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116:
227:
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
202:
308:
228:
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).
100:
of rotation in incompressible fluid (which, as he couldn't have known back then, assumes subsonic flight). Later, English ballistician F. W. Jones simplified it for typical bullet lengths into a
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in 1904 at
Heidelberg (where he also gave a section talk) and an Invited Speaker of the ICM in 1908 at Rome, in 1920 at Strasbourg, and in 1924 at Toronto.
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40:
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is of acknowledged excellence. He was one of the world's leading experts on applications of elliptic integrals in electromagnetic theory.
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rate for lead-core bullets. This shortcut uses the bullet's length, needing no allowances for weight or nose shape. The eponymous
96:
In 1879 Greenhill calculated complicated twist rate formulas for rifled artillery by approximating the projectile as an elongated
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Verhandlungen des dritten internationalen
Mathematiker-Kongresses in Heidelberg von 8. bis 13. August 1904
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Verhandlungen des dritten internationalen
Mathematiker-Kongresses in Heidelberg von 8. bis 13. August 1904
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Compte rendu du Congrès international des mathématiciens tenu à Strasbourg du 22 au 30 Septembre 1920
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197:{\displaystyle \mathrm {Twist} ={\frac {CD^{2}}{L}}\times {\sqrt {\frac {SG}{10.9}}}}
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223:(10.9 for lead-core bullets, which cancels out the second half of the equation)
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70:, London, UK. He held this chair until his retirement in 1908, when he was
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in 1866. In 1876, Greenhill was appointed professor of mathematics at the
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505:"On the Rotation Required for the Stability of an Elongated Projectile"
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45:
525:
428:. ICM proceedings. Leipzig: B. G. Teubner. 1905. pp. 582–585.
406:. ICM proceedings. Leipzig: B. G. Teubner. 1905. pp. 100–108.
114:
694:
420:
Teaching of mechanics by familiar applications on a large scale
122:
as cast (left), with gas check (center) and lubricated (right).
210:
C = 150 (use 180 for muzzle velocities higher than 2,800 ft/s)
398:
260:
University of
Michigan Historical Mathematical Collection
231:
Recently, Greenhill formula has been supplemented with
246:
Differential and integral calculus, with applications
131:
196:
356:"The elliptic integral in electromagnetic theory"
706:
466:"Where did Greenhill's twist rule come from?"
8:
686:The First Century of the ICMI (1909 - 2008)
470:International Journal of Impact Engineering
442:The Fourier and Bessel Functions contrasted
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1177:Members of the French Academy of Sciences
1162:Fellows of the Royal Aeronautical Society
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132:
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68:Royal Military Academy (RMA) at Woolwich
337:MacTutor History of Mathematics Archive
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1137:Alumni of St John's College, Cambridge
590:The Applications of Elliptic Functions
567:: CS1 maint: archived copy as title (
560:
309:"Greenhill, George Alfred (GRNL866GA)"
256:The applications of elliptic functions
258:(MacMillan & Co, New York, 1892)
77:His 1892 textbook on applications of
48:– 10 February 1927 in London), was a
7:
1132:People educated at Christ's Hospital
1147:20th-century British mathematicians
1142:19th-century British mathematicians
509:Van Nostrand's Engineering Magazine
464:Miller, Donald G. (November 2006).
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136:
133:
25:
373:10.1090/s0002-9947-1907-1500798-2
354:Greenhill, Alfred George (1907).
276:The dynamics of mechanical flight
58:George Greenhill was educated at
672:
84:He was a Plenary Speaker of the
655:10.1090/s0002-9904-1917-02930-8
612:10.1090/s0002-9904-1893-00129-8
526:https://dds.crl.edu/item/286938
213:D = bullet's diameter in inches
482:10.1016/j.ijimpeng.2005.06.001
1:
216:L = bullet's length in inches
1167:Fellows of the Royal Society
104:for calculating the optimal
64:St John's College, Cambridge
633:Report on Gyroscopic Theory
592:by Alfred George Greenhill"
313:A Cambridge Alumni Database
287:Report on gyroscopic theory
248:( London, MacMillan, 1886)
33:Sir Alfred George Greenhill
1203:
1127:Mathematicians from London
315:. University of Cambridge.
278:(Constable, London, 1912)
268:(MacMillan, London, 1894)
266:A treatise on hydrostatics
62:and from there he went to
728:
684:Alfred George Greenhill.
503:Greenhill, A. G. (1880).
453:. 1921. pp. 636–655.
332:"Alfred George Greenhill"
290:(Darling & Son, 1914)
342:University of St Andrews
112:, still used today, is:
60:Christ's Hospital School
679:Alfred George Greenhill
742:James Joseph Sylvester
677:Quotations related to
573:(Accessed 2009 AUG 19)
198:
123:
902:George Neville Watson
642:Bull. Amer. Math. Soc
627:Wilson, Edwin Bidwell
599:Bull. Amer. Math. Soc
538:The Greenhill Formula
360:Bull. Amer. Math. Soc
199:
118:
44:(29 November 1847 in
27:British mathematician
1182:De Morgan Medallists
1078:John Griggs Thompson
1070:Keith William Morton
854:Godfrey Harold Hardy
722:De Morgan Medallists
635:by Sir G. Greenhill"
328:Robertson, Edmund F.
129:
1152:Royal Medal winners
422:by A. G. Greenhill"
400:by A. G. Greenhill"
326:O'Connor, John J.;
1187:Ballistics experts
536:Mosdell, Matthew.
194:
124:
79:elliptic functions
1104:
1103:
1022:Albrecht Fröhlich
982:C. Ambrose Rogers
910:A. S. Besicovitch
798:J. W. L. Glaisher
476:(11): 1786–1799.
284:A. G. Greenhill,
274:A. G. Greenhill,
264:A. G. Greenhill,
254:A. G. Greenhill,
233:Miller twist rule
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110:Greenhill formula
92:Greenhill formula
16:(Redirected from
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545:. Archived from
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444:by G. Greenhill"
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221:specific gravity
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1038:R. A. Rankin
1030:W. K. Hayman
926:G. I. Taylor
830:E. W. Hobson
681:at Wikiquote
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551:. Retrieved
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1122:1927 deaths
1117:1847 births
1046:J. A. Green
966:Kurt Mahler
950:Philip Hall
822:W. H. Young
806:Horace Lamb
790:H. F. Baker
758:Felix Klein
280:archive.org
270:archive.org
250:archive.org
1111:Categories
998:K. F. Roth
942:Max Newman
766:S. Roberts
515:: 211–214.
295:References
814:J. Larmor
631:"Review:
588:"Review:
553:19 August
490:0734-743X
239:Textbooks
175:×
98:ellipsoid
629:(1917).
586:(1893).
563:cite web
72:knighted
382:1500798
206:where:
50:British
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808:(1911)
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736:(1884)
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46:London
638:(PDF)
595:(PDF)
447:(PDF)
106:twist
41:FRAeS
39:
569:link
555:2009
486:ISSN
189:10.9
650:doi
607:doi
478:doi
368:doi
86:ICM
74:.
37:FRS
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561:{{
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378:MR
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185:G
182:S
170:L
164:2
160:D
156:C
150:=
146:t
143:s
140:i
137:w
134:T
20:)
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