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Mitsubishi 4WD Owners Club of Qld (Inc) |
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GPS - Part 7 |
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GPS-101 Part 7 (UTM Map Projection) This month I’ve got some more tuition on Map Projections. Last month we had a look at Latitude and Longitude. This is a coordinate system, with known origins. The simplest projection is just a straight proportional scale. This results in a map that is the same shape as the Earth, i.e. a globe. Globes are a perfect projection of the earth surface, because all distance, areas, and shapes are proportionally correct. However, globes aren’t really practical. Usually we’re only interested in a small portion of the Earth’s surface, and to keep the correct curve on your map would require a frame to support it and keep it at the correct curvature. This isn’t really practical and it would be a bugger to fold. So this is why we use projections to flatten the curved surface onto a flat one. Every flat map misrepresents the surface of the Earth in some way. However, a map or parts of a map can show one or more—but never all—of the following: True directions; True distances; True areas; or True shapes. There are many different ways to project the earth’s surface onto a nice flat map that we can fold up; each with pros and cons. I won’t get into the details here, but if you’re interested there are many web sites that will explain it for you. Here’s one of them, from which some of the content of this article are sourced: http://erg.usgs.gov/isb/pubs/MapProjections/projections.html I’m going to cut straight to the UTM, which is one of the most common for navigational maps these days. UTM stands for Universal Transverse Mercator. What’s a Mercator? It’s a projection invented by Gerardus Mercator in the 1569. A Mercator projection is a projection of the earth’s sphere onto a Cylinder, like this:
The problem with this projection is that the further you are from the equator, the more the distortion from the projection. A Transverse Mercator does the projection onto the cylinder from east to west, rather than north to south as depicted below:
Now we’ve just turned the problem sideways. The distortion is bigger, the further you are from the meridian (line of longitude) that touches the cylinder. In this sort of projection, it is referred to as the central meridian.
To reduce the distortion, the Universal Transverse Mercator projection was invented. What they do, is just take a thin section either side of the central meridian and then turn the sphere and take another thin section, as depicted in the diagram: They do this 60 times, which mean that for the 360° of the sphere, you end up with 60 strips that are 6° of longitude each. This means that at the edges of each strip, the worst distortion is only 3° from the central meridian. So now your flat map of the earth looks something like this (This diagram shows 12 central meridian, instead of 60, but you can get the basic idea):
UTM zones extend from latitudes 80°S to 84°N. In the polar regions, the Universal Polar Stereographic (UPS) grid system is used (I’m not going to go there). UTM zones are numbered 1 through 60, starting at the international date line (longitude 180°) and proceeding east. Zone 1 extends from 180° W to 174° W and is centred on 177° W. Each zone is divided into horizontal bands spanning 8 degrees of latitude. These bands are lettered, south to north, beginning at 80° S with the letter C and ending with the letter X at 84° N. The letters I and O are skipped to avoid confusion with the numbers one and zero. The band lettered X spans 12° of latitude instead of 8° like the rest of them. A & B are used for two zones in the circle around the south pole, and Y & Z are used in the circle around the north pole.
What you end up with is a grid of 60 x 20 + 2 x 2 = 1204 sections, with designations like 3N, 34K, 56J, etc. So this tells you which zone you’re in. Australia is included in Zones 49 to 56 and bands G to L as depicted here:
The Northing is the distance north (or south) from the Equator measured in metres. For distances south of the equator, the equator is given an arbitrary datum of 10,000,000m. The Easting is the distance measured in meters to the east from an arbitrary reference line located 500,000m west of the Central Meridian for each zone.
Let’s interpret a couple of examples:
The UTM coordinates for the Parthenon in Athens are 34S 739508E 4206159N 34S is Zone 34 which has a central meridian of 21° East, and band S is in the northern Hemisphere. 739508E is 239,508m East of the central Meridian and 4206159N is 4,206,159m north of the Equator.
The UTM coordinates for the Parthenon Milk Bar in Newcastle are 56H 384095E 6356379N 56H is zone 56 which has a central meridian 153° East, and band H is in the southern Hemisphere. 384095E is -115,905m west of the central meridian (remember the central meridian has an arbitrary or ‘false’ easting of 500,000m in each zone). 6356379N is 3,643,621m south of the equator (if you’re in the southern hemisphere, the equator has a ‘false’ northing of 10,000,000m) There are plenty of sites on the internet if you want more info on UTM. Here’s a couple from which I sourced info for this article: www.maptools.com; www.werple.net.au/~gnb/gps/mapping.html PHEW! That was a bit of a slog. So why use UTM if it is so complex? For the following reasons: - Each map, which typically represents a relatively small portion of the Earth’s surface, has only a small amount of distortion. - The UTM grid provides a square reference grid in metres rather the angles used in Latitude and Longitude. This makes it easier to work out distances quickly. Next month I’ll discuss more about some other acronyms related to mapping in Australia, including: GDA, AGD, WGS, AHD, ANG and why you can be 200meters out if you don’t have the correct Australian datum Happy Navigating. Greg Conlon |
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