1991-02-01

# A Two-Dimensional Model of a “Falling” Vehicle 910124

A number of accidents involve a vehicle going off the edge of the road and becoming airborne. In these types of accident, the engineer is typically faced with the problem of estimating the velocity of the vehicle at launch, based on evidence defining the launch position and point of impact at the end of the flight.
Two options have been available to evaluate the dynamics of such problems. The first is to treat the vehicle as a point mass, and use simple trajectory equations to define the flight path. This approach considers only the two translational degrees of freedom of the center of mass of the vehicle, and neglects effects of tire contact during launch.
The second option is to carry out a full three-dimensional analysis. This approach treats the sprung mass of the vehicle as a rigid body, accounts for the four tire contact conditions, and possibly models the suspension and unsprung masses.
Situations may occur, however, where the engineer requires more detailed information about the launch and path than can be obtained from the simple first option, yet cost considerations or problem geometry do not warrant the expenditure of effort necessary to use the complex second option.
To address this situation, a dynamic model of intermediate complexity has been developed. The vehicle is represented by a two-dimensional model with two translation degrees of freedom and one rotation degree of freedom. This approach can be used to simulate a vehicle travelling approximately forward or laterally off the edge of the roadway.
This two-dimensional model provides information not available from a point mass model. First, it provides a more realistic model of the trajectory by incorporating motion during the time interval when only one set of tires is on the road. Second, it provides information about the rotational motion, which can be used to infer the speed of the vehicle while on the roadway.