Crush Energy and Speed from Damage

The CRASH3 model treats the front (or rear or side) structure of a vehicle as a spring with a linear force-crush relationship. Below a threshold crush depth corresponding to force A, no permanent deformation occurs. Once that threshold is passed, the crush force F increases linearly with depth d at slope B: F(d) = A + B × d, where both A and B are expressed per unit width of the crushed zone. The energy absorbed per unit width per unit depth area is the integral of this relationship over the crush profile.

In practice a reconstructionist measures six crush depths (C1 through C6, at evenly spaced intervals across the damaged width), calculates the average and variance of the profile, and applies the CRASH3 algorithm to get the total energy absorbed Ec. That energy is related to the vehicle's delta-V through: Ec = (1/2) × m × (delta-V)², giving delta-V = sqrt(2 × Ec / m).

At the moment of maximum force during a crash, the vehicle structure compresses to its maximum dynamic crush depth. When the force drops to zero and the vehicles separate, some elastic energy is released and the metal springs back slightly. What survives to be measured later is the residual crush, which is always less than the dynamic crush that determined how much energy was actually absorbed.

CRASH3 includes a coefficient of restitution term to correct for this springback. For most structural crashes the restitution is low (0.1-0.2), meaning most deformation is plastic and the correction is small. At low-speed impacts where the structure behaves more elastically, restitution is higher and the correction becomes more significant. Missing this correction understates the energy and understates the delta-V, which can be consequential in cases where the speed difference matters for liability.

A common misunderstanding in court is that the energy equivalent speed (EES) equals the vehicle's pre-impact approach speed. It does not. EES is the speed at which this vehicle would strike a rigid fixed wall and produce the same crush profile. A rigid wall absorbs none of the energy, so all of the kinetic energy goes into the vehicle. In a real crash, the other vehicle also deforms and absorbs energy. The closing speed is therefore always at least as large as EES, and usually larger.

To get approach speeds from EES values, reconstructionists work with the momentum equations simultaneously. The EES of each vehicle gives its absorbed energy, which constrains the mass-weighted delta-V of each. Combining both constraints with momentum conservation (the vehicles' momenta must balance) allows solution for the pre-impact speeds. This combined approach, using both momentum and crush energy, is more reliable than either method alone and is widely recommended in the accident reconstruction literature when both data sources are available.

The NHTSA vehicle crash test database (available at nhtsa.gov) is the primary source for published A and B stiffness coefficients. Tests are run at controlled speeds against a flat rigid barrier with full-width contact. Each test produces a force-time history and a crush profile from which analysts derive the coefficients. The database covers thousands of vehicle models tested since the 1970s, with coverage concentrated on US-market vehicles.

When the exact vehicle is in the database, the analyst uses the published coefficients directly. When it is not (older vehicles, non-US market vehicles, commercial trucks, motorcycles), the analyst must either derive coefficients from a closely related vehicle and document the assumption, perform a staged test, or acknowledge the gap and widen the uncertainty range. The applicability of surrogate coefficients is frequently contested in litigation, making the matching process one of the most scrutinised aspects of crush-energy testimony.

At low speeds (typically below 8-10 km/h), the structural response is dominated by the bumper fascia and energy-absorbing foam rather than the frame structure that the A and B coefficients were calibrated against. The linear model breaks down, often underestimating the energy absorbed by soft bumper systems or overestimating it if no permanent crush appears but a significant delta-V occurred. Low-speed rear-end impact cases frequently generate battles between experts on this point.

At high speeds, the structural deformation may exceed the geometry assumed by the barrier test (the engine block and firewall intrude, the geometry changes non-linearly), and multiple separate crush zones may absorb energy in sequence rather than simultaneously. The six-point measurement may not capture the full three-dimensional crush geometry in a severe or oblique impact.

• Low speed: soft bumper dominates; linear model may not apply; no permanent crush can conceal a significant delta-V.
• Oblique impact: NPDOF correction adds uncertainty; corner impacts violate the uniform-width crush assumption.
• Repaired or modified vehicles: prior repair changes the structural stiffness; published coefficients no longer apply.
• Rollover and multi-event crashes: sequential damage from multiple contacts cannot reliably be attributed to a single event without additional documentation.
• Coefficient availability: non-US market vehicles, older models, and heavy commercial vehicles frequently lack published A and B values.