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Section Eight: Projected Coordinate Systems

2.8.1: Projection Methods to Projected Coordinate Systems

Up to this point, we've been examining projection technically: the result of using one of variety of methods to transfer the geographic locations of features from a geographic coordinate system to a developable surface everyday use: any coordinate system, geographic or projected methods and not projected coordinate systems. Just like when we learned geographic coordinate systems, there were steps we took to move from the geoid a model of the variation between global mean (average) sea level and local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features , which is used to measure precise elevations on the topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." , to a reference ellipsoid an ellipsoid that is drawn to best-fit an area. World reference ellipsoids are drawn to best-fit the entire geoid; local ellipsoids are best fit on one side to a single place of the geoid , to a geographic grid the result of using an established angular unit of measure to label the intersections of north-south and east-west lines on the surface of the Earth starting the labels at a principal meridian the north-south line from which the labeling begins.  East-west lines have a very obvious start point: the equator.  North-south lines must start somewhere, so when it is established for a particular geographic grid, it can be considered the principal meridian. , to a datum, and finally to a geographic coordinate system. Projection methods stop being just methods and start to be projected coordinate systems after two more steps have been taken: 1. a linear unit of measure is decided, and 2. a coordinate system origin is established. All coordinate systems have a single origin point, a point usually labeled (0, 0), however, some systems, like UTM , use a different origin value to prevent negative numbers (discussed in more detail in Section 2.8.4). No matter if the origin is labeled (0, 0) or something else, the action is the same where each of the intersections along the X and Y axis are labeled, counting up or down from the origin values.

Utilizing a variety of origin points, which come from moving around one secant line or splitting the difference between to tangential lines, allows for the distortion to be the least along either the X or Y axis, depending on the aspect The direction the developable surface a geometric shape which will not be distorted when flattened.  Used as the base shape to transfer features during projections.  Most often a cone, cylinder, or plane (azimuthal) faces in relation to the geographic coordinate system. Normal; transverse, oblique of the projection technically: the result of using one of variety of methods to transfer the geographic locations of features from a geographic coordinate system to a developable surface everyday use: any coordinate system, geographic or projected method. This movement, in addition to a large selection of reference ellipsoids allows for the maps we create to have the highest accuracy and precision paired with the least amount of distortion while still using linear units.

As stated above, the second factor that a projected coordinate system needs that takes it from a projection technically: the result of using one of variety of methods to transfer the geographic locations of features from a geographic coordinate system to a developable surface everyday use: any coordinate system, geographic or projected method to establish the linear units it's going to use, most commonly, feet, meters, and international feet. When a geographic grid the result of using an established angular unit of measure to label the intersections of north-south and east-west lines on the surface of the Earth starting the labels at a principal meridian the north-south line from which the labeling begins.  East-west lines have a very obvious start point: the equator.  North-south lines must start somewhere, so when it is established for a particular geographic grid, it can be considered the principal meridian. 's intersections are labeled via measuring from either the equator or principal meridian the north-south line from which the labeling begins.  East-west lines have a very obvious start point: the equator.  North-south lines must start somewhere, so when it is established for a particular geographic grid, it can be considered the principal meridian. , angles are easier to use since we are dealing with a sphere which later goes through a affine transformation to become an ellipsoid. When we are making measurements on a flat map - a projection technically: the result of using one of variety of methods to transfer the geographic locations of features from a geographic coordinate system to a developable surface everyday use: any coordinate system, geographic or projected - we then switch to linear units of measure, which are much more convenient and make more sense to us.

