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A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: That darned old cocked hat
From: Peter Fogg
Date: 2010 Dec 11, 09:49 +1100
From: Peter Fogg
Date: 2010 Dec 11, 09:49 +1100
Geoffrey Kolbe wrote:
For practical purposes a corrected compass bearing is sufficiently accurate, I've found.
My recent blunder which George so kindly pointed out may have its uses, as it shows that even with an error of 10-minutes of arc of slope, the incorrect slope still functioned reasonably well.
Its always possible that in some "special circumstances" a generally good procedure will show flaws. The logical error would be in assuming that the method is therefore invalid. That would be simply silly. "Special circumstances" may call for special procedures - such as, in this case, iteration.
Once again, the estimated position would have to be wrong to such an extent that probably precludes it from most practical cases. How likely is it that the estimated position would be that wrong? This case would have to be an extreme exception to the general rule, which is that the estimated position is reasonably correct.
How is "in general" suddenly derived from "special circumstances"? No, this does not appear logical at all.
Peter Fogg replied:
Geoffrey Kolbe wrote:
- The calculated slope is for your estimated position. Suppose you are not at, or anywhere close to the estimated position - the calculated slope will not be what it should be for your actual position. Is that not correct Peter?
Well Peter, there is no direct way of measuring azimuth using a sextant,
The calculated slope is derived from the latitude of observation and azimuth of the body being observed. So if you assume you are at one latitude but are instead a very long way away then I guess that your calculated slope, in that case, could be incorrect. Is that helpful, Geoffrey?
For practical purposes a corrected compass bearing is sufficiently accurate, I've found.
so the slope may be in error because of an error in longitude.
My recent blunder which George so kindly pointed out may have its uses, as it shows that even with an error of 10-minutes of arc of slope, the incorrect slope still functioned reasonably well.
Consider the case of observing bodies high in the sky from equatorial latitudes. For bodies towards the North or South, the slope will vary with time (and so longitude) quite quickly. In such circumstances, one might even determine the error in longitude by the difference in slopes between the calculated slope from the estimated position, and the least squares fit to the data.
Given that:
1) In these special circumstances the least squares fit is obviously going to be the best fit.
Its always possible that in some "special circumstances" a generally good procedure will show flaws. The logical error would be in assuming that the method is therefore invalid. That would be simply silly. "Special circumstances" may call for special procedures - such as, in this case, iteration.
2) The fact that if the estimated position is not the actual position, it follows that the calculate slope from the estimated position cannot be the "best" fit.
Once again, the estimated position would have to be wrong to such an extent that probably precludes it from most practical cases. How likely is it that the estimated position would be that wrong? This case would have to be an extreme exception to the general rule, which is that the estimated position is reasonably correct.
It would seem that in general it is better to use a least squares fit rather the calculated slope from the estimated position. Is that logical?
How is "in general" suddenly derived from "special circumstances"? No, this does not appear logical at all.
