Dire Straits Navigation

Emergency Navigation using a watch, a sheet of paper and a poem.

As featured in The Low-Tech Navigator, Practical Boat Owner, Institute of

Navigation News, Ocean Navigator and many other nautical journals

Tony Crowley

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Dire straits navigation.

Dire Straits Navigation is an emergency method of navigation. It is remarkably

simple and only requires a watch set to GMT and a few everyday objects.

Experience has shown that it is capable of providing a calculated position within

several miles of the true one. Not perfect, but good enough if you are lost in the

middle of the Pacific.

To follow the instructions below, you 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 - the odd one out),

and the number of days in each month.

Requirements

• A watch set to GMT

• A square sheet of paper (approx 20cm x 20cm)

• A wooden board (the back of a locker?)

• A few panel pins

• A ruler (useful but not essential)

• A poem

First you will construct a. simple quadrant with the paper and the wooden board.

Then, you will 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 do not have an almanac, these data can be

calculated with the help of four letters of the alphabet and a poem.

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Stage 1. To construct the quadrant

Fold your sheet of paper as shown in the diagram. This will give you a protractor

with nine 10˚ sectors. A ruler may be used to mark up the individual degrees

within a particluar 10˚ sector.

(Figure 2: folding paper quadrant: grading paper quadrant)

Though not essential, you can paste the paper quadrant on the board. It’s main

purpose will be to gauge your latitude. Insert panel pins in the board along the

horizon line as shown in Figure 3 - two sighting pins and one horizon pin.

Viewed from the sighting pins, the horizon pin will blink when the sun’s

shadow falls across it. Instructions on how to use the quadrant follow later.

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(figure 3: the shadow pin quadrant)

Stage 2. To calculate the sun’s declination

The sun crosses the equator northwards around 21st March and southwards

around the 23rd September each year and reaches it maximum declination of

23.45˚ North or South roughly 92 days later (figure 4). Note the convenient

sequence of numbers in the sun’s maximum declination

(figure 4: sun’s declination)

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The key figures to remember are 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. eg 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, the 14th April is

24 days after 21st March. This is 4 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 14th April,

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.

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Stage 3. To calculate the time at which the sun transits Greenwich

The time at which the sun crosses the Greenwich meridian varies from about

1144 to 1214 GMT throughout the year. This is due to a tilt in the earth’s axis

and its eliptical motion around the sun. Although this variation or Equation of

Time changes very gradually, it follows a fairly complex pattern as can be seen

from the graph (Figure 5)

(Figure 5: sun’s equation of time)

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 David

Birch’s excellent book Emergency Navigation.

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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 9th, calculate the period from two weeks after Valentine’s day to two

weeks before the middle of May, ie about 61 days. April 9th is 40 days into this

period. ie about 2/3rds of 61 days. 2/3rds 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 9th, the sun crosses the Greenwich Meridian at

approximately 1202 hrs.

Stage 4. To find latitude

Using trial and error, tap in a shadow pin close to where you think the sun’s

altitude will be at local noon. With your back to the sun, aim the device at the

horizon. Look along the sighting pins to the horizon pin, rock the device up and

down and see if the horizon pin blinks. If it blinks below the horizon, the

shadow pin is to low. If it blinks above the horizon, the pin is too high. When

you have got it right, read the sun’s altitude from the scale and deduct it from

90˚. The result is the angle between your zenith and the sun (figure 6). In

navigation, this angle is known as the zenith distance.

(Figure 6: zenith distance)7

To calculate latitude, think where the sun lies in relation to you and the equator.

(i) If the sun is between you and the equator, add the sun’s declination to the

zenith distance.

(ii) 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. If you have

got this far, you might like to work out the appropriate formula when the

observer’s position lies between the sun and the equator.

Stage 5. To find longitude

The earth 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 hour

10 minutes after Greenwich converts to a longitude of 167.5˚ West of

Greenwich.

This is how to time the sun’s transit over your meridian. A couple of hours

before local noon, tap in a shadow pin on the edge of the scale, aim the device at

the horizon and time when the horizon pin blinks. Do not remove the pin.

When the sun has descended to the same height after noon, note the time of

the second set of observation. The sun’s transit over the meridian will have taken

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place midway between these observations. 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 6th, the estimated times of the sun’s transit over the

meridian averaged 1555 GMT. The transit at Greenwich was 1214 GM. This

difference of 3 hours 41 minutes after Greenwich indicated a longitude of 55˚

15’ West.

Finally, here is an alternative to the paper quadrant for finding your longitude.

An emergency sextant

Partly open the lid of an audio cassette holder. With the opening at the top, and

your eyes protected from the sun ahead, look through the container and a

reflected image of the sun will appear. Adjust the angle of the open lid until the

sun’s image appears to coincide with the horizon. If the lid is made secure, the

image will remain stable as when using a sextant. Use this device to take and

time morning and afternoon observations of the sun. The mean of these times

is when the sun is over your meridian.

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