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    Default Calculation of mileage on trails

    Hi Everyone,

    We have been throwing this around in my backpacking circle of friends for a while, and no one seems to be 100% sure one way or another.

    I have the iPhone 6, which has a health app. One of the functions of the app measures how far you have walked that day. Invariably, when we hike in the mountains, the mileage the app calculates is appreciably higher than on the map or on the signs the trail has.

    For example, we did a hike called Rock Castle Gorge from the hikingupward.com site, and it was listed at 10.7 miles. My wife's app measured over 14 at the end of the hike, and mine measured over 13.

    One thing I reasoned is that the map mileage is calculated without taking into account the ups and downs of the trail...imagine a mountain shaped like a triangle, and you walk up one side and down the other. This would be the measurement the iPhone app makes, whereas on a map, the distance from the base on one side to the base on the other side is the distance calculated (like as the crows flies), which obviously is a shorter amount.

    One reason I believe this may be the case, is we live where it is perfectly flat, and the app measures pretty close to the same mileage as the trail signs do at the local state park.

    One guy I know is a surveyor and he agrees with my reasoning...that's how they do survey, as the crow flies. He said in the old days, they measured laying a length of chain on the ground, and repeating that process over the lay of the land. He said landowners get pissed when they have an old survey saying they have 600 acres, and he comes in a re-surveys it at 500 acres.

    The implication is to me, we hike a lot farther in a day than we think!

    Anyone have any thoughts on this? It's kind of mind blowing in a way...the AT could actually be a distance of 2800 miles if measured the way I am describing.
    Last edited by Namtrag; 06-22-2015 at 13:25.

  2. #2

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    Quote Originally Posted by Namtrag View Post
    Hi Everyone,

    We have been throwing this around in my backpacking circle of friends for a while, and no one seems to be 100% sure one way or another.

    I have the iPhone 6, which has a health app. One of the functions of the app measures how far you have walked that day. Invariably, when we hike in the mountains, the mileage the app calculates is appreciably higher than on the map or on the signs the trail has.

    For example, we did a hike called Rock Castle Gorge from the hikingupward.com site, and it was listed at 10.7 miles. My wife's app measured over 14 at the end of the hike, and mine measured over 13.

    One thing I reasoned is that the map mileage is calculated without taking into account the ups and downs of the trail...imagine a mountain shaped like a triangle, and you walk up one side and down the other. This would be the measurement the iPhone app makes, whereas on a map, the distance from the base on one side to the base on the other side is the distance calculated (like as the crows flies), which obviously is a shorter amount.

    One reason I believe this may be the case, is we live where it is perfectly flat, and the app measures pretty close to the same mileage as the trail signs do at the local state park.

    One guy I know is a surveyor and he agrees with my reasoning...that's how they do surveys.

    The implication is to me, we hike a lot farther in a day than we think!

    Anyone have any thoughts on this? It's kind of mind blowing in a way...the AT could actually be a distance of 2800 miles if measured the way I am describing.
    Depending on which AP you use, the answer may be different. I have three different devices. Each of them uses a different method.

    My FitBit uses the number of steps times my average stride (a number I gave in setup) to calculate mileage. It overestimates the mileage on a trail because I take shorter steps on an incline.

    My Garmin Fenix gps watch uses gps readings to track my movement. It also seems to overestimate the mileage I have walked. I assume that it is because I don't stay in the center of the trail. The "official" mileage attempts to measure the centerline of the trail, but one actually walking the trail will walk more.

    I also have a gps unit that measures distance as a direct line between two points. It underestimate trail mileage.

    On the other hand one can't always rely on the "official" mileage. I am currently planning a hike on the PCT from White Pass to Chinook Pass. The various maps I have found online show the mileage from 28 to 30 miles. I suspect that the primary difference is because both trailheads are in "areas", rather than a precise point.

