**Suggested Citation:**"Chapter 6 - Clear Zone Guideline Assistance Program." National Academies of Sciences, Engineering, and Medicine. 2024.

*Development of Clear Recovery Area Guidelines*. Washington, DC: The National Academies Press. doi: 10.17226/27593.

**Suggested Citation:**"Chapter 6 - Clear Zone Guideline Assistance Program." National Academies of Sciences, Engineering, and Medicine. 2024.

*Development of Clear Recovery Area Guidelines*. Washington, DC: The National Academies Press. doi: 10.17226/27593.

**Suggested Citation:**"Chapter 6 - Clear Zone Guideline Assistance Program." National Academies of Sciences, Engineering, and Medicine. 2024.

*Development of Clear Recovery Area Guidelines*. Washington, DC: The National Academies Press. doi: 10.17226/27593.

**Suggested Citation:**"Chapter 6 - Clear Zone Guideline Assistance Program." National Academies of Sciences, Engineering, and Medicine. 2024.

*Development of Clear Recovery Area Guidelines*. Washington, DC: The National Academies Press. doi: 10.17226/27593.

**Suggested Citation:**"Chapter 6 - Clear Zone Guideline Assistance Program." National Academies of Sciences, Engineering, and Medicine. 2024.

*Development of Clear Recovery Area Guidelines*. Washington, DC: The National Academies Press. doi: 10.17226/27593.

**Suggested Citation:**"Chapter 6 - Clear Zone Guideline Assistance Program." National Academies of Sciences, Engineering, and Medicine. 2024.

*Development of Clear Recovery Area Guidelines*. Washington, DC: The National Academies Press. doi: 10.17226/27593.

**Suggested Citation:**"Chapter 6 - Clear Zone Guideline Assistance Program." National Academies of Sciences, Engineering, and Medicine. 2024.

*Development of Clear Recovery Area Guidelines*. Washington, DC: The National Academies Press. doi: 10.17226/27593.

**Suggested Citation:**"Chapter 6 - Clear Zone Guideline Assistance Program." National Academies of Sciences, Engineering, and Medicine. 2024.

*Development of Clear Recovery Area Guidelines*. Washington, DC: The National Academies Press. doi: 10.17226/27593.

**Suggested Citation:**"Chapter 6 - Clear Zone Guideline Assistance Program." National Academies of Sciences, Engineering, and Medicine. 2024.

*Development of Clear Recovery Area Guidelines*. Washington, DC: The National Academies Press. doi: 10.17226/27593.

**Suggested Citation:**"Chapter 6 - Clear Zone Guideline Assistance Program." National Academies of Sciences, Engineering, and Medicine. 2024.

*Development of Clear Recovery Area Guidelines*. Washington, DC: The National Academies Press. doi: 10.17226/27593.

**Suggested Citation:**"Chapter 6 - Clear Zone Guideline Assistance Program." National Academies of Sciences, Engineering, and Medicine. 2024.

*Development of Clear Recovery Area Guidelines*. Washington, DC: The National Academies Press. doi: 10.17226/27593.

**Suggested Citation:**"Chapter 6 - Clear Zone Guideline Assistance Program." National Academies of Sciences, Engineering, and Medicine. 2024.

*Development of Clear Recovery Area Guidelines*. Washington, DC: The National Academies Press. doi: 10.17226/27593.

**Suggested Citation:**"Chapter 6 - Clear Zone Guideline Assistance Program." National Academies of Sciences, Engineering, and Medicine. 2024.

*Development of Clear Recovery Area Guidelines*. Washington, DC: The National Academies Press. doi: 10.17226/27593.

**Suggested Citation:**"Chapter 6 - Clear Zone Guideline Assistance Program." National Academies of Sciences, Engineering, and Medicine. 2024.

*Development of Clear Recovery Area Guidelines*. Washington, DC: The National Academies Press. doi: 10.17226/27593.

**Suggested Citation:**"Chapter 6 - Clear Zone Guideline Assistance Program." National Academies of Sciences, Engineering, and Medicine. 2024.

*Development of Clear Recovery Area Guidelines*. Washington, DC: The National Academies Press. doi: 10.17226/27593.

Below is the uncorrected machine-read text of this chapter, intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text of each book. Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.

