Mapping, Society, and Technology Chapter 3 Scale and Projections

. Scale and Projections Laura and Melinda Scale and projections are two fundamental features of maps that usually do not get the attention they deserve . Scale refers to how map units relate to units . Projections deal with the methods and challenges around turning a ( and sort of lumpy ) earth into a map . This chapter will introduce you to Scale and ways of telling the map user what the map is measuring on the ground Projection mechanics , types of projections , and their characteristics By the end of this chapter , you should be able to read map scales and identify common projections along with their basic features and uses . Scale The world is Vast . The earth surface has an area of over 500 million and any picture of the earth that you can easily carry can only show general outlines of continents and countries . When we Visually represent a region of the world on a map , we must reduce its size to fit within the boundaries of the map . Map scale measures how much the features of the world are reduced to fit on a map or more precisely , map scale shows the proportion of a given distance on a map to the corresponding distance on the ground in the real world . Map scale is represented by a representative fraction , graphic scale , or Verbal description .

50 Mapping , Society , and Technology Ratio ( Fraction ) scale Graphic scale . Verbal scale inch mile Map scales . A map can have a representative fraction , graphic scale , or verbal description that all mean the same thing . Representative fraction . The most commonly used measure of map scale is the representative fraction ( where map scale is shown as a ratio . the numerator always set to , the denominator represents how much greater the distance is in the world . The figure below shows a topographic map with an of , which means that one unit on the map represents units on the ground , The representative fraction is accurate regardless of which units are used the can be measured as centimeter to centimeters , one inch to inches , or any other unit . I nu IV us SCALE mi 1000 raw 2000 3000 soon 5000 6000 7000 45 CONTOUR INTERVAL 40 FEET NATIONAL GEODETIC OF 1929 THIS MAP COMPLIES WITH NATIONAL MAP ACCURACY STANDARDS FOR SALE BY GEOLOGICAL . BOX 252 , DENVER , COLORADO 225 A FOLDER DESCRIBING MAPS mo SYMBOLS IS AVAILABLE ON REQUEST Representative fraction . Representative fraction and scale bars from a United States Geological Survey ( topographic map . This topographic map has an of , which means that one unit on the map represents units on the ground .

. Scale and Projections 51 Graphic scale . Scale bars are graphical representations of distance on a map . The figure has scale bars for mile , 7000 feet , and kilometer . One important advantage of graphic scales is that they remain true when maps are shrunk or magnified . Verbal description . Some maps , especially older ones , use a verbal description of scale . For example , it is common to see one inch represents one kilometer or something similar written on a map to give map users an idea of the scale of the map . Map makers use scale to describe maps as being or . This description of map scale as large or small can seem at first . A by map of the United States has a small map scale while a campus map of the same size is . Scale descriptions using the provide one way of considering scale , since 121000 is larger than . Put differently , if we were to change the scale of the map with an of so that a section of road was reduced from one unit to , say , units in length , we would have created a map whose representative fraction is . When we talk about and maps and geographic data , then , we are talking about the relative sizes and levels of detail of the features represented in the data . In general , the larger the map scale , the more detail that is shown . Extent . Resolution The extent of a map describes the area visible on the map , while resolution describes the smallest unit that is mapped . You can think of extent as describing the region to which the map is zoomed . The extent of the map below is national as it encompasses the contiguous United States , while the resolution is the state , because states are the finest level of spatial detail that we can see .

52 Mapping , Society , and Technology . Map resolution and extent . This map shows a national extent and a state resolution . The extent of the map is national while the resolution is at the state level because they are the finest level of spatial detail that we can see . We often Choose mapping resolutions intentionally to make the map easier to understand . For example , if we tried to display a map with a national extent at the resolution of Census blocks , the level of detail would be so fine and the boundaries would be so small that it would be difficult to understand anything about the map . Balancing extent and resolution is often one of the most important and difficult decisions a cartographer must make . The figure below offers two more examples of the difference between extent and resolution .

