Collection: Field Notes — Old Fashioned Seamanship

Series Hub: Traditional Navigation Techniques

Subject: Finding your latitude without instruments — the zenith star concept, Polaris height measurement, making and using a kamal, tested accuracy at sea, and the key stars for North Atlantic and Baltic latitudes

How to Find Your Latitude Without GPS or Sextant — Polaris Height, the Kamal, and Hand-Measurement Methods

Polaris’s height above the northern horizon, measured in degrees, is your latitude. The relationship is direct, requires no calculation, and is available on any clear night when the northern sky is visible. This is about how to measure that height with a fist, a kamal, or any approximation of one, and what accuracy you can expect from Lewis’s testing of these methods at sea.

In the summer of 1969, the Carolinian master navigator Piailug was in Honolulu. Someone asked him to estimate how high Polaris stood above the horizon. He extended his hand at arm’s length, sighted along it, and gave a figure. His estimate was within about one degree fifteen minutes of the actual altitude. Honolulu lies at twenty-one degrees fifteen minutes north.

That incident, documented by David Lewis in We, the Navigators, is one of the most precise demonstrations of what hand-measurement can achieve when it is regularly practised. Piailug’s observation was not made with a sextant or any instrument. It was made by a navigator whose daily orientation framework depended on knowing how high Polaris stood above the horizon at different latitudes. In the Carolinian system, that height is a direct readout of latitude. Requiring nothing but a clear night and an extended hand.

This note covers the underlying concept, the measurement method, how to make and use a kamal, Lewis’s accuracy testing at sea, and the specific stars most useful for latitude estimation at the latitudes where readers of this series actually sail.

Why the sky is a latitude instrument

Every star rises over the eastern horizon, arcs across the sky, and sets over the western horizon, as covered in The Sidereal Compass. Each star’s arc is tilted at an angle determined by your latitude. The further north you are, the more northerly the whole sky appears to lean, and the higher Polaris sits above the northern horizon.

Polaris sits almost directly above the north celestial pole and barely moves. It describes a tiny circle around the pole so small that for practical navigation it can be treated as fixed. Its altitude above the horizon, the angle in degrees from the horizon to the star, is to a close approximation equal to your latitude. At fifty-two degrees north, Polaris stands fifty-two degrees above the northern horizon. At forty-five degrees north, forty-five degrees up. The relationship is direct, continuous, and requires no tables, no watch, and no calculation. It is available on any clear night when Polaris is visible. Which over the British Isles and northern Europe means most of the year.

This is the most immediately useful latitude technique for a northern European sailor. Everything else in this post builds outward from it.

The fist method

The basic measurement instrument is the extended fist held at arm’s length. One fist, fingers closed, subtends approximately ten degrees of arc for most adults when held at arm’s length. Not exact. Individual variation means your fist might subtend nine degrees or eleven. But once calibrated it is consistent. The geometry of the calibration is in the appendix at the end of this note.

Lewis documents the Carolinian navigators using a slightly different body measurement, an extended hand span called the ey-ass, but the principle is identical. Namonour and Epemai, senior navigators of Satawal, told Lewis that Polaris stood half an ey-ass above the horizon at their home island and one full ey-ass at Saipan. Converting to degrees, Satawal lies at approximately seven and a half degrees north, Saipan at fifteen degrees north. The measurements were exact.

Tristan Gooley describes and demonstrates the fist method in How to Read Water, including a passage where he demonstrates it to fellow sailors during a dhow voyage. Confirming altitude by fist measurement, then verifying against GPS. His account bridges the Pacific technique directly to practical use on any boat. He also describes it in The Secret World of Weather in the context of estimating cloud heights and angular distances, emphasising that the fist is a versatile angular measurement tool that works in any direction.

For the northern European sailor, the practical exercise. On the next clear night at anchor or alongside, find Polaris using the Plough pointers as described in The Sidereal Compass, measure its height above the horizon in extended fists, multiply by ten (or your calibrated value), and compare with the chart latitude. Repeat on several nights at different anchorages until the measurement is reliable. Once it is, you have a latitude instrument available on any clear night that requires nothing stored, nothing charged, and nothing that can break.

The kamal

A kamal is a simple sighting board, traditionally a piece of wood or stiff material, with a string attached at the centre. The string is held between the teeth or to the lip, keeping the board at a consistent arm’s length. The board is aligned so that its bottom edge sits on the horizon and its top edge touches the star being measured. The position of a knot tied in the string, held against the lips or teeth, records the angle at that latitude. On subsequent occasions, holding the knot at the same point recreates the same angle and confirms the same latitude.

