It is well established that the Law of Conservation of Momentum is applicable to all interactions between any two bodies during an impact. The Law dictates that the total momentum before a collision is the same as the total momentum after the collision. This Law has been accepted as a fundamental part of Newtonian Physics since Newton incorporated Descartes’ work into his own. Scientists rarely question its applicability to kinematics of bodies in the non-quantum world. The Law of Conservation of Momentum is regularly used in vehicle accident reconstruction to calculate the impact speed of one or both of the vehicles, assuming that the masses of the vehicles and sufficient other velocities are known. Collisions of vehicles with highly disparate masses pose and interesting dilemma. In such a collision, the initial speed of the higher mass vehicle will change very little in a collision with a vehicle of much smaller mass and the speed change of the smaller mass vehicle will be large. This is due to the ratio of the masses of the two vehicles which minimizes the effect of the smaller mass vehicle on the vehicle of larger mass. Case examples of collisions of vehicles with widely different masses are presented and used to validate the calculated errors. Examples of such collisions may include: train vs. car, train vs. tractor trailer, tractor trailer vs. car and tractor trailer vs. motorcycle. The lopsided nature of the speed change of this kind of collision can lead one to conclude that momentum is not applicable to collisions where there are dramatically different masses. The objective of this work is to investigate the effect of dissimilar masses of vehicles on the effectiveness of momentum to accurately predict speed change. The mathematical formulation of the error associated with dissimilar mass vehicles is presented and quantified to give the reconstructionist guidance in when momentum can be used reliably and when the error resulting from the use of momentum may be larger than desired. Readily available masses for passenger vehicles and motorcycles will be found and used through the manufacturers supplied documentation.  Research will be conducted to determine the minimum and maximum masses of tractor trailer combinations legal for travel on highway and off-highway roads for use in this study. Additionally, research will be conducted to determine “full” and “dry” weights of differing train car assortments and will be presented in this study. A wide range of velocities will be studied for both the higher and smaller mass vehicles including but not limited to: posted speed limits for interstate travel, speed limits for urban and rural travel, vehicles exceeding the posted speed limits in ten mile per hour increments, and finally vehicles traveling below the speed limits in ten mile per hour increments.


Momentum Analysis of Vehicles With Disparate Masses

Division / Sponsors: 
Aerospace, Bioengineering, Applied Mechanics, Design Engineering Division, Advanced Energy Systems, Manufacturing Engineering Division, Noise Control and Acoustics, Nondestructive Evaluation, Diagnosis, and Prognosis (NDPD), Nuclear Engineering Division, Process Industries Division, Fluids Engineering, Heat Transfer, Materials, Microelectromechanical Systems, Safety Engineering and Risk Analysis, Computers & Information in Engineering


Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2020/volume/84478

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