Calculating Position- by Horizontal Angle

If you were excited by the prospect of measuring your distance off a landmark by vertical angle then today’s lesson in Coastal Navigation is going to completely knock your socks off!

Today faithful blog readers, we are going to learn all about using horizontal angles to find out where you are.

First of all you are going to need a couple of prominent landmarks on the chart and in view from where you are. In our example, lets use the headland entering in to Purau Bay in the bottom middle of this chart, and the little Island on the other side – Ripapa Island. Lyttelton_nz

Step 1. Draw a line between the two landmarks.

Step 2. Measure the angle from the boat. Either by taking two simultaneous compass bearings, with your compass binoculars or a hand bearing compass – and then using the difference between the two bearings. Because you are just measuring the angle between the bearings, you do not need to take in to account variation and deviation.

Or you can measure the angle by turning your sextant horizontally and measuring the angle between the two points (and calculating for index error).

Step 3. If the angle you get is less than 90º then subtract the angle from 90º to get the construction angle.

If the angle is greater than 90º then you subtract 90º to get the construction angle.

Step 4. Use a protractor to plot the construction angle from the baseline – making sure you put them on the boat side of the base line. Lets say in our example the construction angle is 30º so we measure out 30º from each landmark along the baseline and then draw a triangle.

Step 5. Draw a position circle using your drawing compass. With the sharp end on the top of the triangle and the circle passing through both landmarks. Your boat is somewhere on this circle!

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You now need to combine this position circle with some other Coastal Navigation technique of obtaining a position line to figure out just where exactly you are.

Personally, this seems like a lot of maths and drawings to get quite a rough idea of where you might be on a circle. But perhaps you might be able to combine this with being on the transit line of the leading lights, or by taking a bearing to the channel marker in the middle of the harbour.

Thank goodness for GPS! Still I guess it is really important to know how to do all this stuff in case you do end up needing it one day (and for my upcoming exam…) Lightening strike, battery/engine failure etc. Plenty of reasons why your GPS might not be working. What are your thoughts? Do you still practice these Coastal Navigation skills on a day to day basis?

8 thoughts on “Calculating Position- by Horizontal Angle

  1. Why not take a bearing or sight of the first mark then using the sextant, or talking a second bearing get the angle to the second land mark. Go to the chart, from the land mark rule a line for the first bearing/land mark. Then, from the first line using a protractor, parallel rule (from compass rose) or Portland Course Plotter draw the bearing from the second land mark. Where the two cross is approximately where you were when you took the sighting. If you also had speed and course you could also get more exact position by dead reckoning from the derived point. Lot of reckoning in navigation… I reckon we’re here.


  2. Pingback: Basic Navigation | Astrolabe Sailing

  3. Pingback: Navigation – Position Lines | Astrolabe Sailing

  4. I don’t know if taking compass bearings method (and doing the deviation and variation corrections) is possible less accurate than the sextant method. I did find two sights that give a reasonably understandable explanation of why the sextant angle method works (links below). I suspect this wasn’t discussed in your high school classroom, and therefore nothing to apologize for. I do like your method of presenting your knowledge as learner, rather than an all knowing instructor. It’s refreshing and you definitely do your homework.


    • Thanks Robert. I’ll check out those links. I have always wondered how the compass bearing method works with deviation – if you’re using a hand bearing compass for example? Do you just apply variation and leave it at that? Do you know?


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