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    Re: FOG's, was Re: automatic celestial navigation
    From: George Huxtable
    Date: 2008 Jan 26, 15:49 -0000

    For new readers-
    
    Frank Reed and Nicolas de Hilster have been indulging in a thoughtful
    dialogue about inertial navigation systems. These incorporate some sort of
    3-axis gyro or "pseudo-gyro", for determining directions in space, and a
    three-axis accelerometer, for determining accelerations.
    
    These pseudo-gyros no longer involve a spinning element, but instead, send
    light around a closed path, clockwise and anticlockwise, and by measuring
    any minute difference in the time that those two beams take to go round the
    loop, discover whether there has been any rotation of the loop. They are
    still called "gyros", because they fulfil the same function as the
    traditional gyro, of detecting rotation, but there is nothing gyroscopic
    about them, any more. FOG stands for fibre-optic gyro, and is technically
    somewhat different from the other type, the ring laser gyro, but for our
    purposes we can consider them to be effectively the same thing. All are
    extremely precise, and VERY expensive.
    
    Back in Navlist 4411, Frank Reed wrote-
    
    "I don't want to annoy anyone by discussing something that is clearly not
    traditional navigation, but since it's strictly at the level of relating it
    theoretically back to the principles of celestial navigation, I hope no one
    minds for now. "
    
    However, I suggest he has no call to apologise for doing so. It is indeed
    highly relevant to many of our discussions. To me (at least) it's of great
    interest, though I have no detailed knowledge of the subject.
    
    In [4449], Frank wrote-
    
    "The principle underlying the FOG (and also the ring laser) is simple
    enough, and it lets a set of three preserve exact orientation in
    three-dimensional space. So, for example, we could arrange to point one
    fiber optic gyro towards the North Celestial Pole, another towards GHA=0,
    Dec=0, and a third towards GHA=90 degrees, Dec=0. And now no matter how much
    we bounce around, the system will always "remember" where those directions
    are."
    
    But I wonder whether he has got that right. The three directions he has
    specified are not fixed in space, but rotate with the Earth. Three axes,
    fixed in space could be- Toward the North celestial pole, with Dec = 90:
    toward Aries (in the Earth's equatorial plane), with Dec = 0,
    Right-Ascension = 0: and (also in that equatorial plane) 90 degrees from
    Aries, with Dec = 0, R.A. = 90. These axes remain (nearly) unchanging, in
    space.
    
    Although inertial navigation systems always show some drift, as a result of
    having to integrate (twice) the accelerations, which always have some
    zero-error, I doubt (from my inexpert perspective) whether any of that drift
    derives from the pseudo-gyros, which sense the orientation. They are looking
    at the position of interference-fringes of light, which shift as the device
    rotates, but which ought to stay rock-solid, in the absence of any such
    rotation in space. However, if they are strapped-down to a platform that is
    horizontal to the Earth's surface, then they will partake in the Earth's
    rotation, in a way which depends on latitude, and if that platform moves
    about on the Earth, the resulting shifts in the "horizontal" will also
    affect them.
    
    It's that participation in the Earth's rotation that Frank seems to have
    omitted from his argument, but needs to be considered in any attempt to
    understand how such systems work. However, I am no more than feeling my way
    toward such an understanding, and remain a long way from it as yet. May
    these arguments continue...
    
    George.
    
    contact George Huxtable at george---.u-net.com
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    
    
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