66 C H A P T E R Â 6 The original research plan was to modify and use the updated Roadside Safety Analysis Pro- gram (RSAPv3) as the main analysis tool to conduct the risk analysis from which the clear zone guidelines would be developed (25). RSAP is an encroachment-probability-based model that follows an analysis approach that is structured into four modules: â¢ Encroachment Module, â¢ Crash Prediction Module, â¢ Severity Prediction Module, and â¢ Benefit-Cost Module. The analytical methodology uses a series of conditionally independent probabilities to repre- sent a roadside encroachment event. This includes the probability of an encroachment occur- ring, the conditional probability of a crash given a roadside encroachment has occurred, the probable severity of a crash if one occurs, and the expected crash risk or cost of the roadside design alternative that is being investigated. The following conditional probability model is used for each design alternative: ( )E CC ADT P Encr P Cr Encr P Sev Cr E CC SevN,M LN s s s: : : : :=` a a aj k k k where: E(CC)N,M = Expected annual crash cost on segment N for alternative M, ADT = Average daily traffic in vehicles/day, LN = Length of segment N in miles, P(Encr) = Probability that a vehicle will encroach on the segment, P(Cr|Encr) = Probability that a crash will occur given that an encroachment has occurred, P(Sevs|Cr) = Probability that a crash of severity s occurs given that a crash has occurred, and E(CCs|Sevs) = Expected cost of a crash of severity s. RSAPv3 is written as a series of Visual Basic for Applications (VBA) macros within a Microsoft Excel environment. Users can provide input data in the accessible worksheets, while macros conduct the analysesâ tasks in the background. Most of the data tables where the information is stored and used by the macros are in worksheets. Although changes and updates can be made to default values in the data tables, completely rewriting various aspects of the code to incorporate new crash prediction and severity prediction modules is more complicated. The researchers explored the possibility of adding a function into the RSAPv3 code to import data from outside the software and populate the data tables using the developed relationships from ChapterÂ 5. Another option that was explored was to bypass the crash prediction module, independently perform the crash prediction analysis using the newly developed encroachment models, and pass the needed crash probability information to the severity module. Clear Zone Guideline Assistance Program

Clear Zone Guideline Assistance Program 67Â Â However, after further analysis, the modification of RSAPv3 was considered inefficient for this project. Most of the RSAPv3 programming was being replaced by the new encroachment models derived from the computer simulation data. It was, therefore, more straightforward to use the same programming language and architecture used to develop the encroachment models for the overall risk analysis methodology. A new risk-based analysis tool referred to as the Clear Zone Guideline Assistant Program (CZ-GAP) was developed to assist with the clear zone guideline development process. Details of CZ-GAP are provided in the sections below. Framework CZ-GAP is built in R, a programming language known for statistical computing and graphics. The encroachment models described in ChapterÂ 5 form the basis of the analysis modules. The analysis modules include 1. Crash Probability Module, 2. Severity Prediction Module, and 3. Risk Determination Module. The variable input data includes the selected roadway and roadside design variables. These include facility type, posted speed category, horizontal curvature, vertical grade, shoulder width, foreslope ratio, foreslope width, ditch bottom width, backslope ratio, backslope width, and clear zone distance, each having its specific range. This data is used in all the models as common variables.Â For each design scenario, the models are fed with this data, and the probability predictions are output. Finally, the probability outputs are transferred to the Severity Prediction Module where the overall risk of a serious injury or a fatal crash for the design configuration is calculated. Crash Probability The Crash Probability Model computes the probability of an encroaching vehicle impacting a hazard at the clear zone edge. This module was programmed to predict the probability of reach- ing the clear zone and the probability of hitting the hazards (i.e., trees) at the clear zone edge. It consists of three models: the lateral distance model, the longitudinal distance model, and the impact angle model. The probability of reaching a selected lateral distance or clear zone is schematically shown in FigureÂ 39. The lateral distance model is used to determine the probability of each vehicle type reaching the prescribed distance based on the design characteristics of the roadway seg- ment (common variables). The probability obtained for each vehicle is multiplied by the vehicleâs weight factor and summed to arrive at the total probability of reaching the lateral distance of interest for a particular facility type (2U or 4D). If an encroaching vehicle reaches the clear zone distance of interest, the next step in the analy- sis tool is to calculate the probability of impact with an obstacle at the clear zone edge. The obstacles are defined by a line of trees at a specified spacing, S. Different tree spacings are used to represent a range of hazard levels. The wider the spacing, the lower the probability of impact with a tree and vice-versa. When a vehicle departs the roadway at a specific location, the encroachment conditions and roadside design configuration will influence its trajectory. For a given terrain configuration,