Lewis mentions a Carolinian navigator who used a similar device, a cane filled with water and sealed, from which the angle was read. Arab navigators of the Indian Ocean documented since the ninth century used instruments functionally identical to the kamal for the same purpose. Measuring the height of the Pole Star above the horizon to determine latitude. The Arab measurement unit, the isbah, and the Chinese equivalent, the chih, were both finger-breadth measurements at arm’s length, essentially identical in principle to the Pacific Island hand methods.

To make a practical kamal. Cut a piece of stiff card to approximately five centimetres tall and ten centimetres wide. Pierce the centre and thread a piece of string about seventy centimetres long through it. Knot the string at the card end to hold it. Tie a second knot at the other end that sits comfortably against your lips when you hold the string taut. Hold this knot in your teeth or against your lips to maintain a consistent arm’s length. Align the bottom of the card with the northern horizon and raise or lower it until Polaris just touches the top edge. The card height and string length determine the angle measured. To calibrate, at a known latitude, adjust the knot until the measurement is exact. The kamal now records that latitude. Sailing south and finding Polaris no longer reaches the card’s top edge confirms you have moved south of your calibration latitude. Sliding the knot further from the card until Polaris once again touches the top edge gives a new latitude by comparing the knot position with the calibration mark.

A properly calibrated kamal in familiar waters becomes a precise latitude check. Lewis’s account of Arab navigators using the kamal on the route from the Persian Gulf to India describes a system in which specific knot positions on the string corresponded to specific ports, so arriving at the correct latitude for a destination was confirmed directly by the knot position, requiring no calculation at all.

Zenith stars

Below roughly five degrees north latitude, Polaris disappears below the horizon. Pacific navigators who operated in and south of the tropics needed a different approach, and they developed the zenith star method.

A star’s declination is its celestial equivalent of latitude. A star with a declination of twenty-one degrees north passes directly over the zenith, directly overhead, of all places at twenty-one degrees north latitude as it crosses the sky. A navigator who notes that a particular star is passing through their zenith can deduce they are at the latitude corresponding to that star’s declination. Lewis documents this across multiple Pacific traditions under the term fanakenga in Tongan usage. The star that points down to an island. Its overhead star.

The practical application. If you are trying to reach an island at a specific latitude and you know its zenith star, sailing until that star passes directly overhead places you on the correct latitude. You then sail east or west along that latitude until land signs or dead reckoning confirms your position. The zenith star gives latitude. Dead reckoning and land signs provide the final approach.

Lewis tested zenith star observations on his own catamaran voyage across the South Pacific. He compared his estimated latitudes from zenith star observations with the GPS-verified positions recorded by a separate crew member. His results showed accuracy of approximately thirty miles in moderate conditions. Thirty nautical miles of latitude, about half a degree. On his best six observations, excluding one taken after the star had already passed the zenith and one in poor conditions, his average error was twelve nautical miles. He characterises this as adequate for navigation given the expanded target sizes of Pacific islands and their surrounding zones of birds and clouds.

For a northern European sailor, zenith stars are less central than Polaris. Polaris is available and more immediately useful. But understanding the zenith concept is worth the time because it explains how latitude works at all, and because on any clear night you can observe which bright star is currently passing closest to your zenith and use it as a rough latitude cross-check.

Key stars for North Atlantic and Baltic latitudes

For sailors in northern European waters, here are the stars most useful for latitude estimation by the zenith method, with their declinations and the latitudes they pass over.

Capella, declination 45.9 degrees north, passes over the latitude of roughly northern France and the upper Channel. Useful as a zenith star on a Biscay passage when you want to confirm you have reached the latitude of Brest or Ushant before turning east for a landfall. A very bright yellowish star in Auriga, visible in autumn and winter, easy to identify.

Deneb, declination 45.3 degrees north, passes over almost the same latitude as Capella. Brittany, Channel approaches. The bright star at the tail of Cygnus, at the top of the Northern Cross asterism, prominent in summer and early autumn evenings.

Dubhe, declination 61.7 degrees north, passes over the latitude of Shetland. One of the two pointer stars in the Plough that indicate Polaris, circumpolar from most British latitudes, meaning it never sets below the horizon and is available throughout the night throughout the year.

Alioth and Mizar, adjacent stars in the handle of the Plough, have declinations of approximately 55.9 and 54.9 degrees respectively. They pass over the latitude of central Scotland and the Firth of Forth. Both circumpolar from British latitudes.

Merak, declination 56.4 degrees north, the lower of the two Plough pointer stars, passes over approximately the latitude of the Moray Firth and central Scotland.

For a passage south toward Spain and Portugal, Vega, declination 38.7 degrees north, passes over the latitude of Lisbon and northern Portugal. The brightest star in Lyra, intensely blue-white, dominates summer and autumn skies overhead from British latitudes. Almost directly overhead from around fifty degrees north in August evenings.

