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| Sir '''(Alfred) George Greenhill''', [[Fellow of the Royal Society|F.R.S.]] (29 November 1847, [[London]] — 10 February 1927, [[London]]), was a [[Great Britain|British]] [[mathematician]].
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| George Greenhill was educated at [[Christ's Hospital|Christ's Hospital School]] and from there he went up to [[St John's College, Cambridge]] in 1866.<ref>{{acad|id=GRNL866GA|name=Greenhill, George Alfred}}</ref> In 1876, Greenhill was appointed professor of mathematics at the [[Royal Military Academy, Woolwich|Royal Military Academy (RMA) at Woolwich]], London, UK.<ref>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</ref> He held this chair until his retirement in 1908. His 1892 textbook on applications of [[elliptic functions]] is of acknowledged excellence.
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| In 1879, Greenhill developed a [[rule of thumb]] for calculating the optimal [[Rifling#Twist rate|twist]] rate for lead-core bullets. This shortcut uses the bullet's length, needing no allowances for weight or nose shape.<ref>Mosdell, Matthew. ''The Greenhill Formula''. http://www.mamut.net/MarkBrooks/newsdet35.htm (Accessed 2009 AUG 19)</ref> 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:
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| <math>Twist = \frac{C D^2}{L} \times \sqrt{\frac{SG}{10.9}}</math>
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| where:
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| *C = 150 (use 180 for muzzle velocities higher than 2,800 f/s)
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| *D = bullet's diameter in inches
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| *L = bullet's length in inches
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| *SG = bullet's [[specific gravity]] (10.9 for lead-core bullets, which cancels out the second half of the equation)
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| 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 {{convert|0.5|in|mm}} and a length of {{convert|1.5|in|mm}}, the Greenhill formula would give a value of 25, which means 1 turn in {{convert|25|in|mm}}.
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| == Textbooks ==
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| * A. G. Greenhill ''Differential and integral calculus, with applications'' ( London, MacMillan, 1886) [http://www.archive.org/details/differentialinte00greeuoft archive.org]
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| * A. G. Greenhill, ''The applications of elliptic functions'' (MacMillan & Co, New York, 1892). [http://quod.lib.umich.edu/cgi/t/text/text-idx?c=umhistmath;idno=ACQ7072 University of Michigan Historical Mathematical Collection.]
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| * A. G. Greenhill, ''A treatise on hydrostatics'' (MacMillan, London, 1894) [http://www.archive.org/details/treatiseonhydros00greeuoft archive.org]
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| * A. G. Greenhill ''The dynamics of mechanical flight'' (Constable, London, 1912) [http://www.archive.org/details/dynamicsofmechan00greerich archive.org]
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| ==External links==
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| {{Wikisource author}}
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| * Alfred George Greenhill. [http://www-history.mcs.st-and.ac.uk/Biographies/Greenhill.html The MacTutor History of Mathematics archive]
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| * Alfred George Greenhill. [http://www.icmihistory.unito.it/portrait/greenhill.php The First Century of the ICMI (1909 - 2008) ]
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| * 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
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| ==References==
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| {{reflist}}
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| {{Authority control|VIAF=49986812}}
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| {{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. -->
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| | NAME = Greenhill, Alfred George
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| | ALTERNATIVE NAMES =
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| | SHORT DESCRIPTION = British mathematician
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| | DATE OF BIRTH = 1847
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| | PLACE OF BIRTH =
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| | DATE OF DEATH = 1927
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| | PLACE OF DEATH =
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| }}
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| {{DEFAULTSORT:Greenhill, Alfred George}}
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| [[Category:1847 births]]
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| [[Category:1927 deaths]]
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| [[Category:People from London]]
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| [[Category:People educated at Christ's Hospital]]
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| [[Category:Alumni of St John's College, Cambridge]]
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| [[Category:British mathematicians]]
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| [[Category:Royal Medal winners]]
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| [[Category:Second Wranglers]]
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| [[Category:Fellows of the Royal Aeronautical Society]]
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| [[Category:Fellows of the Royal Society]]
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| [[Category:Knights Bachelor]]
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| [[Category:Members of the French Academy of Sciences]]
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| [[Category:De Morgan Medallists]]
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| [[Category:Ballistics experts]]
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| [[Category:ICM 1904 Plenary and Invited Speakers]]
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