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Suggested Citation:"Chapter 4 - Results." National Academies of Sciences, Engineering, and Medicine. 2010. Identification of Vehicular Impact Conditions Associated with Serious Ran-off-Road Crashes. Washington, DC: The National Academies Press. doi: 10.17226/14448.
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Suggested Citation:"Chapter 4 - Results." National Academies of Sciences, Engineering, and Medicine. 2010. Identification of Vehicular Impact Conditions Associated with Serious Ran-off-Road Crashes. Washington, DC: The National Academies Press. doi: 10.17226/14448.
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Suggested Citation:"Chapter 4 - Results." National Academies of Sciences, Engineering, and Medicine. 2010. Identification of Vehicular Impact Conditions Associated with Serious Ran-off-Road Crashes. Washington, DC: The National Academies Press. doi: 10.17226/14448.
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Suggested Citation:"Chapter 4 - Results." National Academies of Sciences, Engineering, and Medicine. 2010. Identification of Vehicular Impact Conditions Associated with Serious Ran-off-Road Crashes. Washington, DC: The National Academies Press. doi: 10.17226/14448.
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Suggested Citation:"Chapter 4 - Results." National Academies of Sciences, Engineering, and Medicine. 2010. Identification of Vehicular Impact Conditions Associated with Serious Ran-off-Road Crashes. Washington, DC: The National Academies Press. doi: 10.17226/14448.
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Suggested Citation:"Chapter 4 - Results." National Academies of Sciences, Engineering, and Medicine. 2010. Identification of Vehicular Impact Conditions Associated with Serious Ran-off-Road Crashes. Washington, DC: The National Academies Press. doi: 10.17226/14448.
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Suggested Citation:"Chapter 4 - Results." National Academies of Sciences, Engineering, and Medicine. 2010. Identification of Vehicular Impact Conditions Associated with Serious Ran-off-Road Crashes. Washington, DC: The National Academies Press. doi: 10.17226/14448.
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Suggested Citation:"Chapter 4 - Results." National Academies of Sciences, Engineering, and Medicine. 2010. Identification of Vehicular Impact Conditions Associated with Serious Ran-off-Road Crashes. Washington, DC: The National Academies Press. doi: 10.17226/14448.
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Suggested Citation:"Chapter 4 - Results." National Academies of Sciences, Engineering, and Medicine. 2010. Identification of Vehicular Impact Conditions Associated with Serious Ran-off-Road Crashes. Washington, DC: The National Academies Press. doi: 10.17226/14448.
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Suggested Citation:"Chapter 4 - Results." National Academies of Sciences, Engineering, and Medicine. 2010. Identification of Vehicular Impact Conditions Associated with Serious Ran-off-Road Crashes. Washington, DC: The National Academies Press. doi: 10.17226/14448.
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Suggested Citation:"Chapter 4 - Results." National Academies of Sciences, Engineering, and Medicine. 2010. Identification of Vehicular Impact Conditions Associated with Serious Ran-off-Road Crashes. Washington, DC: The National Academies Press. doi: 10.17226/14448.
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Suggested Citation:"Chapter 4 - Results." National Academies of Sciences, Engineering, and Medicine. 2010. Identification of Vehicular Impact Conditions Associated with Serious Ran-off-Road Crashes. Washington, DC: The National Academies Press. doi: 10.17226/14448.
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Suggested Citation:"Chapter 4 - Results." National Academies of Sciences, Engineering, and Medicine. 2010. Identification of Vehicular Impact Conditions Associated with Serious Ran-off-Road Crashes. Washington, DC: The National Academies Press. doi: 10.17226/14448.
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Suggested Citation:"Chapter 4 - Results." National Academies of Sciences, Engineering, and Medicine. 2010. Identification of Vehicular Impact Conditions Associated with Serious Ran-off-Road Crashes. Washington, DC: The National Academies Press. doi: 10.17226/14448.
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Suggested Citation:"Chapter 4 - Results." National Academies of Sciences, Engineering, and Medicine. 2010. Identification of Vehicular Impact Conditions Associated with Serious Ran-off-Road Crashes. Washington, DC: The National Academies Press. doi: 10.17226/14448.
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Suggested Citation:"Chapter 4 - Results." National Academies of Sciences, Engineering, and Medicine. 2010. Identification of Vehicular Impact Conditions Associated with Serious Ran-off-Road Crashes. Washington, DC: The National Academies Press. doi: 10.17226/14448.
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Suggested Citation:"Chapter 4 - Results." National Academies of Sciences, Engineering, and Medicine. 2010. Identification of Vehicular Impact Conditions Associated with Serious Ran-off-Road Crashes. Washington, DC: The National Academies Press. doi: 10.17226/14448.
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Suggested Citation:"Chapter 4 - Results." National Academies of Sciences, Engineering, and Medicine. 2010. Identification of Vehicular Impact Conditions Associated with Serious Ran-off-Road Crashes. Washington, DC: The National Academies Press. doi: 10.17226/14448.
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Suggested Citation:"Chapter 4 - Results." National Academies of Sciences, Engineering, and Medicine. 2010. Identification of Vehicular Impact Conditions Associated with Serious Ran-off-Road Crashes. Washington, DC: The National Academies Press. doi: 10.17226/14448.
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Suggested Citation:"Chapter 4 - Results." National Academies of Sciences, Engineering, and Medicine. 2010. Identification of Vehicular Impact Conditions Associated with Serious Ran-off-Road Crashes. Washington, DC: The National Academies Press. doi: 10.17226/14448.
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Suggested Citation:"Chapter 4 - Results." National Academies of Sciences, Engineering, and Medicine. 2010. Identification of Vehicular Impact Conditions Associated with Serious Ran-off-Road Crashes. Washington, DC: The National Academies Press. doi: 10.17226/14448.
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Suggested Citation:"Chapter 4 - Results." National Academies of Sciences, Engineering, and Medicine. 2010. Identification of Vehicular Impact Conditions Associated with Serious Ran-off-Road Crashes. Washington, DC: The National Academies Press. doi: 10.17226/14448.
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Suggested Citation:"Chapter 4 - Results." National Academies of Sciences, Engineering, and Medicine. 2010. Identification of Vehicular Impact Conditions Associated with Serious Ran-off-Road Crashes. Washington, DC: The National Academies Press. doi: 10.17226/14448.
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Suggested Citation:"Chapter 4 - Results." National Academies of Sciences, Engineering, and Medicine. 2010. Identification of Vehicular Impact Conditions Associated with Serious Ran-off-Road Crashes. Washington, DC: The National Academies Press. doi: 10.17226/14448.
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Suggested Citation:"Chapter 4 - Results." National Academies of Sciences, Engineering, and Medicine. 2010. Identification of Vehicular Impact Conditions Associated with Serious Ran-off-Road Crashes. Washington, DC: The National Academies Press. doi: 10.17226/14448.
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Suggested Citation:"Chapter 4 - Results." National Academies of Sciences, Engineering, and Medicine. 2010. Identification of Vehicular Impact Conditions Associated with Serious Ran-off-Road Crashes. Washington, DC: The National Academies Press. doi: 10.17226/14448.
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Suggested Citation:"Chapter 4 - Results." National Academies of Sciences, Engineering, and Medicine. 2010. Identification of Vehicular Impact Conditions Associated with Serious Ran-off-Road Crashes. Washington, DC: The National Academies Press. doi: 10.17226/14448.
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Suggested Citation:"Chapter 4 - Results." National Academies of Sciences, Engineering, and Medicine. 2010. Identification of Vehicular Impact Conditions Associated with Serious Ran-off-Road Crashes. Washington, DC: The National Academies Press. doi: 10.17226/14448.
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Suggested Citation:"Chapter 4 - Results." National Academies of Sciences, Engineering, and Medicine. 2010. Identification of Vehicular Impact Conditions Associated with Serious Ran-off-Road Crashes. Washington, DC: The National Academies Press. doi: 10.17226/14448.
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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.

26 4.1 General The following chapter presents an overview of the data set developed under the current study. A brief comparison of the content of the 17-22 and TTI data set is presented below. Descriptive statistics for the combined data set are then pre- sented followed by a detailed evaluation of the impact con- ditions and comparison of the current data and historical studies. Encroachment lengths from the combined data set are then compared to historical studies and implications of the new data on the calculation of appropriate guardrail length is discussed. Additional tables and plots describing the basic characteristics of the combined data set are presented in Appendix E. 4.1.1 Comparison of 17-22 and TTI Data A summary of the efforts to compare the 17-22 and TTI data sets was presented previously in Section 3.5. As shown in Table 13, differences between the two data sets were found to be statistically insignificant for the vast majority of the impor- tant variables. Vehicle weight, highway speed limit, rollover frequency, and vehicle class were exceptions to this finding. The modest changes observed in vehicle weight and roadway speed limits could be explained by changes in the vehicle fleet and elimination of the national speed limit law. Unfortu- nately, the magnitude of the change in vehicle class and the rollover rates between the 17-22 and TTI data could not be adequately explained. Most other important variables correlated very well between the two data sets. As shown in Table 14, injury and fatality rates for the two studies are virtually identical. Departure speeds and angles are also very similar as shown in Figures 1 and 2. Vehicle heading angle distributions were also found to be very similar, as shown in Figure 3. Although the IS distri- butions, shown in Figure 4, were not as similar as the other comparisons, the differences were not statistically significant. Recall that IS was defined in Chapter 2 as: where: IS = Impact Severity M = Vehicle mass V = Vehicle velocity θ = Impact angle Table 14 and Figures 1 through 4 clearly illustrate that injury rates and departure conditions from the TTI and 17-22 data are sufficiently similar to allow the data to be combined into a single database. As discussed in the prior chapter, the similarity between the two data sets for the vast majority of important data elements is sufficient to justify combining them into a single database. Nevertheless, database users should be cognizant of the differences in rollover rates and vehicle classes when developing data queries. Additional com- parisons between the 17-22 and TTI data sets are presented in Appendix E. 4.2 Descriptive Statistics When combined into a single data set, the 17-22 and TTI data included a total of 877 cases. The following sections pro- vide a basic description of the combined data set. 4.2.1 Characteristics of Sampled Cases As shown in Table 15, rural highways make up approxi- mately 72% of the accident cases with the remaining 28% of cases located in urban areas. Table 16 shows that the data set includes a significant representation of cases on Interstate highways, US routes, state routes, and county roads. The IS M V= ( )1 2    sinθ C H A P T E R 4 Results

27 17-22 Data TTI Data Total Data Injury Type No. Percentage No. Percentage No. Percentage Fatal 55 14.0% 74 15.3% 129 14.7% A-injury 228 58.2% 279 57.5% 507 57.8% B-injury 40 10.2% 49 10.1% 89 10.2% C-injury 33 8.4% 42 8.7% 75 8.6% PDO 36 9.2% 41 8.5% 77 8.8% Total 392 100.0% 485 100.0% 877 100.0% Table 14. Injury severity by study. Note: Many of the figures in this report have been converted from color to grayscale for printing. The electronic version of the report (posted on the web at www.trb.org) retains the color version as submitted by the contractor. Figure 1. 17-22 and TTI departure velocity distributions. Figure 2. 17-22 and TTI departure angle distributions. Figure 3. 17-22 and TTI heading angle distributions. Figure 4. 17-22 and TTI IS distribution.

