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 London is the capital and List of urban areas in the United Kingdom, largest city of England and the United Kingdom, with a population of just under 9 million. It stands on the River Thames in south-east England at the head of a estuary dow ...

– 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, structure, space, models, and change. History On ...

. George Greenhill was educated at

Christ's Hospital School Christ's Hospital is a public school (English independent boarding school for pupils aged 11–18) with a royal charter located to the south of Horsham in West Sussex. The school was founded in 1552 and received its first royal charter in 1553. ...

and from there he went to

St John's College, Cambridge St John's College is a constituent college of the University of Cambridge founded by the Tudor matriarch Lady Margaret Beaufort. In constitutional terms, the college is a charitable corporation established by a charter dated 9 April 1511. The ...

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 In the mathematical field of complex analysis, elliptic functions are a special kind of meromorphic functions, that satisfy two periodicity conditions. They are named elliptic functions because they come from elliptic integrals. Originally those ...

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 In 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 associated with various t ...

for calculating the optimal

twist Twist may refer to: In arts and entertainment Film, television, and stage * ''Twist'' (2003 film), a 2003 independent film loosely based on Charles Dickens's novel ''Oliver Twist'' * ''Twist'' (2021 film), a 2021 modern rendition of ''Olive ...

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 In firearms, rifling is machining helical grooves into the internal (bore) surface of a gun's barrel for the purpose of exerting torque and thus imparting a spin to a projectile around its longitudinal axis during shooting to stabilize the ...

. 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 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 dens ...

(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 Miller twist rule is a mathematical formula derived by Don Miller to determine the rate of twist to apply to a given bullet to provide optimum stability using a rifled barrel.Miller, Don. How Good Are Simple Rules For Estimating Rifling Twist', Prec ...

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