rural nonfreeways. The model addresses tree- and pole-related crashes involving all vehicle types, including a representative proportion of motorcycles in the traffic stream (typically 3 percent). The modified model estimates the frequency of total fatal-and-injury crashes and provides factors to break down the estimate of total fatal-and-injury crashes into estimates of fatal, incapacitating injury (A injury), nonincapacitating injury (B injury), and possible injury (C injury) crashes. Factors are also provided to estimate the number of persons killed and the number of persons injured (by injury severity level). The key differences in the crash frequencies between crashes involving collisions with trees and crashes involving collisions with utility poles result from the values assigned to the calibration factors, the distribution of crash severity levels, and the number of persons killed and injured in crashes of specific severity levels. The model should be applied separately to predicting tree- and pole-related crashes. The model is not intended to predict the combined number of tree- and pole-related crashes, but the model can be applied separately to tree- and pole-related crashes and the results can then be combined. While calibration factors for tree- and pole-related crashes have been provided based on the Kentucky and Washington databases described in Chapter 4, users are also welcome to gather their own calibration data and determine agency-specific calibration factors. A calibration procedure for this purpose is presented below in Section 7.6. The modified RAP model is intended for use in roadside design to quantify the benefits of removing or relocating trees and utility poles. The model is suitable for incorporation by reference in a future edition of the AASHTO RDG. Computational examples from applying the model are included in this chapter. The modified RAP model in the form presented here is applicable to prediction of crashes involving roadside trees and utility poles on rural roads other than fully access controlled freeways. This model could also be applied to freeways, but it would need to be calibrated for that application using the calibration procedure presented in Section 7.6. The model could also be applied to urban roads, but it would need to be calibrated for that application using the calibration procedure presented in Section 7.6 and the urban factors for lane width in Table A-3 would need to be used.

74 7.1 Roadway and Roadside Characteristics Data Needed to Estimate Roadside Tree and Utility Pole Crashes The model presented is this chapter estimates the predicted number of fatal-and-injury crashes per year due to collisions with trees and utility poles on a roadway section where roadside trees or utility poles are present, overall and by severity level, and the predicted number of persons killed and persons injured, by severity level. Separate analyses should be conducted for trees and utility poles. The roadway section analyzed may be of any length, as the extent of the section is defined not by its length, but by the number and extent of roadside trees and utility poles present within the section. Each section analyzed should be reasonably homogeneous with respect to roadway characteristics. Small variations in the distance from the outside edge of the traveled way to the nearest tree or utility pole are permissible; if large variations in this distance are present, it is best to break up the road section into two or more separate sections that are reasonably homogeneous with respect to distance to roadside trees or utility poles. A roadway section may have as few as one tree or utility pole or many trees or utility poles as long as the section is relatively homogeneous in roadway design characteristics and in the offset of the trees or utility poles from the traveled way. The input data needed to use the model include: Roadway Characteristics Data • Roadway type (rural two-lane undivided, rural multilane undivided, rural multilane divided) • Annual average daily traffic volume for both directions of travel combined (AADT) (veh/day) • Design speed of roadway (mph) • Lane width (ft) • Paved shoulder width for left side of the road (ft) • Paved shoulder width for right side of the road (ft) • Horizontal curvature (represented by the estimated speed of traffic on the curve in mph) • Advance visibility of roadway curve (suitability of pavement markings, chevron markers, advance signing, and sight distance to the curve) • Grade (percent) • Presence of shoulder rumble strips • Presence of delineation • Road surface condition • Pavement skid resistance

75 Roadside Characteristics Data (for analysis of trees) • Number of individual trees on the left side of the road • Number of individual trees on the right side of the road • Length of tree groups on the left side of the road (ft) • Length of tree groups on the right side of the road (ft) • Distance from edge of traveled way to nearest tree on the left side of the road (ft) • Distance from edge of traveled way to nearest tree on the right side of the road (ft) Roadside Characteristics Data (for analysis of utility poles) • Number of individual utility poles on the left side of the road • Number of individual utility poles on the right side of the road • Distance from edge of traveled way to nearest utility pole on the left side of the road (ft) • Distance from edge of traveled way to nearest utility pole on the right side of the road (ft) Each of these input data items is explained in more detail in Sections 7.3 and 7.4. 7.2 General Form of Crash Prediction Model for Run-Off-Road Crashes This section presents the portion of the modified RAP crash prediction model that addresses ROR crashes. The general form of the crash prediction model for a specific roadway segment is as follows (adapted from iRAP 2014): 𝑁 = 𝑁 + 𝑁 (27) 𝑁 = 𝑅𝑆𝑆 × (𝐴𝐴𝐷𝑇) . × 𝐶𝐹 × × 𝐶 (28) 𝑁 = 𝑅𝑆𝑆 × (𝐴𝐴𝐷𝑇) . × 𝐶𝐹 × × 𝐶 (29) 𝐶 = 𝐶 + 𝑇𝐺𝐸 × 𝐶 (30) 𝐶 = 𝐶 + 𝑇𝐺𝐸 × 𝐶 (31) where: NROR = predicted number of run off-road crashes per year on a specific roadway segment involving a fatality or injury to an occupant of a motor vehicle running off either side of the road within a specific roadway segment NROR-left = predicted number of run off-road crashes per year on a specific roadway segment involving a fatality or injury to an occupant of a motor vehicle running off the left side of the road within a specific roadway segment

76 NROR-right = predicted number of run off-road crashes per year on a specific roadway segment involving a fatality or injury to an occupant of a motor vehicle running off the right side of the road within a specific roadway segment RSSROR-left = road safety score for crashes involving motor vehicles running off the left side of the road RSSROR-right = road safety score for crashes involving motor vehicles running off the right side of the road AADT = annual average daily traffic volume (veh/day) in both directions of travel combined for undivided roadway segments or roadway segments with traversable medians and in one direction of travel only for roadway segments with nontraversable medians CF = calibration factor for ROR crashes (recommended default values: 1.02 for trees and 0.80 for utility poles) COBJ-left = number of trees (or equivalent trees) or utility poles on the left side of the road within the specific roadway segment COBJ-right = number of trees (or equivalent trees) or utility poles on the right side of the road within the specific roadway segment Cindiv-left = number of individual trees or utility poles on the left side of the road within the specific roadway segment Cindiv-right = number of individual trees or utility poles on the right side of the road within the specific roadway segment Cgroup-left = total length of tree groups (ft) measured longitudinally along the left side of the road within the specific roadway segment (NOTE: If utility poles are being analyzed, set Cgroup-left equal to zero.) Cgroup-right = total length of tree groups (ft) measured longitudinally along the right side of the road within the specific roadway segment (NOTE: If utility poles are being analyzed, set Cgroup-right equal to zero.) TGE = tree group equivalency factor (recommended default value: 0.0097) Recommended values of the calibration factor (CF) in Equations (28) and (29) are 1.02 for trees and 0.80 for utility poles. Individual highway agencies may use their own data to develop calibration factors specific to their own jurisdiction (see Section 7.6). The recommended value for the TGE in Equations (30) and (31) is 0.0097.

