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Bill wrote:

> In the worst case scenario, what would be the difference between the
> averaged Ho and an Ho from from an observation taken at the average time
> used?

I mention the worst case scenario just for fun: If the sun goes through the zenith
and you average the altitudes 2 min before that and 2 min after, your error is 30',
corresponding to 30 nm position error. The practical value of such mind games is
that they help visualizing the nature of the problem, and thereby demonstrate what
to watch out for and how to avoid the problem in actual practice.

The following table shows the maximum difference near meridian transit between the
arithmetic mean of two sun altitudes separated by n minutes, and the actual altitude
at half time:

Alt                 4m             5m             6m
60 deg         0'14"          0'21"          0'31"
75 deg         0'30"          0'46"          1'06"
80 deg         0'45"          1'10"          1'40"
85 deg         1'30"          2'20"          3'21"

You see that in most 'normal' situations there is not much of an error, but it
becomes worse RAPIDLY with increasing altitude as well as with increasing time span.

Most navigators will happily live with a position error of 3 nm as indicated in the
bottom right corner. But remember that all this averaging is done in order to
improve the accuracy! This is where a careful cost/benefit analysis is called for.
There is no point in removing the last decimal of random error if you introduce in
its place a systematic error of the same order of  magnitude.

The Power Squadron (and other instructors) discourage observation of high altitudes
above 75 deg on account of their difficulty. But they admit that they can sometimes
not be avoided. The unwary navigator might be tempted to average them more than
others to compensate for this difficulty. This might be counterproductive. But if
fitted properly (e.g. parabolically), it may help. The safest approach, though, is
to use the N.A. procedure.

Herbert Prinz

   

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