THE METHOD

A Bad Analogy

When you decide to bake a cake, you do not concern yourself with the chemistry of what is going on between the ingredients in the oven (how do those egg proteins bond with the flour, and what might be the optimum temperature for this to occur?). No, the brilliant thing is that someone has done it before, and wrote down how they did it. You follow a recipe, do exactly what it says, and you get a cake.

If your interest is long distance sailing, you have better things to think about than the mathematical formulae and three-dimensional trigonometry as it relates to the surface of a sphere. You want your position (cake).

In this section I tell you the exact steps you have to follow in order to get a position line using astro navigation with tables. I keep the explanation to a mimimum, and the instructions as simple as possible. This is the recipe - not the food science.

Using a Form

When I started to do this myself, I rapidly got in a muddle with bits of paper and scribbled notes. And the really frustrating thing was - if it came out wrong, you had to start all over again, and probably make another mistake, and get another rubbish answer.

There is a way around this. Use a form instead of scap paper. There are three advantages:

a) it helps you to work methodically and make fewer stupid mistakes (e.g. copying numbers incorrectly)

b) if you do get a rubbish answer, you (or someone else) can check back through the form and find out where you went wrong. There's no need to throw the sight away - just correct the fault and carry on from there. This is less frustrating, and you learn by seeing where you went wrong.

c) once you have done a few sights, you will find that the form actually guides you through the process - you don't need to look at the instructions all the time.

The examples below use my recommended forms. Part of the form is different depending on which sight reduction method you use - Nautical Almanac or Air Tables. Both of these forms are available to download.

download forms here ...... picture of each form to click on

Doing Maths

I am well aware that "doing maths" isn't everybody's favourite occupation, in fact a large number of people either hate it, or are intimidated by it.

Luckily, the forms and tables are designed so that you don't have to do very much maths, but you do have to ADD and SUBTRACT, and you have to do this with angles which are expressed as degrees and minutes.

There are 60 minutes in one degree. So, for example:

14° 36' + 10° 40' = 25° 16'

68° 12' - 22° 30.7' = 45° 41.3'

With subtractions, it's a good idea to check the result with a quick "add back" - so:

45° 41.3 + 22° 30.7 = 68° 12' checks that you got the answer right.

The Recipe

A: Taking the Sight

1. Take your sextant and measure the index error. This is done by measuring the angle between the horizon and itself, i.e. it is supposed to be zero. The sextant will read a small angle. Note this angle, and also whether the small number of minutes is on the scale (a reading of, say, 0° 4' is 4' on) or off the scale (a reading of, say, 55' is 5' off). (Note: use the horizon, because anything close to you - part of the boat for example - will give a false index error.)

2. Write down the date, body (e.g. sun) and circle U for upper limb or L for lower limb. Limb means the edge of the body concerned. You usually use the lower limb of the sun by sitting it on, not below, the horizon when taking the sight with the sextant. (With the moon, if it isn’t full, you have to choose either the upper or the lower edge, depending on which one you can get a clean sight of.)

3. Note the log reading, so that you can use your sight to do a transferred position line or DR.

4. Take some measurements of the sun. As you take each one, note the time to the nearest second (it helps if you have someone else looking at the watch and you call out as you get the measurement). Four or five readings is generally OK.

5. Write down the times, measured angles and the index error on the form (use the form from now on). Write the index error correction as + if the error is OFF the scale, - if it is ON the scale.

6. Take an average (mean) of the times and the angles. However, if you see one reading that is obviously wrong, discard it. If you are measuring the sun in the morning, each angle should be slightly greater than the last. If one sticks out as being obviously out of sequence it is probably in error, so discard it and the corresponding time. To take a mean you can use the “spot mean” method, by guessing a mean and averaging the differences, plus and minus, on that guessed mean. (I suggest this because it is quicker than adding them all up).

7. Write down mean (watch) and mean (sextant). Get into the habit of looking at the calculated mean and making sure that it is sensible, i.e. roughly what you expect - the common sense check.