68 Development of Clear Recovery Area Guidelines the different encroachment conditions (vehicle type, encroachment speed and angle, and driver input) define different trajectories. At a given lateral offset or clear zone edge, these multiple trajectories create a longitudinal distance distribution as illustrated in FigureÂ 40. This distribution defines the probability of a vehicle reaching a certain longitudinal distance for a prescribed lateral offset distance. The longitudinal distance distributions are biased toward the point of departure and have a longer tail on the downstream side. These distributions predict the probability of the encroaching vehicle crossing the clear zone edge at a given longitudinal distance. FigureÂ 39. Clear zone probability model. FigureÂ 40. Illustration of longitudinal distance distribution for vehicle crossing a prescribed clear zone edge.

Clear Zone Guideline Assistance Program 69Â Â FigureÂ 41 shows a mixed distribution for one design scenario at a given lateral offset dis- tance. The distribution provides longitudinal distance versus probability density. The mode (peak) of the distribution is indicated by the vertical line. The hazards at the clear zone edge, represented by a line of trees at a prescribed spacing, are mapped onto the longitudinal distribution. The process of computing the crash probability for a given facility type, design scenario, and clear zone distance is schematically illustrated in FigureÂ 42. First, the relevant longitudinal distri- bution is determined based on the design variables, and its mode is established. Next, an obstacle (tree) is aligned with the mode of the distribution, and other obstacles (trees) are then defined to the left and right of the mode based on the prescribed obstacle spacing. Pr ob ab ilit y D en si ty FigureÂ 41. Typical longitudinal distance distribution for a defined design configuration and lateral offset distance. FigureÂ 42. Illustration of impact probability model.

70 Development of Clear Recovery Area Guidelines The diameter of the trees and the distance between them are assigned as variables in the program. The probability of impact with each obstacle that intersects the longitudinal distribution is calculated as the area under the distribution with the width of the area equal to the vehicle width, W. Note that the calculated probabilities at this point relate to a single point of departure from the roadway. In reality, the vehicle has an equal likelihood of departing the roadway anywhere along its length, provided the characteristics of the roadway segment are consistent. What is desired for the risk analysis is an average probability of striking a particular obstacle (tree) for the roadway segment. So, the next step is to iterate the point of departure from the roadway. The calculation is cycled for 10 points of departure in increments of S/10, where S is the obstacle (tree) spacing. This per- mits calculating an average risk for multiple points of departure. At each point of departure, the probability of impacting obstacles (trees) that overlap the longitudinal distance distribution is determined. Note that because the trees are modeled as a continuous line hazard, the probability of impact becomes cyclical as the point of departure is iterated along the roadway segment. In other words, when the point of departure has moved a distance equal to the spacing of the trees, the next tree in the line of trees will now be at the mode of the distribution, which is the same as the starting point of the analysis. This concept is illustrated in FigureÂ 43. The leftmost image in FigureÂ 43 shows an obstacle (tree) placed at the mode of the distribution to define the initial point of departure, with other trees equally spaced upstream and downstream from this point. The longitudinal distance distribution is used to calculate the impact probability for each tree that falls within the distribution. The image in the middle shows a downstream iteration at a point of departure equal to half the tree spacing. A different probability of impact is calculated for each tree that overlaps the distribution. In the rightmost image, another itera- tion of the departure point equal to half the tree spacing has placed the next obstacle (tree) at the mode of the distribution again. The impact probabilities for the trees at this point are the same as the initial probabilities calculated for the leftmost image. The average probability of hitting a particular obstacle (tree) is taken as the summation of the probabilities at each departure point divided by the number of departure points (iterations). Mode Mode Mode FigureÂ 43. Iteration of point of departure for calculation of average impact probability.