77 The value of NROR can be broken down into crash severity levels as follows: 𝑁 = 𝑁 × 𝑆𝑃 (32) 𝑁 = 𝑁 × 𝑆𝑃 (33) 𝑁 = 𝑁 × 𝑆𝑃 (34) 𝑁 = 𝑁 × 𝑆𝑃 (35) where: NROR-K = predicted number of run off-road crashes per year on a specific roadway segment involving a fatality to an occupant of a motor vehicle running off either side of the road within a specific roadway segment NROR-A = predicted number of run off-road crashes per year on a specific roadway segment involving an incapacitating injury to an occupant of a motor vehicle running off either side of the road within a specific roadway segment NROR-B = predicted number of run off-road crashes per year on a specific roadway segment involving a nonincapacitating injury to an occupant of a motor vehicle running off either side of the road within a specific roadway segment NROR-C = predicted number of run off-road crashes per year on a specific roadway segment involving a possible injury to an occupant of a motor vehicle running off either side of the road within a specific roadway segment SPK = estimated proportion of tree- or utility-pole-related crashes resulting in a fatality (see default values in Table 38) SPA = estimated proportion of tree- or utility-pole-related crashes resulting in an incapacitating injury (see default values in Table 38) SPB = estimated proportion of tree- or utility-pole-related crashes resulting in a nonincapacitating injury (see default values in Table 38) SPC = estimated proportion of tree- or utility-pole-related crashes resulting in a possible injury (see default values in Table 38)

78 The number of persons fatally injured in collisions with trees or utility poles can be estimated as: 𝑁 = 𝑁 × 𝑃 (36) where: NROR-PK = predicted number of fatally injured persons per year resulting from a motor vehicle running off either side of the road within a specific roadway segment PK = average number of persons fatally injured per fatal crash involving a collision with a tree or utility pole (see default values in Table 39) Table 38. Crash Severity Proportions for Use as Default Values for Rural Nonfreeways Crash Severity Levela Proportion of crashes Trees Utility poles Fatal (SPK) 0.078 0.020 Incapacitating injury (SPA) 0.177 0.078 Nonincapacitating injury (SPB) 0.376 0.407 Possible injury (SPC) 0.369 0.495 TOTAL 1.000 1.000 a most severe injury resulting from the crash. Table 39. Deaths and Persons Injured Per Crash for Use as Default Values for Rural Nonfreeways Crash severity levela Deaths Per Crash Persons Nonfatally Injured Per Crash Incapacitating Injury Nonincapacitating Injury Possible Injury TREES Fatal (PK, PIK-A, PIK-B, PIK-C) 1.08 0.04 0.10 0.15 Incapacitating injury (PIA-A, PIA-B, PIA-C) -- 1.06 0.14 0.20 Nonincapacitating injury (PIB-B, PIB-C) -- -- 1.15 0.15 Possible injury (PIC-C) -- -- -- 1.33 UTILITY POLES Fatal (PK, PIK-A, PIK-B, PIK-C) 1.02 0.01 0.06 0.02 Incapacitating injury (PIA-A, PIA-B, PIA-C) -- 1.04 0.29 0.37 Nonincapacitating injury (PIB-B, PIB-C) -- -- 1.10 0.11 Possible injury (PIC-C) -- -- -- 1.19 a most severe injury resulting from the crash. The number of persons injured in collisions with trees or utility poles can be estimated as: 𝑁 = 𝑁 × 𝑃𝐼 + 𝑁 × 𝑃𝐼 (37) 𝑁 = 𝑁 × 𝑃𝐼 + 𝑁 × 𝑃𝐼 + 𝑁 × 𝑃𝐼 (38) 𝑁 = 𝑁 × 𝑃𝐼 + 𝑁 × 𝑃𝐼 + 𝑁 × 𝑃𝐼 + (39) 𝑁 × 𝑃𝐼

79 where: NROR-PI-A = predicted number of persons per year receiving incapacitating injuries persons resulting from a motor vehicle running off either side of the road within a specific roadway segment NROR-PI-B = predicted number of persons per year receiving nonincapacitating injuries resulting from a motor vehicle running off either side of the road within a specific roadway segment NROR-PI-C = predicted number of persons per year receiving possible injuries resulting from a motor vehicle running off either side of the road within a specific roadway segment PIK-A = average number of persons receiving incapacitating injuries in fatal crashes involving a collision with a tree or utility pole (see default values in Table 39) PIA-A = average number of persons receiving incapacitating injuries in incapacitating injury crashes involving a collision with a tree or utility pole (see default values in Table 39) PIK-B = average number of persons receiving nonincapacitating injuries in fatal crashes involving a collision with a tree or utility pole (see default values in Table 39) PIA-B = average number of persons receiving nonincapacitating injuries in incapacitating injury crashes involving a collision with a tree or utility pole (see default values in Table 39) PIB-B = average number of persons receiving nonincapacitating injuries in nonincapacitating injury crashes involving a collision with a tree or utility pole (see default values in Table 39) PIK-C = average number of persons receiving possible injuries in fatal crashes involving a collision with a tree or utility pole (see default values in Table 39) PIA-C = average number of persons receiving possible injuries in incapacitating injury crashes involving a collision with a tree or utility pole (see default values in Table 39) PIB-C = average number of persons receiving possible injuries in nonincapacitating injury crashes involving a collision with a tree or utility pole (see default values in Table 39) PIC-C = average number of persons receiving possible injuries in possible injury crashes involving a collision with a tree or utility pole (see default values in Table 39)

80 7.3 Road Safety Scores for Run-Off-Road Crashes The model uses a road safety score (RSS) as a basis for estimating the frequency of crashes of particular types. The RSS is proportional to crash frequency and considers both crash likelihood and crash severity, as well as the influence of motor vehicle speeds and traffic volume. The RSS for injuries to motor vehicle occupants in ROR crashes on each side of the road (iRAP 2013b) is determined as: RSSROR-left = LikelihoodROR x SeverityROR-left x DSF x EFI x MT (40) RSSROR-right = LikelihoodROR x SeverityROR-right x DSF x EFI (41) where: RSSROR-left = road safety score for injuries to occupants of motor vehicles running off the left side of the road RSSROR-right = road safety score for injuries to occupants of motor vehicles running off the right side of the road LikelihoodROR = crash likelihood factor for crashes involving motor vehicles running off the road SeverityROR-left = crash severity factor for crashes involving motor vehicles running off the left side of the road SeverityROR-right = crash severity factor for crashes involving motor vehicles running off the right side of the road DSF = roadway design speed factor EFI = external flow influence factor MT = median traversability factor Crash Likelihood Factor for Run-Off-Road Crashes The crash likelihood factor for crashes involving motor vehicles running off road (iRAP 2013b) is computed as a product of adjustment factors as follows: LikelihoodROR = AFL1 x AFL2 x AFL3 x AFL4 x AFL5 x AFL6 x AFL7 x AFL8 (42) where: AFL1 = likelihood adjustment factor for lane width AFL2 = likelihood adjustment factor for horizontal curvature AFL3 = likelihood adjustment factor for advance visibility of curve AFL4 = likelihood adjustment factor for grade

81 AFL5 = likelihood adjustment factor for shoulder rumble strips AFL6 = likelihood adjustment factor for delineation AFL7 = likelihood adjustment factor for road surface condition AFL8 = likelihood adjustment factor for pavement skid resistance Crash Severity Factor for Run-Off-Road Crashes The crash severity factors for motor vehicles running off the left and right sides of the road (iRAP 2013b) are computed as: SeverityROR-left = AFS1-left x AFS2-left x AFS3-left (43) SeverityROR-right = AFS1-right x AFS2-right x AFS3-right (44) where: AFS1-left = crash severity adjustment factor for distance to the most severe roadside object on the left side of the road AFS1-right = crash severity adjustment factor for distance to the most severe roadside object on the right side of the road AFS2-left = crash severity adjustment factor for most severe roadside object type on the left side of the road AFS2-left = crash severity adjustment factor for most severe roadside object type on the right side of the road AFS3-left = crash severity adjustment factor for paved shoulder width on the left side of the road AFS3-right = crash severity adjustment factor for paved shoulder width on the right side of the road Roadway Design Speed Factor for Run-Off-Road Crashes The roadway design speed factors applicable to ROR crashes (iRAP 2013g) are derived from the RAP factors based on mean speed of traffic or posted speed limit on particular road sections. The design speed is assumed to be 5 mph greater than the mean speed of traffic or posted speed limit. The motor vehicle speed factor (DSF) values are shown in Table 40 and are illustrated in Figure 4. The values of these factors have a cubic relationship to mean speed based on the power curve (Nilsson 2004). Although the model has been calibrated specifically for the range of design speeds from 55 to 70 mph, Table 40 and Figure 4 show the DSF values for the full range of speeds.

