On the trajectories of projectiles depicted in early ballistic woodcuts

Motivated by quaint woodcut depictions often found in many late 16th and 17th century ballistic manuals of cannonballs fired in air, a comparison of their shapes with those calculated for the classic case of a projectile moving in a linear resisting medium is made. In considering the asymmetrical nature of such trajectories, the initial launch angle resulting in the greatest forward horizontal skew of the trajectory is found and compared to the corresponding launch angle which maximizes the range of the projectile. Limiting behaviour in the shape of the trajectory in the strong damping limit is also considered and compared to peculiar straight-lined triangular trajectory woodcuts from the late 16th century.