The Traffic Accident Reconstruction Origin -ARnews-
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The Traffic Accident Reconstruction Origin -ARnews-
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Most highway design books (blue book, green book) also refer to a similar equation.
For a given lateral travel distance:
the angle at exit for a 'drift off the road' would be calculated assuming in the equation that the maximum acceleration is less than 0.10 g's.
For an 'evasive manuever', it would be greater
In cornering maneuvers drivers normally do not exceed ~0.30 g's lateral accel,
In evasive maneuvers it is greater (~0.40-0.50 g's) up to the limits of friction (visible tire marks))
Brian McHenry
mchenry@interpath.com
For example, to continue this discussion look for a thread titled
Accident Investigation Societies??
If this thread does not exist in the current archive, you can begin another one by using that title.
Test Data and Analysis
The test data, with the calculated drag factors, are displayed in Table 1. The results of 40 tests are shown in that table, although 42 tests were conducted. The results of test 22 are not shown, as none of the three timers had valid results. The results of test 36 are not shown, as a radar speed was not recorded. In three of the tests (16, 18, and 33), only two times, not three, were recorded, so only two times were averaged in the drag factor calculation for those three tests.
To calculate the drag factors, the following formulae were used:
Drag factor from skid distance:
where m = drag factor (or coefficient of friction) , vi = initial speed (in feet per second), x = skid distance. (in feet), g = 32.2 ft/sec2.
Drag factor from skid time:
where t = average skid time for a given test (in seconds).
The results for all reported tests are displayed graphically in four figures as a function of initial speed—Figure 1 for time-based results on dry concrete, Figure 2 for distance-based results on dry concrete, Figure 3 for time-based results on wet concrete, and Figure 4 for distance-based results on wet concrete. A least-squares fit for a straight line to the data also is displayed on each graph, which allows trends—variations in m with speed—to be observed. For comparison purposes, all four trend lines are displayed in Figure 5.
The numerical values of the drag factors, based upon the least-squares fit, are displayed in Table 2 for 30 mph and 70 mph for the four different conditions (wet/dry surface, distance/time calculation of m). Likewise, the simple averages of the drag factors in the 30 mph and 70 mph speed areas are shown in Table 3, along with the spreads in the data points. This will facilitate a discussion of the values in the next section.
An alternate way of analyzing the speed dependence of the drag factor is to study the average speed during skidding. The average speed is defined as the distance traveled divided by the elapsed time (x/t). Now if the drag factor actually does not depend upon speed, then during skidding the speed will decrease linearly with time, and its average value will be half its initial value (vi/2). Thus, in this case x/t and vi/2 will have the same value. If, however, the drag factor is less at higher speeds, then the vehicle will not slow down as rapidly at higher speeds, and it will spend more time at the higher speeds than at the lower speeds, making the average speed (x/t) be greater than vi/2, since the vehicle will have traveled farther. Likewise, if the drag factor is more at higher speeds, then the vehicle will slow down more rapidly at the higher speeds, so it will spend less time going faster than it does going slower, and vi/2 will be greater than the average speed x/t. Thus, by comparing the difference Dv in these two values, we can gain insight into the speed behavior of the drag factor.
Table 4 gives a comparison of the two different average speed calculations in the right-hand column. The average value of Dv is given at the bottom of the table. The differences are displayed graphically in Figure 5, along with a trend line. In both Table 4 and Figure 5, the effects of two tests (15 and 16), which lie far outside the other results, have been ignored.
Discussion of Results
The results clearly show that the drag factor for the wet surface is considerably lower than the drag factor for the dry surface—approximately 0.2. The speed dependence appears to be a more complex issue. For both the wet and dry surfaces, the least squares fit indicates that the drag factor changes with speed, but that change may be positive or negative, depending upon the surface and the method for determining m In all cases, the effect is rather small, and probably can be neglected. In that case, and taking into account the spread in the data values, the drag factor for the wet concrete surface can be taken as 0.48 +/- 0.02, and for the dry concrete surface as 0.69 +/- 0.03. (The spread in the individual data points is more than 0.02 or 0.03, but the deviation of the true value of m from the collective average of the measurements can be taken as much less than that.)
A comparison of the results of calculating the average speed during skid-to-stop by two different methods strongly reinforces the conclusion that the drag factor has little, if any, speed dependence. The average value of the difference between the two method is 0.81 mph (for wet surfaces) as can be seen from Table 4. Since the radar records only the integer value of the initial speed, the actual initial speed was approximately 0.5 mph higher than the recorded one (that is, for a recorded speed of, say, 70 mph, the actual speed could have been anywhere between 70.00 mph and 70.99 mph—after many measurements the average of the actual speed would have been about 70.50 mph). This means that the discrepancy between the two average speed calculations, rather than being 0.8 mph, was only 0.3 mph. For the dry surface calculations, the difference between these was greater than that, but the variations in the calculated drag factors were so large that experimental error may have been partially responsible for the larger difference.
Conclusion
The wet concrete surface had a drag factor approximately 0.2 less than the dry surface, and the variation in the drag factor with speed was so small as to be inconsequential for any accident reconstruction purposes.
Appendix
Note: While this article will appear best when printed vertically, the exhibits in the Appendix have
different proportions. These tables and graphs print best horizontally. Links to each of the
tables and figures appear below.
| Table 1 | Table 2 & 3 | Table 4 | Figure 1 | |
| Figure 2 | Figure 3 | Figure 4 | Figure 5 | Figure 6 |
Michael Sunseri has been reconstructing traffic accidents since 1982. He retired from the Louisiana State Police in 1995, having achieved the rank of Lieutenant. He was the Fatality Review Officer from 1982 to 1994. He taught Accident investigation and reconstruction procedures at the Louisiana State Police Academy from 1983 through 1995 and has been an adjunct instructor for N.U.T.I. He taught At Scene A.I. and Advanced Technical A.I. to the Hawaii Police Department. . He has conducted and participated in numerous skid tests involving commercial vehicles, automobiles, and trolley cars.
Mr. Sunseri is A.C.T.A.R. accredited and is a member of S.A.E. as well as S.O.A.R. and N.A.P.A.R.S. He received U.S. Patent #5,445,024 for an Automotive Motion Recorder on August 29, 1995.
He can be reached at leveerat@ix.netcom.com
Dr. Bruno Schmidt received his Bachelor's degree in mathematics and physics from Cornell College in 1964. His Doctorate degree in physics followed from Iowa State University in 1969. He was a Physics faculty member at Southwest Missouri State University (1969-1984) and head of the Computer Science Department at Southwest Missouri State University (1984-1992). Currently he is Vice President for Academic Affairs at Southwest Missouri State University.
Dr Schmidt has been practicing in the field of accident reconstruction since 1989. He also teaches the Applied Physics for Accident Reconstruction for Texas A&M Engineering Extension Service. He maintains active memberships in S.A.E, Texas Association of Accident Reconstruction Specialists (TAARS) and National Association of Professional Accident Reconstruction Specialists (NAPARS).
He can be reached at SchmidtBF@aol.com
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