Why is this bearing calculation so inacurate?

Question

Is it even that inaccurate? I re-implented the whole thing with Apfloat arbitrary precision and it made no difference which I should have known to start with!!

public static double bearing(LatLng latLng1, LatLng latLng2) {
 double deltaLong = toRadians(latLng2.longitude - latLng1.longitude);

 double lat1 = toRadians(latLng1.latitude);
 double lat2 = toRadians(latLng2.latitude);

 double y = sin(deltaLong) * cos(lat2);
 double x = cos(lat1) * sin(lat2) - sin(lat1) * cos(lat2) * cos(deltaLong);
 double result = toDegrees(atan2(y, x));
 return (result + 360.0) % 360.0;
}

@Test
 public void testBearing() {

  LatLng first = new LatLng(36.0, 174.0);
  LatLng second = new LatLng(36.0, 175.0);
  assertEquals(270.0, LatLng.bearing(second, first), 0.005);
  assertEquals(90.0, LatLng.bearing(first, second), 0.005);
 }

The first assertion in the test gives this:

java.lang.AssertionError: expected:<270.0> but was:<270.29389750911355>

0.29 seems to quite a long way off? Is this the formula i chose to implement?

Answer 1

If you've done what you seem to have done and done it correctly you have figured out the bearing of A from B along the shortest route from A to B which, on the surface of the spherical (ish) Earth is the arc of the great circle between A and B, NOT the arc of the line of latitude between A and B.

Mathematica's geodetic functions give the bearings, for your test positions, as 89.7061 and 270.294.

So, it looks as if (a) your calculation is correct but (b) your navigational skills need polishing up.

Answer 2

Are you sure this is due to numeric problems? I must admit, that I don't exactly know what you are trying to calculate, but when you dealing with angles on a sphere, small deviations from what you would expect in euclidian geometry.

Answer 3

java.lang.AssertionError: expected:<270.0> but was:<270.29389750911355>

This 0.29 absolute error represents a relative error of 0.1%. How is this "a long way off"?

Floats will give 7 significant digits; doubles are good for 16. Could be the trig functions or the degrees to radians conversion.

Formula looks right, if this source is to be believed.

If I plug your start and final values into that page, the result that they report is 089°42′22″. If I subtract your result from 360 and convert to degrees, minutes, and seconds your result is identical to theirs. Either you're both correct or you're both wrong.