. Scale and Projections 53 Sea Washington , OM ! More map extent and resolution . Maps showing an extent of the Pacific Northwest . The top image has a spatial resolution of county and the bottom has a spatial resolution of census . Coordinates Projections Locations on the earth surface are measured in terms of coordinates , a set of two or more numbers that specifies a location in relation to some reference system . The simplest system of this kind is a Cartesian coordinate system , named for the century mathematician and philosopher Rene Descartes . A Cartesian coordinate system , like the one below , is simply a grid formed by putting together two measurement scales , one horizontal ( and one Vertical ( The point at which both and equal zero is called the origin of the coordinate system . In the figure , the origin ( is located at the center of the grid ( the intersection of the two bold lines ) All other positions are specified relative to the origin , as seen with the points at ( and (

54 Mapping , Society , and Technology ( Coordinate system . Locations on the surface are measured in terms of coordinates , a set of two or more numbers that specifies a location in relation to some reference system . The geographic coordinate system is designed specifically to define positions on the Earth spherical surface . Instead of the two linear measurement scales and , as with a Cartesian grid , the geographic coordinate system uses an scale , called longitude that ranges from to . Because the Earth is round , or ) and ( or ) are the same grid line , termed the International Date Line . Opposite the International Date Line is the prime meridian , the line of longitude defined as . The scale , called latitude , ranges from ( or ) at the North pole to ( or ) at the South pole . In simple terms , longitude specifies positions east and west and latitude specifies positions north and south . At higher latitudes , the length of parallels decreases to zero at North and South . Lines of longitude are not parallel , but converge toward the poles . Thus , while a degree of longitude at the equator is equal to a distance of about 111 kilometers , that distance decreases to zero at the poles .

. Scale and Projections 55 Longitude and latitude . The graticule is based on an scale called longitude and a scale called latitude . The graticule specifies positions on the globe with latitude and longitude coordinates . The graticule refers to longitude and latitude on a globe . When we use longitude and latitude on a map , we refer to these as geographic coordinates . Maps can have an enormous array of different coordinate systems depending on who developed and used them . Projection is the term for turning a globe into a map . As noted above , the graticule on a globe is helpful , but how do we go from graticule to dimensional geographic coordinates , as per the figure below ?

We will discuss the process of how objects on a surface ( the earth ) come to be represented on a piece of paper or computer screen . Our emphasis will be on the properties that different projections distort or maintain area , shape , and distance .

56 Mapping , Society , and Technology Projected as Graticule geographic coordinates Graticule projected . The longitude and latitude of the graticule geographic coordinates through projection . Projection is the process of making a map from a globe . We can think of the earth as a sphere . In reality , it is more of an ellipsoid with a few bulges , but it is fine to think of it as a sphere , To get a sense of how difficult this process can be , imagine peeling the skin from an orange and trying to lay the skin , Flattened orange peel . You can imagine the difficulty of moving from a to surface by considering how difficult it is to peel the rind from an orange and try to lay the skin . As you peel and the skin , you will encounter several problems Shearing stretching the skin in one or more directions

. Scale and Projections 57 Tearing causing the skin to separate Compressing forcing the skin to bunch up and condense Cartographers face the same three issues when they try to the globe into a map . If you had a globe made of paper , you could carefully try to peel it into a flat piece of paper , but you would have a big mess on your hands . Instead , cartographers use projections to create useable maps . Shearing , tearing , compression . face these the three issues of shearing , tearing , and compression on a globe when they try to the globe into a two dimensional map .

58 Mapping , Society , and Technology Projection Mechanics The term map projection refers to both the process and product of transforming spatial coordinates on a sphere to a plane . In terms of actual mechanics , most projections use mathematical functions that take as inputs locations on the sphere and translate them into locations on a surface . It is helpful to think about projections in physical terms . If you had a clear globe the size of a beach ball and placed a light inside this globe , it would cast shadows onto a surrounding surface , If this surface were a piece of paper that you wrapped around the globe , you could carefully trace these shadows onto the paper , then flatten out this piece of paper and have your projection ! I ! a I II II II II II Thinking of projections in physical terms . You can conceptualize projection as working with a clear globe , a light bulb , and tracing paper . If you had a clear globe the size of a beach ball and placed a light inside this globe , it would cast shadows onto a surrounding surface . This surface can be a ( a ) cylinder , cone , or ( plane . 10 Most projections transform part of the globe to one of three developable surfaces , so called because they are or can be made flat plane , cone , and cylinder . The resultant projections are called planar ,

