NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: David Pike
Date: 2017 Dec 27, 02:13 -0800
Coriolis acceleration is encountered whenever a body moves across the surface of a rotating platform. Its value is 2Vω perpendicular to body’s motion relative to the platform, where V is the velocity of the body, and ω is the angular velocity of the platform. In the case of bubble sextant fluid or pendulous graticule, V is the velocity of the aircraft carrying it, and ω is the Earth’s angular rotation. Most derivations of 2Vω e.g. https://www.youtube.com/watch?v=hrIXgbbDB7M are content to prove only the case of a body moving radially, i.e N-S in the case of the Earth, and the active mind is left wondering "What about E-W, or any other track between 001 and 360?".
Fortunately, this is covered in Ch XVI, pages 300-307, Den Hartog, Mechanics, Dover Publications, 1948. After proving the radial motion case, Den Hartog goes on to consider the concentric motion case (effectively E-W in the case of the Earth), and shows that Coriolis acceleration is also 2Vω. Then, since any direction of motion on the Earth can be resolved into a radial and a concentric component, and their two acceleration components can be compounded again, 2Vω perpendicular to track must be the general case for any track between 001 and 360. Whether this is a rhumb-line or great circle track doesn’t really come into the argument. DaveP