Arcturus, declination 19.2 degrees north, passes over the latitude of the Canaries and northern Mexico. Too far south to be useful as a zenith star in northern European sailing, but worth knowing as a reference point for a passage toward the Azores.

These declinations are for the current epoch. Stellar declinations change very slowly over centuries due to the precession of the equinoxes. On human sailing timescales they are stable enough to use without correction.

Latitude as a complement to dead reckoning

Lewis makes an important observation about what latitude observations can and cannot do. Knowing your latitude tells you nothing about how far east or west you are. As he quotes the navigator Harold Gatty directly, there is no way of finding longitude by star observation alone without knowing Greenwich Mean Time. A latitude observation from a zenith star or from Polaris height places you somewhere on a circle girdling the globe at that latitude. A dead reckoning plot tells you where along that circle you are. But the dead reckoning is subject to the accumulated errors of speed estimation, leeway, and current that Dead Reckoning Without Electronics covers in full.

The combination of the two is more powerful than either alone. A latitude observation from Polaris constrains the north-south dimension of your dead reckoning uncertainty. A dead reckoning plot constrains the east-west dimension. Together they produce a position estimate that is more reliable than either technique separately. Which is precisely how the Pacific navigators who used zenith stars combined them with star path courses, swell direction, and dead reckoning in a system where each technique checked and refined the others.

For a Biscay crossing, arriving at the latitude of your destination port while your dead reckoning confirms approximate longitude is a practical double-check that requires no electronics and no instruments beyond a calibrated fist or a kamal made from card and string. In miniature, the same multi-technique approach Hipour used on a four-hundred-and-fifty-mile open Pacific passage.

The practical starting point

The most immediate action from this post is the Polaris calibration exercise. On the next clear night at a known position, alongside in harbour or at anchor in a bay whose latitude you know from the chart, find Polaris, measure its height in extended fists, and compare with the chart latitude. Note your personal fist-width calibration. Total time required, under five minutes.

The second step is to make a kamal. Five centimetres of card, sixty centimetres of string. Calibrate it at a known latitude by tying a knot at the correct position for Polaris. Use it on a subsequent night at sea to confirm latitude independently of instruments. Lewis’s accuracy testing produced twelve to thirty nautical miles of error. The first time you use it you will probably do worse. The fifth time, probably better.

If you want to practise the celestial measurement habit on dry land before you need it at sea, the Sextant Navigation Trainer I built walks through the geometry of celestial sights and works as a calculator while you are learning. The fist method and the kamal are simpler than a sextant. The mathematics is the same.

The geometry of the fist

In celestial navigation, distance in the sky is measured in degrees of arc rather than inches or centimetres. Because of the way perspective works, a hand held at arm’s length covers a roughly consistent portion of the sky regardless of the person’s size. Longer arms usually come with larger hands, and the two balance.

A standard clenched fist held at arm’s length is approximately ten degrees. The variation matters. If your fist covers nine degrees or eleven degrees, and you are multiplying by a factor of ten, your latitude calculation will be off by hundreds of miles. A person with very long arms will see their fist as smaller against the backdrop of the sky. A person with very large hands will cover more of the horizon. The ratio matters more than either absolute measurement.

To find your specific multiplier, measure a known distance in the sky. Sailors often use two stars with a fixed known angular distance. Dubhe and Merak, the pointer stars in the Plough, are almost exactly five degrees apart. Hold your hand up and see how much of it fills the gap. If two fingers fit the gap exactly, each finger is two and a half degrees. If your full fist covers exactly ten degrees of known star distance, your calibration value is ten. If your fist is slightly smaller and it takes 1.1 fists to cover a 10-degree span, your value is about nine.

The application. Measurement in fists multiplied by your calibrated value gives latitude. If you are at a harbour you know from the chart is at fifty degrees north, and you measure Polaris at five fists high, then using the standard ten gives five times ten which is fifty. Your value is ten. If you consistently measure Polaris at five and a half fists at that same location, then fifty divided by 5.5 is 9.09. Your calibrated value is about nine.

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The companion posts in this series. The Sidereal Compass covers finding Polaris and the star path system on which latitude measurement depends. Dead Reckoning Without Electronics covers the east-west position estimating that latitude observation complements. Land Signs at Sea covers the approach and landfall techniques that take over once latitude is confirmed. The full series index is at Traditional Navigation Techniques.

References

Lewis, D. (1994). We, the Navigators: The Ancient Art of Landfinding in the Pacific. University of Hawai'i Press.

Gooley, T. (2016). How to Read Water. Sceptre..

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