# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**Re: Still on LOP's**

**From:**Geoffrey Kolbe

**Date:**2002 Apr 22, 08:16 +0100

> >But that would still leave us with the problem of what happens when the >cocked hat chances to be very small or very large. Can you explain how >the probability remains at 0.25? > > Trevor. Thankyou for your posting in which you find some accord with my answer to the question, "How often will my actual position be enclosed by the cocked hat resulting from the plotted bearings on three landmarks?" As you point out, there are other ways in which this question can put and which do not actually mean the same think. However, from a practical navigators point of view, it is worth knowing that the answer to THIS question is one time in four. Coming to your question above where you are concerned that even when the cocked hat is very small, how can it be that the probability remains at 0.25? If I may say so, I think that this question is the result of trying to put too much statistical significance on one cocked hat. If you did three more measurements on the same landmarks and drew another cocked hat, the size of the cocked hat would not be the same. When plotted on the chart the cocked hat might not even be in the same place, as I have shown. If the bearings are repeated many times so that a series of cocked hats could be drawn on the chart, then we could make some statistical conclusions. The first is that the actual position would be somewhere in the center of the distribution of cocked hats. The second is that the level of confidence with which we know the centre of the distribution (the actual position) will increase as the square root of the number of cocked hats. The third is some cocked hats will be large, some small. But the size of distribution of cocked hats will give us some information on the accuracy of our bearing measurements. For these cocked hats to be "independent" so that we may make arrive at the statistical conclusions outlined above, the measurements made for one cocked hat cannot be used for any other cocked hat. One more point. The cocked hats for the two classes of cocked hat which will always enclose the actual position, will tend to be larger than the cocked hats for the other six classes which can never enclose the actual position. Small cocked hats should be treated with suspicion! Geoffrey Kolbe.