### Map Projections - Solutions

CBSE Class 11 Geography

NCERT Solutions
Chapter 27
Map Projections

1. Choose the right answer from the four alternatives given below:

(i) A map projection least suitable for the world map:

(a) Mercator
(b) Simple Cylindrical
(c) Conical
(d) All the above

Ans. (c) Conical. A map projection in which an area of the earth is projected on to a cone, of which the vertex is usually above one of the poles.

(ii) A map projection that is neither the equal area nor the correct shape and even the directions are also incorrect

(a) Simple Conical
(b) Polar zenithal
(c) Mercator
(d) Cylindrical

Ans. (a) Simple Conical is often used both in air and ocean navigation.

(iii) A map projection having correct direction and correct shape but area greatly exaggerated polewards is:

(a) Cylindrical Equal Area
(b) Mercator
(c) Conical
(d) All the above

Ans. (b) Mercator. The Mercator projection is a cylindrical map projection presented by the Flemish geographer and cartographer Gerardus Mercator in 1569.

(iv) When the source of light is placed at the centre of the globe, the resultant projection is called:

(a) Orthographic
(b) Stereographic
(c) Gnomonic
(d) All the above

Ans. (c) Gnomonic. A gnomonic map projection displays all great circles as straight lines, resulting in any straight line segment on a gnomonic map showing a geodesic, the shortest route between the segment's two endpoints.

(i) Describe the elements of map projection.

Ans. (a) Reduced Earth: A model of the earth is represented by the help of a reduced scale on a fiat sheet of paper. This model is called the "reduced earth". This model should be more or less spheroid having the length of polar diameter lesser than equatorial and on this model the network of graticule can be transferred.
(b) Parallels of Latitude: These are the imaginary circles running round the globe parallel to the equator and maintaining uniform distance from the poles. An example of a parallel of latitude is the Arctic Circle that runs east - west around the Earth at a latitude of 66° 33' 44".
(c) Meridians of Longitude: These are semi-circles drawn in north-south direction from one pole to the other, and the two opposite meridians make a complete circle, i.e. circumference of the globe. Example of meridians of longitude is the Prime Meridian.
(d) Global Property: In preparing a map projection the following basic properties of the global surface are to be preserved by using one or the other methods:
(i) Distance between any given points of a region; (ii) Shape of the region; (iii) Size or area of the region in accuracy; (iv) Direction of any one point of the region bearing to another point.

(ii) What do you mean by global property?

Ans. The correctness of area, shape, direction and distances are the four major global properties to be preserved in a map. But none of the projections can maintain all these properties simultaneously. Therefore, according to specific need, a projection can be drawn so that the desired quality may be retained. Thus, on the basis of global properties, projections are classified into equal area, orthomorphic, azimuthal and equi-distant projections. Equal Area
Projection is also called homolographic projection. It is that projection in which areas of various parts of the earth are represented correctly. Orthomorphic or True-Shape projection is one in which shapes of various areas are portrayed correctly. The shape is generally maintained at the
cost of the correctness of area. Azimuthal or True-Bearing projection is one on which the direction of all points from the centre is correctly represented. Equi-distant or True Scale projection is that where the distance or scale is correctly maintained. However, there is no such
projection, which maintains the scale correctly throughout. It can be maintained correctly only along some selected parallels and meridians as per the requirement. In preparing a map projection the following basic properties of the global surface are to be preserved by using one or the other methods:
(a) Distance between any given points of a region;
(b) Shape of the region;
(c) Size or area of the region in accuracy;
(d) Direction of any one point of the region bearing to another point.

(iii) Not a single map projection represents the globe truly. Why?

Ans. No map projection is perfect for every task. One must carefully weigh pros and cons and how they affect the intended map's purpose before choosing its projection. Unfortunately, only a globe offers such properties for any points and regions. However, there is no such projection, which maintains the scale correctly throughout. It can be maintained correctly only along some selected parallels and meridians as per the requirement. Projection is a shadow of globe which has to be presented on a map. When shape of globe changes certainly inaccuracy comes in. Therefore, it is rightly said that not a single map projection represents the globe truly.

