Object shape becomes a consideration in oblique collisions, but can be ignored in simple co-axial theory.
In any collision is it virtually impossible to calculate a value for the Coefficient of Restitution, e . The Coefficient of Restitution is analogous to the Coefficient of Friction, m , in that its value depends on the interplay between the two contacting bodies in a very complex manner. Also similar to the Coefficient of Friction, the Coefficient of Restitution is usually measured by experiment. It is erroneous to assign either a Coefficient of Friction or a Coefficient of Restitution to any single object. It is always a combination of the interaction of two objects.
In the investigation of vehicle collisions, it is generally accepted that the Coefficient of Restitution tends to zero as the collision intensity is increased, say where vc > 50 kilometres/hour. However, it is well established that for Low Speed Impacts, i.e., from 5 kilometres/hour < vc < 15 kilometres/hour, the Coefficient of Restitution can have a value in the range of 0.2 to 0.6, and below 5 kilometres/hour, it can reach up to 0.9, [Emori, Horiguchi, 1990; Szabo, Welcher, 1992; Howard, Bomar, Bare, 1993; and Siegmund, Bailey, King, 1994].
In simple theories for co-axial collisions of automobiles, it is usually assumed that e = 0 and that one of the pre-impact velocities is known. Those assumptions allow the velocity of the other vehicle to be determined. However, scene data usually shows that the vehicles have sprung apart indicating that their post-impact velocities were probably not equal, and therefore e ¹ 0. Independent calculation of the individual post-impact velocities, and the use of a Coefficient of Restitution based on experimental results, leads to the calculation of the impact velocities of both vehicles.
Table 1 shows the effect of a bullet vehicle weighing 1000 kilograms, travelling at a velocity of 10 m/s, and striking a stationary object of various weights. Two values of the Coefficient of Restitution have been chosen. The D V for each object is calculated from the relationships in equation .
V1 = 10 m/s v1 = 0 m/s \ vc = 10 – 0 = 10 m/s |
||||||
e = 0 |
e = 0.5 |
|||||
M, kg |
1000 |
1000 |
1000 |
1000 |
1000 |
1000 |
m, kg |
1000 |
2000 |
infinite |
1000 |
2000 |
infinite |
mc, kg |
500 |
667 |
1000 |
500 |
667 |
1000 |
Ic, kgm/s |
5000 |
6667 |
10000 |
7500 |
10000 |
15000 |
D V, m/s |
5 |
6.67 |
10 |
7.5 |
10 |
15 |
D v, m/s |
5 |
3.33 |
0 |
7.5 |
5 |
0 |
Table 1 Sample calculations for co-axial collisions without external forces
Notice how the rebound, i.e., the structural aspect, increases the magnitude of the impulse, and also that the impulse is doubled when an object hits an infinite mass compared with striking another object of equal mass.