Book Milage vs. GPS Milage - Which to believe?

[John H Swanson]

I listed and led a local "10 mile hike" yesterday. The book showed it to be 10.1 miles. At the end, one of the participants looked at the GPS and said we only did 9.4 miles. What gives? And which should I believe?

I have no details about the GPS (type, etc.)

I once read an article that detailed the pains and methods used to determine the milage when the (Bill Myle's) book was written about 25 years ago. IIRC, the milage was determined by wheeling the trails, multiple times.

I thought about potential causes.....
The milage in the book is reported to +/-0.05 mi. Also I used only 3 trails for the hike so start/end error should not be a contributing factor to the descrepency.
I am familar with these trails and any changes or re-routes have been acounted for in the book milage.

thoughts?

 

[Kevin Rooney]

Go with the book mileage. As a rule of thumb, I find my Garmin GPS to be off about 5%. And when I load the track into my PC, the software reports a different mileage figure than the GPS, so even the algorithms to compute distance are slightly different.

Have found that Garmins seem to overstate and Delormes understate, so we sometimes average the two, and they're fairly close to the book (wheeled or steel-taped).

 

[sardog1]

This may have something to do with the resolution setting for tracks on the GPS receiver. If the setting is relatively coarse, the receiver will record locations less frequently. Since it connects such records with straight lines constantly, fewer records will result in more corner cutting. Over a long hike such as this, I can imagine the result being an underestimation of the distance. I haven't tested this over such a long track — YMMV. (You didn't think I was going to pass that up, did you?)

The other possible explanation is truncation of the track itself because the receiver is set to wrap tracks when the memory capacity is reached. This is also an option that can be changed on most receivers.

There's a good summary of these points at Some notes on recording tracks using a Garmin etrex brand of GPS. The piece is five years old, but it's still valid for the Garmin eTrex and similar devices AFAIK.

 

[John H Swanson]

This may have something to do with the resolution setting for tracks on the GPS receiver. If the setting is relatively coarse, the receiver will record locations less frequently. Since it connects such records with straight lines constantly, fewer records will result in more corner cutting. Over a long hike such as this, I can imagine the result being an underestimation of the distance. I haven't tested this over such a long track — YMMV. (You didn't think I was going to pass that up, did you?)

The other possible explanation is truncation of the track itself because the receiver is set to wrap tracks when the memory capacity is reached. This is also an option that can be changed on most receivers.

There's a good summary of these points at Some notes on recording tracks using a Garmin etrex brand of GPS. The piece is five years old, but it's still valid for the Garmin eTrex and similar devices AFAIK.

thanks, I assumed the GPS has an adjustable logging rate for making the track which might have contributed to the error, but not having one....and not knowing which one he had...I wasn't 100% sure this could cause the 0.7mi discrepency. The trail did have some squiggles along the way.

 

[bikehikeskifish]

It's not uncommon for my (Garmin) GPS to come up short on distance and high on elevation, and disagree with the (Garmin) MapSource software which further disagrees with Google Earth. Not enough to get my Under Armor in a knot This has been discussed elsewhere and I'm betting Dr. gPs will chime in with his usual explanation and/or pointer to the discussion

Tim

 

[RoySwkr]

There are a number of ways "book" mileage can be determined, in the old WMG some were just WAG and could be off by a mile or more - and that doesn't include misprints and the trail where somebody entered the km distance as mi

If the book distance is done with a calibrated measuring wheel, it closely approximates the actual distance traveled by a hiker and should be the most accurate but any % error in the wheel will appear in the published distance.

A GPS distance can come up far too long if it somehow records a bogus point off the track, if you have mapping software you can delete such points. The distance can come up short if the sampling interval doesn't record all the wiggles in the trail, for instance on a switchback trail my sister would wait the sampling interval at the end of every switchback to make sure it got a point there (which with the Trimble was apparently easier than taking extra points).

