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

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40 Table 53. Departure condition distribution for all speed limits. Departure Angle Range Velocity (mph) o 0 -5 o o 5 - 10 o 10 - 15o o 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 54. Departure condition distribution for 75 mph speed limits. Departure Angle Range Velocity (mph) o 0 -5 o o 5 - 10 o 10 - 15o o 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 55. Departure condition distribution for 70 mph speed limits. Departure Angle Range Velocity (mph) 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 56. Departure condition distribution for 65 mph speed limits. Departure Angle Range Velocity (mph) o o o o 0 -5 5 - 10 10 - 15o o 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 57. Departure condition distribution for 55 mph speed limits. Departure Angle Range Velocity (mph) 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

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41 Table 58. Departure condition distribution for 50 mph speed limits. Departure Angle Range Velocity (mph) 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 59. Departure condition distribution for 45 mph speed limits. Departure Angle Range Velocity (mph) 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 60. Goodness-of-fit test results. limit. It is not surprising that Interstate highways were found to have the highest impact speeds and that impact Deg. of Chi-square Speed Limit (mph) No. of Cases Freedom Statistic P-value speeds for state and US routes were quite similar. Perhaps All 870 31 40.61 0.116 the most surprising observation that can be gleaned from 75 58 4 4.47 0.346 Table 62 is that highways with 60 to 65 mph speed limits 70 114 11 11.82 0.377 had higher impact speeds than roadways with 70 to 75 mph 65 75 4 8.01 0.091 speed limits. 55 361 20 19.73 0.475 T-tests were conducted to identify which highway classes 50 68 4 3.18 0.528 and speed ranges could be classified as statistically unique. 45 195 9 10.37 0.324 The purpose of this effort was to identify the most appro- priate method for segregating impact speed data. As shown included in the study had at least a modest shoulder, an aver- in Table 63, impact speeds from Interstate highways were age lateral movement of 8 ft is certainly not excessive. found to be statistically different from all of the other classes, There was very little change in angle between roadway while US Routes were found not to be statistically different departure and the first impact as shown in Table 61. This find- from state routes. Similarly, the T-test showed that county ing is not surprising and may be an indication that drivers are roads and city streets could not be considered to have unique more likely to be effective applying the brakes than steering impact speeds. When this approach was applied to impact the vehicle back to the roadway. speed data segregated by speed limit, it was found that most Table 62 shows descriptive statistics for impact speed for speed limit ranges were not statistically different from the the total data set and segregated by highway class and speed adjacent range. Only the 5055 and 6065 speed limit ranges Table 61. Descriptive statistics for impact conditions. 90th Variable Mean Median Std. Deviation Minimum Maximum 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

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42 Table 62. Descriptive statistics for impact speed (mph). Std. 90th Highway Class N Mean Median Deviation Minimum Maximum 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 Std. 90th Speed Limit (mph) N Mean Median Deviation Minimum Maximum 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 were found to be statistically dissimilar. The T-test findings and impact angle, meaning higher impact speeds tend to be indicated that segregating impact speed data by highway associated with somewhat smaller impact angles (12). Such a class may be more appropriate than segregation by speed relationship is expected based on the reduction in vehicle cor- limit range. nering capability associated with an increase in speed. Note Table 64 shows descriptive statistics for impact angle seg- however that the Interstate classification, believed to have regated by both highway class and speed limit. Notice that the highest operating speed of any highway class, was found the variation in mean impact angle is relatively small for all to have the highest mean impact angle. Further, the second- categories of highway class and speed limit range. Further, highest speed limit range, 6065 mph, had the highest mean note that all mean impact angles shown in the table are above impact angle of any speed limit range. However, when impact the 15 degree value reported by Mak et al. Prior studies have angle data sets from the various classes of highway and speed reported a modest negative correlation between impact speed limit ranges were compared using T-tests as shown in Table 65, Table 63. T-tests for impact speed. Sample 1 Sample 2 P-value Statistically Different Interstate US Route 0.0006 Yes Interstate State Route 0.0028 Yes By Highway Class US Route State Route 0.6196 No US Route County Road 0.0224 Yes State Route County Road 0.0032 Yes County Road City Street 0.8384 No Sample 1 Sample 2 P-value Statistically Different 35-45 50-55 0.1339 No By Speed Limit 50-55 60-65 < 0.0001 Yes 60-65 70-75 0.3624 No Table 64. Descriptive statistics for impact angle (degree). Std. 90th Highway Class N Mean Median Deviation Minimum Maximum 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 Std. 90th Speed Limit (mph) N Mean Median Deviation Minimum Maximum 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

