Alfred George Greenhill
Encyclopedia
Sir George Greenhill, F.R.S. (29 November 1847, London
— 10 February 1927, London
), was a British
mathematician
.
George Greenhill was educated at Christ's Hospital School
and from there he went up 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.
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. 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:
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 (12.7 mm) and a length of 1.5 inches (38.1 mm), the Greenhill formula would give a value of 25, which means 1 turn in 25 inches (635 mm).
London
London is the capital city of :England and the :United Kingdom, the largest metropolitan area in the United Kingdom, and the largest urban zone in the European Union by most measures. Located on the River Thames, London has been a major settlement for two millennia, its history going back to its...
— 10 February 1927, London
London
London is the capital city of :England and the :United Kingdom, the largest metropolitan area in the United Kingdom, and the largest urban zone in the European Union by most measures. Located on the River Thames, London has been a major settlement for two millennia, its history going back to its...
), was a British
Great Britain
Great Britain or Britain is an island situated to the northwest of Continental Europe. It is the ninth largest island in the world, and the largest European island, as well as the largest of the British Isles...
mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
.
George Greenhill was educated at Christ's Hospital School
Christ's Hospital
Christ's Hospital is an English coeducational independent day and boarding school with Royal Charter located in the Sussex countryside just south of Horsham in Horsham District, West Sussex, England...
and from there he went up to St John's College, Cambridge
St John's College, Cambridge
St John's College is a constituent college of the University of Cambridge. The college's alumni include nine Nobel Prize winners, six Prime Ministers, three archbishops, at least two princes, and three Saints....
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.
In 1879, Greenhill developed a rule of thumb
Rule of thumb
A rule of thumb is a principle with broad application that is not intended to be strictly accurate or reliable for every situation. It is an easily learned and easily applied procedure for approximately calculating or recalling some value, or for making some determination...
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. Greenhill applied this theory to account for the steadiness of flight conferred upon an elongated projectile by rifling
Rifling
Rifling is the process of making helical grooves in the barrel of a gun or firearm, which imparts a spin to a projectile around its long axis...
. 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 gravitySpecific gravitySpecific gravity is the ratio of the density of a substance to the density of a reference substance. Apparent specific gravity is the ratio of the weight of a volume of the substance to the weight of an equal volume of the reference substance. The reference substance is nearly always water for...
(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 (12.7 mm) and a length of 1.5 inches (38.1 mm), the Greenhill formula would give a value of 25, which means 1 turn in 25 inches (635 mm).
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
External links
- Alfred George Greenhill. The MacTutor History of Mathematics archive
- Alfred George Greenhill. The First Century of the ICMI (1909 - 2008)
- School of Mathematics and Statistics, University of St Andrews, Scotland. Alfred George Greenhill (October 2003). http://www-history.mcs.st-andrews.ac.uk/~history/Biographies/Greenhill.html