 

[Nessmuk]

GPS distance accuracy measured via long distance canoeing

My experience with distance accuracy of GPS comes mainly from personal marathon canoe race GPS “odometer” analysis. I study and lay out waypoints for best long distance canoe race routes and analyze subsequent actual tracks through Adirondack waterways, but most significantly have done so for three 1000-mile marathon races down the Yukon River. Yukon River route selection is based on a combination of many decades old paddlewheeler charts, recent recreational paddler experience, and intuition based on rather dated topographic maps, but is most heavily influenced by fairly recent (2-4 year old) Google Earth imagery.

I have found distance calculations computed from routes created on GE to be in excellent agreement with the trip computer odometer on a Garmin 60CSX. When I manually create a route on GE I try to take into account actual path that will be taken around river bends and islands. This GE route is fed into a program I wrote to calculate turn direction (left or right) to next waypoint, and cumulative distance from the race start line. Each waypoint/turnpoint (738 of them at last count for the Y1K) is then named and displayed both on printed charts and on the internal GPS map/route display with information of mileage and next point turn direction. After the first year's experience I added an adjustment factor for reality of canoe turn radius and wandering that seems to hold very well – this adjustment uniformly increases the raw calculated GE mileage by only 1.6%.

In 2011 at the 425-mile point at Dawson, the actual GPS odometer differed from the computed GE distance by less than a mile. That’s pretty darn good agreement over such a distance in my book. In the second half of the race beyond Dawson, and especially the final third beyond Circle, our actual track may differ slightly from the pre-plan due to annual changes in water level and numerous navigation options around oxbows and island washouts that may open or close shortcut opportunities. That makes correlation a little more difficult from year to year, but in 2011 we finished (the race is not quite 1000 miles) with about a 3-mile difference between GPS odometer and GE planned mileage. Post race analysis decreased that difference to less than 2 miles. PDG.

 

[DougPaul]

This may have something to do with the resolution setting for tracks on the GPS receiver. If the setting is relatively coarse, the receiver will record locations less frequently. Since it connects such records with straight lines constantly, fewer records will result in more corner cutting. Over a long hike such as this, I can imagine the result being an underestimation of the distance. I haven't tested this over such a long track — YMMV. (You didn't think I was going to pass that up, did you?)

The other possible explanation is truncation of the track itself because the receiver is set to wrap tracks when the memory capacity is reached. This is also an option that can be changed on most receivers.

These comments only apply to computing the distance from a recorded ("active track") or saved track, both of which drop points. (Consumer GPSes compute the location once per second.) The trip odometer (on my Garmin GPSes, presumably other brands are similar) is based upon these one-per-second locations.

My hiking GPSes all attempt to determine if I am moving or not which factors into at least some of the trip computer readings. Also, if the GPS loses lock, it may not count that part of the trip.

I presume that the hiker with the GPS was looking at the trip odometer, not analyzing a track.

Trail distance is a fractal--there is no fundamentally correct trail distance (ie it will vary depending on the details of how one measures it).

This topic has come up a number of times before:
http://www.vftt.org/forums/showthre...f-trail-distances-on-signs-and-in-guide-books
http://www.vftt.org/forums/showthread.php?41047-Yet-another-Garmin-GPS-question

Doug

 

[DougPaul]

There's a good summary of these points at Some notes on recording tracks using a Garmin etrex brand of GPS. The piece is five years old, but it's still valid for the Garmin eTrex and similar devices AFAIK.

I can take issue with some of his procedures:
* Yes, I (mostly) agree with resetting the trip odometer, but I only reset some of the fields.

* There are other versions of "Optimal settings for best track resolution" which are equally valid
- unchecking "wrap when full" will cause you to lose the end of your trip if the log fills up, checking "wrap when full" will cause you to lose the beginning of the trip if the log fills up. (Losing part of the track can be considered a huge error...)
- frequent recording intervals will cause the log to fill up faster--a smarter method is to set the interval to record the maximum number of points without filling the log. The most frequent interval (1 per second) will fill the log in 2 hrs, 46 min.
- Some of the more modern GPSes can record a track log to the microSD card--these tracks are limited only by the amount of space on the card.

