Influence of air drag on the optimal hand launching of a small, round projectile

Conditions leading to a maximum range for a small, round projectile, fired by hand, are discussed taking into account air drag and the dependence of the initial speed on the mass launched. Both the optimal angle of release for given projectile and initial speed, and the optimal radius for given density (i.e., among a bed of pebbles) are determined; an increase on the height of release is found to always decrease the angle and increase the radius. The influence of the projectile mass on the optimal manner of launching is considered. The validity of the approximations used in the analysis is discussed. Results from very simple measurements show good agreement with theory.