Thoughts on Mercator (Universal Transverse Mercator), Albers Equal Area Conic and Azimuthal Equidistant.

One of the things these projections all have in common is the idea of placing a primitive object that can be easily unfolded into a flat plane, ie plane, cylinder or cone. At its simplest each of these objects would touch a sphere along a line or point of tangent and here or along it we will see, essentially no distortion of the globe. As we move away from this tangent, distortion will begin to appear. A further point of interest is taking these primitives and bisect a portion of the world with it creating secant lines. In this case our distortion will be eliminated along these lines and grow as me move out for it.

At their simplest these all involve the idea of projecting the graticule from the earth onto the surface. How the lines are projected varies from projection to projection, some use simple ray tracing from a "light" source at the centre or opposite side of the globe, while others use mathematics to place the graticule, while other simply project the graticule orthogonally to the primitive surface.

Mercator and Universal Transverse Mercator (UTM)

The first projection type we will look at is the cylindrical projection. The Mercator projection is a cylindrical projection having tangency along the equator (Heywood et al., 2011). The Transverse Mercator rotates the cylinder by 90 degrees placing its line of tangency along a line of longitude (GISGeography, 2016). Various flavors of UTM are used to control how much distortion exists over an area. These specific projections don't actually have a single line of tangency, but instead the cylinder bisects the Earth, with each of the secant lines emerging some distance away from each other as specified by the projection (GISGeography, 2016). This has the effect of minimal to no distortion along the secant lines and having a controlled level of projection between the two (UTM has a scale factor of 0.9996 at its central meridian) (GISGeography, 2016). Some are good to show larger areas, and some are excellent at smaller areas. For example, within Alberta, Canada we commonly come across 3 forms of transverse Mercator projections: 3TM, UTM and 10TM (ESRI, 2024). 3TM spans 3 degrees of longitude and is good for showing smaller areas like cities, UTM spans 6 degrees of longitude and it used for most oil and gas development/exploration mapping and finally 10tm spans 10 degrees of longitude, making it large enough to encompass the entire province of Alberta, and is seen used in the Alberta 10TM Forest projection (epsg, n.d.).

A normal Mercator projection is excellent for showing a wide country that do not extend very far north and south, since its line of tangency runs east and west around the globe (Heywood et al., 2011), however because the transverse Mercator projections use a cylinder rotated 90 degrees with its line of tangency running north/south (Heywood et al., 2011) what is distorted is also rotated that 90 degrees, a latitude spanning continent like North America sees little north/south distortion. The same can not be said for North America viewed in a transverse Mercator projection, as it spreads out east and west the distortions will increase and it will become less reliable.

The Mercator projection is said to be conformal and so preserve shape and angles, but distort areas (Price, 2019), if we think about the traditional Mercator projection and the example of Greenland. It is the correct shape, but its size is wildly distorted (Longley, 2015).

Scale is an interesting question for this projection as it can be used for various used at various scales, especially when we include variations like 10TM, 3TM and UTM. Each is better at a certain scale. 10TM is not ideal for a city, while 3TM will show little distortion (Heywood et al., 2011). None would be good at showing the entire globe. A normal Mercator projection can be used for the globe for certain applications that are based on direction such as navigation (Longley, 2015), but I wouldn't use it for a representation that was showing comparative areas.

Albers Equal Area Conic

When we place a cone against the globe to create the Albers Equal Area Conic projection we see a line of tangency run around a line of latitude, much as we saw before with the Mercator projection (Heywood et al., 2011) this line shows little to no distortion along it, but as we move out from the line we will see distortion grow. The Albers Equal Area Conic projection, much like we saw with UTM, actually bisects the globe through two parallels giving us two secant lines again, and again two places where we see little to no distortion (ESRI, n.d.).

Unlike we saw with the three flavours of UTM, the location of the standard parallels can be chosen based on what is being mapped (ESRI, n.d.). This allows us to map large east/west extents with some control over the level of distortion we might see between the parallels (ESRI, n.d.).

Mapping large north/south bodies with this type of projection is not ideal as the further the standard parallels are from each other the more distortion we will get between them, and the closer together they are, the most distorted they will get as we move away from them (ESRI, n.d.). Typically features towards the base of the cone will be stretched out to fit the cone, while features towards the top will be pinched together.

As its name suggests the projection preserves area, but at the expense of distance, shape and direction (ESRI, n.d.).

This projection is suitable for mapping large areas such as countries (provided that are more east/west, such as the contiguous US states) and we are interested in investigating the areas that exist within those countries.

Azimuthal Equidistant

While Mercator projects to a cylinder and Albers Conformal Conic to a cone, Azimuthal projects against a plane (ESRI, n.d.). Unlike the other two this projection involves placing a plane against a single point on the Earth (ESRI, n.d.). As with the others at this point there is little to no distortion, but as we spread away distortion grows in all directions, not making it ideal for mapping any particular large country spanning many latitudes or longitudes, with only distance and direction being maintained from that central point (ESRI, n.d.)

While this projection can be placed to map any part of the Earth it is most commonly used for mapping polar regions with the plane being placed against the north or south pole (ESRI, n.d.), as such it is generally used to show an entire hemisphere of the Earth (ESRI, n.d.).

References

epsg n.d. NAD83 / Alberta 10-TM (Forest) - EPSG:3400. [Accessed 9 October 2025]. Available from: https://epsg.io.

ESRI n.d. Albers—ArcGIS Pro | Documentation. [Accessed 9 October 2025a]. Available from: https://pro.arcgis.com/en/pro-app/latest/help/mapping/properties/albers.htm.

ESRI n.d. Azimuthal equidistant—ArcGIS Pro | Documentation. [Accessed 9 October 2025b]. Available from: https://pro.arcgis.com/en/pro-app/latest/help/mapping/properties/azimuthal-equidistant.htm.

ESRI 2024. FAQ: What Are some Common Projections and Geographic Coordinate Systems for Canada? Technical Support. [Online]. [Accessed 9 October 2025]. Available from: https://support.esri.com/en-us/knowledge-base/faq-what-are-some-common-projections-and-geographic-coo-000011853.

GISGeography 2016. How Universal Transverse Mercator (UTM) Works. GIS Geography. [Online]. [Accessed 9 October 2025]. Available from: https://gisgeography.com/utm-universal-transverse-mercator-projection/.

Heywood, D.I., Cornelius, S. and Carver, S. 2011. An introduction to geographical information systems 4. ed. Harlow, England {: Prentice Hall.

Longley, P. 2015. Geographic information science & systems Fourth edition. Hoboken, New Jersey: John Wiley & Sons, Incorporated.

Price, M. 2019. Mastering ArcGIS Pro 1st edn.