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.