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Gary LaPook wrote-
|
| Well, the ultimate limit is the 1/8th wavelength of light "Raleigh
| limit" since anything more perfect is not detectable due to the wave
| character of light. This is the standard for telescope mirrors. But,
| since you will not be trying see the moons of Saturn when doing celnav,
| the artificial horizon doesn't need to be that perfect. Since the angle
| of incidence equals the angle or reflection any error in the shape of
| the mirror is doubled in the reflected ray. So, the answer to your
| question is that it must be accurate to 1/2 the accuracy limit you are
| trying to achieve. If you only want sight accurate to one minute of arc
| then the mirror must be accurate to 1/2 of a minute. If working for one
| tenth of a minute accuracy then the mirror must be accurate to one
| twentieth of a minute.
|
| gl
|
| pls wrote:
| > Does anyone know how accurate (i.e., level) the surface figure of a
| > sheet of black glass must be to serve as an artificial horizon?  In
| > particular I am trying to determine the point beyond which additional
| > accuracy is irrelevant in terms of the result, given the other
| > variables in a sighting with a hand-held sextant.
======================

I wonder whether Gary has that right, or if he is a factor of 2 out?

Yes, if the mirror angle is half a minute out, then the angle between the 
incident and reflected light becomes a whole minute out. But then, to arrive 
at a measured altitude, you have to divide that resulting angle by two. So I 
suggest that, if there were no other sources of error, the accuracy in 
measuring altitude will be no better than the accuracy achieved in levelling 
the mirror, and there is no such factor-of-two to apply.

Maybe "pls" is concentrating on the wrong question. "Surface figure" refers 
to flatness, in a plane, not level-ness. The difficult bit is not getting 
the surface figure of the glass right; any decent glass flat will be good 
enough. It's getting a sufficiently rigid mounting, that can be finely 
adjusted, and tried with sufficiently sensitive levels, so that it can be 
got level, and will stay level, throughout a measurement. It calls for a 
sensitive spirit-level that's sufficiently light in weight so that its 
weight shifting on the glass causes negligible deflection. It requires firm 
ground so that no observable shift occurs as the observer moves his weight 
around.

If these requirements can be met (and they can be bypassed, in the right 
conditions, by using a mercury reflecting surface) then altitudes can be 
measured with much greater accuracy than is possible at sea using a natural 
horizon. Besides the factor of two reduction in instrument errors caused by 
the doubling of the measured angle, and the firm footing on land compared 
with a vessel, all the problems inherent in the natural horizon disappear, 
particularly the unpredictable refractive component of the dip. As long as 
the observed body, preferably a star, isn't too low down (but it can't be 
above 60�, of course), then I would expect altitudes to be measurable, with 
care, to around 0.3 arc-minutes, or so, as long as the glass plate can be 
levelled with corresponding accuracy. And that becomes the difficult bit.

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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