Artillery and Coriolis

E. Linacre and B. Geerts



For many years the discovery of the Coriolis effect has been explained by means of an apocryphal story from the European wars of the early 19th century. The story goes as follows:

The military apparatus of Napoleon's era observed that the new long-range cannon landed their missiles always to the right when accurately trained on the target before firing. The apparent deflection of the missile from the straight path between gun and target was explained by Gustave Gaspard Coriolis (a Frenchman born in 1792) as due to the movement of the Earth, and therefore the target, whilst the missile was in flight. Following his death in 1843, the apparent deflection of missiles and other moving objects was named after him.

However, the story is improbable (1). The effective range of guns was less that 1 km prior to rifling of the bore towards the middle of the nineteenth century, and even then the accuracy was poor. The largest muzzle-loaded cannon with rifling at the end of Coriolis’ life could fire effectively to 5 km at most. The muzzle velocity of such guns was perhaps 500 m/s, so the time of flight would be about 10 seconds, say. In that time, a target at the latitude of France would move only about 2.5 metres to the right of a line from the gun to the target’s initial position. Such a Coriolis deflection would be indiscernible amongst the scatter caused by variations of wind strength and temperature, of the force of the explosive, of rifling wear and of the spin of the missile induced by the rifling. In short, G.G. Coriolis could not possibly have found inspiration for the effect that is named after him in the trajectory of missiles.

More recent developments in the science of ballistics make the Coriolis effect more significant. For instance, a German gun of 21-cm bore called ‘Big Bertha’ was used in 1918 to shell Paris from a distance of 122 km. Over such distances the inclusion of the Coriolis effect is at least as important as the consideration of deflection by the wind.

In ball sports the Coriolis effect is of negligible importance, relative to the effects of the wind and the spin of the ball. For instance, a soccer ball kicked horizontally 100 metres in 4 seconds at 42ºN will deviate 1.5 cm to the right. However when that same ball is kicked with sufficient spin, it will easily deflect 100 times as much. The spin-induced deflection can be explained by the Bernouilli effect applied to air trajectories deflected to both sides of the ball.



  1. This note is based on arguments by Ron Walsh of Canberra on 20/5/1997.