calculating Lat and Long from Bearing and Distance

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jimthree

calculating Lat and Long from Bearing and Distance

in Programming Questions • 1 year ago

Hey Guys.

I'm having a hard time wrapping my head around some Trigonometry. I am trying to deduce a destination latitude and longitude from a start lat and log and distance and bearing.

Fortunately, I found an amazing site which describes exactly the function I need:

http://www.movable-type.co.uk/scripts/latlong.html " Destination point given distance and bearing from start point "

My ultimate aim is to have this calculation done on an Arduino, but I'm prototyping it in processing... Here is what I have so far.

void setup()
{
float CurLon = 0;
float CurLat = 50;
int Eradius = 6371; // mean radius of the earth
float Bearing = 90; // Bearing of travel
float Distance = 1; // km per update
float rBearing = radians(Bearing); // convert Bearing to Radians
float aDistance = Distance/Eradius; // convert dist to angular distance in radians
float DestLat = asin(sin(CurLat)*cos(aDistance)+cos(CurLat)*sin(aDistance)*cos(rBearing));
float DestLon = CurLon + atan2(sin(rBearing)*sin(aDistance)*cos(CurLat),cos(aDistance)-sin(CurLat)*sin(DestLat));
DestLon = (DestLon+3*PI)%(2*PI) - PI; // normalise to -180..+180º
System.out.printf("starting at a Longitude of %f and a Latitude of %f\n",CurLon,CurLat);
System.out.printf("if we travel %f km on a bearing of %f degrees (%f angular distance and %f in radians)\n",Distance,Bearing,aDistance,rBearing);
System.out.printf("we end up at Longitude of %f and a Latitude of %f\n",DestLon,DestLat);
}

The output reads:

starting at a Longitude of 0.000000 and a Latitude of 50.000000 
if we travel 1.000000 km on a bearing of 90.000000 degrees (0.000157 angular distance and 1.570796 in radians) 
we end up at Longitude of 0.000163 and a Latitude of -0.265482

I have obviously got something wrong somewhere, but I don't understand trig deeply enough, or equations of the Great Circle / Haversine to debug what is going wrong here. Does anyone have any experience with this kind of calculation?

thanks

Jim

Replies(2)

filmmaker..

Re: calculating Lat and Long from Bearing and Distance

1 year ago

I have used the same website and formulas for a very similar project I had worked on. Here is my code that works:

** Assuming that lat1,lon1,lat2,lon2 are given float values somewhere in the code.

Distance:

float theta = lon1 - lon2;
float dist = sin(radians(lat1)) * sin(radians(lat2)) + cos(radians(lat1)) * cos(radians(lat2)) * cos(radians(theta));
dist = acos(dist);
dist = degrees(dist);
float miles = dist * 60 * 1.1515; //Not needed if Km is fine

Bearing:

float dLat = radians(lat2-lat1);
float dLon = radians(lon2-lon1);
float y = sin(dLon) * cos(radians(lat2));
float x = cos(radians(lat1))*sin(radians(lat2)) -
sin(radians(lat1))*cos(radians(lat2))*cos(dLon);
float brng = degrees(atan2(y, x));
float bearing = map(brng,-180,180,0,360);

jimthree

Re: calculating Lat and Long from Bearing and Distance

1 year ago

Thanks for the reply and encouragement, I have got the function working as I wanted it!

Jim

float CurLon = 0.000;
float CurLat = 52.000;
float Bearing = 45; // Bearing of travel
float Distance = 10; // km per update
int Eradius = 6371; // mean radius of the earth
void setup()
{
float DestLat = asin(sin(radians(CurLat))*cos(Distance/Eradius)+cos(radians(CurLat))*sin(Distance/Eradius)*cos(radians(Bearing)));
float DestLon = radians(CurLon) + atan2(sin(radians(Bearing))*sin(Distance/Eradius)*cos(radians(CurLat)),cos(Distance/Eradius)-sin(radians(CurLat))*sin(DestLat));
DestLon = (DestLon+3*PI)%(2*PI) - PI; // normalise to -180..+180º
System.out.printf("starting at a Longitude of %f and a Latitude of %f ",CurLon,CurLat);
System.out.printf("if we travel %f km on a bearing of %f degrees ",Distance,Bearing);
System.out.printf("we end up at Longitude of %f and a Latitude of %f ",degrees(DestLon),degrees(DestLat));
}

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