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# Map scale and projection

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### Map scale and projection

1. 1. Map Scale and Projection Lab Three
2. 2. Map Scale <ul><li>The scale of a map indicates how much the Earth has been reduced for reproduction on that map. </li></ul><ul><li>In practical terms, scale is the relationship between the distance shown on a map and the actual distance that it represents on the Earth. </li></ul>
3. 3. Ways to Indicate Scale <ul><li>There are two common ways to indicate the scale of a map: </li></ul><ul><ul><li>Graphic scales </li></ul></ul><ul><ul><ul><li>See figure 1 in lab manual </li></ul></ul></ul><ul><ul><li>Fractional scales </li></ul></ul><ul><ul><ul><li>Example 1:24,000 </li></ul></ul></ul>Graphic Scale
4. 4. Graphic Scale <ul><li>The graphic scale of a map is a bar graph graduates by distance. </li></ul><ul><ul><li>Figure one in the lab manual shows the graphic map scale from a U.S. Geological Survey topographic map. </li></ul></ul><ul><li>To use a graphic scale, simply measure a distance on the map (or mark off the distance on the edge of a piece of paper), then compare the measured distance to the bar graph to determine the actual distance represented. </li></ul><ul><ul><li>On some graphic scales, “zero” is not at the far left, this is to make it easier to read fractions. </li></ul></ul><ul><li>Graphic scales are useful since they remain accurate even if the map is enlarged or reduced. </li></ul>
5. 5. Fractional Scale <ul><li>The fractional scale or the representative scale expresses the scale of a map as a fraction or ratio. </li></ul><ul><ul><li>1/24,000 or 1:24,000 </li></ul></ul><ul><li>This scale, which is read “one to twenty-four thousand”, says that one unit of measurement on the map represents 24,000 units of measurement on the Earth. </li></ul><ul><li>At this scale, one centimeter on the map represents an actual distance of 24,000 centimeters on the Earth, and one inch on the map equals 24,000 inches on the map. </li></ul><ul><ul><li>Units of measurement must be the same in both the numerator and the denominator. </li></ul></ul>
6. 6. Computing Distances with Fractional Scales <ul><li>To determine distances represented on a map by using the fractional scale: </li></ul><ul><li>Use a ruler to measure the distance on the map in inches (or centimeters). This is the measured distance . </li></ul><ul><li>Multiply the measured distance by the map’s fractional scale denominator. This will give you the actual distance in inches (or centimeters). </li></ul><ul><li>To convert your actual distance in inches (or centimeters) to other units, use the following formulas: </li></ul>
7. 7. <ul><li>To determine the distance in feet , actual distance in inches / 12 </li></ul><ul><li>To determine the distance in miles , actual distance in inches / 63,360 </li></ul><ul><li>To determine the distance in meters , actual distance in centimeters / 100 </li></ul><ul><li>To determine the distance in kilometers , actual distance in centimeters / 100,000 </li></ul>
8. 8. English Measurements <ul><li>1 mile = 5280 ft </li></ul><ul><li>1 mile = 63360 inches </li></ul><ul><li>1 foot = 12 inches </li></ul>
9. 9. Metric Measurements <ul><li>1 Kilometer (Km) = 1,000 meters (m) </li></ul><ul><li>1 Kilometer (Km) = 100,000 cm </li></ul><ul><li>1 Kilometer (Km) = 1,000,000 mm </li></ul><ul><li>1 meter = 100 centimeters (cm) </li></ul><ul><li>1 centimeter = 10 millimeters (mm) </li></ul>
10. 10. Examples <ul><li>If a map has a scale of 1/24,000, a measured distance of 8.25 inches on the map represents an actual distance of 198,000 inches </li></ul><ul><ul><li>8.25 X 24,000 = 198,000 inches </li></ul></ul><ul><ul><li>198,000 inches / 12 = 16,500 feet </li></ul></ul><ul><ul><li>198,000 inches / 63,360 = 3.1 miles </li></ul></ul>
11. 11. Examples <ul><li>If a map has a scale of 1/50,000, a measured distance of 22 centimeters on the map represents an actual distance of 1,100,000 cm </li></ul><ul><ul><li>22 cm X 50,000 = 1,100,000 cm </li></ul></ul><ul><li>To calculate the actual distance in meters and kilometers: </li></ul><ul><ul><li>1,100,000 cm / 100 = 11,000 meters </li></ul></ul><ul><ul><li>1,100,000 cm / 100,000 = 11 kilometers </li></ul></ul>
12. 12. Large Versus Small Scale Maps <ul><li>Large scale maps refer to maps with a relatively large representative fraction such as 1/10,000. </li></ul><ul><ul><li>Large scale maps show a small area of the Earth in great detail. </li></ul></ul><ul><li>Small scale maps refer to maps with a relatively small representative fraction like 1/1,000,000. </li></ul><ul><ul><li>Small scale maps show large areas in less detail. </li></ul></ul>Small Scale Medium Scale Large Scale
13. 13. Map Projections <ul><li>http://www.classzone.com/books/earth_science/terc/content/investigations/es0301/es0301page01.cfm </li></ul><ul><li>This is the website that your worksheet came from. </li></ul><ul><li>It has animations and illustrations beyond what is on your worksheet and you are strongly encouraged to visit it. </li></ul>
14. 14. Map Projection <ul><li>Only a globe can show the true area, shape, direction, and distance relationships of the spherical surface of Earth. </li></ul><ul><li>It is impossible to show all of these relationships on a map without distortion. </li></ul>
