It is convenient to practice with sextant in the back yard, but there is rarely a real horizon available.

We can however pick any horizontal line - such as a fence, or neighboring roof-top to use as a substitute.

Obviously this introduces a considerable error, but we can use a noon sight at a known latitude to calculate that error - which should be constant provided you stand in the same place each time.

Normally we are looking for our latitude. From the Nautical Almanac (NA) we look up the time of meridian passage at Greenwich, and adjust that for our longitude to find the GMT of meridian passage at our location. We then lookup the Sun's declination at that time.

We measure the Sun's altitude with the sextant (Hs), apply the corrections for index error (IE) and height of eye (Dip) to get an apparent altitude (Ha) which is then used to find a correction for the Sun to give an observed altitude (Ho). Latitude is normally obtained using a simple formula involving Declination and Zd (which is 90 - Ho):

Lat = Zd - Dec Sun in opposite hemisphere Lat = Zd + Dec Sun in same hemisphere closer to equator Lat = Dec - Zd Sun in same hemisphere further from equator

At local apparent noon, the sun is at its highest in the sky and its declination remains unchanged for a few minutes. By taking successive measurements starting a few minutes before noon we can determine the correct altitude.

Since we know our Latitude we can solve the same equations to find Ho,
and from that we can subtract the normal main correction for the Sun
to get an expected Ha, and we can use the difference between that and
Hs to calculate the correction for using the chosen *horizon*.

Given:

Date: 2019 11 29 Position: 37 21.6 N, 122 2.8 W

we calculate local meridian passage and declination:

Mer pass from NA: 11 48 00 adjust for longitude: 8 08 08 GMT: 19 56 08 Dec: 21 31.5 S

since we know our latitude we can calculate Ha:

Zd = Lat + Dec = 58 53.1 Ho = 90 - Zd = 31 6.9

now for an Ha of about 30-32 degrees the main correction for the Sun (LL) is 14.7:

Ha = 31 6.9 - 14.7 = 30 52.2

We can then go measure Hs and compare. On the above date we got 29 27.4:

fence correction = Ha - Hs = 30 52.2 - 29 27.4 = 1 24.8

we now have a figure that we can apply to measurements taken at other times.

Author: | sjg@crufty.net /* imagine something very witty here */ |
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