Author Topic: Getting a fix using the angle of the slope  (Read 10600 times)

Hugh Westacott

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Re: Getting a fix using the angle of the slope
« Reply #15 on: November 06, 2013, 01:53:02 PM »
Pete

I genuine appreciate your attempt to address the problem I've raised. Since you still seem to be missing the point that I'm trying to make, it leads me to suppose that I have not expressed it sufficiently well.

And please understand that I'm not being critical of the navigational methods that you use. I've been wandering about our British hills  for more than sixty years, and taught navigation techniques for a quarter of a century, so would not dream of criticizing anyone who uses a technique that works for them.

Hugh
« Last Edit: November 13, 2013, 02:03:56 PM by captain paranoia »

Pete McK

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Re: Getting a fix using the angle of the slope
« Reply #16 on: November 06, 2013, 02:09:48 PM »
No offence taken whatsoever Hugh, this is the most polite forum by far on the web :) I really do think you should keep using the techniques, I know that I find this helps make the penny drop for me ;)

captain paranoia

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Re: Getting a fix using the angle of the slope
« Reply #17 on: November 06, 2013, 06:53:29 PM »
> In any case you knew your position to within a kilometre (and probably much less).

Think this may be the important factor here.  I don't think that slope angle is good at establishing your position over a large area (unlike other methods such as resection).  In my view, it's a supplemental method that can help to aid location in a small area; if I know the slope aspect, and it's a convex hill, can I use the angle of the bit I'm on to find out how far up the hill I am?  In the case of Pete's example, the slopes seem fairly linear (i.e. uniform gradient), especially around the arrow.  Slope aspect looks pretty tenuous, too...  Oh, hang on, there's a gulley to the W of the arrow, where the contour lines are discontinuous.  and elsewhere.  Oh... the contour lines are very unhelpful, and would easily fool a slope tool used naively.  Or someone like me not looking carefully...

It's pretty hard to accurately measure the slope from the map, and can be equally hard to measure the slope of the ground (which may have local undulations you have to average out in your head).  So I don't think slope angle is ever going to be particularly accurate.  I think it may best be considered as giving another clue, rather than a precise position.

I recall walking into the Mamores once, from Mamore Lodge, and fixing my position on the path by looking across the valley to an identifiable feature that was at the same height as we were, and using that height to locate us on the continuously ascending path we were on.  But that's a case of using a linear feature to fix position in quite a large area.

Hugh Westacott

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Re: Getting a fix using the angle of the slope
« Reply #18 on: November 07, 2013, 09:05:19 AM »
Captain Paranoia has, in his customarily succinct summary, hit the nail on the head!

I shall make one last attempt to clarify the point I’m trying to make.

I have a copy of The Boy Scouts of America Handbook in which is described a method of calculating the height of a tree. This is an interesting exercise that some boys would find fascinating but I can’t imagine ever employing this skill although I can see that the method will work.

Similarly, on page 169 of the Ultimate Navigation Manual, Lyle describes a method of calculating how far away you are from an object by using what he describes as ‘stereoscopic ranging’. I can understand that this method will work although I can’t imagine why I would need to use it, but readily accept that others may find it helpful.

The problem with Lyle’s description of how to establish your height on a slope (p156) is that it won't work in all situations:

1    You are walking up a hill choosing the easiest route so you are probably not walking in a straight line but are wandering about a bit. You may be as much at 50 metres on either side of the direct route making a total horizontal distance of at least 100 metres.

2   Within this 100-metre area of probability, the gap between contour lines can change making it impossible to identify two contours with the slope angle tool.

3   The problem can be largely resolved if you are following a linear feature marked on the map such as a fence or a path, or you take the aspect of the slope and draw the fall line on your map. Then you don’t have to worry about the gap between contour lines changing because there is no horizontal area of probability.

4   But you still have to identify the contour line that you are on. It’s not unusual for two sets of contour lines to have the same gap between them. If this is the case, you won’t know which one you are on.

5   This is why I believe that the technique, as described, cannot be relied upon to give an accurate fix of your height. 

A much more reliable method would be to get a fix using the standard procedure of taking two compass bearings on two features that can be identified both on the map and on the ground and transferring them onto your map (this might not be possible in conditions of poor visibility). Where the lines intersect is your position and you can read off the height from the figures on the contour lines. No need to use a slope angle tool. It’s probably a quicker method and certainly more reliable.

