A damaged vehicle is a record of the energy that damaged it. Turning that record into a number a court can use is one of the oldest techniques in collision analysis, and one of the most frequently misapplied. It is worth tracing where it came from, because the assumptions it was born with are the assumptions that still limit it.
Campbell’s observation
In 1974 Kenneth Campbell, working with crash test data from a single vehicle line, published a paper that noticed something useful. When he plotted the residual crush depth of test vehicles against the speed at which they had struck a rigid barrier, the relationship was close to a straight line. Above a threshold speed at which permanent damage began, each additional increment of impact speed produced a roughly constant additional increment of crush.
If crush is linear in barrier speed, then the force needed to produce crush is linear in crush depth, and the energy absorbed is proportional to the square of it. The vehicle structure can be treated, for this purpose, as a stiff spring that does not spring back. Campbell expressed that with two coefficients, A and B, describing respectively the force per unit width needed to begin permanent deformation and the rate at which force rises with crush depth. Given those coefficients, a measured crush profile could be integrated across the width of the damage to give the energy absorbed.
From energy to delta-V
Energy absorbed is not itself the quantity a court usually wants. What links the damage to the occupants is delta-V, the change in each vehicle’s velocity during the impact. The step from one to the other is conservation of momentum: if the energy absorbed by both vehicles is known and the masses are known, the closing speed that would have dissipated that energy can be found, and from it the delta-V of each vehicle.
The CRASH3 program developed for the United States National Highway Traffic Safety Administration in the late 1970s and early 1980s put Campbell’s method into a form investigators could use routinely, and its technical manual remains the standard description of the approach. It also introduced the conventions for measuring crush, typically at six equally spaced points across the damaged width, and the Collision Deformation Classification codified in SAE J224 provides the common language for describing where on the vehicle the damage lies and how it is distributed.
Where the stiffness numbers come from
The A and B coefficients are not universal constants. They are properties of a particular structure struck in a particular way, and they are derived from crash tests. In Europe the richest sources are the regulatory and consumer tests: UN Regulations 94 and 95 define the frontal and lateral tests a vehicle type must pass, and Euro NCAP publishes the results of its own frontal and side impact tests, which engineers use to derive stiffness values for a given model.
Three points follow. First, the coefficients apply to the structure that was tested. A frontal stiffness derived from a full-width barrier test does not describe an offset impact into a wheel, or a rear impact, or a side impact into a door. Second, vehicles change: a model updated mid-life may have a different structure from the one tested. Third, every published stiffness value carries scatter, and an honest analysis carries that scatter through to the answer.
The assumptions, stated
A crush-based estimate rests on assumptions that should appear in the report rather than be discovered in cross-examination:
- that the measured residual crush is the whole story, when in fact some deformation recovers elastically and some structure may have been damaged out of sight;
- that the stiffness used describes the structure and the direction of loading actually involved;
- that the crush profile was measured, or can be estimated from photographs, with a known precision;
- that the impact was approximately central and the vehicles did not rotate significantly during contact, or that the correction for rotation has been made; and
- that both vehicles’ damage has been accounted for, because the energy absorbed by one vehicle says little on its own.
Each assumption, when it does not hold, widens the range. The method remains valuable precisely because its limits are well understood and can be quantified. A report that gives a single delta-V to one decimal place from two photographs and a published stiffness table has not understood the method; one that gives a range, explains what drives its width and cross-checks it against another line of evidence has.
The modern setting
Crush analysis now sits alongside evidence Campbell did not have. Event data recorders in many vehicles record delta-V directly, dashcam and CCTV footage can fix closing speeds independently, and finite-element simulation can test whether a particular deformation is consistent with a particular impact. None of these replaces the older technique. They check it. Where a crush-based estimate and a recorded delta-V agree, a court can have real confidence in both. Where they disagree, the disagreement is itself evidence, and finding out why is the engineer’s job.