View Full Version : AT Actual Walking Length

Ham-Bone

02-21-2011, 11:37

Went out on my first hike of the year last weekend. Buddy and I had an interesting conversation. Has anyone ever calculated the actual lenth of the trail taking slopes into account? If 2,170+ is the flat distance on a 2D map, then the actual length that you walk is ________ if it were stretched flat.

For a very long time the distances were measured by a wheel.

LoneRidgeRunner

02-21-2011, 12:05

Went out on my first hike of the year last weekend. Buddy and I had an interesting conversation. Has anyone ever calculated the actual lenth of the trail taking slopes into account? If 2,170+ is the flat distance on a 2D map, then the actual length that you walk is ________ if it were stretched flat.

I've often wondered that myself on other trails also..Having seen signs with distances marked from place to place and then seemingly walked much farther than that does tend to make one wonder it it's flat map distances and not taking slope error or the fact that every little curve and crook in the trails aren't shown on maps. Or could it be distances calculated by GPS routes, again not accounting for all the crooks and curves between the different way points or the slope error?

Someone said for a long time the distances were measured with a wheel. I suppose that would be the most accurate method possible.

You asked a good question that I would like to know the answer too also. Not that it REALLY matters because the distance we actually walk be the same regardless of whether or not we know the accurate distances.

I'm pretty sure the distances account for elevation changes because I'm very attuned to how fast I'm moving and how long it takes me to cover a certain distance on all types of terrain.

That's not to say that AT mileage signs are accurate +-/ 10' or anything but they're close enough for government work IMO.

Jim Adams

02-21-2011, 12:23

It has been measured with a wheel and I also believe a GPS. Mileages are for the exact walking distance. I remember a year when Warren Doyle was pushing a wheel, 1990 I think and the mileage that year was 2,168.

geek

Slo-go'en

02-21-2011, 12:32

I belive distances are still measured by wheel, which is the only way to get a pretty accurate measurment. GPS hasn't been around long enough to be used for trail signage mileage.

Distance shown on trail signs is rounded to the nearist .1 mile and sometimes aren't updated if there was a reroute. And we all know that at times there are short 3/10ths of a mile and sometimes there are looong 3/10ths of a mile (usually at the end of a long day when that 3/10ths is up hill to a shelter!)

LoneRidgeRunner

02-21-2011, 12:32

It has been measured with a wheel and I also believe a GPS. Mileages are for the exact walking distance. I remember a year when Warren Doyle was pushing a wheel, 1990 I think and the mileage that year was 2,168.

geek

WOW..That had to be tedious pushing a wheel that far..also measuring with a GPS and taking measurements at every turn would have been tedious also. Of course the GPS couldn't measure the slope error. I suppose the operator of the GPS could have counted contour lines and figured the slope error. There is a mathematical formula to do that. Again, a very tedious task for over 2100 miles.

Ham-Bone

02-21-2011, 13:20

Good to know....I didn't expect that answer. This means that the elevation profiles that I look at can't be extremely accurate since they are plotted on a grid with equal 1 mile increments that correlate with AT mile markers. Since the AT mile markers are wheel-measured (thus actual length including slopes), then the grid marks should...............Ah nevermind, this is giving me a headache! :eek:

Good to know....I didn't expect that answer. This means that the elevation profiles that I look at can't be extremely accurate since they are plotted on a grid with equal 1 mile increments that correlate with AT mile markers. Since the AT mile markers are wheel-measured (thus actual length including slopes), then the grid marks should...............Ah nevermind, this is giving me a headache! :eek:

Also, read up on vertical exaggeration as it relates to the elevation profiles on your maps.

The distances listed (by and large) account for elevation changes.

If you think about it, it'd be easier to push a wheel than it would be to figure out flat line distances through the mountains.

Ham-Bone

02-21-2011, 13:26

Also, read up on vertical exaggeration as it relates to the elevation profiles on your maps.

The distances listed (by and large) account for elevation changes.

If you think about it, it'd be easier to push a wheel than it would be to figure out flat line distances through the mountains.

I see your location is Erwin. That is where I hiked this weekend (to and fro Erwin).

There was one stretch (I can't remember exactly where it was... northern part of the trail somewhere) where the mileage signs were WAY off. They were all about 30% short of actual mileage. I wonder if some industrious trail maintainer replaced all the exiting signs with GPS mileage that did not account for elevation changes. It wasn't a big deal, but it was a full day of "God dammit. I know I have walked [X] miles by now!" Anyone recall that? Vermont maybe?

Linesman

02-21-2011, 13:44

If someone could measure the AT taking all bends and bumps into account then the measured length would be much higher, perhaps tens of thousands of miles. Measuring any kind of highly irregular path like a coast line is tricky because the more closely you measure the longer it gets.

