Modeling the effect of air-intake aperture size in the ping-pong ball cannon

A vacuum cannon (or a ping-pong ball cannon) is commonly used by many physics departments to demonstrate the large forces that result from pressure differentials surrounding an object. In this paper, previous theoretical descriptions for the vacuum cannon are revisited and extended to include the effect of the air-intake aperture size on the projectile speed in the cannon. This extended treatment is mostly analytic although there is a small but necessary numerical aspect to this analysis. Good agreement has been found between theoretical predictions and observations using this new analysis. The principles involved in this theoretical framework are easily accessible to intermediate and advanced undergraduate students, and hence, the vacuum cannon demonstration could easily be transformed into an experiment appropriate for an undergraduate thermal physics course. Students would be expected to perform analytical derivations, write simple computational programs, and perform high-speed video capture and analysis. Thus, students would gain experience with analytical, numerical, and experimental techniques in a single project.