How to transform a distance from degrees to metres?

Question

I'm using OpenLayers with an ordinary mercator map and I'm trying to sample a bounding box by finding a grid of points in latlong. The bbox is expressed in latlon, e.g.

48.1388,-15.3616,55.2057,-3.9359

I can define a distance in degrees (e.g. x: 2.5, y: 2.4) and work out the points from there. But I'd like to express this distance in metres (e.g. 50000) in order to relate it to the user mindset (people understand metres, not degrees). How can I convert this distance? I know how to reproject a point, but not a distance.

Thanks for any hints! Mulone

Answer 1

Use the haversine formula to get the distance between two points of lat/long. This assumes the earth is a sphere (which is, for most cases, "good enough").

A Javascript implementation of it (shamelessly stolen from here) looks like this:

var R = 6371; // km
var dLat = (lat2-lat1).toRad();
var dLon = (lon2-lon1).toRad(); 
var a = Math.sin(dLat/2) * Math.sin(dLat/2) +
        Math.cos(lat1.toRad()) * Math.cos(lat2.toRad()) * 
        Math.sin(dLon/2) * Math.sin(dLon/2); 
var c = 2 * Math.atan2(Math.sqrt(a), Math.sqrt(1-a)); 
var d = R * c;