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- In BIMpedia
A building is small enough that the Earth is flat for its purposes. A railway or a pipeline isn't. Map grids flatten the curved Earth onto a plane, and that flattening stretches distances slightly in some places and shrinks them in others. On a long corridor, the difference between a distance on the grid and the same distance on the ground becomes a design problem.
| Term | Meaning |
|---|---|
| Grid distance | Distance computed from map grid coordinates |
| Ground distance | Distance actually measured on site, at the site's height |
| Grid scale factor | Grid ÷ ellipsoid distance at a place on the projection |
| Elevation factor | Corrects for height above the ellipsoid |
| Combined scale factor | Grid scale factor × elevation factor |
How big is the difference?
National grids are designed to keep the scale factor close to 1: typically within a few hundred parts per million (ppm) across the country. A factor of 0.99985 is −150 ppm: every kilometre on the grid is 1,000.150 m on the ground. Over a 300 m building that's 45 mm, often ignored. Over a 20 km route it's 3 m.
| Route length | Error at 150 ppm |
|---|---|
| 300 m | 45 mm |
| 1 km | 150 mm |
| 10 km | 1.5 m |
| 20 km | 3.0 m |
Three ways projects handle it
- Work in grid, convert for set-out. Models in the national grid; the surveyor applies the combined factor when setting out. Simple, but every team must know.
- Work in ground, tie to grid. Models at true size; a documented transformation (with scale) maps them to the grid. Common for buildings and short structures.
- A low-distortion project grid. A projection designed around the route so the factor stays within a few ppm everywhere. Used on many long rail and road schemes.
Whichever you choose, write it on the georeferencing sheet: the CRS (EPSG code), whether model units are grid or ground, the combined factor by zone, and who maintains them.
The viaduct designers model at true ground size from a local origin at the south end. The track designers work in national grid. Nobody records a scale factor. At the north end, 20 km away, the viaduct's last pier and the track alignment disagree by 3 m.
At mobilisation the surveyor issues a project grid with a stated factor of 1.000002 along the whole route, and every model is built in it. The viaduct and the track agree to millimetres at both ends.
A pipeline runs 8.4 km. The surveyor gives a combined scale factor of 0.99978 for the route.
- The design gives a grid distance of 8,400.000 m. What is the ground distance?
- How many metres of pipe would be short if it were ordered from the grid length?
- What would you write on the georeferencing sheet so no team repeats the mistake?
Key takeaways
- Projected grids distort distances slightly; the grid scale factor says by how much at each place.
- Height above the datum adds an elevation factor; together they make the combined scale factor.
- Ground distance = grid distance ÷ combined scale factor (for factors close to 1).
- Long projects often use a low-distortion project grid so that grid and ground almost match.