Author Topic: Getting a fix using the angle of the slope  (Read 7318 times)

Hugh Westacott

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Getting a fix using the angle of the slope
« on: November 02, 2013, 12:51:47 PM »
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 didn’t 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 Lyle’s 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 20° 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 weather…? I found it difficult enough using a map table in good light with a pair of dividers and Lyle’s contour measurement tool.

Maybe I’m missing something so I’d be interested to hear if anyone has had practical experience of using this method.

Hugh

Pete McK

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Re: Getting a fix using the angle of the slope
« Reply #1 on: November 03, 2013, 11:53:15 AM »
No, I don’t 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 Navigator’s Slope Angle Card on the website where you buy them http://www.shavenraspberry.com/navigators-map-slope-angle-tool

Hugh Westacott

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Re: Getting a fix using the angle of the slope
« Reply #2 on: November 04, 2013, 07:12:01 AM »
Pete

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.

I’m 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 let’s 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.

Hugh

MoonMan

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Re: Getting a fix using the angle of the slope
« Reply #3 on: November 04, 2013, 07:48:48 AM »
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.
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captain paranoia

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Re: Getting a fix using the angle of the slope
« Reply #4 on: November 04, 2013, 06:41:16 PM »
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.

Hugh Westacott

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Re: Getting a fix using the angle of the slope
« Reply #5 on: November 04, 2013, 07:11:04 PM »
Surely, the most important principle for someone new to navigation to learn is that the closer the contours, the steeper the slope. It doesn't take very long to learn the pattern of contour lines that indicate that a slope is too steep to be attempted. This will, of course, vary according to age and fitness of the walker. I don't see the point of translating this into a slope angle expressed either in degrees or as a percentage or fraction.

Nobody has yet come up with the answer to the conundrum I posed. If you do not have an altimeter, Lyle suggests on page 154 of his book [that], by measuring the slope angle that you are on and relating this to the contour spacing on your map, you can determine your elevation.. Frankly, if this is all the information that is available, I cannot see how this can be relied upon to give an accurate position fix.

Hugh
« Last Edit: November 13, 2013, 01:59:18 PM by captain paranoia »

John-C

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Re: Getting a fix using the angle of the slope
« Reply #6 on: November 04, 2013, 09:03:31 PM »
Hugh,

I think one key point is that, assuming its the same card, its for 10m intervals as used in the more hilly areas. I live near the West Pennines where the interval is 5m (on the 1:25k) and therefore different to the norm.....not sure if its because its classed as Urban or its the smaller hills.

The description on the web site was updated to note this.
« Last Edit: November 05, 2013, 06:45:10 AM by John-C »

MoonMan

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Re: Getting a fix using the angle of the slope
« Reply #7 on: November 05, 2013, 03:34:53 AM »
Does one need to know the Angle, if he knows the Slope to be, say H= 50, D= 120, therefor Slope, or Incline, is 5 in 12?  The Angle,in this case, is arctan 5/12,which is between 22 & 23 degrees. Railways & Roads use this method, the Gradient. Just another way of expressing the same information. 5/12 in the Tangent Tables is 0.41667. Finding 12 out & 5 up on a Protractor, & extending a line to the rim, will give a fair result, which is how Quadrants were put to use, in centuries past. If you have other tools, put in the time to master them, because nothing as as simple as it first seems, & the more subtle aspects only show themselves to the diligent student.
Keeping Track of where Here is in relation to There.

Pete McK

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Re: Getting a fix using the angle of the slope
« Reply #8 on: November 05, 2013, 08:22:07 AM »
I agree with CP and measure the slope to confirm other techniques, such as slope aspect and usually checking the slope in more than one area.

The area I live in the Lake District is area prone to inclement weather and sudden poor visibility and I have found using the slope angle card in this way works well for me.

