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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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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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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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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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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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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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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).