82 Table 40. Roadway Design Speed Factor (iRAP 2013g) Design speed for the roadway segment of interest (mph) Design speed factor (DSF) 25 or less 0.010 30 0.019 35 0.033 40 0.053 45 0.079 50 0.113 55 0.154 60 0.205 65 0.267 70 0.339 75 0.424 80 0.521 85 0.632 Figure 4. Operating Speed Factors Representing the Relative Risk of Injury for Motor Vehicle Occupants Involved in ROR Crashes as a Function of Mean Traffic Speed (adapted from iRAP 2013g) For applying the crash prediction model, the speed used in determining the value of DSF should be the best estimate of the mean speed of motor vehicle traffic. External Flow Influence Factor for Run-Off-Road Crashes The external flow influence factor for motor vehicle movements along the road (iRAP 2013a) represents the level of lane saturation on the road in question. The values of the factors are determined with the best available estimate of traffic volume (AADT) per lane. AADT per lane is computed as the total AADT divided by the number of through lanes on the road. The external flow influence factor essentially represents the level of saturation in the flow on the roadway, where 19,000 to 20,000 veh/day/lane represents a fully saturated roadway.

83 The model uses categories for the traffic flow on the inspected road that represent ranges of AADT per lane. The applicable AADT ranges and midpoints are shown in Table 41. The table also shows the corresponding values of the external flow influence factor. The factor values are plotted as a continuous function in Figure 5. Table 41. External Flow Influence Factors for Motor Vehicle Crashes as a Function of AADT Ranges and Midpoints (adapted from iRAP 2013a) Ranges for AADT per lane (veh/day) Midpoint of AADT per lane range (veh/day) External flow influence (EFI) factor by road type Rural two-lane undivided highway Rural four-lane undivided highway Rural divided nonfreeway less than 1,999 1,000 0.474 0.451 0.500 2,000 – 3,999 3,000 0.448 0.408 0.500 4,000 – 5,999 5,000 0.422 0.370 0.500 6,000 – 7,999 7,000 0.397 0.339 0.500 8,000 – 9,999 9,000 0.372 0.312 0.500 10,000 – 11,999 11,000 0.347 0.290 0.500 12,000 – 13,999 13,000 0.322 0.273 0.500 14,000 – 15,999 15,000 0.298 0.261 0.500 16,000 – 17,999 17,000 0.274 0.253 0.500 18,000 or more 19,000 0.250 0.250 0.500 Figure 5. EFI Factors for Motor Vehicle Crashes as a Function of AADT (adapted from iRAP 2013a) Median Traversability Factor for Run-Off-Road Crashes Median traversability represents the potential for an errant vehicle to cross any median that may be provided on a roadway and enter the opposing lanes or cross the opposing lanes to the roadside on the far side of the opposing lanes (referred to in this model as the left roadside). The median traversability (MT) factor has a value of 1 for roads with traversable medians and 0 for

84 roads with nontraversable medians (iRAP 2013a). The MT factor is used in computation of the RSS for the left side of the road, but does not affect the RSS for the right side of the road. Roadways with traversable medians include undivided roadways with only a marked centerline or with a flush median and divided highways with relatively flat raised or depressed median with no fixed objects present that would constrain an errant vehicle from crossing the roadway. Roadways with nontraversable medians include divided highways with terrain, traffic barriers, or other fixed objects in the median that would prevent an errant vehicle from crossing the median to reach the opposing lanes or the left roadside. 7.4 Crash Likelihood Adjustment Factors This section presents the crash likelihood adjustment factors used in applying Equation (42). Lane Width The crash likelihood adjustment factors (AFL1) represent the relative likelihood that motor vehicles will run off the road, as a function of lane width. The values of this factor are shown in Table 42. Table 42. Crash Likelihood Adjustment Factors for Lane Width (iRAP 2013f) Lane width Adjustment factor for lane width (AFL1) Wide (≥ 10.6 ft) 1.00 Medium (≥ 9 to 10.6 ft) 1.20 Narrow (< 9 ft) 1.50 The rationale for the adjustment factor values is presented in iRAP Road Attribute Adjustment Factors: Lane Width (2013f). These adjustment factors were based on the work of Turner et al. (2009). Horizontal Curvature The likelihood that motor vehicles will run off the road is higher on horizontal curves than on tangents and increases as the radius of curvature decreases. As the likelihood that motor vehicles will run off the road increases, the crash likelihood adjustment factors for curvature (AFL2) for motor vehicle movements along the road are shown in Table 43. The horizontal curvature categories are defined by advisory speed ranges and corresponding ranges of horizontal curve radius. If a horizontal curve is signed with an advisory speed plate, use of the category in Table 43 corresponding to the signed advisory speed is recommended. If there is no signed advisory speed, the curvature category should be based on the horizontal curve radius.

85 Table 43. Crash Likelihood Adjustment Factors for Horizontal Curvature (iRAP 2013c) Horizontal curvature Adjustment factor for horizontal curvature (AFL2) Straight or gently curving (advisory speed ≥ 60 mph or curve radius > 2600 ft) 1.00 Moderate curvature (advisory speed in the range from 45 to < 60 mph or curve radius in the range from 1300 to ≤ 2600 ft) 1.81 Sharp curvature (advisory speed in the range from 25 to < 45 mph or curve radius in the range from 650 to ≤ 1300 ft) 3.51 Very sharp curvature (advisory speed < 25 mph or curve radius < 650 ft) 6.02 The rationale for the adjustment factor values in the table is presented in iRAP Road Attribute Adjustment Factors: Curvature (2013c). Advance Visibility of Curve The advance visibility of curve represents an assessment of the ability of approaching drivers to see a horizontal curve on the roadway ahead. This factor for any specific curve considers pavement markings, chevron markers, advance signing, and sight distance to the curve. If the advance visibility of the curve is limited, motor vehicles may be more likely to run off the road on the curve. The crash likelihood adjustment factors for advance visibility of curve (AFL3) for motor vehicle movements along the road are shown in Table 44. Table 44. Crash Likelihood Adjustment Factors for Advance Visibility of Curve (iRAP 2013i) Advance visibility of curve Adjustment factor for advance visibility of curve (AFL3) Substantial 1.00 Limited 1.25 Not applicable (i.e., tangent section) 1.00 The rationale for the adjustment factor values is presented in iRAP Road Attribute Adjustment Factors: Quality of Curve (2013i). These adjustment factors primarily represent the potential for loss of control on horizontal curves by motor vehicles. Grade Motor vehicles are more likely to lose control on steep grades than on level roadway sections. The crash likelihood adjustment factors representing the relative likelihood that motor vehicles will run off the road as a function of grade (AFL4) are shown in Table 45. Table 45. Crash Likelihood Adjustment Factors for Percent Grade (iRAP 2013e) Percent grade Adjustment factor for percent grade (AFL4 ) 0% to < 7.5% 1.00 7.5% to < 10% 1.20 ≥ 10% 1.70