B: Correcting the Sight

8. On the left column of the form, put in the time zone adjustment (-1h if your watch is set to BST, for example). Put in the watch correction slow or fast. From those, adjust the mean watch time to get corrected Universal Time (UT - essentially the same as GMT).

9. In the very first table of The Nautical Almanac, Altitude Correction Tables, look up Dip for the height of the sextant observation above sea level. (In this example, the observation is from 2m above sea level). Applying IE and Dip to the mean sextant angle gives App Alt (apparent altitude).

10. Also in the Altitude Correction Tables, look up the altitude correction for the App Alt of the Sun and write it down as Alt corr 1. (Ignore Alt corr 2 and U Limb corr - used for moon only).

11. Add Alt corr 1 to App Alt to get True Alt H0.

C: The Sight Reduction - Sun

12. Back to the left hand column. Ignore HP (moon only).

13. Using the Daily Pages in The Nautical Almanac, look up declination for the sun for the UT hour on that day’s date (write the UT hour in the brackets). Make a mental note of whether the declination is increasing or reducing from one hour to the next, and don’t forget to note whether it is N or S by circling the appropriate letter.

14. Write down the value for d from the same day (it’s at the bottom of the table: d is the amount declination changes by in one hour.). Write down the UT minutes in the brackets.

15. Also in the Daily Pages look up GHA for the sun for the UT hour on the same day, and write it down.

16. Using the UT minutes, look up the relevant section of the Increments and Corrections Table, which you will find towards the back of The Nautical Almanac. In this section look up and write down the d correction for that number of minutes.

17. Apply the correction to get Dec, which is the best estimate of the declination at that UT time to the nearest minute. (You add or subtract according to whether declination is increasing or decreasing from one hour to the next, and you should end up with a value between the two hourly values.)

18. In the same section of the Increments and Corrections table, look up the Increment for the minutes and seconds of the UT time. Write this below the GHA from the Daily Pages.

19. (Ignore v - moon and planets only).

20. Add the Increment to the looked up GHA, to give GHA - the best estimate of Greenwich Hour Angle at the UT time to the nearest second. (Again, your GHA value should be somewhere between the hourly values in the Daily Pages.)

21. Choose, and enter on the form, an Assumed Longitude (Ass Long) that is close to your estimated position but comes to a round number when you add it to, or subtract it from, GHA. You add if it is an East longitude and subtract if West, to get LHA. LHA should now be a round number of degrees.

22. Choose an Assumed Latitude (Ass Lat) which is a round number of degrees close to your estimated position.

Thus far, the process has been EXACTLY THE SAME whether you intend to use the concise Sight Reduction Table in The Nautical Almanac, or the Air Tables. From now on they differ.

Steps 23 to 29 in BLACK use Sight Reduction Tables for Air Navigation. For The Nautical Almanac method, scroll down to step 23 in BLUE.

23. Copy Lat, LHA and Dec to the next section on the form, putting the degrees part of Dec by Dec°, and the minutes part by Dec'. Also note whether Dec and Lat are both North or both South (circle "same"), or whether one is North and the other South (circle "contrary").

24. In the Air Tables, choose the volume (2 or 3) which covers the Latitude you need. In that volume find the tables for Lat. Within these, find the column for Dec (you need to find the right page, depending on whether Declination is SAME or CONTRARY to Latitude). In this column look up against LHA. Write down HC, d and Z from the table.

25. Copy HC (table) to the next section of the form, and copy d to the left side of the form underneath Dec', and using these two values look up the correction for the minutes of Declination, in Table 5 at the back of the Air Tables volume. Write this down, and add it to HC (table), to give HC.

26. Copy True Alt H0 from higher up the form (it's the measured altitude, corrected) and subtract the smaller of HC and H0 from the larger, to get the difference in minutes. Write this number as Intercept - the distance of your position line from the Assumed Position, towards or away from the sun.