Megapixel

02-21-2011, 13:47

this brings up another thing i've often thought of... has anyone an idea of how long a thru hiker actually walks, i.e. in town, through the grocery store, to the springs, to the bathroom, getting lost, etc... maybe 3000???

Cool Hands

02-21-2011, 13:49

Good old high school math comes to the rescue! Pythogorean Theorem, people. On wikipedia, the horizontal component of the trail is given (2,180 miles) along with the vertical component (475,200 feet of elevation change). So what do you do? Add the squares of each length, find that number's square root, and that is the actual distance, taking into account the rises! (If I'm wrong, someone correct me here...)

Therefore, the length would be (2,181miles*5,280feetpermile)^2 + (475,200feet)^2 = 132,610,885,862,400 + 225,815,040,000 = 132,836,700,902,400. The square root of this is 11,525,480.51, and divided by 5,280 feetpermile gives us 2,182.9 miles.

Only an extra two miles, but pretty interesting! (I realize after doing this that working with miles instead of feet would have been way easier... whoops.)

NiteRaven

02-21-2011, 14:01

Cool hands: where did you get that elevation change number? I once heard the A.T. is equivalent of ascending and descending Mount Everest 7 times, but according to your number it's actually a bit over 8.

Cool Hands

02-21-2011, 14:04

I found this number via wikipedia, which cites the "Appalachian Trial Database" as its source for the number. But now that I think of my little equation, it sounds too simple.... I'm not sure if I'm correct.

Memphis Tim

02-21-2011, 14:04

If someone could measure the AT taking all bends and bumps into account then the measured length would be much higher, perhaps tens of thousands of miles. Measuring any kind of highly irregular path like a coast line is tricky because the more closely you measure the longer it gets.

Absolutely. Remember it's only a 1400 mile drive from Amicola to Baxter State Parks. Also keep in mind that every step you take off the center line of trail doesn't count. I wouldn't be at all surprised if the average thru-hiker actually ends up walking at least twice the recorded length of the trail.

Absolutely. Remember it's only a 1400 mile drive from Amicola to Baxter State Parks. Also keep in mind that every step you take off the center line of trail doesn't count. I wouldn't be at all surprised if the average thru-hiker actually ends up walking at least twice the recorded length of the trail.

And don't forget the curvature of the earth. The further north you go, the shorter a mile is.

Cool Hands

02-21-2011, 14:08

If someone could measure the AT taking all bends and bumps into account then the measured length would be much higher, perhaps tens of thousands of miles. Measuring any kind of highly irregular path like a coast line is tricky because the more closely you measure the longer it gets.

Tens of thousands? You're joking. Hundreds of extra miles? Still probably not. A few dozen more miles? Maybe.

Memphis Tim

02-21-2011, 14:24

Any mathematicians out there feel free to correct the recollections of this old history major but few years ago I watched a fascinating documentary on fractal geometry. In it they discussed the paradox of infinite regression when trying to map an irregular contour such as coastline. Since you can always reduce the scale to find more to measure it turns out that the contour of any island is infinitely long. I don't know about that but I think any thru-hiker will tell you that is, without a doubt, true about the Appalachian Trail :-?.

Cool hands: where did you get that elevation change number? I once heard the A.T. is equivalent of ascending and descending Mount Everest 7 times, but according to your number it's actually a bit over 8.

I had always heard it was 8 times...

And don't forget the curvature of the earth. The further north you go, the shorter a mile is.

I call BS on that one!

walkin' wally

02-21-2011, 21:23

When a maintaining club does a relo the difference in distance from the old to to the new is recorded and sent to the ATC. Thats why the total distance changes nearly every year.

I'm pretty sure the distances account for elevation changes because I'm very attuned to how fast I'm moving and how long it takes me to cover a certain distance on all types of terrain.

That's not to say that AT mileage signs are accurate +-/ 10' or anything but they're close enough for government work IMO.

Because a hiker inevitably will weave somewhat from side to side in the trail corridor - avoiding puddles, icy patches, walking around boulders, etc., the "wheel method" probably ends up giving the minimum distance one might ever hike on the trail. I think a couple percent additional distance above the wheel figure would be a fair estimate.

... the vertical component (475,200 feet of elevation change).

Cool hands: where did you get that elevation change number? I once heard the A.T. is equivalent of ascending and descending Mount Everest 7 times, but according to your number it's actually a bit over 8.

For the record, Everest's base to peak stature is about 12300 feet. Base camp west of the summit (for Hillary and Norgay's ascent, the most common route) is at 17,700', and the summit is at 29,029'. So 475.2K would be just over 19 Everest round trips of elevation change. Just saw a superb British documentary of the initial successful ascent, The Conquest of Everest. Great film - highly recommend it. Got a hold of it from the local library as part of this set: http://www.amazon.com/Into-Thin-Air-Everest-Mountain/dp/B00000IML4 .

