A Parametric Study of Frictional Resistance to Vehicular Rotation Resulting from a Motor Vehicle Impact

The equations of rotational motion used to calculate pre-impact vehicle speeds using the rotational displacement of the vehicles following a collision are well known. The technique uses the rotational momentum exchange during impact and the principle of conservation of rotational energy to calculate the post impact vehicle angular velocity from the energy dissipated during the vehicle's rotation to a stop (product of torque and rotational displacement). Integral to the calculation of the stopping torque on the vehicle is the determination of the effective rotational coefficient of friction (f_r) between the tires and the roadway. The interactions of the road with the tires to produce the rotational coefficient of friction (f_r) are more complex and less understood than those of linear coefficient of friction (deceleration factor). A derivation of the post impact equations of motion and the kinematics of vehicles in rotation are examined. The resultant parameters of motion that affect the rotational coefficient of friction (f_r) are presented. The effects of these various parameters on the rotational coefficient of friction (f_r) were studied using EDSMAC™. Normalized coefficients, which can be multiplied by the roadway friction to obtain the rotational coefficient of friction (f_r) under common accident scenarios, are presented. Use of equations of rotational motion supplements linear momentum equations in a momentum analysis. They are not a substitute for other accident reconstruction techniques, such as computer crash simulations.