NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Antoine Couëtte
Date: 2023 Aug 11, 05:13 -0700
Just for fun, this quick computation rings a bell .. about pre-cosmonaut training and pre-TPS exams.
Under its best known - at least in France - "classical" form the centripetal acceleration "γ" is given as " γ = v**2 / r " with "v" being the [longitudinal] speed and "r" the instantaneous radius of turn.
Through immediately jumping onto this classical form " γ = v**2 / r " formula, unfamilar candidates hassled into computing "r" from the starting data, to eventually discover that "r" did simply vanish in the final results.
Too bad ... meanwhile the clock had been too fast running.
A few Candidates - and the only ones able to complete all such exercises in a very limited time - were using the centripetal acceleration formula under this form " γ = v * ω " with "ω" being the angular motion.
No need for any explicit "r" value, then ...
In this example, with v = 540 kts = (540 * 1852 / 3600) m/s = 277.8 m/s and ω = 1° / min = π /(180 * 60) rad/s = 291 E-6 rad/s, the lateral acceleration "γ" is instantly computed as : γ = 277.8 * 291 E-6 = 0.08081 m/s.
Referring it to "g" as being the local gravity acceleration (at 9.81 m/s**2) yields :
tan-1 (0.08081 / 9.81) = 28.3 '/° at 540 kts GS, or - as advertised - 57' of vertical offset for a 2° heading change per minute of time at 540 kts GS.
Kermit