86 The rationale for the adjustment factor values is presented in iRAP Road Attribute Adjustment Factors: Grade (2013e). These adjustment factors represent the potential for loss of control on grades by motor vehicles. The grade factors were based on work by Harwood et al. (2000) and analysis by RAP of an ARRB Group database and extrapolation of results by RAP to grades over 8 percent. Presence of Shoulder Rumble Strips Shoulder rumble strips are placed on the edgeline or shoulder of a roadway to alert drivers that their vehicle is leaving the roadway. Thus, shoulder rumble strips reduce the likelihood that motor vehicles will run off the road. The crash likelihood adjustment factors for the effect of shoulder rumble strips in reducing the likelihood of motor vehicles running off the road (AFL5) are shown in Table 46. Table 46. Crash Likelihood Adjustment Factors for Shoulder Rumble Strips (iRAP 2013p) Presence of shoulder rumble strips Adjustment factor for shoulder rumble strips (AFL5) Not present 1.25 Present 1.00 The rationale for the adjustment factor values is presented in iRAP Road Attribute Adjustment Factors: Shoulder Rumble Strips (2013p). These adjustment factors are based primarily on literature reviewed by Turner et al. (2012) and Turner et al. (2009). Presence of Delineation Delineation involves the placement of pavement markings and delineators to help guide drivers along the roadway. Motor vehicles are more likely to run off the road where delineation is poor than where delineation is adequate. The crash likelihood adjustment factors for the effect of delineation presence (AFL6) on the likelihood that motor vehicles will run off the road are shown in Table 47. Table 47. Crash Likelihood Adjustment Factors for Delineation (iRAP 2013d) Presence of delineation Adjustment factor for delineation (AFL6) Substantial 1.00 Limited or none 1.20 The rationale for the adjustment factor values is presented in iRAP Road Attribute Adjustment Factors: Delineation (2013d). The adjustment factor for delineation was based primarily on work by Turner et al. (2009). Road Surface Condition Poor road surface condition may make it more likely that motor vehicles run off the road. The crash likelihood adjustment factors representing the effect of road surface condition (AFL7) on the relative likelihood that motor vehicles will run off the road are shown in Table 48.

87 Table 48. Crash Likelihood Adjustment Factors for Road Surface Condition (iRAP 2013m) Road surface condition Adjustment factor for road surface condition (AFL7) Good 1.00 Medium 1.20 Rough 1.40 The rationale for the adjustment factor values is presented in iRAP Road Attribute Adjustment Factors: Road Condition (2013m). This result is based on an Australian study of the relationship between road surface roughness and crashes (Cairney and Bennett, 2009). Medium or rough road surface conditions are likely to represent a higher likelihood for loss of control by motorcyclists than for loss of control by other motor vehicles. Pavement Skid Resistance Poor pavement skid resistance increases the likelihood that drivers of motor vehicles may be unable to stop when needed to avoid striking another motor vehicle moving along the road. Limited pavement skid resistance also increases the likelihood that motor vehicles will lose control and run off the road. The crash likelihood adjustment factors for the effect of pavement skid resistance of the road surface (AFL8) on the likelihood that motor vehicles will run off the road are shown in Table 49. If pavement skid resistance data are not available, use of the default value of AFL8 equal to 1.0 is recommended. Table 49. Crash Likelihood Adjustment Factors for Pavement Skid Resistance (iRAP 2013q) Pavement skid resistance Adjustment factor for pavement skid resistance (AFL8) High 1.00 Medium 1.41 Limited 2.02 The rationale for the adjustment factor values is presented in iRAP Road Attribute Adjustment Factors: Skid Resistance/Grip (2013q). These adjustment factors were based on a literature review by Turner et al. (2010). 7.5 Crash Severity Adjustment Factors This section presents the crash severity adjustment factors used in applying Equations (43) and (44). Most Severe Roadside Object Distance AFS1-left represents the crash severity adjustment factor associated with the distance from the left edge of the traveled way to the most severe roadside object that could be struck by a motor vehicle running off the left side of the roadway. A severe object is any object that could result in an injury to an occupant of a vehicle that strikes the object. The distance to object used here should be for the object on the left side of the road whose type is used to determine RS2-left in Section 7.5.2. On divided highways, the distance used to determine AFS1-left is measured from the

88 edge of the traveled way on the median or left side of the traveled way; the most severe roadside object to which the distance is measured may be in the median or may be on the roadside beyond the opposing roadway of the divided highway. On undivided highways, the distance used to determine AFS1-left is measured from the edge of the traveled way on the left side of the roadway (i.e., from what would be considered the outside or right edge of the traveled way in the opposing direction of travel to the primary direction of travel). Similarly, AFS1-right is based on the distance from the right edge of the traveled way to the most severe roadside object that could be struck by a motor vehicle running off the right side of the roadway. This adjustment factor is entirely analogous to AFS1-left for the left side of the road except that this attribute applies to the right side of the road. The crash severity adjustment factors for roadside object distance for motor vehicles running off either side of the road are computed with Equations (45) and (46). 𝐴𝐹 = 1.046 − 0.0310 × 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒, 1.5 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 22.5 (45) 𝐴𝐹 = 0.670 − 0.0143 × 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒, 22.5 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 40 (46) where: AFS1 = crash severity adjustment factor for distance to the most severe roadside object on the left or right side of the road (AFS1-left or AFS1-right) Distance = distance from outside edge of the traveled way to the nearest tree or utility pole Equations (45) and (46) are illustrated in Figure 6. Figure 6. Factor for Distance from Traveled Way to Roadside Object Expressed as a Piecewise Linear Function

89 For an object on the left side of the road, the computed value of AFS1 should be used as AFS1-left in Equation (43). If there are no objects on the left side of the road, AFS1-left should be set equal to 0.0. For an object on the right side of the road, the computed value of AFS1 should be used as AFS1- right in Equation (44). If there are no objects on the right side of the road, AFS1-right should be set equal to 0.0. Most Severe Roadside Object Type AFS2-left represents the relative crash severity associated with the object type for the most severe roadside object on the left side of the road that could be struck by a motor vehicle running off the road. A severe object is any object that could result in an injury to an occupant of a vehicle that strikes the object. The object whose type is coded here should be the same object whose distance from the traveled way was used to determine AFS1-left. AFS2-right is based on the object type of the most severe roadside object on the right side of the road that could be struck by a motor vehicle running off the road. The object whose type is coded here should be the same object whose distance from the traveled way was used for AFS1-right. For analysis of both trees and utility poles, the values of both AFS2-left and AFS2-right should be 25. If no roadside objects are present on a particular side of the road, then AFS2 for that side of the road should be set equal to 0.0. The general rationale for these adjustment factors is presented in iRAP Road Attribute Adjustment Factors: Roadside Severity - Distance (2013o). The rationale for the specific values of AFS2-left and AFS2-right is explained in Section A.4.2 in Appendix A. Paved Shoulder Width Motor vehicles are more likely to lose control, run off the road, and experience a severe crash on roads without paved shoulders than on roads with paved shoulders. As the width of a paved shoulder increases, the probability of a severe crash decreases. The crash severity adjustment factors for paved shoulder width for motor vehicles running off the road are shown in Table 50. The values of the crash severity adjustment factors for the left and right sides of the road are identical. The rationale for the adjustment factor values is presented in iRAP Road Attribute Adjustment Factors: Paved Shoulder Width (2013h). The paved shoulder width factors were based on work by Turner et al. (2009). Table 50. Crash Severity Adjustment Factors for Paved Shoulder Width (iRAP 2013h) Paved shoulder width on the left or right side of the road Adjustment factor for motor vehicles of all types running off the right or left side road (AFS3-left or AFS3-right) ≥ 7.9 ft 0.7 3 ft to <7.9 ft 0.83 > 0 ft to <3 ft 0.95 None 1.00

