GPS/GIS Calculations: Algorithm to predict future position based on movement/mph?

Question

Looking for resources or algorithm to calculate the following in a navigation app:

If my current GPS position is (0,0) and I'm heading 32 degrees at 15 miles per hour, how can I calculate what my position will be in 10 seconds?

i.e.: GPSCoordinate predictedCoord = GPSCoordinate.FromLatLong(0, 0).AddByMovement(32, 15, TimeSpan.FromSeconds(10));

Edit: Current code based on answer below:

public GPSCoordinate AddMovementMilesPerHour(double heading, double speedMph, TimeSpan duration)
{
    double x = speedMph * System.Math.Sin(heading * pi / 180) * duration.TotalSeconds / 3600;
    double y = speedMph * System.Math.Cos(heading * pi / 180) * duration.TotalSeconds / 3600;

    double newLat = this.Latitude + 180 / pi * y / earthRadius;
    double newLong = this.Longitude + 180 / pi / System.Math.Sin(this.Latitude * pi / 180) * x / earthRadius;

    return GPSCoordinate.FromLatLong(newLat, newLong);
}

Answer 1

Here is the complete parametric answer :

variables :

• heading : heading (i.e. backwards angle from azimuth 0°, in degrees)
• speed : velocity (i.e. norm of the speed vector, in miles/hour)
• lat0, lon0 : initial coordinates in degrees
• dtime : time interval from the start position, in seconds
• lat, lon : predicted coordinates in degrees
• pi : the pi constant (3.14159...)
• Rt : Earth radius in miles (6378137.0 meters which makes 3964.037911746 miles)

In an (East, North) local frame, the position after the time interval is :

x = speed * sin(heading*pi/180) * dtime / 3600;
y = speed * cos(heading*pi/180) * dtime / 3600;

(with coordinates in miles)

From there you can compute the new position in the WGS84 frame (i.e. latitude and longitude) :

lat = lat0 + 180 / pi * y / Rt;
lon = lon0 + 180 / pi / sin(lat0*pi/180) * x / Rt;

Edit : corrected the last line : *sin(phi) to /sin(phi)

Answer 2

Here are the formulas that you need.

http://www.movable-type.co.uk/scripts/latlong.html

Hope that helps.

Bob

[update] Here are the formulas in JavaScript (copied from source)

var lat2 = Math.asin( Math.sin(lat1)*Math.cos(d/R) +                       Math.cos(lat1)*Math.sin(d/R)*Math.cos(brng) ); var lon2 = lon1 + Math.atan2(Math.sin(brng)*Math.sin(d/R)*Math.cos(lat1),                              Math.cos(d/R)-Math.sin(lat1)*Math.sin(lat2));

d=distance traveled=velocity x time R=radius of the earth