Work on friction dates back more than two hundred years. Some of the work applies to dynamic situations in which the influence of speed may be a factor (see Kragelskii [5]). But, most of the work does not apply to the velocity regime observed in high-speed penetration problems. This has become an issue because of the Air Force’s interest in smaller and more versatile air launched weapons. Earlier work focused on conventional friction models. Jones and Rule [2] considered optimal design of the penetrator nose in a high friction environment using Coulomb friction. Later, Jones, et al [3] used constant friction equivalent to target shear strength. While the results of these analyses were largely satisfactory, they did not completely capture the essence of the work done by friction. Recently, the authors [4] proposed a simple velocity-dependent engineering model to account for friction in high-speed penetration events. A critical velocity controlled the initiation of friction and the amount of work done by friction. The results were very satisfactory and correlated very well with experimental observations from range tests. However, there were a number of tedious integrations and numerical evaluation of some difficult integrals. In this paper, several simplifying assumptions are made which replace the numerical integration with closed form solutions. The results, while somewhat different, agree in principle with those given earlier. The same trends are observed and the correlation with independently performed experiments is excellent. Additionally, the zero asymptotic limit is replaced and its effect is considered.

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