# Pedometer Accuracy

One always wonders how accurate a pedometer is, but the real difficulty in analyzing the accuracy is in having true mileages for trails for comparison. The conventional standard is the mileage measured by a bicycle wheel rolled along the trail. The bicycle wheel standard works fine for trails that are locally flat, so that a wheel rolls smoothly along the trail.

However, most real mountain trails have rocks, bumps, ridges and steps, which makes the bicycle wheel somewhat inaccurate. 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. This is not a totally negligible factor - consider a trail that looks in cross-section like the way a schoolchild draws the wavy surface of the ocean. 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%.

Mileages measured by bicycle riders have their own set of problems at this level, ranging from the calibration of their particular odometer, the inflation level and wear of their tires, how often they are "air-borne", how often their tires are skidding, how much they weave in and out of the center of the trail, etc.

Thus although bicycle wheel measurements are vastly superior to pedometers, measurements made on large-scale topo maps, and estimates from hiking times, it would be nice to have an accurately surveyed trail to compare against. Fortunately, one exists.

The most accurately surveyed trail in perhaps the world is the Bright Angel Trail in the Grand Canyon. The Museum of Science in Boston published and copyrighted a 1:4,800 map of the Trail in 1981, with contour intervals of 25', which was surveyed and edited by Bradford Washburn, with the assistance of many other people. The map is based on 1973 aerial photography, with key supplementary measurements of angular measurements between places in the area by Wild T-3 theodolite and of distances by K. & E. Laser Ranger instruments. Distances along the trail are given to 0.01 mile for over 60 control points along the trail.

On 20 October 1997, I followed the map continuously as I hiked the trail, to verify that indeed all the wiggles of the trail were faithfully recorded. As far as I could tell, they were. It is an amazing thing indeed to have a map in hand that you can visibly see your progress on, as well as recognize that subtle bends in the trail are clearly shown. Hence I believe that the mileages presented with that map are indeed accurate to that level.

I recorded my pedometer reading at nearly every one of those control points. The cumulative mileage given by my pedometer is plotted against the control point mileages in the leftmost plot below. The pedometer error, pedometer mileage minus control point mileage, is plotted versus the control point mileages in the rightmost plot below.

 (Click on graph for bigger and better image.) (Click on graph for bigger and better image.)

Overall, the pedometer shows amazing accuracy, especially for such a steep trail. The total error is less than 1%, 0.1 mile out of 16 miles, well within my quoted accuracy of 10% from previous comparisons of guidebook-quoted mileages and by comparing uphill with downhill total mileages for many other trails. 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 tends to cancel between uphill and downhill, and one divides by a mileage that is twice as high as the individual segments.

The detailed comparison on the right above shows that the uphill pedometer error is constant throughout the entire uphill. However, the source of the downhill pedometer error seems to come primarily from true mileage about 2-2.5 to 4 miles, where the pedometer shows a 20% high error that is not seen in reverse coming back up at true mileage 12 to 13.5 miles. This is the segment with tight switchbacks of Jacob's Ladder and the set of switchbacks farther up the trail. I speculate that the source of the error is the pronounced "washboarding" of the trail there, probably caused by mule traffic, where on the downhill segment I took longer strides in order to stay on the high points. Going uphill, I took my usual fairly measured strides since one doesn't have the energy to take long strides going uphill in the Grand Canyon.

Conclusion: The pedometer I use, a basic analog model by Precise sold for around \$20, is in general accurate to better than 10%, especially when combining uphill and downhill mileages. This conclusion comes not just from the one comparison I present here, but from many dozens of comparisons of uphill pedometer readings to downhill pedometer readings I have made in the past. However, there clearly can be stretches where the error is at least 20%.

It is astonishing to me that a pedometer can be so accurate in light of the many changes of step size that occur on a trail going uphill versus downhill. I speculate that when one is taking a lot of tiny steps, either the pedometer misses counting some of them, or that this occurs so infrequently as to not be a major factor in overall mileages. (Two years after this speculation, I got an electronic pedometer that read out step counts, and was able to verify that the pedometer missed counting tiny uphill steps. Furthermore, there was a clear difference between the rate at which the new and old pedometers accumulated mileage on that steep portion.)

Caveat: Your mileage may vary. 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.

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Copyright © 1997-1999 by Tom Chester.
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Comments and feedback: Tom Chester
Last update: 2 October 1999. (typo corrected 20 July 2001)