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 PROCESS
most projections are combinations of the following characteristics:
characteristic of earth features that are maintained
shape of the projection plane (developable shape)
aspect of the projection plane
points or lines of tangency or secancy
location of the false ‘illumination source’

8. 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

9. 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

10. PROJECTION PROPERTIES
Equidistant

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

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
Area
Distance
Direction
Shape
Equal-Area No
Yes
Equidistant
Azimuthal
Conformal

14. 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

15. 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:

16. 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.

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

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

19. PROJECTION CLASSIFICATION

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

21. PROJECTION CLASSIFICATION
Conical Distortion

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

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

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

25. PROJECTION CLASSIFICATION

26. 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

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

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

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

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

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

32. PROJECTION CLASSIFICATION
NORMAL
TRANSVERSE
OBLIQUE

33. CANADA PROJECTED
Cylindrical
Conic
Planar

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

35. 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

36. 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

37. CHOOSING PROJECTION depends on:
purpose for which the data is to be used
property in which distortion is minimized
extent and location of area

38. CHOOSING PROJECTION steps: size of area of interest
small area has little distortion, any projection.
latitude of area of interest
low-latitudes – cylindrical
mid-latitudes – conical
polar latitudes - planar

39. 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

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

41. 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

42. 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

43. 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.

44. 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

45. COMMON PROJECTIONS

46. COMMON PROJECTIONS

47. 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

48. 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

49. 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

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

51. 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

52. 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

53. OTHER PROJECTIONS
Berghaus Star

54. OTHER PROJECTIONS
Sanson-Flamsteed

55. OTHER PROJECTIONS
Conoalactic

56. OTHER PROJECTIONS
Hammer

57. OTHER PROJECTIONS
Eisenlohr

58. OTHER PROJECTIONS
Gall Stereographic Cylindrical

59. OTHER PROJECTIONS
Cassini

60. SCALE

61. SCALE
size of an object on a map compared to the actual object on the ground
may not be the same in all directions from a point

62. SCALE TYPES Verbal scale describes the scale in words
i.e. “one centimeter represents one kilometer”
commonly found on popular atlases and maps

63. SCALE TYPES Visual scale (bar scale or graphic scale)
graphically illustrates relationship between map distance and ground distance.
one end can be divided
most common
remains correct if reduced or enlarged

64. SCALE TYPES
Visual scale (bar scale or graphic scale)

65. SCALE TYPES Representative Fraction (RF)
ratio (proportion) between map distance to earth distance
i.e. 1:50,000
most versatile; not tied to any specific units

66. SCALE FACTOR Representative Fraction Globe distance Earth distance =
Map Scale:
(e.g. 1:24,000)
Map Projection:
Scale Factor

67. SCALE FACTOR stated scale is correct only at selected points
statement of relation between given scale and actual scale value
i.e. SF of would mean that actual scale is twice the principal scale

68. LARGE VS SMALL SCALE
large scale: show a small area with a large amount of detail.
small scale: show a large area with a small amount of detail
all relative

69. DETERMING SCALE
use map scale to convert map distance to ground distance.
for verbal and RF scales - multiply by the scale, then convert the ground distance to units suitable for ground measurements.
i.e. we have a map with a scale of 1:50,000. We measure the distance along a property boundary as 1.7 cm. What is the length in the real world?
for graphic scales – mark off a distance on the map and compare it directly to the bar scale.

70. TRANSFORMING SCALES Verbal to RF
write verbal scale as a fraction then convert so that both numerator and denominator have the same units and numerator has a 1
i.e. convert verbal scale “1 cm represents 100 km” to RF
RF to Verbal
i.e. convert from RF of 1:25,000 to verbal scale, in metric

71. TRANSFORMING SCALES Graphic Scales and RF/Verbal
take the measurement from the bar scale to determine the map distance and corresponding ground distance.
i.e. 10 km on ground measures 2.4 cm on map.
use method for verbal scale to RF conversion.