Awol2003

02-22-2011, 00:21

Ham Bone, the distance that you see published in guidebooks is intended to account for ups and downs and twists and turns. There is no such thing as a "true" distance of the trail, only good approximations. For such a long trail, even the word "approximation" implies more accuracy than is possible. The published distance is more like a consensus.

GPS will usually measure too short. Wheels will usually measure too long (they travel more like an ant than a person), and wheels return useless values if not carefully calibrated and maintained. I plan to include a little about trail measurement in my talk at Trail Days this year.

Jim Adams

02-22-2011, 00:22

There was one stretch (I can't remember exactly where it was... northern part of the trail somewhere) where the mileage signs were WAY off. They were all about 30% short of actual mileage. I think this is the stretch before South Kinsman in N.H. Seems like you walked for ever for about 11 miles when the signs said 6.6 miles.:confused:

Cool hands: where did you get that elevation change number? I once heard the A.T. is equivalent of ascending and descending Mount Everest 7 times, but according to your number it's actually a bit over 8. I remember someone adding all of the elevation gains going NOBO and it totaled around 68 vertical miles.:eek:

I belive distances are still measured by wheel, which is the only way to get a pretty accurate measurment. GPS hasn't been around long enough to be used for trail signage mileage.

I remember DellDoc measured the trail via GPS...2002? The GPS would also read elevation gains and loses if it had a barometer or barametric altimeter in it and would adjust the distances on the readout.:cool:

geek

Captain Blue

02-22-2011, 00:28

And don't forget the curvature of the earth. The further north you go, the shorter a mile is.

I call BS on this too!

10-K: Support this claim with some facts.

Jim Adams

02-22-2011, 00:33

I call BS on this too!

10-K: Support this claim with some facts.

I don't think that it would be shorter but should be closer to level.:-?

geek

BobTheBuilder

02-22-2011, 00:56

I call BS on this too!

10-K: Support this claim with some facts.

Just look at Greenland on a map. It's way north, and looks like it's the size of Texas, but it's really the size of Rhode Island. You can walk across it in a couple of hours! Another lie - it's not really very green!

Ham-Bone

02-22-2011, 17:48

Ham Bone, the distance that you see published in guidebooks is intended to account for ups and downs and twists and turns. There is no such thing as a "true" distance of the trail, only good approximations. For such a long trail, even the word "approximation" implies more accuracy than is possible. The published distance is more like a consensus.

GPS will usually measure too short. Wheels will usually measure too long (they travel more like an ant than a person), and wheels return useless values if not carefully calibrated and maintained. I plan to include a little about trail measurement in my talk at Trail Days this year.

Thanks....I wasn't too wrapped up in an exact measurement....I only thought that the mile markers were flat measurements. But now I know.

bigcranky

02-22-2011, 19:04

Therefore, the length would be (2,181miles*5,280feetpermile)^2 + (475,200feet)^2 = 132,610,885,862,400 + 225,815,040,000 = 132,836,700,902,400. The square root of this is 11,525,480.51, and divided by 5,280 feetpermile gives us 2,182.9 miles. =

This is pretty accurate. I remember doing the math once and being surprised at how small the difference was in total length when taking into account large elevation changes.

Good old high school math comes to the rescue! Pythogorean Theorem, people. On wikipedia, the horizontal component of the trail is given (2,180 miles) along with the vertical component (475,200 feet of elevation change). So what do you do? Add the squares of each length, find that number's square root, and that is the actual distance, taking into account the rises! (If I'm wrong, someone correct me here...)

Therefore, the length would be (2,181miles*5,280feetpermile)^2 + (475,200feet)^2 = 132,610,885,862,400 + 225,815,040,000 = 132,836,700,902,400. The square root of this is 11,525,480.51, and divided by 5,280 feetpermile gives us 2,182.9 miles.

Only an extra two miles, but pretty interesting! (I realize after doing this that working with miles instead of feet would have been way easier... whoops.)

Your starting distance, 2180, was measured by a wheel, over ground. The wheel was rolled over the ups, downs, bumps and turns. Therefore your calculation to account for additional distance due to elevation change is totally unnecessary.

Essentially by global standards, the AT is nearly flat. That's why Map people artificially increase the height drawings 5? fold. That exaggeration is needed to satisfy long distance hikers, who want to show profiles that suggest to folks at home how hard the trail is.

SassyWindsor

02-22-2011, 21:02

1117 miles = straight line from Springer to Katahdin. Not taking in earth curvature the difference between the actual wheel measurement and 1117 miles should be close to the distance caused by the the curves, zig-zags, and elevation or 1050 or so miles, which is close to half the total distance.

