How to Calculate Scale Factor in Land Surveying

A map projection offers a way of depicting the earth’s curved surface of on a flat surface in order that coordinate grids can be determined and maps can be made. The referring or relative positions of the grid points are changed to some extent from their ground positions because of utilizing Transverse Mercator Projection to present the earth curvature.

The scale factor formula is

Scale Factor = Grid Distance / Measured Distance (at Mean Sea Level)

For instance, assume the following two coordinates

1. A = 1882281.927, 182474.093

2. B = 1882314.193, 182458.059

3. The grid distance or calculated distance on the map is presented as 36.03

4. It means (1882281.927-1882314.193)² + (182474.093 – 182458.059)²) = 36.030

5. In case you calculated the horizontal distance between coordinates A and B in ground with total station or tape and obtained 36.000 meters. Subsequently, the scale factor is computed as

6. Scale factor = Grid distance / Measured distance (at Mean Sea Level)

7. Scale factor = 36.030/36.000 = 1.000833

8. Therefore, we can compute the ground distance from the aforementioned plan

9. The ground distance between points/coordinates A to B (or 1 to 2) = 36.03/1.0008428 = 36.00

The uncomplicated way to compute the scale factor is to hold the two coordinates and measure the distance between them through calculator. After that, calculate the actual distance between the coordinates/points with total station or tape. After that, divide the calculated or grid distance by measured distance. For construction or road works, scale factor can be incorporated in the construction sites.

To gather more information, go through the following link: www.gpslandsurveying.com