To review, a projection technically: the result of using one of variety of methods to transfer the geographic locations of features from a geographic coordinate system to a developable surface everyday use: any coordinate system, geographic or projected method includes selecting a projected coordinate system, a developable surface a geometric shape which will not be distorted when flattened.  Used as the base shape to transfer features during projections.  Most often a cone, cylinder, or plane (azimuthal) , such as a cone, cylinder, or flat plane (azimuthal), and an aspect The direction the developable surface a geometric shape which will not be distorted when flattened.  Used as the base shape to transfer features during projections.  Most often a cone, cylinder, or plane (azimuthal) faces in relation to the geographic coordinate system. Normal; transverse, oblique , selecting which direction to turn the Earth within the given developable surface a geometric shape which will not be distorted when flattened.  Used as the base shape to transfer features during projections.  Most often a cone, cylinder, or plane (azimuthal) . It becomes a projected coordinate system when a linear unit and a single secant line or pair of tangential lines have been selected prior to transferring the land and ocean masses to the developable surface a geometric shape which will not be distorted when flattened.  Used as the base shape to transfer features during projections.  Most often a cone, cylinder, or plane (azimuthal) , which is then cut and unrolled into a flat map. The selection of the placement of the secant or tangential lines define the location of the system's origin, as these lines will have the least amount of distortion. Selecting and moving the secant or tangential lines is made easier with software like ArcGIS, since it allows you to simple type in which line(s) you'd like to use and it makes all of the adjustments necessary.

As you will learn throughout the semester, there are several words in GIS which are used incorrectly or may have a double meaning. This is in no way done to confuse you (really), but it’s just a language that has been used by lots of folks, most of whom came from other sciences. As GIS is a fairly young science, most of it, including the terminology, comes from other places. This, in addition to a whole lot of "DIY GIS", has led to a fair number of words which are used either incorrectly, partially correct, or that have two, and sometimes three, meanings. The term " projection technically: the result of using one of variety of methods to transfer the geographic locations of features from a geographic coordinate system to a developable surface everyday use: any coordinate system, geographic or projected " is one of those words which, in addition to having a couple of meanings (which, luckily, are mostly correct and mostly similar), is used as a rather "all encompassing" term to mean "geographic coordinate system", "projected coordinate system", " projection technically: the result of using one of variety of methods to transfer the geographic locations of features from a geographic coordinate system to a developable surface everyday use: any coordinate system, geographic or projected method", and "convert data from one coordinate system to another".

Technically, the word " projection technically: the result of using one of variety of methods to transfer the geographic locations of features from a geographic coordinate system to a developable surface everyday use: any coordinate system, geographic or projected " or "to project" is in reference to the action of creating a projection technically: the result of using one of variety of methods to transfer the geographic locations of features from a geographic coordinate system to a developable surface everyday use: any coordinate system, geographic or projected and "projected coordinate system (PCS)" is the result of the action, after a linear unit and system origin has been set. For example, "Lambert Conformal Conic" is However, you’ll almost always here a projected coordinate system (and geographic coordinate systems, for that fact) referred to as a " projection technically: the result of using one of variety of methods to transfer the geographic locations of features from a geographic coordinate system to a developable surface everyday use: any coordinate system, geographic or projected ", simply because it’s shorter and easier. This text attempts to use the correct terms in the correct places while you’re still learning the process, but later will switch to using " projection technically: the result of using one of variety of methods to transfer the geographic locations of features from a geographic coordinate system to a developable surface everyday use: any coordinate system, geographic or projected " to mean both the action and the product - but by then, you’ll be able to note the difference in context.

We noted earlier that the word projection technically: the result of using one of variety of methods to transfer the geographic locations of features from a geographic coordinate system to a developable surface everyday use: any coordinate system, geographic or projected refers to the method used to create a the first part of a projected coordinate system. This idea will come up again when we begin to explore coordinate systems (both geographic and projected) in the GIS software. For every projected coordinate system, it will have a very specific name that represents where is should be used and the method by which it was created, as well as additional information about the method with which it was created - including the name. That is to say, the name of the PCS is the most specific thing, consisting of where you should use that particular PCS and the method it was created, and not exactly to be redundant, as there are always cases which vary from the norm, you will find the projection technically: the result of using one of variety of methods to transfer the geographic locations of features from a geographic coordinate system to a developable surface everyday use: any coordinate system, geographic or projected method listed, which is slightly less specific. For example, you might see USA Contiguous Lambert Conformal Conic as the specific name of a projected coordinate system and Lambert Conformal Conic as the projection technically: the result of using one of variety of methods to transfer the geographic locations of features from a geographic coordinate system to a developable surface everyday use: any coordinate system, geographic or projected method. The name Lambert Conformal Conic, as we learned earlier, means the projection technically: the result of using one of variety of methods to transfer the geographic locations of features from a geographic coordinate system to a developable surface everyday use: any coordinate system, geographic or projected method used a cone as the developable surface a geometric shape which will not be distorted when flattened.  Used as the base shape to transfer features during projections.  Most often a cone, cylinder, or plane (azimuthal) and it is meant to be used with projected coordinate systems which need to preserve shape ( conformal serve the purpose of preserving shape, distance, and bearing, at the expense of area and scale ) within the contiguous United States.