. Scale and Projections 59 conical , and cylindrical . We use developable surfaces because they eliminate tearing , although they will produce shearing and compression . Of these three problems , tearing is seen as the worst because you would be making maps with all sorts of holes in them ! As we see below , however , there are times when you can create maps with tearing and they are quite useful . The place where the developable surface touches the globe is known as the tangent point or tangent line . Maps will most accurately represent objects on the globe at these tangent points or lines , with distortion increasing as you move farther away due to shearing and compression . It is for this reason that cylinders are often used for areas near the equator , cones used to map the , and planes used for polar regions . Tangency . Red lines or dots mark the tangent line or point respectively . The flat surface touches the globe and it is the point on the projected map which has the least distortion . the place where the developable surface touches the globe is known as the tangent point or tangent line . These surfaces can be a ( a ) cylinder , cone , or ( plane . 11 For beginning , understanding the exact mechanics of projections doesn matter as much as knowing which map properties are maintained or lost with the choice of projection the topic of the next section . Projections must distort features on the surface of the globe during the process of making them

60 Mapping , Society , and Technology because projection involves shearing , tearing , and compression . Since no projection can preserve all properties , it is up to the map maker to know which properties are most important for their purpose and to choose an appropriate projection . The properties we will focus on are shape , area , and distance . Note that distortion is not necessarily tied to the type of developable surface but rather to the way the transformation is done with that surface . It is possible to preserve any one of the three properties using any of the developable surfaces . One way of looking at the problem is with distortion ellipses . These help us to visualize what type of distortion a map projection has caused , how much distortion has occurred , and where it has occurred . The ellipses show how imaginary circles on the globe are deformed as a result of a particular projection . If no distortion had occurred in projecting a map , all of the ellipses would be the same size and circular in shape . Conformal Conformal projections preserve shape and angle , but strongly distort area in the process . For example , with the projection , the shapes of coastlines are accurate on all parts of the map , but countries near the poles appear much larger relative to countries near the equator than they actually are . For example , is only the land area of Africa , but it appears to be just as large !

. Scale and Projections 61 projection . The projection is conformal because it preserves shape and angle but strongly distorts 12 area . Conformal projections should be used if the main purpose of the map involves measuring angles or representing the shapes of features . They are very useful for navigation , topography ( elevation ) and weather maps .

62 Mapping , Society , and Technology projection . One of the first maps of tire world developed was by ( do Mundo de , 1569 ) 13 A conformal projection will have distortion ellipses that vary substantially in size , but are all the same circular shape . The consistent shapes indicate that conformal projections ( like this projection of the world ) preserve shapes and angles . This useful property accounts for the fact that conformal projections are almost always used as the basis for large scale surveying and mapping .

. Scale and Projections 63 distortion . The projection is conformal because it preserves shape and angle but strongly distorts area . Equal Area On projections , the size of any area on the map is in true proportion to its size on the earth . In other words , countries shapes may appear to be squished or stretched compared to what they look like on a globe , but their land area will be accurate relative to other land masses . For example , in the projection , the shape of is significantly altered , but the size of its area is correct in comparison to Africa . This type of projection is important for quantitative thematic data , especially in mapping density ( an attribute over an area ) For example , it would be useful in comparing the density of Syrian refugees in the Middle East or the amount of cropland in production .

64 Mapping , Society , and Technology projection . The Gall Peters projection is equal area . Note how the shape of is significantly altered , 15 but the size of its area is correct in comparison to other regions such as Africa . As we can see with an projection , however , the ellipses maintain the correct proportions in the sizes of areas on the globe but that their shapes are distorted . projections are preferred for thematic mapping , especially when map users are expected to compare sizes of area features like countries and continents .

