Projection System Demystified

Universal Transverse Mercator projection
Universal Transverse Mercator or UTM coordinate system is a convenient system for GIS and cartography work over a very large area. It is often said that UTM is created by U.S. Army. In fact, several nations and the North Atlantic Treaty Organization (NATO) played roles in creation of this system after World War II. At that time, the goal was to design a consistent coordinate system that could promote cooperation among the military organizations of several nations. After several conferences across Europe and America, U.S. Army introduced this system on 1951.

UTM system divides the world into 60 zones in each of the Northern and Southern Hemisphere. The numbering of the zones begins at longitude 180° E, the International Date Line, and increases sequentially toward the east. Zone 1 is from 180° W longitude to 174° W longitude, zone 2 is from 174° W longitude to 168° W longitude, and so on. Each zone has a central meridian exactly in the middle.

All UTM zones have a width of 6° of longitude. From north to south, the zones extend from 84° N latitude to 80° S latitude. Originally, the northern limit was at 80° N latitude, and so does the southern limit. But, 80° N latitude was found to exclude parts of Russia and Greenland and was extended to 84° N latitude. UTM system is actually based on conformal azimuthal stereographic projections. There are few subtle feature of this system, which are,

  • In UTM all measurements are done in meters. Coordinates are always positive and there is no need for N, E, W, S designations.
  • Coordinate values of a point identify its position within the familiar Cartesian coordinate system.
  • Calculation of distances, directions and areas can be performed much more conveniently in comparison to geographic coordinate system.
  • The narrow width (6° of longitude) of each zone and the use of a secant developable surface for projection ensures minimal scale distortion within a zone.

Easting, northing and Scale Factor
False Easting is a value relating to distance east of a standard meridian but with a constant added to make the numbers convenient. For instance, in UTM the value 500,000 is added to the easting from the center of each zone to return a false easting that is never negative (the smallest true easting is approximately -340,000 which set to false easting of 160,000).

Within a zone, easting values increase towards east. A point lying 8 meters east of central meridian has an easting of 500000 + 8 = 500008mE. The easting of a point 350m west of central meridian would be 500000 – 350 = 499650mE. The east-west distance between two points is obtained by the difference of their easting values. The distance between the above points is 500008 – 499650 = 358m.

False Northing is a value relating to distance north of a standard latitude but with a constant added to make the numbers convenient. For instance, in UTM, the Southern Hemisphere is assigned negative degrees of latitude, but to avoid negative numbers in northings, a constant value of 10,000,000 is added so that negative numbers for northings do not occur.

A point south of equator with a northing of 7587834mN is 10,000,000 – 7587834 = 2412166m south of the equator. A point located 34m south of the equator has a northing of 9999966mN, while a point 34m north of the equator has a northing of 10000034mN. The north-south distance between two points north of equator with northings of 4867834mN and 4812382mN is 4867834 – 4812382 = 55452m.

UTM easting and northing coordinates specify the position of a point on Earth. UTM coordinate of a point is stated by writing the zone, easting and then northing values. When finding a position on a map, it is helpful to “read right up”, that is to read west to east to find the easting and then south to north to find the northing of the location. An example of a complete UTM coordinate: 11U 358657mE 5885532mN.

Scale factor refers to a ratio between distances in actual surface and imaginary ellipsoid.

Scale factor = distance between two point measured on a developable surface / distance on ellipsoid

If there is no distortion in the projected map, the value is 1, if not then the value can be both positive and negative. For example, the value 0.9996 means the distance on ellipsoid is 1000m while on the map it is 999.6m. It means for every 1000m the projected map has an error of 0.4m.

Some example of Projection Systems used in Bangladesh

Here are some of the most common projection systems used in Bangladesh.

Name of the Projection Parameters
Bangladesh Transverse Mercator (BTM) Projection: Transverse Mercator
False Easting: 500000.0
False Northing: -2000000.0
Central Meridian: 90.0
Scale Factor: 0.9996
Latitude of Origin: 0.0
Linear Unit: Meter
Datum: Everest_1830 or D_Everest_Bangladesh or D_Gulshan_303
Spheroid: Everest_1830 or Everest_Adj_1937
Lambert Conformal Conic (LCC) Projection: Lambert Conformal Conic
False Easting: 2743185.699 Meters
False Northing: 914395.233 Meters
Central Meridian: 90.0 (DD)
First Standard Parallel: 23.15 (DD)
Second Standard Parallel: 28.80 (DD)
Latitude of Origin: 26.00 (DD)
Linear Unit: Meter
Datum: Everest_1830 or D_Everest_Bangladesh
Spheroid: Everest_1830 or Everest_Adj_1937
Bangladesh Universal Transverse Mercator (BUTM) Projection: Transverse_Mercator
False_Easting: 500000.0
False_Northing: 0.0
Central_Meridian: 90.0
Scale_Factor: 0.9996
Latitude_Of_Origin: 0.0
Linear Unit: Meter
Datum: WGS1984
Spheroid: WGS1984
Universal Transverse Mercator (UTM) Zone 45N Projection: Transverse_Mercator
False_Easting: 500000.0
False_Northing: 0.0
Central_Meridian: 87.0
Scale_Factor: 0.9996
Latitude_Of_Origin: 0.0
Linear Unit: Meter
Zone: Zone 45
Datum: WGS1984
Spheroid: WGS1984
Universal Transverse Mercator (UTM) Zone 46N Projection: Transverse_Mercator
False_Easting: 500000.0
False_Northing: 0.0
Central_Meridian: 93.0
Scale_Factor: 0.9996
Latitude_Of_Origin: 0.0
Linear Unit: Meter
Zone: Zone 46
Datum: WGS1984
Spheroid: WGS1984

 

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6 Comments

  1. Hello Mr Sunbeam, i was searching about BTM and other coordinate format. I have received a data format where the values of coordinate are given in meter but i am not sure whether it is in BTM or UTM. Is there any way to be sure what the data format is. and can you give me any way to transfer those data to degree decimal format for GIS.

  2. For BTM the ellipsoid can be different? I am a bit confused.
    And could you please explain difference between datum and ellipsoid?

    • Ellipsoid is a theoretical model of the world where all planar sections are either an ellipse or circle. Datum on the other hand is a set of reference point which is used to measure distance. It can be at the center of the Earth or at it’s surface.

      I haven’t known any source who can confirm altering the ellipsoid itself for certain projection system (ie. BTM). We don’t actually need that, do we.

  3. Thank you for the article….This is the best article I have ever read on projection system…Keep it up.

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