2.8.2: Map Scale

Before we look at how to choose a projection technically: the result of using one of variety of methods to transfer the geographic locations of features from a geographic coordinate system to a developable surface everyday use: any coordinate system, geographic or projected , lets first look at the idea of map scale a mathematical representation expressing distance on a map vs distance on the ground . Map scale is simply the mathematical ratio of the distance between two points represented on a map and the same two points in the real world expressed in one of two ways:

  1. A Statement of EquivalencyorVerbal Scale
  2. A Representative Fraction
  3. Scale Bars

Statement of Equivalency or Verbal Scale

A statement of equivalency (also known as ''verbal scale''): the relative scale is expressly defined on a map: 1 cm = 1 kilometer; 1 inch = 10 miles (also known asverbal scale) is when the relative scale is expressly defined on a map: 1cm = 1 kilometer; 1 inch = 10 miles, 5 nanometers = 12 kilometers (even though that last one would be a bit silly to use). For every measured unit on the map, one would travel the same distance in the real world. For the map where one inch equals ten miles, if you were to use a wooden ruler and measure an inch on the map, you can safely assume that the distance between those two points in the real world would be 10 miles.

The catch with a statement of equivalency (also known as ''verbal scale''): the relative scale is expressly defined on a map: 1 cm = 1 kilometer; 1 inch = 10 miles is, however, that the statement is only good for those units. If you were to measure the same map as above in centimeters, you could not assume that the distance between one centimeter is going to be ten miles. You could, using unit conversion, assume that 2.54 centimeters on the map would equal ten miles, however, but that means you'd be doing a whole lot of math and conversions. This is why, when you don't know what units your map's audience best thinks in, is to use representative fractions instead.

Representative Fractions

Similar to statements of equivalency, a representative fraction expression of map scale in ratio form utilizing non-specific linear unit, such as 1 map unit equals 250,000 real world units, or 1:250,000 is unitless. Presented as a ratio such as1:24,000; 1:100,000; 1:1,000,000; and so on, one unit on the map equals the stated units in the real world. In other words, a map that has a scale of 1:24,000 means that one inch equals 24,000 inches in the real world OR 1 centimeter equals 24,000 centimeters in the real world. With representative fractions, you don't need to assume what units your audience thinks best in, but you also assume they know how many inches are in a mile, since the representative fractions only work with a single unit at a time.

Scale Bars

Lastly, with maps, we often see scale bars drawn on the bottom. Like a statement of equivalency (also known as ''verbal scale''): the relative scale is expressly defined on a map: 1 cm = 1 kilometer; 1 inch = 10 miles , the scale bar will be shown in a set unit of measure, and not a representative fraction expression of map scale in ratio form utilizing non-specific linear unit, such as 1 map unit equals 250,000 real world units, or 1:250,000 . Unlike statement of equivalencies, however, you could potentially use a ruler of a different unit scale to measure the map. If the map scale a mathematical representation expressing distance on a map vs distance on the ground bar is shown in inches and miles, you could use a centimeter ruler to find the distancein miles. You're not exactly limited by the unit of measure of the ruler, but since the scale bar is set up for one kind of units, you can't convert the units back and forth, but you could successfully use a different kind of ruler.

  • One note: When it comes to reproducing maps, the only one of these three which stays constant is a scale bar. Statement of equivalencies and representative fractions are only true for the size of map the originally refereed to. If a map is copied at a smaller or larger size, the two ratios will be incorrect while the scale bar remains correct.

