Latitude Coriolis Deflection Calculator

Coriolis deflection quantifies how far a freely moving object appears to wander sideways from a straight track because the planet turns beneath it. In a frame rotating with Earth the transverse acceleration is f times v, where the Coriolis parameter f equals 2 times omega times the sine of latitude and omega is Earth's rotation rate of 7.2921 times 10 to the minus 5 radians per second. Integrating that lateral acceleration over a flight time t gives the quadratic form d = 0.5 f v t squared, so deflection grows with the square of travel time but only linearly with speed. Since t equals distance divided by speed, a fixed range crossed more slowly deflects further. The parameter f runs from zero at the equator through 1.03 times 10 to the minus 4 per second at 45 degrees to 1.458 times 10 to the minus 4 per second at the poles. The expression treats the ground track as flat and f as locally constant, assumptions that hold while the path stays under roughly 100 km and away from the equator where the beta effect becomes important. It also ignores drag and wind. The Rossby number, speed divided by f times the length scale, indicates whether rotation dominates: values well below 1 imply near-geostrophic balance, while values above 1 mean inertia governs and deflection is a small perturbation. For scale, a rifle bullet over 1000 m drifts a few centimeters, a 20 km artillery shell about 25 m, and the inertial period is roughly 17 hours at 45 degrees.

Gaspard-Gustave de Coriolis published the underlying mathematics in 1835 in a paper on the equations of relative motion in machines, motivated by rotating waterwheels and industrial machinery rather than by the atmosphere. Pierre-Simon Laplace had already written equivalent terms into his tidal equations in 1778, and the qualitative notion that Earth's rotation deflects moving air appeared in George Hadley's 1735 account of the trade winds, though Hadley used a conservation-of-velocity argument that yields only about half the correct magnitude. William Ferrel corrected and generalized the reasoning during the 1850s, stating what is now called Ferrel's law: bodies moving across Earth's surface deflect to the right in the Northern Hemisphere and to the left in the Southern. Physical confirmation arrived with Leon Foucault's 1851 pendulum at the Paris Pantheon, whose plane of swing rotated at a rate proportional to the sine of latitude. The term Coriolis force entered meteorological usage around the turn of the twentieth century, and Vilhelm Bjerknes and the Bergen School embedded it in operational weather analysis during the 1910s and 1920s. Long-range naval gunnery forced practical adoption, with fire control tables from the First World War onward carrying explicit rotation corrections. Ascher Shapiro's 1962 tank experiment at MIT settled the popular bathtub question by showing the effect is genuine but demands an undisturbed symmetric basin. The Coriolis term is now a standard component of every numerical weather and ocean circulation model.