Sir Alfred George Greenhill,
FRS FRAeS
The Royal Aeronautical Society, also known as the RAeS, is a British multi-disciplinary professional institution dedicated to the global aerospace community. Founded in 1866, it is the oldest aeronautical society in the world. Members, Fellows ...
(29 November 1847 in
London
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– 10 February 1927 in London), was a
British
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mathematician
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Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change.
History
On ...
.
George Greenhill was educated at
Christ's Hospital School and from there he went to
St John's College, Cambridge in 1866. In 1876, Greenhill was appointed professor of mathematics at the
Royal Military Academy (RMA) at Woolwich, London, UK. He held this chair until his retirement in 1908. 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. He was a Plenary Speaker of the
ICM 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.
Greenhill formula
In 1879, Greenhill developed a
rule of thumb for calculating the optimal
twist
Twist may refer to:
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rate for lead-core bullets. This shortcut uses the bullet's length, needing no allowances for weight or nose shape. 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 f/s)
*D = bullet's diameter in inches
*L = bullet's length in inches
*SG = bullet's
specific gravity
Relative density, or specific gravity, is the ratio of the density (mass of a unit volume) of a substance to the density of a given reference material. Specific gravity for liquids is nearly always measured with respect to water at its densest ...
(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 and a length of , the Greenhill formula would give a value of 25, which means 1 turn in .
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
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)
References
External links
*
* Alfred George Greenhill
The First Century of the ICMI (1909 - 2008)
{{DEFAULTSORT:Greenhill, Alfred George
1847 births
1927 deaths
Mathematicians from London
People educated at Christ's Hospital
Alumni of St John's College, Cambridge
19th-century British mathematicians
20th-century British mathematicians
Royal Medal winners
Second Wranglers
Fellows of the Royal Aeronautical Society
Fellows of the Royal Society
Knights Bachelor
Members of the French Academy of Sciences
De Morgan Medallists
Ballistics experts