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    Re: FOG's, was Re: automatic celestial navigation
    From: Frank Reed
    Date: 2008 Jan 26, 21:03 -0500

    George, you wrote:
    "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
    Yes, thanks. I meant SHA and typed GHA. In a spacecraft (or in a fundamental
    theoretical case), you want to keep fixed directions in inertial space, so
    fixed SHA is what you're looking for. In practice, it's normal for
    applications near the Earth's surface to rotate the platform at the sidereal
    rate. In older systems based on real gyros mounted on a physical platform
    mounted in gimbals, this was done with something like a telescope's clock
    drive turning at the sidereal rate. In modern "strapdown" inertial systems,
    the "platform" is virtual so the sidereal rate rotation is done in software.
    And you wrote:
    "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
    Yeah, from my perspective, thinking purely in terms of the physics that
    "makes them go", FOGs and RLGs are variations on a theme. They are "Sagnac
    effect" devices. I have been told that FOGs are significantly less expensive
    which is why people in the industry saw them as a major improvement over
    RLGs when they began appearing about twenty years ago. The price of an
    isolated component can be difficult to quantify, but does anyone in the
    group have any real idea if this price difference is real?
    You wrote:
    "However, I suggest he has no call to apologise for doing so." [discussing
    something outside the bounds of traditional navigation]
    It was a pre-emptive strike. 
    And you wrote:
    "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."
    But those darn photons are bosons. They "like" being in the same state, and
    they tend to produce standing waves when the rotation rate is slow.
    Apparently this is a bigger problem with RLGs than FOGs. RLGs in real
    navigation systems are equipped with little vibrating devices to keep them
    lively. These tend to prevent the counter-rotating beams from locking into
    the same state.
    And you wrote:
    "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."
    Apart from the sidereal rate rotation that I mentioned above, there's a lot
    of this that can handled when the system boots up. For example, in some
    aircraft INS systems, they can calculate a fairly good latitude value and
    true north direction by watching the rate of rotation of the vertical with
    respect to directions in inertial space. The system "observes" the motion of
    the vertical (maximum acceleration direction for a motionless vehicle) for
    five minutes relative to the spatially fixed axes.
    Most of my information is anecdotal so some of it may be rumor. I've never
    touched an INS or seen one outside of a museum. I understand more than a
    little about the theoretical aspects, but only "a little more than a
    Here's a fun link regarding a home-built inertial navigation system:
    http://www.tmoser.ch/typo3/11.0.html . The test results are interesting.
    After one minute of motionless operation, their homebrew INS had an error in
    the vertical of 5.0 degrees growing steadily and 40 meters in position
    growing rapidly. These are related, of course. If your vertical is wrong,
    then a horizontal accelerometer will think that some portion of the local
    gravity acceleration is actually vehicle acceleration. A small error, theta,
    in the vertical leads to some horizontal acceleration a=g*sin(theta) which
    then grows as (1/2)*a*t^2. But I suspect these guys could have done better
    with more sophisticated software. There are ways of taming these errors.
    I'll close this message with a connection taking us back to the 19th
    century. Here's a letter to the editor of "Nature" published in 1959
    referencing another letter published way back in 1873:
    Department of Astronomy and Geophysics, Science Museum, London, S.W.7. Oct.
    THE recent voyage of the submarine Nautilus below the polar ice has caused
    interest to be focused on the subject of 'inertial navigation'. This recalls
    to mind a communication which was published in Nature (7, 483; 1873). A
    correspondent, Joseph John Murphy of Co. Antrim, discounted the idea that
    "the instinct of direction in animals is of the same kind as the faculty by
    which men find their way" and suggested instead a mechanical analogy
    basically identical with 'inertial navigation', namely: "If a ball is freely
    suspended from the roof of a railway carriage it will receive a shock
    sufficient to move it, when the carriage is set in motion: and the magnitude
    and direction of the shock ... will depend on the magnitude and direction of
    the force with which the carriage begins to move ... " " ... every change in
    ... the motion of the carriage ... will give a shock of corresponding
    magnitude and direction to the ball. Now, it is conceivably quite possible,
    though such delicacy of mechanism is not to be hoped for [my italics,
    D. C.], that a machine should be constructed ... for registering the
    magnitude and direction of all these shocks, with the time at which each
    occurred ... from these data the position of the carriage ... might be
    calculated at any moment." "
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