This is a preliminary analysis of the extent to which some general curvature patterns in military spending contribute to predicting war onset in a global sample of arms races. Exponential, logarithmic, and trigonometric curves are fit to the military spending data of nations engaged in arms races, and derivatives are taken at the point of war onset. In contrast to a prior unfavorable assessment (Thompson, Duval and Dia, 1979), Alcock's (1972) hypotheses on military spending curvature and incidence of war are shown to describe several cases of the onset of arms race‐related wars. However, contrary to Alcock, the majority of these wars are not signalled by deceleration in racing for both rivals. Instead, expansion of racing just prior to war is shown. Strongly exponential racing appears more likely to end in war than do other racing patterns, as argued in other data and in more complex analyses.