Map Projections
EXERCISE
1. Choose the right answer from the four alternatives given below:
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 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: (d) Cylindrical.
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.
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.
2. Answer the following questions in about 30 words:
I. Describe the elements of map projection.
Ans: Maps project the curved Earth onto a flat surface, using key elements like:
1. Reduced Earth: A miniaturized model of the globe to fit onto the map.
2. Parallels & Meridians: Imaginary lines of latitude (horizontal) and longitude (vertical) defining locations.
3. Projection Method: Different techniques (e.g., Mercator, Cylindrical) to transfer features from the globe to the plane.
4. Distortions: Inevitable compromises in shape, area, or direction depending on the projection method.
Understanding these elements is crucial for interpreting maps accurately and appreciating the challenges of representing our 3D world on a flat surface.
II. What do you mean by global property?
Ans: The meaning of "global property" depends on the context. It could refer to:
*Real estate: Owning properties across different countries or continents.
*Intellectual property: Rights to inventions, designs, etc., protected internationally.
*General concept: Anything related to ownership or characteristics found worldwide.
III. Not a single map projection represents the globe truly. Why?
Ans: Imagine squeezing a 3D orange peel flat! No matter how you do it, some things distort (stretching, shrinking). Map projections face the same problem: projecting Earth's sphere onto a flat surface inevitably compromises either shape, area, or direction. It's a trade-off to get a usable map, choosing which distortions to prioritize for the specific purpose.
IV. How is the area kept equal in cylindrical equal area projection?
Ans: In a cylindrical equal-area projection, area equality is achieved by "stretching" longitudes towards the poles. It's like inflating a balloon cylinder around the Earth, causing the vertical lines to widen as they reach the top and bottom (poles). While shapes get distorted, landmasses retain their relative sizes in terms of area.
3. Differentiate between—
I. Developable and non-developable surfaces
Ans: Here's a quick and clear differentiation between developable and non-developable surfaces:
Developable:
*Can be flattened without tearing or stretching (imagine unrolling a cone)
*Zero Gaussian curvature: curves smoothly in just one direction
*Examples: planes, cylinders, cones, some ruled surfaces
Non-developable:
*Cannot be flattened without deformation (think of a sphere or a potato)
*Non-zero Gaussian curvature: curves in two directions
*Examples: spheres, ellipsoids, most complex curved surfaces
Key points:
*Imagine flattening: Developable surfaces unfold like fabric, non-developable ones crumple or tear.
*Think of curvature: Developable are flat or smoothly curved, non-developable have bumps or dips.
*Applications: Developable in architecture, map projections, origami; non-developable in many natural shapes and objects.
II. Homolographic and orthographic projections
Ans: Homolographic and orthographic projections are both map projection techniques used to represent the Earth's surface on a flat plane, but they differ in their primary focus:
Homolographic projection:
*Focus: Preserves area accurately. Landmasses maintain their relative sizes, making it ideal for studying areal relationships, like resource distribution or agricultural zones.
*Shape and direction: Distorted, particularly towards the edges of the map. Shapes become stretched or compressed, and directions deviate from true bearings.
*Example: Robinson projection is a common homolographic projection used in atlases and thematic maps.
Orthographic projection:
*Focus: Preserves correct shapes of landmasses. Features appear as they would when viewed from a specific point in space, usually directly above the center of the map.
*Area and direction: Distorted, especially away from the center of the map. Landmasses appear smaller towards the edges, and directions lose accuracy.
*Example: The Van der Grinten projection is an orthographic projection used in celestial maps and some world maps.
Choosing the right projection depends on the specific purpose of the map. If accurate area comparisons are crucial, a homolographic projection is preferred. If accurate shapes and visual representation of landmasses are important, an orthographic projection might be better.
III. Normal and oblique projections
Ans: Normal and oblique projections are two categories in map projections, distinguished by the orientation of the projection surface relative to the globe:
Normal projections:
*Their projection surface (e.g., cylinder, cone) touches the globe along the equator.
*This results in maps with parallels and meridians running perpendicularly, creating a symmetrical grid.
*Examples: Mercator projection (cylindrical), Mollweide projection (equal-area)
Oblique projections:
*Their projection surface touches the globe at a point between the equator and a pole.