Large and Small Scale

In GIS and cartography, we often use the terms small scale, which are equally as often mixed up. When we look at the representative fraction expression of map scale in ratio form utilizing non-specific linear unit, such as 1 map unit equals 250,000 real world units, or 1:250,000 scale of a map and see a large number in the denominator, we tend toincorrectlyconclude the map is the large scale, when in fact a large denominator leads to a small number (a number a long distance from one on the number line)- thus a small scale map a map where the representative fraction is far from one and the objects in the map are relatively small (zoomed out) . Large scale maps have a small denominator where the number is closer to one on the number line.

The confusion is clear. When you see a map with a representative scale fraction with a large denominator and a larger geographic extent, your first inclination is to assume the map has a large scale. If we keep looking back on the representative fraction expression of map scale in ratio form utilizing non-specific linear unit, such as 1 map unit equals 250,000 real world units, or 1:250,000 , we see that fractions with a smaller denominator are closer to one on the number line (and a scale of 1:1 is the real world) and fractions with larger denominators are further away from the representative size being the same as the real world. To keep it straight, think that smaller denominators lead to larger features (more like the real world) and larger features lead to large scale maps.

Figure 2.41: Small and Large Scale Maps

2.8.3: Projection Selection

So far in this Chapter, we have looked at the idea of geodesy the science of measuring and monitoring the size and shape of the Earth and the location of points on its surface and measuring the Earth, representing the Earth’s odd shape as a geoid a model of the variation between global mean (average) sea level and local mean sea level the measurement above or below the global average at a single point on the Earth's surface used for recording the elevation of topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." 's relief the difference between the highest and lowest point within a particular area while landforms are the descriptive words for individual features , which is used to measure precise elevations on the topographic surface a detailed map of the surface features of land. It includes the mountains, hills, creeks, and other bumps and lumps on a particular hunk of earth. The word is a Greek-rooted combo of topos meaning "place" and graphein "to write." and a mathematical ellipsoid, creating measurable locations on the Earth’s surface by combining reference ellipsoids and datums to create geographic coordinate systems, how to use the idea of projections to convert a round Earth to a flat map, and lastly, how different projections are designed to minimize different distortions. Whew! That’s a lot of information - but we are not done quite yet. A solid understanding of how GCS’s and projections are created is essential to understanding how we use them in GIS, so we are going to finish off this chapter with a bit of practical projection technically: the result of using one of variety of methods to transfer the geographic locations of features from a geographic coordinate system to a developable surface everyday use: any coordinate system, geographic or projected use.

One of the most common questions asked by introduction to GIS students after learning about projections is: "What projection technically: the result of using one of variety of methods to transfer the geographic locations of features from a geographic coordinate system to a developable surface everyday use: any coordinate system, geographic or projected is best for my project"? This is one of those questions which has the unfortunate answer of "Well, that depends". When you look at how projections are created and what distortions come into play with their use, you will start to realize that being able to select the "proper" projection technically: the result of using one of variety of methods to transfer the geographic locations of features from a geographic coordinate system to a developable surface everyday use: any coordinate system, geographic or projected is just an understanding of the gains and setbacks of each kind of projection technically: the result of using one of variety of methods to transfer the geographic locations of features from a geographic coordinate system to a developable surface everyday use: any coordinate system, geographic or projected . While there are no real “rules” on projection technically: the result of using one of variety of methods to transfer the geographic locations of features from a geographic coordinate system to a developable surface everyday use: any coordinate system, geographic or projected selection, there are a few guidelines to help you choose:

