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Horizontal Distance vs Hypotenuse Distance

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Horizontal Distance vs Hypotenuse Distance

Postby lodidodi » Wed Nov 28, 2012 2:36 pm

Everyone uses distance and elevation gain for their hikes but I'm assuming everybody uses horizontal distances from a map. If you take these two measurements and assume it's a right triangle then you can use pythagoream theorm to calculate your hypotenuse distance.

For example I took the East slope approach for Pikes Peak where the distance is 26 miles with 7,500 ft of elevation gain and the hypotenuse distance was 26.15 miles. It is probably more because I used the elevation gain and if you have losses then the distance would be greater. I know it doesn't matter but that's about an eight of a mile further than you thought you hiked. Yes, I am bored at work by the way, now do I add or subtract the the curvature of the earth?

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Re: Horizontal Distance vs Hypotenuse Distance

Postby Voodoo302 » Wed Nov 28, 2012 4:14 pm

You'd need the ellipsoid of the Earth because if it were a perfect sphere you'd have no terrain and therefore no elevation gain so it'd be moot...as for the additional distance I guess you'd compare diameter X pi X (distance in degrees/360) to the map distance. Buuuut I have a feeling this is going to be FAR less than the hypotenuse adds.

However I think many of the stated trail lengths are already measured and given as distance on the ground.

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Re: Horizontal Distance vs Hypotenuse Distance

Postby GregMiller » Wed Nov 28, 2012 4:28 pm

Something to consider, if you're assuming that the distances given are on a flat earth - how do you account for different slopes? While some trails may be fairly consistent class 1 throughout their length, others are long easy approaches followed by near vertical class 4.
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Re: Horizontal Distance vs Hypotenuse Distance

Postby ChrisRoberts » Wed Nov 28, 2012 9:16 pm

Voodoo302 wrote: Buuuut I have a feeling this is going to be FAR less than the hypotenuse adds.

Considering we have 26 miles from TH to summit on the horizontal plane, my sloppy math gives around 26.000036 miles. A better estimate would probably be around 26.00005 mi

Can anyone say "dee theta"?
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Re: Horizontal Distance vs Hypotenuse Distance

Postby GerryRigged » Wed Nov 28, 2012 9:32 pm

Now if you are measuring the distance with a GPS you whould get very very close to actual ground/slope distance since a GPS measures the distance between two points every few seconds. Since most people don't walk more than say two miles per hour the distance between two points witha GPS will be very short. So even tough the distance might be a horizontal disitance it's a short one. By adding all the very short distances together you will end up with a very accurate ground/slope distance. :-D

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Re: Horizontal Distance vs Hypotenuse Distance

Postby Jim Davies » Wed Nov 28, 2012 9:58 pm

Unfortunately for your calculations, Barr Trail isn't quite 26 miles r/t, but only 25.6 or so (depending on who you ask). The marathon starts and ends at Soda Springs Park (which is about a mile down the road from the Barr TH), and straightens out the first part of the trail by using an alternate route.

GPS measurements could take 3-D distance into account, but they're fundamentally off anyway; they tend to cut switchbacks, in that the periodic samples will interpolate straight lines onto curving trails.
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Re: Horizontal Distance vs Hypotenuse Distance

Postby MountainHiker » Wed Nov 28, 2012 10:38 pm

Jim Davies wrote:GPS measurements could take 3-D distance into account, but they're fundamentally off anyway; they tend to cut switchbacks, in that the periodic samples will interpolate straight lines onto curving trails.
I walk off the end of switchbacks to pee, so I would have to add distance!
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Re: Horizontal Distance vs Hypotenuse Distance

Postby Bean » Thu Nov 29, 2012 7:40 am

Jim Davies wrote:GPS measurements could take 3-D distance into account, but they're fundamentally off anyway; they tend to cut switchbacks, in that the periodic samples will interpolate straight lines onto curving trails.


A number of units have a 1-second sampling option, and are repeatable within .25% over the same course in my experience.
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Re: Horizontal Distance vs Hypotenuse Distance

Postby crossfitter » Thu Nov 29, 2012 10:09 am

The curvature of the earth is completely insignificant at those scales. The difference between walking 26 miles along the surface of the earth and burrowing straight through the ground is just under 3 inches (on level ground, treating the earth as a sphere).
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Re: Horizontal Distance vs Hypotenuse Distance

Postby Patinator » Thu Nov 29, 2012 12:31 pm

Have you ever used the parallax method? It is pretty good if you now the approximate size of the object in the distance.

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Re: Horizontal Distance vs Hypotenuse Distance

Postby tlongpine » Thu Nov 29, 2012 4:56 pm

"Everyone uses distance and elevation gain for their hikes but I'm assuming everybody uses horizontal distances from a map."

Why are you making that assumption?
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Re: Horizontal Distance vs Hypotenuse Distance

Postby ChrisRoberts » Thu Nov 29, 2012 7:42 pm

Thats the assumption I've always made.
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