@article{ref1,
title="A simple closed form solution for the displacement constrained problem of braking to a terminus velocity",
journal="Accident reconstruction journal",
year="2012",
author="Singh, Jai",
volume="22",
number="4",
pages="12-15",
abstract="Accident reconstructionists must often determine speeds, times and distances associated with the sequential perception of a hazard, the engagement of a reaction to the hazard perception, and achievement of a terminus event such as a collision or bringing the vehicle to a stop. This study seeks to develop an analytical solution for intermediate speed values and distances traversed in the case of a tripartite contextual sequence under a total displacement constraint. In this case, the first phase consists of the start of perception to the end of early reaction, as exemplified by the start of braking, but over which vehicle speed remains constant. The second phase consists of the combination of mechanical brake transient/lag associated with system latency and the portion of the response phase associated with depressing the brake pedal. The third phase consists of the development of effective constant braking force that terminates congruent with the terminus of the analysis. This is similar to the maximum speed to stop at the point of impact calculation derived by Limpert (1999) while explicitly accounting for the brake lag/transient phase. A hypothetical case involving a vehicle-pedestrian conflict is used to demonstrate the proposed analytical solution.<p />",
language="",
issn="1057-8153",
doi="",
url="http://dx.doi.org/"
}