90 7.6 Calibration Procedure The recommended values of the CF in Equations (28) and (29), presented above in Section 7.2, are 1.02 for trees and 0.80 for utility poles. These values are recommended for use as defaults for application of the RAP model in the U.S. when no better local data are available. Individual agencies are encouraged, when practical, to calibrate the model using local data for their jurisdiction. This section presents a procedure that may be used for developing calibration factors with local data. • Step 1—Identify a set of roadways from among those within the local jurisdiction of interest to be used for calibration purposes. These roadways should include sites for all roadway type(s) of interest. Identification of sites representing at least 200 centerline-mi of road is recommended. The selected sites should have a substantial number of trees and utility poles within 40 ft of the roadway traveled way. • Step 2—Assemble roadway data for the identified sites including: - lane width - horizontal curve location and radii - advance visibility of curve - grade - presence or absence of shoulder rumble strips - delineation - road surface condition - skid resistance (if available) - paved shoulder width Some or all of these data may be available in existing highway agency databases. Other data will need to be determined from review of aerial and street-level photographs or in the field. • Step 3—Assemble roadside data for the identified sites including: - locations of roadside trees and utility poles located within 40 ft of the roadway traveled way. Trees should be classified as individual trees or tree groups. - distance of each individual tree, tree group, or individual utility pole from the roadway traveled way. • Step 4—From existing highway agency records, assemble data for average annual daily traffic volumes (AADTs) for the identified sites and obtain crash history data for all tree- and utility-pole-related crashes within a recent multiyear period (typically 5 years). • Step 5—Sum the number of tree and utility pole crashes from the crash history dataset obtained in Step 4. These sums represent the observed crash history for the identified sites. • Step 6—Apply the modified RAP model presented in this chapter to each individual site to determine the predicted annual frequencies for tree- and utility-pole-related crashes. • Step 7—Compute CFs separately for tree- and utility-pole-related crashes using the following equation:

91 𝐶𝐹 = × (47) • Step 8—Use the values of CF obtained for tree- and utility-pole-related crashes in applying Equations (28) and (29) within the jurisdiction of interest. 7.7 Computational Examples This section presents several computational examples of applying the modified RAP model. The examples include: • Example #1 – an individual tree on the right roadside of a rural two-lane highway • Example #2 – a tree group on the right roadside of a rural four-lane undivided highway • Example #3 – an individual utility pole on the right roadside of a rural four-lane divided nonfreeway • Example #4 – numerous individual trees, utility poles, and tree groups on both sides of a rural two-lane highway Example #1 The Site/Facility A rural two-lane undivided highway with an individual tree on the right roadside. The Question How many tree-related crashes and personal injuries per year are predicted to occur on this facility in a one-year period? The Facts The conditions present on this facility are provided in the following list: • 2,000 veh/day in both directions of travel combined • 10.5-ft lanes with 2-ft paved shoulders • 55-mph posted speed limit with 60-mph design speed • On a horizontal curve with a radius of 2,000 ft with no advance signing and a vertical crest that limits sight distance to the curve • 3-percent grade • No shoulder rumble strips • Faded longitudinal pavement markings and no roadside delineators • Good road surface condition • Medium pavement skid resistance • One tree on the right roadside located 6 ft from the outside edge of the traveled way

92 • No tree groups or utility poles on the right roadside • No individual trees, tree groups, or utility poles on the left roadside • No local calibration factors available Data Used in Calculations The following parameter values are applicable to this example: • DSF = 0.205 representing a 60-mph design speed • EFI = 0.448 representing an AADT equal to 2,000 veh/day on a rural two-lane undivided highway • MT = 1.00 representing an undivided highway which, by definition, has no median and to which the parameter value for a traversable median applies The following adjustment factor values are applicable to this example: • AFL1 = 1.20 representing 10.5-ft lanes • AFL2 = 1.81 representing moderate horizontal curvature • AFL3 = 1.25 representing limited advance visibility of curve • AFL4 = 1.00 representing 3-percent grade • AFL5 = 1.25 representing shoulder rumble strips not present • AFL6 = 1.20 representing limited delineation • AFL7 = 1.00 representing good road surface condition • AFL8 = 1.41 representing medium pavement skid resistance • AFS1-left = 0.00 representing no roadside objects on the left side of the road • AFS2-left = 0.00 representing no roadside objects on the left side of the road • AFS3-left = 0.95 representing a 2-ft paved shoulder width • AFS1-right = 0.86 representing a tree 6 ft outside of the roadway traveled way on the right side of the road • AFS2-right = 25 representing a tree on the right side of the road • AFS3-right = 0.95 representing a 2-ft paved shoulder width The extent of roadside fixed objects is represented as: • Cindiv-left = 0 representing no individual trees on the left side of the road • Cindiv-right = 1 representing one individual tree on the right side of the road • Cgroup-left = 0 representing no tree groups on the left side of the road • Cgroup-right = 0 representing no tree groups on the right side of the road

93 Estimation of Total Annual Fatal-and-Injury Crashes Through applying Equations (42), (43) and (44), the values of the likelihood and severity factors for this example are determined as: 𝐿𝑖𝑘𝑒𝑙𝑖ℎ𝑜𝑜𝑑 = 1.20 × 1.81 × 1.25 × 1.00 × 1.25 × 1.20 × 1.00 × 1.41 = 5.74 𝑆𝑒𝑣𝑒𝑟𝑖𝑡𝑦 = 0.00 × 0.00 × 0.95 = 0.00 𝑆𝑒𝑣𝑒𝑟𝑖𝑡𝑦 = 0.86 × 25 × 0.95 = 20.43 Through applying Equations (40) and (41) the RSS scores for this example are determined as: 𝑅𝑆𝑆 = 5.74 × 0.00 × 0.205 × 0.448 × 1.00 = 0.00 𝑅𝑆𝑆 = 5.74 × 20.43 × 0.205 × 0.448 = 10.77 Through applying Equations (27) through (31) the predicted number of total annual fatal-and- injury crashes involving roadside trees is estimated as: 𝐶 = 0 + 0.0097 × 0 = 0.00 𝐶 = 1 + 0.0097 × 0 = 1.00 𝑁 = 0.00 × (2000) . × 1.02 × 36510 × 0.00 = 0.00 𝑁 = 10.77 × (2000) . × 1.02 × 36510 × 1.00 = 0.0101 𝑁 = 0.00 + 0.0101 = 0.0101 Estimation of Annual Crashes by Crash Severity Level Through applying Equations (32) through (35) the predicted number of annual crashes by crash severity level involving roadside trees is estimated as: 𝑁 = 0.0101 × 0.078 = 0.0008 𝑁 = 0.0101 × 0.177 = 0.0018 𝑁 = 0.0101 × 0.376 = 0.0038 𝑁 = 0.0101 × 0.369 = 0.0037 Estimation of Annual Persons Injured by Crash Severity Level Through applying Equations (36) through (39) the predicted number of annual crashes by crash severity level involving roadside trees is estimated as: 𝑁 = 0.0008 × 1.08 = 0.0008 𝑁 = 0.0008 × 0.04 + 0.0018 × 1.06 = 0.0019 𝑁 = 0.0008 × 0.10 + 0.0018 × 0.14 + 0.0038 × 1.15 = 0.0047

94 𝑁 = 0.0008 × 0.15 + 0.0018 × 0.20 + 0.0038 × 0.15 + 0.0037 × 1.33 = 0.0060 Summary of Results Table 51 summarizes the crash predictions for Example #1. The table shows that the single roadside tree in Example #1, located 6 ft from the outside edge of the traveled way on a rural two-lane undivided highway, is estimated to experience 0.0101 fatal-and-injury crashes per year or approximately one crash every 99 years. A total of 0.0134 injured persons per year are estimated, equivalent to an average of one injured person every 75 years. Table 51. Summary of Crash Predictions for Example #1 PREDICTED TOTAL FATAL-AND-INJURY CRASHES PER YEAR Total fatal-and-injury crashes per year 0.0101 PREDICTED CRASHES PER YEAR BY CRASH SEVERITY LEVEL Fatal crashes per year 0.0008 Incapacitating injury crashes per year 0.0018 Nonincapacitating injury crashes per year 0.0038 Possible injury crashes per year 0.0037 PREDICTED PERSONS INJURED PER YEAR BY CRASH SEVERITY LEVEL Persons per year with fatal injuries 0.0008 Persons per year with incapacitating injuries 0.0019 Persons per year with nonincapacitating injuries 0.0047 Persons per year with possible injuries 0.0060 Total persons injured 0.0134 Example #2 The Site/Facility A rural four-lane undivided highway with a tree group for an extended length on the right roadside. The Question How many tree-related crashes and personal injuries per year are predicted to occur on this facility in a one-year period? The Facts The conditions present on this facility are provided in the following list: • 4,000 veh/day in both directions of travel combined • 11-ft lanes with 4-ft paved shoulders • 60-mph posted speed limit with 65-mph design speed • Tangent alignment • 2-percent grade