    I find the same issue when hiking in the Grand Canyon. Many of the maps give different mileage between points along the trails because the "points" are really areas rather than points. For example Indian Garden is 4 miles from the South Rim on some maps and 4.5 miles on other maps. Both are accurate because Indian Garden extends for 1/2 mile along the trail.
    Shutterbug

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    Yeah, I am not sure how the apple app works, but I have heard it is gps based...the NSA must love it!

    One reason I even thought to look into this is I have seen signs saying I had only 2 miles left, and hiked two hours to finish, knowing in my mind that I hiked more than 2 miles.

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    Also, trails are ... approximate. Some are more approximate than others. I know that I've walked 3.9 miles over what the signs and guidebook said was a 2.3 mile stretch of trail not too long ago, and I was following the blazes. But I could see where the old trail disappeared in the beaver ponds.

    Measuring the length of something that has twists and turns at every length scale is also ... complicated.

    I know that some trail maps have mileages measured by a measuring wheel. But that was the length on the day that the guy with the wheel walked the trail.
    I always know where I am. I'm right here.

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    There are a number of reasons why distances could vary from signs and maps to that experienced on the trail - any, all, or something else could apply:

    -The trail moved since the sign and/or map was created. More switchbacks put in, moved around a wet spot or private land corner, etc.

    -Distance may have been scaled off a map with inaccurate route placement. This could occur from scrawls on old topos or from digitizing the old topos and very precisely measuring the wrong track.

    -The track might be in the right place but not fine enough to account for all the squiggles around rocks, etc. On PA Mid State Trail we have seen that wheeled distances go from spot on when following a rail trail, to 3-5% greater on the rockiest segments.

    -The sign was just wrong to start with - trails are created by imperfect humans, after all.

    -Probably the least likely reason is slope vs. plane distance. A highly machined ball bearing is rougher than the Earth's surface generally. Typical hiking profiles use a vertical exaggeration of 5.28:1 to make the ups and downs of the trail correspond with people's perceptions of up-down-ness. The slope vs. plane matters when one needs to survey a piece of ground for legal precision in property or engineering work, but even in the mountains that factor makes less of a difference than people think.

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    Sometimes the trail gets shorter than advertised. Old timers frequently would just pace off the distance. They knew how many paces per mile when they were 23, and didn't recalibrate for being 83.

  7. #7

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    I've found Runkeeper to be one of the more accurate apps. Pedometer based stuff has always been sketchy, even GPS smooths things out too and doesn't actually measure the true surface of the earth.

    But to go old school...
    Two things happen- scaling errors and 2d to 3d. Depends on how nerdy you want to get to fix them.

    Scaling errors- not as bad in a canoe as on foot.
    Quite simply-In a boat, you may lay out your route as true bearings and shoot across an open body of water, so your measurement error is smaller. On trail, even in a dead flat world we don't find many trails (unless they are a rails to trails project) that are straight lines. Every trail twists and turns a bit. When I was learning to read maps and set a route I used a string and transferred the scale to it. On very winding trails this is really the only way to scale the 2d distance on a trail. Even then, depending on the actual scale of the map, you may still be "smoothing" the curve as it's scaled down. A good tip- if you have a map case and it has a leash- put the scale on the leash so you have a piece of cord handy to scale with.

    2d to 3d- again, same problem. Even on a 5' contour scale, there are still some small dips that add up and down. On something more extreme, like the north end of the LT, 50 contour intervals may not tell the tale as you can easily ascend up or down several times in that overall 50' gain. The contour just shows the net result because of the scale used. So you could easily gain 75' and lose 25' in a dip as you ascend. All those ups and downs add distance at some point.

    What to do?
    Experience will let you get a good idea of the winding and scaling issues of your simple 2d measurements.
    The old school way; take your best shot at the map, then record your guestimate.
    You have to know your pace, and do a bit of dead reckoning based upon that knowledge.
    So if you know you walk about X and you guessed Y- do the math and see how close your guess was.
    You just did that actually- sign said 2 miles, your experience and watch said it had to be longer.