Hugh
« Last Edit: November 13, 2013, 01:53:54 PM by captain paranoia »

captain paranoia

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Re: Getting a fix using the angle of the slope
« Reply #19 on: November 13, 2013, 05:19:13 PM »
Hugh,

I'll reiterate that I think this is a technique that can sometimes be used to estimate your position.  Like many navigation techniques, it's not very accurate, because we cannot accurately measure slope angle from map or ground, and the resulting error bounds of the measurement mean that a precise position fix is unlikely.  Thus, like many of the other techniques, we have to use it in combination, to fuse a number of position estimation methods into a more reliable estimated position*.  Even then, I don't think it's ever likely to give us a result as accurate as a good resection/triangulation (which, itself, has accuracy issues when taking bearings, identifying features, and plotting the bearings). 

A good example of where the technique would not work would be climbing up a ridge with uniform slope.  Whilst you'd have a linear feature or well-defined slope aspect (the ridge), you would not be able to determine your height or position using the slope angle, because the slope angle would be the same all the way up the ridge.  You would have to determine your height by other means.

 It's certainly true that the technique can be used, just not in all situations...  So I think only a minor revision of the UNM text would be required, along the lines of 'the technique can sometimes be used to provide an estimated position provided the slope angle is sufficiently unique'.

* By the way, even a GNSS receiver does this sort of fusion; it makes estimates of the reliability/accuracy of the signals from each satellite (based on signal strength and position in the sky), and weights the solution in favour of the better signals.  The resulting position can be considered a strangely-shaped 3-dimensional probability density function (PDF), which, in turn, can be used to indicate the dilution of precision (DOP, or 'goodness of solution'); the broader the PDF, the larger the DOP, and the sharper/narrower the PDF, the lower the DOP.

captain paranoia

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Re: Getting a fix using the angle of the slope
« Reply #20 on: November 13, 2013, 06:06:59 PM »
> Where the lines intersect is your position and you can read off the height from the figures on the contour lines. No need to use a slope angle tool. It’s probably a quicker method and certainly more reliable.

But if you can perform a resection/triangulation, you won't need to use slope aspect & slope angle or height to find your position...  As Lyle says in paragraph 2 of p156: "if you are relocating using slope aspect, you probably have a poor GNSS signal, so don't use its satellite altimeter"; in other words, slope aspect & height are somewhat 'last resort' solutions, and other methods are preferable and more accurate.  It may be that you cannot see remote landmarks to perform a resection (as in Pete's earlier example).

Pete McK

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Re: Getting a fix using the angle of the slope
« Reply #21 on: November 14, 2013, 07:29:49 AM »
Spot on Captain. It is neither a mainstay technique nor one which should be used in isolation. But in certain circumstances, such as those frequently encountered in the Lake District, sudden low cloud and reduced visibility, the technique, in combination with slope aspect and terrain association, works well :)

Hugh Westacott

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Re: Getting a fix using the angle of the slope
« Reply #22 on: November 14, 2013, 08:05:41 AM »
Some of you may have noticed that this thread disappeared for a time because exception was taken to the tone of some of my contributions to the discussion. At first, I was taken aback because I had no intention of being either offensive or disrespectful, and it was only when I read them again that I realized that they could reasonably be described as abrupt, even abrasive. It happened because I was cross with myself as I seemed unable to describe sufficiently well the point I was trying to make.

In a previous career I had to write abstracts of articles. The art of abstracting requires an article to be described accurately and dispassionately and in as few words as possible, so adjectives and adverbs are used only where absolutely necessary. This technique, although useful to clarify one's thoughts, is not suitable for use in a forum post.

As the police would say, I've been given words of advice! My contributions to this thread have been edited to make them more emollient yet still retain the points I was trying to make, and I have sent a private apology and explanation to Lyle.

Contritely

Hugh

MoonMan

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Re: Getting a fix using the angle of the slope
« Reply #23 on: November 15, 2013, 08:37:06 AM »
Now that we have come this far into the discussion, I relate this experience. Not long ago,I took an off road walk onto a wooded ridge, with a  1: 50 map. I always knew my approximate location, but could never get an exact fix, Even tho there are plenty of landmarks in the distance, to get a bearing from, the ridge is heavily wooded, so visibility was restricted to the nearest thicket of down slope tree tops. The  ridge was more or less of like aspect in any given section of the walk. I came to a point where I was trying to reckon when to turn onto the next leg, but found that I had not gone as far as necessary. It did not go as planned, but I was able to follow the ridge to my starting point. If I had been trying to reach a specific location, I'd have been lost, or doing some exploratory work. That night, I spent some time at reviewing my route, with Google maps [all those trees] but I could not be certain of my exact route. I did mark my path on the way in. In short, knowing the exact location is not as important as knowing the general route & lay of the land, but it can make a big difference.  :'(
Keeping Track of where Here is in relation to There.