95 • No shoulder rumble strips • Longitudinal pavement markings present and in good condition • Good road surface condition • High pavement skid resistance • One tree group 0.5 miles in length on the right roadside located 12 ft from the outside edge of the traveled way • No individual trees or utility poles on the right roadside • No individual trees, tree groups, or utility poles on the left roadside • No local calibration factors available Data Used in Calculations The following parameter values are applicable to this example: • DSF = 0.267 representing a 65-mph design speed • EFI = 0.370 representing an AADT equal to 4,000 veh/day on a rural four-lane undivided highway • MT = 1.00 representing an undivided highway which, by definition, has no median and to which the parameter value for a traversable median applies The following adjustment factor values are applicable to this example: • AFL1 = 1.00 representing 11-ft lanes • AFL2 = 1.00 representing tangent alignment • AFL3 = 1.00 representing advance visibility of curve not applicable • AFL4 = 1.00 representing 2-percent grade • AFL5 = 1.25 representing shoulder rumble strips not present • AFL6 = 1.00 representing substantial delineation • AFL7 = 1.00 representing good road surface condition • AFL8 = 1.00 representing high pavement skid resistance • AFS1-left = 0.00 representing no roadside objects on the left side of the road • AFS2-left = 0.00 representing no roadside objects on the left side of the road • AFS3-left = 0.83 representing a 4-ft paved shoulder width • AFS1-right = 0.674 representing roadside trees 12 ft outside of the traveled way on the right side of the road • AFS2-right = 25 representing trees on the right side of the road • AFS3-right = 0.83 representing a 4-ft paved shoulder width The extent of roadside fixed objects is represented as:

96 • Cindiv-left = 0 representing no individual trees on the left side of the road • Cindiv-right = 0 representing no individual trees on the left side of the road • Cgroup-left = 0 representing no tree groups on the left side of the road • Cgroup-right = 2,640 ft representing a tree group 0.5 mi in length on the right side of the road Estimation of Total Annual Fatal-and-Injury Crashes Through applying Equations (42), (43) and (44), the values of the likelihood and severity factors for this example are determined as: 𝐿𝑖𝑘𝑒𝑙𝑖ℎ𝑜𝑜𝑑 = 1.00 × 1.00 × 1.00 × 1.00 × 1.25 × 1.00 × 1.00 × 1.00 = 1.25 𝑆𝑒𝑣𝑒𝑟𝑖𝑡𝑦 = 0.00 × 0.00 × 0.83 = 0.00 𝑆𝑒𝑣𝑒𝑟𝑖𝑡𝑦 = 0.674 × 25 × 0.83 = 13.99 Through applying Equations (40) and (41) the RSS scores for this example are determined as: 𝑅𝑆𝑆 = 1.25 × 0.00 × 0.267 × 0.370 × 1.00 = 0.00 𝑅𝑆𝑆 = 1.25 × 13.99 × 0.267 × 0.370 = 1.73 Through applying Equations (27) through (31) the predicted number of total annual fatal-and- injury crashes involving roadside trees is estimated as: 𝐶 = 0 + 0.0097 × 0 = 0.00 𝐶 = 0 + 0.0097 × 2640 = 25.61 𝑁 = 0.00 × (4000) . × 1.02 × 36510 × 0.00 = 0.00 𝑁 = 1.73 × (4000) . × 1.02 × 36510 × 25.61 = 0.0845 𝑁 = 0.00 + 0.0845 = 0.0845 Estimation of Annual Crashes by Crash Severity Level Through applying Equations (32) through (35) the predicted number of annual crashes by crash severity level involving roadside trees is estimated as: 𝑁 = 0.0845 × 0.078 = 0.0066 𝑁 = 0.0845 × 0.177 = 0.0150 𝑁 = 0.0845 × 0.376 = 0.0318 𝑁 = 0.0845 × 0.369 = 0.0312

97 Estimation of Annual Persons Injured by Crash Severity Level Through applying Equations (36) through (39) the predicted number of annual crashes by crash severity level involving roadside trees is estimated as: 𝑁 = 0.0066 × 1.08 = 0.0071 𝑁 = 0.0066 × 0.04 + 0.0150 × 1.06 = 0.0161 𝑁 = 0.0066 × 0.10 + 0.0150 × 0.14 + 0.0318 × 1.15 = 0.0393 𝑁 = 0.0066 × 0.15 + 0.0150 × 0.20 + 0.0318 × 0.15 + 0.0312 × 1.33 = 0.0502 Summary of Results Table 52 summarizes the crash predictions for Example #2. The table shows that the roadside tree group in Example #2, located 12 ft from the outside edge of the traveled way on a rural four- lane undivided highway, is estimated to experience 0.0845 fatal-and-injury crashes per year or approximately one crash every 12 years. A total of 0.1127 injured persons per year are estimated, equivalent to an average of one injured person every 9 years. Table 52. Summary of Crash Predictions for Example #2 PREDICTED TOTAL FATAL-AND-INJURY CRASHES PER YEAR Total fatal-and-injury crashes per year 0.0845 PREDICTED CRASHES PER YEAR BY CRASH SEVERITY LEVEL Fatal crashes per year 0.0066 Incapacitating injury crashes per year 0.0150 Nonincapacitating injury crashes per year 0.0318 Possible injury crashes per year 0.0312 PREDICTED PERSONS INJURED PER YEAR BY CRASH SEVERITY LEVEL Persons per year with fatal injuries 0.0071 Persons per year with incapacitating injuries 0.0161 Persons per year with nonincapacitating injuries 0.0393 Persons per year with possible injuries 0.0502 Total persons injured 0.1127 Example #3 The Site/Facility A rural four-lane divided nonfreeway with an individual utility pole on the right roadside. The Question How many utility-pole-related crashes and personal injuries per year are predicted to occur on this facility in a one-year period?

