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Celestial Navigation

A ship's position read from the sky

Date
c. 1460
Era
Renaissance
Rebuild stage
IV Science & industry
Difficulty

Plate

Legend
  1. 1Sun
  2. 2Sea horizon
  3. 3Index mirror
  4. 4Horizon mirror, half silvered
  5. 5Sighting telescope
  6. 6Graduated arc
  7. 7Marine chronometer

Anatomy

0102030405060708090100110120α2α
Sunlight, reflected by the index mirror and then the horizon mirrorDirect line of sight to the horizon, through the clear half of the horizon mirrorα, the arm's turn from 0; 2α, the angle the arc readsThe sextant is seen square to its frame, so every angle in this plane is drawn true. Sunlight strikes the index mirror, which turns with the index arm about the pivot, passes the two shade glasses swung in to cut its glare, and reaches the horizon mirror. That mirror is silvered on its half nearer the frame and clear on the outer half: the silvered half sends the Sun's image into the telescope while the horizon is seen straight through the clear half, so the two appear side by side in the eyepiece (inset). The mirrors are parallel when the arc reads 0°. Turn the arm by α and the ray leaving the horizon mirror turns by 2α, so each half degree of arc is engraved as a degree, and an arc of one sixth of a circle, 152 mm in radius, reads up to 120°. The navigator brings the Sun's lower edge down onto the horizon and reads the arc. The figure works the plate's example: local noon on 11 April, declination +8.0°, eye 2 m above the sea. The arc reads 52.2°; adding half the Sun's diameter (16′) and taking off the dip of the horizon (2.5′) and refraction (0.8′) puts the Sun's centre at 52.4°, and 90 − 52.4 + 8.0 = 45.6° N. Never sight the Sun without the shade glasses swung in.

Celestial navigation finds a ship's position from the height of the Sun, Moon and stars above the horizon. Latitude comes from the Pole Star, which Portuguese pilots measured with a quadrant around 1460, or from the noon Sun; longitude needs the time at a home meridian, which chronometers and lunar tables supplied from the 1760s.

What it is

Out of sight of land, compass and estimated speed hold a course, but errors pile up. The sky gives a check, because the height of a star or of the Sun above the horizon depends on where the observer stands.

Latitude, the distance north or south of the equator, came first: Indian Ocean pilots took it from the Pole Star with fingers or a kamal, and Europeans brought quadrants and astrolabes to sea in the fifteenth century. Longitude depends on time and stayed a hard problem until the eighteenth. The plate shows a sextant and a marine chronometer from that later period.

How it works

The Pole Star sits close to the point of the sky above the Earth’s axis. At the North Pole it stands close to overhead; on the equator, close to the horizon. In between, its height is roughly the latitude. In Columbus’s time it was 3.5° off the pole, so pilots corrected their readings; today the gap is under a degree.

South of the equator, navigators use the Sun at local noon, when it stands highest. Its angle from the celestial equator, the declination, swings between about 23.4° N and 23.4° S over the year and can be tabulated in advance. With the noon Sun to the south, latitude is 90° minus its altitude, plus the declination, south counting as negative. With the Sun to the north, as always south of the tropics, latitude is the declination minus (90° minus altitude).

A bronze mariner’s astrolabe with an open four-spoked wheel, a hanging ring and a sight rule with two pierced vanes The mariner’s astrolabe was cast heavy and open so the wind would not swing it.

On the early quadrant, a plumb line hangs across a scale while the star is sighted along one edge. The mariner’s astrolabe hangs from a ring; for the Sun, the navigator turns its sight rule until a beam passes through the upper pinhole onto the lower one. Both swing on a rolling deck, and errors of several degrees were common.

The octant and sextant measure from the sea horizon instead. Sunlight strikes the index mirror on the moving arm, reflects to the horizon mirror, then into the telescope. Half of the horizon mirror is clear, so the horizon is seen straight through it beside the reflected Sun. With dark shades swung in, the navigator moves the arm until the Sun’s lower edge touches the horizon and reads the arc. Tables then correct for the eye’s height, refraction and half the Sun’s diameter, about 16′. The double reflection doubles the angle, so an arc of one sixth of a circle reads up to 120°.

For longitude: the Earth turns 15° an hour. If the Sun crosses the local meridian when a clock kept on Greenwich time shows 15:00, the ship is about 45° west of Greenwich, before the correction for the equation of time: the Sun runs up to 16 minutes early or late over the year. The hard part was a clock that stays true at sea. The other method, the lunar distance, compares the Moon’s measured angle to a bright star with printed tables to find the home time.

Between sights, a dead reckoning from compass, log line and clock is plotted on the chart; each fix corrects it.

How to build it

A card quadrant finds your latitude within a degree or two, 100 to 200 km.

A quarter circle of card with a drinking straw taped along one edge and a thread with a nut hanging from the corner Sight along the straw and read where the thread crosses the scale.

Make the quadrant. Cut a quarter circle of stiff card about 15 cm in radius. With a protractor, mark degrees along the curve, from 0 at one straight edge to 90 at the other. Tape a straw along the 90 edge. Hang a thread weighted with a nut from the corner. The thread then reads the straw’s angle above the horizontal.

Measure the Pole Star. On a clear night in the northern hemisphere, follow the two end stars of the Plough’s bowl to Polaris, about five times their spacing away. Sight it through the straw, let the thread settle and read. Five readings averaged give an approximate latitude.

Or measure the noon Sun by a shadow. Never sight the Sun. Plant a straight stick on level ground and check it is vertical with the plumb line. Around midday, mark the shadow’s tip every five minutes: the shortest shadow is local noon, rarely 12:00 by the clock. The Sun’s altitude is the angle whose tangent is the stick’s height divided by that shadow; or draw the triangle to scale and measure the angle with the protractor.

Correct for the date. Look up the day’s solar declination in an almanac, positive when north. North of the tropics, latitude = 90° − altitude + declination. On 11 April the declination is about +8°. If a 100 cm stick casts a shortest shadow of 77 cm, the altitude is about 52.4° and the latitude 90 − 52.4 + 8 = 45.6° N, close to Lyon’s 45.8°. Then compare with a map.

Safety. Never look at the Sun, with the naked eye or through a straw, tube, binoculars or any sight, even briefly; sunglasses do not protect, and the damage is permanent. At night go with someone, carry a torch, and keep away from cliff edges, quays, riverbanks and open water.

History and evolution

Pacific navigators sailed without instruments, steering by where stars rise and set and judging latitude by the height of the Southern Cross. In 1976 Mau Piailug guided the canoe Hōkūleʻa from Hawaiʻi to Tahiti this way.

A small wooden board with a knotted cord through its centre The kamal: each knot matched the Pole Star’s height at a known port.

With the kamal of Indian Ocean pilots, a knot held in the teeth set the distance to a small board whose edges spanned horizon and star. Ahmad ibn Majid of Oman recorded this lore in 1490.

Diogo Gomes wrote that he took the Pole Star with a quadrant on a Guinea voyage around 1460; his dates are uncertain. Past the equator, crossed in the 1470s, the Portuguese used the noon Sun, the astrolabe and Abraham Zacuto’s declination tables, printed at Leiria in 1496. The cross-staff and John Davis’s backstaff of about 1594 followed. John Hadley described his octant to the Royal Society in 1731. John Harrison’s watch H4 was tried at sea in 1761; Nevil Maskelyne’s Nautical Almanac, first issued in 1766 for 1767, carried lunar tables. Regular radio time signals began in 1904, and GPS reached full operation in 1995.

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