    Same on elevation changes, with appropriate pace adjustments.

    This is even easier now with a GPS, phone, etc. to give you a double check after the fact.

    What I do-
    Eventually you get a feel of scale and adjust accordingly.
    1-Take your best measurement.
    2-Use experience of scale to make an educated adjustment. If the trail is pretty straightforward on a good map, maybe add a few percent. If the trail is really windy or the scale is large, maybe up to 10% to the distance.
    3-Look at the contour lines; what scale are they? Flat lands, mountains, past experience in the terrain, etc. I know some folks who count contour lines per inch to get an idea too. I'm mainly in flatlands if I am navigating by map, so my adjustments are usually minimal. But basically, the more contour lines you are crossing, and the bigger the scale of contour- the bigger the fudge factor.
    4-Take the adjusted 2d distance, and multiply it again for your contour fudge factor. On flatlands I might add nothing. Rolling hills like Wisconsin or Southern Illinois I might add 5%. Something crazy like Vermont- 25%.

    If I didn't learn it as a kid, and wasn't planning group trips into areas without known mileages I probably wouldn't have nerded out on it as much. But still- it's an easy/fun skill to play with here and there when you're out. Especially on something like the AT where you have fairly accurate known distances as double checks, or even your local community trails.

    Read the map, take your best guess first and write it down (funny how the memory shifts in your favor, lol). Then walk it and see how you did. As you go, pay attention to how things have affected your hike relative to what the map said. Eventually your dead reckoning and map reading skills get really good and there won't be much thought to it unless the area or map scale is very unfamiliar.

  8. #8

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    Just one more small 3d thing...
    Pythagoras tells us that one mile out and one mile up means the trail up the hill is roughly 1.4 miles.
    More of a western trick where paths are graded a bit better, but learning grades relative to simple geometry can give you a quick ballpark too that helps with the 2D to 3D scale factor.

    That's more or less what the counting contour lines per mile trick is- get an idea of the relative change over a mile and you'll have a decent scale factor for distance. What is nice about that trick is that you don't have to worry about elevation gain/loss- just count lines.

    10 50' contour lines per mile- 500' elevation change.
    Roughly 10% of a mile (500/5280), roughly 10% of the 1.4 mile hypotenuse in a 1:1 triangle.
    So roughly a 4% scale up for 2d to 3d.

    You can quickly spot check a few "miles" randomly to get a decent feel for an area, although this trick falls apart a little in the east as there is a lot more action between the contour lines.

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    I know that some trail maps have mileages measured by a measuring wheel. But that was the length on the day that the guy with the wheel walked the trail.



    here's an interesting article on the guy who measured the trails in GSMNP..........


    http://www.smhclub.org/Stories/Lochbaum.htm

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    When you start getting enough contour lines per mile, the distances get meaningless anyway. http://kbk.is-a-geek.net/catskills/k...=-74.1399&z=15 is one of those. The apparent loop-de-loop in the trail at about 3000 feet on the west side of Sugarloaf is real. The trail goes under an overhanging cliff, scrambles a chimney and walks back on the cliff top. Every tiny wiggle on that map is the trail circling a ledge to the next scramble. All of that is lurking between the contour lines.

    You can also see where trail routings are approximate. Magenta trails on that part of the map are from the "official" map, Black ones are mostly field verified with GPS. You can how the Pecoy Notch trail east of Sugarloaf has been relocated around a beaver pond, and runs about 200 vertical feet farther up the slope than the "official" map indicates. On the north side of Sugarloaf, the "official" map is missing a lot of switchbacks.

    The signposts there reflect mileages that someone measured with a map wheel on the "official" map, so they're doubly inaccurate. In fact, I'd say that they're out and out lies. Although, and more significant, the signpost at the trailhead does warn that the elevation gains are 1650 feet to Twin, 1800 to Sugarloaf and 1850 to Plateau. And likewise, the signpost at the Pecoy Notch trail junction warns that Twin is 0.6 mile and still 1100 feet of climb to go. Since a thousand feet of elevation expends the same amount of sweat as a mile or two of trail, at least they do tell you what you're getting into.
    I always know where I am. I'm right here.

