ABSTRACT
This approach recognizes from the outset that the inter-vehicle contact forces are self-equilibrating, due to Newton’s Third Law. If, therefore, we define the system as including both vehicles, then the contact forces do not show up when Newton’s Second Law is expressed mathematically. The only external forces on the system are tire forces due to friction. As discussed in Chapter 2, the tire forces are in the neighborhood of the vehicle’s weight or less, so they produce vehicle accelerations on the order of 1 G or less. In a high-speed crash, vehicle accelerations often exceed 40 G, so the tire forces are negligible by comparison. For collisions at low speeds or with large trucks, tire forces might not be negligible by comparison, so the reconstructionist must remain aware of the assumptions being made. If indeed the tire forces are negligible, then no external impulses are delivered to the system during the crash, and Newton’s Second Law reduces to the Conservation of Momentum, which may be expressed as
d mV( )
= 0 (23.1)
d(Iω) = 0 (23.2)
Equation 23.1 indicates that the change in momentum mV
is zero; in other words, momentum is conserved (i.e., stays constant) throughout the crash. The magnitude and direction of the system momentum vector is unchanged from impact to separation. Similarly, Equation 23.2 shows that the change in angular momentum is zero; angular momentum is conserved throughout the crash. (Note that the system moment of inertia will change during a crash if the vehicle positions change relative to each other.)
Equations 23.1 and 23.2 are vector equations, involving two components in Equation 23.1 and one component in Equation 23.2. So momentum
conservation for a planar system involves three equations. To these scalar equations, we add a fourth, which expresses the conservation of energy:
Δ(KE1) + Δ(KE2) = CE1 + CE2 (23.3)
where ΔKE is the loss of kinetic energy, CE is the crush energy, and the subscripts refer to the two vehicles. Energy is a scalar quantity, so Equation 23.3 is always a single equation, regardless of the degrees of freedom of the system.