(iv) How is the area kept equal in cylindrical equal area projection?

Ans. The area is kept equal in cylindrical equal area projection because latitudes and longitudes intersect each other at right angles in the straight line form. The cylindrical equal area projection, also known as the Lambert’s projection, has been derived by projecting the surface of the globe with parallel rays on a cylinder touching it at the equator. Both the parallels and meridians are projected as straight lines intersecting one another at right angles. The pole is shown with a parallel equal to the equator; hence, the shape of the area gets highly distorted at the higher latitude.

3. Differentiate between:

(i) Developable and non-developable surfaces

Ans.

 Basis Developable. Surface Non-developable Surface Meaning A developable surface is one, which can be flattened, and on which, a network of latitude and longitude can be projected. A non-developable surface is one, which cannot be flattened without shrinking, breaking or creasing. Example A cylinder, a cone and a plane have the property of developable surface. A globe or spherical surface has the property of non-developable surface

On the basis of nature of developable surface, the projections are classified as cylindrical, conical and zenithal projections.

(ii) Homolographic and orthographic projections

Ans.

 Basis Homolographic Projection Orthographic Projection Meaning A projection in which the network of latitudes and longitudes is developed in such a way that every graticule on the map is equal in area to the corresponding graticule on the globe. It is also known as the equal-area projection. A projection in which the correct shape of a given area of the earth's surface is preserved.

(iii) Normal and oblique projections

Ans.

 Basis Normal Projection Oblique Projection Meaning If the developable surface touches the globe at the equator, it is called the equatorial or normal projection. If projection is tangential to a point between the pole and the equator, it is called the oblique projection.

(iv) Parallels of latitude and meridians of longitude

Ans.

 Basis Meridians of Longitude Parallels of Latitude Meaning The meridians of longitude refer to the angular distance, in degrees, minutes, and seconds, of a point east or west of the Prime (Greenwich) Meridian. The parallels of latitude refer to the angular distance, in degrees, minutes and seconds of a point north or south of the Equator. Name Lines of longitude are often referred to as meridians. Lines of latitude are often referred to as parallels. Reference point 0° longitude is called prime meridian 0° latitude is called equator. Division It divides the earth into eastern hemisphere and western hemisphere. It divides the earth into northern hemisphere and southern hemisphere. Number These are 360 in number: 180 in the eastern hemisphere and 180 in the western hemisphere. These are 180 in number: 90 in southern hemisphere and 90 in northern hemisphere. Importance It helps to determine time of a place. It helps to determine temperature of a place. Equality These are not equal. These are equal.

4. Answer the following questions in not more than 125 words:
(i) Discuss the criteria used for classifying map projection and state the major characteristics of each type of projection.

Ans. Types of Map Projection:
(a) On the basis of drawing techniques, map Projections may be classified perspective, non-perspective and conventional or mathematical. Perspective projections can be drawn taking the help of a source of light by projecting the image of a network of parallels and meridians of a globe on developable surface. Non¬perspective projections are developed without the help of a source of light or casting shadow on surfaces, which can be flattened. Mathematical or conventional projections are those, which are derived by mathematical computation and formulae and have little relations with the projected image.
(b) On the basis of developable surface, it can be developable surface and non developable surface. A developable surface is one, which can be flattened, and on which, a network of latitude and longitude can be projected. A globe or spherical surface has the property of non-developable surface whereas a cylinder, a cone and a plane have the property of developable surface. On the basis of nature of developable surface, the projections are classified as cylindrical, conical and zenithal projections.
(c) The correctness of area, shape, direction and distances are the four major global properties to be preserved in a map. But none of the projections can maintain all these properties simultaneously. Therefore, according to specific need, a projection can be drawn so that the desired quality may be retained. Thus, on the basis of global properties, projections are classified into equal area, orthomorphic, azimuthal and equi-distant projections. Equal Area
Projection is also called homolographic projection. It is that projection in which areas of various parts of the earth are represented correctly. Orthomorphic or True-Shape projection is one in which shapes of various areas are portrayed correctly. The shape is generally maintained at the
cost of the correctness of area. Azimuthal or True-Bearing projection is one on which the direction of all points from the centre is correctly represented. Equi-distant or True Scale projection is that where the distance or scale is correctly maintained. However, there is no such
projection, which maintains the scale correctly throughout. It can be maintained correctly only along some selected parallels and meridians as per the requirement.
(d) On the basis of location of source of light, projections may be classified as gnomonic, stereographic and orthographic. Gnomonic projection is obtained by putting the light at the
centre of the globe. Stereographic projection is drawn when the source of light is placed at the periphery of the globe at a point diametrically opposite to the point at which the plane surface touches the globe. Orthographic projection is drawn when the source of light is placed at infinity from the globe, opposite to the point at which the plane surface touches the globe.
The correctness of area, shape, direction and distances are the four major global properties to be preserved in a map. But none of the projections can maintain all these properties simultaneously. Therefore, according to specific need, a projection can be drawn so that the desired quality may be retained.

