Dilemma of an Insane Young Adult

Discuss geopolitical area highpoints, prominence, and similar lists.

Dilemma of an Insane Young Adult

Postby Swithich » Sat Apr 30, 2011 1:27 am

So I was looking at the steepness measure and calculation stats today and something really bothered me. I found that Devils Tower is 40th on the list. How can something that is nearly straight up on all sides be so low on the steepness list? The answer (and I could be wrong on this) appear to be because the steepness measure is taken from a point, and a defining characteristic of Devils Tower is that it has a summit area. This effectively means that when calculating steepness we are increasing our horizontal value associated with that angle of steepness. The end result is a diminished steepness measure for anything that looks less like a spire, and more like a mesa. However, few would argue that something that something like Devils Tower is like a spire in that there is no way to get up it easily (that is, there is no real line of weakness for accent).

A further disturbing point is that it seems much harder to come up with a quantitative way of fixing such an issue (assuming one considers this an issue). My own method for calculating steepness that I had hoped to develop using PDEs and the Finite Difference Method, does not solve the issue either. Unless, I somehow cut out the summit area from the discretization. But to define a summit area is a tricky task and would likely require and individual review of every summit that might fit the definition.

I've really run into a wall here. Most of you probably don't care, but this is really bothersome to me. Comments?
Swithich
 
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Re: Dilemma of an Insane Young Adult

Postby TWorth » Sat Apr 30, 2011 4:02 pm

Switch - I run the steepness calcs featured on this site; thanks for checking them out.

The flat summit area does negatively affect the Devils Tower angle measurement, but not too severely. #42 out of ~60,000 peaks tested in the western states is not a low ranking in my view. Almost all the peaks ranked above it appear to have numerous vertical sides in the same height range as DT, mostly desert towers. Many of them are equally or more difficult to climb than DT.

An alternate steepness measure is "steepest minimal angle", looks like Devils Tower does better there(#8 overall, western states) see -
http://ned-files.com/listall.cgi?list=3

One option to fix the insane mesa top dilemma is to take steepness readings from all points on and along the edge of a flat mesa and go with the highest steepness reading. Other is to "remove" the mesa top, as you say, by using a floating measurement point along a mesa rim to calculate drop. Both methods have major problems so I haven't tried writing any algorithms to compute steepness other than using the summit coordinates, but feel free to have a crack at it if you'd like.

Don't have the time to go more in depth on the subject right now, but some of this is covered on a website I put up: http://ned-files.com

-Tim W
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