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update easting and northing using distance and bearing

Posted on 2009-07-09
Last Modified: 2012-05-07
Could anyone suggest a formula / method for updating eastings and northings using a distance and a bearing?
Question by:gardnerw
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LVL 55

Expert Comment

by:Jaime Olivares
ID: 24833449
at a first approach, I think you must always operate coordinates as latitude/longitude and then apply conversion to UTM
LVL 15

Expert Comment

ID: 24840773
When you say Northing & Easting, do you mean Lat/Lon or in some kind of projection?

The following page is one I've gotten a lot of information from. To project a point a given distance & bearing from a given coordinate, you could use the equations to determine destination using Rhumb lines.
LVL 15

Expert Comment

ID: 24840777
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Author Comment

ID: 25280146
Hi sorry for such a late response to your posts,

The data is on OSGB70 projection, it would be sitting within a variety of GIS applications. Ideally i would like to be able to export it to a xls, csv or  dxf then specify a bearing and a distance to update specific points.

Many Thanks
LVL 15

Accepted Solution

oobayly earned 500 total points
ID: 25280979
Unfortunately I'm not familiar with OSGB70, as I normally deal with OSGB70 & WGS84. However:

OSGB70 & ODGB36 share the same ellipsoid:
OSGB70: http://www.eye4software.com/products/coordinatecalculator/datum/175/
OSGB36: http://www.eye4software.com/products/coordinatecalculator/datum/12/

This page gives you some idea of how to do the transformation:

The nice thing is that as the transformation and rotation parameters are all zero (for WGS84 & OSGB70), you only have to convert your coordinates in OSGB70 to Cartesian (using the Airy ellipsoid), and then straight back to WGS84 coordinates (using the WGS84 ellipsoid).
Actually, I'm guessing that your data is already cartesian coordinates as you mentioned Eastings & Northings, so you should only have to use the ToWGS84 method.

Then operating on the WGS84 using the equations in the 1st set of links I posted.

private static void FromOSGB70(double lat, double lon, double h,
  out double x, out double y, out double z) {
  // WGS coordinates in radians
  double phi = lat * Math.PI / 180;
  double lambda = lon * Math.PI / 180;
  // Airy 1830 ellipsoid parameters
  // http://www.eye4software.com/products/coordinatecalculator/datum/175/
  // Semi-major axis
  double a = 6377563.396;
  // Flattening
  double f = 1 / 299.3249646;
  // Eccentricity squared
  double e2 = (2 * f) - (f * f);
  double nu = a / Math.Sqrt(1 - e2 * Math.Pow(Math.Sin(phi), 2));
  x = (nu + h) * Math.Cos(phi) * Math.Cos(lambda);
  y = (nu + h) * Math.Cos(phi) * Math.Sin(lambda);
  z = ((nu * (1 - e2)) + h) * Math.Sin(phi);
private static void ToWGS84(double x, double y, double z,
  out double lat, out double lon, out double h) {
  // WGS84 ellipsoid parameters
  // http://www.eye4software.com/products/coordinatecalculator/datum/7/
  // Semi-major axis
  double a = 6378137;
  // Flattening
  double f = 1 / 298.257223563;
  // Eccentricity squared
  double e2 = (2 * f) - (f * f);
  double p = Math.Sqrt((x * x) + (y * y));
  double r = Math.Sqrt((p * p) + (z * z));
  double mu = Math.Atan2(
    z * ((1 - f) + (e2 * a / r)),
  double lambda= Math.Atan2(y, x);
  double phi = Math.Atan2(
    (z * (1 - f)) + (e2 * a * Math.Pow(Math.Sin(mu), 3)),
    (1 - f) * (p - (e2 * a * Math.Pow(Math.Cos(mu), 3)))
  h = (p * Math.Cos(phi)) + (z * Math.Sin(phi)) -
    (a * Math.Sqrt(1 - (e2 * Math.Pow(Math.Sin(phi), 2))));
  lat = phi * 180 / Math.PI;
  lon = lambda * 180 / Math.PI;

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