coordinate system - Formula for calculating short distances in UTM?

I'm fairly new at calculating distances with precision, but I wanted to know what is the best formula for calculating short distances in UTM coordinates.

The distances that I'am calculating are all less than 30 km and all coordinates lie at Central America.

For instance, the pythagorean distance could cause too much bias?

If not, would it still be a respectable choice either way?

If possible, base your answer on some sort manual or academic paper (and make a reference to it).

Answer

The best way I can think is to get two UTM points, convert them to Lat/Long, and compare their geodesic distances to their UTM pythagorean distance.

E.g. Take a point from this example:

The CN Tower is ... in UTM zone 17, and the grid position is 630084m east, 4833438m north.

So if we take A (17n 630084 4833438) and move it 30 km east, we get B (17n 660084 4833438). Convert these to Lat/Long (using GeoConvert), where A' (43°38'33.2224"N 079°23'13.7143"W), and B' (43°38'12.1573"N 079°00'55.3849"W). Now, find the inverse geodesic between A' and B' (using GeodSolve), and the resulting length s12 is 30004.205 m, or 0.0140% larger.

Similarly, moving A 30 km north is C (17n 630084 4863438) or C' (43°54'45.2518"N 079°22'47.5212"W), where the distance between A' and C' is 30005.647 m or 0.0188% larger.

We see that the UTM projection around the CN Tower is underestimating the true distance by about 0.016%. Note that there is anisotropy in the warping of the transverse Mercator projection, depending on the azimuth of the two points in the analysis. An analysis in a different part of the world will yield a different answer, so do your own analysis on a bunch of pairs of points from your region of interest.

Literary references are available on the pages I linked to.