Clear Zone Guideline Assistance Program 71Â Â FigureÂ 44 presents an example of the point of departure (POD) cycling relative to the obstacles (trees) at the clear zone edge. It can be seen in this example that as the longitudinal distance of the tree (represented by the blue curve) increases from the POD, the effective width around the tree (indicated by the hashed red lines) increases. Also, the area under the blue curve indicates that only a few trees (roughly, from the fourth tree through the tenth tree, counting from the POD) have a probability of being impacted. It can also be seen that with each additional point of departure, the tree positions are slightly shifted toward the left relative to the longitudinal dis- tance distribution, and that for POD 11 the position of the trees and their effective areas under the curve is equivalent to the positions from POD 1. Thus, the probabilities of hitting trees begins to repeat after 10 PODs. The calculations of the crash probability involve the estimation of the distributions of longitu- dinal distance reached at a given lateral offset (i.e., the clear zone under evaluation). Because the estimated distribution is expressed as a probability density function, the area under that curve for a range of longitudinal distance values represents the probability of a trajectory reaching the clear zone within that range of longitudinal distances. The final element of the crash probability process is determining the range of probable vehicle exposure for a given fixed object at the clear FigureÂ 44. POD cycling to calculate cumulative impact probability for each obstacle (tree).

72 Development of Clear Recovery Area Guidelines zone line. This exposure provides a projection or envelope that is mapped onto the longitudinal distance distribution to determine the probability of impact with a given tree at the clear zone line. After further analysis, the research team determined the need to modify the initially assumed profile of vehicle exposure to the risk of hitting a tree in a line of trees. Initially, the exposure pro- file was determined based on the assumption of a tracking vehicle approaching the fixed object, as shown on the left side of FigureÂ 45. However, some departures are not necessarily expected to arrive at the clear zone line while tracking. Therefore, the team decided to generalize the profile of vehicle exposure to represent the average expected impact angle of the vehicle CG trajectory with respect to the line of hazards, as shown on the right side of FigureÂ 45. The orange dot in the figure represents the hazard, e.g., a tree. For the non-tracking condition, it can be shown that the adjusted profile is governed by the relationship given in Eq. 1 involving the width (W) and length (L) of the vehicle as well as the yaw or sideslip angle with respect to the path of the vehicle. . . cos sinAdjusted Profile Width W Ltrajectory # #i i= + (1) where: Î¸ = slip (sliding) angle relative to the CG trajectory of the vehicle. The research team reviewed the NCHRP Web-Only Document 341 database to determine the mean value of Adjusted.Profile.Width given the data provides sufficient information to determine the Î¸ values expected from actual crashes (3). The average vehicle design dimen- sions for the vehicle models simulated in this project are 6.19Â ft for width (W) and 15.83Â ft for length (L). From this analysis, the average adjusted profile width was found to be 1.35 times the width of the vehicle. After further discussion, the research team agreed on the need to also introduce some overlap with the fixed object to ensure that the adjusted profile width results in a significant crash with potential for severe outcomes, as opposed to a grazing or minimal impact. The amount of overlap was agreed to be 2.4 times the width of the designâs fixed object (1Â ft diameter tree), as shown on Tracking Non-Tracking FigureÂ 45. Comparison of vehicle exposure to hazard for tracking (left) and non-tracking (right) conditions.

Clear Zone Guideline Assistance Program 73Â Â the right side of FigureÂ 45. erefore, for this project, the adjusted prole width relative to the trajectory was set as given in Eq. 2: . .. . W DAdjusted Profile Width 1 35 2 4trajectory # #= - (2) where: D = Diameter of a tree. Furthermore, the research team determined that an additional adjustment was needed in the calculations to account for the angle of the trajectory at the point of impact with respect to the line of xed objects under consideration, as shown in FigureÂ 46. e adjusted prole width was projected over the line of trees that is assumed to be parallel with the road. is quantity was considered as the eective exposure width along the tree line (E.Wtreeline). As shown for the two scenarios, a narrower angle of impact (scenario on the le) will result in a longer projection over the tree line, compared to a wider angle of impact (scenario on the right). It can be shown that this relationship between the adjusted prole width and the angle of impact is governed by Eq. 3. . . . sin Eff W Adjusted Profile Width treeline trajectory z = (3) where: Ï = impact angle. e research team again consulted the NCHRP Web-Only Document 341 data to get a sense of the impact of this adjustment on the calculations. e average value of the impact angle, Ï, in that dataset was found to be 13.01Â degrees (including the sampling weights in that dataset). As shown in Eq. 4, the adjustment results in an eective exposure width of 26.46Â , which is a signicant value compared to the vehicle dimensions. . . . . . . . . sinsin Eff W Adjusted Profile Width 13 0113 01 1 35 2 4 26 46 W D fttreeline trajectory = = - = c c (4) S Exposure 2 at Tree line Î¦ Average angle from NCHRP 17â43 dataset: 13.01 degrees Î¦ Î¦ Exposure 1 at Tree line Î¦ FigureÂ 46. Effective exposure width based on vehicle trajectory angle.

