The Anderson Theorem

Extract

In 1835 Gustave-Gaspard Coriolis proved that, if a ‘body’ travelling unaccelerated at a speed v is made to conform to a medium rotating at a rate w, it will be accelerated sideways at vw. Hence air travelling freely, if subjected to the rotation of the Earth's surface, will be accelerated at – 2vω sin ø, –ω sin ø being the rate at which the local surface rotates, with –ω the speed at which the Earth spins and ø the local latitude. (In the diagrams ω is presented as Ω).

2. Coriolis also proved the converse formula from which, if air travels freely over the surface of the Earth, it will accelerate at + 2ω sin ø relative to the local rotating surface. This reversed Coriolis formula happens to be far more important than the original direct formula. It has been applied to long-range artillery, to aircraft using spirit-level sextants, to inertial navigation systems and to the ground tracking of space craft. It has also been applied to forecasting wind speeds.

3. We can handle the duality of Coriolis by a loop diagram as in Fig. 1. The central link shows the direct Coriolis acceleration produced when air travelling freely is forced to conform to the rotating surface of the Earth, The link to the left depicts the reversed Coriolis acceleration which applies to air travelling freely as seen from the local surface of the rotating Earth.