Hugh Westacott

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Re: Getting a fix using the angle of the slope
« Reply #9 on: November 05, 2013, 09:09:23 AM »
John wrote:

<I live near the West Pennines where the interval is 5m (on the 1:25k) and therefore different to the norm.....not sure if its because its classed as Urban or its the smaller hills.>

The Ordnance Survey has strict rules on whether the contour interval should be 10m or 5m on 1:25k maps. The fundamental basis is clarity and ease of use. In areas where a 5m interval would make the map too cluttered, the 10m interval is employed. Thus, there is no such thing as a 'normal' contour interval; every sheet uses either a 10m or a 5m contour interval. Great Britain is covered by 470 Explorer sheets. I don't know how many there are in each category but I do know that below the 350° national grid  easting just south of Nottingham, virtually all of the approximately 90 Explorer maps covering that part of England have a contour interval of 5m. The exceptions are Dartmoor, Exmoor, the Welsh Marches and few small, isolated areas such as the Shropshire Hills. North of Nottingham there must be many more on both the east and west coasts of England. I suspect, too, that there will be at least some sheets with a 5m interval along the east coast of Scotland and also in the northeast.

I have number of books on maps and navigation and am astonished how many of them seem to assume that navigation in lowland areas is so easy that it is not worth covering the special techniques that are used. Navigation in the south of England is often more difficult than it is in good conditions in upland areas. This is because you are normally required to follow rights of way which, in little-walked areas, may not be waymarked or even visible on the ground. The most important feature is the field boundary, not contours (it would take a genius to navigate across the East Anglian fens or the Somerset Levels relying entirely on contours!), so a 50k map is not much use. It's most unlikely that you would come to any harm if you got lost because you will not be far from a road or habitation, but it can be a tricky exercise especially in popular waking areas where there is often a maze of unofficial paths. When I was writing footpath guides, I used to survey and navigate my chosen routes using the Outline Edition of the Pathfinder map (the 1:25k predecessor of the Explorer). It was monochrome and omitted contours which made it easy to follow field boundaries and to annotate in the field.

The correction on Lyle's website now states:

Alternatively, by measuring the slope angle that you are on and relating this to the contour interval on your map, you can determine your elevation.

Sorry, I must be dense because I cannot see how, if all you have is the map, the angle of the slope and the slope angle tool, you can determine your elevation. Surely, you must have something such as a linear feature that is marked on the map that will establish the exact line of the route that you are following. I don’t believe that walking on a bearing would be work because of the inherent inaccuracy of this technique, especial when walking on a steep incline.

Incidentally, nobody has mentioned that the contour interval on Harvey maps is 15m with a supplementary contour where considered necessary.

Hugh

Hugh Westacott

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Re: Getting a fix using the angle of the slope
« Reply #10 on: November 05, 2013, 12:33:52 PM »
Look chaps, I’m a practical navigator and am always keen to learn new techniques but I fail to understand two things in the current discussion:

1   Why, other than general interest, would you need to know your elevation? The only answer I can come up with is that you are with someone who is tiring and you need to know whether the summit of the hill or mountain that you are climbing is sufficiently close to carry on, or whether it would  be wise to retreat. Can anyone think of any other reasons?

2   Why should the slope angle be important other than as a matter of interest? I’m sure that my wife’s American workmates would be far more impressed (and sympathetic!) to know that I had dragged her out on a 10.5-mile walk  and we’d climbed 2400 feet than to be told that each of the five hills had a slope angle of 27°.

We all are members of this forum because we are interested in navigation and some members are experts. So will somebody  point out the flaws in the following argument:

3   I believe that, in order to establish your elevation accurately without using an altimeter you can only use the following methods:

   a)   Follow a linear feature such as a field boundary. Estimate by timing or pacing from features depicted on the map, the distance travelled and, therefore, your approximate position. Then use a slope measuring tool to identify a contour on the map that matches that on the device. This is your position identified with reasonable accuracy.

   b)   If you are following a bearing, draw a line on the map along the line of your bearing. Estimate by timing or pacing from features depicted on the map, the distance travelled and, therefore, your approximate position to within an uncertain circle of accuracy. Then use a slope measuring tool to identify a contour on the map that matches that on the device. This is a very approximate position because of the errors inherent in walking on a bearing (accuracy to within 2° is generally considered a remarkable achievement).

