MAP PROJECTION Habib Ali Mirdda Department of Geography

MAP PROJECTION Habib Ali Mirdda Department of Geography, St. Xavier College, Mahuadanr

Map Projection: Meaning and use • Map projection is a systematic drawing of parallel of latitudes and meridians of longitude on a plane surface for the whole earth or a part of it on a certain scale so that any point on the earth surface may correspond to that on the drawing. • Maps cannot be created without map projections. All map projections necessarily distort the surface in some fashion. • Depending on the purpose of the map, some distortions are acceptable and others are not; therefore, different map projections exist in order to preserve some properties of the sphere-like body at the expense of other properties. • There is no limit to the number of possible map projections

Classification of Map Projections Map projections are classified on the following criteria: • • Method of construction Development surface used Projection properties Position of light source

Method of Construction The term map projection implies projecting the graticule of the earth onto a flat surface with the help of shadow cast. However, not all of the map projections are developed in this manner. Some projections are developed using mathematical calculations only. Given below are the projections that are based on the method of construction: • Perspective Projections : These projections are made with the help of shadow cast from an illuminated globe on to a developable surface • Non Perspective Projections : These projections do not use shadow cast from an illuminated globe on to a developable surface. A developable surface is only assumed to be covering the globe and the construction of projections is done using mathematical calculations.

Development Surface Projection transforms the coordinates of earth on to a surface that can be flattened to a plane without distortion (shearing or stretching). Such a surface is called a developable surface. The three basic projections are based on the types of developable surface and are introduced below: • 1. Cylindrical Projection • 2. Conic Projection • 3. Azimuthal/Zenithal Projection

Cylindrical, Conical and Azimuthal Projections

Projection Properties According to properties map projections can be classified as: • Equal area projection: Also known as homolographic projections. The areas of different parts of earth are correctly represented by such projections. • True shape projection: Also known as orthomorphic projections. The shapes of different parts of earth are correctly represented on these projections. • True scale or equidistant projections: Projections that maintain correct scale are called true scale projections. However, no projection can maintain the correct scale throughout. Correct scale can only be maintained along some parallel or meridian.

Projection Properties

Position of Light Source Placing light source illuminating the globe at different positions results in the development of different projections. These projections are: • Gnomonic projection: when the source of light is placed at the centre of the globe • Stereographic Projection: when the source of light is placed at the periphery of the globe, diametrically opposite to the point at which developable surface touches the globe • Orthographic Projection: when the source of light is placed at infinity from the globe opposite to the point at which developable surface touches the globe

Position of Light Source

CONSTRUCTION OF MAP PROJECTIONS

Simple Cylindrical Projection Let us draw a network of Simple cylindrical Projection for the whole globe on the scale of 1: 400, 000 spacing meridians and parallels at 30º interval Calculations

Graticules of Simple Cylindrical Projection

Steps of Constrution: • • • Draw a line AB, 9. 975 cm long to represent the equator. The equator is a circle on the globe and is subtended by 360º. Since the meridians are to be drawn at an interval of 30º divide AB into 360/30 or 12 equal parts. The length of a meridian is equal to half the length of the equator i. e. 9. 975/2 or 4. 987 cm. To draw meridians, erect perpendiculars on the points of divisions of AB. Take these perpendiculars equal to the length specified for a meridian and keep half of their length on either side of the equator. A meridian on a globe is subtended by 180º. Since the parallels are to be drawn at an interval of 30º, divide the central meridian into 180/30 i. e. 6 parts. Through these points of divisions draw lines parallel to the equator. These lines will be parallels of latitude. Mark the equator and the central meridian with 0º and the parallels and other meridians. EFGH is the required graticule.

Conical Projection Let us draw a graticule on simple conical projection with one standard parallel on the scale of 1: 180, 000 for the area extending from the equator to 90º N latitude and from 60º W longitude to 100º E longitude with parallels spaced at 15º interval, meridians at 20º, and standard parallel 45º N. Calculations:

Steps of construction • Draw a circle with a radius of 3. 527 cm that represents the globe. Let NS be the polar diameter and WE be the equatorial diameter which intersect each other at right angles at O. • To draw the standard parallel 45º N, draw OP making an angle of 45º with OE. • Draw QP tangent to OP and extend ON to meet PQ at point Q. • Draw OA making an angle equal to the parallel interval i. e. 15º with OE.

Graticules of Simple Conical Projection

Azimuthal Projection Let us draw Polar zenithal equal area projection for the northern hemisphere on the scale of 1: 200, 000 spacing parallels at 15° interval and meridians at 30° interval. Calculations:

Steps of construction: • Draw a circle with radius equal to 3. 175 cm representing a globe. Let NS and WE be the polar and equatorial diameter respectively which intersect each other at right angles at O, the centre of the circle. • Draw radii Oa, Ob, Oc, Od, and Oe making angles of 15°, 30°, 45°, 60° and 75° respectively with OE. Join Ne, Nd, Nc, Nb, Na and NE by straight lines. • With radius equal to Ne, and N’ as centre draw a circle. This circle represents 75° parallel. Similarly with centre N’ and radii equal to Nd, Nc, Nb, Na and NE draw circles to represent the parallels of 60°, 45°, 30°, 15° and 0° respectively. • Draw straight lines AB and CD intersecting each other at the centre i. e. point N. • Radius N’B represents 0° meridian, N’A 180° meridian, N’D 90° E meridian and N’C 90° W meridian. • Using protractor, draw other radii at 30° interval to represent other meridians

