Debunking a Questionable Crash Reconstruction

John C. Glennon, D. Engr., P.E.
July 2002 (copyright)

In a recent civil court case involving sight distance issues about an intersection collision, the reconstructionist for the defense presented his conclusions based on an alleged SMAC analysis. His conclusion was that a northbound Ford 350 pickup ran the stop sign in making a left turn onto the east-west state highway and collided with the eastbound Mercury Cougar. Figure 1 shows the impact and final resting positions.

Figure 1
This reconstructionist, let's call him Doctor X, adopted the stipulated testimony that the eastbound Mercury was traveling 50-55 mph. His conclusion from his alleged SMAC analysis was that the Ford pickup had an impact speed of 20 mph and, therefore, had to have run the stop sign.

What's Wrong With This Picture ?
You really don't have to be a rocket scientist to be able to debunk Dr. X's analysis, but proving it to an uneducated jury can be another matter. The following facts, however, can be easily pointed out.
  1. The first unusual factor in this collision is the police-reported final resting position of the Ford 350 pickup, which is about 145 feet south of the impact. This placement defies all principles of physics and cannot be explained directly by the subject collision. Obviously, either the pickup driver drove his vehicle to this position after the collision or the vehicle was a runaway.
  2. The Ford 350 pickup, which had a long bed, an extended-cab, a 4-wheel drive, and a diesel engine, weighed in at 6,500 pounds unloaded. At the time of collision, this vehicle with driver, fuel, large arc welder, and tools weighted about 9,280 pounds, compared to 3,545 pounds for the Mercury. If the Mercury was traveling 52 mph and the Ford pickup was traveling 20 mph while having this near-90° impact, the Ford pickup would have had 11% more momentum than the Mercury. Therefore, for this scenario, even the casual observer would expect to see both vehicles much farther to the north at final rest.
  3. The relatively high 20-mph conclusion for the Ford pickup is generally not consistent both with a vehicle turning left at an intersection and the (evasive) position of that vehicle in the intersection at impact.
Dr. X gave his conclusions, saying they were based on a trial-and-error SMAC analysis, yet he failed to produce any kind of documentation, arguing that it wasn't necessary to support his expert opinions. Dr. X's scenario, however, could never have produced his alleged SMAC conclusion without some kind of overriding assumption about the post-collision movement of the pickup truck that would be grossly inconsistent with both of the final resting positions shown by the police report.

Is A Crash Reconstruction Even Possible ?
Without any clear knowledge of the post-collision movement of the pickup truck, a precise accident reconstruction is not possible. But, can Dr. X's conclusions about the pickup driver's failure to stop be validated with some kind of partial crash reconstruction analysis? Can we conduct any analysis when part of the post-collision data is missing? In fact, we can! Knowing the impact speed for one vehicle should allow for a reasonable boundary analysis to physically prove or disprove Dr. X's conclusion that the Ford pickup ran the STOP sign.

Can We Use a Boundary Analysis ?
Looking again at Figure 1, notice that the vehicles came together, corner-to-corner, at approximately 90°. Under this scenario, both vehicles should have rotated toward each other after collision and, in those movements, physically limited the direction of each other. In other words, one vehicle cannot physically pass through the other vehicle. The initial northward movement of the Ford pickup, therefore, should be limited by the manifest post-collision trajectory of the Mercury. And, more importantly, the Conservation of Momentum solution that gives the very highest impact speed for the Ford pickup is that one where the Ford pickup has this exact same post-collision trajectory as the Mercury.

Knowing the Mercury moved 81.5 feet after impact, and assuming that the average post-collision drag factor is 0.58, the post-collision speed, SC2, of the Mercury is solved as follows:

S2C2 = (30)(f)(d)
S2C2 = (30)(0.58)(81.5)
SC2 = 37.7 mph

[Already suggesting that the testified 50-55 mph impact speed for the Mercury may be a reasonable estimate].

Assigning East to the direction of the Mercury and using the weights of each vehicle, the 52-mph impact and 37.7 mph post-impact speeds for the Mercury, and the 15° post-impact direction for the Mercury, the following East-West Linear Momentum equation can be written:

East Momentum
(WC)(SC1) = WC (SC2) (cos Ø)+ WT (ST2) (cos Ø)
(3545)(52) = (3545)(37.7)(cos 15°) + (9280)(ST2) (cos 15°)
52 = (37.7)(.9659) + (2.618)(ST2) (.9659)
52 = 36.41 + 2.5285 ST2
2.5285 ST2 = 15.59
ST2 = 6.17 mph

Because an approximate impact speed was pre-known for the Mercury [note: the 52 mph is actually the conclusion of a sequential process using Conservation of Energy that validated it as the most likely speed], and because we've adopted the boundary post-collision direction for the Ford pickup, this equation has only the one unknown, the post-collision speed of the Ford, which is solved as 6.17 mph.

Armed with this solution for the post-collision speed of the Ford pickup, we can now write the north-south momentum equation, knowing that the truck impact angle is 3°, as follows:

North Momentum
(WT)(ST1)(cos µ) = (WT)(ST2)(sin Ø) + (WC)(SC2)(sin Ø)
(9280)(ST1)(cos 3°) = (9280)(6.17)(sin 15°) + (3545)(37.7)(sin 15°)
(ST1)(.9986) = (6.17)(.2588) + (14.40)(.2588)
ST1 = 1.60 + 3.74
ST1 = 5.34 mph

This solution indicates that the maximum impact speed for the Ford 350 pickup is a little more than 5 mph as opposed to Dr. X's conclusion of 20 mph. The only remaining exercise is to validate this 5.34-mph speed as the maximum possible speed by using the Conservation of Energy equation to check the solution as follows (the Equivalent Barrier Speeds, EBS, associated with the vehicle damages were estimated as 22 mph for the Mercury and 17 mph for the Ford pickup):

Energy Check
WC (SC1)2 + WT (ST1)2 =(?) WC (SC2)2 + WT (ST2)2 + WC (EBSC)2 + WT (EBST)
3545(52)2 + 9280(5.34)2 =(?) 3545(37.7)2 + 9280(6.17)2 + 3545(22)2 + 9280(17)2
2704 + 75 =(?) 1421 + 100 + 484 + 757
2779 = 2762

[QED: The Energy solution checks with the Momentum solutions with less than a 1% difference]

What Can We Learn?
This boundary reconstruction was very useful in showing the nature of the subject collision. Its 5-mph maximum speed clearly shows the Dr. X's conclusion that the Ford 350 pickup did not stop at the STOP sign was unsupported by any physical evidence. It also suggests that Dr. X's 20-mph impact speed for the pickup, in which he refused to document his alleged SMAC analysis, was either a fraudulent or grossly flawed conclusion.

Many situations lend themselves to boundary analysis. The question is not always, what is the exact speed? , but either, did the vehicle exceed the speed limit? , or, does the solved speed demonstrate some kind of negligent behavior by one driver or the other?. For these kinds of questions, boundary analyses often provide a solution, even when all of the otherwise required physical evidence is not available.

About the Author

Dr. John C. Glennon is a traffic engineer with over 45 years experience. He has over 120 publications. He is the author of the book "Roadway Safety and Tort Liability" and is frequently called to testify both about roadway defects and as a crash reconstructionist.


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