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

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

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45 Figure 11. Normal distribution fit to impact speed. be mathematically possible by adopting the bivariate normal where: distribution. The probability of an impact falling into any cell x = impact speed mean can be calculated by solving the double integral of f(x,y) as y = impact angle mean shown below. x = impact speed standard deviation x - x 2 y - y 2 y = impact angle standard deviation 1 1 f ( x, y ) = exp - + = Pearson's correlation coefficient 2 x y 1 - 2 2 (1 - 2 ) x y Two basic assumptions are necessary in order to apply the x - x y - y - 2 x f ( x , y ) dxdy bivariate normal distribution to model impact and speed y y x data: (1) both impact speed and impact angle distributions Figure 12. Normal distribution fit to impact angle.

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46 Table 70. Goodness-of-fit results for speed data. Data Highway Class Distribution P-value Coefficients Transformation Untransformed Interstate Normal 0.2396 mean = 45.105 Std. dev. = 16.731 data Untransformed US Route Normal 0.1470 mean = 38.592 Std. dev. = 17.694 data Untransformed State Route Normal 0.4398 mean = 39.601 Std. dev. = 16.055 data Untransformed County Road Normal 0.5233 mean = 35.017 Std. dev. = 14.782 data Untransformed City Street Normal 0.8558 mean = 35.541 Std. dev. = 13.336 data Table 71. Goodness-of-fit results for angle 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 are normal, and (2) impact speed and impact angle can be con- since impact speed and angle were found to be dependent for sidered as linear combinations of two independent variables. this roadway class and independence is one of the assump- The second assumption can be considered to be satisfied if tions required for application of the bivariate normal distri- speed and angle data pass a test for independence as illus- bution. Tables 73 through 77 show estimated impact speed trated previously. Tables 70 and 71 show the goodness-of-fit and impact angle distributions for each highway class included results of the impact speed and angle data. The untransformed in the study. Note that the probability distribution tables gen- data was used for the impact speed. The transformed data was erated by the bivariate normal distribution did not initially used for the impact angle, except for Interstate data. It was sum to 1.0. This finding arose because tails of some of the fits found that, for Interstate, the normal distribution fitted the to the angle and speed distributions extended below zero. This untransformed impact angle data better than the transformed problem was eliminated with normalization of Tables 73 data. A bivariate normal distribution was then fitted to the through 77 by dividing the contents of each cell by the sum speed and angle data for each of the five highway classes using of all cells. mean and standard deviation values shown in Tables 70 and When the data was segregated by speed limit range instead 71 and correlation coefficients shown in Table 69. of highway classification, two of the four ranges were found Table 72 summarizes results of goodness-of-fit tests of to have significant dependency between impact speed and the bivariate normal distribution fits to the speed and angle angle. Speed limit ranges of 6065 and 7075 mph were data. This table shows that all of the models provided accept- found to have p values of 0.0315 and 0.0153, respectively. able fits to the raw data. County road was the only highway When the analysis was carried further, it was found that nor- class that had a goodness-of-fit measure that could be clas- mal distributions fit all of the speed data and all of the angle sified as marginal with p = 0.0747 compared to the gener- data after a square-root transformation was applied. Further, ally accepted limit of p = 0.05. This finding is not surprising neither the normal distributions nor any other distributions Table 72. Goodness-of-fit results for the bivariate normal distributions. 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

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47 Table 73. Joint speed and angle distribution for Interstate freeways. Angle (degree) Speed (mph) Total 30 < 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 74. Joint speed and angle distribution for US routes. Angle (degree) Speed (mph) Total 30 < 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 75. Joint speed and angle distribution for state routes. Angle (degree) Speed (mph) Total 30 < 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 76. Joint speed and angle distribution for county roads. Angle (degree) Speed (mph) Total 30 < 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 77. Joint speed and angle distribution for city streets. Angle (degree) Speed (mph) Total 18 < 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