Chapter 3: Map Projections
A map projection is a geometrical transformation of the earth’s spherical or ellipsoidal surface onto a flat map
Globes versus Flat Maps
Of all maps, globes give us the most realistic picture of the earth as a whole. It’s realistic because basic
geometric properties such as distance, direction, shape and areas are preserved because the globe is same
scale everywhere but as everything do, globes has disadvantages. They don’t let you view all parts of the
earth’s surface at the same time. Also, they aren’t useful to see kind of detail you might find on the road
map in your car. Globes are also bulky and they’re hard to store and handle. Globe construction is also
very laborious and costly.
It would be very nice if we can map the earth without any distortion. Unfortunately, the spherical earth is
not a developable surface. So, all flat maps are distorted. However, what cartographers do is to
minimize these distortions or preserve a particular geometrical property at the expense of others. This is
also known as map projection problem.
The Map Projection Process
The first step is to define the earth’s irregular surface topography as elevations above or sea depths
below a more regular surface known as geoid.
The second step is to project slightly undulating geoid onto the more regular oblate ellipsoid surface.
The third step involves projecting the ellipsoidal or spherical surface onto a plane through the use of
map projection equations that transform geographic or spherical coordinates into planar (x,y) map
coordinates. The greatest distortion of the earth’s surface geometry occurs in this step.
Map Projection Properties
Because of the stretching and shrinking that occurs in the process of transforming the spherical
or ellipsoidal earth surface to a plane, the stated map scale is true only at selected points or along
particular lines called points and lines of tangency. Everywhere else the scale of the flat map is
actually smaller or larger than the stated scale.
There are in fact two map scales. Actual scale is the scale that you measure at any point on the
map; it will differ from one location to another. Principle scale is the scale of the generating
globe—a globe reduced to the scale of the desired flat map.
Scale factor is actual scale divided by principal scale. An SF of 2.0 on a smallscale map means
that the actual scale is twice as large as the principal scale.
Completeness refers to the ability of map projections to show the entire earth. Correspondence relations
You might expect that each point on the earth would correspond to a point on the map projection.
Such a pointtopoint correspondence would grasp your attention from a feature on the earth to
the same feature on the map.
To represent an entire spherical surface on a plane, the continuous spherical surface must be