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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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