Alfred George Greenhill


Sir Alfred George Greenhill , was a British mathematician.
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 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 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 of rotation in incompressible fluid. Later, English ballistician F. W. Jones simplified it for typical bullet lengths into 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. The eponymous Greenhill formula, still used today, is:
where:
  • C = 150
  • D = bullet's diameter in inches
  • L = bullet's length in inches
  • SG = bullet's specific gravity
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 ; above those velocities, a C of 180 should be used. For instance, with a velocity of 600 m/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