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geometrygeography

Distance between lat/long points using the haversine formula

I am trying to find the distance between two longitude and latitude points. I am trying ot use the great circle distance. This is the formula: alt text

I am not sure why but my program is not working. This is the result I am getting: 

Change Angle: 0.00016244370761414
Earth Radius: 6371

RESULTS: 
Correct  Distance: 24.883 km
Computed Distance: 1.0349288612097

Source:

$latStart = 44.638;
$longStart = -63.587;

$latFinish = 44.644;
$longFinish = -63.597;


# Convert Input to Radians
$latStart = deg2Rad($latStart);
$longStart = deg2Rad($longStart);

$latFinish = deg2Rad($latFinish);
$longFinish = deg2Rad($longFinish);

# Because the Earth is not perfectly spherical, no single value serves as its 
# natural radius. Distances from points on the surface to the center range from 
# 6,353 km to 6,384 km (≈3,947–3,968 mi). Several different ways of modeling the 
# Earth as a sphere each yield a convenient mean radius of 6371 km (≈3,959 mi).
# http://en.wikipedia.org/wiki/Earth_radius
$earthRadius = 6371;

# difference in Long/Lat
$latChange = $latFinish - $latStart;
$longChange = $longFinish - $longStart;



# haversine formula 
# numerically stable for small distances
# http://en.wikipedia.org/wiki/Great-circle_distance
$changeAngle = 2 * asin(
                sqrt(
                        pow(sin($latChange/2),2) +
                        cos($latStart) * cos($latFinish) * pow(sin($longChange/2),2)
                )
        );



echo "Change Angle: $changeAngle\n";
echo "Earth Radius: $earthRadius\n";
Solution

  • Let's do a back-of-the-envelope check using a planar approximation. The difference in latitude is 0.006°, and the difference in longitude is 0.01°, but multiply by cosine of latitude to get 0.0075°. Apply Pythagoras: 

    >>> sqrt(0.006 ** 2 + 0.0075 ** 2)
0.0096046863561492727

    which is about 0.000167 radians, pretty close to your computation. (Even more back-of-the-envelope check: a degree is about 69 miles, which is a bit over 100 km, so 0.01° should be a bit over 1 km.)

    So I think it's your alleged "Correct distance" that's wrong, not your computation.