98 The Facts The conditions present on this facility are provided in the following list: • 16,000 veh/day in both directions of travel combined • 12-ft lanes with 6-ft paved shoulders • 65-mph posted speed limit with 70-mph design speed • On a horizontal curve with a radius of 3,000 ft with advance signing provided and no limitation that limits sight distance to the curve • 1-percent grade • 20-ft median with continuous median barrier • Shoulder rumble strips present • Longitudinal pavement markings and roadside delineators present and in good condition • Good road surface condition • No available data on pavement skid resistance • One utility pole on the right roadside located 15 ft from the outside edge of the traveled way • No individual trees or tree groups on the right roadside • No individual trees, tree groups, or utility poles on the left roadside • Local calibration factor determined by the highway agency to be 0.95 Data Used in Calculations The following parameter values are applicable to this example: • DSF = 0.339 representing a 70-mph design speed • EFI = 0.500 representing an AADT equal to 8,000 veh/day on a rural four-lane divided nonfreeway • MT = 0.00 representing a divided highway with a nontraversable median The following adjustment factor values are applicable to this example: • AFL1 = 1.00 representing 12-ft lanes • AFL2 = 1.00 representing gentle horizontal curvature • AFL3 = 1.00 representing substantial advance visibility of curve • AFL4 = 1.00 representing 1-percent grade • AFL5 = 1.00 representing shoulder rumble strips present • AFL6 = 1.00 representing substantial delineation • AFL7 = 1.00 representing good road surface condition

99 • AFL8 = 1.00 representing pavement skid resistance data not available • AFS1-left = 0.00 representing no roadside objects on the left side of the road • AFS2-left = 0.00 representing no roadside objects on the left side of the road • AFS3-left = 0.83 representing a 6-ft paved shoulder width • AFS1-right = 0.581 representing a utility pole 15 ft outside of the roadway traveled way on the right side of the road • AFS2-right = 25 representing a utility pole on the right side of the road • AFS3-right = 0.83 representing a 6-ft paved shoulder width The extent of roadside fixed objects is represented as: • Cindiv-left = 0 representing no individual utility poles on the left side of the road • Cindiv-right = 1 representing one individual utility pole on the right side of the road • Cgroup-left = 0 representing tree groups on the left side of the road not applicable • Cgroup-right = 0 representing tree groups on the right side of the road not applicable Estimation of Total Annual Fatal-and-Injury Crashes Through applying Equations (42), (43) and (44), the values of the likelihood and severity factors for this example are determined as: 𝐿𝑖𝑘𝑒𝑙𝑖ℎ𝑜𝑜𝑑 = 1.00 × 1.00 × 1.00 × 1.00 × 1.00 × 1.00 × 1.00 × 1.00 = 1.00 𝑆𝑒𝑣𝑒𝑟𝑖𝑡𝑦 = 0.00 × 0.00 × 0.83 = 0.00 𝑆𝑒𝑣𝑒𝑟𝑖𝑡𝑦 = 0.581 × 25 × 0.83 = 12.06 Through applying Equations (40) and (41) the RSS scores for this example are determined as: 𝑅𝑆𝑆 = 1.00 × 0.00 × 0.339 × 0.500 × 0.00 = 0.00 𝑅𝑆𝑆 = 1.00 × 12.06 × 0.339 × 0.500 = 2.04 Through applying Equations (27) through (31) the predicted number of total annual fatal-and- injury crashes involving roadside trees is estimated as: 𝐶 = 0 + 0.0097 × 0 = 0.00 𝐶 = 1 + 0.0097 × 0 = 1.00 𝑁 = 0.00 × (160002 ) . × 0.95 × 36510 × 0.00 = 0.00 𝑁 = 2.04 × (160002 ) . × 0.95 × 36510 × 1.00 = 0.0074 𝑁 = 0.00 + 0.0074 = 0.0074

100 Estimation of Annual Crashes by Crash Severity Level Through applying Equations (32) through (35) the predicted number of annual crashes by crash severity level involving roadside trees is estimated as: 𝑁 = 0.0074 × 0.020 = 0.0001 𝑁 = 0.0074 × 0.078 = 0.0006 𝑁 = 0.0074 × 0.407 = 0.0030 𝑁 = 0.0074 × 0.495 = 0.0037 Estimation of Annual Persons Injured by Crash Severity Level Through applying Equations (36) through (39) the predicted number of annual crashes by crash severity level involving roadside trees is estimated as: 𝑁 = 0.0001 × 1.02 = 0.0002 𝑁 = 0.0001 × 0.01 + 0.0006 × 1.04 = 0.0006 𝑁 = 0.0001 × 0.06 + 0.0006 × 0.29 + 0.0030 × 1.10 = 0.0035 𝑁 = 0.0001 × 0.02 + 0.0006 × 0.37 + 0.0030 × 0.11 + 0.0037 × 1.19 = 0.0049 Summary of Results Table 53 summarizes the crash predictions for Example #3. The table shows that the single roadside utility pole in Example #3, located 15 ft from the outside edge of the traveled way on a rural four-lane divided highway, is estimated to experience 0.0074 fatal-and-injury crashes per year or approximately one crash every 135 years. A total of 0.0092 injured persons per year are estimated, equivalent to an average of one injured person every 109 years. Table 53. Summary of Crash Predictions for Example #3 PREDICTED TOTAL FATAL-AND-INJURY CRASHES PER YEAR Total fatal-and-injury crashes per year 0.0074 PREDICTED CRASHES PER YEAR BY CRASH SEVERITY LEVEL Fatal crashes per year 0.0001 Incapacitating injury crashes per year 0.0006 Nonincapacitating injury crashes per year 0.0030 Possible injury crashes per year 0.0037 PREDICTED PERSONS INJURED PER YEAR BY CRASH SEVERITY LEVEL Persons per year with fatal injuries 0.0002 Persons per year with incapacitating injuries 0.0006 Persons per year with nonincapacitating injuries 0.0035 Persons per year with possible injuries 0.0049 Total persons injured 0.0092

101 Example #4 The Site/Facility An extended section of rural two-lane undivided highway with many trees and utility poles on both sides of the road. The Question How many tree- and utility-pole-related crashes and personal injuries per year are predicted to occur on this facility in a one-year period? The Facts The conditions present on this facility are provided in the following list: • 5,000 veh/day in both directions of travel combined • 12-ft lanes with 6-ft paved shoulders • 60-mph posted speed limit with 65-mph design speed • Tangent alignment • 2-percent grade • Shoulder rumble strips present • Longitudinal pavement markings and roadside delineators present and in good condition • Good road surface condition • High pavement skid resistance • 16 individual trees and three tree groups totaling 1.20-mi in lengths on the right roadside located 12 ft from the outside edge of the traveled way • 12 individual utility poles on the right roadside located 10 ft from the outside edge of the traveled way • 20 individual trees and two tree groups totaling 0.6-mi in lengths on the left roadside located 12 ft from the outside edge of the traveled way • No utility poles on the left roadside • No local calibration factors available Data Used in Calculations for Roadside Trees The following parameter values are applicable to this example: • DSF = 0.267 representing a 65-mph design speed • EFI = 0.422 representing an AADT equal to 5,000 veh/day on a rural two-lane undivided highway • MT = 1.00 representing an undivided highway which, by definition, has no median and to which the parameter value for a traversable median applies

102 The following adjustment factor values are applicable to this example: • AFL1 = 1.00 representing 12-ft lanes • AFL2 = 1.00 representing tangent alignment • AFL3 = 1.00 representing advance visibility of curve not applicable • AFL4 = 1.00 representing 2-percent grade • AFL5 = 1.00 representing shoulder rumble strips present • AFL6 = 1.00 representing substantial delineation • AFL7 = 1.00 representing good road surface condition • AFL8 = 1.00 representing high pavement skid resistance • AFS1-left = 0.674 representing trees 12 ft outside of the roadway on the left side of the road • AFS2-left = 25 representing trees on the left side of the road • AFS3-left = 0.83 representing a 6-ft paved shoulder width • AFS1-right = 0.624 representing trees 12 ft outside of the roadway on the right side of the road • AFS2-right = 25 representing trees on the right side of the road • AFS3-right = 0.83 representing a 6-ft paved shoulder width The extent of roadside fixed objects is represented as: • Cindiv-left = 20 representing individual trees on the left side of the road • Cindiv-right = 16 representing individual trees on the right side of the road • Cgroup-left = 3168 ft representing 0.6 mi of tree groups on the left side of the road • Cgroup-right = 6336 ft representing 1.2 mi of tree groups on the right side of the road Estimation of Total Annual Fatal-and-Injury Crashes for Roadside Trees Through applying Equations (42), (43) and (44), the values of the likelihood and severity factors for this example are determined as: 𝐿𝑖𝑘𝑒𝑙𝑖ℎ𝑜𝑜𝑑 = 1.00 × 1.00 × 1.00 × 1.00 × 1.00 × 1.00 × 1.00 × 1.00 = 1.00 𝑆𝑒𝑣𝑒𝑟𝑖𝑡𝑦 = 0.674 × 25 × 0.83 = 13.99 𝑆𝑒𝑣𝑒𝑟𝑖𝑡𝑦 = 0.674 × 25 × 0.83 = 13.99 Through applying Equations (40) and (41) the RSS scores for this example are determined as: 𝑅𝑆𝑆 = 1.00 × 13.99 × 0.267 × 0.422 × 1.00 = 1.58 𝑅𝑆𝑆 = 1.00 × 13.99 × 0.267 × 0.422 = 1.58 Through applying Equations (27) through (31) the predicted number of total annual fatal-and- injury crashes involving roadside trees is estimated as: 𝐶 = 20 + 0.0097 × 3168 = 50.73