. Scale and Projections 65 distortion . The Gall Peters projection is equal area . Note how the shape of is significantly altered , but Lhe size of its area is correct in comparison to other regions such as Africa . 16 Equidistant Equidistant projections , as the name suggests , preserve distance . This is a bit misleading because no projection can maintain relative distance between all places on the map . Equidistant maps are able , however , to preserve distances along a few clearly specified lines . For example , on the Azimuthal Equidistant projection , all points are the proportionally correct distance and direction from the center point . This type of projection would be useful visualizing airplane flight paths from one city to several other cities or in mapping an earthquake epicenter . Azimuthal projections preserve distance at the cost of distorting shape and area to some extent . The flag of the United Nations contains an example of a polar azimuthal equidistant projection .

66 Mapping , Society , and Technology Azimuthal Equidistant projection . In this equidistant projection , all points are the proportionally correct distance and 17 direction from the center point . This projection is used on the map of the United Nations . Compromise , Interrupted , and Artistic Projections Some projections , including the Robinson projection , strike a balance between the different map properties . In other words , instead of preserving shape , area , or distance , they try to avoid extreme distortion of any of these properties . This type of projection would be useful for a general purpose world map .

. Scale and Projections 67 Robinson Projection . Some projections , including Robinson projection , strike a balance between the different map properties . In other words , they do not preserve shape , area , or distance , but instead try to avoid extreme distortion . 13 Compromise projections preserve no one properties , but instead seek a compromise that minimizes distortion of all kinds , as with the Robinson projection , which is often used for thematic maps of the world . Compromise distortion . Note that some maps may not preserve either shape or area but do a pretty good job at both . 19 Other projections deal with the challenge of making the globe flat by tearing the earth in strategic

68 Mapping , Society , and Technology places . Interrupted projections such as the interrupted Homolosine projection represent the earth in lobes , reducing the amount of shape and area distortion near the poles . The projection was developed in 1923 by John Paul to provide an alternative to the projection for portraying global areal relationships . homolosine projection of the world . This projection is interrupted in the sense that it uses lobes or sections . 20 The Interrupted Homolosine preserves area ( so it is or equivalent ) but does not preserve shape ( it is not conformal ) Interrupted distortion . This equal area projection preserves area but distorts shape , but not as much as it would if it were not interrupted . 21 There are also many projections that are aesthetically pleasing , but not intended for navigation

. Scale and Projections 69 between places or to visualize data . Examples of these artistic projections include the projection . Artistic projections . Many projections are interesting and beautiful , like this Projection , but are not intended for navigation between places or to visualize data . Conclusion In this chapter , we have explored the concepts of scale , resolution , and projection , There are hundreds of projections , each which distorts the world in a slightly different way , Keep in mind that all maps have a scale and there are a few important ways to indicate this scale . All maps also use a projection that can be formed from a developable surface and can preserve one or two properties at most . Resources GIS Commons Spatially Integrated Social Science

70 Mapping , Society , and Technology References Parts of section are adapted from Campbell and Shin ( 2011 ) Essentials of Geographic Information Systems . Parts of section are adapted from ( 1998 ) The Nature of Geographic Information An Open Textbook . Notes ! Adapted from Michael ( GIS Commons An Introductory Textbook on Geographic Information Systems . Adapted from Campbell and Shin ( 2012 ) Based on topographic maps ( Steven Manson 2017 . Data from and US Census . Steven Manson 2017 . Data from and US Census . Adapted from et al . 2012 ) Mapping our Changing World . Geography Department , The Pennsylvania State University . Adapted from et al . 2012 ) Mapping our Changing World . Geography Department , The Pennsylvania State University . Adapted from et al . 2012 ) Mapping our Changing World . Geography Department , The Pennsylvania State University . Adapted from Anthony Robinson . Maps and the Revolution , Original photos Nathan . Steven Manson 2012 . GNU Free Documentation License , Version . Adapted from Sutton , Sutton ( 2009 ) A Gentle Introduction to GIS . Chief Directorate Spatial Planning Information , Department of Land Affairs , Eastern Cape . Public domain . US National Atlas . Daniel ?

Public domain . Stefan ?

Daniel . Eric ?

Eric . By Spiff Based on File , the , United , Public Domain , Eric ?

Eric Gab Data World Coast Line ( public domain ) . Scale and Projections 71 20 . Daniel . 21 . Daniel . 22 . Daniel .