iPhone distances

One of the cute things that iPhones started doing was measuring how far you walked or ran–even if you didn’t ask it to do that. (Pace count is a different beast that, realistically, did not work well here). Folks have questioned the numbers that come out from their phone, so it seems mildly worthwhile to take advantage of some long-distance numbers that came out of a llama trip along the John Muir Trail last summer. Distances between campsites were estimated from a guidebook and compared with the distances the iPhone recorded each day:

DistancePlot

There are a few ways to interpret this. A best-fit line would indicate that there was an additional 0.23 miles of walking each day and the iPhone mileage was about 8.6% higher than the guidebook distance. Alternatively, if the iPhone distance was correct, then there was a mile of so of walking each day beyond the hiking on the trail.  The former seems more likely (the iPhone was generally kept in a backpack that was dropped immediately in camp). But why would there be a nearly 9% difference in distance?

One way to look at this is to say that iPhone distances tend to be a bit high and you probably would say you walked a bit more than 90% of the distance shown.

Another way is to say that the typical guidebook estimates of distance along the trail are a bit off–some of the distance along the wiggles in the trail were not caught. The iPhone might catch that because of the accelerometer’s contribution to the distance estimate, while the guidebook estimate might be from GPS measurements along the trail that might cut across switchbacks. (Years ago, a hiker might have a distance wheel tied to his pack to measure distance). This would suggest that the actual on-the-ground hiking distance is about 8% higher than what the guidebook says (so the Muir Trail, instead of being 220.8 miles from Yosemite Valley to Whitney Portal might actually require 239.8 miles of hiking). The very few and fairly long switchbacks on day 18 and the close coincidence of iPhone and guidebook distances tends to support this, as does the mismatch on day 14, when we hiked up the Golden Staircase, and day 17 over Glen Pass, both of which have a large collection of tight switchbacks.

It isn’t easy to test this, but we can look at the mismatch between the iPhone and the guidebook as a function of the wiggliness of the trail.  A second GPS device was active the whole trip, a YB satellite tracker, and it only got a position every 30 minutes, so it did not capture any detailed wiggles.  From the map, it appears to have done a decent job of getting positions on the trail. A really wiggly section of trail will have a big mismatch between the YB distance and the guidebook distance, while a fairly straight stretch won’t. If the iPhone accumulates random errors all along, then the bigger mismatches won’t correlate to wiggly trails.  If the guidebook is missing distances on wiggly trails, there should be a correlation.

iPhoneWindingTest

This test uses ratios.  The closer the YB cumulative distance is to the guidebook, the straighter the trail. So we expect that the iPhone distance  will be closer to the guidebook the straighter the trail, so some trend like the red line is what we expect. The data, if anything, look to do the opposite. This might make sense as errors in individual distances due to bad GPS locations will tend to be higher when the trail is straighter (an error off a perfectly straight line will always produce a longer distance, but if the path is winding, an error can both increase or reduce the distance, so a sum over such errors will tend to cancel out).

A final thought was that the iPhone was calculating distances in three space (i.e., including changes in elevation). With several thousand feet of elevation change over a few miles near passes, about a 2% longer distance seems possible. But there is no correlation of the iPhone excess distances with elevation changes in a given day. For instance, days 17 and 18 had almost identical shortages of distance travelled (guidebook-YB) and very similar elevation changes, but day 17 had the largest iPhone excess distance (2.4 miles more than the guidebook) while day 18 had one of the smallest (0.1 miles).

Conclusion is that the iPhone tends to overestimate distances travelled by an average of about 9%, with the value reaching nearly 25% on the straighter trail segments but lowering to under 10% on more winding sections of trail. So if you are relying on your iPhone’s default health app to tell you how far you’ve gone–don’t trust it too much. If there are errors in the distances in the guidebook used for the Muir Trail, this analysis can’t ferret them out.

Details. iPhone 6, iOS 9.3.2 when the data was recorded. The app reports most intervals were about 0.1-0.2 miles (~5 minute intervals), but occasionally it went over a mile before posting an accumulation (sometimes an hour+interval).

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