* for random hiking, I just use "auto", "norm", and "wrap when full". It is good enough (for my purposes) and I have never overfilled a track log in a day. If I am mapping a route or performing a GPS accuracy experiment, I generally use a more frequent interval.

Doug

 

[John H Swanson]

Doug,

Thanks for the links to the previous threads.

Interesting things to consider for this situation. If the point recording interval was set to 1 sec and we were doing about 3mph for most of the hike, then the points would be about 4.4 ft apart. If I understand correctly, the TO then measured the point to point distance without smoothing. Ignoring any gps movement relative to the body, The question at hand would be, does one travel straight (or directly) for each 4.4 ft or would the path traveled for that same 4.4 ft be longer than 4.4 ft. And how would it compare to the moving wheel that recorded the trail across the same 4.4 ft. With the descrepency being 7% - or 4.7 ft vs 4.4 ft. I could easily see the wheel traveling 3.5" further for 4.4 ft on rough terrain or hills but not as an average for the whole hike. Personally, I know for sure that on some rocky terrain, I probably travel at least 6 ft to cover that same 4.4 ft. But again, not as an average for the whole hike. Hmm, time to ask about the gps settings.

 

[DougPaul]

Interesting things to consider for this situation. If the point recording interval was set to 1 sec and we were doing about 3mph for most of the hike, then the points would be about 4.4 ft apart. If I understand correctly, the TO then measured the point to point distance without smoothing.

The TO runs off the 1/sec GPS PVT (Position-Velocity-Time) output independently of the track recording interval. The manufacturers do not publish their algorithms so we do not know what if any smoothing is used. (The PVT solution algorithms also include smoothing.)

Ignoring any gps movement relative to the body, The question at hand would be, does one travel straight (or directly) for each 4.4 ft or would the path traveled for that same 4.4 ft be longer than 4.4 ft. And how would it compare to the moving wheel that recorded the trail across the same 4.4 ft. With the descrepency being 7% - or 4.7 ft vs 4.4 ft. I could easily see the wheel traveling 3.5" further for 4.4 ft on rough terrain or hills but not as an average for the whole hike. Personally, I know for sure that on some rocky terrain, I probably travel at least 6 ft to cover that same 4.4 ft. But again, not as an average for the whole hike. Hmm, time to ask about the gps settings.

As noted above, the GPS track recording settings affect only the recorded track (and anything computed from it), but not the TO.

There are all sorts of details that can affect the distance estimate: eg for a wheel: diameter (there are standard sizes), whether one goes over or around rocks, etc... (How far does a giraffe travel vs how far does an ant travel?) For a GPS, one needs to consider not just the GPS and its settings but how it is carried. (For instance, when mapping a route, I use an external antenna in my hat to get the best signals and the best accuracy.)

And if you are going to get the best out of a GPS, I suggest that you use a survey-grade professional GPS with a choke-ring antenna (a ~1 ft diameter disk mounted on a pole). A professional will also check out that satellite positions to make sure that there are no bad constellations and post-process the data to correct for satellite orbital and clock errors. Or he might use reference data from a nearby stationary reference GPS to reduce the errors (DGPS). Or stated differently, don't expect professional accuracy from consumer GPSes with amateur operators.

Again, the length of a trail is a fractal--there really is no exact correct answer. I suggest that you simply accept that all methods are approximate and be happy if the distances from different methods are similar.

Doug

 

[Snowflea]

This happened to a friend and me on Saturday. We did a big lollipop run in the Sespe Wilderness (California Central Coast area) which was supposed to be 29.5 miles. My friend's GPS said 32.1. Which to believe? Always the higher number, of course.

When hitting the trails with GPS enabled friends, this happens quite often. In my personal experience it seems to happen more out here on the Left Coast. I have seen a lot of discrepancies in the Sierras, for example. My husband is convinced that one well-known mapmaker in particular was high when he put the mileages on some of his maps.

