State Plane Coordinate System

Posted on August 31, 2008 by Rashid Faridi

The State Plane Coordinate System (SPCS) was developed in the 1930s by the U.S. Coast and Geodetic Survey to provide a common reference system for surveyors and mappers. The goal was to design a conformal mapping system for the country with a maximum scale distortion of one part in 10,000, which at the time was considered the limit of surveying accuracy. The State Plane Coordinate System (SPCS) is used for local surveying and engineering applications, but isn’t used if crossing state lines.

The State Plane grid system is very similar to that used with the UTM system, with the exception of where the origin for the grids are located. The easting origin for each zone is always placed an arbitrary number of feet west of the western boundary of the zone, eliminating the need for negative easting values. The northing origin, however, is not at the equator as in UTM, but rather it is placed at an arbitrary number of feet south of the state border.

To maintain the accuracy of one part in 10,000 and minimize distortion, large states were divided into zones, and depending on their orientation different projections were chosen. The three conformal projections used are listed below.
Lambert Conformal Conic… for states that are longer east–west, such as Tennessee and Kentucky.
Transverse Mercator projection… for states that are longer north–south, such as Illinois and Vermont.
The Oblique Mercator projection… for the panhandle of Alaska, because it lays at an angle.
The number of zones in a state is usually determined by the area the state covers and ranges from one to as many as ten in Alaska. Each zone has a unique central meridian.

Idaho uses a transverse Mercator projection and is divided into three zones – east, central and west
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UTM – Universal Transverse Mercator Geographic Coordinate System

Posted on August 28, 2008 by Rashid Faridi

Projections are a mathematical way of representing 3D earth on a 2D plane.The idea of the transverse mercator projection has its roots in the 18th century, but it did not come into common usage until after World War II. It has become the most used because it allows precise measurements in meters to within 1 meter.

A mercator projection is a ‘pseudocylindrical’ conformal projection (it preserves shape). What you often see on poster-size maps of the world is an equatorial mercator projection that has relatively little distortion along the equator, but quite a bit of distortion toward the poles.

What a transverse mercator projection does, in effect, is orient the ‘equator’ north-south (through the poles), thus providing a north-south oriented swath of little distortion. By changing slightly the orientation of the cylinder onto which the map is projected, successive swaths of relatively undistorted regions can be created.

This is exactly what the UTM system does. Each of these swaths is called a UTM zone and is six degrees of longitude wide. The first zone begins at the International Date Line (180°, using the geographic coordinate system). The zones are numbered from west to east, so zone 2 begins at 174°W and extends to 168°W. The last zone (zone 60) begins at 174°E and extends to the International Date Line.

The zones are then further subdivided into an eastern and western half by drawing a line, representing a transverse mercator projection, down the middle of the zone. This line is known as the ‘central meridian’ and is the only line within the zone that can be drawn between the poles and be perpendicular to the equator (in other words, it is the new ‘equator’ for the projection and suffers the least amount of distortion). For this reason, vertical grid lines in the UTM system are oriented parallel to the central meridian. The central meridian is also used in setting up the origin for the grid system.

Any point can then be described by its distance east of the origin (its ‘easting’ value). By definition the Central Meridian is assigned a false easting of 500,000 meters. Any easting value greater than 500,000 meters indicates a point east of the central meridian. Any easting value less than 500,000 meters indicates a point west of the central meridian. Distances (and locations) in the UTM system are measured in meters, and each UTM zone has its own origin for east-west measurements.

To eliminate the necessity for using negative numbers to describe a location, the east-west origin is placed 500,000 meters west of the central meridian. This is referred to as the zone’s ‘false origin’. The zone doesn’t extend all the way to the false origin.
The origin for north-south values depends on whether you are in the northern or southern hemisphere. In the northern hemisphere, the origin is the equator and all distances north (or ‘northings’) are measured from the equator. In the southern hemisphere the origin is the south pole and all northings are measured from there. Once again, having separate origins for the northern and southern hemispheres eliminates the need for any negative values. The average circumference of the earth is 40,030,173 meters, meaning that there are 10,007,543 meters of northing in each hemisphere.

