# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**Re: Coriolis and gyros (second attempt)(typos corrected)**

**From:**Gary LaPook

**Date:**2009 Aug 24, 19:29 +0200

There is a problem with your analysis. Since the period of the pendulum is fixed by its length then it is necessarily true that as the amplitude of the swing diminishes during the day, due to air resistance, that its maximum velocity and its average velocity also slows down. Try this yourself with any pendulum and observe how slowly it moves near the end as it slows to a stop. The formula for coriolis force includes a term for velocity across the turning reference frame so that coriolis force and coriolis acceleration is proportional to this velocity over the ground. So if your analysis is correct then the rate of change of the azimuth of the pendulum's swing should vary throughout the day, changing at a more rapid rate in the morning and more slowly later in the day as the pendulum slows down. But the rate of change of azimuth is constant, 11.32 degrees per hour which disproves your analysis. Now looking at the case of the gyroscope's undergoing earth rate apparent precession. If this apparent precession is caused by coriolis due to the speed of the rotating flywheel moving in one direction at the point at the bottom and in the opposite direction at the top, (as you claim) then, without doing the diagram of the precessional forces (I leave that to you), it must also be true that gyroscopes spinning in opposite directions would also precess in opposite directions. One rotating clockwise would precess toward the east and one turning counterclockwise would precess toward the west yet all gyroscopes, no matter which way they are spinning, precess toward the east, again disproving your analysis. A further disproof of your analysis of earth rate precession of a gyroscope is due to that pesky term in the coriolis formula that makes the coriolis force proportional to velocity over the ground. If your analysis were correct then slowly turning gyroscopes would precess more slowly than rapidly spinning gyros yet they all show the same apparent precession due to the earth rate of 15.04 degrees per hour times the sine of the latitude. You have not addressed the movement of a gyrocompass at the equator where coriolis is zero since the sine of zero degrees of latitude is also zero, there's that pesky coriolis formula again. Also consider the earth rate apparent precession of a gyroscope at the north pole which changes at a rate of 15.04 degrees per hour since the sine of 90 degrees of latitude is 1. Yet a gyroscope located exactly at the pole is not moving at all (ignoring the earth's movement around its orbit) but is remaining at one fixed spot on the earth so it has no velocity across the ground so, again by the formula, there should be no coriolis available to cause the apparent precession. gl frankreed@HistoricalAtlas.com wrote: > "Coriolis is not involved since the Pantheon has not moved across the surface of the earth since its foundations were laid in 1758 so its ground speed is zero." > > LOL. Gary the pendulum bob is itself in motion, right? Its ground speed is most certainly NOT zero. Likewise in a gyro-compass, its individuaL mass elements are moving at very high speed. If they weren't moving, it wouldn't work. The Coriolis acceleration causes the precession in both cases --in the rotating frame of reference in which the Earth is fixed. > > -FER > > > > > > > --~--~---------~--~----~------------~-------~--~----~ NavList message boards: www.fer3.com/arc Or post by email to: NavList@fer3.com To unsubscribe, email NavList-unsubscribe@fer3.com -~----------~----~----~----~------~----~------~--~---