A general formulation for time-to-collision safety indicator

Time to collision is an important time-based safety indicator for detecting rear-end conflicts in traffic safety evaluations. A major weakness of the time to collision notion is the assumption of constant velocities during the course of an accident. In this paper we utilise equations of motion to develop a generalised formulation for time to collision by relaxing the assumption of constant velocity, constant acceleration and so on. This paper also illustrates how this concept can be applied to real-world data, and detailed data gathered in the NGSIM project are used. Then time to collision is calculated based on the assumption of constant speed, constant acceleration and linear acceleration for leading and following vehicles. Results indicate that in the third case (linear acceleration), the average duration of exposure to critical time to collision values is greater than the others. So, applying time to collision based on the assumption of linear acceleration in collision avoidance systems would decrease driver errors more than other cases.