Personally I don't get that hung up about it and find these discrepancies kind of humorous and fun but can see where it might matter to some folks. Would be interesting to see what different mileages people get on their gizmos vs., say, the White Mtn. Guide.

PS: Hi John!

 

[Raymond]

If the trail goes up and down, the GPS measures it as though it were on a flat surface, doesn’t it? That’s what I understood the answer to be when I asked a similar question last year. So the GPS doesn’t consider that Point B may be higher in elevation than Point A. If you were on, say, North Kinsman and wanted to check the distance to Mount Lafayette, the GPS would just calculate straight across through space, not take into account the valley you’d have to drop into to actually travel from one to the other. Same thing when measuring your hike, whether it be across mountain ranges or up the Capitol steps.

The book mileage may have been measured with a wheel.

The Adirondack Mountain Club’s High Peaks Region guide book has the distance from Upper Works to Flowed Lands as 4.7 miles, the late Barbara McMartin’s book has the distance as 4.4 miles, and I think the sign says 3.7 miles. I haven’t hiked that trail since I got a GPS, so who knows what the GPS thinks the distance is. Maybe someone else here has a figure.

 

[DougPaul]

If the trail goes up and down, the GPS measures it as though it were on a flat surface, doesn’t it? That’s what I understood the answer to be when I asked a similar question last year.

Yes, however the actual difference is pretty small unless you get on really steep terrain:
* 500ft/mi: 3D distance .5% greater than 2D distance
* 1000ft/mi: 3D distance 2% greater than 2D distance
* 1500ft/mi: 3D distance 4% greater than 2D distance
* 2000ft/mi: 3D distance 7% greater than 2D distance

Doug

 

[TomD]

There is a rather lengthy discussion on The Lightweight Backpacker (www.backpacking.net) about whether a GPS is accurate in measuring distances on an angle, e.g. if you walk a mile down a 30% grade, does the GPS show the actual distance walked or the shorter base tangent (straight) distance. Think of a 3-4-5 right triangle to picture what I'm talking about. The answers got into some math, which was beyond me, but you might find the discussion interesting.
http://www.backpacking.net/forum/ubbthreads.php?ubb=showflat&Number=162200#Post162200

 

[DougPaul]

There is a rather lengthy discussion on The Lightweight Backpacker (www.backpacking.net) about whether a GPS is accurate in measuring distances on an angle, e.g. if you walk a mile down a 30% grade, does the GPS show the actual distance walked or the shorter base tangent (straight) distance. Think of a 3-4-5 right triangle to picture what I'm talking about. The answers got into some math, which was beyond me, but you might find the discussion interesting.
http://www.backpacking.net/forum/ubbthreads.php?ubb=showflat&Number=162200#Post162200

Only about one person in that thread seems to know what GPSes actually measure... (The answer is summarized in Raymond's and my previous posts: the horizontal distance only.)

As noted in my previous post, the effect is minor on most trails.
* 500ft/mi: 3D distance .5% greater than 2D distance
* 1000ft/mi: 3D distance 2% greater than 2D distance
* 1500ft/mi: 3D distance 4% greater than 2D distance
* 2000ft/mi: 3D distance 7% greater than 2D distance

The math is trivial (uses the Pythagorean theorem because height and horizontal distance are at right angles over typical hiking distances. http://en.wikipedia.org/wiki/Pythagorean_theorem):

d3^2 = x^2 + y^2
where
 d3 = 3 Dimensional distance (ie the length of the hypotenuse of a right triangle)
 x = horizontal distance
 y = vertical distance
 and the nontation x^2 means x squared

Or solved for d3:
 d3 = sqrt(x^2 + y^2)

To generate the above numbers, simply set x=5280 ft, y=the number of feet/mile, compute d3, and the percentage increase over x. (This assumes a uniform grade.)