largest number of cases, 275 (32.7%), occurred on county roads and 195 (23.2%) cases were on Interstate highways. The number of cases on US and state routes are approximately the same at 160 (19.0%) and 161 (19.1%) cases, respectively. As would be expected for crashes collected from these high- way types, the data set includes a wide distribution of speed limits ranging from 45 to 75 mph, as shown in Table 17. Table 18 presents this distribution of speed limit by high- way class. As expected, most of the data collected from high-speed facilities involved Interstate highways and the majority of cases involving low-speed facilities were col- lected on county roads. Tables 19 and 20 show the number of lanes at the accident site for divided and undivided high- ways, respectively. Surprisingly, even though a large proportion of crashes involved Interstates and US routes, very few cases involved vehicles departing from a portland cement pavement surface. As shown in Table 21, the vast majority of the cases, 773 (88.1%), occurred on asphalt with only 45 (5.1%) involving portland cement concrete. As shown in Table 22, winter months were significantly underrepresented in the data. Only 132 (15.1%) crashes occurred during the winter months from December through February. The low proportion of crashes during the winter provided an explanation for the low numbers of crashes with ice, 28 (3.2%), or snow, 25 (2.9%), on the roadway surface, as shown in Table 23. This table also shows that almost 80% of all of the crashes in the data set occurred on dry roadways. These findings correlated with the weather conditions at the time of the crash, shown in Table 24. More than 85% of the crashes occurred in clear weather and less than 10% occurred in the rain. A total of 529 of the 877 cases were recorded as having struck an object on the roadside. As shown in Table 25, more than 37% of these fixed-object crashes involved trees and another 7% involved utility pole impacts. More than 18% of the fixed-object crashes involved longitudinal barrier impacts. Thus, approximately 62% of fixed-object crashes involved impacts that would be expected to significantly reduce vehicle speed or redirect it back toward the roadway. The remaining 38% of crashes involved fixed objects that would be less likely to significantly reduce the speed of the impacting vehicle (e.g. embankments, ditches, curbs, breakaway sign and luminaire supports, fences, mailboxes and culverts). 28 Hwy Class No. of Cases Percentage Interstate 195 23.16% US Route 160 19.00% State Route 161 19.12% County Road 275 32.66% City Street 43 5.11% Other 8 0.95% Total 842 100.00% Table 16. Highway classification. No. of Cases Percentage Urban 235 27.94% Rural 606 72.06% Total 841 100.00% Table 15. Case distribution by land use. Cases Speed Limit No. Percentage 75 58 6.7% 70 114 13.1% 65 75 8.6% 55 361 41.4% 50 68 7.8% 45 195 22.4% Total 871 100.0% Table 17. Speed limit. Speed Limit (mph) 75 70 65 55 50 45 Hwy Class No. % No. % No. % No. % No. % No. % Interstate 57 98.3 63 56.3 25 34.2 41 11.9 2 3.2 5 2.7 US Route 0 0.0 46 41.1 34 46.6 50 14.5 11 17.5 18 9.7 State Route 1 1.7 2 1.8 13 17.8 95 27.5 20 31.7 29 15.6 County Road 0 0.0 0 0.0 0 0.0 153 44.3 27 42.9 94 50.5 City Street 0 0.0 0 0.0 0 0.0 2 0.6 3 4.8 38 20.4 Other 0 0.0 1 0.9 1 1.4 4 1.2 0 0.0 2 1.1 Total 58 100.0 112 100.0 73 100.0 345 100.0 63 100.0 186 100.0 Table 18. Highway class vs. speed limit.

29 Number of Lanes Hwy Class 1 - 2 3 - 4 More than 4 Interstate 67 (38.3%) 86 (49.1%) 22 (12.6%) US Route 29 (30.9%) 56 (59.6%) 9 (9.6%) State Route 17 (37.8%) 25 (55.6%) 3 (6.7%) County Road 1 (33.3%) 2 (66.7%) 0 (0.0%) City Street 7 (58.3%) 5 (41.7%) 0 (0.0%) Other 0 (0.0%) 1 (100.0%) 0 (0.0%) Table 19. Number of lanes— divided highways. Number of Lanes Hwy Class 1 - 2 3 - 4 More than 4 Interstate 18 (94.7%) 1 (5.3%) 0 (0.0%) US Route 54 (81.8%) 7 (10.6%) 5 (7.6%) State Route 101 (87.8%) 11 (9.6%) 3 (2.6%) County Road 237 (98.8%) 3 (1.3%) 0 (0.0%) City Street 20 (64.5%) 7 (22.6%) 4 (12.9%) Other 6 (100.0%) 0 (0.0%) 0 (0.0%) Table 20. Number of lanes— undivided highways. Roadway Surface No. of Cases Percentage of Total Asphalt 773 88.1% Portland Cement 45 5.1% Dirt 31 3.5% Gravel 28 3.2% Total 877 100.0% Table 21. Distribution by roadway material. Month Number of Occurrences Percentage January 37 4.2% February 50 5.7% March 102 11.6% April 87 9.9% May 82 9.4% June 101 11.5% July 83 9.5% August 86 9.8% September 76 8.7% October 71 8.1% November 57 6.5% December 45 5.1% Total 877 100.0% Table 22. Case distribution by month. Surface Condition No. of Cases Percentage of Total Dry 695 79.2% Wet 121 13.8% Ice 28 3.2% Snow 25 2.9% Other 8 0.9% Total 877 100.0% Table 23. Distribution by surface condition. Weather Condition No. of Cases Percentage Clear 750 85.81% Rain 82 9.38% Snow 30 3.43% Fog 6 0.69% Hail 3 0.34% Sleet 2 0.23% Sandstorm 1 0.11% Total 874 100.00% Table 24. Weather condition. Object/Feature Struck No. Percentage Tree 197 37.2% Guardrail 71 13.4% Embankment 65 12.3% Sign and Luminaire Support 39 7.4% Utility Pole 37 7.0% Culvert 30 5.7% Concrete Barrier 25 4.7% Ditch 24 4.5% Mailbox 18 3.4% Fence 13 2.5% Curb 10 1.9% Total 529 100.0% Table 25. First impact. Table 26 presents the distribution of vehicle classes included in the data set. Almost 58% of vehicles included in the data set were classified as “car.” Further, another 28% of vehicles fell into the compact light truck class including compact pick- ups, compact utility vehicles, and minivans. Only 13% of vehicles included in the database were full-size pickups, util- ity vehicles, or vans. 4.2.2 Crash Severity As expected, the data set is biased toward higher severity crashes. As shown in Table 27, roughly 15% of the cases

30 with a minimum of 69% for county roads and a high of 75% for US routes. This same bias toward higher severity crashes is also evident in Tables 28 through 31. Table 28 presents the rela- tionship between specific vehicle class and crash severity. There appears to be no consistent trend between vehicle size and crash severity. Table 29 condenses this information to produce crash severity by overall vehicle type. Again there appears to be only modest differences in crash sever- ity as a function of overall vehicle type. Tables 30 and 31 also illustrate that the severity bias masks the effects of rollover and the object struck on crash severity, respec- tively. For example, fatality rates for tree and guardrail impacts are found to be very similar at 13.2% and 12.7% respectively. Thus, Tables 27 through 31 clearly illustrate Vehicle Class No. of Cases Percentage by Veh. Subclass Percentage of Total Subcompact Car 145 28.7% 16.5% Compact 167 33.0% 19.0% Intermediate 117 23.1% 13.4% Full-Size Sedan 55 10.9% 6.3% Large Size 22 4.3% 2.5% Car Subtotal 506 100.0% 57.7% Compact Pickup 99 52.4% 11.3% Large Pickup 87 46.0% 9.9% Other Pickup Type 3 1 .6% 0.3% Pickup Truck Subtotal 189 100.0% 21.5% Compact Utility 120 83.9% 13.7% Large Utility 15 10.5% 1.7% Stationwagon Utility 8 5.6% 0.9% Utility Vehicle Subtotal 143 100.0% 16.4% Minivan 27 69.2% 3.1% Large Van 10 25.6% 1.1% Full-Size Van 2 5.2% 0.2% Van Subtotal 39 100.0% 4.4% Total 877 100.0% Table 26. Vehicle class. Maximum Severity Fatality Injury Type A Injury Type B Injury Type C PDO Hwy Class No. % No. % No. % No. % No. % Interstate 35 17.9% 109 55.9% 15 7.7% 20 10.3% 16 8.2% US Route 19 11.9% 102 63.8% 11 6.9% 15 9.4% 13 8.1% State Route 26 16.1% 93 57.8% 18 11.2% 11 6.8% 13 8.1% County Road 40 14.5% 150 54.5% 36 13.1% 23 8.4% 26 9.5% City Street 7 16.3% 30 69.8% 3 7.0% 1 2.3% 2 4.7% Other 0 0.0% 4 50.0% 1 12.5% 3 37.5% 0 0.0% All 127 15.1% 488 58.0% 84 10.0% 73 8.7% 70 8.3% Table 27. Highway class vs. crash severity. involved a fatality (denoted “K”) and approximately 73% of all cases involved either an A-injury or a fatality (A+K). A recent study of single-vehicle crashes on controlled-access freeways in Kansas found a fatality rate of only 0.73% and an A+K rate of only 3.8% (32). From the data in Table 27, the fatality rate for Interstate highways in the data set was 17.9% and the A+K rate was 73.8%. These fatality and A+K rates were 25 and 19 times higher, respectively, than the values for controlled-access freeways in Kansas. This degree of bias is associated with the original case-selection criteria used to identify the NASS CDS cases and therefore cannot be avoided. This inherent bias toward increased severity may be masking the relationship between highway functional class and crash severity for this database. As shown in Table 27, the A+K rates for all highway functional classes is approximately the same

31 Maximum Injury (%) Vehicle Class No. of Cases Fatal A-injury B-Injury C-Injury PDO Subcompact 145 13.1 53.8 11.0 12.4 9.7 Compact Car 167 16.2 52.1 10.8 10.2 10.8 Intermediate 117 13.7 63.2 9.4 6.0 7.7 Full-Size Sedan 55 14.5 54.5 12.7 10.9 7.3 Car Large Size 22 4.5 68.2 13.6 0.0 13.6 Compact Pickup 99 19.2 57.6 7.1 8.1 8.1 Large Pickup 87 10.3 64.4 5.7 10.3 9.2 Pickup Truck Other Pickup Type 3 33.3 33.3 0.0 0.0 33.3 Compact Utility 120 14.2 59.2 14.2 5.0 7.5 Large Utility 8 0.0 75.0 12.5 0.0 12.5 Utility Vehicle Stationwagon Utility 15 13.3 60.0 6.7 13.3 6.7 Minivan 27 22.2 63.0 7.4 3.7 3.7 Large Van 2 50.0 50.0 0.0 0.0 0.0 Van Full-Size Van 10 30.0 50.0 10.0 10.0 0.0 Table 28. Crash severity by vehicle class. Maximum Injury No. of Cases Percentage by Roll Result Percentage of Total Fatality 79 16.7% 9.0% A-injury 274 57.9% 31.2% B-injury 48 10.1% 5.5% C-injury 40 8.5% 4.6% PDO 32 6.8% 3.6% Rollover Subtotal 473 100.0% 53.9% Fatality 50 12.4% 5.7% A-injury 233 57.7% 26.6% B-injury 41 10.1% 4.7% C-injury 35 8.7% 4.0% PDO 45 11.1% 5.1% No Rollover Subtotal 404 100.0% 46.1% Total 877 100.0% Table 30. Rollover and crash severity. No. of Maximum Injury (%) Vehicle Type Cases Fatal A-injury B-Injury C-Injury PDO Automobile 506 14.0% 56.1% 10.9% 9.5% 9.5% Pickup 189 15.3% 60.3% 6.3% 9.0% 9.0% Utility 143 13.3% 60.1% 13.3% 5.6% 7.7% Van 39 25.6% 59.0% 7.7% 5.1% 2.6% Table 29. Crash severity by vehicle type. Fatal A-Injury B-Injury C-Injury PDOObject/Feature Struck No. of Cases No. % No. % No. % No. % No. % Tree 197 26 13.2% 127 64.5% 16 8.1% 14 7.1% 14 7.1% Guardrail 71 9 12.7% 36 50.7% 7 9.9% 6 8.5% 13 18.3% Embankment 58 6 10.3% 34 58.6% 9 15.5% 4 6.9% 14 24.1% Vertical Support 37 6 16.2% 19 51.4% 6 16.2% 1 2.7% 5 13.5% Utility Pole 37 9 24.3% 17 45.9% 7 18.9% 3 8.1% 1 2.7% Concrete Barrier 27 5 18.5% 13 48.1% 2 7.4% 4 14.8% 3 11.1% Culvert 27 3 11.1% 20 74.1% 1 3.7% 2 7.4% 1 3.7% Ditch 25 2 8.0% 15 60.0% 2 8.0% 5 20.0% 1 4.0% Mailbox 18 2 11.1% 10 55.6% 2 11.1% 2 11.1% 2 11.1% Fence 13 2 15.4% 8 61.5% 0 0.0% 3 23.1% 0 0.0% Curb 10 0 0.0% 7 70.0% 1 10.0% 1 10.0% 1 10.0% Total 520 70 13.5% 306 58.8% 53 10.2% 45 8.7% 55 10.6% Table 31. First impact vs. crash severity.

