[VHFcontesting] Calculating distances from grid squares

[James Duffey]

Some have asked how the distance between the two grid squares are calculated. 

Here is one way that the distance between the six grid squares is calculated:

The calculation starts by converting the 6 grid square center to a latitude and longitude. You can find the technique for doing that here:

Tyson, N5JTY, Conversion Between Geodetic and Grid Locator Systems, QST January 1989, pp. 29-30, 43

or there are several online calculators that will do that for you. 

Then, using high school trigonometry, the distance between the two points can be calculated:

d = arccos(sin φ1 ⋅ sin φ2 + cos φ1 ⋅ cos φ2 ⋅ cos Δλ ) ⋅ R 

where d is the distance between the two lat-lon points, R is the radius of the earth, φ1 and φ2 are the latitudes of the two points, and Δλ is the difference in longitude between the two points. Angles are in radians. 

The earth is not quite a sphere and there are factors which can be added to that calculation to make it more precise. There is some dependence on the datum which is used in the calculation, but both these effects are probably small compared to the distance to the center of the 6 square grid that is ignored in the scoring calculation.

I don’t know whether or not the ARRL will use this exact method, but it will use something not too different. I hope that this helps. - Duffey KK6MC
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KK6MC
James Duffey
Cedar Crest NM