Conservation of momentum is a physics principle that provides a powerful, but often misused, reconstruction tool in the determination of impact speeds in two-vehicle accidents. It’s major advantage is that the work done, along with the resulting loss of kinetic energy during impact is irrelevant and, therefore, the vehicle damage can be ignored. A corollary benefit of this method is that it is valid for both elastic and plastic collisions. It is, however, essential to remember that this principle only applies to the brief (± 0.10 seconds) impact phase of the accident that occurs from first contact to separation of the vehicles. Prior to the conservation of momentum analysis of the impact phase of the accident event, a complete and reliable post-impact analysis must be conducted to calculate the departure speed and determine the departure direction of each vehicle.
Since the departure direction is the travel path of the vehicle’s center of gravity at the instant of separation, it must be derived from the physical evidence at the scene of the accident. Due to vehicle rotation, the departure direction is rarely the same as a single tire mark, gauge mark, or fluid trail. Since there often is a curved post-impact travel path, the departure direction is also not necessarily a straight line from impact to final rest. Careful consideration of the physical scene evidence, along with the vehicle’s damaged wheelbases and track widths, is required to achieve a reliable departure direction. If this cannot be done, a crude estimate is not sufficient, and this method of analysis will have questionable validity.
Each vehicle’s approach direction is also required for a successful reconstruction. This information may be confirmed by the vehicle damage patterns in the classic T-bone intersection collision, but may not be reliably determined in other angled intersection collisions such as one involving a left turning vehicle. Assuming that a vehicle’s approach direction is the same as the approach travel lane may also be invalid since the driver may have executed an, often undetectable, avoidance maneuver.
Intersection collisions such as a truck versus car or a car versus motorcycle are rarely candidates for a successful conservation of momentum analysis. Any slight error in the estimate of the heavier vehicle’s departure direction will produce an unacceptable error in the calculated impact speed of the lighter vehicle.
An off-center head-on collision may appear amenable to a complete conservation of momentum impact analysis, but it is often necessary to take energy losses due to damage into consideration. Since changes in direction are usually quite small in this crash configuration, estimates of the lateral post-impact speeds are often of questionable reliability. Therefore, conservation of longitudinal momentum provides the only equation for the two unknown impact speeds and a second equation using conservation of energy is required.
Conservation of energy dictates that the total energy at impact is equal to the total energy at separation, plus the total kinetic energy lost during impact. The energy loss due to frontal crush can often be calculated from stiffness coefficients derived from staged collisions.
A reconstruction analysis of the impact phase of any accident event using conservation of energy, although not always reliable, can be used as a valuable cross check for gross errors in the conservation of momentum analysis.
Since momentum is a vector with magnitude and direction, a graphical solution with or without computer assistance, is another option that may be useful in visualizing the conservation of momentum concept.
More information on this topic can be found in the chapter on Impact Dynamics in Highway Accidents: Investigation, Reconstruction and Causation available at: Amazon.com. Information about the book and author is available at: www.bmorrow.com.