UTM coordinates are typically given with the zone first, then the easting, then the northing. So, in UTM coordinates, Red Hill is located in zone twelve at 328204 E (easting), 4746040 N (northing). Based on this, you know that you are west of the central meridian in zone twelve and just under halfway between the equator and the north pole. The UTM system may seem a bit confusing at first, mostly because many people have never heard of it, let alone used it. Once you use it for a little while, however, it becomes an extremely fast and efficient means of finding exact locations and approximating locations on a map.

Many topographic maps published in recent years use the UTM coordinate system as the primary grids on the map. On older topographic maps published in the United States, UTM grids are shown along the edges of the map as small blue ticks.

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Map Projection and Distortions

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Geographic Coordinate System

Posted on August 26, 2008 by Rashid Faridi

One of the most common coordinate systems in use is the Geographic Coordinate System, which uses degrees of latitude and longitude to describe a location on the earth’s surface. Lines of latitude run parallel to the equator and divide the earth into 180 equal portions from north to south (or south to north). The reference latitude is the equator and each hemisphere is divided into ninety equal portions, each representing one degree of latitude.

In the northern hemisphere degrees of latitude are measured from zero at the equator to ninety at the north pole. In the southern hemisphere degrees of latitude are measured from zero at the equator to ninety degrees at the south pole. To simplify the digitization of maps, degrees of latitude in the southern hemisphere are often assigned negative values (0 to -90°). Wherever you are on the earth’s surface, the distance between lines of latitude is the same (60 nautical miles,), so they conform to the uniform grid criterion assigned to a useful grid system.

Lines of longitude, on the other hand, do not stand up so well to the standard of uniformity. Lines of longitude run perpendicular to the equator and converge at the poles. The reference line of longitude (the prime meridian) runs from the north pole to the south pole through Greenwich, England. Subsequent lines of longitude are measured from zero to 180 degrees east or west (values west of the prime meridian are assigned negative values for use in digital mapping applications) of the prime meridian.

At the equator, and only at the equator the distance represented by one line of longitude is equal to the distance represented by one degree of latitude. As you move towards the poles, the distance between lines of longitude becomes progressively less until, at the exact location of the pole, all 360° of longitude are represented by a single point you could put your finger on (you probably would want to wear gloves, though). So, using the geographic coordinate system, we have a grid of lines dividing the earth into squares that cover approximately 4,773.5 square miles at the equator…a good start, but not very useful for determining the location of anything within that square.

To be truly useful, a map grid must divided into small enough sections that they can be used to describe with an acceptable level of accuracy the location of a point on the map. To accomplish this, degrees are divided into minutes (‘) and seconds (“). There are sixty minutes in a degree, and sixty seconds in a minute (3600 seconds in a degree). So, at the equator, one second of latitude or longitude = 101.3 feet.
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Grid Systems for Maps

Posted on August 24, 2008 by Rashid Faridi

A grid system allows the location of a point on a map (or on the surface of the earth) to be described in a way that is meaningful and universally understood. Projecting the earth’s surface (or a portion of it) in one of the ways outlined in the Map Projections page, allows for a representation of an area on a flat piece of paper. Once this is accomplished, it is necessary to set up a coordinate system on the map that will allow a point to be described in X-Y space.

However, in order to describe this location in a universally understandable manner a grid system is necessary. A simple grid is shown with the location of a point of interest that we want to describe.
In order for a point designation on a grid to be meaningful, there must be an origin to the grid which can be used to reference the point to. Once an origin is assigned then there is only one correct designation for the point, and anyone looking at the grid will assign it the same value and be able to interpret what someone else means when they describe a point located at 3,3.

A few examples of possible origins for the grid are shown. In the first example, the designation for the point would be 3,3. In the second the designation would be 3,1, and in the third it would be 1,1. All of these designations describe the same point and the only thing that has changed is the origin of the grid. In order for any type of grid to be useful it is necessary for it to have an origin and a uniform grid spacing (i.e. the distance between grid lines should remain constant).

There are several types of grids (or coordinate systems), used to divide the earth’s surface.
Geographic . . . Uses degrees of latitude and longitude. One of the most common coordinate systems in use.
UTM . . . Preserves shape, and allows for precise measurements in meters.
State Plane . . . Developed for local surveying, with minimal distortion.
Public Land Survey . . . This one was used in Colonial America for surveying. Not as accurate as others.
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