A Safety Distance Design Model Based on Just Noticeable Difference

According to the theories of traffic dynamics, traffic psychology and psychophysics, the process that drivers perceive leading car's movement through the distance changes between vehicles is explored, where just noticeable difference is introduced. The extreme cases for car-following behaviors are discussed and the range of the car-following distance and the relationship between the car-following distance and three factors, including the roughness of road surface, the velocity of vehicles and the reaction time of drivers are derived, respectively. Finally, regarding the lower limit of the range of the car-following distance as governing equation for safety distance, we have obtained the optimal values of safety distance under different road conditions, such as roads with anti-skid surface, asphalts pavement, rain, snow and ice. Compared with the safety distance in “the Road Traffic Safe Law”, the rationality of this safety distance design is validated. These conclusions can provide a theoretical basis for the design of traffic safety and management.