Rising & Dipping Landmarks

So how far away is the horizon? Well it all depends on how high up you are. If you are on a small boat, standing just a couple of metres above sea level, the distance to the horizon is going to be different to what the captain on a big ship is seeing. Thankfully some clever person has come up with a formula to work that out.

Distance to sea horizon in miles = √height of eye of the observer x 2.03

+

Distance to sea horizon in miles + √elevation of the object x 2.03

My normal calculator doesn’t actually have the √ sign. (Which is by the way, the square root for those of you who like me couldn’t remember) Thankfully my iPhone calculator does have it – if you turn the phone sideways.

Say your height of eye is 2m and the elevation of the object you want to raise is 11m.

On the calculator you go: 2 √ x 2.03 = 2.870 (so this means it is 2.870M from your height of eye to the horizon) Then take the height of the object and do the same 11 √ x 2.03 = 6.732

Then you add 2.870 + 6.732 = 9.60M

If you don’t have a calculator, thankfully all is not lost – a very considerate person has worked it all out for me already in a handy table, which you might be able to find in a nautical almanac (which is where I got mine from)

__________________________________

The Geographical Range is the maximum distance at which an object can theoretically be seen over the horizon.

So you can just grab this table. Work out the height of your eye above sea level – say 2m.

Next thing to do is to work out a landmark (or a light – but read on for more info on that) on your chart. For this example, lets say it is a large hill on the top of an island, like on the Isle of Pines, which is 260 metres high.

So if you look along the top of the table, and find the 2 metre column – for our height of eye, and then scroll down the column until we get to the 260 metre elevation row, then we can see that we should be able to see the top of that hill ‘raise’ above the horizon when we are 35.6 nautical miles away. (So long as it is a nice clear day)

So then you get your compass (the one you draw circles with), measure off on the side of the chart 35.6 miles – put the pin on the top of the mountain and draw an arc on the chart. This gives you your first position line – i.e. you are somewhere on that line. When you do see it raise above the horizon, you can take a bearing with your hand bearing compass, or compass binoculars. Now you have got a bearing to the light, which you can draw on your chart as well. All going well your vessel should be where the two lines intercept. You could also check the chart for the depth of the water, and compare that with what your depth sounder says for further clarification of your position.

So there are a few things to take in to account when it comes to using this table.

Height of tide. If you want to get really clever then you can take the tide heights in to account, however this is generally ignored in this calculation

The table includes an allowance for atmospheric refraction (which is the bending of light rays as they pass through the atmosphere) Abnormal refraction may occur in unusual conditions of pressure, temperature and humidity. This can increase or decrease the range.

You need to have good visibility to do this – as its quite difficult to raise or dip anything if you are surrounded in fog or if it is dark…