32 eral trend for lower impact angles to produce higher crash severities, when A+K severities are considered, the apparent relationship disappears and impact angle appears to have little correlation with severity. Even in light of the very lim- ited amount of data, this finding was quite surprising. The relationship between IS value and crash severity, shown in Table 37, was also quite surprising. After further investiga- tion, it was discovered that the guardrail impact was not the most harmful event for most of the serious injuries associated with low angle and low IS crashes. Tables 38 and 39 present crash severity versus impact angle and IS value for crashes where the guardrail impact was the most severe event. These tables display the expected correlation between impact angle and IS versus crash severity. 4.3 Departure Conditions One of the primary objectives of developing the database described herein was to identify the departure conditions associated with serious ran-off-road crashes. The encroach- ment conditions described below are associated with a data- base that has an A+K rate of more than 70%. Clearly, this database is heavily biased and it can be considered to be rep- resentative of serious ran-off-road crashes. 4.3.1 Departure Speed and Angle Distributions As shown in Table 40, the mean departure speed was found to be 49.26 mph. This value was higher than the mean value Injury Severity Levels Fatal Injury A Injury B Injury C PDO VehicleClass No. % No. % No. % No. % No. % Car 15 19.5% 47 58.4% 5 6.5% 3 3.9% 7 9.1% Pickup 10 22.7% 26 59.1% 3 6.8% 2 4.5% 3 6.8% Utility 13 33.3% 21 53.9% 1 2.6% 3 7.7% 1 2.6% Van 2 33.3% 4 66.7% 0 0.0% 0 0.0% 0 0.0% Table 33. Crash severity by vehicle size for departure velocities of 60–75 mph. Rollover Yes No Vehicle Class No. % No. % Car 51 66.2% 26 33.8% Pickup 35 79.6% 9 20.5% Utility 35 89.7% 4 10.3% Van 5 83.3% 1 16.7% Table 34. Rollover risk by vehicle size for departure velocities of 60–75 mph. Injury Severity Levels Fatal Injury A Injury B Injury C PDODeparture Velocity (mph) No. of Cases No. % No. % No. % No. % No. % < 30 103 3 2.9% 50 48.5% 10 9.7% 17 16.5% 23 22.3% 30–45 240 18 7.5% 135 56.3% 35 14.6% 23 9.6% 29 12.1% 45.1–60 313 52 16.6% 192 61.3% 30 9.6% 26 8.3% 13 4.2% 60.1–75 166 40 24.1% 98 59.0% 9 5.4% 8 4.8% 11 6.6% > 75 48 15 31.3% 26 54.2% 5 10.4% 1 2.1% 1 2.1% Table 32. Crash severity by departure velocity. that the database described herein cannot be used to eval- uate the severity of different types of crashes whether it involves crash outcome such as rollover, vehicle class, or object struck. However, the purpose of this database is not to provide rel- ative comparisons of crash severities available from conven- tional databases, but rather to provide the basis for developing a relationship between crash conditions and severity for vari- ous types of hazards. Table 32 illustrates the strong relationship between departure velocity and crash severity. Both fatality rate and A+K rate increased with each increment in departure velocity. Tables 33 and 34 show injury severity and rollover risk, respectively, by vehicle type for departure velocities from 60 to 75 mph. Table 35 shows the relationship between impact velocity and crash severity for W-beam guardrails. Again, there appears to be a strong correlation between impact speed and probabil- ity of fatal and serious injury. Table 36 provides a compari- son between impact angle and crash severity for W-beam guardrails. Although at first glance, there appears to be a gen-

33 Maximum Injury Fatalities A-Injuries B-Injuries C-Injuries PDOCrashes Impact Speed Cases No. % No. % No. % No. % No. % < 25 mph 1 0 0 0 0 0 0 0 0 1 100 25-40 mph 2 1 50 1 50 0 0 0 0 0 0 40-55 mph 12 0 0 8 67 2 17 0 0 2 17 55-70 mph 9 1 11 5 56 0 0 1 11 2 22 70-85 mph 5 3 60 1 20 1 20 0 0 0 0 85 mph 3 2 67 1 33 0 0 0 0 0 0 Unknown 4 0 0 3 75 0 0 0 0 1 25 Table 35. Crash severity vs. impact speed for W-beam guardrail. Maximum Injury Fatal A-Injury B-Injury C-Injury PDO Impact Angle Cases No. % No. % No. % No. % No. % 0-6 deg 4 2 50% 2 50% 0 0% 0 0% 0 0% 6-12 deg 11 3 27% 5 45% 0 0% 0 0% 3 27% 12-18 deg 7 2 29% 2 29% 1 14% 1 14% 1 14% 18-24 deg 2 0 0% 2 100% 0 0% 0 0% 0 0% 24 deg 12 0 0% 8 67% 2 17% 0 0% 2 17% Table 36. Severity by impact angle of crashes involving guardrails. Maximum Injury Fatal A-Injury B-Injury C-Injury PDO Impact Severity Cases No. % No. % No. % No. % No. % 0-5 kJ 4 0 0% 4 100% 0 0% 0 0% 0 0% 5-13 kJ 4 2 50% 1 25% 0 0% 0 0% 1 25% 13-30 kJ 5 1 20% 2 40% 0 0% 0 0% 2 40% 30-90 kJ 10 4 40% 3 30% 1 10% 1 10% 1 10% 90 kJ 9 0 0% 6 67% 2 22% 0 0% 1 11% Table 37. Severity by IS value of crashes involving guardrails. Maximum Injury Fatalities “A” Injuries Impact Severity Cases No. % No. % 0-5 kip-ft 0 0 N/A 0 N/A 5-13 kip-ft 0 0 N/A 0 N/A 13-30 kip-ft 1 0 0 1 100 30-90 kip-ft 7 3 43 4 57 90 kip-ft 4 0 0 4 100 Unknown 3 0 0 3 100 Table 39. Crash severity vs. IS when guardrail impact was most harmful event. Maximum Injury Fatalities A-Injuries Impact Angle Cases No. % No. % 0-6 deg 0 0 N/A 0 N/A 6-12 deg 0 0 N/A 0 N/A 12-18 deg 3 2 67 1 33 18-24 deg 3 0 0 3 100 24 deg 9 1 11 8 89 Table 38. Crash severity by impact angle when guardrail impact was most harmful event.

34 found by Mak et al. (3) in the 1980s. Table 41 presents a comparison of velocity data from the current study and Mak et al.’s Pole Study. In order to compare the two studies, it was necessary to adjust the roadway classifications in this study to match the functional classes in Mak et al. All fully controlled access roadways were classified as freeways and US and state routes were classified as arterials. County roads and city streets were then placed into the collector/local category. Although this classification scheme is not perfect, it did place all road- ways with high volume and most medium-volume roadways in the arterial category. Note the velocity distributions from this study are significantly higher than those found by Mak et al. (3). This finding is believed to arise from three factors: (1) the elimination of the national speed limit law; (2) the bias in the current study toward severe crashes; and (3) the Mak data is for impacts while the data from the current study is from departure conditions. Figure 5 graphically illustrates the dif- ferences between the velocity distributions on freeways in the two studies. The mean departure angle shown in Table 42 is also higher than the corresponding angle from the Pole Study. A simple cornering analysis would indicate that higher depar- ture speeds should produce lower departure angles. Thus, the increase in both departure speed and departure angle is unexpected. The most plausible explanation for this find- ing would be the wide implementation of antilock brakes. In the late 1970s, very few passenger cars had antilock brakes and by the late 1990s, the majority of the vehicle fleet was so equipped. In theory, antilock brakes are intended to allow drivers to continue to steer through emergency brak- ing procedures. Unfortunately, research has not been able to identify any significant reduction in crash risk or crash Variable Mean Median Standard Deviation Minimum Maximum 10th percentile 90th percentile Velocity 49.3 49.2 15.91 5.00 97.2 28.5 69.3 Angle 16.9 15.0 10.49 0.00 84.0 5 30 Table 40. Velocity and angle descriptive statistics. Velocity (mph) Mean 70th Percentile 90th Percentile Highway Class 17-22 Pole Study 17-22 Pole Study 17-22 Pole Study All 49.3 31.3 57.4 39.1 69.3 59.4 Freeway 56.3 43.9 63.2 51.2 75.5 65.9 Urban Arterial 44 25.3 52 30.4 62.6 44 Rural Arterial 49.1 37.4 56 45.5 65.8 64.1 Urban Loc/Col 44.2 20.8 49.2 25 61.4 37 Rural Loc/Col 44.6 29.1 51.1 35.6 62.4 48.2 Table 41. Velocity Comparison with Mak et al. (3). Figure 5. Freeway velocity distributions from Pole Study and 17-22. severity associated with the use of antilock brakes. This find- ing may indicate that allowing drivers to continue to steer through emergency situations does not necessarily reduce the angle of departure from the roadway. Figure 6 shows a graphical comparison of freeway departure angles for the 17-22 database, encroachment data from Cooper (33) and Hutchinson and Kennedy (7), and impact angles from the Pole Study. Note that the angle distributions from the current study are very near those found by Cooper. Table 42 presents a comparison between departure angles from the 17-22 data and impact angles from the Pole Study for all roadway classes. Notice that with the exception of urban local/collector, all measures of departure angle for the current study were higher than impact angles from the Pole Study. However, the mag- nitude of the differences was found to be relatively modest.

