# Alfred George Greenhill

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Sir (Alfred) George Greenhill, F.R.S. (29 November 1847 in London – 10 February 1927 in London), 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.[1] In 1876, Greenhill was appointed professor of mathematics at the Royal Military Academy (RMA) at Woolwich, London, UK.[2] 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.[3] 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:

Cast bullets as cast (left), with gas check (center) and lubricated (right).

$Twist = \frac{C D^2}{L} \times \sqrt{\frac{SG}{10.9}}$

where:

• C = 150 (use 180 for muzzle velocities higher than 2,800 f/s)
• D = bullet's diameter in inches
• L = bullet's length in inches
• SG = bullet's specific gravity (10.9 for lead-core bullets, which cancels out the second half of the equation)

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 (2800 ft/s); above those velocities, a C of 180 should be used. For instance, with a velocity of 600 m/s (2000 ft/s), a diameter of 0.5 inches (13 mm) and a length of 1.5 inches (38 mm), the Greenhill formula would give a value of 25, which means 1 turn in 25 inches (640 mm).