A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: FOG's, was Re: automatic celestial navigation
From: Frank Reed
Date: 2008 Jan 26, 21:03 -0500
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 space." 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 expensive." 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 little". 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: "D. CHILTON Department of Astronomy and Geophysics, Science Museum, London, S.W.7. Oct. 9. 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." " -FER --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to NavList@googlegroups.com To unsubscribe, send email to NavListemail@example.com -~----------~----~----~----~------~----~------~--~---