*This leads to maps with parallels and meridians intersecting at an angle, causing the grid to tilt.
*Examples: Bonne projection, Van der Grinten projection
Key differences:
*Symmetry: Normal projections have symmetrical grids, while oblique projections have tilted grids.
*Distortions: Both types introduce distortions in area, shape, or direction, but the patterns of distortion differ depending on the specific projection and point of contact.
*Uses: Normal projections are often used for world maps, while oblique projections are useful for regional maps where the area of interest is not centered on the equator.
IV. Parallels of latitude and meridians of longitude
Ans: Both parallels of latitude and meridians of longitude are imaginary lines used to pinpoint locations on Earth, but they differ in their direction and function:
Direction:
*Parallels: Run horizontally like concentric circles around the Earth, with 0° at the equator and 90° at each pole (North and South). Imagine slicing an orange, the lines on the peel are like parallels.
*Meridians: Run vertically like lines joining the North and South Poles, with 0° at the Prime Meridian (Greenwich, England) and extending 180° East and 180° West. Think of stitching the orange peel together, the seams are like meridians.
Function:
*Parallels: Measure north-south distance from the equator, determining climate zones, daylight hours, and even cultural differences. Think of them as "rungs on a ladder," showing how high (north/south) you are from the equator.
*Meridians: Measure east-west distance from the Prime Meridian, establishing time zones and helping identify relative positions between places. Think of them as "spokes on a wheel," showing how far east/west you are from the starting point.
Mnemonic:
*Remember "Polar bears Prefer Pancakes," where the Ps stand for parallels and pancakes indicate their flat, circular nature.
*For meridians, think of "Married Men Make Money," where the Ms represent meridians and the middle Ms hint at their north-south direction.
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: Map projections can be classified based on several criteria with distinct characteristics for each type:
Source of light:
Perspective: Projects features with shadows like a globe under light (gnomic).
Nonperspective: Projects features without shadows like tracing outlines onto a surface (cylindrical).
Projection surface:
Conformal: Preserves shapes but distorts areas and directions (cylindrical).
Equal area: Preserves areas but distorts shapes and directions (mollweide).
Equidistant: Preserves distances from specific points but distorts shapes and areas (polar zenithal).
Global property:
Normal: Projection surface touches the globe at the equator (Mercator).
Oblique: Projection surface touches the globe between equator and a pole (Bonne).
II. Which map projection is very useful for navigational purposes? Explain the properties and limitations of this projection.
Ans: The Mercator projection is highly favored for navigation due to its unique properties:
Benefits:
*Conformal: Preserves shapes of landmasses, crucial for visual map recognition during navigation.
*Straight rhumb lines: Bearings (compass directions) remain constant as straight lines on the map, simplifying course plotting.
Limitations:
*Area distortion: Stretches landmasses towards the poles, exaggerating their size relative to the equator.
*Direction distortion: Not truly accurate direction at all points, especially away from the equator.
*Limited polar coverage: Poles cannot be represented due to infinite scale at those points.
Despite these limitations, the Mercator projection's ability to simplify course plotting and maintain recognizable shapes makes it valuable for navigation charts and general nautical use. Remember, however, to interpret areas and distances cautiously, especially near the poles.
III. Discuss the main properties of conical projection with one standard parallel and describe its major limitations.
Ans: Conical Projection with One Standard Parallel: Properties and Limitations
Properties:
*Preserves shape along the standard parallel: Landmasses retain their accurate shape at the chosen latitude.
*Straight meridians: Meridians appear as straight lines, simplifying direction measurement.
*True scale along meridians: Distances along meridians are accurately represented from the standard parallel.
*Concentric circular parallels: Parallels are evenly spaced circles centered on the pole.
Limitations:
*Area distortion: Landmasses away from the standard parallel become increasingly distorted and exaggerated, especially towards the poles.
*Direction distortion: Directions become less accurate away from the standard parallel and meridians.
*Limited suitability for world maps: Distortions become significant away from the standard parallel, making it a less ideal choice for representing the entire globe.
*Not conformal: Does not preserve shapes accurately outside the standard parallel.
While useful for regional maps centered around the chosen standard parallel, this projection suffers from significant limitations when applied to larger areas or the whole world. Consider these limitations when interpreting distances and shapes on such maps.
