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32 Table 32. Crash severity by departure velocity. Injury Severity Levels Departure Velocity No. of Fatal Injury A Injury B Injury C PDO (mph) Cases No. % No. % No. % No. % No. % < 30 103 3 2.9% 50 48.5% 10 9.7% 17 16.5% 23 22.3% 3045 240 18 7.5% 135 56.3% 35 14.6% 23 9.6% 29 12.1% 45.160 313 52 16.6% 192 61.3% 30 9.6% 26 8.3% 13 4.2% 60.175 166 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 33. Crash severity by vehicle size for departure velocities of 6075 mph. Injury Severity Levels Vehicle Class Fatal Injury A Injury B Injury C PDO 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% that the database described herein cannot be used to eval- eral trend for lower impact angles to produce higher crash uate the severity of different types of crashes whether it severities, when A+K severities are considered, the apparent involves crash outcome such as rollover, vehicle class, or relationship disappears and impact angle appears to have object struck. little correlation with severity. Even in light of the very lim- However, the purpose of this database is not to provide rel- ited amount of data, this finding was quite surprising. The ative comparisons of crash severities available from conven- relationship between IS value and crash severity, shown in tional databases, but rather to provide the basis for developing Table 37, was also quite surprising. After further investiga- a relationship between crash conditions and severity for vari- tion, it was discovered that the guardrail impact was not the ous types of hazards. Table 32 illustrates the strong relationship most harmful event for most of the serious injuries associated between departure velocity and crash severity. Both fatality rate with low angle and low IS crashes. Tables 38 and 39 present and A+K rate increased with each increment in departure crash severity versus impact angle and IS value for crashes velocity. Tables 33 and 34 show injury severity and rollover where the guardrail impact was the most severe event. These risk, respectively, by vehicle type for departure velocities from tables display the expected correlation between impact angle 60 to 75 mph. and IS versus crash severity. 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- 4.3 Departure Conditions ity of fatal and serious injury. Table 36 provides a compari- One of the primary objectives of developing the database son between impact angle and crash severity for W-beam described herein was to identify the departure conditions guardrails. Although at first glance, there appears to be a gen- 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 Table 34. Rollover risk by vehicle size for database is heavily biased and it can be considered to be rep- departure velocities of 6075 mph. resentative of serious ran-off-road crashes. Rollover Vehicle Class Yes No No. % No. % 4.3.1 Departure Speed and Car 51 66.2% 26 33.8% Angle Distributions Pickup 35 79.6% 9 20.5% Utility 35 89.7% 4 10.3% As shown in Table 40, the mean departure speed was found Van 5 83.3% 1 16.7% to be 49.26 mph. This value was higher than the mean value

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33 Table 35. Crash severity vs. impact speed for W-beam guardrail. Maximum Injury PDO Fatalities A-Injuries B-Injuries C-Injuries Crashes 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 36. Severity by impact angle of crashes involving guardrails. 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 37. Severity by IS value 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 38. Crash severity by impact angle 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 39. Crash severity vs. IS when guardrail impact was most harmful event. 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

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34 Table 40. Velocity and angle descriptive statistics. Standard 10th 90th Variable Mean Median Deviation Minimum Maximum percentile 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 41. Velocity Comparison with Mak et al. (3). 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 found by Mak et al. (3) in the 1980s. Table 41 presents a severity associated with the use of antilock brakes. This find- comparison of velocity data from the current study and Mak ing may indicate that allowing drivers to continue to steer et al.'s Pole Study. In order to compare the two studies, it was through emergency situations does not necessarily reduce necessary to adjust the roadway classifications in this study to the angle of departure from the roadway. Figure 6 shows a match the functional classes in Mak et al. All fully controlled graphical comparison of freeway departure angles for the access roadways were classified as freeways and US and state 17-22 database, encroachment data from Cooper (33) and routes were classified as arterials. County roads and city streets Hutchinson and Kennedy (7), and impact angles from the were then placed into the collector/local category. Although Pole Study. Note that the angle distributions from the current this classification scheme is not perfect, it did place all road- study are very near those found by Cooper. Table 42 presents ways with high volume and most medium-volume roadways a comparison between departure angles from the 17-22 data in the arterial category. Note the velocity distributions from this and impact angles from the Pole Study for all roadway classes. study are significantly higher than those found by Mak et al. (3). Notice that with the exception of urban local/collector, all This finding is believed to arise from three factors: (1) the measures of departure angle for the current study were higher elimination of the national speed limit law; (2) the bias in than impact angles from the Pole Study. However, the mag- the current study toward severe crashes; and (3) the Mak data nitude of the differences was found to be relatively modest. 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 Figure 5. Freeway velocity distributions from Pole to identify any significant reduction in crash risk or crash Study and 17-22.

