Techniques > Navigational Questions & Answers

Getting a fix using the angle of the slope

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Hugh Westacott:
Recently, my wife and I spent a few days in Beer (no jokes, please!) on the east Devon coast. We spent a lovely day walking the 17 glorious kilometres along the Southwest Coast Path from Sidmouth to Seaton which has a total ascent of more than 700 metres in a series of five very steep climbs from sea-level to the top of the cliffs. Joan wanted to know just how steep some of the ascents were and as I didnít have my Suunto MC-2 compass with me I was unable to take the angle of the slope and had to rely on calculating the steepest sections from the 1:25k map with a contour interval of 5 metres..

I found it surprisingly difficult. Pages 156-7 of Lyleís Ultimate Navigation Manual  explains the methodology of calculating the angle of the slope and provides a chart from which an estimate can be made by measuring the interval between contours. I used a pair of dividers and his plastic device (has it a name?) for making the calculation and arrived at an approximate figure of 20į which is a 36% gradient. But I found it virtually impossible to make the same calculation using a 1:50k map with a contour interval of 10 metres because of the the thicknesss of the contour lines and their closeness to each other.

On page 157, Lyle mentions the possibility of using the slope angle and his chart to match the interval between contours on the map and thus establish your position.

Now I accept that this works in theory but is it a practical method when standing on a mountainside using a Landranger map? And in foul weatherÖ? I found it difficult enough using a map table in good light with a pair of dividers and Lyleís contour measurement tool.

Maybe Iím missing something so Iíd be interested to hear if anyone has had practical experience of using this method.


Pete McK:
No, I donít think that you are missing anything Hugh, however you may be introducing error by using your dividers. My technique uses the card directly on the map. With the card running perpendicular to the direction of the contour lines, I move it over the map to find where the spacings on the card match the spacings of the contour lines on the map to find the slope angle. For 1:25,000 maps I find the card reliable and correct. On 1:50,000 like all other measurements because everything is half as big, less so, although the indication of the slope is invariably enough for me to perform an accurate slope angle relocation technique. 

The card is imaginatively called ;) a Navigatorís Slope Angle Card on the website where you buy them

Hugh Westacott:

Many thanks for providing me with the name of the slope angle tool. Lyle was kind enough to send me one some time ago but the name does not appear on the device. Frankly, I find it difficult to use and only resorted to dividers to confirm that the contour interval matched from map to card. I think it would be easier to use if the card were transparent and the scale was etched along the edge.

I'm a reasonably competent navigator and have practised, and also used in real-life situations, all the standard navigation techniques such as boxing, expanding square searches, aspect of the slope etc, but I'm always keen to learn new methods and have been working through some of those described in The Ultimate Navigation Manual.

Iím having a real problem in understanding how elevation can be established to obtain a fix as described on pp156-7. In order to get a reasonably accurate fix you normally need the bearing or a linear feature and either distance measured or, in areas where the contours are close together, elevation. Walking on a bearing is prone to error so letís assume that you are climbing a hill following a wall that is marked on the map (think of the wall that runs north from the top of the Honister Pass to Dale Head). It seems to me that the technique using the slope angle tool will only work if every contour were spaced irregularly so that none matched any of the others. On a regular slope the contours would be equidistant from each other thus making it impossible to identify a specific space between contours.

This is why I think that I may be missing something and am asking for advice and clarification from those who have used the technique in real life.


Tangent of Slope Angle equals Height over Distance:: Tan A=h/d; Cot A=d/h
Sine of Slope Angle equals h/ length of Slope; Cos A=d/ length of Slope.
Length of Slope: as measured from bottom to top, ie, paced or estimated.

captain paranoia:
One problem with these methods is that hills with varying slope confuse tools like Lyle's, or Wally Keay's Keayscale, or my own version, because you need a number of contour lines at a fixed spacing in order to be able to use the scale accurately.

Not only do you have to estimate the gradient shown on the map, you also have to estimate the gradient of the real slope in front of you, averaging out lumpy terrain, and deciding which part of the changing slope you wish to estimate.

I think slope angle might best be used to confirm other techniques, such as slope aspect.

> Tangent of Slope Angle equals Height over Distance [etc]

Yes, that's the basic trigonometry, but I don't think it will be a lot of help in the field, unless you're adept at evaluating trigonometric functions in your head.  I'm not, and I suspect Hugh isn't either...  You could take a calculator or trig tables, I suppose; a graphical tool is essentially a form of trigonometric table.

The percentage slope is somewhat easier, being a 'simple' division.


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