Calculate new coordinates given lat/long/bearing/distance in C

Posted on 2011-09-28
Last Modified: 2012-08-13
I would like an example or some C code showing how to calculate the new longitude and latitude coordinates if one has the starting point, in longitude and latitude, along with the distance to travel, in feet, and the heading/bearing. So for example if I have the long/lat as:
4290816,-78793945 distance = 50 feet and bearing = 55 degrees I need the new long2 lat2.

I have seen the data at:

but haven't been able to get the formulas to work correctly.

Again I need this in C, not Jave/Basic/Perl what have you.

Question by:atomicgs12
  • 2
LVL 16

Accepted Solution

HooKooDooKu earned 400 total points
ID: 36720534
Using the formulas shown at your second link, the C code should look something like this:
      long double lat1;
      long double lon1;
      long double lat2;
      long double lon2;
      long double Th;
      long double d;
      long double R;

      const long double PI = 3.1415926535;

      lon1 = 42.90816;
      lat1 = -78.793945;

      Th = PI * 50 / 180;      //Must convert Bearing in degrees to radians
      d = 50;                        //Distance in feet, so...
      R = 3959 * 5280;      //Mean Radius of the earth in feet (note, earths radius varies from 3947 to 3968 miles)

      lat2 = asin( sin(lat1) * cos(d/R) + cos(lat1) * sin(d/R) * cos(Th) );
      lon2 = lon1 + atan2( sin(Th) * sin(d/R) * cos(lat1), cos(d/R) - sin(lat1) * sin(lat2) );

The key is to remember that the trig functions us radias.  So your 55 degees must be converted to radians.  The formula uses the value distance/earth radius over and over.  What ever your dimensions for distance need to match for earth's radius.  So if you distance is in feet, you must plug in earth's radius in feet.  Then just to throw confusion into the mix, the earth's radius is not fixed because the earth isn't a perfect sphere.  So the numbers you use might be different than the numbers someone else has used for earth's radius.

Author Comment

ID: 36720649
When I run you code, with 55 as bearing, I get the following values:
lon2 = 42.908160000000002
lat2 = 0.95993108859688125
this was kind of the values I was getting before. I was wondering about the lat2 formula, maybe it is suppose to be lat2 = lat1 + asin( sin(lat1) * cos(d/R) + cos(lat1) * sin(d/R) * cos(Th) );

Did you run you code?
LVL 84

Assisted Solution

ozo earned 100 total points
ID: 36814257
are you converting lat and long to radians when you take sin and cos?
I get lat2=-1.375212233366 radians = -78.7938569 degrees

Author Comment

ID: 36815551
Ah 'ozo' you are correct, I had the radian conversion in there but for testing I commented out that section. When converting back it looks like the correct values now. Thanks

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