# Accuracy of Trail Mileages

Trail distances have mostly been a very rough estimate until the advent of mountain bicycles. It used to be amusing to watch the two mileposts on the Mt. Wilson Toll Road, which give mileages from the entrance to the Toll Road and to Henninger Flats, move around by ~0.5 miles from year to year! Once mountain bicycles appeared with odometers, the posts became fixed and accurate. (Although one might have thought that vehicle odometers on that road would have previously fixed the posts.)

The most accurate way by far to measure trail mileages is to do what they did with the Bright Angel Trail in the Grand Canyon - extremely accurate surveying, producing mileage estimates accurate to 0.01 miles. All other measures have some degree of error. In order of probable accuracy, here are other ways to get trail mileages:

1. Rolling a calibrated bicycle wheel along the trail.
2. Riding a mountain bike with a calibrated odometer.
3. Walking the trail using a calibrated pedometer.
4. Walking the trail keeping track of time spent walking, and then converting the time to a distance using a calibration that depends on altitude gain or loss and trail roughness.

All of these measures have problems:

Measurements made with a bicycle wheel are limited by the rocks, bumps, ridges and steps found on most real mountain trails. For example, if there is a 1' drop caused by a rock stairstep along the trail, the bicycle wheel being pushed along the trail will not be able to follow the arc through the air that your foot travels. Similarly, bicycle wheels follow all the dips and bumps of the trail that will be "straight-lined" by the foot.

These are not totally negligible factors: Consider a trail that looks in cross-section like the way a schoolchild draws the wavy surface of the ocean. Parts of the Bright Angel Trail in the Grand Canyon look almost exactly like that, with the high points being logs or rock laid across the trail to stabilize it, with low points between them caused by mule and foot traffic scooping out the dirt there.

Let the peak to peak distance be 3', and the segments between peaks be a portion of a circular arc, with a dip at the center of 3" measured from the line connecting the peaks. A bicycle wheel would measure a distance that is 2% greater than the foot distance if your stride is 3'. If the dip were 6", the error would be 4%.

See Description of Carter's Trail Odometer for more information about bicycle wheel odometers.

Measurements made with a pedometer have a number of limitations:

• Pedometers won't even work for some people. For example, my hiking buddy Craig Cheetham has had no luck at all with pedometers, including the same model that I use. Clearly a pedometer is sensitive to the exact throw of your hip with left steps and right steps. I have tried two of his discarded models, a Precise brand like my current one that worked fine for me, and another brand (which I have forgotten) which did not work for me either.

• Pedometers are often sensitive to the exact placement on one's hip. An anonymous reader told me:
I found that at least one of the units that I had was very sensitive to the exact placement on the belt. It wouldn't count when I wore a certain pair of pants that had a belt loop at the point that I normally wear the unit. It was one of many of the original units from Precise and other units of this same model didn't have the same problem. Moving the unit around to the rear of the hip allowed it to register OK.

• Pedometers are limited by changes in one's step size as one negotiates amidst the same rocks, bumps, ridges and steps. In addition, pedometers may or may not even count all of the steps one takes. On the steep ascent to Mt. Baldy on 16 September 1999, on the uphill, a pedometer recorded only 67% of my steps (307 out of 460). On the downhill, it recorded 95% of my steps (380 out of 400).

Actually, this lack of counting steep uphill steps probably improves the accuracy overall, since when going steeply uphill, one take shorter steps.

Measurements made by converting times to distances are limited by both step-size variations and gait changes.

Thus mileages are often not what they seem for trails. As more mountain bikes traverse the trails and report their mileages, trail mileages should get much more accurate. (If you have better measures of any trail, please let me know.) However, I have come to believe that, in some cases, pedometers actually are often a better indication of how "long" the trail is than accurate mileages, since they accurately count how many steps you take, which presumably is highly correlated with the number of steps that others take on that trail.

I have kept track of the accuracy of my pedometers over the years, and found the following:

1. Pedometer mileages are almost always within 10% of guidebook-quoted mileages, and
2. Uphill total mileages are almost always within 10% of downhill total mileages.

I have made a detailed comparison of my pedometer mileages with the very accurate Bright Angel Trail mileages. The total error for that trail is less than 1%, 0.1 mile out of 16 miles. For the Bright Angel, my downhill mileage is higher by 4% and my uphill mileage is lower by 2.5%, for a relative error between uphill and downhill mileages of 6.5%. (The total mileage is more accurate because the error is in different directions between uphill and downhill, and thus partially cancels, and one divides by a mileage that is twice as high as the individual segments.) See the detailed comparison for the data and a more complete analysis.

Other studies have found that pedometers are accurate to within 10% or that accuracy varies considerably. Hence your mileage may vary.

For a peek at the possible future of consumer pedometers, take a look at an expensive military pedometer (~\$2000!) which is said to be accurate to 2-5% of the distance traveled sans GPS, and presumably much more accurate with GPS.

The ultimate pedometer would be one that measures the location of one's feet very accurately, perhaps using magnets and electrical pickup, and integrates those measurements. If you can build such a pedometer, I'd be happy to help test it! (This idea was stimulated by the ideas of Matt Maxon in improving pedometers.)

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