Mathematical models for hit probabilities of small arms are developed in order to estimate the expected hits on an aircraft for certain altitudes and air speeds. A model for the firing lead angle is developed for cases when the distribution of hits is normal and the firing angle is from 20 degrees to 160 degrees. probabilities of hit for single and multiple shots at various altitudes are calculated. Tables are given showing the probability of hits and kill for targets flying at high speed above 500 feet from ground level.