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Alfred George Greenhill
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.[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:
\( Twist = \frac{C D^2}{L} \times \sqrt{\frac{SG}{10.9}} \)
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).
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
Wikisource has original works written by or about:
Alfred George Greenhill
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
^ Venn, J.; Venn, J. A., eds. (1922–1958). "Greenhill, George Alfred". Alumni Cantabrigienses (10 vols) (online ed.). Cambridge University Press.
^ 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
^ Mosdell, Matthew. The Greenhill Formula. http://www.mamut.net/MarkBrooks/newsdet35.htm (Accessed 2009 AUG 19)
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