Alfred George Greenhill
Sir Alfred George Greenhill .
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
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:
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
- ^ "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
- 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 Congrès international des mathématiciens tenu à 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.
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External links
- Quotations related to Alfred George Greenhill at Wikiquote
- Alfred George Greenhill. The First Century of the ICMI (1909 - 2008)