Map Projections

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Map Projections
For Summer School
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Map Projections
Meridians
North-South lines (such as Longitude)
Parallels
East-West lines (such as Latitude)
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Map Projections
Definition
A map projection is a portrayal of the earths
surface (or portion of the earths surface) onto
a flat surface. There is no universally perfect
projection system, thus there are a number of
systems.
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Map Projections
Why are they so important?
Think of trying to trace lines from a globe onto
a flat piece of paper. You cant do it without
folding, tearing, or stretching the paper. Map
projections give us a controlled method for doing
this.
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Map Projections
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Map Projections
Stages of Map Projection
Curved Surface (Datum Surface)
Projection surface (Intermediate Surface)
Plane Surface (Map Surface)
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Map Projections
Visualize a light shining through the
transparent Earth onto a surface (Latitudes and
longitudes Projected onto a Paper)

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Map Projections
How projections are classified

• 1. (a) By the distortions of Shape / Area /
  Distance / Direction
• Shape
• Area
• Distance
• Direction

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Map Projections
How projections are classified
(b) By properties

• Conformal
• -maintains angles at which lines intersect
• Equal-area
• -maintains area
• Equidistant
• -maintains distances
• Direction
• -maintains directions

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Map Projections
How projections are classified

• 2. By the shape they are projected onto
• Azimuthal Projection of a sphere onto a plane.
• Conical Projection of a sphere onto a cone
• Cylindrical Projection of a sphere onto a
  cylinder.
• Miscellaneous Unprojected and other
  projections.

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Map Projections
Aspect

• Normal - equatorial / East-West
• Transverse - North-South regions
• Oblique - other angles

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Map Projections
Cases

• Tangent
• projection surface touches sphere
• Secant
• surface cuts through sphere
• No distortion at contact points
• Distortion increases away from contact points

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Map Projections
Tangent Cases
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Map Projections
Secant cases
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Map Projections

• Cones, Cylinders, Planes can be
  flattened without distortion
• A point or line of contact is created when
  surface is combined with a sphere

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Map Projections
Azimuthal Projections

• Straight or curved meridians, curved parallels
• Meridians radiate from poles
• Parallels may be equally spaced

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Map Projections
Azimuthal Projections
Azimuthal Equidistant Used to show
air-route distances. Distances from the centre
are true, distortion radiates out from
the center of the map.
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Map Projections
Conic Projections

• Common Conic Projections
• Albers
• Lambert
• Polyconic

• Straight meridians, curved parallels
• Meridians radiate from poles
• Parallels may be equally spaced

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Map Projections
Conic Projections
Albers Equal Area Conic Direction, area, and
shape distorted away from the standard
parallels. Areas and directions are true only in
limited portions of a map. Used in regions
with longer E-W orientation than N-S orientation.
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Map Projections
Conic Projections
Equidistant Conic Direction, area, and shape
distorted away from the standard
parallels. Areas and directions are true only in
limited portions of a map. Used in regions near
the equator.
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Map Projections
Conic Projections
Polyconic Scale is true along each parallel and
along the central meridian.
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Map Projections
Properties - Scale is exact
along each parallel and central meridian
- Parallels are of circle but are not
concentric - It is neither conformal nor
equal area - Central meridian and
equator are straight lines all other meridians
are complex curves - Free of distortion
only along central meridian - It has
rolling fit with adjacent sheet in E-W direction
- Used in USA up to 1950 only -
Used in India for topographical maps
Polyconic
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Map Projections
Polyconic
Drawbacks - The main
disadvantage is that it has rolling fit only.
When two individual adjacent sheets are kept side
by side with graticule showing N-S direction, we
find there will be a gap. To avoid this gap the
adjacent sheet is rolled and made fit. Thus if
we take sixteen 15 x 15 quadrangle and try to
fit them in one 10 x 10 quadrangle these will not
fit exactly.
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Map Projections
Conic Projections
Lambert Conic Direction, area, and shape
distorted away from the standard
parallels. Areas and directions are true only
in limited portions of a map.
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Map Projections
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Map projections
Conformal Property

• Angles on the surface of the datum are preserved
  on the map.
• Shapes of small areas are preserved.
• Meridians and parallels cut each other at right
  angles.

