Below are the first 10 and last 10 pages of uncorrected machine-read text (when available) of this chapter, followed by the top 30 algorithmically extracted key phrases from the chapter as a whole.

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

Do not use for reproduction, copying, pasting, or reading; exclusively for search engines.

OCR for page 39

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

OCR for page 39

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

OCR for page 39

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

OCR for page 39

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

OCR for page 39

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

OCR for page 39

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

OCR for page 39

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
µx = impact speed mean
can be calculated by solving the double integral of f(x,y) as
µy = 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.

OCR for page 39

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

OCR for page 39

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