27. Circle "towards" if H0 is larger then HC, and "away" if H0 is less than HC.

28. The final thing is to work out the Azimuth. Copy the value of Z that you looked up in the table, and follow the rules on the form to get Zn, the azimuth: in northern latitudes, if LHA>180° Zn is the same as Z; if LHA <180° Zn =360°-Z. In southern latitudes, if LHA>180° Zn=180°-Z; if LHA <180° Zn=180°+Z.

29. You've finished the sight reduction - now skip the blue section below, go to step 41 and plot the position line on the chart.

Steps 23 to 38 in BLUE use the Sight Reduction Tables in The Nautical Almanac.

23. Copy Ass Lat and LHA to the next section on the form, and use them to look up in The Nautical Almanac’s Sight Reduction Table. When you find the correct point in the table write down A, B and Z1.

24. Write down A° (A rounded to the nearest degree - not necessarily rounded down) and A' which is the minutes part of A.

25. Make B negative if LHA is between 90° and 270°. Make Z1 the same sign as B. (It's a good idea to write in + if you're not making something negative - it shows you've done that step in the process)

26. Copy B and Dec to the left hand column, making Dec negative if it is contrary to Lat (i.e. if one is North and the other is South).

27. Add B and Dec (using their new + or - signs) to get F.

28. Write down F° (F rounded to the nearest degree) and F' which is the minutes part of F.

29. Now copy A° and F° to the left hand column and use them to look up in the Sight Reduction Table again. This will give you H, P and Z2. Write these down, and P° and Z2° which are P and Z2 rounded to the nearest degree.

30. This second lookup in the Sight Reduction Table needs two corrections, because you used A° and F° which were approximations to A and F. Copy F', P°, A' and Z2° to the left hand column. Look in the Auxiliary Table (last page of the Sight Reduction Table) using F' and P°, and this will give you corr1. Using the same table look up using A' and Z2°, and this will give you corr2.

31. Make corr1 negative if F<90° and F' >29'; or if F>90° and F'<30'.

32. Make corr2 negative if A'<30'.

33. Put the Nautical Almanac to one side, because that was the last time you need to use it.

34. You’re almost there! Copy H, corr1 and corr2 to the left hand column. Add the positive or negative corrections to H to get HC, and finally make HC negative if F is negative.

35. HC is the calculated angle for the sun at the assumed position, so copy it up to the right hand side of the form just below True Alt HO. Subtract the smaller from the larger to get the Intercept, which is going to be the distance (in degrees and minutes, and hence Nautical Miles) of your position line from the Assumed Position; towards or away from the direction of the sun.

36. Circle towards if HO is greater than HC, away if it is less.

37. The final thing is to work out the azimuth. Copy Z2, and make it negative if F>90°.

38. On the next line, if F is negative, calculate and write down a new value for Z2, which is 180°-Z2 (otherwise leave that blank).

39. Write down Z1, then add Z1 and Z2 together to get Z.

40. Finally, follow the rules on the form to calculate Zn, the azimuth: in northern latitudes, if LHA>180° Zn is the same as Z; if LHA <180° Zn =360°-Z. In southern latitudes, if LHA>180° Zn=180°-Z; if LHA <180° Zn=180°+Z.

D: Now turn to the chart, and draw the position line as follows:

41. Mark the Assumed Position (using Ass Lat and Ass Long from the form).

42. Draw a line through the Assumed Position towards and away from the sun, using Zn from the form as the true bearing of the sun.

43. Measure off the Intercept distance, either towards or away from the sun as indicated on the form (use the degrees and minutes of latitude on the side of the chart, close to the latitude of the Assumed Position).

44. At the point where you have measured off the Intercept, draw your position line at 90° to the first line.

45. Mark each end of the position line with arrows pointing towards the sun, and write the time and “SUN” beside it. Congratulate yourself and make a cup of tea!

To see the full completed forms, click on the LEFT for the CONCISE (Nautical Almanac) tables form, and on the RIGHT for the AIR TABLES version.