Map Coordinates for Dummies (Again)

Longitude convergence

If there's one thing our staff cartographer wishes freelancers had learned in elementary school, it's how latitude and longitude work. It's especially taxing for her to see the geographically illiterate types who think that ten degrees of longitude represents the same distance no matter what your latitude. Says she, "Stupid, stupid, stupid!" Well, today's DotD is one such stupid, geometrically illiterate type: let's see what Grant D. McKenzie has to say in his Sciencing.com post, "How to Convert Latitude & Longtitude Into Feet."

For starters, we're pretty sure that McKenzie's ignorance of maps and mapping led to a bogus interpretation of the topic. Those among us who can spell "map projection" figured that the OQ wanted to know out how to generate XY coordinates from latitude and longitude, similar to UTM coordinates (which are, if you aren't aware, in meters). Grant, however, had other ideas...

"Earth scientists determine positions on earth by the angular measurements of latitude and longitude. The earth has a fixed circumference, so you can convert these to feet by calculating the distance the angles defined by latitude and longitude sweep. Angular measurements range range from -180 degrees and 180 degrees with respect to a reference, which is the equator when measuring latitude and the prime meridian when measuring longitude."

OK, we see where this ignorant fool is headed: do you? Well, his instructions follow, using the latitude and longitude of Denver International Airport, which McKenzie tells us are 39° 51’ 42", -104° 40’ 23”; coordinates he says convert to 104.673°, 39.862°. First, that's wrong: the longitude is negative. Second, three decimal places' precision is accurate only within about 300 feet. However, that's just window dressing. Where McKenzie earned his award is in the following nonsensical claim:

• "Longitude: -104.673 * (10,000/90) = -11,630.34km. This is the distance of DIA from the prime meridian."
• "Latitude: 39.8617 * (10,000/90) = 4429.1km. This is the distance of DIA from the equator."

After which McKenzie converted kilometers to feet, multiplying the distances he calculated by 3280.4. You see where Grant went wrong, don't you? No? Well it's pretty simple: besides the high probability that the OQ didn't want to know the distance to DIA from some spot in the Gulf of Guinea, McKenzie also made a classic dumbass mistake¹: a degree of longitude is not a constant distance. At the equator, it's about 60 nautical miles or 69 statute miles, BUT at the poles a degree of longitude is zero miles. In other words, at 40°N, the approximate latitude of DIA, a degree of longitude is somewhere around 50 miles.
In other words, not only is our Dumbass of the Day ignorant of map projections, he's also ignorant of simple geometry. So, for that matter, is whatever content editor let this bullshit get published.

¹ This mistake was repeated ad nauseam by freelancers at eHow: see the topic "MAPS" in our "Dumbasses sorted by topic" file.

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