Hs to Ho, worked: the noon Sun
1The lesson in plain words
A worked lower-limb Sun sight, corrected step by step from 47°31.4′ on the sextant to a true altitude of 47°45.8′.
The data
26 November 2026, noon sight at DR 21°10′N 027°45′W; the noon-sight unit uses this sight. Sun lower limb, Hs 47°31.4′. Index error 1.8′ off the arc. Height of eye 2.5 m. Daily page: SD 16.2′. Standard temperature and pressure.
Hs to Ha
Index correction: off the arc, so +1.8′. Dip: 1.76 × √2.5 = 2.78′, so −2.8′. Ha = 47°31.4′ + 1.8′ − 2.8′ = 47°30.4′.
Ha to Ho
Refraction at 47°30′: −0.9′. Semi-diameter, lower limb: +16.2′. Parallax: +0.1′. Total +15.4′. Ho = 47°30.4′ + 15.4′ = 47°45.8′. The almanac's combined October–March lower-limb table, built on a mean SD, gives the same within 0.1′.
Check it
At this altitude and height of eye, Ho should exceed Hs if the index correction is small: +SD outweighs dip and refraction. A lower result is a reason to check the signs. For the upper limb at the same Ha, the main correction would be −16.2′ − 0.9′ + 0.1′ = −17.0′.
What remains
The arithmetic is to 0.1′, but sights from a yacht are rarely better than about 1′: the horizon is wavy, your height of eye changes and refraction near the sea can be abnormal. Each 1′ of altitude error moves the position line 1 M.
2Key data
- Hs
- 47°31.4′, Sun lower limb, 26 Nov 2026
- Index correction and dip
- +1.8′ (off the arc), −2.8′ (2.5 m)
- Ha
- 47°30.4′
- Main correction
- −0.9′ refraction + 16.2′ SD + 0.1′ parallax = +15.4′
- Ho
- 47°45.8′
- Spanish terms
- Altura aparente, altura verdadera, corrección total
3Key points
- 1
Hs 47°31.4′ + 1.8′ − 2.8′ = Ha 47°30.4′.
- 2
Ha + 15.4′ = Ho 47°45.8′ for the lower limb.
- 3
At this altitude and height of eye, with a small index correction, lower-limb Sun Ho exceeds Hs.
- 4
Upper limb at the same altitude: about −17.0′.
- 5
Expect about 1′ accuracy from a yacht: 1′ = 1 M.
4Frequent mistakes
Wrong: Enter the almanac correction table with Hs.
Right: Enter it with Ha, after index correction and dip.
Wrong: Every 0.1′ in the result is real accuracy.
Right: The working keeps 0.1′, but a yacht's sights are usually good to about 1′.
5Practice case & exam keys
At effectively the same time and place as your lower-limb sight, a crew member records the upper limb at Hs 48°06.8′, with the same IE and eye height. Your lower-limb Ho is 47°45.8′. Calculate their Ho. Is the pair consistent?
Show the answer
Ha = 48°06.8′ + 1.8′ − 2.8′ = 48°05.8′; subtracting 17.0′ gives Ho 47°48.8′. That is 3′ above your result, larger than the expected agreement of about 1–2′. Investigate the limb, reading, contact and correction signs; repeat the sights if possible.
Exam keys
- Hs + IC − dip = Ha; enter the tables with Ha.
- Sun LL main correction = SD − refraction + parallax (here +15.4′).
- Worked: 47°31.4′ → 47°30.4′ → 47°45.8′.
- UL main correction is about −(SD + refraction).
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