Sun sights

Altitude and time, both exact

Take the Sun above about 15°, where refraction is steady; well east or west, its line runs near north–south and fixes longitude. Time it to the second: 4 seconds is 1′ of longitude.

Turn the watch into UT: remove its error, add the zone description (positive in west zones); past 2400 or below 0000 the Greenwich date and the almanac page change.

Hs to Ho: index error, dip, then the main correction.

Ho is Hs corrected for index error, dip and the main correction for your limb and season. In a seaway take several sights and average them, dropping any out of step.

GHA, declination and LHA

The daily page gives the Sun's GHA and Dec for each hour of UT. Add the increment for the minutes and seconds (the Sun moves 15° an hour) and correct Dec with d, checking the next hour for its trend; near an equinox its name can change.

LHA is the Sun's angle west of your meridian: GHA minus west longitude or plus east, with 360° added or taken off. Morning, the Sun east of you: LHA over 180°. Afternoon: under 180°.

Solving the PZX triangle

Pole, zenith and Sun make a triangle. You know two sides, 90° − Lat and 90° − Dec, and the angle between them at the pole, the LHA. Solving it gives 90° − Hc, the altitude seen from that position, and the azimuth.

Angle at P: the LHA. Angle at Z: the azimuth.

By calculator, sin Hc = sin Lat sin Dec + cos Lat cos Dec cos LHA, a contrary-name Dec negative, from any position: use the DR.

HO 249 tabulates whole degrees, so you work from an assumed position: the nearest whole degree of latitude, and a longitude within 30′ of the DR longitude that makes LHA whole (in west longitude the GHA's minutes, in east 60′ minus them). Enter the same- or contrary-name page with the whole degree of Dec, correct Hc with d. Both workings plot the same line.

From two altitudes to a line

The intercept is Ho − Hc, 1′ for 1 mile. Ho greater: you are nearer the Sun than the point you worked from, towards. Hc greater: away.

• Lay off the intercept from the AP or DR along Zn if towards, its reciprocal if away.
• Draw the position line there, at right angles to the azimuth.
• Measure miles on the latitude scale.

A nil intercept puts the line through the AP. A very long one is not wrong, but the line is only a short piece of a large circle: rework from a point on it. One line is not a fix; its point nearest the DR is your best position. Current matters only when a line is carried forward.

Sun, run, sun

The Sun gives a fix once its bearing has changed. Carry the earlier line forward by the run, course and distance made good, leeway allowed and legs added as vectors; it keeps its direction and meets the later line, or the noon latitude, at the fix.

The lines cut at the change of azimuth: wait until it has changed about 45°, and no longer than that: every hour adds run error. Add a known current to the run; an unknown one shows afterwards as the gap from DR to fix. In the tropics the azimuth swings so fast past noon that sights an hour apart cut well.

Around its quarters the Moon is up by day: Sun and Moon lines taken together cross with no run.

What one line tells you

A position line lies at right angles to the Sun's bearing: pick the moment to suit the question.

Along the reef: 14.0 M from the AP less 5.2 M towards leaves 8.8 M off.

It also crosses a depth contour where the bottom rises steeply, or a radar range, whose circle cuts it twice; the DR says which cut is yours.

A mile for a minute

Three sun lines from one day seldom meet in a point; the cocked hat comes mostly from the runs that carried the earlier lines. A constant error shifts every line the same way along its azimuth: you are inside the triangle only if the azimuths span more than 180°. Lines a mile the same way every day betray such an error.