Ahasanul Hoque

Ahasanul Hoque

Lives in Bangladesh
Ahasanul Hoque

A Brief on Map Projection

April 22, 2017, by aHaSaN, category GeoTechnology

Over the centuries, many different ways of representing the round Earth on flat paper have been developed. Each of these methods is referred to as a map projection. What does it mean to project something? Have you ever been to the movie theatre? How does the movie get on the movie screen? The image you watch on the screen is projected using a high powered light from the back of the theater. Now, imagine placing a projector inside of a globe and projecting the different continents, islands, and other features onto a flat screen. What would the projection look like? This depends on where you place the screen. Map projections are attempts to portray the surface of the earth or a portion of the earth on a flat surface. Some distortions of conformality, distance, direction, scale, and area always result from this process. Some projections minimize distortions in some of these properties at the expense of maximizing errors in others. Some projection are attempts to only moderately distort all of these properties.

Conformality : When the scale of a map at any point on the map is the same in any direction, the projection is conformal. Meridians (lines of longitude) and parallels (lines of latitude) intersect at right angles. Shape is preserved locally on conformal maps.

Distance : A map is equidistant when it portrays distances from the center of the projection to any other place on the map.

Direction : A map preserves direction when azimuths (angles from a point on a line to another point) are portrayed correctly in all directions.

Scale : Scale is the relationship between a distance portrayed on a map and the same distance on the Earth.

Area : When a map portrays areas over the entire map so that all mapped areas have the same proportional relationship to the areas on the Earth that they represent, the map is an equal-area map.

The problem is that achieving all of these properties on a two-dimensional map is impossible. Mathematicians have proven this. Preserving any one requires distorting at least one other.

This table shows which properties can be combined in a single map projection:

Equal-Area Equidistant Azimuthal Conformal
Equal-Area no yes no
Equidistant no yes no
Azimuthal yes yes yes
Conformal no no yes

Early maps and the Mercator projection

When people first started drawing maps, they didn’t draw them with mathematical precision, because the necessary mathematics hadn’t been invented yet. The Greeks were the first to do rigorous geometry, and the Greek mathematician Ptolemy (90–168 CE) was the first to develop a map using lines of latitude and longitude and defining locations on a coordinate system. Islamic mapmakers in the Middle Ages built on his ideas, and the Chinese also drew coordinate-based maps to careful scale.

In 1569, the Flemish geographer and cartographer Gerardus Mercator created a map using a mathematical formula to “project” points on the earth’s surface onto a map based on their latitude and longitude. His formula — called the Mercator projection — became the standard means of making maps for navigation, because the directions of the compass corresponded to directions on the map. North, east, south, and west were straight lines on paper, just as they are on the earth’s surface.

Map of the world by Gerardus Mercator, 1569Gerardus Mercator’s 1569 map of the world

he problem with the Mercator projection is that it distorts areas and distances. The North and South Poles are stretched all the way across the top and bottom of the map, and regions to the far north and south appear much larger than they actually are. This isn’t a problem for navigation — Google Maps uses a Mercator projection even today — and the distortion is negligible for maps of small regions (say, of North Carolina). But it can give a false impression of the relative sizes of various countries and continents. For example, on the map below, Greenland is larger than Africa!

World satellite map in Mercator projection              Satellite photography from NASA is used to make a map of the world using the Mercator projection.

Cartographers have developed a number of other projections with various advantages and disadvantages, but the Mercator projection is the vision of the earth that most of us have in our heads more than four centuries later. Different map projections result in different spatial relationships between regions.

Cylindrical Projection

A cylindrical projection map is the most common type of map that we see. Imagine placing the movie screen around the globe in a cylinder shape. The projection that results is depicted in this image. Notice that areas close to the equator have very little distortion. However, the closer to the poles that one travels, the more distorted the map becomes. In this example, Greenland appears to be many times larger than it really is.



Conic Projection

A conic projection map is created by placing a cone shaped screen on a globe. The resulting projection is more accurate than the cylindrical projection map discussed above. However, the further we travel down the map, the more distorted and less accurate the map becomes.

