# Calculate length of line across zones with at least m accuracy

I have created lines between multiple points that are across MGA 54 and 55S (EPSG 28355). I am trying to calculate the distance between points but different methods give different answers (~1km difference).

All data is in GDA94 (EPSG 4283 as it en composes both projections)

If anyone wants to try the two test points are

Normanton PO -17.669563 141.079541 to Mareeba site (off Kirrakoppa Rd) 145.417391 -16.999263

What is the most accurate method? if any.

Source question for background is Draw line between points from multiple datasets

• This publication may be of interest but I think geodesists at the Dept of Natural Resource Management would probably recommend projecting to Queensland Albers for measurements such as these. – PolyGeo Feb 28 '14 at 1:12
• Thanks @PolyGeo -when the dataset is converted to 3577 (Australian Albers) and I now get 468.467, that's now a 2km difference between the GDA94 based calculations – GeorgeC Feb 28 '14 at 2:02
• To create Queensland Albers copy the *.prj you used for Australian Albers and set Central Meridian: 146, Standard Parallel 1: -13.166667 and Standard Parallel 2: -25.833333 - you would expect more distortion using an Australia-wide PCS than when using one designed for Queensland. – PolyGeo Feb 28 '14 at 2:34
• Thanks. I am now getting 465.360 which is much lower than the values in GDA94. It is a methodology and projection based issue - I want to figure out what the best system to use is. – GeorgeC Feb 28 '14 at 5:24
• Please post the full precision, original MGA values. – mkennedy Feb 28 '14 at 21:43

Presuming your original coordinates are indeed where you hope to start and finish in the real world, the correct distance is 467009.0 metres in UTM. No doubt QLD Albers is better, but will whoever uses the data after you be working with that precision / technology?

If you pay for a road gang to lay tarmac the full distance, they may engage a surveyor to check that there is 468 km or less in that distance. They may still try to charge you for the GDA94 distance....

When a new model for the Geodesy of that part of the world is released a few years into the future, they may argue that they didn't get paid enough.

So what version of the distance you accept is a point of arbitrage, depending on your purpose.

I'm writing an answer just because I'm going to run out of space in a comment! Sorry, there's going to be question coming up later. (also asked in a comment)

NGS Inverse program gives 467.009 km. That's also what I get in the Esri projection engine. NGS and Esri projection engine are both using Vincenty. Esri has some extra code to handle near-antipodal points.

Edit: Rhumb line/loxodrome on the same pair gives 467.019 km.

You have great circle, rhumb line, geodesic, AND let's-treat-degrees-as-if-they're-Cartesian distances. You can't compare one to the other, except to decide if the great circle or rhumb line are good enough versus the geodesic calculation.

Can you post the original XY coordinates in the two MGA systems? That might be where some of the discrepancies are coming from.

Albers is equal area and does not maintain distances. These points are between the standard parallels so all distances are too short.

Disclosure: I work for Esri.

• I created the points using GDA94 and not MGA. It is for pigeon racing from start point to the loft. We were just concerned by the different distances but if we use one method then the relative distances will be the same. – GeorgeC Mar 2 '14 at 22:48