UTM coordinates
Adapted from an original article by Mario Labelle
Catalogues of Club des Cent Cols contain UTM coordinates. These coordinates can be used directly on certain topographic maps, such as the 1:25,000 IGN (Top25) series in France. Here we explain what UTM coordinates are and how to use them on maps that allow them.
A bit of theory...
UTM stands for Universal Transverse Mercator. Universal Transverse Mercator. It is a system of cartographic projection that divides the globe into 60 spindles of 6° longitude each. Each zone is further divided at the equator into a southern zone and a northern zone. Europe, for example, is on zones 29 to 38, or more precisely on northern zones 29 to 38. In each zone, a point is defined by an abscissa (x) and an ordinate (y), each given in metres. The abscissa is a positive number calculated so that the central meridian of the spindle has an abscissa of 500,000 metres. The abscissa values range from 167,000 to 833,000 m. The minimum is on the western (left) edge of the spindle, 3° west of the central meridian; the maximum is on the eastern (right) edge, 3° east of the central meridian. In the northern hemisphere, the ordinate is defined very simply as the distance (in metres) from the equator. In the southern hemisphere, to avoid negative numbers, we add 10,000,000 m. This is roughly equivalent (to within a few km) to taking the distance from the South Pole. The ordinate always increases towards the north, so towards the top on maps where north is at the top. It should be noted in passing that the Gauss-Krüger coordinates used in Germany, for example, are defined in a similar way to UTM, with the same projection but with narrower zones, of only 3°.
Unlike longitude and latitude coordinates in degrees, UTM coordinates allow distances between points to be calculated directly, although this calculation becomes slightly less accurate as you move away from the central meridian. Between different time zones, on the other hand, such a direct calculation is not possible. UTM coordinates can be calculated from longitude and latitude using approximation formulae. These are available, for example, with centimetre accuracy. The reverse calculation is also possible, but more complicated. In all cases, care must be taken to work in the same geodetic system for both sets of coordinates (WGS84 is the geodetic system most commonly used, particularly by the GPS system).
UTM notation varies between maps and applications, particularly as regards the zone. Sometimes the zone is omitted, sometimes only the time zone is given but the hemisphere (S or N) is omitted. In some cases, the zone is shown next to the abscissa, either in the same font or in a different font. A presentation as 3 distinct variables zone / x / y is best to avoid confusion. Some examples for a single point:
31474123 / 4769456
31474123 / 4769456
31 474 123 / 4 769 456
31N / 474 123 / 4 769 456
... and practice
For orientation on maps with metric coordinates such as UTM, quadrants are used, typically kilometre quadrants. These quadrants are normally noted in the margins of the maps. However, there are often several indications in these margins, so care must be taken to use those that correspond to the system used. For example, on the French IGN TOP25 maps, the UTM coordinates are in blue, in italics, and the kilometre grid is also in blue.
To locate a point, start by separating the kilometres from the remaining metres in the UTM coordinates. Let's take the example of the Col du Louron given in the Club des Cent Cols catalogue of French passes ("Le Chauvot").
The blue-framed numbers define the UTM kilometre quadrant to be located on the map. The figures in red indicate the position of the point in metres from the left or bottom edge of the quadrant.
The first step is to identify the 292 / 4747 quadrant. The corresponding numbers in the margins of the map give us the bottom left-hand corner. Once you've found the quadrant, you can do a little mental calculation to find the point. The numbers in red are metres, i.e. thousandths of a kilometre quadrant. This can be used as a rough guide to find the point. In our example, the Col de Louron is shown on the TOP25 map and is easily found at around 7/10 from the left and 2/10 from the bottom of the quadrant. For a point that is not marked, a little calculation is required. This is where the map scale comes into play, 1:25,000 in our example. By dividing the metres (framed in red) by 25, we obtain millimetres on the map. In your mind, divide by 100 and then multiply by 4:
- Abscissa: 712 / 100 ~ 7, and 7 x 4 = 28 mm
- Ordinate: 209 / 100 ~ 2, and 2 x 4 = 8 mm
Using a ruler, we measure 28 mm from the left of the quadrant and 8 from the bottom. And there you have it.
If the above can be generalised to any map with a kilometre network, here is another specific method of locating the passes in the French catalogue (the "Chauvot") and the IGN TOP100 series maps. The Chauvot gives the millimetre coordinates of the passes on the quadrants of these maps in a new one called TOP100, which makes any calculation superfluous. For example, here is the blue 715/4760 quadrant on TOP100 map no. 166. Chauvot's TOP100 column gives the Col d'Aubisque as 715-4760-20-17, putting this pass 20 mm from the left edge of the quadrant and 17 mm from the bottom edge. Note that the blue grid here is 5 x 5 km and that the black grid should be ignored.