SassyWindsor

02-22-2011, 21:16

In other words, if one could walk in a straight line with no elevation change you could walk from Springer to Katahdin and back to Springer and have walked approximately 2234 miles, not far from the actual trail miles one way.

bigcranky

02-22-2011, 23:29

Look at it this way:

Take a single flat mile, 5280 feet.

Now add a 500 foot climb -- which is a pretty good grade for a hiker (500 feet per mile.)

If you are going uphill, how much longer than a flat mile do you end up hiking?

Well, use old Pythagoras. 5280*5280 + 500*500 = your answer (squared.) Do the math, take the square root, and you get....

5303 feet and change, or about 23 extra feet on a one mile climb. Not much difference.

Of course, the trail goes up and down a lot.

I remember DellDoc measured the trail via GPS...2002? The GPS would also read elevation gains and loses if it had a barometer or barametric altimeter in it and would adjust the distances on the readout.:cool:

geek

Yes, he did his GPS survey in 2002...his rig cost him about $50,000 and as he was doing the survey he told me he didn't yet have a buyer for the data, though he was hoping the ATC would buy it, but there were no guarantees (perhaps they were waiting to see how good the data was before committing to buy it)...I think he said he was taking measurements every 3 meters, though watching him do it I would think this would be an approximation...probably doesn't matter because at the end you are just going to connect the dots of all the measured points. I have no idea if the data was ever used. He was essentially slackpacking the trail that year (it was his 4th thru-hike) with his wife meeting him at road crossings...a couple of times I met him on an upward climb and wondered if he'd make it the whole way without keeling over. He and his wife are good people, they were always shuttling people to and from town.

johnnyblisters

02-23-2011, 01:21

I see no reason why a wheeled measurement's data would be disputed, assuming the instrument was properly calibrated and utilized.

To answer the OP's question, the measurements you are given are not a linear measurement on a planar scale. When measuring with a physical instrument such as a measuring wheel, all geodesic variables are taken into account in that measurement.

And to 10-k, I think you forgot an emoticon at the end of this

And don't forget the curvature of the earth. The further north you go, the shorter a mile is. :cool:

I see no reason why a wheeled measurement's data would be disputed, assuming the instrument was properly calibrated and utilized.

.....

Like most things in life, a measuring wheel measurement is only as accurate as the assumptions of the operator. Wheels work great on sidewalks and paved highways. They have variables when used on typical woodland trails, with scattered rocks and downed logs.

Do you roll the wheel up and over a big log or rock that a hiker would just step over? Or do you stop at the base of the obstruction and lift the wheel over?

What about measuring a rough trail? I find myself measuring from one side to the other of a trail, seeking the easiest route for pushing a wheel, but not necessarily the route I would walk without the hinderance of the mechanical device.

Lemni Skate

02-23-2011, 02:37

I teach Geometry and you would actually have to sum a bunch of little triangles. It doesn't come out the same as if you had one giant triangle.

Most people really over estimate how steep of a slope we have in most sections.

I have always been under the impression that the distances were actual ground distances measured with a wheel and not 2D distances.

Pedaling Fool

02-23-2011, 08:32

Essentially by global standards, the AT is nearly flat. That's why Map people artificially increase the height drawings 5? fold. That exaggeration is needed to satisfy long distance hikers, who want to show profiles that suggest to folks at home how hard the trail is.

That's not exactly true. If you look at the map profiles their linear scaling is different than the actual map the profile is printed on, but it's usually about the same, i.e. nearly 1" = 1 mile. So if 1 inch equals thousand of feet you can imagine how small the inclines, which in many cases are less than a thousand feet would appear. Overall, the profile would be virtually flat; without vertical exaggeration there would be no reason to have a profile map.

That's not exactly true. If you look at the map profiles their linear scaling is different than the actual map the profile is printed on, but it's usually about the same, i.e. nearly 1" = 1 mile. So if 1 inch equals thousand of feet you can imagine how small the inclines, which in many cases are less than a thousand feet would appear. Overall, the profile would be virtually flat; without vertical exaggeration there would be no reason to have a profile map.

What I mean is always true (well within human limits.) What I write, however, is not always what I mean. We need a system of writing that doesn't require those pesky words.

jersey joe

02-23-2011, 11:20

Yes, he did his GPS survey in 2002...his rig cost him about $50,000 and as he was doing the survey

I met Delldoc on my 2002 thru hike coming out of a town. He had a large backpack on with the gps unit, it was bigger than I would have wanted to carry. He was an older fella, I wished him luck in making it to the end of the trail.

This thread is very interesting to me. I was recently asked if the trail included elevation gain. I thought it did since the I knew the trail was measured by a wheel, but I wasn't sure...this thread confirms that.

Pedaling Fool

02-24-2011, 09:17

What I mean is always true (well within human limits.) What I write, however, is not always what I mean. We need a system of writing that doesn't require those pesky words.

I understand. My words often relay an opposite message I was attempting to communicate.