74 Development of Clear Recovery Area Guidelines The research team performed a small sensitivity analysis to explore how the separation between trees (closely tied to the tree density in the tree line) relates to the maximum impact angle that would ensure an impact with one tree [i.e., the maximum angle for which P(hit a tree)=1.0]. There- fore, in Eq. 5 and Eq. 6, the angle of impact makes the resulting Eff.Wtreeline equal to S, the obstacle spacing. . . . sin Eff W Adjusted Profile Width Streeline trajectory z = = (5) . . . . sin sin S Adjusted Profile Width S W D1 35 2 4trajectory 11z = = - - - J L KK J L KK N P OO N P OO (6) TableÂ 47 shows the critical impact angle for different values of obstacle (tree) spacing, S. It is not surprising that as the separation between trees increases, the maximum angle that ensures an impact decreases. For example, with trees spaced every 30Â ft, any trajectory arriving at the line of trees at an angle of 11.45Â degrees or less would be certain to result in a tree impact. On the other extreme, for a line of trees spaced every 150Â ft, only trajectories arriving at the tree line at an angle of 2.28Â degrees or less would be certain to result in an impact. The impact angle model described in ChapterÂ 5 was incorporated into the crash probability analysis procedure. The model was integrated into the CZ-GAP analysis tool such that it per- mits the selection of an impact angle percentile for use in the risk analysis. For purposes of this project, the mean impact angle from the modeled impact angle distribution corresponding to a given lateral and longitudinal distance was used. The impact angle model is used in conjunction with the lateral and longitudinal distance models to determine the probability of hitting an object along the clear zone edge following the methodology described above. This information is passed to the Risk Determination Module where it is used as part of the computation of the probability of a serious injury or fatal crash for a given design condition at a prescribed clear zone distance and defined obstacle spacing at the clear zone edge. Rollover Probability The rollover probability for the different design vehicles was programmed in two separate functions by facility type (i.e., 2U and 4D). In each function, the rollover probability for each vehicle type is calculated and then multiplied by their representative weights. The result is the sum of vehicle model predictions and a combined rollover probability for a given design configu- ration at a given lateral offset distance. This architecture is shown in FigureÂ 47. This information is passed to the Risk Determination Module where it can be used as part of the computation of the overall probability of a serious injury or fatal crash for a given design condition at a pre- scribed lateral offset (clear zone) distance. Severity Prediction The Impact Speed Models described in ChapterÂ 5 were incorporated into the CZ-GAP analysis tool to calculate the mean speed of a vehicle at the lateral clear zone distance of interest and for the longitudinal distance associated with a given obstacle (tree) at the clear zone edge. In other words, each obstacle location defined by a prescribed lateral and longitudinal distance will have an associated mean impact speed defined by the Impact Speed Models. S (ft) Critical Impact Angle(degrees) 30 11.45 60 5.70 100 3.41 150 2.28 TableÂ 47. Critical vehicle trajectory angle for different obstacle spacings.

Clear Zone Guideline Assistance Program 75Â Â The design (common) variables are used to fit the impact speed regression models for a given facility type, roadway and roadside terrain configuration, lateral clear zone distance, and longitudi- nal hazard location. The mean and standard deviation are then extracted from the models for each vehicle type. The final mean impact speed for a given hazard is the average of the mean impact speed for each vehicle multiplied by its representative weight factor. This process is schematically illustrated in FigureÂ 48. Development of Impact Speed-Severity Relationship for Fixed Objects The Severity Prediction Module calculates the risk of a fatal or severe injury crash [P(K+A)] by using the mean speed from the Impact Speed Model as the impact speed with a given obsta- cle (tree). The Severity Prediction Module then determines the P(K+A) crash injury risk for each hazard using a fixed-object relationship between impact speed and injury probability. The P(K+A) tree crash risk for each obstacle is then multiplied by the outcome probabilities from the Crash Probability Module to generate a weighted P(K+A) tree crash risk that is summed over the number of hazards. The research team used the crash database from NCHRP Web-Only Document 341 to deter- mine the relationship between impact speed and injury severity. For the subset of data that included right-side departures, the team identified 290 crashes on 2U roads and 37 crashes on 4D roads. Preliminary analyses were performed using the 2U data. The 2U and 4D data were FigureÂ 47. Rollover probability algorithm architecture. FigureÂ 48. Impact speed prediction model.