35 4.3.2 Theoretical Modeling of Departure Speed and Angle Distributions Tables 43 and 44 show descriptive statistics for departure velocity and angle respectively, segregated by road class. Note that with the exception of the Interstate classification, the mean velocities were quite similar. Further departure angle did not vary significantly from one road classification to the next. These findings lead to the conclusion that roadway classification may not be the best discriminator for departure conditions. Tables 45 and 46 show descriptive statistics for departure velocity and angle respectively, segregated by speed limit. Note that the mean velocities now show more significant variation and the trend is correlated with speed limit. There is also more discrimination in the mean angle when the data are segregated by speed limit. Although prior studies showed that functional class was the best discriminator for depar- ture speed, functional class was not identifiable in the current database. Findings from Tables 43 through 46 indicate that the surrogate measures used to indicate functional class may not be appropriate. However, speed limit does appear to pro- vide a significant degree of discrimination for both departure speed and angle. Tables 43 through 46 also present skewness values for veloc- ity and angle data. Note that mean skewness for velocity data is near zero while mean skewness for angle data is above 1.0. These skewness measures indicate that the velocity data may best be modeled with a normal distribution while angle data would be more likely to fit a gamma model. Angle and velocity data from the Pole Study were found to fit a gamma distribution while other studies (1) found that the speed data fit a normal distribution. As a first step to modeling departure conditions, normal and gamma distributions were fit to departure speed and angle data for the total database and for each speed limit range as shown in Tables 47 and 48. Table 47 shows that the velocity distributions for the total database and all categories of speed limit were found to fit a normal distribution quite well. Although the gamma distri- bution was found to fit most speed limit categories acceptably well, p-values for both the total data set and the 50 mph speed limit category were below 0.05, indicating a poor fit to the data. Figure 7 shows the quality of fit for normal and gamma distri- bution to velocity data for the total database. Notice that the gamma distribution does not match the data very well. Table 48 shows that neither normal nor gamma distribu- tions provided an acceptable fit to departure angle data for all speed limit categories. Figure 8 shows the poor quality of fit for these distributions to the departure angle data from the total data set. In light of the poor quality of the normal and gamma distribution fits to the departure angle data, 53 other distributions were then fit to the departure angle data from all speed limit categories. Unfortunately, it was found that no single distribution adequately fit all speed limit categories. In fact, the gamma distribution was found to come as close to fitting all data categories as any of the distributions. In order to produce an acceptable fit to departure angle data, it was decided to utilize the square root of the departure angle as the independent variable. Using the square root of the departure angle shifts the distribution to the left and reduces the accuracy of predictions at the high end of the curve. How- ever, adjusting the independent variable in this manner is an acceptable method for improving statistical fits to measured Figure 6. Comparison of freeway departure angle distributions. Departure Angle (deg) Mean 70th Percentile 90th Percentile Highway Class 17-22 Pole Study 17-22 Pole Study 17-22 Pole Study All 16.9 15.9 20 19.2 30 29.4 Freeway 16.8 15.5 20 18.7 29 28.4 Urban Arterial 16.6 15.5 17 18.9 29.3 29.5 Rural Arterial 16.3 15.0 20 18.4 30 30.3 Urban Loc/Col 15.4 16.5 18.0 19.8 28.4 28.7 Rural Loc/Col 16.6 15.4 19.5 18.8 29.5 30.4 Table 42. Angle comparison with Mak et al. (3).

36 Road Class Speed Limit (mph) No. of Cases Min. Vel (mph) Mean Vel. (mph) Max. Vel (mph) Standard Deviation Skewness All 45-75 870 5 49.3 97.2 15.913 -0.09537 Interstate 45-75 194 10 58.24 92.6 15.587 -0.44254 U.S. Highway 45-75 155 5 48.679 97.2 16.775 -0.09055 State Highway 45-65 159 10 49.494 89.9 15.39 0.08016 County Road 45-55 274 14.5 44.668 90.6 13.666 0.82561 Table 43. Departure velocity statistics by highway class. Road Class Speed Limit (mph) No. of Cases Min. Ang. (deg) Mean Ang. (deg) Max. Ang. (deg) Standard Deviation Skewness All 45-75 877 0 16.9 84 10.949 1.5728 Interstate 45-75 194 0 16.5 56 9.7802 1.0612 U.S. Highway 45-75 157 2 16.5 55 10.159 1.2036 State Highway 45-65 161 3 16.7 59 10.828 1.422 County Road 45-55 274 0 16.6 84 11.05 1.7913 Table 44. Departure angle statistics by highway class. Speed Limit (mph) No. of Cases Min. Vel. (mph) Mean Vel. (mph) Max. Vel (mph) Standard Deviation Skewness 75 58 42 66.045 92.6 11.081 0.37389 70 112 7.5 54.951 90.8 16.206 -0.13195 65 75 10 53.939 88.5 16.539 -0.90328 55 357 13.8 47.331 97.2 14.894 0.24393 50 68 18.7 46.231 81.9 13.632 0.06293 45 194 5 43.999 91.1 14.741 0.5794 Table 45. Departure velocity statistics by speed limit. Speed Limit (mph) No. of Cases Min. Ang. (deg) Mean Ang. (deg) Max Ang. (deg) Standard Deviation Skewness 75 58 2 14.2 32 8.3183 0.43907 70 114 2 18 56 11.128 1.2138 65 75 3 14.9 49 9.0404 1.4983 55 361 0 17.3 76 11.389 1.4225 50 68 4 17.0 84 13.94 2.4057 45 195 0 17.2 76 10.011 1.5565 Table 46. Departure angle statistics by speed limit. Chi Squared – Normal Gamma Dist. Chi Squared – Gamma Speed Limit (mph) No. of Cases Mean Vel. (mph) Standard Deviation DOF Chi Stat. P-Value Alpha Beta DOF Chi Stat. P-Value All 870 49.3 15.913 9 2.3071 0.9856 9.5964 5.137 9 23.917 0.0044 75 58 66.045 11.081 5 0.96147 0.9615 35.526 1.859 5 1.4802 0.9153 70 112 54.951 16.206 6 6.9659 0.3240 11.498 4.7792 6 7.7562 0.2565 65 75 53.939 16.539 5 7.7495 0.2570 10.637 5.071 5 7.7209 0.1723 55 357 47.331 14.894 8 6.8966 0.5478 10.099 4.6867 8 19.862 0.0109 50 68 46.231 13.632 6 4.7869 0.5714 11.501 4.0198 5 6.5352 0.2576 45 194 43.999 14.741 7 5.61 0.5860 8.908 4.9388 7 1.6949 0.9748 Table 47. Normal and gamma distribution fits to speed data.

37 where: χ = Chi-square measure of error between the two contin- gency tables Oi = Observed frequency in cell i Ei = Expected frequency in cell i k = number of cells in table. The chi-square statistic calculated from Tables 50 and 51 was found to be 30.54. The number of degrees of freedom for this test is one less than the number of rows times one less than the number of columns. In the example of the entire data base, the 6 x 6 contingency table shown in Table 48 has 25 degrees of freedom. The chi-square statistic of 30.54 and 25 degrees of freedom produce a p-value of 0.205. This mag- nitude of the p-value indicates that angle and speed data can be considered to be independent. The relationship between speed and angle of departure can be graphically illustrated by plotting the distribution of departure angle for three different χ2 2 1 = −( ) = ∑ O E E i i i i k Figure 7. Normal and gamma distribution fits to departure speed. Chi Squared – Normal Gamma Dist. Chi Squared - GammaSpeed Limit (mph) No. of Cases Mean Angle (deg) Standard Deviation DOF Chi Stat. P-Value Alpha Beta DOF Chi Stat. P-Value All 877 16.936 10.949 9 133.04 0.0001 2.6183 6.483 9 17.895 0.0364 75 58 14.224 8.3183 7 12.754 0.0783 13.961 4.1716 7 12.962 0.0731 70 114 18 11.128 6 9.2486 0.1601 2.6166 6.8791 6 3.4874 0.7456 65 75 14.88 9.0404 5 5.4896 0.3591 2.7091 5.4925 6 8.1237 0.2292 55 361 17.263 11.389 8 47.362 1x10-7 2.4615 7.0327 8 13.894 0.0846 50 68 17.044 13.94 4 19.612 6x10-4 1.495 11.400 6 21.943 0.0012 45 195 17.195 10.011 7 13.412 0.0627 2.9502 5.8285 7 7.70539 0.4233 Table 48. Normal and gamma distribution fits to angle data. Figure 8. Normal and Gamma Distribution Fits to Departure Angle (all data). data. As shown in Table 49, the gamma distribution was found to fit the square root of the departure angle for all speed limit categories. The p-value of 0.0754 found for the gamma distribution fit to the total data set indicates that this fit is rel- atively marginal. Note however that the p-values for all indi- vidual speed limit categories were found to be 0.27 or higher, which indicates a reasonably good fit to the data. Figure 9 illus- trates the use of a gamma distribution fit to the square root of the departure angle to model departure angle data. Tables 47 and 49 provide parameters for fitting normal and gamma distributions to departure speed and square root of departure angle, respectively. The next step in modeling depar- ture conditions involved exploring the dependence of speed and angle. A chi-square test for independence was employed for this evaluation. Table 50 shows a contingency table for all departure speed and angle combinations and Table 51 presents expected frequencies if speed and angle are independent. A chi-square goodness-of-fit test was then used to measure the appropriateness of the independence assumption using the fol- lowing equation to calculate the chi-square statistic.

38 speed ranges as shown in Figure 10. Note that the angle dis- tribution for the low-speed range was found to be higher than the middle- or high-speed range, while differences in depar- ture angle distribution for high- and middle-speed ranges were found not to be statistically significant. The fact that the differences between departure angle distributions for the middle- and high-speed ranges were not statistically sig- nificant further reinforces the finding that the correlation between speed and angle is sufficiently weak to treat them as independent. In view of the finding of limited dependence between depar- ture speed and angle for the total database, the chi-square test for independence was applied to the speed and angle of depar- ture data for each speed limit category. The resulting p-values from these analyses were found to be much higher as shown in Table 52. With all of the p-values greater than 0.05, it is impos- sible to reject the assumption that the velocity and angle data are independent whenever cases are segregated by speed limit. Based upon the finding of, at most, a very limited degree of dependence between departure speed and angle, the normal distribution fit to velocity data and the gamma distribution fit to square root angle data can be applied independently to pro- duce speed and angle probability distributions for each speed limit category as shown in Tables 53 through 59. Chi-square tests were then conducted to compare pre- dicted and observed frequencies for each speed limit category. As shown in Table 60, the predicted frequencies compared reasonably well with the observed values for most speed limit categories. These findings indicate that it is acceptable to model departure speed and angle as independent variables. Further, departure speed can be modeled using the normal distribution parameters shown in Table 47 and departure angle can be modeled using the gamma distribution fits to square root of departure angle presented in Table 49. These models produce the departure conditions shown in Tables 53 through 59. Square Root Angle Gamma Distribution Chi Squared - GammaSpeed Limit (mph) No. of Cases Mean Std. Dev. Alpha Beta DOF Chi Stat. P-Value All 877 3.916 1.266 9.6039 0.40868 9 15.613 0.0754 75 58 3.5992 1.1366 10.028 0.35892 5 4.2553 0.51327 70 114 4.0482 1.2754 10.074 0.40183 6 6.066 0.41583 65 75 3.6995 1.0998 11.316 0.32693 6 6.5419 0.3653 55 361 3.9405 1.3184 8.9338 0.44108 8 9.837 0.27665 50 68 3.8812 1.4177 7.4944 0.51788 5 6.3047 0.2777 45 195 3.9755 1.1822 11.309 0.35132 7 6.3246 0.5024 Table 49. Gamma distribution fit to square root of departure angle. Figure 9. Square root of departure angle used to model departure angle (all data). Departure Angle (deg.)Departure Velocity (mph) <6 6 - 12 12 - 18 18 - 24 24-30 >30 <25 4 15 16 10 7 13 25 - 35 9 24 29 15 12 16 35 - 45 15 40 43 31 30 20 45 - 55 25 65 62 31 21 19 55 - 65 13 45 46 32 15 18 >65 22 41 30 19 12 12 Table 50. Observed departure conditions. Departure Angles (deg.)Departure Velocity (mph) <6 6 - 12 12 - 18 18 – 24 24-30 >30 <25 6.52 17.05 16.75 10.23 7.19 7.26 25 - 35 10.54 27.54 27.06 16.52 11.61 11.73 35 - 45 17.96 46.94 46.13 28.17 19.80 20.00 45 - 55 22.38 58.48 57.47 35.09 24.66 24.92 55 - 65 16.96 44.32 43.55 26.59 18.69 18.88 >65 13.65 35.67 35.05 21.40 15.04 15.20 Table 51. Expected departure velocity and angle frequencies.

