How soon to brake and how hard to brake: Unified analysis of the envelope of opportunity for rear-end collision warnings

Rear-end collision warning systems are both an available and an evolving technology. The goal of these systems is to alert the driver of a dangerous situation, with sufficient time to take evasive action and avoid a collision. Their development, analysis, and evaluation requires considering the envelope of opportunity available to a driver - once an alert is issued - to avoid a collision.

This paper simplifies the envelope of opportunity analysis and presentation. Previous work in this area focuses on establishing the relevant kinematic equations of motion and obtaining case-specific plots of the envelope of opportunity. We have plotted the envelope of opportunity using the reaction time and the reciprocal of the following vehicle acceleration. Plotting the envelope in this manner readily accommodates the limiting cases of infinite following vehicle deceleration and zero reaction time and the envelope of opportunity is, in most cases, a straight line, allowing for direct generation of the envelope and insight into the effect of initial kinematic variables on the envelope.