The Mathematics of Ballistics—from Aristotle to Euler

The mathematics of ballistics (projectile flight), taking into account air resistance, projectile shape, barometric pressure, humidity, wind, etc. are so difficult it wasn’t surprising that one of the first applications of ENIAC, one of the first electronic computers, was calculating ballistic tables for naval gunnery and army artillery. Among the sample programs developed for Fourmilab’s emulation of Charles Babbage’s Analytical Engine is this demonstration of “Numerical Integration: Naval Gunnery”.


Interestingly, when atmospheric drag is very high (as for a large projectile with low density), the actual trajectory resembles Aristotle’s model of an initial impulse carrying the projectile to its maximum altitude, after which it falls almost vertically from the sky.