  1. What distortion can you give up in favor of the one(s) you really need?
    • All projected coordinate systems come with some distortion, as we've learned there are no projections which preserve all kinds at one time. The biggest decision of which projection technically: the result of using one of variety of methods to transfer the geographic locations of features from a geographic coordinate system to a developable surface everyday use: any coordinate system, geographic or projected to use for a project is that of distortion. If you have a project which deals with solving the the area which has changed, selecting a projection technically: the result of using one of variety of methods to transfer the geographic locations of features from a geographic coordinate system to a developable surface everyday use: any coordinate system, geographic or projected which preserves shape will produce errors in the solved measurements. On the other hand, when you go to present your work at the end of the project, keeping the projection technically: the result of using one of variety of methods to transfer the geographic locations of features from a geographic coordinate system to a developable surface everyday use: any coordinate system, geographic or projected which preserved area and distorted shape will look quite odd to your reader.
  2. How big is your project area?
    • Now that we understand what scale is in regards to GIS and cartography, we can explore projections in these same terms. As we learned with reference ellipsoids, better accuracy and precision come with better localization, and the same is held true with projections. Selecting a localized projection technically: the result of using one of variety of methods to transfer the geographic locations of features from a geographic coordinate system to a developable surface everyday use: any coordinate system, geographic or projected will decrease distortion close to the tangential point, and that distortion will increase as you move away, so choosing a projection technically: the result of using one of variety of methods to transfer the geographic locations of features from a geographic coordinate system to a developable surface everyday use: any coordinate system, geographic or projected designed for use in Florida and applying it to Oregon is most likely a bad idea. And when you are completing a project which covers the entire United States, choosing a projection technically: the result of using one of variety of methods to transfer the geographic locations of features from a geographic coordinate system to a developable surface everyday use: any coordinate system, geographic or projected designed for either Oregon or Florida (or the whole Earth, for that fact) is also a bad idea.
  3. What unit of measure (feet, inches, degrees measurement of plane angle, representing 1⁄360 of a full rotation (circle). In full, a degree of arc or arc degree. Usually denoted by ° ...) would you like your map to be measured in?
    • We know that geographic coordinate systems consist of a datum, a reference ellipsoid an ellipsoid that is drawn to best-fit an area. World reference ellipsoids are drawn to best-fit the entire geoid; local ellipsoids are best fit on one side to a single place of the geoid , and an angular unit of measure the selected units for measuring angles.  Choices include degree and radians.  (such as degree with the latitude also known as 'parallels' the east-west portion of a geographic grid measured with angles between 0 and 90° /longitude system) - which means that spatial objects collected in a GCS will be measured in that unit of measure. For example, if you create a GIS layer of roads, and the chosen GCS is WGS84, the length of the roads will be measured in degrees measurement of plane angle, representing 1⁄360 of a full rotation (circle). In full, a degree of arc or arc degree. Usually denoted by ° . When we go through the process of creating a projection technically: the result of using one of variety of methods to transfer the geographic locations of features from a geographic coordinate system to a developable surface everyday use: any coordinate system, geographic or projected , moving from the round (measured in angles) to the flat, we can move from an angular unit of measure the selected units for measuring angles.  Choices include degree and radians.  to a linear one, such as feet and meters. When you move the roads layer you created in WGS84, and move it, or project it, from the GCS WGS84 to a flat map (say WGS84 California (Teale) Albers), you are now capable of measuring in feet, yards, and miles.
  4. What is the end goal of your project?
    • While we will spend quite a bit of time discussing this in Chapter Nine, for now, we can just look at the end goal as how is it the map should look? Will it be displayed on a wall and you need to preserve shape and size or used for navigation where distance and bearing are important. Choosing the correct projection technically: the result of using one of variety of methods to transfer the geographic locations of features from a geographic coordinate system to a developable surface everyday use: any coordinate system, geographic or projected leads to the proper end product.

2.8.4: Examples Of Projected Coordinate Systems

Up to this point, we've spent quite a lot of time examining the process of creating projected coordinate systems: the projection technically: the result of using one of variety of methods to transfer the geographic locations of features from a geographic coordinate system to a developable surface everyday use: any coordinate system, geographic or projected methods, the distortions that are a result of the process, kinds of developable surfaces, and kinds of aspects. To be a quality GIS technician, it's important to understand the process of creating these coordinate systems which we use every day. With this understanding comes the ability to make better decisions about maps, products, and solutions. Within the GIS software, you will find all of the information about how a particular projection technically: the result of using one of variety of methods to transfer the geographic locations of features from a geographic coordinate system to a developable surface everyday use: any coordinate system, geographic or projected was created, which will help you understand it's strength and weaknesses.

In the next section, will look at four common projected coordinate systems and examine how they were made, which - as stated above - will let us in on the benefits of selecting that projection technically: the result of using one of variety of methods to transfer the geographic locations of features from a geographic coordinate system to a developable surface everyday use: any coordinate system, geographic or projected for a specific project.