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35 Table 42. Angle comparison with Mak et al. (3). 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 4.3.2 Theoretical Modeling of Departure Tables 43 through 46 also present skewness values for veloc- Speed and Angle Distributions ity and angle data. Note that mean skewness for velocity data is near zero while mean skewness for angle data is above 1.0. Tables 43 and 44 show descriptive statistics for departure These skewness measures indicate that the velocity data may velocity and angle respectively, segregated by road class. Note best be modeled with a normal distribution while angle data that with the exception of the Interstate classification, the mean would be more likely to fit a gamma model. velocities were quite similar. Further departure angle did not Angle and velocity data from the Pole Study were found to vary significantly from one road classification to the next. These fit a gamma distribution while other studies (1) found that the findings lead to the conclusion that roadway classification may speed data fit a normal distribution. As a first step to modeling not be the best discriminator for departure conditions. departure conditions, normal and gamma distributions were Tables 45 and 46 show descriptive statistics for departure fit to departure speed and angle data for the total database velocity and angle respectively, segregated by speed limit. and for each speed limit range as shown in Tables 47 and 48. Note that the mean velocities now show more significant Table 47 shows that the velocity distributions for the total variation and the trend is correlated with speed limit. There is also more discrimination in the mean angle when the data database and all categories of speed limit were found to fit a are segregated by speed limit. Although prior studies showed normal distribution quite well. Although the gamma distri- that functional class was the best discriminator for depar- bution was found to fit most speed limit categories acceptably ture speed, functional class was not identifiable in the current well, p-values for both the total data set and the 50 mph speed database. Findings from Tables 43 through 46 indicate that limit category were below 0.05, indicating a poor fit to the data. the surrogate measures used to indicate functional class may Figure 7 shows the quality of fit for normal and gamma distri- not be appropriate. However, speed limit does appear to pro- bution to velocity data for the total database. Notice that the vide a significant degree of discrimination for both departure gamma distribution does not match the data very well. speed and angle. 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- Figure 6. Comparison of freeway departure angle ever, adjusting the independent variable in this manner is an distributions. acceptable method for improving statistical fits to measured

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36 Table 43. Departure velocity statistics by highway class. Speed Limit Min. Vel Mean Vel. Max. Vel Standard Road Class No. of Cases Skewness (mph) (mph) (mph) (mph) Deviation 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 44. Departure angle statistics by highway class. Speed Limit Min. Ang. Mean Ang. Max. Ang. Standard Road Class No. of Cases Skewness (mph) (deg) (deg) (deg) Deviation 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 45. Departure velocity statistics by speed limit. Speed Limit No. of Min. Vel. Mean Vel. Max. Vel Standard (mph) Cases (mph) (mph) (mph) 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 46. Departure angle statistics by speed limit. Speed Limit No. of Min. Ang. Mean Ang. Max Ang. Standard (mph) Cases (deg) (deg) (deg) 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 47. Normal and gamma distribution fits to speed data. Mean Chi Squared Normal Gamma Dist. Chi Squared Gamma Speed Limit No. of Vel. Standard (mph) Cases (mph) 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

