入门的UTM投影

Map Projections

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Representing a rounded earth on a flat surface cannot be accomplished without introducing some form of distortion error. Different map projections have been developed over the years to limit specific distortions. These distortions can be broadly categorized as shape, area, distance and direction. The common projection used in the Ministry of Forests (Universal Transverse Mercator) limits the shape distortions.

The Universal Transverse Mercator (UTM) projection is a derivative of the Mercator projection which was developed by Gerardus Mercator in the 1500s. The Mercator projection is based on strips of the earth running in an east-west direction. The parallels of latitude, which on the globe are equal distances apart, are drawn with increasing separation as their distance from the equator increases in order to preserve shapes. However, areas are exaggerated with increasing distance from the equator. The Transverse Mercator projection differs from the Mercator projection in that the strips run north-south instead of east-west.

In both the Mercator and Transverse Mercator projections, the earth is represented on a flat surface by placing a cylinder around the earth. This cylinder touches the earth at one spot. The longitude at which this happens is called the central meridian. Only at this point are the distances accurate.

The UTM projection uses the same cylinder technique, but the cylinder touches the earth at two points instead of just one. This lessens the distance distortions across the whole map.

UTM Map Projection - how the round earth is represented on a cylinder

 

The UTM projection is broken down into zones each of which is 6° of longitude wide with Zone 1 beginning at 180° west longitude and covering the 6° to 174° west longitude. The earth is covered by 60 such zones numbered 1 to 60. Canada is covered by zones 7 to 22 with British Columbia occupying zones 7 to 11.

Each UTM zone is referenced using a rectangular grid based on a distance in metres east and north of a set location. The easting (distance east) is taken from a false easting of 500,000 metres at the central meridian. This means that locations west of this point will have an easting less than 500,000m while those to the east will have an easting greater than 500,000m. The northing (distance north) is taken from the equator.

For example: The Town of Fort Nelson is at 58° 48' N by 122° 43' W in UTM Zone 10. The central meridian for Zone 10 is 123° W. Given that Fort Nelson is east of the central meridian the easting value will be greater than 500,000m. The position of Fort Nelson using UTM Grid Coordinates is at 515468m East by 6518529m North UTM Zone 10. This translates to about 15.5km east of the central meridian of 123° and about 6500km north of the equator