I am working on a field survey and a client requirement is to differentiate various norths, like magnetic north, true north and grid north. My question is what is the methodology of calculating north and how can we differentiate various type of north as above mentioned.
Your question is not clear but let me try if it is useful to you.
1) Differentiate various types of north:
- True north .... Direction of meridians (lines of equal longitude) at your survey site. On a globe, these meet at the poles. On a map, it depends on the map projection.
- Grid north .... Direction of vertical lines (of equal eastings) making up the map grid.
- Magnetic north ... Direction of local magnetic field.
2) Methodology for calculating various norths:
You should know the following terms: azimuth, grid bearing, magnetic bearing and convergency.
- Azimuth of a survey line is the clockwise angle from the true north. Grid bearing of survey line is clockwise angle from grid north and similarly clockwise angle from magnetic north is Magnetic bearing.
- Azimuth can be obtained by astronomical observations (tedious) or can be computed by latitude and longitude (spherical coordinates and spherical trigonometry).
- Grid bearing can be computed by grid coordinates (simple trigonometry).
- Covergency is the difference in angle between True north and Grid north. It will depend on which map projection is used. For example, on a transverse Mercator projection, it is computed by the arctangent of the product of tangent of delta lamda and sine of phi, where delta lamda is the difference between longitudes of place of observation and of grid origin, and phi is latitude of place of observation. See wiki/Transverse_Mercator_projection
Grid bearing = True bearing - convergency
Sorry i cant explain with a diagram here but i hope you are familiar enough with the terms needed to solve your problem.
On the web you can find some Bearing converter calculator like these ones:
http://www.geomag.bgs.ac.uk/data_service/models_compass/gma_calc.html (for uk only and reliable)
but, usually all oficial national mapping services produce maps with this info.