15. 15. <ul><li>Equivalence and conformity are the most important properties of maps. </li></ul><ul><li>An equivalent map or an equal area map shows correct area relationships over the entire map. </li></ul><ul><li>With an equivalent map, the area of one region on the map can be directly compared with the area of any other region. </li></ul>The Lambert cylindrical equal-area projection as an example of an equivalent, cylindrical projection http://www.kartografie.nl/geometrics/Map%20projections/body.htm
16. 16. <ul><li>In contrast, a conformal map shows the correct angular relationships over the entire map. </li></ul><ul><li>In other words, a conformal map shows the correct shape of features in a limited area. </li></ul><ul><ul><li>The true shapes of the continents can only be shown with a glove. </li></ul></ul>www.kartografie.nl/.../body.htm
17. 17. <ul><li>It is impossible for a map to be both equivalent and conformal, and many maps are neither, but are a compromise. </li></ul><ul><ul><li>Distortions are most pronounced on world maps, on large scale maps showing limited areas, distortions may not be a serious problem. </li></ul></ul><ul><ul><li>Properties other than equivalence and conformity may also be maintained on a map. </li></ul></ul><ul><ul><ul><li>True direction can be retained in some projections or along a specific set of lines. </li></ul></ul></ul>
18. 18. Map Projections <ul><li>Cartographers transfer the surface features of the Earth to a map by mathematically “projecting” the graticule (the grid of latitude and longitude) out from the spere onto a flat surface. </li></ul>
19. 19. Map Projections <ul><li>In the example shown in figure 2, the plane projection is tangent to the North Pole, and so would be suitable for maps of polar regions. </li></ul><ul><li>The cylindrical projection is tangent to the equator, and would produce a map with low distortion in the equatorial regions. </li></ul><ul><li>The conic projection is tangent to a parallel in the midlatitudes, making is a good choice for the midlatitude regions. </li></ul><ul><ul><li>Some cylindrical and conic projections are based on more than one standard parallel. </li></ul></ul><ul><li>A fourth family of map projection is called pseudocylindrical. These are mathematically based on a cylinder, tangent to the equator, but the cylinder curves back down toward the pokes so that the projection gives a sense of the curvature of the earth </li></ul><ul><ul><li>The Eckert (figure 1b) is based on a pseudocylindrical projection. </li></ul></ul>http://lh4.ggpht.com/FaizRious73/R8jSlC3rAaI/AAAAAAAAAaU/3Je0VCBRfj8/The+three+classes+of+map+projections%5B5%5D
20. 20. Characteristics of Map Projections <ul><li>There is no single map that is good for all purposes. </li></ul><ul><li>Different projections produce maps that are suitable for different uses. </li></ul><ul><ul><li>The conformal Mercator (fig 1a) is based on a cylindrical projection. </li></ul></ul><ul><ul><li>On the Mercator, any straight line is a rhumb line , or a line of constant direction, making these maps useful for navigation. </li></ul></ul>
21. 21. Characteristics of Map Projections <ul><li>The Robinson (fig 3) is a pseudocylindrical projection that is increasingly becoming the standard compromise projection used for wall maps of the world. </li></ul><ul><ul><li>It is neither conformal nor equivalent, but offers a good balance between correct shape and correct area. </li></ul></ul>
22. 22. Characteristics of Map Projections <ul><li>The Lambert Conformal Conic projection (fig 4) uses two standard parallels, and is often used by the US Geological Survey for large scale topographic maps. </li></ul>http://www.geog.ucsb.edu/~kclarke/G176B/stpar.jpg http://www.staff.amu.edu.pl/~zbzw/glob/plcc.jpg
23. 23. Characteristics of Map Projections <ul><li>Orthographic projections (fig 5a) are known as perspective maps. </li></ul><ul><li>They make Earth appear as it would from space. </li></ul><ul><li>On gnomic maps (fig 5b) a straight line represents a path along a great circle (the largest circle that can be drawn on a sphere) and shows the shortest path between two points. </li></ul><ul><ul><li>Both orthographic and gnomic maps are based on plane projections. </li></ul></ul>
24. 24. Characteristics of Map Projections <ul><li>An interesting type of cylindrical projection is the Transverse Mercator (fig 5c). </li></ul><ul><li>Instead of being tangent to the equator, the Transverse Mercator is tangent to a standard meridian (for example the 90°W / 90°E meridian in the example shown in the lab book). </li></ul><ul><li>The Transverse Mercator is conformal, and is used on many US Geological Survey topographic maps. </li></ul>
25. 25. Characteristics of Map Projections <ul><li>Goode’s Interrupted Homolosine projection (fig 6) is widely used to show the distribution of phenomena on the continents. </li></ul><ul><li>The Goode’s Interrupted projection is equivalent, yet the shapes of the land masses are also very well maintained. </li></ul>
26. 26. <ul><li>Map Projection Page: good examples of distortion </li></ul><ul><li>http://maps.unomaha.edu/Peterson/carta/Assign/ProjectionPage/ProjectionPage.htm </li></ul><ul><li>What is a map projection? </li></ul><ul><li>http://www.kartografie.nl/geometrics/Map%20projections/body.htm </li></ul>