Here is a very simplified discussion of Grid Scale factor and why you need to include it in your surveying knowledge.
#ScaleFactor #UTMGrid #SurveyConcept


Formula for Point Scale Factor :-

SF = k0 * (1 + ((E - E0) * sin(phi) * tan(phi)) / (2 * rho^2),

where:
SF is the scale factor at the given location
k0 is the scale factor at the central meridian, which is 0.9996 for UTM zone 43
E is the easting coordinate of the given location in meters
E0 is the easting coordinate of the central meridian in meters
phi is the latitude of the given location in radians, which is 20°N converted to radians (0.349 radians)
rho is the radius of curvature of the ellipsoid at the given latitude in meters

To calculate rho, you need to use the following formula:
rho = a * (1 - e^2) / ((1 - e^2 * sin^2(phi))^1.5),

where:
a is the equatorial radius of the ellipsoid, which is 6,378,137 meters for the WGS84 ellipsoid used in the UTM system
e is the eccentricity of the ellipsoid, which is 0.081819191 for the WGS84 ellipsoid

Using these formula -- rho = 6,371,007.2 meters

So, the Scale Factor at 20°N can be calculated as:
SF = 0.9996 * (1 + ((500,000 - 750,000) * sin(0.349) * tan(0.349)) / (2 * 6,371,007.2^2))

SF = 0.99953