[pct-l] GPS and Pi

[msaenz at mve-architects.com (Mike Saenz)]

Ah....
A mathematician!
But you assume the second hiker is consistently walking abreast the entire circumference.

Now assume (for ease of illustrative purposes) a 10 mile long trail.
Hiking in a straight line (toe to heel), one could surmise that said hiker would hike exactly 10 miles.
Now, assume a 3' stride. (again for ease of illustration) and let's make said hiker take diagonal step every other stride.
Each time the hiker takes a diagonal step, he travels roughly 4.25 feet instead of the 3' straight step. (assuming a 45 degree diagonal step, instead of a straight toe-to-heel step)
10 miles = (5280x10) = 52800 feet.
52800 / 3 (stride) = 17600 strides
17600 strides / 2 (every other step) = 8800.
8800 strides x 1.25 = 11000 feet, .48 of a mile.
That's almost a 5% increase in mileage.

That's an additional 132 miles over the course of the PCT...

Ok. Ok.

All academic, maybe.
My original point is, actual mileage my vary (sounds like an ad for a Toyota!),
I would bet that a 10 mile measurement with a wheeled odometer could, and probably would, vary somewhat each time you hiked and measured with it.
So. Also, would a GPS measure different distances on the same trail, as the GPS unit moves a foot sideways here, a foot sideways there...

Distance measurement isn't the most informative data a GPS can give you anyway. For me, the average moving speed has been the most useful. I haven't been off trail so deep that I need to check my location with the GPS. If I'm trying to locate a spring or cliff or some other interesting feature, I have found that I can pinpoint my location on a topo map much faster by checking my elevation on the GPS and seeing where the trail intersects that particular contour line. Works just about every time! Only once have I needed to break out my topo divider to project long/lat coordinates on my map to find out where I was at. But that still worked pretty well.

Fun stuff...

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 -----Original Message-----
From: 	SnoLepard [mailto:SnoLepard@TrekkingKats.com] 
Sent:	Monday, April 12, 2004 11:35 AM
To:	pct-l@mailman.backcountry.net
Subject:	[pct-l] GPS and Pi

I'd just like to chime in about wheeling trail mileages. It concerns the difference in distances wheeled on the outside of the curve and the inside of the curve.

Using pi the formula for the circumference of a circle is pi times the diameter. Therefore if there were a hypothetical trail around a mountain and the trail was a circle ten miles in diameter the trail would be 31.415 miles long. If two hikers were to walk abreast at 3 feet from center of hiker to center of hiker, the hiker on the outside would hike less than 19 feet farther than the inside hiker over the entire loop trail.

Why is this? Because the diameter of the inside trail is 52800 feet and the diameter of the outside trail is 52806 feet, only six feet farther out. Two times the three foot difference. Multiply 52800 by pi and get 165,876.09 feet. Multiply 52806 by pi and get 165,894.94 feet. The difference is 18.849 feet.

Even if two hikers walked around the Earth at the equator, one on the ground and one on a wall three feet high, the hiker on the wall would still only hike 19 feet farther.
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