Gmap and Hills (Read 915 times)

Here's a geeky question. Does Gmap (or a Garmin, for that matter) take three dimensions into account when it measures distance? If a rolling course is measured as if it took place on a two-dimensional plane (like a computer screen or the surface of a globe), then the measurement will come up short because it won't take into account the distance traveled in the third dimension (up and down). I know that it can chart this third dimension with the elevation toggle, but it does not do this automatically. I can imagine several possible responses to this question: 1) Gmap doesn't take the third dimension into account when it measures distances, but it's not a big deal because the distance traveled in the third dimension is so minuscule that it's not worth worrying about. or 2) Gmap does take it into account. or 3) Oh my god, you're right! We've all been running farther and faster than we thought!!! Hold the presses!!! Adjust the pace bunnies!!! or 4) Aren't you supposed to be a running purist? Why the heck are you worried about the fractions of a mile you might or might not be running? Just get out there and RUN! Any other responses?

#4. And No, gmap does not take this into account when calculating distance. Neither does RA. And No, it does not really make much difference to include this in the distance calculations. --------------------------------------------------------------------------------------------------------------------------- Doing the math: Grade is defined as rise over run, multiplied by 100. So a course that rises 100 feet over a mile is (100 / 5280) * 100 = 1.8% To determine the distance run on the hypotenuse of this route, you can apply the Pythagorean Theorum, which states that A^2 + B^2 = C^2 (where the notation ^2 means squared). So in a triangle formed on one side by the distance 5280 feet and on another side by the distance 100 feet, your hypotenuese = sqrt(5280^2 + 100^2) = 5 280.9. Catch that? A 2% grade, which is just over a 100 foot climb over a mile adds one foot to your distance. That is less than 0.1% error per mile, which is insignificant. That is less than a foot of error per mile. This may matter more on a nasty run, such as the Pikes Peak Marathon. The Pikes Peak Marathon includes a 13 mile climb up more than 7500 feet, with an average 11% grade. Assuming you actually do climb 13 miles in 7500 feet, let's determine the error. 13 * 5280 = 68 640 feet. Applying the Pythagorean Theorum, we get sqrt(68 640^2 + 7500^2) = 69 048.5 feet. That is a difference of 408.5 feet over 13 miles (31 feet per mile), or a 0.6% error. I think that with these mapping tools, you are more likely to introduce more feet to your expected distance run by your mapping (im)precision rather than by the effects of elevation change.

Jeff, I've wondered about this as well. The answer is no, GMAPS does not take elevation change into account when calculating distances. The is from the FAQ section of GMAPS: "The google maps API does not expose data about elevation, which means that elevation changes are not taken into account in calculating the distances. Some users have pointed out that there are services available on the web which can return elevation given a certain latitude and longitude point. I experimented a bit with adding functionality to the site to show that, but wasn't thrilled with the fact that the data is only available for the US, and seems to be intermittent in its reliability. Maybe some day it'll be added, if enough folks indicate that want it, and they're comfortable with the fact that it may not be all that reliable." Hope this helps

Jeff, "but wasn't thrilled with the fact that the data is only available for the US, and seems to be intermittent in its reliability."

RA seems to be quite precise here in Austria, as opposed to some other sites that I tried.

A slightly different question is (and I haven't found this out yet), is whether Google Earth takes 3-D into account with distance traveled, since it is a 3-dimensional rendering of the earth. Anyone know? I'm guessing no since vertical is negligible in almost all cases. The following link didn't answer my question explicitly (unless I missed it), but there's a very interesting and geektastic overview of the challenges of distance measurement over a large scale spherical surface. Google Earth and Geographic Distances

--anybody got any good ideas for a dissertation prospectus?

How about... Correlations of "Up, Up and Away", Fartlek and IPod Marketing, or An Inquisition Into the Matter of "^" ? Lynn B

The distance tracked on my Forerunner is usually shorter than what MB tells me once I've uploaded my workout depending on how hilly it is. A GPS the size of mine only calculates distance based on a flat plane. The difference is usually less than 1/4 mile unless I'm doing a lot of peaks and valleys in the mountains where I've seen it as much as 3/4 of a mile. It's fairly accurate once you factor in actual distance traveled. I know you can use the rise over run formula, but that only works on a consistent grade. There are some trails I run where you start out on top of a 150 foot hill then you go down, then back up 60 feet, then back down, then back up to 200 feet. Straight line might be 1 mile, but actual distance traveled comes out 1.5 miles.

Using the example, as you suggest, of a one mile horizontal route that drops 150 feet, then climbs 60 feet, then drops 60 feet, then climbs 200 feet, and assuming that each of these changes is a continuous plane occurring over 1/4 mile (they are not likely doing this, and this would MINIMIZE the effect of the change), the total distance run is 1 mile and 26 feet. So you are off by just 26 feet, a 0.5% error. Taking the same course but assuming that each change in elevation is a vertical drop or climb (which would MAXIMIZE the effects of the change), the total distance is 1 mile and 470 feet. That is an 8.9% error, still far less than the 0.5 miles (i.e., a 50% error). My guess is that the truth is somewhere between the 0.5 and the 8.9% estimates. (thanks olethros!)