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

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Re: The development of bubble sextants
From: Gary LaPook
Date: 2009 Aug 16, 03:12 +0200

```Douglas wrote, concerning coriolis acceleration:

"I have a theodolite made by British Aerospace with a North seeking gyro built
in which 'feels' the acceleration right enough to provide North to within a
few second of arc."

I have no knowledge about how his theodolite works but I wonder if it doesn't
work like a gyro compass which doesn't use coriolis to seek north. A gyro
compass seeks north while the common directional gyro in an airplane only
maintains its orientation in inertial space much like the Foucault Pendulum.
(I am in Paris now and saw the Foucault pendulum in the Pantheon the other
day, in the same place where he demonstrated it more than a hundred and fifty
years ago. They have a clock face on the floor under the swinging pendulum.
You look at the time displayed when you go into the Pantheon and then look
when you are leaving and you can see that the pendulum has changed its swing
to now indicate the current time. Since it is obvious that nobody reached out
and disturbed the swing of the pendulum it is clear to anybody that the earth
has turned under the pendulum. The plaque says it turns 11 degrees per hour
but doesn't point out that this is the sine of the latitude of Paris times
15.042 degrees per hour, the rotation of the earth in inertial space, so it
may leave people wondering, why not fifteen degrees per hour, 360 divided by
a twenty four hour day? I guess I am expecting too much out of tourists.)

But a gyro compass does seek north and it is interesting to see how this
works. Imagine you are at the equator and it is the equinox. You set up a
gyroscope that is gymboled so it is free to move in all directions. At
sunrise you point one end of the axis toward the sun, it is horizontal at
this point. (Let's call this the pointing end and the end of the axis toward
the observer, the observer's end. We will also ignore the change in
declination of the sun and the earth's  movement around it's orbit. The
gyroscope rotates clockwise as seen from the observer's end.) As the earth
rotates the sun moves higher in the sky and the pointing end of the gyroscope
follows it, pointing straight up at noon. Then the pointing end follows the
sun, pointing straight west and horizontal at sunset, straight down at
midnight and horizontally toward the east at the next sunrise. So far, no
north seeking tendency.

Now we modify the set up by adding a pendulous mass under the gyroscope
connected to the bearings holding the axis of the gyroscope. When the
pointing end of the axis attempts to rise to follow the sun it is resisted by
the weight being pulled down by gravity. This applies a torque to the
gyroscope like a push to the east at the top of the gyroscope and a pull to
the west at the bottom of the gyroscope. As a result, the gyroscope responds,
like all good gyroscopes, as though the forces were applied 90� later in the
rotation of the gyroscope resulting in a push toward the east at the south
end of the gyroscope and a pull toward the west at the north end of the
gyroscope. Continue this throughout the day and you end up with the axis of
the gyroscope aligned with the axis of the earth at which point the pendulous
weight swings parallel with the rotation of the gyroscope and no longer
applies any torques to the gyroscope. Of course a real gyrocompass is more
complicated with a power source for the gyroscope itself, dampening
mechanisms, and a take off system to display the gyro heading on repeaters.

gl

douglas.denny@btopenworld.com wrote:

> Dear Gary,
>
> Coriolis is a very real acceleration. It is not fictional at all.
>
> The sextant (and person ) is being carried through space in a curved motion
by the Earth itself, and the acceleration due to curved motion is real
enough, just the same as if you are in the big Millenium Ferris Wheel in
London, or in a fairground 'Skyboat' device whizzing around in circular
motion.
> Coriolis just happens to be a small quantity - though relevant in
calculation if you are in a jet moving at around 400 knots.
>
> I have a theodolite made by British Aerospace with a North seeking gyro
built in which 'feels' the acceleration right enough to provide North to
within a few second of arc.
>
> Coriolis can be allowed for because the motion of the Earth is 'constant' so
the parameters can be calculated for the direction of travel and Latitude,
the main components affecting the apparent local gravitational field due to
Coriolis.
>
> Douglas Denny.
> Chichester. England.
>
>
> >
>
>

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