Why map projections are needed

Detail

What a map projection is

• Map projection: the method of moving the graticule from the globe onto a flat surface (a plane surface: flat paper or a flat screen).
• Graticule: the net of parallels (east–west circles of latitude) and meridians (north–south half-circles of longitude) drawn on the globe.

• Class 11 (Map Projections) also defines it as the study of the different methods tried for this transfer.

• Class 11 (Introduction to Maps) lists projection as one of the essentials of map making, along with scale and symbols.

• Every flat map, from a school atlas to a Survey of India topographical sheet, is drawn on some projection.

The globe is true but impractical

• 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

• No flat map can match a globe in showing the whole Earth's surface truly. Every flat map shows the surface wrongly in some way [2].

• 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)

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

• Result: detailed study needs large-scale maps on flat paper. A large-scale map covers a small area in great detail, like a 1:50,000 topographical sheet.

Feature	Globe	Flat map
Shape, size, direction, distance	All four true	Never all four true at once [2]
Carrying and cost	Bulky, costly	Easy to fold, cheap to print
Small details	Cannot show	Can show (large-scale maps)
Comparing regions	Hard	Easy, side by side

The core problem: the sphere is non-developable

• Developable surface: a surface that can be cut and opened out flat without stretching or tearing. Examples are a cylinder, a cone and a plane.
• Non-developable surface: a surface that cannot be flattened without stretching or tearing. A sphere (the globe) is one.
• How the transfer is tried, step by step:
• 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)
• light is thrown from the centre of the globe, and the graticule's shadow 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 (Class 11, Fig. 4.1)

• The paper is then unrolled. This gives the main projection families: cylindrical, conical and zenithal (also called azimuthal: on a flat sheet touching one point).

Surface	Developable?	Projection family it gives
Cylinder	Yes	Cylindrical (e.g. Mercator)
Cone	Yes	Conical
Plane	Already flat	Zenithal / azimuthal
Sphere (globe)	No	Must be projected onto one of the above

The orange-peel test (Class 6, Mapping the Earth)

• Peel an orange in one piece and try to press the peel flat.
• The peel tears or wrinkles before it lies flat.
• In the same way, the Earth's curved surface cannot become a flat map without being broken, stretched or squeezed.

What happens to the graticule

• On the globe:
• meridians are semicircles running from the North Pole to the South Pole

• parallels are full circles that get smaller towards the poles

• On paper: meridians and parallels become straight or curved lines that cross each other. Each projection draws them in its own pattern.

Distortion cannot be avoided, so many projections exist

• Distortion: a wrong showing of shape, area, distance or direction on a flat map.
• A flat map can show one or more of the four properties truly, but never all four at once [2].
• So the map-maker must choose which property to keep true for the map's purpose and give up the others, or accept a balance between several of them [3].
• The two main choices:
• Conformal projections: show the true shape of small areas but get size wrong
• Equal-area projections: show 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 this trade-off well:

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

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

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

Indian example: projections used by the Survey of India

• Before the National Map Policy 2005, Survey of India topographical sheets used the Polyconic projection and the Everest datum [5].

• Datum: the reference model of the Earth's shape used to fix positions.

• After 2005, Open Series Maps (OSM) for the public use the UTM (Universal Transverse Mercator) projection and the WGS-84 datum, at scales of 1:250,000, 1:50,000 and 1:25,000 [5].

• Most Survey of India geographical (small-scale) maps are drawn on the Lambert Conformal Conic (LCC) projection [6].
• Lesson: a country chooses different projections for different map types and scales, because no single projection is right for every use.

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 surface; cylinder, cone and plane = developable surfaces.
• Paper touches the globe only 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.
• Conformal = true shape (of small areas); equal-area = true relative size. No projection is both [2].
• Mercator (1569): cylindrical and conformal; rhumb lines are straight; used for navigation; areas are exaggerated at high latitudes [4].
• Trap: Mercator keeps direction and shape true, not area. It is wrong to call it equal-area.
• Survey of India: Polyconic + Everest datum (before NMP 2005) → UTM + WGS-84 for Open Series Maps [5].
• Survey of India geographical maps: mostly on Lambert Conformal Conic [6].

Mains Points

• Why projections are needed (GS-I):
• the globe is true but costly, bulky and cannot show small detail
• planning, defence, navigation and resource surveys need large-scale flat maps

• so the graticule must be projected onto paper

• Why distortion is unavoidable:

• the sphere is non-developable, so it cannot be flattened without stretching or tearing (the orange-peel test)

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

• Choice of projection has real effects:

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

• equal-area projections are better for showing how population, forests or crops are spread

• Indian practice:

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