39 4.4 Impact Conditions Whereas departure conditions described the vehicle veloc- ity, angle, and orientation at the point the vehicle leaves the roadway, impact conditions describe the same characteristics at the point where an errant vehicle encounters a roadside hazard. Note that a number of the crashes included in the database involved vehicles rolling over without striking an identifiable hazard. Therefore, for the purpose of the analysis described below, impact was defined as the onset of the first harmful event. This definition assigns the impact point to either the point at which the vehicle began to roll over or the point at which it struck a fixed object, whichever occurred first. This definition was selected to produce impact condi- tions that were representative of the point at which a vehicle’s occupants began to be exposed to significant risk of injury. Most of the applications for encroachment speeds and angles described above are more appropriately addressed with impact conditions rather than departure conditions. For example, safety features need to be designed to accom- modate impact conditions rather than roadway departure speeds and angles. Similarly, benefit/cost analyses utilize impacts speed and angle to estimate the probability of injury during a ran-off-road crash. 4.4.1 Impact Speed and Angle Distributions Table 61 compares departure conditions to impact condi- tions for the first harmful event. Notice the significant change in velocity from roadway departure to the first impact. The mean departure velocity was reduced by approximately 20% or 10 mph from departure to impact. Although at first glance this difference appears to be excessive, the difference becomes more understandable with the application of a simple brak- ing formula to explore the lateral distance required to slow vehicles down from the mean departure velocity to the mean impact speed. A vehicle departing the roadway at the mean speed of 49.3 mph subjected to an effective friction of 0.7 due to braking would need to travel 30 ft before it slowed by 10 mph. If this vehicle was encroaching at the mean depar- ture angle of 16.9 degrees, it would travel only 8 ft laterally as it slowed from 49 mph to 39 mph. Since most of the roadways Figure 10. Departure angle distribution for three departure speed categories. Speed Limit (mph) No. of Cases Deg. of Freedom Chi-square Statistic P-value 75 58 4 2.69 0.611 70 114 4 3.57 0.467 65 75 1 3.37 0.066 55 361 9 10.55 0.308 50 68 4 3.56 0.469 45 195 9 11.98 0.214 Table 52. Results of independence tests.

40 Departure Angle Range Velocity (mph) 0o - 5o 5o - 10o 10o - 15o 15o - 20o 20o - 25o 25o - 30o >30o <20 0.00227 0.00516 0.00984 0.00564 0.00374 0.00236 0.00379 20 - 30 0.00552 0.01256 0.02394 0.01372 0.00910 0.00575 0.00921 30 - 40 0.01154 0.02627 0.05006 0.02869 0.01903 0.01202 0.01926 40 - 50 0.01647 0.03748 0.07142 0.04093 0.02715 0.01714 0.02748 50 - 60 0.01603 0.03649 0.06954 0.03985 0.02644 0.01669 0.02676 60 - 70 0.01065 0.02425 0.04620 0.02647 0.01756 0.01109 0.01778 >70 0.00668 0.01522 0.02900 0.01662 0.01102 0.00696 0.01116 Table 53. Departure condition distribution for all speed limits. Velocity (mph) Departure Angle Range 0o - 5o 5o - 10o 10o - 15o 15o - 20o 20o - 25o 25o - 30o >30o <30 0.00006 0.00016 0.00014 0.00009 0.00005 0.00003 0.00004 30 - 40 0.00087 0.00251 0.00219 0.00141 0.00082 0.00045 0.00055 40 - 50 0.00638 0.01838 0.01604 0.01031 0.00597 0.00332 0.00405 50 - 60 0.02166 0.06242 0.05447 0.03502 0.02027 0.01127 0.01376 60 - 70 0.03432 0.09888 0.08629 0.05548 0.03211 0.01785 0.02180 70 - 80 0.02540 0.07318 0.06387 0.04106 0.02377 0.01321 0.01613 >70 0.01029 0.02964 0.02587 0.01663 0.00963 0.00535 0.00654 Table 54. Departure condition distribution for 75 mph speed limits. Velocity (mph) Departure Angle Range 0o - 5o 5o - 10o 10o - 15o 15o - 20o 20o - 25o 25o - 30o >30o <30 0.00336 0.01268 0.01405 0.01103 0.00759 0.00492 0.00821 30 - 40 0.00631 0.02384 0.02643 0.02074 0.01427 0.00925 0.01545 40 - 50 0.01096 0.04139 0.04588 0.03600 0.02477 0.01606 0.02682 50 - 60 0.01315 0.04968 0.05507 0.04322 0.02973 0.01928 0.03219 60 - 70 0.01092 0.04124 0.04572 0.03587 0.02468 0.01600 0.02672 70 - 80 0.00627 0.02367 0.02624 0.02059 0.01416 0.00918 0.01534 >70 0.00332 0.01253 0.01389 0.01090 0.00750 0.00486 0.00812 Table 55. Departure condition distribution for 70 mph speed limits. Velocity (mph) Departure Angle Range 0o - 5o 5o - 10o 10o - 15o 15o - 20o 20o - 25o 25o - 30o >30o <30 0.00533 0.01975 0.01927 0.01293 0.00756 0.00418 0.00486 30 - 40 0.00908 0.03362 0.03281 0.02201 0.01288 0.00711 0.00827 40 - 50 0.01488 0.05512 0.05379 0.03608 0.02111 0.01166 0.01356 50 - 60 0.01712 0.06338 0.06185 0.04149 0.02427 0.01341 0.01559 60 - 70 0.01381 0.05112 0.04989 0.03347 0.01958 0.01081 0.01258 70 - 80 0.00781 0.02892 0.02823 0.01893 0.01108 0.00612 0.00712 >70 0.00415 0.01538 0.01501 0.01007 0.00589 0.00325 0.00378 Table 56. Departure condition distribution for 65 mph speed limits. Velocity (mph) Departure Angle Range 0o - 5o 5o - 10o 10o - 15o 15o - 20o 20o - 25o 25o - 30o >30o <20 0.00253 0.00749 0.00741 0.00553 0.00373 0.00241 0.00416 20 - 30 0.00678 0.02004 0.01984 0.01481 0.00998 0.00645 0.01114 30 - 40 0.01440 0.04255 0.04211 0.03143 0.02119 0.01368 0.02364 40 - 50 0.01980 0.05849 0.05789 0.04321 0.02913 0.01881 0.03250 50 - 60 0.01763 0.05209 0.05155 0.03849 0.02594 0.01675 0.02894 60 - 70 0.01017 0.03005 0.02974 0.02220 0.01497 0.00966 0.01670 >70 0.00488 0.01441 0.01426 0.01064 0.00718 0.00463 0.00801 Table 57. Departure condition distribution for 55 mph speed limits.

41 included in the study had at least a modest shoulder, an aver- age lateral movement of 8 ft is certainly not excessive. There was very little change in angle between roadway departure and the first impact as shown in Table 61. This find- ing is not surprising and may be an indication that drivers are more likely to be effective applying the brakes than steering the vehicle back to the roadway. Table 62 shows descriptive statistics for impact speed for the total data set and segregated by highway class and speed limit. It is not surprising that Interstate highways were found to have the highest impact speeds and that impact speeds for state and US routes were quite similar. Perhaps the most surprising observation that can be gleaned from Table 62 is that highways with 60 to 65 mph speed limits had higher impact speeds than roadways with 70 to 75 mph speed limits. T-tests were conducted to identify which highway classes and speed ranges could be classified as statistically unique. The purpose of this effort was to identify the most appro- priate method for segregating impact speed data. As shown in Table 63, impact speeds from Interstate highways were found to be statistically different from all of the other classes, while US Routes were found not to be statistically different from state routes. Similarly, the T-test showed that county roads and city streets could not be considered to have unique impact speeds. When this approach was applied to impact speed data segregated by speed limit, it was found that most speed limit ranges were not statistically different from the adjacent range. Only the 50–55 and 60–65 speed limit ranges Velocity (mph) Departure Angle Range 0o - 5o 5o - 10o 10o - 15o 15o - 20o 20o - 25o 25o - 30o >30o <20 0.00284 0.00634 0.00566 0.00411 0.00279 0.00184 0.00357 20 - 30 0.00939 0.02093 0.01870 0.01359 0.00922 0.00609 0.01181 30 - 40 0.02165 0.04827 0.04312 0.03134 0.02125 0.01405 0.02723 40 - 50 0.02983 0.06651 0.05942 0.04319 0.02929 0.01935 0.03752 50 - 60 0.02457 0.05479 0.04895 0.03557 0.02413 0.01594 0.03091 60 - 70 0.01210 0.02697 0.02410 0.01751 0.01188 0.00785 0.01522 >70 0.00425 0.00947 0.00846 0.00615 0.00417 0.00276 0.00534 Table 58. Departure condition distribution for 50 mph speed limits. Velocity (mph) Departure Angle Range 0o - 5o 5o - 10o 10o - 15o 15o - 20o 20o - 25o 25o - 30o >30o <20 0.00250 0.01104 0.01263 0.00970 0.00638 0.00392 0.00559 20 - 30 0.00578 0.02546 0.02913 0.02237 0.01472 0.00904 0.01289 30 - 40 0.01074 0.04733 0.05415 0.04158 0.02737 0.01681 0.02397 40 - 50 0.01282 0.05650 0.06465 0.04963 0.03267 0.02006 0.02861 50 - 60 0.00983 0.04331 0.04956 0.03805 0.02505 0.01538 0.02194 60 - 70 0.00484 0.02132 0.02439 0.01873 0.01233 0.00757 0.01080 >70 0.00188 0.00829 0.00949 0.00728 0.00479 0.00294 0.00420 Table 59. Departure condition distribution for 45 mph speed limits. Speed Limit (mph) No. of Cases Deg. of Freedom Chi-square Statistic P-value All 870 31 40.61 0.116 75 58 4 4.47 0.346 70 114 11 11.82 0.377 65 75 4 8.01 0.091 55 361 20 19.73 0.475 50 68 4 3.18 0.528 45 195 9 10.37 0.324 Table 60. Goodness-of-fit test results. Variable Mean Median Std. Deviation Minimum Maximum 90th Percentile Departure 49.3 49.2 15.91 5 97.2 69.3 Speed (mph) Impact 39.13 38.8 16.45 4.2 93.6 59.04 Departure 16.9 15 10.49 0 84 30 Angle (degree) Impact 16.96 15 11.68 0 86 32 Table 61. Descriptive statistics for impact conditions.

