Modeling of Truck-Car Sideswipe Collisions Using Lug Patterns

Vehicle to vehicle sideswipe collisions may involve contact between a vehicle body and a contacting vehicle's rotating wheels, tires and lug nuts. During a sideswipe collision between a truck and an automobile it is not uncommon to see lug marks in the shape of consecutive damage loops or strikes on the side of the impacted vehicle. The damage loops or strikes are generated by the protruding lug nuts of the truck wheel as it passes by the impacted vehicle at a shallow angle. Additionally, rubber transfers due to contact with the tire sidewall and metal scraping from the wheel rim also leave distinctive shapes on the sides of the contacted vehicle body. The tire, rim, lug nut markings and associated damage manifest themselves as a special case of the epitrochoid and can be geometrically and mathematically described. Presented is a derivation of the equations that govern the lug, rim and tire positions and relative motions. The equations are derived in terms of the speeds of the two impacting vehicles as well as the relevant geometry. A spreadsheet implementation of the equations facilitates their application to accident reconstruction. Staged collision testing using instrumented vehicles at known speeds was conducted. The mathematically derived shapes were compared to the staged collision test contact patterns. The application to transportation accident reconstruction is discussed.