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Sir George Greenhill, F.R.S., was a British mathematician.
George Greenhill was educated at Christ's Hospital School and from there he went up to St John's College, Cambridge in 1866. In 1876, Greenhill was appointed professor of mathematics at the Royal Military Academy at Woolwich, London, UK. He held this chair until his retirement in 1908. His 1892 textbook on applications of elliptic functions is of acknowledged excellence.
In 1879, Greenhill developed a rule of thumb for calculating the optimal twist rate for lead-core bullets. This shortcut uses the bullet's length, needing no allowances for weight or nose shape. Greenhill applied this theory to account for the steadiness of flight conferred upon an elongated projectile by rifling. The eponymous Greenhill Formula, still used today, is:
where:
C = 150
D = bullet's diameter in inches
L = bullet's length in inches
SG = bullet's specific gravity
The original value of C was 150, which yields a twist rate in inches per turn, when given the diameter D and the length L of the bullet in inches. This works to velocities of about 840 m/s; above those velocities, a C of 180 should be used. For instance, with a velocity of 600 m/s, a diameter of 0.5 inches and a length of 1.5 inches, the Greenhill formula would give a value of 25, which means 1 turn in 25 inches.
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