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Map Projections
Standard Parallels

• The projection can be with one or two standard
  parallels.
• The scale is true along standard parallels.
• Always better to adopt projection with two
  standard parallels
• to limit distortion in scale over large areas.
• To design projection, limiting parallels
  meridians are
• prescribed which cover the entire area to be
  projected.
• Standard parallels are selected at 1/6th of the
  extent in N-S
• direction.
• Central meridian is chosen midway between
  limiting
• meridians.
• - Value of central parallel is calculated
  mathematically.

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Map Projections
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Map Projections
Lambert Conformal Conic (With Two Standard
parallels)
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Map Projections
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Map Projections
Cylindrical Projections

• Common Cylindrical Projections
• Peters
• Mercator
• Universal Trnsverse Mercator

• Straight meridians and parallels
• Meridians equally spaced
• Parallels unequally spaced

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Map Projections
Cylindrical Projections
Peters De-emphasizes exaggerations in the high
latitudes
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Map Projections
Cylindrical Projections
Mercator Emphasizes exaggerations in the
high latitudes
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Map Projections
Cylindrical Projections
Transverse Mercator Projection

• Main features -
• It is a Transverse application of Cylindrical
  projection.
• Conformal i.e. shapes are preserved
• Central meridian, Equator and each meridian 90
  degree from Central meridian are projected as
  straight lines.
• Other meridians and parallels are complex curves.
• Scale is true along central meridian and along
  two straight lines equidistant from and parallel
  to central meridian
• Scale becomes infinite 90 degree from central
  meridian
• Used extensively for quadrangle maps from
  125,000 to 1250,000
• Not used in India, but extensively used in USA,
  Great Britain.

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Map Projections
Cylindrical Projections
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Map Projections
Cylindrical Projections
Universal Transverse Mercator Defines
horizontal positions into 6? zones. Each zone
has a central meridian. Is actually 60
projections!
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Map Projections
Cylindrical Projections
Universal Transverse Mercator Defines
horizontal positions into 6? zones. Each zone
has a central meridian.
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Map Projections
Illustration of Various Projections with same
origin
Difference in distance between Polyconic and
LCC Found to be approximately 4 mm on scale
150,000, i.e 200 m. on ground.
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Map Projections

• Choice of Projections-
• There can be number of projections. It is
  purpose specific. However when one purpose is
  well served, other qualities need to be preserved
  as far as possible. A map can be of equal area
  type but then the conformality is certainly lost.
  When the area covered on map is rather small,
  all properties can be preserved within a small
  allowance, by almost all the projections. But
  when the portion of the globe that comes as a map
  is much, choice of projections becomes important.
  Again the choice of the projections will be
  influenced by location on the globe. If it is
  the whole globe, or only a hemisphere or a
  continent or two the projection can vary.
• Rhumb lines and great circles on globe are
  important for navigation and Mercator or Gnomonic
  projections are good respectively. In azimuthal
  maps, straight lines through center of projection
  are great circles on globe.

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Map Projections
Projections used for different regions on Earth
Polar Regions - Azimuthal
Projections. Tropical Regions - Conical
Projections. (Mid-latitude Regions)
Equatorial Regions - Cylindrical
Projections.
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Map Projections
Some Examples of Projections Maps

• Topographical maps - Polyconic Projection,LCC,
• Stereographic Azimuthal, Transverse Mercator,
  UTM etc..
• Geographical maps - Lambert Conformal Conic
• ( large extent in N-S direction) (LCC)
  Projections
• Cadastral Maps - Cassini projection, LCC
• (small extent in E-W direction)
• Air Sea Navigation maps - i) Mercator
  Projection (Equatorial regions )
• ii) Gnomonic projection ( Polar regions )
• World Maps in one piece - Lamberts
  Azimuthal Equal area, Mercator Projection, Galls
  Stereographic Cylindrical
• Continents and Atlases - Simple Conic,
  Bonnes Equal area, Lambert Azimuthal Equal area,
  LCC

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Map Projections
Comparision of Transverse Mercator projection
with Lambert Conformal Conic projection
Both are excellent conformal map projections,
used worldwide and can be used to map any area on
any scale and for most of the applications.
Transverse Mercator projection is more suitable
for areas predominant in North-South extent,
whereas LCC projection is more suitable for areas
predominant in East-West extent. Closed
formulae are available in respect of LCC making
calculations easy, whereas in Transverse Mercator
projection lengthy series formulae are used which
are difficult to handle.