Normal Mercator and Transverse Mercator

Normal Mercator

The Normal Mercator projection technically: the result of using one of variety of methods to transfer the geographic locations of features from a geographic coordinate system to a developable surface everyday use: any coordinate system, geographic or projected is one of the most common, and most controversial, projections out there. Just like it was stated in the West Wing clip we watched, the Mercator projection technically: the result of using one of variety of methods to transfer the geographic locations of features from a geographic coordinate system to a developable surface everyday use: any coordinate system, geographic or projected is a conformal serve the purpose of preserving shape, distance, and bearing, at the expense of area and scale cylindrical projection technically: the result of using one of variety of methods to transfer the geographic locations of features from a geographic coordinate system to a developable surface everyday use: any coordinate system, geographic or projected , tangent at the Equator, and designed to preserve shape, distance, and bearing. Adjacent to the tangential line, distortion is minimal, but increases rapidly as one moves north or south. The Mercator projection technically: the result of using one of variety of methods to transfer the geographic locations of features from a geographic coordinate system to a developable surface everyday use: any coordinate system, geographic or projected (and it’s cousin, Web Mercator) is used for large areas (small scale) nearest the mid-latitudes.

Transverse Mercator

The Transverse Mercator projections, like we learned in the previous section, turn the tangential line from a parallel to a meridian, which reduces distortion along a North-South line, with that distortion increasing moving east or west.

Figure 2.42: Normal and Transverse Mercator Projected Coordinate Systems

Normal Mercator Projected Coordinate System

Transverse Mercator Projected Coordinate System

Lambert Conformal Conic

Looking at the name, we immediately know this projection technically: the result of using one of variety of methods to transfer the geographic locations of features from a geographic coordinate system to a developable surface everyday use: any coordinate system, geographic or projected is designed to preserve shape, distance, and bearing ( conformal serve the purpose of preserving shape, distance, and bearing, at the expense of area and scale ) and is created from a conic developable surface a geometric shape which will not be distorted when flattened.  Used as the base shape to transfer features during projections.  Most often a cone, cylinder, or plane (azimuthal) (and was designed by a guy named Lambert). Designed by Johann Heinrich Lambert in 1772, the Lambert Conformal Conic projection technically: the result of using one of variety of methods to transfer the geographic locations of features from a geographic coordinate system to a developable surface everyday use: any coordinate system, geographic or projected is used to map large areas (small scale), especially in the mid-latitudes, where the secant lines are placed at roughly 20°N and 60°S.

Figure 2.43: Lambert Conformal Conic Projected Coordinate System

Universal Transverse Mercator(UTM)

Universal Transverse Mercator is a technically a planar coordinate system the result of converting an angular unit of measure used to locate objects on a geographic coordinate system to a linear unit of measure via a Cartesian Coordinate System. Planar Coordinate Systems utilize linear units such as feet, meters, and international feet. - a specially designed method for finding a location on a two-dimensional map, which is based on a projection technically: the result of using one of variety of methods to transfer the geographic locations of features from a geographic coordinate system to a developable surface everyday use: any coordinate system, geographic or projected . Like with the Lambert Conformal Conic projection technically: the result of using one of variety of methods to transfer the geographic locations of features from a geographic coordinate system to a developable surface everyday use: any coordinate system, geographic or projected , we can look to the name - Universal Transverse Mercator - to see the projection technically: the result of using one of variety of methods to transfer the geographic locations of features from a geographic coordinate system to a developable surface everyday use: any coordinate system, geographic or projected is based on the transverse Mercator projection technically: the result of using one of variety of methods to transfer the geographic locations of features from a geographic coordinate system to a developable surface everyday use: any coordinate system, geographic or projected . The “universal” part comes in by altering the transverse methods slightly instead of being tangent at one line and projecting the entire globe, a smaller projection technically: the result of using one of variety of methods to transfer the geographic locations of features from a geographic coordinate system to a developable surface everyday use: any coordinate system, geographic or projected is made by placing the cylinder secant at two lines 6° apart, creating a strip or “zone”. The secant lines are then rotated, and another strip is taken (360° / 6° = 60 zones). By stitching together all 60 zones together, a complete world projection technically: the result of using one of variety of methods to transfer the geographic locations of features from a geographic coordinate system to a developable surface everyday use: any coordinate system, geographic or projected is made with distortion reduced in every zone (vs at a only single meridian). Like the Transverse Mercator projection technically: the result of using one of variety of methods to transfer the geographic locations of features from a geographic coordinate system to a developable surface everyday use: any coordinate system, geographic or projected , however, the distortion is too extreme at the poles (the sweet spots are between 84°N and 80°S) and UTM is not used.