103 𝐶 = 16 + 0.0097 × 6336 = 77.46 𝑁 = 1.58 × (5000) . × 1.02 × 36510 × 50.73 = 0.1921 𝑁 = 1.58 × (5000) . × 1.02 × 36510 × 77.46 = 0.2934 𝑁 = 0.1921 + 0.2934 = 0.4855 Estimation of Annual Crashes by Crash Severity Level for Roadside Trees Through applying Equations (32) through (35) the predicted number of annual crashes by crash severity level involving roadside trees is estimated as: 𝑁 = 0.4855 × 0.078 = 0.0379 𝑁 = 0.4855 × 0.177 = 0.0859 𝑁 = 0.4855 × 0.376 = 0.1825 𝑁 = 0.4855 × 0.369 = 0.1791 Estimation of Annual Persons Injured by Crash Severity Level for Roadside Trees Through applying Equations (36) through (39) the predicted number of annual crashes by crash severity level involving roadside trees is estimated as: 𝑁 = 0.0379 × 1.08 = 0.0409 𝑁 = 0.0379 × 0.04 + 0.0859 × 1.06 = 0.0926 𝑁 = 0.0379 × 0.10 + 0.0859 × 0.14 + 0.1825 × 1.15 = 0.2257 𝑁 = 0.0379 × 0.15 + 0.0859 × 0.20 + 0.1825 × 0.15 + 0.1791 × 1.33 = 0.2885 Data Used in Calculations for Roadside Utility Poles The following parameter values are applicable to this example: • DSF = 0.267 representing a 65-mph design speed • EFI = 0.422 representing an AADT equal to 5,000 veh/day on a rural two-lane undivided highway • MT = 1.00 representing an undivided highway which, by definition, has no median and to which the parameter value for a traversable median applies

104 The following adjustment factor values are applicable to this example: • AFL1 = 1.00 representing 12-ft lanes • AFL2 = 1.00 representing tangent alignment • AFL3 = 1.00 representing advance visibility of curve not applicable • AFL4 = 1.00 representing 2-percent grade • AFL5 = 1.00 representing shoulder rumble strips present • AFL6 = 1.00 representing substantial delineation • AFL7 = 1.00 representing good road surface condition • AFL8 = 1.00 representing high pavement skid resistance • AFS1-left = 0.00 representing no roadside objects on the left side of the road • AFS2-left = 0.00 representing no roadside objects on the left side of the road • AFS3-left = 0.83 representing a 6-ft paved shoulder width • AFS1-right = 0.736 representing utility poles 10 ft outside of the roadway traveled way on the right side of the road • AFS2-right = 25 representing utility poles on the right side of the road • AFS3-right = 0.83 representing a 6-ft paved shoulder width The extent of roadside fixed objects is represented as: • Cindiv-left = 0 representing no individual trees on the left side of the road • Cindiv-right = 1 representing one individual tree on the right side of the road • Cgroup-left = 0 representing no tree groups on the left side of the road • Cgroup-right = 0 representing no tree groups on the right side of the road Estimation of Total Annual Fatal-and-Injury Crashes for Utility Poles Through applying Equations (42), (43) and (44), the values of the likelihood and severity factors for this example are determined as: 𝐿𝑖𝑘𝑒𝑙𝑖ℎ𝑜𝑜𝑑 = 1.00 × 1.00 × 1.00 × 1.00 × 1.00 × 1.00 × 1.00 × 1.00 = 1.00 𝑆𝑒𝑣𝑒𝑟𝑖𝑡𝑦 = 0.674 × 25 × 0.83 = 13.99 𝑆𝑒𝑣𝑒𝑟𝑖𝑡𝑦 = 0.674 × 25 × 0.83 = 13.99 Through applying Equations (40) and (41) the RSS scores for this example are determined as: 𝑅𝑆𝑆 = 1.00 × 13.99 × 0.267 × 0.422 × 1.00 = 1.58 𝑅𝑆𝑆 = 1.00 × 13.99 × 0.267 × 0.422 = 1.58

105 Through applying Equations (27) through (31) the predicted number of total annual fatal-and- injury crashes involving roadside trees is estimated as: 𝐶 = 0 + 0.0097 × 0 = 0.00 𝐶 = 12 + 0.0097 × 0 = 12.00 𝑁 = 1.58 × (5000) . × 0.80 × 36510 × 0.00 = 0.00 𝑁 = 1.58 × (5000) . × 0.80 × 36510 × 12.00 = 0.0487 𝑁 = 0.00 + 0.0487 = 0.0487 Estimation of Annual Crashes by Crash Severity Level for Roadside Utility Poles Through applying Equations (32) through (35) the predicted number of annual crashes by crash severity level involving roadside trees is estimated as: 𝑁 = 0.0487 × 0.020 = 0.0010 𝑁 = 0.0487 × 0.078 = 0.0038 𝑁 = 0.0487 × 0.407 = 0.0198 𝑁 = 0.0487 × 0.495 = 0.0241 Estimation of Annual Persons Injured by Crash Severity Level for Roadside Utility Poles Through applying Equations (36) through (39) the predicted number of annual crashes by crash severity level involving roadside trees is estimated as: 𝑁 = 0.0010 × 1.02 = 0.0010 𝑁 = 0.0010 × 0.01 + 0.0038 × 1.04 = 0.0040 𝑁 = 0.0010 × 0.06 + 0.0038 × 0.29 + 0.0198 × 1.10 = 0.0229 𝑁 = 0.0010 × 0.02 + 0.0038 × 0.37 + 0.0198 × 0.11 + 0.0241 × 1.19 = 0.0323 Summary of Results Table 54 summarizes the crash predictions for Example #4. The table shows that the roadside trees and utility poles in Example #4 are estimated to experience a combined total of 0.535 fatal- and-injury crashes per year or approximately one crash every 1.9 years. A total of 0.709 injured persons per year are estimated, equivalent to an average of one injured person every 1.4 years.

106 Table 54. Summary of Crash Predictions for Example #4 Tree Crashes Utility Pole Crashes Combined PREDICTED TOTAL FATAL-AND-INJURY CRASHES PER YEAR Total fatal-and-injury crashes per year 0.486 0.049 0.535 PREDICTED CRASHES PER YEAR BY CRASH SEVERITY LEVEL Fatal crashes per year 0.038 0.001 0.039 Incapacitating injury crashes per year 0.086 0.004 0.090 Nonincapacitating injury crashes per year 0.183 0.020 0.203 Possible injury crashes per year 0.179 0.024 0.203 PREDICTED PERSONS INJURED PER YEAR BY CRASH SEVERITY LEVEL Persons per year with fatal injuries 0.041 0.001 0.042 Persons per year with incapacitating injuries 0.093 0.004 0.097 Persons per year with nonincapacitating injuries 0.226 0.023 0.249 Persons per year with possible injuries 0.289 0.032 0.321 Total persons injured 0.649 0.060 0.709