How to calculate impact speed from pedestrian throw distance
Updated 2026 · 4 min read
When there are no skid marks —and in an urban pedestrian impact there hardly ever are— one measurement remains that is taken reliably: how far the pedestrian came to rest from the point of impact. From that the vehicle speed is bracketed. But it produces a range, not a number, and it is worth understanding why.
What the throw distance depends on
The pedestrian is thrown, flies, lands and slides to a stop. The total distance depends on the vehicle speed, on the launch angle and on the friction between the body and the road surface.
The problem is that the launch angle is almost never known. That is the elegance of the Searle method: instead of assuming it, it computes both extremes —the angle that gives the maximum distance and the one that gives the minimum— and returns the interval between them.
Where d is the throw distance and f combines the pedestrian-road friction with the gradient. The real vehicle speed lies between those two values, and the report should give both.
With a friction of 0.75 —usual on asphalt— the minimum comes out at about 80% of the maximum. That is: if the maximum is 50 km/h, the minimum is around 40. A report quoting only one of the two extremes is choosing the convenient one without saying so.
Pedestrian-road friction
This is not tyre friction. It is a clothed body sliding over the surface, and the authors who fitted the model against real tests restrict it to the 0.7–0.8 interval. Outside that margin the result is no longer backed by the validation it was built on, and the calculator says so.
When the method is not the right one
- Forward projection trajectory. The Searle equation is intended above all for wrap trajectories, where the pedestrian is carried onto the bonnet. When the front is high and the body is thrown forward without wrapping, the Northwestern equation is the indicated one.
- Distances outside 5 to 35 metres. That is the range of the tests the empirical constants were fitted on. Beyond it you are extrapolating.
- Steep gradients. Above 6% the uncorrected formula deviates by more than 5%, according to the source itself; the calculator carries the gradient into the computation.
Why there are several methods and not one
Besides Searle there are empirical correlations fitted directly on tests —Wood, Appel, Collins, Northwestern, Han-Brach—. They are more convenient, but they differ in a way worth declaring: they are not mechanical models. They admit no gradient, no launch angle and no vehicle geometry, and they return a single value instead of a range.
The sensible approach is to compute with several and see whether they agree. When two independent methods land in the same neighbourhood, the result stands up far better to an awkward question.
Module 11 brings together seven throw methods, returns the Searle range with its critical angle, and warns when the data fall outside each one's validation range.
Frequently asked questions
- Can you tell a car’s speed from where the pedestrian came to rest?
- Yes, within a range. From the throw distance and the friction between the body and the road, the Searle formula gives the maximum and minimum speeds consistent with that distance, without needing to know the launch angle.
- What friction coefficient is used for a pedestrian?
- That of a clothed body sliding over the surface, not the tyre value. The authors who validated the model against tests restrict it to the 0.7–0.8 interval; outside that the result is not backed by that validation.
- Why is the result a range and not a single value?
- Because the angle at which the pedestrian was launched is almost never known. Rather than assume it, the method computes both extremes. With a friction of 0.75 the minimum speed is about 80% of the maximum.
- Does the method apply if the pedestrian was thrown forward?
- It is not the most suitable. The Searle equation is considered appropriate above all for wrap trajectories; for forward projection the Northwestern equation is indicated, and it is worth cross-checking with another method.
Sources
The methods used by module 11 and the references from which their constants and validity ranges are taken:
- Searle, J. A. (1983). Wrap trajectory; speed range and critical angle. Cited in the course notes of Forensic Road Accident Investigation (PDC).
- Appel, H., Stürtz, G. & Gotzen, L. (1975). Four empirical variants. IRCOBI.
- Collins, J. C. & Morris, J. L. (1979). Highway Collision Analysis, pp. 240-242. Reproduced in Transactions on Transport Sciences 3(3), 2010.
- Fricke, L. B. (1990). Northwestern equation, suited to forward projection.
- Han, I. & Brach, R. M. (2001). SAE 2001-01-0898.
- Happer, A. et al. (2000). SAE 2000-01-0846. Publishes two distinct fits: 202 wrap-trajectory cases and 106 forward-projection cases.
- Wood, D. & Simms, C. (2000). International Journal of Crashworthiness 5(4). Reproduced in SAE 2015-01-1419.
- Bhalla, K. et al. (2002). IRCOBI. On restricting Searle’s equation to wrap trajectories.
- Ravani, B., Brougham, D. & Mason, R. T. (1981). «Pedestrian post-impact kinematics and injury patterns». SAE 811024, 25th Stapp Car Crash Conference.
How these methods compare against documented cases is detailed in How this calculator is validated.