This section introduces, defines, and describes map projection properties.

A map projection property is an alteration of area, shape, distance, and direction on a map projection. These map projection properties exist because the conversion from a three dimensional object, such as the earth, to a two-dimensional representation, such as a flat paper map, requires the deformation of the three-dimensional object to fit onto a flat map. The three-dimensional spherical surface is torn, sheared, or compressed to flatten it onto a flat developable surface.

These map projection properties are area, shape, distance, and direction. These four map projection properties described for facets of a map projection that can either be held true, or be distorted.

Of the four projection properties, area and shape are considered major properties and are mutually exclusive. That means, that if area is held to its true form on a map, shape must be distorted, and vice versa. Distance and direction, on the other hand, are minor properties, and can coexist with any of the other projection properties. However, distance and direction cannot be true everywhere on a map as will be discussed soon.

Anytime we create a flat map of a three-dimensional object, we must distort the three-dimensional object. Distortions are unavoidable when making flat maps of the earth. Distortion is not constant across the map, as distortion may take different forms in different parts of the map. There are few points were distortions are going to be zero, however, distortion is usually less near the points or lines of intersection where the developable surface intersects the globe. By determining where the standard points and lines are placed will directly affect where the map will have the least and most amount of distortion.

A map can show one or more, but never all, of the following map projection properties at the same time: true direction, true distance, truth area, and true shape. Additionally, remember that area and shape are two major map projection properties, and they still remain mutually exclusive. We will now discuss different families of map projections which aim to preserve at least one of the map projection properties.

The equal area map projection, also known as the equivalent map projection, aims to preserve the area relationships of all parts of the globe. You can easily identify most equal area map projections by noting that the meridians and parallels are not at right angles to each other. Additionally, distance distortion is often present on equal area map projection, and, shape is often skewed.

Even with the distortion of distance and shape, equal area map projection is useful for general quantitative thematic maps when it is desirable to retain area properties. This is especially useful for choropleth maps, when the attribute is normalized by area. Holding areal properties to be true, allows for an apples to apples comparison of density between different enumeration units, such as counties.

The cylindrical equal area map projection is an example of an equal area, or equivalent map projection, which aims to keep the areal relationships of all parts of the globe correct.

A second example of an equal area projection is the hammer aitoff map projection. Again, like the cylindrical equal area projection, this map projection aims to hold areas true. Also note, that on this map projection, the parallels and meridians do not intersect at 90° angles, which is a hint that lets us know that this may be an equal area projection.

Conformal map projections, also known as orthomorphic map projection, preserves angles around points, and shape of small areas. Additionally, it allows for the same scale in all directions to or from a single point on the map. Conformal map projections can usually be identified by the fact that meridians intersect parallels at right angles, areas are distorted significantly its small scales, and shapes of large regions may be severely distorted.

Even with the potential for large shape distortion. Conformal map projections are useful for large scale mapping and phenomenon with circular radial patterns such as radio broadcasts for average wind directions.

The Mercator projection, perhaps the most famous of all map projections, is a conformal map projection that preserves shape. However, notice the massive amount of distortion in the lower latitudes towards the south pole, and the northern latitudes, near the North Pole. Also note, that the parallels and meridians intersect at 90° angles.

The third map projection family is the equidistant map projection which aims to preserve great circle distances. That means a distance can be held true from one point to all other points, or from a few select points, to others, but not from all points to all other points. It is also important to note the scale is uniform along these lines a true distance from the select points on the map. Identifying marks of the equidistant map projection are that they are neither conformal or equal area, and look less distorted.

Equidistant map projections are useful for general purpose maps and Atlas maps.

Example of an equidistant map projection is the equidistant cylindrical map projection. Notice that compared to the conformal map projection, there is less distortion at the North and South pole, and the shapes also do not look overly distorted.

The azimuthal map projection, also known as the true direction map projection, preserves direction from one point to all other points in the map. Is important to note that direction is not true between non-central points. Direction is only true when measured to or from the specific points chosen to have true direction. Azimuthal map projection is most useful for preserving direction two or one from point, often used for navigation.

The azimuthal equidistant map projection, is an example of a true direction map projection that also holds distance to be true. While not all azimuthal map projections look like this, this particular map projection allows you to measure across the poles, and around the world, to determine true distance and direction from a single point.

As seen on a few example map projections previously, we can combine map projection properties onto a single projection. For example, an equal area map projection can also combine parts of it azimuthal map projection. Conformal can combine with azimuthal, equidistant can combine with azimuthal, and azimuthal can combine with equal area, conformal, and/or equidistant.

There is another map projection family, that does not try to hold a single map projection property is true. This map projection family is known as the minimum error, or compromise, map projection. The goal of the compromise map projection is to simultaneously minimize all for map projection properties, but may not hold any of the four map projection properties as true. The compromise map projection is useful for general geographic cartography.

An example of a compromise map projection is the Robinson map projection. It does not greatly distort any of the four map projection properties nor does it hold any of the four properties true. However what is nice about the Robinson map projection, is that it does a reasonable job of showing the true shape, distance, direction, and size of the features of the earth.

Link

To end this section, let’s watch a short clip from the TV show the West Wing, where the Organization of Cartographers for Socially Equality, a fictional group, petition white house staff to require a different map projection be used in public schools.

3.7 - Map Projection Properties.pptx