Calculating distance discrepancy: EPSG 3112 Projection VS GeoDesic (Karney), is ~0.5% difference normal?

Question

I have lat-lng coords in EPSG:4326, and I'm calculating the distance between them (in metres).

Since these are in Australia (and Australia wide, therefore no specific MGA zone projections), I'm using the Australia wide (metres) projection EPSG-3112 (if there's a better EPSG projection for measuring distance Australia wide, please let me know).

I'm wondering if a discrepancy of ~0.5% / 0.4% (compared to Karney output) is normal? From what I understand; Haversine is for spherical, Vincenty is for Ellipsoids, and Karney is a better Vincenty formula?

I am calculating the Karney distance using GeoPy.

Two examples of my measurements are:

• Mildura -> Bendigo:
  • EPSG:3112 - 342,215 m
  • Karney - 342,675 m
• Mildura -> Shepparton:
  • EPSG:3112 - 384,180 m
  • Karney - 384,358 m

But I also have similar discrepancies of 0.4% at smaller scales.

Answer 1

There's no map projection which preserves distances. So the errors you're seeing are expected. Measuring distances in a small area usually won't help unless your area lies on one of the standard parallels for the projection (lat = 18S or lat = 36S in the case of epsg:3112).