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Greg Rudzinsli wrote, about amplitudes-

Sent: Thursday, June 03, 2010 1:53 AM
Subject: [NavList] Re: Amplitudes


George,

I just did a work up for todays sunset amplitude/azimuth using my Palm to 
figure the Sun's lower limb altitude above the horizon for a few different 
heights of eye to get an Hc of zero at a Latitude of 34�10'N Longitude 
119�14'W.  3 June 2010 at UT 02:59:36  Declination 22�17.3' N

H.E.           Sun Altitude L.L. (moa)
100ft          25.2'
  50ft          22.4'
    6ft          17.9'
    0ft          15.5'

Azimuth 297.3� by program (Hc zero)
                 297.3� by amplitude formula INV SIN(SIN DEC/COS LAT)
                 297.4� by program for lower limb 15.5' above horizon at 
100ft height of eye
                 297.7� by program for lower limb on the horizon at 100ft 
height of eye

No corrections for temperature or pressure.

There seems to be only a few tenths of a degree difference.

============================

Response from George-

Yes, "only a few tenths of a degree difference", is just as one would 
expect, when allowing for the effect of dip. And for most of us who use 
magnetic compasses on small boats, which under the best conditions are not 
dependable to better than a degree or so, such corrections are unimportant, 
in most circumstances.

But Jeremy, and Byron, are both discussing using an amplitude to assess 
gyro compass error, which is, on a big vessel, presumably readable to quite 
a small fraction of a degree. So making the correct allowance for dip might 
indeed be important. I would be interested to learn, from Jeremy and Byron 
both, what numerical precision they expect to place on an azimuth 
observation, and on an amplitude observation (which is only a special case 
of an azimuth in which the true altitude is taken to be zero).

And such observations have been historically important in mapping magnetic 
variation, using accurate compasses designed for that, for which purpose 
those "few tenths of a degree difference" error would be unwelcome.

Byron's posting raises some further questions. He writes- "Navy Ships at 
sea must determine gyro error every day". I am interested in the "must" 
aspect, if the Sun is clouded at sunrise/sunset, as will often be the case. 
Is a comparison of the gyro with the magnetic compass then acceptable 
instead?

And Byron writes- "The lower limb is about 16’ high the eye can estimate 
well enough because the sun is going an away or toward you changing very 
slowly while in low latitudes. ". I presume here that Byron is referring to 
the fact that in the tropics the Sun is travelling near vertically near 
sunrise and sunset, so the resulting errors in its direction, caused by an 
improper estimate of height, are small. But the US Navy expects to operate 
over more of the World than the tropics, and at high latitudes the Sun can 
be rising or setting at an angle that's much closer to the horizontal. As a 
result, an arror in assessed altitude will give rise to a much greater 
error in azimuth. How well does Byron's rule-of-thumb hold up in that case?

I am rather surprised that Byron attaches such great confidence to an 
amplitude. Can he give us a notion of what variation he expects to find in 
the apparent altitude of the Sun's lower limb as a result of unusual 
low-level refraction, that differs from the predicted value? In my time, 
I've seen many distorted Sun-discs, at rising and setting, which would lead 
me to doubt whether the refraction itself was following the standard 
predictions.

George.

contact George Huxtable, at  george@hux.me.uk
or at +44 1865 820222 (from UK, 01865 820222)
or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK. 

   

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