Map projection

Also called: Projection · Topic: Map Projections · NCERT: Class 11, Ch 1 "Introduction to Maps"; Class 11, Ch 4 "Map Projections"

Meaning

A map projection is a method of moving the graticule (the net of parallels and meridians drawn on the globe) from the round globe onto a flat surface, such as paper or a screen. The sphere cannot be flattened without stretching or tearing, so every flat map shows the Earth wrongly in some way. A flat map can keep one or more of the four properties (shape, area, distance and direction) true, but never all four at once [2]. This makes the choice of projection a choice about which property to keep true for the map's purpose.

Explanation

Why we need it: the globe is true but not practical

• What the globe gets right: it is a small model of the Earth, so it shows all four properties correctly:
• shape of land masses
• size (area)
• direction between places

• distance between places

• Why the globe is not enough:

• it is costly to make and hard to carry
• it cannot show small details such as roads, villages or contours (lines joining points of equal height)

• you can see only one side of it at a time, so comparing two far-apart regions is hard

• Result: detailed study needs large-scale maps (maps that cover a small area in great detail, like a 1:50,000 topographical sheet) on flat paper.

• In Class 11 (Introduction to Maps), projection is one of the essentials of map making, along with scale and symbols.
• Every flat map is drawn on some projection, from a school atlas to a Survey of India topographical sheet.

How it works: from a round globe to a flat sheet

• The core problem:
• a sphere is a non-developable surface (it cannot be opened out flat without stretching or tearing)

• a cylinder, a cone and a plane are developable surfaces (they can be cut and laid flat with no stretching)

• Orange-peel test (Class 6): peel an orange in one piece and press the peel flat. It tears or wrinkles. In the same way, the Earth's surface cannot become flat without being broken, stretched or squeezed.

• How the transfer is done, step by step (Class 11, Fig. 4.1):
• a sheet of paper is placed on the globe
• the paper touches the globe only along one line (a cylinder or cone wrapped round it) or at one point (a flat sheet resting on it)
• a light is shone from the centre of the globe, and the shadow of the graticule falls on the paper
• near the tangent point or line (where paper and globe touch), the image is fairly true

• the farther from that point or line, the more distorted the image

• What happens to the graticule:

• on the globe, meridians are semicircles running from the North Pole to the South Pole
• on the globe, parallels are full circles that get smaller towards the poles
• on paper they become straight or curved lines that cross each other, in a pattern that differs for each projection

Types: the three main projection families

• Once the paper is unrolled, you get three main families:

Surface used	Developable?	Projection family
Cylinder	Yes	Cylindrical (e.g. Mercator)
Cone	Yes	Conical
Plane	Already flat	Zenithal (also called azimuthal; a flat sheet touches one point)
Sphere (globe)	No	Must be projected onto one of the above

The trade-off: which property to keep true

• Distortion means showing shape, area, distance or direction wrongly on a flat map.
• A flat map can keep one or more properties true, but never all four at once [2].
• So the map-maker chooses the property to keep true for the map's purpose and gives up the others, or accepts a balance between several of them [3].
• The two main choices:
• Conformal projections keep the true shape of small areas but get size wrong
• Equal-area projections keep the true relative size of all areas but get shape and direction wrong

• no projection is both conformal and equal-area, and some are neither [2]

• Mercator projection (1569) shows the trade-off clearly:

• it is cylindrical and conformal [4]
• every straight line on it is a rhumb line (a line of constant true bearing that cuts every meridian at the same angle), so it suits sea navigation [4][2]
• area is shown more and more wrongly away from the equator, so high-latitude lands look far too big, and areas and distances near the poles are badly wrong [4][2]

• so it is a poor choice for comparing the sizes of countries on a world map [4]

• Each purpose needs a different property kept true, so many projections have been designed [2].

Where it occurs

• India: Survey of India (SoI) topographical sheets:
• before the National Map Policy 2005, they used the Polyconic projection and the Everest datum [5]

• a datum is the reference model of the Earth's shape used to fix positions on it

• India: Open Series Maps (OSM), after 2005:

• these are public maps made by the Survey of India
• they use the UTM (Universal Transverse Mercator) projection and the WGS-84 datum [5]

• they come at scales of 1:250,000, 1:50,000 and 1:25,000 [5]

• India: SoI geographical (small-scale) maps: most are drawn on the Lambert Conformal Conic (LCC) projection [6]. India spreads widely from east to west in the mid-latitudes, and a conical projection suits that shape [6].

• World: sea navigation: the Mercator projection is used because a ship can follow a straight line on it as a constant compass bearing [4][2].
• World: distribution maps: equal-area projections are used to show how population, forests or crops are spread, because sizes stay comparable.
• Lesson: one country uses different projections for different map types and scales, because no single projection fits every use.

Don't confuse with

• Globe vs map projection: the globe is a model of the Earth, not a projection. It is the only thing that shows shape, area, direction and distance all correctly [2]. Every projection gets at least one of them wrong.
• Conformal vs equal-area projection: conformal keeps shape (of small areas) true, and equal-area keeps relative size true. No projection does both [2]. Mercator is conformal, not equal-area.
• Developable vs non-developable surface: the cylinder, cone and plane are developable and are used to make projections. The sphere is non-developable, which is the reason projections are needed at all.
• Projection vs datum: a projection is the method of flattening the graticule onto paper. A datum is the reference model of the Earth's shape used to fix positions. The Survey of India changed both: Polyconic + Everest → UTM + WGS-84 [5].

Prelims Hooks

• The globe is the only model that shows shape, area, direction and distance all correctly. A flat map can never show all four at once [2].
• Sphere = non-developable; cylinder, cone, plane = developable. They give the cylindrical, conical and zenithal (azimuthal) families.
• Paper touches the globe along a line (cylinder or cone) or at a point (plane). Distortion increases with distance from that tangent point or line.
• On the globe, meridians are semicircles and parallels are full circles that get smaller towards the poles.
• Trap: the Mercator (1569) projection is cylindrical and conformal. Rhumb lines are straight on it, so it is used for navigation, but high-latitude areas are exaggerated. It is not equal-area [4].
• Survey of India: Polyconic + Everest datum before NMP 2005 → UTM + WGS-84 for Open Series Maps [5]. Geographical maps mostly use Lambert Conformal Conic [6].

Mains Points

• Why projections are needed and why distortion cannot be avoided (GS-I):
• the globe is true but costly and bulky, and it cannot show small detail
• planning, defence, navigation and resource surveys need large-scale flat maps
• the sphere is non-developable, so flattening it always stretches or tears it (the orange-peel test)

• map-makers therefore keep one property true for the purpose: shape for navigation (Mercator), area for distribution maps (equal-area) [2][3]

• The choice of projection has real effects:

• Mercator world maps make high-latitude lands look too big, which distorts how people picture the relative size of countries [4]

• equal-area projections give a fairer picture when showing how population, forests or crops are spread

• Indian practice and policy:

• the shift from Polyconic/Everest to UTM/WGS-84 under the National Map Policy 2005 brings Indian maps in line with global GPS and GIS standards [5]
• LCC is kept for geographical maps because India's wide east–west spread in the mid-latitudes suits a conical projection [6]

Read more

• Why map projections are needed