Projections

The earth is a three-dimensional object whereas most maps are two-dimensional. As such, a mathematic approach is required to present the curved surface of the Earth on a flat surface such as a paper map, a computer screen or a mobile phone screen – this process is known as a map projection.

It is however impossible to represent a curved surface on a flat plane without distorting one or more characteristics such as distances, directions, shape, or area. Try it: peel an orange and try to squash it flat without tearing or creasing it …. spoiler - you can’t.

How do they work?

So how do they work? Imagine a light source was placed inside the centre of the Earth and then a piece of paper held up to the Earth or wrapped around it (without making a fold or crumpling it). If the landmasses were opaque, they would form shadows on the paper when the light is turned on – this is your projection. Unfortunately though, the shadows will be distorted, either in size or shape. Here-in lies the problem – projections result in distortion.

Projections can be split into 3 main types; Cylindrical, Conic and Planar (Azimuthal), which define the type of developable surface used – a cylinder, a cone or a flat plane respectively. Each of these surfaces can be moved, rotated and positioned so that they just touch the Earth in one place, or along a single line (tangential), or it can intersect the Earth (secant). Along the lines where the paper intersects or touches the Earth’s surface, scale is true i.e. a distance measured on the map is true to its distance on the ground.

A classic cylindrical projection is best suited for use in the equatorial regions where the country has a broadly east-west extent, or in its transverse form (rotated 90⁰), a country with a broadly north-south extent. Conic projections are best suited for countries in the mid latitudes with a greater East-West extent than North-South extent. Finally, azimuthal projections are commonly used for countries which are broadly circular in their extent and are often used for mapping in the high latitudes. There are equidistant (preserves distances), conformal (preserves angles and shapes) and equal area versions of cylindrical, conic and azimuthal projections – these are discussed below.

Different projection methods preserved different characteristics. This means that the best projection to use will depend on the purpose of the map (plus the shape of the area to be mapped and its location on the globe). The choice of map projection becomes very important for maps greater than the size of a small country due to the distortions created across large areas. A poor choice of projection can result in the misrepresentation of what you are trying to show. For maps of small areas, the distortion is minimal and therefore the choice of map projection matters less.

As noted above, different map projections preserve different characteristics. Those which keep areas correct are called ‘equal area’ projections, those which preserve distance are known as ‘equidistant’ projections, and those which preserve angles are known as ‘conformal’ projections. In addition, there are a number of projections which are a compromise between these. Think carefully about what your map is showing and what needs to be preserved before choosing your projection.

Projection Types

Conformal

Conformal projections preserve angles. This means that the shape of features appears correct and means that a straight line drawn on a map between two locations represents a line of constant bearing in reality i.e. measure the angle on the map, set your compass and off you go. Conformal projections do however distort areas and distances. The projection often used for maps of the world (rightly or wrongly – you decide) is the Mercator projection, which is a conformal, cylindrical projection, created by Gerhard Mercator in 1569. This projection was designed to represent sailing courses of constant bearing (rhumb lines) as straight lines. It is still used to this day for maritime and air charts. As you can see on the map below, distances and areas are distorted, with the distortion becoming more pronounced towards the poles. On a Mercator projection, Greenland and Africa appear to be a similar size, however Africa is approximately 14 times larger than Greenland. Not a great projection to use if you want to represent the relative areas of countries correctly.

Mercator projection

It is important to note that distances vary across this projection so, if using this sort of projection at a continental or global scale, you should not include a standard scale bar as it will only be valid for distances measured along the equator.

Equal Area

Equal area projections are commonly used for mapping distributions such as population density, land cover, or climatic regions. When mapping distributions, it is important that the relative areas of different regions or countries are presented correctly. Using a non-equal area projection could result in giving greater weight to certain data due to certain regions looking bigger than they should (such as Greenland on a Mercator Projection). Equal area projections however distort shapes, angles, and distances. Examples of equal area projections include Albers Equal Area Conic, Equal Earth, Gall-Peters, Mollweide, and Eckert IV. The distortion to shape can however make some areas look unrecognisable. If you look at the little circles on the Albers Equal Area Conic Projection, you can see their shape is preserved well in mid Northern latitudes. As such, this projection is often used for maps of Europe.

Albers Equal Area Conic Projection

Equal Earth Projection

Note how the direction of North and distances vary across these projections – if using these projections at a continental or global scale, you should not include a north arrow or scale bar.

Equidistant

Equidistant projections do as they say, they preserve (some) distances and therefore should be used if representing the distance between two points correctly is important to the purpose of the map. Most equidistant maps preserve scale along one or more lines or between two other points on the map. No projection can preserve all distances. One type of equidistant projection is an azimuthal equidistant projection which preserves distance from a single specified point on the projection and any other point on the map and is often used to map the polar regions.

Azimuthal Equidistant Projection

Compromise

Some projections are a compromise and do their best to preserve areas, distances, and shapes, but in doing so, they preserve none of them. One example is the Robinson projection which keeps shapes of countries looking about right and the relative areas of countries better represented that some projection methods. As such, it is quite a popular global projection. Be wary of using it though when preserving distances or areas is key to the message of your map.

Robinson Projection

Ordnance Survey

The map projection commonly used for Britain is the Ordnance Survey National Grid projection which is a Modified Transverse Mercator projection. This is a cylindrical projection where the cylinder is rotated by 90 degrees (ends of the cylinder facing East-West rather than North-South). The cylinder is centred on the north-south central meridian of the UK (at 2⁰ West) i.e. it touches the Earth down the centre of the UK. The effect of this, in theory, means that distances become more distorted with distance away from this central meridian, where the Earth’s surface touches the mapping grid. To minimise the overall distortion, a scale factor of 0.9996 is applied, essentially making it a secant projection. This results in projected distances measured along the central meridian being slightly smaller than reality, two lines of true scale at about 180km east and west of the central meridian and then distances measured on the map east and west of these lines of true scale being slightly bigger than reality. The stated scale of an OS map is therefore only exactly true on the two lines of true scale, but the scale error elsewhere is quite small. For instance, the true scale of OS 1:50 000 scale map sheets is actually between 1:49 980 and 1:50 025 depending on easting – a difference of about 20cm in real life in every 50,000cm at the extremities of the map east and west.

More can be read about this projection and the British National Grid Coordinate reference system here: guide-coordinate-systems-great-britain (ordnancesurvey.co.uk)

British National Grid projection