UTM COORDINATE SYSTEM (UNIVERSAL TRANSVERSE MERCATOR)

What is a map projection? And why do we need it?

Map projection is a geographical transformation of earth's curved surface on to a flat map surface.

The earth's surface, as we all know is neither a perfect sphere nor a perfect ellipsoid. Although, globes provide the most accurate picture of the earth and basic geometric properties such as distance, shape,direction and area are all preserved; they have certain disadvantages too such as:

• In globe simultaneous view of whole of the earth is not possible, at most only half hemisphere is visible.
• They're bulky and difficult in handling or storage and a small scale globe is of practically no use.
• Instruments and techniques that are suited for measuring distance, direction and area on spherical surfaces are relatively complicated. 
• Globes construction is laborious and costly relative to maps.
• Globes don 't offer the variety and details as offered by maps.

The universal transverse Mercator (UTM) is a map projection that is based completely on the cylindrical transverse Mercator, with a secant cylinder.

Why do we use UTM system in directional drilling industry, when there're other systems too?

Advantages of UTM coordinate system:

1. Cylindrical projection preserves Area, i.e. exact representation of area is possible.
2. UTM is a planar coordinate system which provides a constant distance relationship anywhere on the map. In angular coordinate systems like latitude and longitude, the distance covered by a degree of longitude differs as you move towards the poles.
3. All UTM coordinates are measured in metric units.
4. No negative numbers.
5. Simple Cartesian coordinate mathematics can be used to find distances, thereby eliminating complex mathematical calculations. 

The UTM coordinate system is universally used plane coordinate system (except for polar regions). 

What is a UTM coordinate system? 

In UTM grid, 

(1). Area of earth between 84°N to 80°S is divided into 60 north-south columns of 6° wide longitude called Zones. So, UTM covers most of the world. 

{Rest part of the world 84°N to 90°N and 80°S to 90°S is covered by UPS system (Universal Polar Stereographic).}

(2). Zones are numbered eastwards from 1 to 60; starting from 180th meridian. Zones in northern and southern hemisphere are labelled N and S respectively.
o Zone 1 is from 180°W to 174°W,
o Zone 2 is from 174°W to 168°W, and so on.

                                                              

UTM zones are flattened using the Transverse Mercator Projection, and a rectangular grid network of straight horizontal and vertical lines is superimposed on each zone.

(3). Longitude lines run towards true north whereas, grid lines don't, instead they run towards grid north and are parallel to the central meridian of the zone.

Hence, grid north are latter corrected to true north.

Latitude lines are parallel to equator.

Each zone has a central meridian.

o Zone 1 central meridian is 177°W,

o Zone 2 central meridian is 171°W, and so on.

(4). UTM system is a coordinate system and therefore, it will have a x-axis, y-axis and an origin.

For a zone,
X-axis is the equator;

Y-axis is the central meridian of the zone; and

an origin is taken as there intersection point.

As (x,y) are used to denote a point in the coordinate system, Easting and Northing are used in UTM coordinate system.

Easting are used to determine east-west position w.r.t central meridian which is assigned an arbitrary value of 500,000m. All the points lying east will have easting value > 500,000m and points lying east will have < 500,000m w.r.t central meridian.

{Longitude lines are farthest apart at equator, hence max. width occur at equator with a max value of 834,000m and min. width near poles with a min. value of 166,000m. As a result, there'll be no negative easting.}

A point lying 10m east of central meridian has an easting of 500000 + 10 = 500010mE. 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 = 360m.

(If eastings are < 500,000m it means point lies on the west of central meridian and for eastings > 500,000m point lies on east of central meridian.)

Northing are used to determine north-south position w.r.t equator which is assigned a value of 0m north for northern hemisphere and an arbitrary value of 10,000,000m south for referencing northing coordinates in southern hemisphere. The northing of a point south of the equator is equal to 10,000,000m minus its distance from the equator. In both northern and southern hemispheres, northing values increase from south to north.

{In the southern hemisphere the northing values range from 10,000,000m at the equator to approximately 1,100,000m at the 80°S. In the northern hemisphere the northing values stretch from 0m at the equator to around 9,350,000m at the 84°N. As a result, there'll be no negative northing.}

A point south of equator with a northing of 7,560,897mN is 10,000,000 – 7,560,897 = 2,439,103m south of the equator. A point located 54m south of the equator has a northing of 99,99,946mN, while a point 34m north of the equator has a northing of 00,00,034mN. The north-south distance between two points north of equator with northings of 4,657,134mN and 4,212,189mN is 4,657,134 – 4,212,189 = 444,945m.

Easting and northing are often referred as a False Easting and False Northing.




How to locate places on earth with UTM coordinates?

To explain this let's consider following examples.

Example 1:

The latitude and longitude of The Taj Mahal in Agra, Uttar Pradesh, India is 78.0419°S and 27.1750°N.

The Taj Mahal as per UTM coordinate system lies in,

UTM Zone 44R.

Easting & Northing coordinates are is 206,890.80mE, 3,009,276.00mN

We can see from map agra lies in b/w 84°E to 90°E longitudes. 87°E is the central meridian of this zone

From northing value we know the point lies 3,009,276m north to the equator in the zone 44R. 

From easting value we know the point lies at 500,000 - 206,890.80 = 293,109.20m west from the central meridian.

Hence, the Taj Mahal lies at the intersection of these two points.

Example 2:
The latitude and longitude of The Sydney Opera House in Australia is 33.8587°S and 151.2140°N.

The Sydney Opera House as per UTM coordinate system lies in,

UTM Zone 56H.

Easting & Northing coordinates are is 334,895.26mE, 6,252,359.77mN

We can see from map sydney opera house lies in b/w 150°E to 156°E longitudes. 153°E is the central meridian of this zone

From northing value we know the point lies 10,000,000 - 6,252,359.77 = 3,747,640.23m  south to the equator in the zone 44R. 

From easting value we know the point lies at 500,000 - 334,895.26 = 165104.74m west from the central meridian.

Hence, the Sydney Opera House lies at the intersection of these two points.

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