Chapter 4 Map Projections | Class 11th Practical Work in Geography revision notes

NCERT Class 11 Practical Geography Chapter 4 Map Projections

• Map projection – transform spherical surface into flat location
• Globe show directions and distances accurately
• Horizontal – parallels and vertical lines are longitudes
• Problems with globe – expensive, cannot be carried easily, meridians are semicircle and parallels are circles – on paper they become straight or curved line
• Need for map projection
• Detailed regions
• Compare 2 natural regions
• Transfer latitude and longitude on flat paper
• Distortions increase with distance from tangential point (throwing light from center)
• Tracing shape, size and directions, etc. from a globe is nearly impossible because the globe is not a developable surface
• Lexodrome or Rhumb Line: It is a straight line drawn on Mercator՚s projection joining any two points having a constant bearing. It is very useful in determining the directions during navigation.
• The Great Circle: It represents the shortest route between two points, which is often used both in air and ocean navigation.
• Homolographic Projection: 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.
• Orthomorphic Projection: A projection in which the correct shape of a given area of the earth՚s surface is preserved

Elements of Map Projection

• Reduced Earth: A model of the earth is represented by the help of a reduced scale on a flat 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.
• Parallels of Latitude: These are the circles running round the globe parallel to the equator and maintaining uniform distance from the poles. Each parallel lies wholly in its plane, which is at right angle to the axis of the earth. They are not of equal length. They range from a point at each pole to the circumference of the globe at the equator. They are demarcated as  to  North and South latitudes.
• 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. Each meridian lies wholly in its plane, but all intersect at right angle along the axis of the globe. There is no obvious central meridian but for convenience, an arbitrary choice is made, namely the meridian of Greenwich, which is demarcated as  longitudes. It is used as reference longitudes to draw all other longitudes
• 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:
  • Distance between any given points of a region;
  • Shape of the region;
  • Size or area of the region in accuracy;
  • Direction of any one point of the region bearing to another point.

Classification of Map Projection

• Drawing Surface- Perspective, non-perspective & Mathematical
• Developable (cylindrical, conical and zenithal) & Non-Developable
• Source of light – gnomonic, stereographic and orthographic
• Global properties – area, shape, direction, distance

Classification of Map Projection: Area, Shape & Distance

• Drawing Surface: 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 (Mollweide, sinusoidal/Samson flam steed or homolosine)
• Developable surface: A developable surface is one, which can be flattened, and on which, a network of latitude and longitude can be projected- cylindrical, conical and zenithal projections.
• Zenithal projection is directly obtained on a plane surface when plane touches the globe at a point and the graticule is projected on it. Generally, the plane is so placed on the globe that it touches the globe at one of the poles. These projections are further subdivided into normal, oblique or polar
• If it is tangential to a point between the pole and the equator, it is called the oblique projection; and if it is tangential to the pole, it is called the polar projection
• If the developable surface touches the globe at the equator, it is equatorial or normal projection.
• Non-Developable surface – non-developable surface is one, which cannot be flattened without shrinking, breaking, or creasing. A globe or spherical surface

Source of Light

• 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
• Global Properties: As mentioned above, the correctness of area, shape, direction, and distances are the four major global properties to be preserved in a map based on global properties; projections are classified into equal area, orthomorphic, azimuthal and equidistant projections.
• (Area) Equal Area Projection is also called homolographic projection. Areas of various parts of the earth are represented correctly in that projection.
• (Shape) 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.
• (Direction) Azimuthal or True-Bearing projection is one on which the direction of all points from the centre is correctly represented.
• (Distance) Equi-distant or True Scale projection is that where the distance or scale is correctly maintained. It cannot be maintained throughout but at certain specific locations.

Examples of Cylindrical Projections

• Equal-area cylindrical projection
• Equidistant cylindrical projection
• Mercator projection
• Miller projection
• Plate Carree projection
• Universal transverse Mercator projection

Examples of Conical Projections

• Albers Equal-area projection
• Equidistant projection
• Lambert conformal projection
• Polyconic projection

Examples of Azimuthal Projections

• Equidistant azimuthal projection
• Gnomonic projection
• Lambert equal-area azimuthal projection

Draw a Mercator՚s projection for the world map on the scale of 1: 250,000, 000 at  interval

Construction of Projections

Mercator՚s Projection

A Dutch cartographer Mercator Gerardus Karmer developed this projection in 1569. The projection is based on mathematical formulae. So, it is an orthomorphic projection in which the correct shape is maintained. The distance between parallels increases towards the pole. Like cylindrical projection, the parallels and meridians intersect each other at right angle. It has the characteristics of showing correct directions. A straight line joining any two points on this projection gives a constant bearing, which is called a Laxodrome or Rhumb line.