Plane Projection

A plane projection is created by placing an imaginary screen directly above or below a globe. The image that would result is called a plane projection. This type of map projection is not commonly used.

Interrupted Projection

There are many different types of interrupted projection maps. These types of maps try to depict the continents as accurately as possible by leaving blank space in the less important areas of the map, such as in the oceans.

 

Each of the map projections previously discussed as well as any other type of map projection must consider two important factors. What is more important, depicting the accurate sizes of objects on the map, or depicting accurate shapes of these objects? The challenge is that you cannot have both. The more accurately you depict shape, the less accurate will be your depiction of size, and vice versa.

A map which portrays shape accurately is called a conformal map. Conformal maps are useful in that they help us understand the true shape of the items on the map. However, these maps have many drawbacks. A conformal map tends to get quite distorted, especially towards the top and bottom of the map. This creates problems with scale. The scale may be accurate near the equator, but the further one travels form the equator, the less accurate the scale becomes.

Hybrid Maps

Many maps are neither entirely conformal nor entirely equivalent. By blending both conformality and equivalency, we can create a map that balances the distortion of both size and shape.

Thus, some map projections are entirely conformal, while others are entirely equivalent. It is impossible for a map to be both conformal and equivalent. However, many maps are a hybrid between conformal and equivalent.

Properties of common projections

The U.S. Geological Survey provides an overview of several common map projections, with an explanation of how each is created and what it’s most useful for. The table below summarizes the properties of common map projections.  ( Key:  yes yes   partly partly )

Projection Type      Conformal         Equal     area                Equidistant Azimuthal (true direction)
Globe Sphere yes yes yes yes
Mercator Cylindrical yes partly
Transverse Mercator Cylindrical yes
Oblique Mercator Cylindrical yes
Space Oblique Mercator Cylindrical yes
Miller Cylindrical Cylindrical
Robinson Pseudo-cylindrical
Sinusoidal Equal Area Pseudo-cylindrical yes partly
Orthographic Azimuthal partly
Stereographic Azimuthal yes partly
Gnomonic Azimuthal partly
Azimuthal Equidistant Azimuthal partly partly
Lambert Azimuthal Equal Area Azimuthal yes partly
Albers Equal Area Conic Conic yes
Lambert Conformal Conic Conic yes partly
Equidistant Conic Conic partly
Polyconic Conic partly
Bipolar Oblique Conic Conformal Conic yes

Choosing a projection

Finally, this table gives a summary of what kinds of maps each projection is more and less suitable for.  Adapted from the U.S. Geological Survey. Click the name of a projection to get more information about it.

Key:  yes yes   partly partly )

Projection   Type                   World                              Hemisphere                           Continent/
Ocean
                        Region/
sea
                   Medium scale                      Large scale
Globe Sphere yes
Mercator Cylindrical partly yes
Transverse Mercator Cylindrical yes yes yes yes
Oblique Mercator Cylindrical yes yes yes yes
Space Oblique Mercator Cylindrical yes
Miller Cylindrical Cylindrical yes
Robinson Pseudo-
cylindrical
yes
Sinusoidal Equal Area Pseudo-
cylindrical
yes yes
Orthographic Azimuthal partly
Stereographic Azimuthal yes yes yes yes yes
Gnomonic Azimuthal partly
Azimuthal Equidistant Azimuthal partly yes yes yes partly
Lambert Azimuthal Equal Area Azimuthal yes yes yes
Albers Equal Area Conic Conic yes yes yes
Lambert Conformal Conic Conic yes yes yes yes
Equidistant Conic Conic yes yes
Polyconic Conic partly partly
Bipolar Oblique Conic Conformal Conic yes

 

Map projection types all have their pros and cons, but they are incredibly versatile. Even though it is nearly impossible to create an entirely accurate map projection there are uses for even the most imperfect depictions of the Earth. Map projections are created for certain purposes and should be used for those purposes. In the end each and every map projection has a place, and there is no limit to the amount of projections that can be created.

Welcome to the world of modern geography. Enjoy Cartography , Happy Mapping !!

Ref: learnnc; Progonos.com, GISLounge, Kids GeoGraphy

So, what do you think ?