Figure 2.44: Universal Transverse Mercator Projected Coordinate System

Since UTM is a planar coordinate system the result of converting an angular unit of measure used to locate objects on a geographic coordinate system to a linear unit of measure via a Cartesian Coordinate System. Planar Coordinate Systems utilize linear units such as feet, meters, and international feet. , it utilizes a Cartesian Coordinate system affixed to an origin and labels XY intersections by measuring the linear distance from that origin. Yet, the UTM system delivers the geographic grid the result of using an established angular unit of measure to label the intersections of north-south and east-west lines on the surface of the Earth starting the labels at a principal meridian the north-south line from which the labeling begins.  East-west lines have a very obvious start point: the equator.  North-south lines must start somewhere, so when it is established for a particular geographic grid, it can be considered the principal meridian. in a unique way - with 60 different origins, one for each zone.

Using the equator as the X axis, each UTM zone is bisected right down the middle creating a central meridian, with 3° on the east and 3° on the west (and the Y axis). North of the equator is the North Zone, denoted with the number of the zone and an N, such as Zone 18N, and an S for south, such as Zone 18S. If the origin was labeled 0,0 where the equator and central meridian intersect in each zone, that means there would have to be negative numbers - those west of the central meridian and south of the equator. To combat the negative numbers, the 0,0 was arbitrarily changed to 500,000 and 10,000,000, meaning coordinates west of the central meridian start counting down from 499,999 meters and south of the equator count down from 9,999,999 meters. Since UTM measurements come from a projection technically: the result of using one of variety of methods to transfer the geographic locations of features from a geographic coordinate system to a developable surface everyday use: any coordinate system, geographic or projected and not a GCS, the terms false easting and false northing are used in place of North and East, like we see with Latitude and Longitude.

Whew! That was a lot of information in two paragraphs. Let’s look at some examples to help understand what we just read.

Figure 2.45: The UTM System Explained
First, we place the cylinder secant along two lines 6° apart to make a zone. Since our goal is to reduce distortion and create a flat map with planar coordinates, the two curved sections are overlapped with the neighboring zone to make a rectangular strip.
The North and South halves of each zone contains a false and a true origin, with the false origin located at 0 mE, 0mN, as expected, and the false origin located where the central meridian and equator intersect. The North Zone true origin is located at 5000,000 mE, 0mN while the South Zone true origin is located at 500,000 mE, 10,000,000mN. The arbitrary numbers assigned to the false origins prevents the use of negative numbers for UTM coordinates.

Since each zone is labeled the same way in reference to the UTM coordinates, each unique coordinate pair occurs 120 times, thus making the addition of the zone number and North or South designation imperative for the coordinate label. For example, 420235 mE, 3868323mN occurs 120 times, but UTM 11N 420235 mE, 3868323mN occurs only once.

State Plane Coordinate System(SPCS)

The UTM planar coordinate system the result of converting an angular unit of measure used to locate objects on a geographic coordinate system to a linear unit of measure via a Cartesian Coordinate System. Planar Coordinate Systems utilize linear units such as feet, meters, and international feet. is a great example of a “global” system designed to minimize distortion and locate positions over a large area using series of multiple, smaller projections stitched together. An excellent example of a “local” coordinate system with the same purpose is the State Plane Coordinate System or SPCS.

