1. MAP PROJECTIONS AND SCALE
OUTLINE:
scale definition
types of scale
projection definition
projection properties and classification
choosing a map projection

2. PROJECTIONS

3. THE GLOBE Advantages: most accurate map latitude and longitude lines
Disadvantages
expensive to make
cumbersome to handle and store
difficult to measure
not fully visible at one

4. PROJECTIONS Flat Map Curved Earth
process of transforming earth’s spherical surface to a flat map while maintaining spatial relationships.
Curved Earth
Flat Map

5. PROJECTIONS
projection process involves stretching and distortion

6. PROJECTIONS
no matter how the earth is divided up, it can not be unrolled or unfolded to lie flat (undevelopable shape).

7. PROJECTION PROPERTIES
properties in which distortion is minimized when producing a map
Area
equal area or equivalent
area sizes are correct everywhere on map
shapes greatly distorted

8. PROJECTION PROPERTIES
Distance
equidistant
distance is correct in all directions from a point
i.e. equidistant projection centered on Winnipeg would show the correct distance to any other location on the map, from Winnipeg only
distorting area and/or direction

9. PROJECTION PROPERTIES
Equidistant

10. PROJECTION PROPERTIES
Direction
azimuthal
compass bearing is maintained in all directions only from a point – focal point
shapes, distances and areas are badly distorted

11. PROJECTION PROPERTIES
all distances measured from the center of the map along any longitudinal line are accurate;
an example of a polar azimuthal equidistant projection can be seen on the United Nations flag

12. PROJECTION PROPERTIES
Shape
conformal
shape maintains its shape across the map
distorting area
latitude and longitude cross at right angles
used for navigation

13. PROJECTION PROPERTIES
Tissot’s Indicatrix
convenient way of showing distortion
size and shape of the indicatrix will vary from one part of the map to another
Mercator projection
Equal-Area projection

14. PROJECTIONS
made by projecting a globe onto a surface – developable surface
distortion is least where developable surface touches the earth
accomplished by use of geometry and mathematics
Mercator:

15. PROJECTION CLASSIFICATION
Tangent case – shape just touches the earth along a single line or at point.
Secant case – shape intersects or cuts through earth as two circles.

16. PROJECTION CLASSIFICATION
Conical
globe sits under a cone, touching along pre-selected line of latitude
projection developed by cutting cone lengthwise and unrolling

17. PROJECTION CLASSIFICATION
normal case:
parallels – concentric circular arcs, meridians – straight equally spaced lines

18. PROJECTION CLASSIFICATION
Lambert conformal conic projection
Albers equal-area conic projection

19. PROJECTION CLASSIFICATION
Conical Distortion

20. PROJECTION CLASSIFICATION
Conical
Polyconic – envelopes globe with an infinite number of cones, each with its own standard parallel

21. PROJECTION CLASSIFICATION
Cylindrical
projected onto a cylinder which is also cut lengthwise and unrolled

22. PROJECTION CLASSIFICATION
Cylindrical
evenly spaced network of straight, horizontal parallels and straight vertical meridians (grid like)

23. PROJECTION CLASSIFICATION

24. PROJECTION CLASSIFICATION
Cylindrical Distortion
projection of the entire world, significant distortion occurs at the higher latitudes
parallels become further apart and poles can not be seen

25. PROJECTION CLASSIFICATION
Cylindrical Distortion
sizes of Greenland vs. Africa
Mercator Projection
True size

26. PROJECTION CLASSIFICATION
Cylindrical
straight line between any two points follows a single direction called a rhumb line
useful in construction of navigational charts

27. PROJECTION CLASSIFICATION
Planar/Azimuthal
portion of earth’s surface is transformed from a perspective point to a flat surface

28. PROJECTION CLASSIFICATION
Planar/Azimuthal
perspective point/light source
Light rays

29. PROJECTION CLASSIFICATION
Planar/Azimuthal
true direction only between center and other locations
most often used to map polar regions

30. PROJECTION CLASSIFICATION
NORMAL
TRANSVERSE
OBLIQUE

31. CANADA PROJECTED
Cylindrical
Conic
Planar

32. PROJECTION CLASSIFICATION
Pseudo map projections
Pseudocylindrical
pseudoconic and pseudocylindrical projections - have curved meridians instead of straight ones

33. PROJECTION CLASSIFICATION
Pseudo map projections
modified projections - changes have been made to reduce the pattern of distortion or add more standard parallels
modified to reduce the distortion in the size of areas

34. PROJECTION CLASSIFICATION
Pseudo map projections
individual or unique projections – can not be easily related to one of the three developable geometric forms
Goode’s Projection

35. CHOOSING PROJECTION shape of area of interest:
E-W extent: conic or cylindrical
N-S extent: cylindrical
square or circular: planar
purpose:
navigation – planar or cylindrical
world distributions – cylindrical
specific locations - planar

36. COMMON PROJECTIONS Albers Equal-Area Conic
equal area, secant conical projection (two standard parallels)
resembles earth graticule

37. COMMON PROJECTIONS Mercator cylindrical, conformal projection
angular relationships are preserved
parallels and meridians appear as straight lines
parallels are farther apart with increased distance from equator

38. COMMON PROJECTIONS Mercator
change in N-S scale exactly offset change in E-W direction (shapes preserved)
scale is true at equator or at two standard parallels equidistant from equator
all rhumb lines appear as straight lines, while great circle arcs are not (except equator and meridians)
used primarily for navigation and large scale maps

39. COMMON PROJECTIONS Transverse Mercator
cylindrical, conformal projection
similar to Mercator except the axis of projection cylinder is rotated 90o from polar axis
scale is true along central meridian or along two straight lines equidistant from and parallel to central meridian
used to portray areas with larger N-S than E-W extent.

40. COMMON PROJECTIONS Lambert Conformal Conic
conformal, secant conical projection with two standard parallels
possesses true shape of small areas with area distortion
concentric parallels (increasing intervals) and equally-spaced straight meridians

41. COMMON PROJECTIONS

42. COMMON PROJECTIONS

43. COMMON PROJECTIONS Mollweide pseudocylindrical, equal-area projection
N-S scale is decreased in high latitudes, increased in low latitudes; opposite in E-W direction
parallels are straight, spaced closer together from equator

44. COMMON PROJECTIONS Polar Stereographic
directions are true from center point
conformal projection: over a small area, angles in the map are the same as the corresponding angles on Earth's surface
meridians are straight and radiating; parallels are concentric circles
shows only one hemisphere

45. COMMON PROJECTIONS Polar Stereographic
preserves circles - all great and small circles are shown as concentric arcs or straight lines
scale true only where the central parallel and meridian cross
used in polar aspect for topographic maps of polar regions, regions that are circular in shape

46. COMMON PROJECTIONS Eckert IV Equal Area
pseudocylindrical and equal-area
scale is true along the parallel at 40:30 North and South

47. COMMON PROJECTIONS Robinson
developed to minimize appearance of angular and area distortion
distorts shape, area, scale and distance in an attempt to balance errors of projection properties

48. COMMON PROJECTIONS Robinson
based on tables of coordinates not mathematical formulae
overall effect – more than 75% of earth is shown with less than 20% departure from true scale size
used for thematic and reference maps

49. OTHER PROJECTIONS
Berghaus Star

50. OTHER PROJECTIONS
Sanson-Flamsteed

51. OTHER PROJECTIONS
Conoalactic

52. OTHER PROJECTIONS
Hammer

53. OTHER PROJECTIONS
Eisenlohr

54. OTHER PROJECTIONS
Gall Stereographic Cylindrical

55. OTHER PROJECTIONS
Cassini