Converting from one Transverse Mercator based system to another produces inconsistencies?

Question

As a civil engineer, the one semester of survey training we had leaves my knowledge quite lacking in the field of coordinate systems.

We're working on a project based in Gabon and we get information from two parties in two different coordinate systems. The one coordinate system is UTM WGS84 Zone 32N, which is convenient. The other coordinate system is unknown but we got the following information from the other company:

• False easting: 500000
• False northing: 500000
• Central meridian: 11.5
• Scale factor: 0.9996
• Latitude of origin: 0.0
• Linear unit: Meter (1.0)

I used Autodesk Civil 3D to create a new coordinate system based on the above information but I don't get accurate results. When I convert the survey from one company to Lat Long and then convert that back to the other company's system everything is far out.

After digging around on the internet I found that the Gabon Transverse Mercator System of 2010 uses a central meridian of 12 degrees so I changed mine accordingly.

After this conversion the two surveys are now only a few meters off, but it is still much too inaccurate for my comfort.

I suspect that you should be able to linearly convert between the two systems without any distortions seeing that both systems are Transverse Mercator based on WGS84.

Is my understanding of this correct, or is it harder than I expect it to be? Maybe I'm missing something big and the central meridian really is 11.5 degrees.

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AndreJ's answer clears up some of my assumptions, which are clearly wrong. I am however not trying to just move the drawings from one origin to another, although this would have been possible if my assumptions were true.

I am trying to convert points from one system to lat-long coordinates. My expectation is that if I take those lat-longs and project them in my drawing in the other coordinate system then the point should be in the correct place. If the one survey is done in one of the older systems then I would completely understand that it is out by a few meters, though I expect it to be based on one of the newer systems.

Answer 1

Your assumption of linear conversion is wrong. In Transverse Mercator, only the central meridian is straight northward, all others are bended. So 11.5 vs 12 degrees makes a difference.

Besides Gabon 2010, there is a Gabon 2011 coordinate system, with this proj.4 parameter string:

+proj=tmerc +lat_0=0 +lon_0=11.5 +k=0.9996 +x_0=1500000 +y_0=5500000 +datum=WGS84 +units=m +no_defs

This might be your projection, with the first digit stripped off.

Apart from that, there is EPSG:26632 M'poraloko / UTM zone 32N defined as

+proj=utm +zone=32 +a=6378249.2 +b=6356515 +towgs84=-74,-130,42,0,0,0,0 +units=m +no_defs

You see a datum shift to WGS84. According to Clifford Mugniers article on Gabon, surveying in Gabon used the M'poraloko datum, but the shift transformation only has a poor accuracy of 25 meters. The EPSG registry also offers a datum shift of -80.7,-132.5,41.1 with 0.5m accuracy for Port Gentil.

A Cape Esteiras datum was also used, but no shift parameters are known.