I genuinely welcome contributions that can discover flaws in these arguments.

Hugh   

captain paranoia

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Re: Getting a fix using the angle of the slope
« Reply #11 on: November 05, 2013, 07:01:54 PM »
Elevation (slope) can be another clue to help position yourself by using terrain association.

You might be at some spot that has a certain slope aspect, or other geomorphological feature.  There may be a number of matching features on the map, and elevation may be one means by which they can be distinguished.

In winter, elevation can give you a clue as to whether a slope might be prone to avalanche; 25-60 degrees is often given as more dangerous.

> I believe that, in order to establish your elevation accurately without using an altimeter

Oh, you mean altitude...  All this recent astronomical talk has got me thinking of elevation in terms of angles of inclination...

Well, again, it can be another clue to help pinpoint your position using terrain association, or even on a linear feature.

If you're estimating distances using similar triangles methods, and using a distant peak of given altitude, you need to know how high you are (assuming you project horizontally to the 'base' of the distant object; if you don't, you may get errors that I'll have to think about...).

I'll go and read the section of UNM in question, so I know what you're talking about...

Pete McK

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Re: Getting a fix using the angle of the slope
« Reply #12 on: November 06, 2013, 09:18:20 AM »
Hugh, I thought back to when I last used the contour spacing to help determine my location to help you get your head around this technique :)

We were walking across the fells in an area just north of Helvellyn. It was a very wet day, with a low cloud base. Reaching a non-descript summit in the clag I needed to confirm our location, as I knew just to the NW of where I thought we were was Hart Side which in appearance at the top is very similar. I performed slope aspect – when I undertake this technique I always repeat it in two other locations where the aspect changes, then used the slope angle card and measured the contour spacing. Nowhere else on my map, within a radius of 2km, was the slope and the angle the same and I was able to confirm we were indeed on Greeny Ridge and not Hart Side.

http://s1294.photobucket.com/albums/b609/PeteMck/?action=view&current=Hartside_zps29a89e89.jpg

Both procedures takes practice and I use them in combination to good effect.

Hugh Westacott

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Re: Getting a fix using the angle of the slope
« Reply #13 on: November 06, 2013, 12:28:42 PM »
Pete

Many thanks for your attempt to clarify matters. Unfortunately, your example doesn’t really assist me. To start with, I’m a bit confused because Greeny Ridge is not named on either the Landranger or Explorer map; do you mean Green Side? Also the arrow you used to take the aspect of the slope is located on an unnamed eminence with a spot height of 795m, but if so, Hart Side is to the NE and not NW as stated in your post. In any case you knew your position to within a kilometre (and probably much less).

Let’s assume that you took the aspect of the slope along the fall line indicated by the arrow. In doing so you established the line that you were on. By taking a different aspect you established your position which reasonable accuracy. If you took two bearings you must have been on or close to the summit. A glance at the map shows that the fall lines on Hart Side are not on the same bearings, so all you had to do was to head NE to Hart Side. The height was largely irrelevant and I can’t see why it was necessary to measure the distance between contours..

I still maintain that Lyle’s description of how to establish your height by measuring contour intervals won't work in all cases. I believe that you must be following a linear feature, or a bearing combined with pace counting or timing. Even so, this would not give you an accurate fix and I’m sceptical whether measuring the contour interval would always be reliable. The best way would be to take a couple bearings on distant objects (this may not be possible in poor visibility, or take the aspect of the slope and then read off the height from the map.

I'm hoping Lyle will be able to clarify how and when the technique can be used.

Hugh
« Last Edit: November 13, 2013, 02:02:36 PM by captain paranoia »

Pete McK

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Re: Getting a fix using the angle of the slope
« Reply #14 on: November 06, 2013, 12:54:53 PM »
Well, as I stated Hugh, the techniques work for me and maybe you should practice with them more - I can be of little further help for you.
Greeny Ridge is the local name for the area we were on.