(ii) Which map projection is very useful for navigational purposes? Explain the properties and limitations of this projection.

Ans. Mercator's Projection is very useful for navigational purposes. A Dutch cartographer Mercator Gerardus Karmer developed this projection in 1569. The projection is based on mathematical formulae.
Properties:
(a) It is an orthomorphic projection in which the correct shape is maintained.
(b) The distance between parallels increases towards the pole.
(c) Like cylindrical projection, the parallels and meridians intersect each other at right angle. It has the characteristics of showing correct directions.
(d) A straight line joining any two points on this projection gives a constant bearing, which is called a Laxodrome or Rhumb line.
(e) All parallels and meridians are straight lines and they intersect each other at right angles.
(f) All parallels have the same length which is equal to the length of equator.
(g) All meridians have the same length and equal spacing. But they are longer than the corresponding meridian on the globe.
(h) Spacing between parallels increases towards the pole.
(i) Scale along the equator is correct as it is equal to the length of the equator on the globe; but other parallels are longer than the corresponding parallel on the globe; hence the scale is not correct along them.
(j) Shape of the area is maintained, but at the higher latitudes distortion takes place.
(k) The shape of small countries near the equator is truly preserved while it increases towards poles.
(l) It is an azimuthal projection.
(m) This is an orthomorphic projection as scale along the meridian is equal to the scale along the parallel.

Limitations
(a) There is greater exaggeration of scale along the parallels and meridians in high latitudes. As a result, size of the countries near the pole is highly exaggerated.
(b) Poles in this projection cannot be shown as 90° parallel and meridian touching them are infinite.

(iii) Discuss the main properties of conical projection with one standard parallel and describe its major limitations.

Ans. A conical projection is one, which is drawn by projecting the image of the graticule of a globe on a developed cone, which touches the globe along a parallel of latitude called the standard parallel. As the cone touches the globe located along AB, the position of this parallel on the globe coinciding with that on the cone is taken as the standard parallel.
Properties
(a) All the parallels are arcs of concentric circle and are equally spaced.
(b) All meridians are straight lines merging at the pole. The meridians intersect the parallels at right angles.
(c) The scale along all meridians is true.
(d) An arc of a circle represents the pole.
(e) The scale is true along the standard
parallel but exaggerated away from the standard parallel.
(f) Meridians become closer to each other towards the pole.
(g) This projection is neither equal area nor orthomorphic.

Limitations
(a) It is not suitable for a world map due to extreme distortions in the hemisphere opposite the one in which the standard parallel is selected.
(b) Even within the hemisphere, it is not suitable for representing larger areas as the distortion along the pole and near the equator is larger.
Uses
(a) This projection is commonly used for showing areas of mid-latitudes with limited latitudinal and larger longitudinal extent.
(b) A long narrow strip of land running parallel to the standard parallel and having east-west stretch is correctly shown on this projection.
(c) Direction along standard parallel is used to show railways, roads, narrow river valleys and international boundaries.
(d) This projection is suitable for showing the Canadian Pacific Railways, Trans-Siberian Railways, international boundaries between USA and Canada and the Narmada Valley.