Graticules of Polar Zenithal Equal Area Projection

Selection of Map Projection • Considering the purpose of the map is important while choosing the map projection. If a map has a specific purpose, one may need to preserve a certain property such as shape, area or direction • On the basis of the property preserved, maps can be categorized as following a. Maps that preserve shapes. b. Maps that preserve area c. Maps that preserve scale d. Maps that preserve direction

Maps that preserve shapes Used for showing local directions and representing the shapes of the features. Such maps include: • Topographic and cadastral maps. • Navigation charts (for plotting course bearings and wind direction). • Civil engineering maps and military maps. • Weather maps (for showing the local direction in which weather systems are moving).

Maps that preserve area The size of any area on the map is in true proportion to its size on the earth. Such projections can be used to show • Density of an attribute e. g. population density with dots • Spatial extent of a categorical attribute e. g. land use maps • Quantitative attributes by area e. g. Gross Domestic Product by country • World political maps to correct popular misconceptions about the relative sizes of countries.

Maps that preserve scale Preserves true scale from a single point to all other points on the map. The maps that use this property include: • Maps of airline distances from a single city to several other cities • Seismic maps showing distances from the epicenter of an earthquake • Maps used to calculate ranges; for example, the cruising ranges of airplanes or the habitats of animal species

Maps that preserve direction On any Azimuthal projection, all azimuths, or directions, are true from a single specified point to all other points on the map. On a conformal projection, directions are locally true, but are distorted with distance.

Major Types of Map Projection

Cylindrical Projection

Properties of Cylindrical Projection • Parallels and meridians are straight lines • The meridians intersect parallels at right angles • The distance between parallels decrease toward the poles but meridians are equally spaced • The length of the equator on this projection is same as that on globe but other parallels are longer than corresponding parallels on globe. So, the scale is true along the equator but is exaggerated along other parallels • Shape and scale distortions increase near points 90 degrees from the central line resulting in vertical exaggeration of Equatorial regions with compression of regions in middle latitudes • Despite the shape distortion in some portions of a world map, this projection is well suited for equal-area mapping of regions which are predominantly north-south in extent, which have an oblique central line, or which lie near the Equator.

Properties of Azimuthal Projection • The pole is a point forming the centre of the projection and the parallels are concentric circles. • The meridians are straight lines radiating from pole having correct angular distance between them. • The meridians intersect the parallels at right angles. • The parallels are unequally spaced. The distances between the parallels increase rapidly toward the margin of the projection. This causes exaggeration of the scale along the meridians. • The scale along the parallels increases away from the centre of the projection. • The exaggeration and distortion of shapes increases away from the centre of the projection. The exaggeration in the meridian scale is greater than that in any other zenithal projection.

Conical with One and Two Standard Parallel

Bonne’s Projection

Properties of Bonne’s Projection Pole is represented as a point and parallels as concentric arcs of circles Scale along all the parallels is correct Central meridian is a straight line along which the scale is correct. Other meridians are curved and longer than corresponding meridians on the globe. Scale along meridians increases away from the central meridian • Central meridian intersects all parallels at right angle. Other meridians intersect standard parallel at right angle but other parallels obliquely. Shape is only preserved along central meridian and standard parallel • The distance and scale between two parallels are correct. Area between projected parallels is equal to the area between the same parallels on the globe. Therefore, is an equal area projection • Maps of European countries are shown in this projection. It is also used for preparing topographical sheets of small countries of middle latitudes. • •

Polyconic Projection

Properties of Polyconic Projection • The parallels are arcs of circles with different centers • Each parallel is a standard parallel i. e. each parallel is developed from a different cone • Equator is represented as a straight line and the pole as a point • Parallels are equally spaced along central meridian but the distance between them increases away from the central meridian. • Scale is correct along every parallel. • Central meridian intersects all parallels at right angle so the scale along it, is correct. Other meridians are curved and longer than corresponding meridians on the globe and so scale along meridians increases away from the central meridian. • It is used for preparing topographical sheets of small areas.

Sinusoidal Projection

Properties of Sinusoidal Projection • The central meridian is a straight line and all other meridians are equally spaced sinusoidal curves. • The parallels are straight lines that intersect centre meridian at right angles. • Shape and angles are correct along the central meridian and equator • The distortion of shape and angles increases away from the central meridian and is high near the edges • Equal area projection • Used for world maps illustrating area characteristics. Used for continental maps of South America, Africa, and occasionally other land masses, where each has its own central meridian.

Interrupted Sinusoidal Projection

Interrupted Sinusoidal Projection

Mercator Projection

Properties of Mercator Projection • Parallels and meridians are straight lines • Meridians intersect parallels at right angle • Distance between the meridians remains the same but distance between the parallels increases towards the pole • The length of equator on the projection is equal to the length of the equator on the globe whereas other parallels are drawn longer than what they are on the globe, therefore the scale along the equator is correct but is incorrect for other parallels • As scale varies from parallel to parallel and is exaggerated towards the pole, the shapes of large sized countries are distorted more towards pole and less towards equator. However, shapes of small countries are preserved • The image of the poles are at infinity • Commonly used for navigational purposes, ocean currents and wind direction are shown on this projection

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