You have probably heard conflicting reports about Dale Earnhardt's crash that took his life. Among other things, there is controversy about whether the seat belts were broken and whether contact with another car initiated the accident. There have also been conflicting reports about the speed at which he hit the wall, reflecting some common misunderstandings about speed and velocity.
Let's focus on the velocity issue. Determination of the velocities at various stages of an accident is usually one of the critical tasks in accident reconstruction. Impact forces are directly related to the velocity at impact, so determination of it is critical to finding out the likely causes of injury or death. In my last article, I discussed the relative motion of two objects colliding head-on. In that case, only the speed of the objects is important since the motion is collinear. Many collisions involve an angle of impact, and all good engineers know that speed AND direction are necessary to specify velocity. In the Earnhardt crash there were two significant collisions, one with the car to his right and one with the wall.
To illustrate the importance of direction, consider that Earnhardt was driving at 190 mph just prior to the accident. From videotape footage, it appears that he hit the wall at an angle of about 45 degrees. Assuming the wall is smooth and rigid, the significant impact forces will be perpendicular to it. Thus, it is the speed perpendicular to the wall that is important. The component of velocity perpendicular to the wall is 134 mph. Thus, even if he were traveling at a speed of 190 mph when he hit the wall, he really "hit the wall" at about 134 mph. However, this speed does not seem consistent with the apparent speed and damage to the car as evidenced by the video.
The above calculation ignores the effect of the collision with the car to the right. If we assume the two cars are about the same weight and traveling at about the same speed, simple conservation of momentum calculations will give a first estimate of the velocities of both vehicles after impact. The videotape indicates an angle of impact of about 20 degrees between the two vehicles. During impact, the two cars demonstrate something close to plastic impact, with both cars assuming a common velocity. Calculations give a velocity after impact of about 187 mph at an angle of about 10 degrees relative to the wall. This corresponds to a velocity toward the wall of about 32 mph. This speed seems more consistent with the video evidence, but appears to be on the low side. The kinetic energy of the two vehicles was decreased by about 3% due to the impact forces that resulted in the bending of metal, generation of heat, etc. Tire forces and other non-impact forces are so small during the short period of impact that their effects are negligible.
It was reported on the Fox News special report "Death of a Legend" that accident reconstructionists determined that Earnhardt hit the wall at 50 mph. The video evidence shows that his car was in clockwise rotation following initial impact with the other car. Our calculations neglected this and other rigid body effects that require more complicated calculations. Also, between initial impact and collision with the wall there would be energy loss due to skidding of the tires, and rolling of wheels which would direct more car velocity toward the wall without significant loss of energy—two factors that I will discuss in later articles. Considering these effects, the reported impact speed of about 50 mph seems consistent with our first-order estimate. It is encouraging that at least some reporters have been willing to investigate more thoroughly without regard to sensationalism.
This report is one in a series authored by Larry Zirkle, a forensic engineer who specializes in accident reconstruction. Director of special projects for TECH, a consulting firm that provides mechanical design and FE services, Zirkle is a former professor of mechanical engineering at Oklahoma State University. You can reach Larry at Lzirkle@mail.techok.com or e-mail your comments to us at firstname.lastname@example.org.