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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@huxtable.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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