76 Development of Clear Recovery Area Guidelines later combined because the impact speedâinjury severity relationship should be independent of facility type. The research team identified at least two possible ways to define the severity of a crash using this database: the AAIS variable and the AINJSER variable. The definitions for these two vari- ables are presented in FigureÂ 49 (14). Out of the 290 crashes identified on 2U facilities, 274 crashes had valid fields for the AAIS vari- able and 158 had valid values for the AINJSER variable. The research team elected to develop the severity relationship based on the AAIS variable, both for consistency with past work as well as for sample size purposes. The AAIS variable is based on the maximum known injury in a crash based on the Abbreviated Injury Scale (AIS). FigureÂ 50 shows the relationship developed when considering levels 4 through 6 of the AAIS scale to define a severe or fatal crash. Similarly, FigureÂ 51 shows the relationships when considering levels 3 to 6 in the definition of a severe or fatal crash. After some discussion, the team decided to move forward with the definition that uses levels 3 to 6, which seems to provide better correlation with the definition of a serious injury crash. The relationship is based on 307 crashes including 274 crashes on 2U roads and 33 crashes on 4D roads combined. The team verified that the severity relationship derived from NCHRP Web-Only Document 341 data resembles the shape of a curve developed by Ray etÂ al. shown in FigureÂ 52, albeit the ordinate in that curve is cost, rather than severity (3, 26). Development of Severity Relationship for Rollovers The research team filtered rollover events from 2U and 4D facilities from the NCHRP Web- Only Document 341 database to develop a severity relationship for rollover events (3). The dataset FigureÂ 49. Injury code definitions (14). SAS 5 Statistical Analysis System.

Clear Zone Guideline Assistance Program 77Â Â P( K+ A ) Impact Speed (kph) FigureÂ 50. Fixed object K1A injury probability versus impact speed for AAIS 4â6. P( K+ A ) Impact Speed (kph) FigureÂ 51. Fixed object K1A injury probability versus impact speed for AAIS 3â6.

78 Development of Clear Recovery Area Guidelines contained rollover events and fixed-object crashes. Moreover, the vehicle speed at rollover and the impact speed with the fixed objects were available. The data were analyzed using a logistic regression model whose coefficients are indicated in TableÂ 48. It can be observed that the rollover events have a lower likelihood of K+A crashes compared to the fixed-object crashes. Furthermore, FigureÂ 53 provides the resulting rollover severity relationship based on rollover speed compared to the severity of impacting a fixed object, which is plotted versus impact speed. The rollover relationship is relatively flat in the range of data available. In the programming of the CZ-GAP risk analysis tool, the team applied an average severity value for rollovers that are sensitive to the speed limit rather than making it a function of actual speed at rollover, which would significantly complicate the analysis procedure. Risk Determination For purposes of this project, âriskâ is defined in terms of the probability of serious or fatal injury P(K+A) based on the KABCO scale. The KABCO scale is a descending scale of injury severity where a K-injury is a fatality and an O-crash results in âno apparent injuryâ and is often referred to as property damage only. A, B, and C refer to decreasing levels of injury severities, which are currently defined as âsuspected serious injury,â âsuspected minor injury,â and âpossible injury,â respectively. These injury levels are defined in the MMUCC Guideline: Model Minimum Uniform Crash Criteria (27). The injury severity is determined for each design configuration for different clear zone dis- tances and obstacle spacing beyond the clear zone edge. As the clear zone increases, the prob- ability of impacting a fixed object at or beyond the clear zone edge decreases, and, thus, the risk decreases. The probability of impacting a fixed object and, hence, the injury risk associated with a given roadway segment and clear zone distance are also a function of the nature of the obstacles at the clear zone edge. Consequently, risk was determined for different obstacle spacings. As FigureÂ 52. Cost versus impact speed for narrow fixed objects from the NCHRP Report 665 data (16). EFCCR 5 Effective Fatal Crash Cost Ratio. Parameter Estimate StandardError z-Value P-Value Significance Intercept â2.641380 0.450441 â5.864 4.52E-09 *** Impact speed 0.016056 0.005978 2.686 0.00723 ** Rollover event â1.247500 0.756489 â1.649 0.09913 ~ NOTE: *** = statistically significant at the 99% confidence interval; ** = statistically significant at the 95% confidence interval; ~ = statistically significant at the 90% confidence interval. TableÂ 48. Regression model for rollover severity derived from the NCHRP Web-Only Document 341 database (3).