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    Quote Originally Posted by Just Bill View Post
    10 50' contour lines per mile- 500' elevation change.
    Roughly 10% of a mile (500/5280), roughly 10% of the 1.4 mile hypotenuse in a 1:1 triangle.
    So roughly a 4% scale up for 2d to 3d.
    4% of 5000 is 200 feet for a 10% grade, which is way way way overstating it. Exponents don't work that way.

    To simplify, assume a mile is 5000 feet. And let's go with the 10% grade, which is 500 feet.

    5000*5000 + 500*500 = X-squared, where X is the actual hiked distance.

    So we take the square root of 25,250,000, which is ~5024.

    So if the mileage is measured on a flat map, and there is a 10% grade, the actual distance hiked is less than 1/2 of 1% longer than the measured mile (5024 ft vs 5000 ft).

    (And let's not get into the fact that the "miles" are measured with a wheel or, lately, with an accurate GPS, so the mileage charts take into account the actual miles hiked, not the "map miles.")

    To the OP, the built in tool in my new iPhone is wildly inaccurate most of the time. I occasionally walk to work, and the iPhone shows the distance as sometimes half and sometimes twice the real distance, but rarely if ever the actual distance. I would not rely on it for navigation.
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    Thanks for all the great info...I do see that the phone app is inaccurate some of the time (it seems much more accurate here in Va Beach on perfectly flat ground), but at the same time, when you have it happen occasionally that it takes you 2 hours to go 2 miles in relatively benign hills, you just begin to wonder...did I really hike only 2 miles and am slow as hell, or was the map wrong?

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    My wife and I took a 2 mile walk in the neighborhood the other day. She had her iPhone and one of those health apps, I had an eTrex GPS. Her phone showed that we walked 2.00 miles, my GPS said 1.85.
    I checked things out in Google Earth to see if the difference could be attributed to the fact I might be walking on the "inside" as we go around cul-de-sacs and she's on the outside. But in a worst case, I can only find about 120' of total difference (about 0.02 miles). Where did the other 0.13 miles come from (i.e. her iPhone was showing a LONGER distance than an eTrex Garmin GPS).

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    4% of 5000 is 200 feet for a 10% grade, which is way way way overstating it. Exponents don't work that way.

    To simplify, assume a mile is 5000 feet. And let's go with the 10% grade, which is 500 feet.

    5000*5000 + 500*500 = X-squared, where X is the actual hiked distance.

    So we take the square root of 25,250,000, which is ~5024.

    So if the mileage is measured on a flat map, and there is a 10% grade, the actual distance hiked is less than 1/2 of 1% longer than the measured mile (5024 ft vs 5000 ft).

    (And let's not get into the fact that the "miles" are measured with a wheel or, lately, with an accurate GPS, so the mileage charts take into account the actual miles hiked, not the "map miles.")

    To the OP, the built in tool in my new iPhone is wildly inaccurate most of the time. I occasionally walk to work, and the iPhone shows the distance as sometimes half and sometimes twice the real distance, but rarely if ever the actual distance. I would not rely on it for navigation.



    This example would be incorrect if there were switch backs

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    Quote Originally Posted by bigcranky View Post
    4% of 5000 is 200 feet for a 10% grade, which is way way way overstating it. Exponents don't work that way.

    To simplify, assume a mile is 5000 feet. And let's go with the 10% grade, which is 500 feet.

    5000*5000 + 500*500 = X-squared, where X is the actual hiked distance.

    So we take the square root of 25,250,000, which is ~5024.

    So if the mileage is measured on a flat map, and there is a 10% grade, the actual distance hiked is less than 1/2 of 1% longer than the measured mile (5024 ft vs 5000 ft).

