Measurement accuracy for small distances - geodesic vs. planar UTM WGS84

Question

Does anyone know how accurate geodesic measurement is compared to planar measurements in UTM WGS84 for distances below 15km? We'd like to inform our users about measurement accuracy when using tools based on geodesic measurements. Some of these measured distances are critical because we have to comply with margins regulated by law.

Some tests (3km line drawn in UTM32 WGS84 and measured geodesic) have shown that the difference can be up to 0,5%. Can anyone confirm this? Maybe based on literature or formula? I couldn't find anything in the Internet...

Or am I completely wrong and both measurements have to be identical within one UTM zone because they are based on the same ellipsoid (WGS84)?

Answer 1

As commented by @whuber:

By design, the UTM scale factor is off by up to 0.04% throughout each zone (and it varies from being too short in the middle to too long at the edges, at least at lower latitudes). By definition, geodesic measurements are correct, provided you are using an appropriate datum. Thus your phrasing is a little puzzling: there should be no question of inaccuracy in geodesic measurements (unless you are using a poor approximation or datum). If you are finding errors up to 0.5%, that implies something is wrong with one or both of your calculations.

and:

I didn't mean to create the impression that both measurements would be identical up to some fixed or easily determined scale factor: the relationship depends on both endpoints of the measured segment. The two lengths ought to be within 0.04% of each other. The geodesic calculation is the accurate one, assuming it is correctly and precisely carried out and you do not need to compensate for the elevation or local topographic variation. The UTM measurement is an approximation based on the TM projection, whose scale factor varies with longitude (by different amounts at each latitude).