An equation for generalising from impact test performance to real-world crashes

Instrumented headforms are projected at the fronts of cars to assess pedestrian safety. Better information would be obtained from these and other types of impact tests if performance over the range of expected impact conditions in the field were taken into account. That is, some means is needed to convert from performance in tightly-specified test conditions to what happens in the real-world. Pedestrian impact safety performance of a car is affected by speed, head mass, and the distribution of impact locations over the front of the car. The effects are complicated because bottoming out may occur, that is, the hood or other surface structure may fail to absorb sufficient energy to prevent contact with much stiffer structures beneath it. In turn, the locations are affected by the geometry of the car, the impact speed, and the pedestrian’s stature. The relative frequencies of different speeds, masses, and so on are important inputs to the calculation of an average. The principal result is a theory. This has three steps. The first is to convert the test quantity (e.g., HIC, the Head Injury Criterion) observed in test conditions to what would be observed if (for example) speed or mass were different. The second is to convert the test quantity to something that can be meaningfully averaged --- for example, average dollar cost of HIC or the probability of death corresponding to a given HIC. The third is to obtain the average cost, or average probability of death, by integration over the quantities that vary from crash to crash: speed, head mass, stature, and impact location. The theory that is developed may be used to calculate, for example, the changes that result if test performance is improved, or the probabilities of different conditions change. With appropriate modification, the theory is applicable to many other forms of testing also. The chief limitation is that good information is required on such things as the dependence of HIC on speed and mass, the dependence of cost on HIC, and the relative frequencies of speeds, masses, and so on. Such information is difficult to obtain. Better representation of the effect of impact conditions on severity is required if a test regime is to provide appropriate incentives for improvement in vehicle design. This paper identifies what information is needed, and shows how it can be used to estimate average real-world performance starting from what is observed in an impact test.