Sir Alfred George Greenhill (29 November 1847 in

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– 10 February 1927 in London), was a British

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

. George Greenhill was educated at Christ's Hospital School and from there he went to

St John's College, Cambridge St John's College, formally the College of St John the Evangelist in the University of Cambridge, is a Colleges of the University of Cambridge, constituent college of the University of Cambridge, founded by the House of Tudor, Tudor matriarch L ...

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, 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. 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 calculated complicated twist rate formulas for rifled artillery by approximating the projectile as an elongated

ellipsoid An ellipsoid is a surface that can be obtained from a sphere by deforming it by means of directional Scaling (geometry), scalings, or more generally, of an affine transformation. An ellipsoid is a quadric surface; that is, a Surface (mathemat ...

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

rule of thumb In English language, English, the phrase ''rule of thumb'' refers to an approximate method for doing something, based on practical experience rather than theory. This usage of the phrase can be traced back to the 17th century and has been associat ...

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. The eponymous Greenhill formula, still used today, is: 3CastBullets

\mathrm = \frac \times \sqrt

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 Relative density, also called specific gravity, is a dimensionless quantity defined as the ratio of the density (mass of a unit volume) of a substance to the density of a given reference material. Specific gravity for solids and liquids is nea ...

(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