Dire straits navigation is an emergency method of navigation that has been developed for the benefit of the increasing numbers of sailors who venture across the world’s oceans relying entirely on electronic aids and satellite navigation systems. In the unfortunate event of systems failure, they may be left struggling to master the mysteries of celestial navigation, and doomed to circle the globe. This system is remarkably simple and, at its most primitive, requires a watch set to UCT, a sheet of paper, four numbers and a poem. Experience has shown that it is capable of providing a calculated position within several miles of the true one. It is by no means perfect, but good enough if you are lost in the middle of the Pacific.

Prior to following the instructions below, users should have a basic understanding of latitude and longitude, the Greenwich Meridian, the dates of the solstices (June 21, December 21), the equinoxes (March 21, September 23), and the number of days in each month.Requirements

To find your latitude and longitude with the help of the sun, you will need the following items: a sheet of paper, a ruler, a small block of wood, and a watch set to UCT. The paper can be of any size but its height should be 84% the size of its width10 inches by 81/2 inches (21 x 25 cms) is perfect, but if you have no ruler, a rectangular sheet based on 5 units by 6 units will do. The paper is used to construct a quadrant for measuring the height of the sun above the horizon and will be more accurate than copying and extending angles from a small protractor.

You will also need to know the sun’s position in relation to the equator (its declination) and the time at which it passes the Greenwich Meridian on the day of the observation. Assuming you have no access to an almanac, these data can be calculated with the help of four numbers and a poem.Constructing the quadrant

Draw a line across the paper from corner to corner. Fold one of the longer edges to this line and then fold it again (figure 1). You now have four sectors, each with an arc of 10°. Draw lines along the folds and copy them on the other half of the paper. The paper now contains nine sectors each occupying 10°. A section of a ruler graded in tenths can be placed at an appropriate point across each sector and used to mark up individual degrees (figure 2). Mount the quadrant on a larger piece of card or board and extend the degree scale to the edges of the board. Attach a small block of wood, or a pin, at the focus and extending about 3/4 of an inch (or about 2 cm) at right angles from the board.

To use the quadrant, hold it upright at right angles to the direction of the sun and line up the upper edge of the quadrant with the horizon ahead. Note where the shadow of the block of wood’s upper edge touches the scale and try to read the angle to the nearest 0.25° (figure 3). If the device is not help upright or at right angles to the sun, the reading will always increase, so the correct angle is the smallest reading when the device is parallel with the horizon. Even though your craft may not be steady, be patient and persevere. The procedure can be improved by viewing the horizon as near as possible to that part of the scale on which the sun’s shadow falls. This is achieved by cutting a window in the board and marking some parallel guidelines on the board. A ruler or straight edge may then be used as an adjustable horizon guide. A deluxe version would have an acetate window printed with several parallel lines, but don’t construct it during an emergency!Calculating the sun’s declination

The sun crosses the equator northwards around March 21 and southwards around September 23 each year and reaches maximum declination of 23.45° North or South roughly 92 days later. Note the convenient sequence of numbers in the maximum declination: 8, 15, 20 and 23. Converting these numbers to letters of the alphabet and placing them in a sentence such as ‘Help On The Way’ may work as a memory jogger. These are the latitudes the sun will have reached each 20 days it is from the equator. For example, it takes the first 20 days to reach a declination of 8°; the next 20 days to reach a declination of 15°; the next 20 days to reach a declination of 20°; the next 20 days to reach a declination of 23°; the remaining days to reach a declination of 23.45°.

With a diary and some simple arithmetic, you should be able to work out the sun’s declination to within half a degree or closer. For example, April 14 is 24 days after March 21. This is four days or one-fifth of the next 20 days in the table. One fifth between 8° and 15° is about 9.4°. The declination on April 14, therefore, is about 9.4° and is North. Note: Over a four-year period, there are annual variations in the sun’s daily declination. For the level of accuracy here, these can be ignored, but during a leap year (after 28th February) it is worth calculating the figure for the day following the one in which the observations are being made.Calculating the ‘Equation of Time’

Owing to a misalignment in its axis, the earth wobbles slightly as it rotates. The result is a variation in the time at which the sun crosses the Greenwich, or any other, meridian each day. This variation, which is called the Equation of Time, means that noon at Greenwich varies across the year from about 1144 to 1214 UCT. In the absence of an almanac or diagram, it is possible to calculate the time of the Greenwich transit with the help of the following rhyme inspired by ideas presented in David Burch’s Emergency Navigation (International Marine, 1990).

14 minutes late around Valentine’s Day

4 minutes early in the middle of May

6 minutes late near the end of July

16 minutes early when Halloween’s nigh

These variations last two weeks either side of those four peaks.

The last two lines are a reminder that the variations last about two weeks either side of the dates listed before they start to change. With a diary and some simple arithmetic, the equation of time may be calculated for specific days to within a minute of the correct figure. For example, to find the equation of time for April 9, calculate the period from two weeks after Valentine’s Day to two weeks before the middle of May, i.e., about 61 days. April 9 is 40 days into this period, i.e., about two-thirds of 61 days. Two-thirds of the 18 minutes range (+14 minutes to – 4 minutes) is about 12 minutes. So the equation of time is 14 – 12 minutes = 2 minutes. On April 9, the sun crosses the Greenwich Meridian at approximately 1202.Finding latitudeMeasure the sun’s altitude when the sun is bearing due south (or north) and deduct it from 90°. The result is the angle between your zenith and the sun. In navigation, this angle is known as zenith distance.

To calculate your latitude, think about where the sun lies in relation to you and the equator. If the sun is between you and the equator, add the sun’s declination to the zenith distance. If the equator is between you and the sun, deduct the sun’s declination from the zenith distance.

For example, at noon on a particular day, the sun has a declination of 11.5°North. The sun’s altitude is found to be 61° so its zenith distance is 29°. The sun lies between the observer and the equator, so the declination is added to the zenith distance. The latitude, therefore, is 29° + 11.5° = 40.5° North.

Work out the appropriate formula when the observer’s position lies between the sun and the equator.Finding longitudeEarth rotates 15° each hour (1° every 4 minutes; 0.25° every minute). The difference in time between the sun’s transit over the Greenwich Meridian and its transit over the observer’s meridian can be converted directly to a longitude. For example, a time difference of 3 hours, 12 minutes before Greenwich converts to a longitude of 48° East of Greenwich. A time difference of 11 hours, 10 minutes after Greenwich converts to a longitude of 167.5° west of Greenwich.

Timing the sun’s exact transit over your meridian, however, is not easy. Using the simple equipment described here, the best method is to measure the sun’s height an hour or so before noon and note the time of the observation. When the sun has descended to the same height after noon, note the time of the second observation. The sun’s transit over the meridian will have taken place approximately midway between the two observations. With this method, it is advisable to take several before and after observations, rather than rely on a single pair of observations, and average the results. It also assumes that your position has remained unchanged in the intervening period.

For example: On February 6, the estimated times of the sun’s transit over the meridian averaged 1555 UCT. The transit at Greenwich was 1214 UCT. This difference of 3 hours, 41 minutes after Greenwich indicated a longitude of 55° 15′ W.

Avoiding the influence of metal objects, try using a handbearing compass to establish longitude. Any error on the compass, from whatever cause, must be known with reasonable accuracy. Take and time several bearings of the sun before and after local noon. Plot them on a graph to find the most likely time at which the sun was due north or south and crossing the meridian. This method is useful when the sun’s altitude at noon is low or when the sun is partially obscured by cloud.

Tony Crowley lives in Herts, England.