Prediction of concrete penetration using Forrestals formula

Abstract

The various existing empirical formulas for predicting penetration into concrete targets are seen to give different results. Explaining the difference is difficult since most of the original empirical data behind the various formulas are not available. The range of the parameters used in the experiments is known, though. The theoretical formula developed by Forrestal, based on the cavity expansion theory, seems to be in good agreement with experiments for various projectiles and various quality of the concrete target. Forrestal's formula is analysed using non-dimensional quantities, and this formula is used to analyse the other existing empirical formulas for predicting penetration into concrete. Assuming that Forrestal’s formula predicts the penetration depth correctly, least square approximations, and possible ”empirical equations” for constant non-dimensional mass are calculated. These ”empirical equations” turn out to be very sensitive to the range of the impact velocity used in the experiments. Many existing empirical formulas are based on experiments with different values of length to diameter ratio in their data sets. The resulting empirical formula from such data sets may become ”arbitrary”. This means that even though the range of the non-dimensional parameters are identical, the resulting empirical formulas turn out to be quite different. From these observations, an explanation of the difference between the empirical formulas is suggested. Finally, Forrestal's formula is applied to different kinds of modern penetrating weapons.