Grid convergence

I was trying to overlay the British National Grid (OSGB 1936 UTM projection) onto the Eurostat grid (ETRS 1989 LAEA Europe) and realized that they do not perfectly overlay (after projecting the Eurostat grid to OSGB 1936 map projection). The Eurostat grid tilts slightly. I discovered that this is due to Grid convergence which I calculated for both grids and are different.

Does grid convergence differ for each different map projection or it is not dependent on map projection alone but other factors as well?

I believe there is some misunderstanding between projection / transformation.

The European Grid uses a Lambert Azimuthal Equal Area projection.

The British National Grid uses a Transverse Mercator Projection. UTM is a series of secant Transverse Projections which span the Earth.

Changing cartesian (projected coordinates, e.g. x/y) between projections is no problem as long as the coordinate is within the extent of both projections.

The two projections which you mention use different datums.

The European Grid uses ETRS89 as datum.

The British National Grid uses OSGB36 as datum.

You will need to transform geographic coordinates (e.g latitude and longitude) between the datums. This will always be an approximation.

The picture below shows 100km grid squares reprojected to EPSG4326. Red are the grid squares from LAEA (EPSG3035), blue are the squares from BNG (EPSG27700).

As mentioned in comment a square from one projection cannot be a square in a different projection.

True north (EPSG:4326) will be straight up. The grid convergence can be calculated for any point. But the shape is defined by the projection.

Short answer: Grid convergence is different for different projections but also within a projection.

• Hi Dennis, Thank you for the quick answer to my question..I have managed to do to the transformation between the datums and that is not a problem. My issue when when I overlay the 2 grids, one is tilted so they do not perfectly overlay. I discovered from literature that this is caused by different grid convergence, which I calculated and discovered that it is different for the 2 grids. My question is does grid convergence differ with map projection or other factors contribute as well? Thank you Jan 3, 2018 at 11:38
• Tilt is due to convergence; But the shape is due to the different type of projection. In answer to your comment grid convergence is different with projections but also within the projection. Two sheets in the same projection can have a different convergence. Jan 3, 2018 at 13:10
• Grid convergence can also be different at every point. If a grid is built using the projected coordinates, it has to be reprojected to a different projCRS and could be tilted or otherwise distorted. A graticule (based on lat/lon) is projected to both projCRS, then one is reprojected to the other, they should line up (if they have enough vertices). Jan 3, 2018 at 19:01
• Thank you for your comment @mkennedy. However, I tried to project Eurostat grid from ETRS89 to British Gird OSGB36 and vice-versa and they did not align. I tried to project Eurostat grid first to WGS84 then to OSGB36 and they still did not line up. Any other way I can project the 2 in order to have the line up? Jan 4, 2018 at 10:39
• Are they graticules or grids? AKA do the lines represent lat/lon lines in the projected CRS or do the lines represent even projected values like every 500 km? If they're grids (projected values), they'll have completely different values in another projected CRS. Jan 4, 2018 at 21:17