• Draw a line of 6.28 inches representing the equator as EQ:
• Divide it into 24 equal parts. Determine the length of each division using the following formula: 
• Calculate the distance for latitude with the help of the table given below:-

Latitude Distance

 inch

 inch

 inch

 inches

 inches

Properties

• All parallels and meridians are straight lines and they intersect each other at right angles.
• All parallels have the same length, which is equal to the length of equator.
• All meridians have the same length and equal spacing. However, they are longer than the corresponding meridian on the globe.
• Spacing between parallels increases towards the pole.
• 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 corresponding parallel on the globe; hence, the scale is not correct along them. For example, the  parallel is 1.154 times longer than the corresponding parallel on the globe.
• Shape of the area is maintained, but at the higher latitudes, distortion takes place.
• The shape of small countries near the equator is truly preserved while it increases towards poles.
• It is an azimuthal projection.
• This is an orthomorphic projection as scale along the meridian is equal to the scale along the parallel.

Limitations

• 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. For example, the size of Greenland equals to the size of USA, whereas it is  ^thof USA.
• Poles in this projection cannot be shown as  parallel and meridian touching them are infinite.

Uses

• More suitable for a world map and widely used in preparing atlas maps.
• Very useful for navigation purposes showing sea routes and air routes.
• Drainage pattern, ocean currents, temperature, winds and their directions, distribution of worldwide rainfall and other weather elements are appropriately shown on this map

Construct a cylindrical equal area projection for the world when the R. F. of the map is 1: 300,000, 000 taking latitudinal and longitudinal interval as .

Cylindrical Equal Area Projection

The cylindrical equal area projection, also known as the Lamber՚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 is highly distorted at the higher latitude.

Construction

• Draw a circle of 2.1 cm radius;
• Mark the angles of  and  for both, northern and southern hemispheres;
• Draw a line of 13.2 cm and divide it into 24 equal parts at a distance of  apart. This line represents the equator;
• Draw a line perpendicular to the equator at the point where  is meeting the circumference of the circle;
• Extend all the parallels equal to the length of the equator from the perpendicular line

Properties

• All parallels and meridians are straight lines intersecting each other at right angle.
• Polar parallel is also equal to the equator.
• Scale is true only along the equator.

Limitations

• Distortion increases as we move towards the pole.
• The projection is non-orthomorphic.
• Equality of area is maintained at the cost of distortion in shape.

Uses

• The projection is most suitable for the area lying between N and S latitudes.
• It is suitable to show the distribution of tropical crops like rice, tea, coffee, rubber and sugarcane

Construct a conical projection with one standard parallel for an area bounded by  N to  N latitude and  E to  E longitudes when the scale is 1: 250,000, 000 and latitudinal and longitudinal interval is 

Conical Projection with One Standard Parallel

A conical projection is one, which is drawn by projecting the image of the graticule of a globe on a developable 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. The length of other parallels on either side of this parallel are distorted

Construction

• Draw a circle or a quadrant of 2.56 cm radius marked with angles COE as  interval and BOE and AOD as standard parallel.
• A tangent is extended from B to P and similarly from A to P, so that AP and BP are the two sides of the cone touching the globe and forming Standard Parallel at  N.
• The arc distance CE represents the interval between parallels. A semi-circle is drawn by taking this arc distance.
• X-Y is the perpendicular drawn from OP to OB.
• A separate line N-S is taken on which BP distance is drawn representing standard parallel. The line NS becomes the central meridian.
• Other parallels are drawn by taking arc distance CE on the central meridian.
• The distance XY is marked on the standard parallel at  for drawing other meridians.
• Straight lines are drawn by joining them with the pole

Properties

• All the parallels are arcs of concentric circle and are equally spaced.
• All meridians are straight lines merging at the pole. The meridians intersect the parallels at right angles.
• The scale along all meridians is true, i.e.. distances along the meridians are accurate.
• An arc of a circle represents the pole.
• The scale is true along the standard parallel but exaggerated away from the standard parallel.
• Meridians become closer to each other towards the pole.
• This projection is neither equal area nor orthomorphic.

Limitations

• 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.
• 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

• This projection is commonly used for showing areas of mid-latitudes with limited latitudinal and larger longitudinal extent.
• A long narrow strip of land running parallel to the standard parallel and having east-west stretch is correctly shown on this projection.
• Direction along standard parallel is used to show railways, roads, narrow river valleys, and international boundaries.
• This projection is suitable for showing the Canadian Pacific Railways, Trans-Siberian Railways, international boundaries between USA and Canada and the Narmada Valley.