Understanding and making use of UTM grid lines

If you're a hiker, you are probably familiar with UTM grid lines on your hiking maps. If you are a paddler or mariner, you may not have seen them at all.

Even if are a hiker and used to seeing them, you may not have known what they are, and just overlooked them as more clutter on a map.

Overlook them no longer! Wild Coast Publishing has added UTM grid lines to all 200-series marine mapsheets, ensuring the entire new lineup of Wild Coast maps -- both marine and trail -- includes UTM grids.

This isn't because you are likely to convert from longitude-latitude to UTM coordinates when tracking your routes. If using a GPS, it doesn't really matter too much, just so long as you know where you are. But there are advantages that go beyond just the coordinate system when using UTMs.

UTM grid lines are the representation of the Universal Transverse Mercator coordinate system. It overcomes (sort of) one of the basic problems with the traditional longitude and latitude measures, in that the representation of distance between longitude lines changes as you move north or south. 

The UTM system instead divides the planet into 60 zones, and then divides these zones into one kilometre squares. So while the zones are skewed as is the case with all divisions of a globe, the km squares created by the UTM gridlines are uniformly distant.

The obvious immediate utility is to tell the distance between objects east to west or north to south. Just count the grid lines. Each line is one kilometre. That never changes.

Naturally, this bring us the point that routes are rarely straight east-west or north-south. The advantage, then, of one-km squares falls short. Or does it?

There is a quick mathematical solution that can help, namely, the high-school lesson you've forgotten all about called the Pythagorean theorem (A squared plus B squared equals C squared). It need not be hugely complex in this application. Let's just make some assumptions.

The first assumption is you are travelling southwest, so at approximately a 45 degree angle to the UTM grid lines:


Simple math applies: your distance north to south is 1 km, and distance east-west is 1 km as well, but your total distance travelled is 1.4 km. Always.

From there it is just a matter of applying simple math. Let's say your route shifts east-southeast, and you will travel two gridlines east but just one south. Like so:

In this instance your travel distance is 2.36 km. 

This math can also be used if you are going east-southeast but just for the one km east to west, so only through the first box of the two gridlines above. The key to watch for is that you are going to the half-way point of the north-south limit. In that case, your distance of travel is about 1.18 km. 

So what if your east-west distance is three grid lines? Such as this:

In that case, your travel distance is 3.18 km.

Realistically, then, there is probably only one other measure you need to know: the distance when you are travelling three gridlines east to west and two north to south, like this: 


The distance here overall is 3.6 km.

And that is probably as much as you need to know. As your route shifts, pick a new measure that applies and stack them up, and suddenly your zigs and zags can yield a fairly precise calculation of the distance of your trip.

For paddlers and mariners, this will likely be more accurate than for use in calculating distances for hiking and trails, where zigs and zags are more prevalent. For hikers, especially alpine hikers following routes, the UTM grids are ideal for telling your distance to the next waypoint, possibly a summit. You might have many kms to go in distance, but your position can be used to tell that you are exactly 350 metres from your destination. Just don't use that to justify the simplicity of a straight route rather than following the trail! The math may be in your favour, but possibly very little else.

Oh, and one other problem for hikers. The creators of UTMs viewed their construction as entirely flat. This means, if you are calculating distance for anything other than walking on water, the accuracy falls off again as there is no accounting in UTMs for the ups and downs. Therefore is is entirely possible you follow a gridline east to west for exactly one kilometre in distance, but due to hills actually travel closer to 1.1 km. Possibly!

Now for the explanation of the "sort of" hinted above.

The example above shows details from two Canadian National Topographic System maps side by side. The left is sheet 092K03, and the right is 092K02. Both show the north end of Cortes Island, with 50 degree 15 minutes aligned horizontally. The map adequately dissects Cortes Island so when placed together the shorelines meld. But notice UTM line 5567. To the left, it cuts into Cortes Island. To the right, it passes above. The discrepancy is about 12 metres, a significant amount in a map that is advertised for use up to military standards.

The horrible truth about UTM grid lines on maps 

 The hope would be if you look at a UTM grid line, the distance between them on the map would be 1 km exactly . Right? Well, not so fast. 

Maps have been fantastic at lying for generations now. Remember those classroom maps as a kid? Where Greenland was larger than the United States and Mexico was a skinny V shape, somewhat smaller than Quebec? Surprise, that was all a terrible lie. 

It all boils down to earth being an ellipsoid and maps being two-dimensional. UTM grid lines get past the problem inherent in latitude-longitude measures, that being the east-west distance between longitude lines gets shorter north to south. UTM lines don't do that on land. But UTM grids create new problems for maps.

The main one is the complex translation of a straight line on a ellipsoid to two dimensions on a map. It is essentially the latitude-longitude problem in reverse.

First, though, let's backtrack on the major cheat on print maps. Most maps have continued the Greenland problem to some degree, and ignored the ellipsoid by making the longitude lines simply straight parallel lines. This can easily be done if you are mapping say Vancouver Island instead of the globe. There is no frame of reference for your error, so it looks fine. When out of context to the rest of the globe, that is.

Nowhere is this lie more evident than in the Canadian National Topographic System maps that you might have seen in some form or another, possibly as the backbone of official Canadian mapping systems. They identify sections of the country in blocks 15 minutes latitude and 30 minutes longitude. They have then assigned names to each such section, so you may recognize a name such as 09B05 or similar to an area of British Columbia (that one being Sooke). The format is always the same-sized rectangle, regardless of the curvature of the earth.

This means the top is stretched out, and the bottom by comparison compacted. Or, put another way, the east-west distance represented at the north end is slightly less than on the bottom. Again, this is fine in small blocks, as the discrepancy is small in that size of a section.

However, if you lay out British Columbia in its entirety in the way of these sheets, it becomes an issue. To truly represent distances on mapsheets as they exist on our ellipsoid planet, the UTM grid lines can't be straight or uniformly distant. They have to adjust to account for the curve. 

And the truth is, no one does.

We at Wild Coast Publishing discovered this the hard way, by trying to do exactly that -- running our UTM grids on our maps as straight lines, then finding they weren't accurate because if you plot out one kilometre squares on two dimensions, they don't equal one kilometre squares on three dimension. Go figure.

That's exactly why we're behind schedule on our new maps for 2021! We had to develop a new and better system to adapt grid lines from an ellipsoid to a two-dimensional map.

We'll be perfecting this for some time to come, because in part we discovered a better system part-way through the process, and will have to backtrack on earlier attempts.

You can take solace that when it is said and done, our UTM representation should be more accurate than the Canadian National Topographic System.

Unfortunately, that's not as high a bar as you might think. 



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