42 Highway Class N Mean Median Std. Deviation Minimum Maximum 90th Percentile Interstate 180 45.34 47.00 16.47 6.20 84.10 66.00 US Route 144 38.78 36.65 17.63 4.20 92.80 60.28 State Route 142 39.78 40.00 16.36 7.50 87.90 57.47 County Road 230 34.90 34.40 14.79 8.30 93.60 54.22 City Street 36 26.29 26.65 4.65 13.60 65.50 32.15 Speed Limit (mph) N Mean Median Std. Deviation Minimum Maximum 90th Percentile 35-45 163 35.12 34.30 14.71 9.70 73.10 55.66 50-55 375 37.29 36.30 15.97 4.20 93.60 56.88 60-65 72 46.12 48.00 16.69 12.60 87.90 66.08 70-75 161 43.95 45.00 16.76 6.20 84.10 65.00 Table 62. Descriptive statistics for impact speed (mph). Sample 1 Sample 2 P-value Statistically Different Interstate US Route 0.0006 Yes Interstate State Route 0.0028 Yes US Route State Route 0.6196 No US Route County Road 0.0224 Yes State Route County Road 0.0032 Yes By Highway Class County Road City Street 0.8384 No Sample 1 Sample 2 P-value Statistically Different 35-45 50-55 0.1339 No 50-55 60-65 < 0.0001 Yes By Speed Limit 60-65 70-75 0.3624 No Table 63. T-tests for impact speed. Highway Class N Mean Median Std. Deviation Minimum Maximum 90th Percentile Interstate 183 18.02 17 10.59 0 68 30.80 US Route 161 17.84 16 12.50 0 51 36.00 State Route 162 15.83 14 11.36 0 61 30.90 County Road 269 16.52 14 12.40 0 86 30.20 City Street 42 15.93 16 7.44 0 32 25.00 Speed Limit (mph) N Mean Median Std. Deviation Minimum Maximum 90th Percentile All combined 858 17.44 15.0 12.28 0 86 32.0 35-45 194 17.81 15.5 13.00 0 86 31.0 50-55 422 16.91 14.0 12.45 0 84 34.0 60-65 73 18.66 19.0 11.04 0 45 32.0 70-75 166 17.66 17.0 11.34 0 68 30.5 Table 64. Descriptive statistics for impact angle (degree). were found to be statistically dissimilar. The T-test findings indicated that segregating impact speed data by highway class may be more appropriate than segregation by speed limit range. Table 64 shows descriptive statistics for impact angle seg- regated by both highway class and speed limit. Notice that the variation in mean impact angle is relatively small for all categories of highway class and speed limit range. Further, note that all mean impact angles shown in the table are above the 15 degree value reported by Mak et al. Prior studies have reported a modest negative correlation between impact speed and impact angle, meaning higher impact speeds tend to be associated with somewhat smaller impact angles (12). Such a relationship is expected based on the reduction in vehicle cor- nering capability associated with an increase in speed. Note however that the Interstate classification, believed to have the highest operating speed of any highway class, was found to have the highest mean impact angle. Further, the second- highest speed limit range, 60–65 mph, had the highest mean impact angle of any speed limit range. However, when impact angle data sets from the various classes of highway and speed limit ranges were compared using T-tests as shown in Table 65,

43 differences between the data sets were found to be statisti- cally insignificant. Thus, this data would indicate that any correlation between impact angle and operating speed is likely to be weak. Table 66 shows descriptive statistics for impact speed and impact angle segregated by access control. Impact speeds were found to be higher on highways with full and partial access control than on highways with no access control. Table 67 shows that T-tests verified this finding by indicating that impact speeds on highways with full or partial access control are significantly different from impact speeds on highways with no access control. 4.4.2 Impact Speed and Angle Models As mentioned above, impact speed and angle have tradi- tionally been believed to be correlated because of the reduc- tion in cornering associated with higher speeds. The first step in modeling impact speed and angle data was devoted to exploring the existence of any association between these two variables. A chi-square independence test was utilized for this effort. As shown in Table 68, when the test was applied to the total data set, a strong dependence was identified between impact speed and angle (i.e., p-value = 0.0014). The Pearson correlation coefficient was found to be negative at –0.19, meaning that, as speed increased, the impact angle tended to decrease. In fact, the 95% confidence interval indicates that there is significant evidence that the correlation is negative. However the magnitude of this correlation is relatively low. The total database incorporates crash records from widely varying highway classes, ranging from fully access-controlled rural Interstates to constricted county roads and city streets. The causes and nature of crashes associated with such widely varying highway types would be expected to be quite differ- ent. Therefore, the same chi-square test for independence was conducted on each highway classification and each of the four speed limit ranges examined in the previous section. These tests would eliminate some of the wide variations in highway geometrics, operating conditions, and crash causation asso- ciated with the total data set. Sample 1 Sample 2 P-value Statistically Different Interstate US Route 0.8869 No Interstate State Route 0.0643 No US Route State Route 0.013 No US Route County Road 0.2871 No State Route County Road 0.5601 No County Road City Street 0.7623 No Table 65. Two-sample T-tests for impact angle by highway class. Access Control N Mean Median Std. Deviation Minimum Maximum 90th Percentile All combined 738 39.15 38.9 16.45 4.2 93.6 59.1 Full 252 43.65 45.0 16.71 4.2 84.1 64.9 Partial 54 40.41 42.0 17.65 7.0 87.9 60.7 Impact Speed (mph) Uncontrolled 432 36.37 35.9 15.56 5.0 93.6 55.0 All combined 821 16.96 15 11.67 0 86 32.0 Full 262 18.95 17.00 12.22 0 86 33.9 Partial 56 16.91 16 10.96 0 51 29.5 Impact Angle (degree) Uncontrolled 503 15.93 14 11.33 0 84 29.8 Table 66. Descriptive statistics for impact conditions segregated by access control. Sample 1 Sample 2 P-value Statistically different Full control Partial control 0.201 No Full control Uncontrolled < 0.0001 Yes Speed data Partial control Uncontrolled 0.0772 Yes Sample 1 Sample 2 P-value Statistically different Full control Partial control 0.2504 No Full control Uncontrolled 0.0007 Yes Angle data Partial control Uncontrolled 0.5365 No Table 67. T-tests for impact speed and angle segregated by access control.

44 When the crash data was segregated by highway class and the chi-square independence testing was repeated, the find- ings were quite different. Table 69 presents results from this chi-square testing. County road was the only highway class where any significant degree of dependence was detected. Table 69 also shows that all of the highway classes were found to have weak negative correlations between impact speed and impact angle. With the chi-square testing showing that impact speed and angle can be considered independent for most highway classes, it was decided to develop independent models for the impact speed and impact angle data. If impact speed and angle are truly independent for the segregated data, it should then be possible to combine the independent speed and angle distributions to create a joint probability distribution to fit the raw data. Several different distributions were fit to both the impact angle and speed data. Although several distributions were found to fit one or more of the data sets, the normal distri- bution was found to fit the largest number of data sets. The normal distribution provided adequate fits to most of the impact speed data sets and many of the impact angle classi- fications. Unfortunately, when these fits were used to model speed and angle data from the various highway classifica- tions, the approach failed most of the goodness-of-fit tests. The angle data was then adjusted using a square-root trans- formation, and new fits were developed. This approach provided acceptable goodness-of-fit tests for all highway classes except Interstate. However, the Interstate highway classification had shown an acceptable goodness-of-fit test using normal distribution fits and untransformed angle data. Figures 11 and 12 present normal distribution fits to impact speed and square-root impact angle data, respec- tively, to illustrate how close these estimated distributions are to the raw data. Since it was found that normal distributions provided qual- ity fits for both impact speed and impact angle data, calcula- tions of the joint probabilities for these two variables would Table 68. Test of independence results. Highway Class Chi-square Degrees-of-freedom P-value Correlation Interstate 25.8015 25 0.4183 -0.1582 US Route 21.744 20 0.3528 -0.2300 State Route 28.2857 20 0.1028 -0.2095 County Road 26.4712 15 0.0334 -0.2752 City Street 5.4704 6 0.4850 -0.0903 Table 69. Test of independence results for data segregated by highway class.

45 Figure 11. Normal distribution fit to impact speed. Figure 12. Normal distribution fit to impact angle. be mathematically possible by adopting the bivariate normal distribution. The probability of an impact falling into any cell can be calculated by solving the double integral of f(x,y) as shown below. f x y x x y x x ,( ) ( ) ⎧⎨⎩ ⎛⎝ ⎞⎠= − − − −1 2 1 1 2 12 2πσ σ ρ ρ μ σ exp 2 2 2 + − − − − ⎛ ⎝⎜ ⎞ ⎠⎟ ⎡ ⎣⎢ ⎛⎝ ⎞⎠ ⎛⎝⎜ ⎞ ⎠ y x y y y x x y y μ σ ρ μ σ μ σ ⎟ ⎤⎦⎥ ⎫⎬⎭ ( )∫∫ f x y dxdyxy , where: µx = impact speed mean µy = impact angle mean σx = impact speed standard deviation σy = impact angle standard deviation ρ = Pearson’s correlation coefficient Two basic assumptions are necessary in order to apply the bivariate normal distribution to model impact and speed data: (1) both impact speed and impact angle distributions

46 are normal, and (2) impact speed and impact angle can be con- sidered as linear combinations of two independent variables. The second assumption can be considered to be satisfied if speed and angle data pass a test for independence as illus- trated previously. Tables 70 and 71 show the goodness-of-fit results of the impact speed and angle data. The untransformed data was used for the impact speed. The transformed data was used for the impact angle, except for Interstate data. It was found that, for Interstate, the normal distribution fitted the untransformed impact angle data better than the transformed data. A bivariate normal distribution was then fitted to the speed and angle data for each of the five highway classes using mean and standard deviation values shown in Tables 70 and 71 and correlation coefficients shown in Table 69. Table 72 summarizes results of goodness-of-fit tests of the bivariate normal distribution fits to the speed and angle data. This table shows that all of the models provided accept- able fits to the raw data. County road was the only highway class that had a goodness-of-fit measure that could be clas- sified as marginal with p = 0.0747 compared to the gener- ally accepted limit of p = 0.05. This finding is not surprising since impact speed and angle were found to be dependent for this roadway class and independence is one of the assump- tions required for application of the bivariate normal distri- bution. Tables 73 through 77 show estimated impact speed and impact angle distributions for each highway class included in the study. Note that the probability distribution tables gen- erated by the bivariate normal distribution did not initially sum to 1.0. This finding arose because tails of some of the fits to the angle and speed distributions extended below zero. This problem was eliminated with normalization of Tables 73 through 77 by dividing the contents of each cell by the sum of all cells. When the data was segregated by speed limit range instead of highway classification, two of the four ranges were found to have significant dependency between impact speed and angle. Speed limit ranges of 60–65 and 70–75 mph were found to have p values of 0.0315 and 0.0153, respectively. When the analysis was carried further, it was found that nor- mal distributions fit all of the speed data and all of the angle data after a square-root transformation was applied. Further, neither the normal distributions nor any other distributions Highway Class DataTransformation Distribution P-value Coefficients Interstate Untransformeddata Normal 0.2396 mean = 45.105 Std. dev. = 16.731 US Route Untransformeddata Normal 0.1470 mean = 38.592 Std. dev. = 17.694 State Route Untransformeddata Normal 0.4398 mean = 39.601 Std. dev. = 16.055 County Road Untransformeddata Normal 0.5233 mean = 35.017 Std. dev. = 14.782 City Street Untransformeddata Normal 0.8558 mean = 35.541 Std. dev. = 13.336 Table 70. Goodness-of-fit results for speed data. Highway Class Data Transformation Distribution P-value Coefficients Untransformed data Normal 0.9857 mean = 18.287 Std. dev. = 10.681 Interstate Transformed data Normal 0.4191 mean = 4.0628 Std. dev. = 1.3399 US Route Transformed data Normal 0.7474 mean = 3.9115 Std. dev. = 1.614 State Route Transformed data Normal 0.9999 mean = 3.7777 Std. dev. = 1.4812 County Road Transformed data Normal 0.6831 mean = 3.8163 Std. dev. = 1.4558 City Street Transformed data Normal 0.9418 mean = 3.9511 Std. dev. = 0.908 Table 71. Goodness-of-fit results for angle data. Highway Class Chi-square df P-value Interstate 34.1654 31 0.318 US Route 28.4489 25 0.2876 State Route 26.9054 25 0.3606 County Road 28.4740 19 0.0747 City Street 7.8278 7 0.3480 Table 72. Goodness-of-fit results for the bivariate normal distributions.

