## Horizontal Distance vs Hypotenuse Distance

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**2**of**2**• 1,**2**- TravelingMatt
**Posts:**1311**Joined:**Wed Jun 29, 2005 10:17 am**Location:**Dillon

### Re: Horizontal Distance vs Hypotenuse Distance

No map will show every curve in a trail, nor will GPS account for every curve, as mentioned above.

I estimate distances by some consensus of ascent time (~2.3 mph on easy Class 1), descent time (~3 mph on easy 1) and map distance + fudge factor. Naturally my ascent and descent times depend on terrain, my physical condition that day, rest stops, pack weight and so on. I spend a lot of my downhill time deciding whether I'm going 2.7 mph or 2.8. I need to get out more. Or is that less?

I estimate distances by some consensus of ascent time (~2.3 mph on easy Class 1), descent time (~3 mph on easy 1) and map distance + fudge factor. Naturally my ascent and descent times depend on terrain, my physical condition that day, rest stops, pack weight and so on. I spend a lot of my downhill time deciding whether I'm going 2.7 mph or 2.8. I need to get out more. Or is that less?

Expect to go the wrong way some of the time. -- Gerry Roach

- pseudoghost
**Posts:**91**Joined:**Sun Aug 15, 2010 8:16 pm

### Re: Horizontal Distance vs Hypotenuse Distance

Honestly, unmarked switchbacks and other trail variations add up to more than the difference between the horizontal distance and the hypotenuse distance. This is even true for relatively short trails, like Bierstadt.

- lodidodi
**Posts:**675**Joined:**Wed Dec 27, 2006 12:07 am**Location:**Aurora, CO

### Re: Horizontal Distance vs Hypotenuse Distance

tlongpine wrote:"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?

Surveying uses horizontal distance to make maps and I've been trying to find out if GPS calculates the actual "slope" (hypotenuse, ground, surface, or true) distance or if a gps calculates horizontal distance as well. I think GPS's calculate horizontal distance because the system is based on UTM coordinates and then it basically takes the difference between the two readings of coordinates and calculates your distance. I don't know if it adds in the elevation change. If you step off a 5,000 foot building is it going to show you traveled 1 foot in distance or 5,000 ft? I found an article by Conoco about pipe lengths and it took them 2 years to develop a software to put gps data into to calculate actual pipe lengths. I don't know if Garmin (or any other brands) has built this formula into their gps's. If a surveyor uses a total station, it will give a reading for slope distance and horizontal distance. Maybe a surveyor or somebody in this field can clear this up for me?

- Dancesatmoonrise
**Posts:**2146**Joined:**Fri Sep 25, 2009 8:47 pm**Location:**Colorado Springs

### Re: Horizontal Distance vs Hypotenuse Distance

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Last edited by Dancesatmoonrise on Thu Dec 06, 2012 6:10 pm, edited 1 time in total.

- jdorje
**Posts:**1086**Joined:**Wed Jun 16, 2010 3:33 pm**Location:**Crestone, CO and/or Chapel Hill, NC

### Re: Horizontal Distance vs Hypotenuse Distance

lodidodi wrote:Surveying uses horizontal distance to make maps and I've been trying to find out if GPS calculates the actual "slope" (hypotenuse, ground, surface, or true) distance or if a gps calculates horizontal distance as well.

Any competent GPS software should use straight-line distance between two points (what people are calling the hypotenuse). This requires very simple math from the ECEF coordinates which are what GPS hardware outputs.

That said, I have no idea. The android GPS interface does not give programmers the ECEF data (which is easy to calculate from the lat/lon/alt), but does provide a complicated function to determine the earth-surface distance between two points. In short, it's intended for 2d use, and writing an android app to show the straight-line distance takes considerably more work than writing one to show the earth-surface distance.

Most trail distances that are accurately measured are probably done so by running a wheel along the trail and counting the revolutions. At least, that's how I would do it; bicycles can do this automatically of course. Done correctly, this would give a very accurate distance.

-Jason Dorje Short

- Jim Davies
**Posts:**7147**Joined:**Thu Jun 08, 2006 2:23 pm**Location:**Colorado Springs

### Re: Horizontal Distance vs Hypotenuse Distance

Since the error in GPS altitude measurement is so high, including that in the point-to-point distance calculations could throw them off quite a bit.

Some people are afraid of heights. Not me, I'm afraid of widths. -- Steven Wright

- jdorje
**Posts:**1086**Joined:**Wed Jun 16, 2010 3:33 pm**Location:**Crestone, CO and/or Chapel Hill, NC

### Re: Horizontal Distance vs Hypotenuse Distance

Jim Davies wrote:Since the error in GPS altitude measurement is so high, including that in the point-to-point distance calculations could throw them off quite a bit.

Indeed. Significant smoothing would be required.

-Jason Dorje Short

- Rarefied
**Posts:**155**Joined:**Wed Sep 29, 2010 1:52 pm

### Re: Horizontal Distance vs Hypotenuse Distance

lodidodi wrote:If you step off a 5,000 foot building is [the GPS] going to show you traveled 1 foot in distance or 5,000 ft?

A version of that scenario can be developed in MapSource. First, perform an overzoom (80' setting) on the Independence Monument outside Grand Junction. Using the distance tool, start at the 5700' contour at/near the summit and proceed southeast to the nearby 5400' contour for a vertical drop of 300'. (Make your distance line perpendicular to that contour.) Yet, the distance tool will show a value of 75-80' depending upon how you draw that line -- that's the horizontal distance. (By the way, at 300' & 80' that's a 75 degree slope -- and it looks it!)

To state it another way, your GPS would show (assumes adequate resolution) you had traveled 80' whether you rappelled down to 5400' or flew a hang-glider off the summit and maintained 5700' until you were precisely over the same spot. (For a larger scale version, proceed due south from Quandary's summit to the north shore of the larger of the Blue Lakes and compare the numbers that way. Or for that matter, any number of other locations in the state will also work.)

R

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