Doug

 

[Kevin Rooney]

* 1500ft/mi: 3D distance 4% greater than 2D distance
* 2000ft/mi: 3D distance 7% greater than 2D distance

The above is interesting in light of my observation that my Garmin GPS seems to overstate distance by about 5% as I stated in my first post, and the above range is often the rate of ascent of many of my hikes. Thanks for posting the table, Doug.

 

[TomD]

Only about one person in that thread seems to know what GPSes actually measure... (The answer is summarized in Raymond's and my previous posts: the horizontal distance only.)

As noted in my previous post, the effect is minor on most trails.
* 500ft/mi: 3D distance .5% greater than 2D distance
* 1000ft/mi: 3D distance 2% greater than 2D distance
* 1500ft/mi: 3D distance 4% greater than 2D distance
* 2000ft/mi: 3D distance 7% greater than 2D distance

The math is trivial (uses the Pythagorean theorem because height and horizontal distance are at right angles over typical hiking distances. http://en.wikipedia.org/wiki/Pythagorean_theorem):

d3^2 = x^2 + y^2
where
 d3 = 3 Dimensional distance (ie the length of the hypotenuse of a right triangle)
 x = horizontal distance
 y = vertical distance
 and the nontation x^2 means x squared

Or solved for d3:
 d3 = sqrt(x^2 + y^2)

To generate the above numbers, simply set x=5280 ft, y=the number of feet/mile, compute d3, and the percentage increase over x. (This assumes a uniform grade.)

Doug[/QUOTE

That's exactly what I thought, but some of them seem totally convinced it is otherwise. Based on my rudimentary knowledge of how a GPS works-triangulation in a vertical plane (up to the satellites) as opposed to a horizontal plane, like using landmarks to triangulate where you are. I couldn't see how it would work any other way. Using a simple right triangle, as Doug pointed out, is how you would figure actual distance traveled.

Although, if for example I was in a plane at 6K feet, got a GPS reading of where I was, landed then stood directly under that spot so that my position on the ground was the same longitude and latitude, how does the GPS account for the difference in altitude when it makes the calculation? I suspect that because the satellites are so far away, a few thousand feet in altitude will make a very small, virtually insignificant difference in the angle to them.

 

[bikehikeskifish]

A recorded track has the elevation at every point, so it could figure out the 3D distance traveled, as closely as measuring the horizontal fractal.

(My Garmin 76CSx shows the GPS Elevation (on the satellite page, http://www8.garmin.com/manuals/GPSMAP76CSx_OwnersManual.pdf, page 32). The calibration (for the barometric altimeter) offers a choice of known elevation, known pressure or using the GPS elevation.)

Tim

 

[Nessmuk]

That's exactly what I thought, but some of them seem totally convinced it is otherwise. Based on my rudimentary knowledge of how a GPS works-triangulation in a vertical plane (up to the satellites) as opposed to a horizontal plane, like using landmarks to triangulate where you are. I couldn't see how it would work any other way. Using a simple right triangle, as Doug pointed out, is how you would figure actual distance traveled.

Although, if for example I was in a plane at 6K feet, got a GPS reading of where I was, landed then stood directly under that spot so that my position on the ground was the same longitude and latitude, how does the GPS account for the difference in altitude when it makes the calculation? I suspect that because the satellites are so far away, a few thousand feet in altitude will make a very small, virtually insignificant difference in the angle to them.

It's a little more complicated than what you may be thinking of in terms of "triangulation". Angles as such are not directly measured from satellites in the way you envision using a compass on landmarks, but rather precise timing of signals is used from precisely known satellite positions. This results in spherical "shells" of expanding time, and calculating the intersection of multiple overlapping shells will give you your location on the surface of the earth. A non-mathematical description is found here.

The altitude error is also a complex matter. Look at this web site for a brief description of that. Another way to think of it is that in the horizontal plane you can see satellites at multiple angles all around the 360 degree horizontal plane. But in the vertical plane, you can't see any satellites that are under the earth below you, which lessens the accuracy.