An Examination of Equations Relating Motorcycle Impact Speed to Struck Vehicle Post-Impact Rotational Displacement 2021-01-0895
When a motorcycle collides with another vehicle, the impact may cause a change in the translational and rotational velocities of the vehicle. If these velocity changes or the magnitude of the translation and rotation of the struck vehicle can be quantified, then these can be used to calculate the impact speed of the motorcycle. There are several methods that could be used for this analysis. The most general and comprehensive solution will be to use one of the widely-accepted accident reconstruction simulation programs – PC-Crash, HVE (the EDSMAC4 or SIMON modules), or Virtual CRASH. These software packages incorporate equations for calculating the velocity changes that occur when the vehicles collide and equations for calculating the post-impact motion of the vehicles. These models enable the analyst to specify and incorporate the level of steering and braking at each tire (due to driver input or damage) and they utilize a graphical interface that allows the analyst to import a diagram of the physical evidence (tire marks, scrapes and gouges, fluid on the roadway, and vehicle rest positions, for instance) and to compare the simulated motion to the evidence on the diagram.
Still, these simulation programs can be time-consuming to apply and not everyone has access to them. It would be useful to have simple formulas for obtaining at least a reasonable estimate of the motorcycle impact speed based on the observed post-impact translation and rotation of the struck vehicle. Developing such equations necessarily requires simplifying assumptions. As long as the analyst is aware of these simplifying assumptions, however, and applies them to cases that satisfy the assumptions, these equations have their place. Development of such equations will begin with a method for relating the collision speeds to the velocity changes produced in the struck vehicle. It will then move onto the expected translational and rotational displacements expected from these velocity changes. This paper develops such simple equations for obtaining an initial estimate of a motorcycle’s impact speed based on the struck vehicle’s post-impact translation and rotation.