47 Angle (degree) Speed (mph) < 6 6 - 12 12 - 18 18 - 24 24 - 30 > 30 Total < 25 0.006 0.014 0.022 0.026 0.022 0.023 0.114 25 - 35 0.011 0.022 0.034 0.037 0.030 0.028 0.161 35 - 45 0.018 0.035 0.050 0.052 0.039 0.034 0.227 45 - 55 0.020 0.038 0.051 0.051 0.037 0.029 0.226 55 - 65 0.016 0.029 0.037 0.035 0.024 0.018 0.159 > 65 0.014 0.023 0.027 0.024 0.015 0.010 0.114 Total 0.085 0.160 0.221 0.224 0.167 0.142 1.000 Table 73. Joint speed and angle distribution for Interstate freeways. Angle (degree) Speed (mph) < 6 6 - 12 12 - 18 18 - 24 24 - 30 > 30 Total < 25 0.025 0.037 0.039 0.034 0.026 0.049 0.211 25 - 35 0.030 0.040 0.039 0.032 0.023 0.038 0.202 35 - 45 0.040 0.048 0.044 0.034 0.024 0.036 0.225 45 - 55 0.038 0.042 0.036 0.026 0.018 0.025 0.184 > 55 0.045 0.043 0.034 0.023 0.014 0.018 0.178 Total 0.178 0.211 0.192 0.149 0.105 0.165 1.000 Table 74. Joint speed and angle distribution for US routes. Angle (degree) Speed (mph) < 6 6 - 12 12 - 18 18 - 24 24 - 30 > 30 Total < 25 0.019 0.033 0.036 0.031 0.023 0.035 0.177 25 - 35 0.030 0.045 0.044 0.034 0.023 0.031 0.208 35 - 45 0.044 0.058 0.052 0.038 0.024 0.029 0.246 45 - 55 0.043 0.051 0.042 0.029 0.017 0.019 0.201 > 55 0.046 0.046 0.033 0.021 0.012 0.011 0.169 Total 0.181 0.233 0.208 0.153 0.099 0.125 1.000 Table 75. Joint speed and angle distribution for state routes. Angle (degree) Speed (mph) < 6 6 - 12 12 - 18 18 - 24 24 - 30 > 30 Total < 25 0.023 0.044 0.050 0.044 0.032 0.049 0.243 25 - 35 0.036 0.057 0.055 0.043 0.028 0.035 0.253 35 - 45 0.047 0.063 0.055 0.039 0.024 0.026 0.253 > 45 0.066 0.069 0.051 0.032 0.017 0.016 0.251 Total 0.171 0.233 0.212 0.157 0.101 0.126 1.000 Table 76. Joint speed and angle distribution for county roads. Angle (degree) Speed (mph) < 12 12 - 18 > 18 Total < 25 0.059 0.069 0.082 0.211 25 - 35 0.078 0.089 0.102 0.270 35 - 45 0.083 0.092 0.103 0.279 > 45 0.074 0.079 0.086 0.240 Total 0.295 0.330 0.374 1.000 Table 77. Joint speed and angle distribution for city streets.

48 could be identified that pass goodness-of-fit testing for com- bined angle and speed distributions. This analysis clearly demonstrated that, for impact conditions, roadway classifi- cation provided a better discriminator for impact speed and angle than did speed limit range. Mak et al. obtained simi- lar results when he studied data collected under the national speed limit law. Recall that departure data was found to be more sensitive to speed limit range than highway class. These findings may be a reflection on the effects of clear zones on a driver’s ability to slow down before striking a hazard. 4.4.3 Impact Severity Impact severity has been found to be strongly correlated with the magnitude of loading during longitudinal barrier impacts. IS is defined as shown below: where: IS = Impact severity m = Vehicle mass v = Impact velocity θ = Impact angle Table 78 presents descriptive statistics for impact sever- ity from the first harmful event. IS has been accepted as the primary measure of the magnitude of a barrier crash and it is used in MASH to set limits for minimum crash condi- tions. The target IS value found in MASH for Test Level 3 IS m v= ( )1 2 2 sinθ is 156 kJ. As shown in Table 78, the 95th percentile IS value from Interstate highways was found to be 160 kJ, very near the target value for Test Level 3. Thus, the IS values recom- mended by MASH for longitudinal barrier testing appear to be appropriate. 4.4.4 Vehicle Orientation at Impact Vehicle orientation at impact has been linked to crash severity (15). Further, this parameter is also used to estimate crash costs in benefit/cost models RSAP (21). Basic descrip- tive statistics for vehicle orientation are shown in Table 79. Figure 13 presents a plot of vehicle orientation distribution from the ran-off-road crash database. Note that less than 40% of crashes were found to have heading angles between –20 and +20 degrees. 4.5 Encroachment Length The distance that a vehicle travels along the roadside is an important input to the design of guardrail installations. For the last 30 years or more, guardrail designs were based upon findings from a study of roadside encroachments by Hutchinson and Kennedy (H&K) (7). More recently, data from an encroachment study by Cooper (33) have shown longitudi- nal travel distances to be much shorter than those measured by H&K. This discrepancy has been attributed to two fundamen- tal differences between the two studies (34, 35). The Cooper study involved highways with speed limits of 59–62 mph (95–100 km/h), while the H&K study involved speed limits of 70 mph. The other explanation for differences in longi- Road Class N Mean Median Std. Dev. Minimum Maximum 90th Percentile 95th Percentile All classes combined 868 38.91 18.46 57.34 0.00 584.50 98.54 143.31 Interstate 194 51.06 32.13 66.70 0.70 584.50 123.15 159.89 US Route 157 32.63 14.52 43.60 0.20 234.45 80.41 121.74 State Route 159 43.66 19.92 61.53 0.90 392.15 113.65 180.34 County Road 273 28.68 14.78 42.52 0.00 343.14 69.45 100.90 City Street 42 23.15 15.83 24.70 0.40 127.47 48.95 62.04 Table 78. Descriptive statistics for impact severity. Road Class N Mean Median Std. Dev. Minimum Maximum 90th Percentile All Classes 842 3.3 4 69.52 -168 180 102 Interstate 188 7.29 9 80.42 -159 171 129 US Route 163 -4.12 0 70.73 -165 180 96.8 State Route 165 4.44 1 67.6 -168 180 105 County Road 275 3.96 4 64.72 -164 180 90 City Street 44 13.2 11.5 47.44 -149 115 75 Table 79. Descriptive statistics for vehicle orientation.

49 tudinal travel distances is the overrepresentation of low- angle encroachments in the H&K data. Recall that as shown in Figure 6, the angle of departure data from the current study was found to be quite similar to that from Cooper and the Pole Study, while departure angles from H&K were found to be much lower. When H&K data are adjusted to eliminate the bias toward low-angle encroachments, the differences between the Cooper and H&K longitudinal travel distances were reduced to a level that could easily be explained by dif- ferences in speed limit. The database described herein should provide some clarifi- cation of which of the two encroachment studies is most appropriate for use in determining guardrail length. Note that the 17-22 database has been constructed from reported acci- dents, many of which involved impacts with roadside objects. It is reasonable to conclude that many of these vehicles would have traveled farther if the obstacle had not been impacted. However, as described above, the crashes included in this study are strongly biased toward serious injury and fatal crashes. In effect, the data included herein was taken from the very types of roadside crashes guardrail is intended to prevent. Thus, designing guardrail configurations to withstand these crashes is more appropriate than relying on roadside encroachment data that includes very few reported crashes and undoubtedly includes many controlled encroachments that would never produce a crash. 4.5.1 Raw Data The first step in the process of evaluating longitudinal travel distances from the current study was to compare encroach- ment length data from Cooper and H&K to longitudinal travel distances from the current study as shown in Figure 14. For this figure, the data from the current study was limited to access-controlled freeways with speed limits of 70–75 mph. The Cooper data were restricted to divided highways with Figure 13. Vehicle orientation angle distribution. Figure 14. Encroachment lengths for different studies.

50 59–62 mph (95–100 km/h) speed limits and the H&K data were collected on rural Interstate highways with a 70 mph speed limit. Notice that the 17-22 travel distances are close to those from Cooper and that the differences can be explained by the higher speed limits associated with the current study. Figure 15 illustrates the effects of speed limit by comparing data from the current study collected on access-controlled highways with 55–65 mph speed limits to the Cooper data taken from divided highways with 59–62 mph (95–100 km/h) speed limits. These two distributions are not only visually similar; a two tailed T-test analysis indicated that the differ- ences are not statistically significant with a p-value of 0.966. The excellent comparison between Cooper’s data and the 17-22 data supports the hypothesis that the long encroach- ments observed in the H&K study are associated with the overrepresentation of low-angle encroachments in the study. Procedures contained in the 2006 AASHTO Roadside Design Guide identify the required length of a guardrail in terms of a runout length parameter, which is based upon the distri- bution of encroachment lengths from the H&K study. As shown in Table 80, the runout length associated with high- volume, high-speed roadways was based upon the 85th per- centile encroachment length while lower volume roadways were assigned runout lengths based upon a lower percentile encroachment length. Note that 92% of the encroachments collected by H&K were from highways with a 70 mph design speed and traffic volumes less than 6000 vehicles per day. Hence the traffic volume categories shown in Table 80 were based upon the source of the H&K data. The data from Table 80 was then extrapolated to lower design speeds. A more recent study of guardrail length-of-need utilized this same approach to apply Cooper’s data to this problem (36). Table 81 presents comparable results from the Cooper data. Thus, encroach- ment length distributions, presented in tabular form as shown in Tables 80 and 81 have been used to develop the recom- mended values for the guardrail runout length parameter. The 17-22 longitudinal encroachment lengths will therefore be presented in this same format. Figure 15. Cooper and 17-22 (55-65 mph) encroachment data comparison. Traffic Volume (ADT) >6000 2000-6000 800-2000 <800 Design Runout Length, m 146.3 134.1 121.9 109.7 Enc. Length Percentile 85% 80% 75% 70% Table 80. RDG runout lengths for 70 mph design speed. Encroachment Length Percentile Source Average Speed Limit 90% 85% 80% 75% 70% 60.5 mph 96.3 78.6 69.2 57.3 52.4Cooper 50.3 mph 54.9 46.9 42.4 38.4 34.7 Table 81. Encroachment length distributions.

