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December 23, 2006

Odometer versus GPS

Filed under: General MTBGuru stuff,GPS — mtbguru @ 9:11 am

In the previous post we compared GPS elevation data to elevation data from topographic maps – the latter giving you generally more averaging than the former. Something similar is going on when you compare GPS distance data to bike odometer distance data – but the roles are inverted here: the GPS averages more than the odometer.
Let’s look again at the snippet of Garmin Edge 305 data from the Tahoe Rim Trail:

GPS data

The distance between a given datapoint and the previous one is now plotted in blue. The GPS device records longitude and latitude, from which this distance can be calculated using fairly simple trigonometry; we use the haversine form of the great circle distance, which works well (in terms of rounding errors) for points relatively close to each other.

Let’s now consider the data you would get from an odometer. First, we assume that the circumference of the wheel is properly set up in the odometer, in which case it can be considered quite accurate. The odometer essentially takes a datapoint for every revolution of the wheel; for a 26 inch wheel and a speed of 5 mph (hey, it was a tough technical climb at altitude), there is about 1 second in between datapoints. For higher speeds, there is less than that.

Compare this to the GPS: the Edge at its fastest takes 1 point per second, and usually much less, as you mostly want to use it in its ‘smart’ or adaptive mode (to limit the amount of data recorded and make economic use of memory). On the graph below, this is illustrated by the higher density of (red) odometer datapoints than the GPS points:

GPS + odo data

The odometer of course doesn’t really record all these points, but the figure shows what they would look like if it did. It does record a cumulative (total) distance number though. How does it get this? By simple adding the lengths of all line segments between the points. This is done for both GPS and odometer in the figure below. The odometer will almost always give you a higher total distance reading than the GPS (in particular on fairly bumpy or technical rides) because all the red (odometer) line segments add up to a higher total than all blue (GPS) segments – this is so because the odometer simply samples at a higher rate than the GPS (see also the ‘length of a coastline’ problem). You could of course try to compensate for this effect by doing lots of wheelies ;) .

Update (12/30/06): as ragetty observes in the comments below, the latter paragraph isn’t entirely accurate: the odometer doesn’t give a better number because it samples at a higher rate than the GPS, but because the wheel tracks all features of the trail (at least, those features with size in the order of the wheel diameter). What I tried to say is that if the GPS would sample at a higher speed, it would be in better agreement with the odometer.

GPS + odo data 2

12 Responses to “Odometer versus GPS”

  1. BayAreaBiker2001 Says:

    A GPS can swithc from biking to running/hiking without modification. A cylometer is limited to biking, a pedometer is limited to running and walking.

  2. mtbguru Says:

    Yes indeed. To be clear: this article compares data taken on a bike ride from a GPS to data from an odometer/cyclometer (device based on a sensor counting wheel revolutions).

  3. ragetty Says:

    i don’t think this has anything to do with sample frequency, rather that the wheel follows the contour of the ground (with it’s subtle or not so subtle highs and hollows) and not a straight line (or arc of a great circle) between any two points.

    the wheel (more) accurately integrates all lengths travelled by the wheel over all inclinations, whilst gps calculates the distance between 2 points assuming they are at the same elevation (i.e. the surface of a smooth great sphere otherwise known as earth). no matter how often the gps sampled, it would still be in error due to method of calculation – e.g. for a continuous and smooth 10% slope, this is 50cm every 100m, if also undulating then even higher.

    if the wheel sensor was constructed to record only every 10 revolutions, you can not convince me that the tacho would now show less distance travelled – this would have to mean that the wheel slipped *backwards* somewhere.

  4. mtbguru Says:

    What I wanted to claim is that the GPS data will converge with the ‘real’ distance traveled (as measured by the wheel sensor) if its sampling speed would be increased.

    I agree with you that the fact that the wheel sensor measures the real distance is not due to sampling speed – as you say, that’s true because the wheel tracks the features of the trail.

    So I probably should rewrite the last paragraph (“this is so because the odometer simply…”) because that says indeed something different than what I wanted to say ;)

  5. AChang’s BLog » Hello world! Says:

    [...] The slope of this curve is of course the speed, and you can quickly identify the descents, climbs and breaks. Distance is calculated from latitude and longitude using the great circle distance formula as mentioned in another post. [...]

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