Calculating UTM Convergence for Dummy Cartographers

Grid North vs True North vs Magnetic North

Cars Week is, mercifully, finished; but drivers everywhere are still dumber than sacks of hammers and getting lost unless they have Siri or Cortana or another GPS character (Super Mario, perhaps?) there to whisper in their shell-like ears. It won't help them find themselves if they stupidly get advice from people who know little if anything more than they do when it comes to using maps. We know these liars are out there because we looked at some of the bull they've published and, let us tell you, much of it either makes no sense or is just plain wrong. Some fits both  categories, like "How to Convert a Grid to True North," penned for eHow.com (and now appearing on GoneOutdoors.com)¹ by Sean Lancaster. That piece of content is one sad example of dumbassery gone wild!

Like many of eHow's more moronic posts, this one is built on a fallacy from the get-go: the phrase "convert a grid to true north" is nonsensical. You can determine the declination – the difference between true north and magnetic north at a point – or you can calculate the convergence – the difference between grid north and true north at any point on a map. But to "convert a grid"? It can't be done. According to Sean, though, it's no problemo. Of course, Sean proves himself ill-equipped to discuss this topic in the introduction, when he claims that

"The direction indicator that points North on the map defines Grid North." Ummm,  no, Sean, the North Arrow points to true north; grid north is the azimuth of a line on the map connecting any two points with the same X or Easting value in the projection. But who cares about such things as "accuracy," anyway? Lancaster then proceeds to give an example of what he thinks is his conversion technique, although the formula he cites does not appear anywhere in his reference (which was written by someone who knows what he's talking about). Whatever... Sean claims that the formula to "convert a grid to true north" is CONV = (CM – LONG) X SIN (LAT) and even says that he's calculating convergence. Well, that's not quite true, since that's only the approximate convergence², but what the hell: it's eHow. We won't even bother to point out to Lancaster (and the rest of the world) that UTMs are far from the only map projection system and that every projection has a different formula for this calculation. It would only confuse them.

We had to laugh, however, at Sean's fumble-assed example of the process:

"As an example, assume that you are located in the Netherlands in UTM-5 (Universal Transverse Mercator). Your CM is 5 degrees, the longitude would be is [sic] 4 degrees 55 minutes and the latitude is 52 degrees 23 minutes. Express all angles in decimal degrees. Do this by dividing the minutes by 60 and adding to the number of degrees. CONV = (5 – 4 55/60) X SIN (52 23/60) = (5 – 4.92) X SIN (52.38) = 0.08 X 0.79 = 0.063. [sic]"

Oh, there are so many things wrong with that...

The Netherlands is not in UTM-5. We're not even sure what "UTM-5" is, but we do know that Holland is in UTM zone 31N: Yes, north of the equator is different from south. Duh. The central meridian of UTM 31N (corrected from Lancaster's idiotic "UTM-5") is not 5 degrees. In the UTM system, the value of the central meridian is always a multiple of 3. In fact, this time it is 3: 3° E longitude (note: west longitudes are conventionally assigned negative values, but that would probably just confuse Sean) Sean may think longitude and latitude to the minute is OK, but we don't. We think that, for accuracy, you should at least measure to the second and probably to the hundredth of a second. Otherwise your coordinates could be off by a thousand meters or so (not so good for following a road with a nav system). Just WTF does "(5 – 4 55/60)" mean, anyway?

Lancaster concludes by "informing" his readers that they must

"Rotate the coordinate system 3.8 degrees West of the Grid North. The directions are now all referenced to True North."

Well, no. All you've done is found the convergence at a point. How one could ever "rotate [a] coordinate system" remains a mystery to our mapping guru, as does the value "3.8 degrees West of the Grid North." Even if this could work, which it can't, around what point would you rotate things? and what is meant by "rotate west"?

No, this is what happens when you send someone who doesn't know what he's talking about to explain some technical topic. It's not unlikely that the person who asked this question knows more about the topic than the person who collected his eHow stipend to write this dumbass "answer." Lancaster didn't know the question is unanswerable ("makes no sense"), assumed there's only one coordinate system, and made a mess of his example ("just plain wrong"). Is it any wonder that Sean's the Antisocial Network's Dumbass of the Day? Of course not...

¹ The original has been deleted by Leaf Group, but can still be accessed using the Wayback machine at archive.org. Its URL was   ehow.com/how_8264607_convert-grid-true-north.html
² a more accurate formula, we're told, is 

γ = arctan [tan (λ - λ0) × sin φ], 

where γ is grid convergence, λ0 is longitude of the UTM zone's central meridian and φ, λ are latitude, longitude of the point.

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