Development of a Tumble Number for Use in Accident Reconstruction

This paper discusses the development of what the author calls the “Tumble Number.” The Tumble Number is an empirically derived deceleration rate applicable in cases where a reasonably compact mass decelerates from a finite velocity while undergoing random and undefined rotation in multiple planes and making irregular ground contacts until it finally comes to a rest. This situation is encountered in a variety of ways in accident reconstruction. Typically, it is useful in cases of vehicle rollover, or in cases of pedestrian or cyclist's vehicle impact where the torso of cycle is propelled forward some distance from the point of impact as a result of direct or transferred pre-impact velocity.

The developed Tumble Number is strikingly close to 1/2 g, a value which appears in certain theoretical formulas having nothing to do with tumbling objects. The significance of this similarity will be discussed at the end of the paper.