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After a bit more thought, following my earlier posting in Navlist 3407, I've
conjectured that further improvents may be possible in azimuth tables.

My previous suggestion was to address the problem that Cos Dec Sin LHA
changes little, from column to column and row to row, in the bottom left
corner of the table, where Dec is small and LHA approaching 90, and the
tabulated  number (in Bennett's tables) nears 1000.

But a similar problem occurs towards the top right of the table, for high
Dec and small LHA, when the tabulated number is small, and changes little,
or not at all, between adjacent rows and columns.

We appear to be free to tabulate any function of Cos Dec Sin LHA that we
wish, as long as it's single-valued within our working range. In that case,
it may be possible to improve on my earlier suggestion of tabulating 11.11
arcsine( cos Dec Sin LHA), rather than simply 1000 (cos Dec Sin LHA) as
existing tables do.

Try tabulating instead, the nearest 3-digit integer to-

500 +5.5555 Arcsine(2 Cos Dec Sin LHA -1), to give a number in the range 0
to 999, as before.

(This assumes that the angle provided by the arcsine function is in degrees.
If in radians, the multiplier should be 1000/pi, or 318.3, instead of
5.5555)

That will force the tabulated numbers to change more rapidly at the extreme
corners of the table, at the expense of a slightly slower change near its
centre, which doesn't matter.

We would now be solving the equation-

500 + 5.5555 Arcsine(2 Cos Alt Sin Az -1) = 500 + 5.5555 Arcsine (2 Cos Dec
Sin LHA -1),

which is self-evidently true if Cos Alt Sin Az = Cos Dec Sin LHA.

However, the more serious problems that are inevitably associated with
deriving azimuth using altitude, especially when quantised in coarse steps,
remain unaffected.

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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