GPS Coordinates for Dummies

GPS coordinates in latitude-longitude

Just yesterday we handed out one of our DotD awards to someone for giving a very specific answer to a quite general question. Today's candidate for the award is someone who also provides a very specific answer to a question: it's just that she answered the wrong question (we note with interest that both freelance posts are at Sciencing.com...). The self-appointed "expert" in this case is one Pearl Lewis, PhD, and her topic is "How to Convert GPS Coordinates to Feet."

Now to our staff, the question seemed quite straightforward: the information-seeker has GPS coordinates recorded in some other system of units, but wants (or needs) the location(s) expressed in feet. The ambiguity of "GPS coordinates" notwithstanding – did the OQ mean lat-long? UTM? – the problem is quite clearly one of coordinate transformation, for which there are many online sources of information and even pages full of widgets that will perform the necessary math automagically.

Lewis, on the other hand, opened her introduction by telling her readers that,

"Today, locations all over the world can be pinpointed using GPS coordinates. By taking the curvature of the earth into account, the GPS coordinates of any two locations can be translated into the straight-line distance between those locations."

But wait, Pearl: nobody said a word about "distance"! Yet Lewis forged bravely on, ultimately asking her readers to use the formula

131332796.6 x (ArcCos{Cos[a1]xCos[b1]xCos[a2]xCos[b2] + Cos[a1]xSin[b1]xCos[a2]xSin[b2] + Sin[a1]xSin[a2]}/360)

...which, oddly enough, doesn't match any formula provided by any of her sources, at least in part because we have no idea where that 131332796.6 multiplier comes from, It isn't part of the haversine formula usually used to calculate great circle distances (a phrase Lewis never uses). Whatever the case and whether Lewis, the eHow content editor, and the conversion to Sciencing format changed the notation (it wouldn't be the first time), ultimately Lewis is well-deserving of our Dumbass of the Day. Why? Because she answered the wrong question – we repeat, no one mentioned "distance" in the original question!

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