Reconstruction of inline crashes between vehicles with a low closing speed, so-called “low speed” crashes, continues to be a class of vehicle collisions that reconstructionists require specific methods to handle. In general, these collisions tend to be difficult to reconstruct due primarily to the lack of, or limited amount of, physical evidence available after the crash. Traditional reconstruction methods such as impulse-momentum (non-residual damage based) and CRASH3 (residual damage based) both are formulated without considering tire forces of the vehicles. These forces can be important in this class of collisions. Additionally, the CRASH3 method depends on the use of stiffness coefficients for the vehicles obtained from high-speed crash tests. The question of the applicability of these (high-speed) stiffness coefficients to collisions producing significantly less deformation than experimental crashes on which they are generated, raises questions of the applicability.
An alternative stiffness-based method for low closing speed crashes has been developed [1]. This method characterizes the stiffness of vehicle pairs using data from tests with exemplars of the subject vehicles. As currently formulated, the method does not include the forces from braked tires. Users of the method might approach this situation by stating that its use without braking forces is conservative in that braking by either or both vehicles during contact always produces ΔV of the target vehicle that is lower than without braking. However, there may be instances where the ability to include braking forces is convenient or necessary such as when the physical evidence indicates that one or both of the drivers was braking during some or all of the duration of the momentum transfer.
This paper re-derives the governing equations for the method to include braking forces by either or both vehicles. The equations can be used without the inclusion of these forces, in which case the results match the original formulation. The braking forces are characterized using a frictional drag coefficient acting on the weight of the vehicle. The new model is validated using an inline (central) impulse-momentum collision model that includes braking forces for the vehicles [6]. For identical input parameters, the models match exactly, thus validating the stiffness-based model. Trends in the results of the model for braking by either and both vehicles are presented. An example application of the method is also presented.
The use of simulation software, such as HVE EDSMAC4, is an option for analyzing low closing speed crashes. EDSMAC4 is validated and described in the literature [15]. EDSMAC4 uses the friction circle and Fiala tire model to calculate tire longitudinal and lateral forces. EDSMAC4 uses a linear force versus crush model. The A and B stiffness coefficients derived from full-scale high-speed barrier crash tests have been shown to overpredict peak acceleration values and under predict collision durations when modeling low speed collisions [16]. As such, a constant-ratio reduction of stiffness coefficients proportional to closing speed improves the impact duration and corresponding peak acceleration. A close match in ΔV and maximum acceleration was observed with slightly over-reporting for all values except the ΔV of the striking vehicle, which was underreported. The trends of the results of EDSMAC4 when evaluating effects of braking were the same as the trends of the stiffness characterization method.