Worked: compass error by azimuth, 4 December 2026
1The lesson in plain words
Note the exact UT of the bearing, work out LHA, then the Sun's true azimuth by formula or tables. Worked on an Atlantic crossing.
The method
Steady the boat on the heading you want to check. Take the body's compass bearing and note the UT to the second, the heading and the log. From the almanac, find GHA and Dec for that UT; then LHA from your DR longitude. Compute the true azimuth by formula or tables.
The formula
tan Z = abs(sin LHA) ÷ (cos Lat × tan Dec − sin Lat × cos LHA). Here abs means positive magnitude. Use N-positive, S-negative latitude and declination. Z is 0°–180° from north; a negative denominator puts it above 90°. LHA under 180°: Zn = 360° − Z; over 180°: Zn = Z. HO 229 and Norie's ABC tables also give azimuth; follow their printed naming rules.
Worked: the data
4 December 2026, late afternoon, DR 15°56′N 041°32′W. Heading 262°C. At 1908 UT the Sun bears 255.6°C. Almanac for 1908 UT: GHA 109°25.5′; Dec S22°18.7′. LHA = 109°25.5′ − 41°32′ = 067°53.5′.
Worked: the answer
The numerator is 0.9265 and the denominator −0.4979, so tan Z = −1.861. Inverse tan gives −61.7°. Positive numerator and negative denominator select quadrant II: Z = 118.3°. LHA under 180° puts the Sun west: Zn = 360° − 118.3° = 241.7°T. Error = 241.7 − 255.6 = −13.9°: 13.9°W.
Deviation
The plotter's World Magnetic Model (WMM2025) gives a variation of 14.8°W there. Deviation = error − variation = −13.9 − (−14.8) = +0.9°: 0.9°E on heading 262°C.
Timing tolerance
Here the Sun's azimuth changes about 0.1° a minute, so a timing error of a minute or two matters little. Near noon or with a high Sun it changes much faster; time those bearings carefully, or wait for a lower Sun.
2Step by step
Compass error by azimuth
- 1
Steady on the heading to check; note heading and log.
Deviation belongs to the heading, not to the bearing.
- 2
Take the body's compass bearing; note the UT to the second.
The true azimuth depends on the time through GHA and LHA.
- 3
Find GHA and Dec for that UT; LHA from your DR longitude.
These, with latitude, fix the body's direction.
- 4
Compute Z by formula or tables, and name it as Zn.
This is the true bearing at the moment of your compass bearing.
- 5
Error = Zn − compass bearing; name it E (+) or W (−).
This is the total correction: variation plus deviation.
- 6
Deviation = error − variation; log it against the heading.
Variation comes from the chart or the WMM; the rest is the boat's.
3Key data
- Azimuth formula
- tan Z = abs(sin LHA) ÷ (cos Lat tan Dec − sin Lat cos LHA)
- Worked inputs
- 1908 UT, 15°56′N 041°32′W, LHA 067°53.5′, Dec S22°18.7′
- Worked true azimuth
- Z 118.3°, body west: Zn = 241.7°T
- Worked error
- 241.7 − 255.6 = −13.9°: 13.9°W
- Worked deviation
- −13.9 − (−14.8) = 0.9°E on 262°C
4Key points
- 1
Time the compass bearing to the second; find GHA, Dec and LHA for that UT.
- 2
Formula Z is from north; with tables, use their printed naming rules.
- 3
Error = Zn − compass; deviation = error − variation, for that heading.
- 4
Prefer a low body: easier to bear, and its azimuth changes slowly.
5Frequent mistakes
Wrong: Record the deviation against the Sun's bearing, 255.6°C.
Right: Deviation depends on the boat's heading. Record it against the heading steered, here 262°C.
Wrong: Take Z from the formula as the true azimuth.
Right: For north-referenced Z, LHA under 180° means Zn = 360° − Z, here 241.7°T. LHA over 180° means Zn = Z.
Wrong: Use the variation printed on an old chart's rose without updating it.
Right: Variation changes year by year. Update the rose to this year, or use the current WMM in the plotter.
6Practice case & exam keys
Same day and position. A crew member bears the Sun at 255.6°C but logs the time as 1900 instead of 1908 UT. They work out Zn 241.0°T and a deviation of 0.2°E. How much does the timing slip matter here, and what do you do?
Show the answer
About 0.7°: the Sun's azimuth changes nearly 0.1° a minute here, so eight minutes moves Zn from 241.7° to 241.0°. The deviation comes out 0.2°E instead of 0.9°E. Rework it for 1908 UT. Small, but a check is only as good as its time; always note the UT at the moment of the bearing.
Exam keys
- Azimuth method: compass bearing + exact UT → GHA, Dec, LHA → Zn.
- tan Z = abs(sin LHA) ÷ (cos L tan d − sin L cos LHA). Formula Z is from north; tables have their own naming rules.
- Worked 4 Dec 2026: Zn 241.7°T, compass 255.6°C → 13.9°W; variation 14.8°W → deviation 0.9°E.
- Deviation is recorded against the heading steered.
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