51 Departure Length Percentile Speed Limit No. of Cases 90% 85% 80% 75% 70% 50% 70-75 169 109.9 101.0 85.4 73.8 66.3 49.5 55-65 424 77.0 65.4 57.0 50.0 46.5 33.8 55 353 74.4 62.0 52.0 47.0 44.7 32 45-50 253 63.1 50.0 43.2 38.8 34.8 24 45 186 60.8 47.1 41.8 37.0 33.0 24 Table 82. Departure length segregated by speed limit. Departure Length Percentile Volume Class No. of Cases 90% 85% 80% 75% 70% 50% High 189 92.1 80.9 70.2 61.2 57 38 Medium 207 95.3 84 71.2 64.6 61.8 42.6 Low 388 65.2 53 47 43.6 40 26.6 Table 83. Departure length segregated by traffic volume. Departure Length Percentile Access Control No. of Cases 90% 85% 80% 75% 70% 50% Full 263 102.7 89.3 76.5 68 62.8 45.4 None 493 66.7 54 47 43.5 40 28 Table 84. Departure length segregated by access control. Departure Length Percentile Speed Limit Access Control No. of Cases 90% 85% 80% 75% 70% 50% 70-75 Full 151 109.1 101.1 88 75.1 66.7 50 55-65 Full 98 89.6 76.9 65 60.5 54 40 55-65 None 284 68.7 57.8 49.2 46 43 32 45-50 None 205 61 49 42.9 37 33 24.8 Table 85. Departure length segregated by speed limit and access control. Longitudinal departure length data from the 17-22 data set were first examined when categorized by speed limit, access control, and traffic volume. Table 82 presents departure length data segregated by speed limit. Note that there were too few cases with 65 and 50 mph to reliably establish the tail of the distributions. These cases were lumped with the next lower speed limit categories to illustrate the general trend between speed limit and departure length. Table 82 shows that there is a relatively strong trend for departure length to increase with higher speed limits. The effects of traffic volume and access control on depar- ture lengths were then explored as shown in Tables 83 and 84, respectively. Notice that there is no clear trend between traffic volume category and departure length and there appears to be a strong relationship between access control and depar- ture length. However, there is also correlation between speed limit and access control. In order to isolate the importance of access control on departure length, it is necessary to iso- late the evaluation to a constant speed limit. This type of evaluation could not be conducted on the tail of the depar- ture length distribution as shown in Tables 82 through 84 because of the small sample sizes at any one speed limit. Therefore, the effect of access control was evaluated at the median for a 55 mph speed limit. The median departure lengths for a 55 mph roadway were found to be 45.2 m and 32.0 m for full and no access control, respectively. The nearly 50% increase in median departure length demonstrates that full access control has a significant effect beyond its correla- tion with speed limit. In light of the finding that traffic volume had no consistent effect on departure length, this parameter was eliminated from further consideration. Departure length data was then segregated by access control and speed limit as shown in Table 85. Note that for the 55–65 mph category, there were

52 sufficient data to provide departure lengths for both full and no access control. 4.5.2 Screened Data The data shown in Table 85 provides measures of the length of vehicle departures for several speed limit and access control categories. Although this table represents the actual travel distances associated with serious injury and fatal crashes, the data may be distorted by the placement of longi- tudinal barriers. Barriers placed adjacent to the travelway are designed to redirect vehicles away from roadside obstacles and toward the travelway. Thus, longitudinal barriers are likely to reduce the length of travel along the roadside and the departure length data shown in Table 85 may be artificially shortened. The effects of longitudinal barriers on the length of roadside travel were investigated by removing all crashes involving barrier impacts. The data shown in Table 85 was then adjusted by excluding all crashes involving barrier impacts and is presented in Table 86. Note that the number of cases in the 55–65 mph, full access-control category was reduced to the point that the tail of the distribution could not be reliably determined. Further, eliminating barrier impacts increased longitudinal travel distance values for access control freeway by an average of 2% and decreased lengths for roadways with- out access control by approximately 1%. The minor differences between Tables 85 and 86 appear to indicate that longitudinal barriers do not produce a significant reduction in the dis- tances that vehicles travel along the roadway during ran-off- road events. This finding may indicate that, for most impacts, longitudinal barriers do not redirect cars back onto the road- way, but rather allow impacting vehicles to rub along the face of the barrier. There was also a concern that rigid objects may have an effect on longitudinal travel distances. This concern is based on the assumption that, for most crashes involving a rigid obstacle, impacting vehicles are brought to a premature stop. In this situation, the length the vehicle travels along the roadside would be artificially reduced. This effect was again explored by removing crashes involving rigid obstacles from the data set and re-tabulating the data as shown in Table 87. Again, the effects of removing rigid obstacle crashes from the database were extremely minor. The average change in depar- ture length between Tables 86 and 87 was found to be less than 0.5%. Based upon the minor differences in Tables 85, 86, and 87, it can be concluded that the upper tails of the road- side departure length distributions from the 17-22 database are not significantly affected by the presence of roadside bar- riers or rigid obstacles. Thus it is recommended that Table 85 be used in the evaluation of guardrail runout length calcula- tion procedures. 4.6 Significance for Guardrail Runout Length As mentioned previously, guardrail length-of-need is determined based upon the design runout length. This length is used to identify locations along the roadway in advance of a roadside object where barriers must begin to be effective. Table 88 shows the recommended runout lengths contained in the 2006 AASHTO Roadside Design Guide. As mentioned above these values are based on the H&K encroachment data (7). Table 89 presents runout length recommendations from a 1996 study that applied Cooper’s data (33) to the design of guardrail layouts. Note that the runout length rec- ommendations were based upon the upper tail of encroach- Departure Length Percentile Speed Limit Access Control No. of Cases 90% 85% 80% 75% 70% 50% 70-75 Full 137 111 101.6 88.7 77.2 67 52.5 55-65 None 263 67.9 55.6 49 46 43 31.8 45-50 None 201 61.8 48.4 41.8 36.8 32.6 24.7 Table 86. Departure lengths excluding barrier impacts. Departure Length Percentile Speed Limit Access Control No. of Cases 90% 85% 80% 75% 70% 50% 70-75 Full 136 111.5 101.7 88.9 78.2 67.4 53 55-65 None 262 67.9 55.7 49 46 43 31.6 45-50 None 196 62.3 48 41.7 36 32.2 24.6 Table 87. Departure lengths excluding barrier and rigid obstacle impacts.

53 ment length distributions from H&K and Cooper. For Table 88, the top row of runout lengths were obtained from the 85th, 80th, 75th, and 70th percentile runout lengths from the H&K study. Because the Cooper study contained no highways with 70 mph speed limits, the top row of Table 89 was obtained by extrapolating the 90th, 85th, 80th, and 75th percentile encroachment lengths from the divided highways with 59–62 mph speed limits included in the Cooper study. When the data from the 17-22 study shown in Table 85 is compared with RDG runout length guidelines, it is clear that existing guardrail design procedures greatly overesti- mate guardrail lengths. Note the 90th percentile departure length shown in Table 85. Note that the recommended runout length for high traffic volumes with a 70 mph design speed is approximately one-third greater than the 90th percentile departure length found along access-controlled freeways with speed limits from 70 to 75 mph. The difference between the 17-22 departure lengths and the H&K–based runout lengths increases further until it reaches 46% for traffic vol- umes of less than 800 average daily traffic (ADT), which were intended to correlate with the 70th percentile encroachment length. Thus, 17-22 data indicates that the guardrail length recommendations contained in the RDG grossly overstate guardrail need. It is important to note that guardrail is a roadside hazard that produces approximately 1200 fatalities per year. Therefore, there is a penalty for placing too much guardrail adjacent to the roadway and excessive guardrail length is likely to produce greater numbers of serious in- juries and fatalities than would be associated with shorter installations. Note that findings from the 17-22 data compare much better to guardrail length guidelines developed from Cooper. The 90th percentile departure length for 70–75 mph speed limits with full access control is virtually identical to the rec- ommended guardrail runout length for a 70 mph design speed and high traffic volume. However, the recommended runout lengths for lower traffic volumes appear to drop faster than would be indicated from the 17-22 accident data shown in Table 85. However, the recommended lengths do match up well with the 80th, 75th, and 70th percentile departure length from Table 85. Recall that the original guardrail length guidelines were developed based on the 85th through 70th encroachment lengths from the H&K data. The approach was shifted slightly to utilize the 90th through 75th percentile encroachment length when Cooper data was utilized in place of the H&K study. This adjustment was implemented because Cooper’s data did not include any highways with speed lim- its greater than 62 mph. When the entire history of guardrail length determination is considered, the guardrail runout length recommendations for a 70 mph design speed shown in Table 89 are found to compare very well with the 17-22 Traffic Volume ADT 6000 2000-6000 800-2000 <800 Design Speed (mph) Runout Length (m) Runout Length (m) Runout Length (m) Runout Length (m) 70 146 134 122 110 60 122 112 101 91 50 98 89 81 73 40 73 67 61 55 30 49 45 41 37 Table 88. Runout length recommendations from the RDG. Traffic Volume ADT 10,000 5,000-10,000 1,000-5,000 <1,000 Design Speed (mph) Runout Length (m) Runout Length (m) Runout Length (m) Runout Length (m) 70 110 91 79 67 60 79 64 55 49 50 64 52 46 40 40 49 40 34 30 30 34 27 24 21 Table 89. Runout length recommendations from Wolford & Sicking (36).

54 departure length distribution for access-controlled freeways with 70–75 mph speed limits. Note that for design speeds of 60 mph, guardrail runout lengths shown in Table 89 appear to be midway between the full access control and no access control data for 55–65 mph speed limits. If it is assumed that fully access-controlled free- ways are designed to a 70 mph or higher design speed, guard- rail runout length recommendations shown in Table 89 can be considered to be conservative. However, if fully access- controlled roadways utilize a 60 mph design speed, the rec- ommended guardrail lengths should probably be extended. Recommended guardrail runout lengths for a 50 mph design speed also compare well with departure lengths from roadways with speed limits of 45–50 mph and no access control. Note that the recommended runout lengths are consistently 3 m longer than the measured departure lengths shown in Table 85. In summary, with the exception of highways with a design speed of 60 mph and full access control, guardrail length rec- ommendations based on Cooper’s data compare surprisingly well with departure length data described herein. Therefore, it is recommended that AASHTO consider adding a recom- mendation that guardrails placed along fully access-controlled freeways should be designed for 70 mph, regardless of the actual design speed.

Next: Chapter 5 - Long-Term Data Collection Plan »
Identification of Vehicular Impact Conditions Associated with Serious Ran-off-Road Crashes Get This Book
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TRB’s National Cooperative Highway Research Program (NCHRP) Report 665: Identification of Vehicular Impact Conditions Associated with Serious Ran-off-Road Crashes quantifies the characteristics of ran-off-road crashes and identifies appropriate impact conditions for use in full-scale crash testing.

Appendices A through F of NCHRP Report 665, which are as follows, are available online:

Appendix A: Annotated Bibliography

Appendix B: 1997–2001 NASS CDS Cases

Appendix C: Supplemental Data Collection Protocol

Appendix D: Database Content

Appendix E: Additional Tables, Plots, and Analysis Results

Appendix F: Proposed Data Collection Forms Continuous Sampling Subsystem

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