NavList:
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 29, 01:58 -0500
From: Frank Reed
Date: 2008 Jan 29, 01:58 -0500
George, you wrote: "Nevertheless, isn't it the case that there is effectively zero long-term drift in the orientation sensing of these devices; quite different from the behaviour of their mechanical predecessors?" No, they drift for many little reasons. But they're a lot cheaper than the fine mechanical gyros that they have mostly replaced. Also, they're getting better all the time. So in ten or twenty years, it may well be said that "for all practical purposes, they have no drift". Nicolas sent me a brief message saying he's gotten busy with work so he can't get back into this discussion right now. But he did send me some docs on the FOG system he uses so I'll see if there's anything of interest in those. It occurs to me that it's worth mentioning that there are two fairly distinct ways of doing inertial navigation. There's the "pure" approach where we maintain three fixed directions in space. It's the sort of thing that's well-suited to a spacecraft. Then there's a "gravity" approach where the system tilts the platform to keep it level based on the calculated current position. If we travel ten nautical miles along the equator, the system turns the platform ten minutes of arc in the same direction (the "platform" can be a real table in gimbals or it can be a "virtual platform" in software). This has the advantage that a fixed leveling error leads to oscillatory errors in position: errors obey a harmonic equation (at the 84-minute local tidal period** at the surface of the Earth), but to do this it sacrifices accuracy in the vertical direction: errors propagate anti-harmonically. So altitude above (or below) sea level has to be determined (or constrained) in some other way. And back to the point, can we use the determined level/vertical for celestial navigation as an independent check on position? The answer again is 'no', or at best 'not really'. The error in the vertical is the same as the error in the position. If my calculated position is oscillating back and forth with an amplitude of two nautical miles, then my calculated vertical is oscillating back and forth with an amplitude of two minutes of arc. But the stars CAN be used as a compass, drastically reducing any error that results from gyro drift. They calculate where the stars should be, based on the gyros, then they automatically point the star tracker towards that location and do a little spiral search pattern for the star (with a fixed star tracker, this is all done in software). If it's thirty seconds of arc off-center, then the platform is mis-aligned by that amount. So you feed in that error and re-do the calculation. That's what these "stellar-inertial" systems apparently do (I say apparently because I don't really know what they do --some of them, after all, are highly classified). On the other hand, the FOG devices that are not serving as inertial navigation systems, like the one Nicolas has described, might still be used for a celestial navigation vertical. That part I'm still thinking about... It all depends on how they do it. -FER **Above I mentioned the tidal period. So there's no confusion, I'm not talking about ocean tides due to the variation in the gravitational forces of the Sun and the Moon over the surface of the Earth, but rather the local "tidal" acceleration in the vicinity of any point on Earth due to the variation in the gravitational force of the Earth itself. For an example, imagine an air table with a disc on it ("air hockey" with a floating puck). If I level the table perfectly at its center, and if the table is perfectly flat, then the floating disc, if released near one edge, will "fall" towards the center because that's the only place where the gravity vector is exactly perpendicular to the table --everywhere else, the vector is slightly tilted, pointing towards the center of the Earth, so a small component of the gravity vector is pointing towards the center of the table. The amount is directly proportional to the distance from the center of the table. The disc will execute simple harmonic motion [natural frequency omega=sqrt(g/R)=sqrt(GM/R^3)], as if it's attached to the center of the table by a perfect spring, gliding back and forth across the table with a period of 84 minutes (ignoring air resistance). Give it a slight sideways motion and the disc will travel in a circular or elliptical path around the center of the table with that same 84 minute period (no matter how big the circle). That's the "tidal field" of the Earth. --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to NavList@fer3.com To , send email to NavList-@fer3.com -~----------~----~----~----~------~----~------~--~---