    (And let's not get into the fact that the "miles" are measured with a wheel or, lately, with an accurate GPS, so the mileage charts take into account the actual miles hiked, not the "map miles.")

    To the OP, the built in tool in my new iPhone is wildly inaccurate most of the time. I occasionally walk to work, and the iPhone shows the distance as sometimes half and sometimes twice the real distance, but rarely if ever the actual distance. I would not rely on it for navigation.
    Well there's "math" and then there's MATH. Not that I did a good job there on either of them, lol.
    The very shady and poorly written "math" is a back of napkin type "math" I probably shouldn't have brought up at all without more accurately stating it as durn cheating rule of thumb which has little to do with math at all really.

    The "math" had nothing to do with grade. Grade was only mentioned to describe a more uniform elevation change as opposed to the more wildly "graded" trails.

    I think we can agree in any language= a 1:1 triangle gets you 1.41 on the hypotenuse
    If the base triangle is a mile, and we cheat to make it easy we call it 5000' per side.

    Here's where you get a little "Just Bill math" and cross into rule of thumb range.
    If we call a 1:1 (pretty unrealistic trail generally) a worst case trail that is our baseline for our rule of thumb. As Kevin mentioned- anything past that is ridiculous and out the window.

    Rule of thumb 1- 2d to 3d distance
    We call our worst possible mile 5000/5000.
    So a 500' elevation change per mile is about 10% (500/5000) of our worst conceivable mile.

    Here's where you just get plain shady-
    1:1= 1.41 Call that 41% longer than our paper mile, better yet just say 40, as in the number 40 not 40% (that's the shady part)
    So back to our 500' mile- 10% of 40= 4%.
    Now this is rule of thumb result- I would say that mile on the map is 1.04 miles in real life.

    Which is a better number (in my silly head ) to use for real life planning than the real number (below). So yes, according to MATH the rule of thumb number is a few hundred feet longer- even though a mile is a mile we all know not every mile is a mile, so better to count some miles as more miles when planning.

    So Rule of Thumb 2- Shady grading vs pace-
    On the flippty flop side of the first rule- if 1:1 is a really hard trail we could also say that it is 100% harder than a flat trail. (which we all generally agree on actually)
    We could also use the 500/5000 number to say that that mile will be roughly 10% harder than a flat mile. (same as first rule)
    SO... we can also say that this mile will take 1.1 times as long as our normal mile in regards to our pace. (10%= .1+1=1.1)
    If it really is a 1:1 mile it will easily take us twice as long.. (100%=1+1=2)

    Yar- it is definitely not math BUT it works surprisingly well without a calculator on top of it, especially off trail.

    Count contours in a mile and divide by 5000.
    C/5000= a percentage.
    % times 40= multiplier for distance (rule 1-map to "real life")
    100%+(C/5000) = multiplier for pace (rule 2- calculate pace for dead reckoning and planning)

    Not to be a jerk, or promote bad math... But I've found this works really well.
    Now of course it's my rule, but over the years it's held up pretty durn well, and held up or exceeded the usefulness of other rules of thumb I have encountered. Call it Philosophical Mathematics rather than MATH and you may like it....





    Back to real math that quasi justifies the fake math-
    If you do 10% of 40% you will get .004 or 4/10 of 1%.
    Which gets really really close to the MATH answer if you want it;
    (500x500) + (5280*5280)= 28128400 = 5303.6
    5303.6-5280= 26' or (26/5280) =.00492 (Durn close to real number using 5280 instead of 5000)

    It's just that adding back in that decimal place (.04 vs .004 in this one)-
    A- prevents any real hard "thinkering" on my part

    B- provides a good (but not insane) margin of error to the cautious side. 150 ish feet per mile ain't bad really as a margin for error in this case- and really- the steeper the trail the more likely one will under estimate their pace and travel time so it all washes out in real life in my experience.