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37 Table 48. Normal and gamma distribution fits to angle data. Speed Limit No. of Mean Standard Chi Squared Normal Gamma Dist. Chi Squared - Gamma (mph) Cases Angle (deg) 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 data. As shown in Table 49, the gamma distribution was (Oi - Ei )2 = i =1 2 k found to fit the square root of the departure angle for all speed Ei 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- where: atively marginal. Note however that the p-values for all indi- vidual speed limit categories were found to be 0.27 or higher, = Chi-square measure of error between the two contin- which indicates a reasonably good fit to the data. Figure 9 illus- gency tables trates the use of a gamma distribution fit to the square root of Oi = Observed frequency in cell i the departure angle to model departure angle data. Ei = Expected frequency in cell i Tables 47 and 49 provide parameters for fitting normal and k = number of cells in table. gamma distributions to departure speed and square root of The chi-square statistic calculated from Tables 50 and 51 departure angle, respectively. The next step in modeling depar- was found to be 30.54. The number of degrees of freedom for ture conditions involved exploring the dependence of speed this test is one less than the number of rows times one less and angle. A chi-square test for independence was employed than the number of columns. In the example of the entire for this evaluation. Table 50 shows a contingency table for all data base, the 6 x 6 contingency table shown in Table 48 has departure speed and angle combinations and Table 51 presents 25 degrees of freedom. The chi-square statistic of 30.54 and expected frequencies if speed and angle are independent. A 25 degrees of freedom produce a p-value of 0.205. This mag- chi-square goodness-of-fit test was then used to measure the nitude of the p-value indicates that angle and speed data can appropriateness of the independence assumption using the fol- be considered to be independent. The relationship between lowing equation to calculate the chi-square statistic. speed and angle of departure can be graphically illustrated by plotting the distribution of departure angle for three different Figure 7. Normal and gamma distribution fits to Figure 8. Normal and Gamma Distribution Fits departure speed. to Departure Angle (all data).

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38 Table 49. Gamma distribution fit to square root of departure angle. No. of Square Root Angle Gamma Distribution Chi Squared - Gamma Speed Limit (mph) 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 speed ranges as shown in Figure 10. Note that the angle dis- duce speed and angle probability distributions for each speed tribution for the low-speed range was found to be higher than limit category as shown in Tables 53 through 59. the middle- or high-speed range, while differences in depar- Chi-square tests were then conducted to compare pre- ture angle distribution for high- and middle-speed ranges dicted and observed frequencies for each speed limit category. were found not to be statistically significant. The fact that As shown in Table 60, the predicted frequencies compared the differences between departure angle distributions for reasonably well with the observed values for most speed the middle- and high-speed ranges were not statistically sig- limit categories. These findings indicate that it is acceptable nificant further reinforces the finding that the correlation to model departure speed and angle as independent variables. between speed and angle is sufficiently weak to treat them Further, departure speed can be modeled using the normal as independent. distribution parameters shown in Table 47 and departure In view of the finding of limited dependence between depar- angle can be modeled using the gamma distribution fits to ture speed and angle for the total database, the chi-square test square root of departure angle presented in Table 49. These for independence was applied to the speed and angle of depar- models produce the departure conditions shown in Tables 53 ture data for each speed limit category. The resulting p-values through 59. 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- Table 50. Observed departure conditions. sible to reject the assumption that the velocity and angle data are independent whenever cases are segregated by speed limit. Departure Departure Angle (deg.) Based upon the finding of, at most, a very limited degree of Velocity (mph) 30 dependence between departure speed and angle, the normal <25 4 15 16 10 7 13 distribution fit to velocity data and the gamma distribution fit to square root angle data can be applied independently to pro- 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 51. Expected departure velocity and angle frequencies. Departure Departure Angles (deg.) Velocity (mph) 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 Figure 9. Square root of departure angle used to model >65 13.65 35.67 35.05 21.40 15.04 15.20 departure angle (all data).