Acceleration Modeling with Constant Power 2023-01-5073

The evaluation of the acceleration, velocity, and travel distance of a motor vehicle is an issue that arises frequently in the analysis of vehicle accidents. It is well known that the acceleration capabilities of a motor vehicle generally reduce as the velocity increases. Vehicle accident reconstruction has traditionally used constant acceleration models with stepped decreases of acceleration as the velocities, distances, and loading increase. For any given vehicle, the energy output of the engine that can be transmitted to the drivetrain remains within a power band of the operating engine. Transmissions efficiently transfer this relatively constant power to the drive wheels. Using the mathematical relationships of the “power equations,” the acceleration, velocity, and travel distances for vehicles can be reasonably evaluated with limited test information. Adjustments for differing load conditions and terrain are readily incorporated into the model. Constant power models are developed from fundamental principles and have been presented in a variety of formats, most of which are not very useful for accident reconstruction. The objective of this paper is to (a) develop the principle constant power equations, (b) present the power equations in a format usable by the typical accident reconstructionist, and (c) refine the model to represent real-world conditions more closely.