A.D. Tupper & Associates Limited

Linear momentum is a quantity of motion consisting of the product of a body's mass and its velocity. It is a vector quantity and is typically dimensioned in pound seconds or lb-sec.

For practical purposes in MVA reconstruction, linear momentum can be defined as the vehicle weight multiplied by the vehicle speed in a certain direction. The basic premise of a momentum analysis is based on the law of conservation of momentum which can be stated that in a group of objects which act upon each other, the total linear momenta immediately following a collision is equal to the total linear momentum immediately preceding a collision. Any momentum lost by one vehicle is gained by the other.

 Since each vehicle has a weight, speed, and a direction going into the collision, and a weight, speed, and direction coming out of the collision, there are 12 numerical values associated with the two vehicles. A momentum analysis will solve for any two of the 12. The other ten must be evaluated or assumed.

 The typical linear momentum analysis has the following phases:

1. The reconstructionist must obtain the weights of the vehicles. If actual weighing is not practical, published specifications can be used and an estimate made of the weight of the vehicle occupants and contents.
2. The impact location and rest position of the vehicles must be determined as part of the collision analysis.
3. The post impact direction is obtained from the physical evidence, such as tire marks and gouges at the collision site or the general direction from impact to rest.
4. The decelerations from impact to rest are evaluated from the post impact braking, rotation, terrain, and contact with such objects as poles, brush, et cetera.
5. The post impact speeds can then be determined from the evaluated decelerations and the travel distance to rest.
6. At this point, if the pre impact direction for both vehicles is known, the momentum equations can be solved to yield the speed for each vehicle.
7. Alternatively, if the incoming speed and direction for one vehicle is known, the speed and direction for the second can be calculated.
8. The final portion of the analysis involves braking or skidmark length, and takes into account any pre impact deceleration.

Collision events where the momentum analysis has limited or no applicability include:

1. Head on or rear end collisions, (In these cases the analysis reduces to one dimension and can only solve for one unknown speed or direction.)
2. Collisions with fixed or very heavy objects,
3. Collisions where deceleration values can not reasonably be determined,
4. Collisions, such as sideswipe of a trailer, in which a common velocity is not reached.