SPCS breaks the United States into sections by state, and in many cases, breaks states into zones, all with the goal of reducing distortion and labeling locations. For east-west trending states, such as Tennessee and Colorado, utilize a Lambert Conformal Conic projection technically: the result of using one of variety of methods to transfer the geographic locations of features from a geographic coordinate system to a developable surface everyday use: any coordinate system, geographic or projected , while north-south trending states such as Illinois and Mississippi, use a Transverse Mercator projection technically: the result of using one of variety of methods to transfer the geographic locations of features from a geographic coordinate system to a developable surface everyday use: any coordinate system, geographic or projected (The panhandle of Alaska didn’t fall into either category, thus an Oblique Mercator was used). Thinking about what we’ve learned so far, why were the Lambert Conformal Conic and Transverse Mercator projections used?

Figure 2.46: State Plane

The State Plane Coordinate System (SPCS) with zone numbers

In addition to each state being projected independently to reduce distortion, most of the states were actually broken down further, such as Colorado which contains three zones - Colorado North (0501), Colorado Central (0502), and Colorado South (0503). This means the distortion for each section is about as small as it can be. One thing to note is while distortion is reduced greatly for each zone, the inter-zone distortion can be greater then desired, especially when two neighboring states are created from two base projections.

Like UTM, SPCS is a not a projection technically: the result of using one of variety of methods to transfer the geographic locations of features from a geographic coordinate system to a developable surface everyday use: any coordinate system, geographic or projected , but rather a planar coordinate system the result of converting an angular unit of measure used to locate objects on a geographic coordinate system to a linear unit of measure via a Cartesian Coordinate System. Planar Coordinate Systems utilize linear units such as feet, meters, and international feet. , utilizing a false origin originally located in Meades Ranch, Kansas (when the system was based on the North American Datum 1927 NAD27), and the idea of counting coordinates with a false easting and a false northing. With an effort to convert angular units of measure ( degrees measurement of plane angle, representing 1⁄360 of a full rotation (circle). In full, a degree of arc or arc degree. Usually denoted by ° ) into a Cartesian Coordinate System for ease of navigation, the SPCS was developed in 1930. Since then, the system has been revised a few times, most notably in 1983 after NAD83 was completed, and more recently, when the origin was moved to the center of the Earth to improve calculations when using the system with GPS units. SPCS can be found in feet, meters, and international feet.

Also like UTM, the idea of using a technique of projecting small sections and merging them together into a large network can be tough for a new GIS student, since the answer “What projection technically: the result of using one of variety of methods to transfer the geographic locations of features from a geographic coordinate system to a developable surface everyday use: any coordinate system, geographic or projected is your data in?” regarding data near Denver would be “SPCS Colorado Central (0502)”. SPCS is often used as a local projection technically: the result of using one of variety of methods to transfer the geographic locations of features from a geographic coordinate system to a developable surface everyday use: any coordinate system, geographic or projected (since each zone is based on a projection technically: the result of using one of variety of methods to transfer the geographic locations of features from a geographic coordinate system to a developable surface everyday use: any coordinate system, geographic or projected ), even though it is technically a planar coordinate system the result of converting an angular unit of measure used to locate objects on a geographic coordinate system to a linear unit of measure via a Cartesian Coordinate System. Planar Coordinate Systems utilize linear units such as feet, meters, and international feet. . Think about it this way: if you are working in Oregon and would like the data to be as exact as possible, you know that if you use Oregon North, the cone used in the projection technically: the result of using one of variety of methods to transfer the geographic locations of features from a geographic coordinate system to a developable surface everyday use: any coordinate system, geographic or projected was tangent to a line running through the center of the zone, vs a cone which was tangent thought the center of the United States for a continent-based projection technically: the result of using one of variety of methods to transfer the geographic locations of features from a geographic coordinate system to a developable surface everyday use: any coordinate system, geographic or projected . When the projection technically: the result of using one of variety of methods to transfer the geographic locations of features from a geographic coordinate system to a developable surface everyday use: any coordinate system, geographic or projected is designed for a smaller area, distortion is reduced, larger projections have the least amount of distortion along the tangential line, and increasing distortion from there. If your entire area is only a few hundred miles across, the distortion is negligible, and when the area is thousands of miles across, the distortion is noticeable.