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Alfred George Greenhill

August 22, 2023

Sir Alfred George Greenhill FRS FRAeS (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 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, when he was knighted.

His 1892 textbook on applications of elliptic functions is of acknowledged excellence. He was one of the world's leading experts on applications of elliptic integrals in electromagnetic theory.[3]

He was a Plenary Speaker of the ICM in 1904 at Heidelberg[4] (where he also gave a section talk)[5] and an Invited Speaker of the ICM in 1908 at Rome, in 1920 at Strasbourg,[6] and in 1924 at Toronto.

Greenhill formula

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.[7] 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).
 

where:

  • C = 150 (use 180 for muzzle velocities higher than 2,800 ft/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).

Recently, Greenhill formula has been supplemented with Miller twist rule.

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)[8] 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
  • A. G. Greenhill, Report on gyroscopic theory (Darling & Son, 1914)[9]

References

  1. ^ "Greenhill, George Alfred (GRNL866GA)". A Cambridge Alumni Database. University of Cambridge.
  2. ^ O'Connor, John J.; Robertson, Edmund F., "Alfred George Greenhill", MacTutor History of Mathematics Archive, University of St Andrews
  3. ^ Greenhill, Alfred George (1907). "The elliptic integral in electromagnetic theory". Bull. Amer. Math. Soc. 8 (4): 447–534. doi:10.1090/s0002-9947-1907-1500798-2. MR 1500798.
  4. ^ "The Mathematical Theory of the Top considered historically by A. G. Greenhill". Verhandlungen des dritten internationalen Mathematiker-Kongresses in Heidelberg von 8. bis 13. August 1904. ICM proceedings. Leipzig: B. G. Teubner. 1905. pp. 100–108.
  5. ^ "Teaching of mechanics by familiar applications on a large scale by A. G. Greenhill". Verhandlungen des dritten internationalen Mathematiker-Kongresses in Heidelberg von 8. bis 13. August 1904. ICM proceedings. Leipzig: B. G. Teubner. 1905. pp. 582–585.
  6. ^ "The Fourier and Bessel Functions contrasted by G. Greenhill" (PDF). Compte rendu du Congrès international des mathématiciens tenu à Strasbourg du 22 au 30 Septembre 1920. 1921. pp. 636–655.
  7. ^ Mosdell, Matthew. The Greenhill Formula. . Archived from the original on 18 July 2011. Retrieved 19 August 2009.{{cite web}}: CS1 maint: archived copy as title (link) (Accessed 2009 AUG 19)
  8. ^ Harkness, J. (1893). "Review: The Applications of Elliptic Functions by Alfred George Greenhill" (PDF). Bull. Amer. Math. Soc. 2 (7): 151–157. doi:10.1090/s0002-9904-1893-00129-8.
  9. ^ Wilson, Edwin Bidwell (1917). "Review: Report on Gyroscopic Theory by Sir G. Greenhill" (PDF). Bull. Amer. Math. Soc. 23 (5): 241–244. doi:10.1090/s0002-9904-1917-02930-8.

External links

 
Wikisource has original works by or about:
Alfred George Greenhill
  •   Quotations related to Alfred George Greenhill at Wikiquote
  • Alfred George Greenhill. The First Century of the ICMI (1909 - 2008)

August 22, 2023
alfred, george, greenhill, fraes, november, 1847, london, february, 1927, london, british, mathematician, george, greenhill, educated, christ, hospital, school, from, there, went, john, college, cambridge, 1866, 1876, greenhill, appointed, professor, mathemati. Sir Alfred George Greenhill FRS FRAeS 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 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 when he was knighted His 1892 textbook on applications of elliptic functions is of acknowledged excellence He was one of the world s leading experts on applications of elliptic integrals in electromagnetic theory 3 He was a Plenary Speaker of the ICM in 1904 at Heidelberg 4 where he also gave a section talk 5 and an Invited Speaker of the ICM in 1908 at Rome in 1920 at Strasbourg 6 and in 1924 at Toronto Contents 1 Greenhill formula 2 Textbooks 3 References 4 External linksGreenhill formula EditIn 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 7 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 T w i s t C D 2 L S G 10 9 displaystyle mathrm Twist frac CD 2 L times sqrt frac SG 10 9 where C 150 use 180 for muzzle velocities higher than 2 800 ft 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 Recently Greenhill formula has been supplemented with Miller twist rule Textbooks EditA G Greenhill Differential and integral calculus with applications London MacMillan 1886 archive org A G Greenhill The applications of elliptic functions MacMillan amp Co New York 1892 8 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 A G Greenhill Report on gyroscopic theory Darling amp Son 1914 9 References Edit Greenhill George Alfred GRNL866GA A Cambridge Alumni Database University of Cambridge O Connor John J Robertson Edmund F Alfred George Greenhill MacTutor History of Mathematics Archive University of St Andrews Greenhill Alfred George 1907 The elliptic integral in electromagnetic theory Bull Amer Math Soc 8 4 447 534 doi 10 1090 s0002 9947 1907 1500798 2 MR 1500798 The Mathematical Theory of the Top considered historically by A G Greenhill Verhandlungen des dritten internationalen Mathematiker Kongresses in Heidelberg von 8 bis 13 August 1904 ICM proceedings Leipzig B G Teubner 1905 pp 100 108 Teaching of mechanics by familiar applications on a large scale by A G Greenhill Verhandlungen des dritten internationalen Mathematiker Kongresses in Heidelberg von 8 bis 13 August 1904 ICM proceedings Leipzig B G Teubner 1905 pp 582 585 The Fourier and Bessel Functions contrasted by G Greenhill PDF Compte rendu du Congres international des mathematiciens tenu a Strasbourg du 22 au 30 Septembre 1920 1921 pp 636 655 Mosdell Matthew The Greenhill Formula Archived copy Archived from the original on 18 July 2011 Retrieved 19 August 2009 a href Template Cite web html title Template Cite web cite web a CS1 maint archived copy as title link Accessed 2009 AUG 19 Harkness J 1893 Review The Applications of Elliptic Functions by Alfred George Greenhill PDF Bull Amer Math Soc 2 7 151 157 doi 10 1090 s0002 9904 1893 00129 8 Wilson Edwin Bidwell 1917 Review Report on Gyroscopic Theory by Sir G Greenhill PDF Bull Amer Math Soc 23 5 241 244 doi 10 1090 s0002 9904 1917 02930 8 External links Edit Wikisource has original works by or about Alfred George Greenhill Quotations related to Alfred George Greenhill at Wikiquote Alfred George Greenhill The First Century of the ICMI 1909 2008 Retrieved from https en wikipedia org w index php title Alfred George Greenhill amp oldid 1170787232, wikipedia, wiki, book, books, library,

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