Clear Zone Guideline Assistance Program 79Â Â FigureÂ 53. Comparison of rollover severity with severity of impacting a fixed object. P( K+ A ) noted previously, the hazards were defined as a line of trees having a diameter sufficient for them to behave as âfixed objects.â For practical purposes, the obstacle spacing can be considered the average spacing of trees, or other fixed-object types, along a roadway segment. A higher density of trees (i.e., closer spacing) will result in a higher probability of an impact. Conversely, a lower tree density (i.e., larger spacing) will have a lower probability of impact and a lower overall level of risk. There are two basic approaches for using risk-based analysis results to develop guidelines. The first is based on absolute risk, where the calculated risk of the roadway segment is compared to a risk target that is considered acceptable by the owner agency. If the risk associated with a given clear zone for a defined roadway segment and the ADT is less than the target, the risk is consid- ered acceptable, and the clear zone distance is satisfactory. The second approach is based on relative risk. When hazards on the roadside are shielded by a barrier such as guardrail, the guardrail has an associated level of risk. The general roadside design philosophy is that the risk associated with the barrier should be less than the risk associated with the unshielded roadside. Thus, in the context of clear zone guidelines, a given clear zone distance is considered acceptable for a roadway segment if its relative risk associated with impacting obstacles at the clear zone edge is less than the risk of shielding the segment with guardrail. As previously discussed, the Severity Prediction Module predicts the overall probability of a serious injury or fatal crash for an encroachment occurring along the predefined roadway seg- ment for the selected clear zone distance and obstacle spacing. The Severity Prediction Module has two submodules: the Rollover Severity submodel and the Impact Severity submodel. The Rollover Severity submodel predicts the probability a given encroachment will result in a roll- over before the vehicle reaches the clear zone edge of interest. This probability is then assigned

80 Development of Clear Recovery Area Guidelines a rollover crash injury severity based on the relationship derived from the NCHRP Web-Only Document 341 crash database (3). The Impact Severity submodel uses the Impact Speed Model to determine the mean impact speed for each obstacle (tree) of interest. The Impact Speed-Severity relationship derived from the NCHRP Web-Only Document 341 database (3) is then used to determine a P(K+A) for each obstacle (tree). This P(K+A) value is multiplied by the probability of an impact for each obstacle (tree), which is calculated using the Crash Probability Module. These weighted tree P(K+A) values are then summed over the number of obstacles. The sum of the K+A tree crash risks and K+A rollover crash risk is the total K+A crash risk for the given design configuration, clear zone distance, and obstacle spacing. This is expressed mathematically in Eq. 7. P K A P Roll P K A P Reach P Tree Impact P K A V CZ CZ Roll CZ i Tree i i n 1 ) ) )+ = + + + = ` ` ` ` ` ` `j j j j j j j R T SS R T S S V X WW V X W W/ (7) where: P(K + A)CZ = Weighted total K+A crash risk P(K+A) for the clear zone distance of interest given an encroachment has occurred. P(Roll)CZ = Probability of rollover before reaching the clear zone edge of interest. P(K + A)Roll = Probability of a fatal or severe injury from a rollover. P(Reach)CZ = Probability of an encroachment reaching the clear zone edge of interest. n = Total number of trees in segment of interest. P(Tree Impact)i = Probability of impacting i-th tree given an encroachment has reached the clear zone edge of interest. P(K + A)Tree( ââVi) = Risk of a fatal or severe injury from a tree crash adjusted for the impact velocity with i-th tree. Vi = Mean impact velocity given a crash has occurred with i-th tree. However, since guidelines have historically been developed based only on roadside obstacle impact risk, the research team decided to exclude rollover risk in the development of clear zone guidelines in this project. This simplified Eq. 7 in the form presented in Eq. 8. P K A P Reach P Tree Impact P K A V i Tree i i n CZ CZ 1 ) )+ = + = ` ` ` ` `j j j j j/ (8) As a result, CZ-GAP used Eq. 8 to generate the K+A crash risk values for all the configurations considered. After further variable sensitivity and importance analysis, these P(K+A) values were then used to generate the clear zone guidelines that will be made available for consideration for inclusion in the RDG.