Littelmann path model

Sir (Alfred) George Greenhill, F.R.S. (29 November 1847, London — 10 February 1927, 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. In 1876, Greenhill was appointed professor of mathematics at the Royal Military Academy (RMA) 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:

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

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 Template:Convert and a length of Template:Convert, the Greenhill formula would give a value of 25, which means 1 turn in Template:Convert.

Textbooks

• A. G. Greenhill Differential and integral calculus, with applications ( London, MacMillan, 1886) archive.org
• A. G. Greenhill, The applications of elliptic functions (MacMillan & Co, New York, 1892). University of Michigan Historical Mathematical Collection.
• A. G. Greenhill, A treatise on hydrostatics (MacMillan, London, 1894) archive.org
• A. G. Greenhill The dynamics of mechanical flight (Constable, London, 1912) archive.org

External links

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• Alfred George Greenhill. The MacTutor History of Mathematics archive
• Alfred George Greenhill. The First Century of the ICMI (1909 - 2008)
• School of Mathematics and Statistics, University of St Andrews, Scotland. Alfred George Greenhill (October 2003). http://www-history.mcs.st-andrews.ac.uk/~history/Biographies/Greenhill.html

References

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