    C- In real life, as the navigator in a group, even a group of 1, you will never get in trouble for saying it is 1.04 miles when in reality it is 1.004 miles. Although the inverse will get you in at least 1.40 times as much trouble.

    D- Makes it easy to implement rule #2- which is also durn handy.

  16. #16

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    Quote Originally Posted by HooKooDooKu View Post
    My wife and I took a 2 mile walk in the neighborhood the other day. She had her iPhone and one of those health apps, I had an eTrex GPS. Her phone showed that we walked 2.00 miles, my GPS said 1.85.
    I checked things out in Google Earth to see if the difference could be attributed to the fact I might be walking on the "inside" as we go around cul-de-sacs and she's on the outside. But in a worst case, I can only find about 120' of total difference (about 0.02 miles). Where did the other 0.13 miles come from (i.e. her iPhone was showing a LONGER distance than an eTrex Garmin GPS).
    https://en.wikipedia.org/wiki/Geodetic_datum

    The Earth isn't round, and GPS doesn't use a sphere even if it was.

    1-A fundamental problem with GPS (as someone who used it to survey and grade to within 1.25") is that it's accuracy is based upon a "close" shape. GPS locates you on the Epcot center like surface of it's system. If you think of a square in a circle; it's dead nuts to reality where the point of the square hits the circle... as you get further away from those points on the surface of the circle accuracy decreases.

    2-You are here, the satellites are in space. On any given day stuff is in your way that affects the signal. Weather being one, tree cover being another- two issues for any hiker.
    On the models I used we received an update on when the satellites were in the correct positions to work, what the fluctuation would be during the day, and we got a "bounce" warning if the unit was getting conflicting data or couldn't triangulate itself. All of these models required a base station plus the handheld units. The base station provided a double check- a fixed point- so you could work with more accuracy. On a bad day it could take an hour to calibrate and set a base station- some days 5 minutes... depended on conditions.
    Your handheld GPS has no base station to check against.
    Very generally speaking- x/y location is good (2d), Z or elevation is a totally different deal.

    3-The accuracy of your device- which can vary widely. Also depends what system you have access to.

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    For hiking I alway assume the word "about" should be included. If the sign says, "Groundhog shelter - 4 Miles" it would never occur to me that someone started at the shelter and paced off exactly 4 miles and planted the sign dead on the 4 mile mark.

    Also.. when I'm hiking I don't think distance so much as time. I translate a sign that says something is 4 miles away to mean that I'll be there in around 2 hours. Because I hike a very unscientific net 2 MPH.

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    Quote Originally Posted by bigcranky View Post
    4% of 5000 is 200 feet for a 10% grade, which is way way way overstating it. Exponents don't work that way....
    Why don't atheists work exponential equations? Because they don't believe in higher powers.

    Sorry, I couldn't resist.

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    Quite a few reasons why indicated trail mileages could be awry. Personally, I'll take a wheeled mileage estimate over a pedometer app or fitness pedometer wrist watch almost always. However, some mapping technologies do take into account for vertical adjustments/contours when estimating, usually quite closely, within 2%, trail mileages.

    On another note, when I'm dialed in on a long hike, in the zone, I have an excellent feel for my pace, time, and distance. Watch is very helpful tool. At these times I can usually tell two more bends in the trail, 6.4 more miles, 800-900 ft more elevation, etc and I'll be at the river, campsite, pass, junction, big tree, dirt road,etc. Combine that with your topos and a compass(two other helpful tools) and I'm golden - rarely late in estimating my time to a destination. Practice this at home on walks sometimes to unknown destinations and/or using new routes and you'll be ahead of the game once you hit the trail.

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    Quote Originally Posted by Just Bill View Post
    Well there's "math" and then there's MATH. Not that I did a good job there on either of them, lol.
    The very shady and poorly written "math" is a back of napkin type "math" I probably shouldn't have brought up at all without more accurately stating it as durn cheating rule of thumb which has little to do with math at all really....
    Just Billiant!

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