Map Projections
April 13, 2015
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 earth’s surface
(or portion of the earth’s 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 can’t 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
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(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
• Straight meridians, curved parallels
• Meridians radiate from poles
• Parallels may be equally spaced
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Common Conic Projections
• Albers
• Lambert
• Polyconic
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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
Polyconic
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
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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
Lambert Conformal Conic Projection:
This projection is used in geographic maps of India and also in the
gridded topographical maps. Its main features are :
(i) It is conical and conformal i.e. shapes are preserved.
(ii) Meridians and parallel cut at right angles everywhere i.e. at any point
the scale is same in all directions, so that there is no local distortion.
(iii) The projection can be with one or two standard parallels. The scale is
true along the standard parallels. It is always better to adopt the
projection with two standard parallels to limit distortions in scale over
large area.
(iv) The standard parallels are selected at 1/6th of the extent in NS
directions i.e. Latitudinal extent.
(v) Parallels are projected as unequally spaced arcs of concentric circles,
more closely spaced near the center of the map.
(vi) Meridians are equally spaced radii of the same circles, thereby cutting
parallels at right angles.
(vii) This projection is mainly used for the countries and regions with predominant east-west extent.
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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
Origin of Co-ordinate system is taken as point of
intersection of central parallel and central meridian.
To avoid negative values of co-ordinates assumed
values are given to the origin.
The assumed co-ordinates are
Easting or x = 500,000 metres
Nothing or y = 500,000 metres
This results in an assumed origin which has coordinates x = 0 and y = 0 with respect to the system
of rectangular co-ordinates. This is also known as
False Origin.
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Map Projections
Lambert Conformal Conic
(With Two Standard parallels)
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Map Projections
76º 00
20º
80º 30
85º 00
20º
Limiting Parallel
00
00
k>1
18º
k=1
18º
Standard Parallel 2
45
16º
15 19
45
k<1
ko=0.9990540231
O x = 5,00,000 m
y = 5,00,000 m
13º
45
k=1
16º Central Parallel
15 19
13º Standard Parallel 1
45
k>1
12º
30
76º 00
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80º 30
12º
30
85º 00
Limiting Parallel
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Map Projections
Cylindrical Projections
• Straight meridians and parallels
• Meridians equally spaced
• Parallels unequally spaced
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Common Cylindrical Projections
• Peters
• Mercator
• Universal Trnsverse Mercator
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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 1:25,000 to 1:250,000
Not used in India, but extensively used in USA, Great Britain.
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Map Projections
Cylindrical Projections
Universal Transverse Mercator Grid (UTM):
UTM
is a particular case of Transverse
Mercator Projection. It is a world wide projection system
brought out by US army in 1947 for designating rectangular
coordinates on large scale military maps of the entire world. Its
specifications are given below :(i)
The world is divided into 60 E-W equal parts from
180º W through 0º to 180º E and called 1 to 60.
(ii)
The N-S subdivision is from 80º S to 84º N being all 8º
spread except the last one, which is 72º N to 84º N.
The
identification starts with ‘C’ from 80º S to 72º S, ‘D’ for
72º S to 64º S ……... and so on till 64º N to 72º N, and ‘X’
for 72º N to 84º N - remembering that alphabets ‘I’ and
‘O’are not used.
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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
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Difference in distance between Polyconic and LCC
Found to be approximately 4 mm on scale 1:50,000, 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 -
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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 Lambert’s Azimuthal Equal area,
Mercator Projection, Gall’s Stereographic Cylindrical
* Continents and Atlases Simple Conic, Bonne’s 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.
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