April 19, 2022

How to Make the Earth Flat

Written by: Mackenzie Mills

 

A commonly accepted fact is that the Earth is not flat. Globes portray the Earth in a spherical model, but in reality, Earth is not exactly a sphere either. Earth is a geoid, an irregular and lumpy, roughly ellipsoidal shape that is difficult to map and model in its entirety. Hopefully, the fact that the Earth is not flat is not news to you, but it is an important fact to consider when mapping and modeling any area on Earth. Luckily, Global Mapper and Geographic Calculator from Blue Marble Geographics can help you manage the geodetic characteristics and projection for any GIS or mapping project.

Geodesy is the study and mathematics behind the modeling of Earth. Being a complex science, geodetics is often overlooked by GIS practitioners when creating a map. However, since all maps use some form of projection to compress and stretch the Earth onto a flat surface, the geodesy behind projections and the impacts of different projection methods should be considered when creating any map.

Approximating Earth’s Shape and Flattening it

A calculated ellipsoid model of the Earth is used to approximate the shape of the planet. While we know that the Earth is a smooth ellipsoid shape, a datum, an ellipsoid model tied to the earth at a specific location, works well to map the two-dimensional coordinates of the Earth. In other words, elevation, or height is ignored, and the surface of Earth is modeled by an ellipsoid that is then projected onto a flat surface. 

If you have ever tried to remove an orange peel in one piece, you know that you cannot make something round completely flat without cutting or stretching it. To avoid creating a fragmented map cut into such small sections that nothing is connected, Earth’s surface must be stretched or distorted in order to flatten it into the form of a map. This distortion can affect the size and/or shape of the areas being depicted. Conformal maps retain the true local shape of the features being depicted but distort their size. Equal-area maps take a different approach and distort the shape of the features in order to retain their size relative to one another.

These three world map projections display the data distorted in different ways.

When flattening a rounded area out onto a map, a few common projection methods are used. These methods do not encompass all of the projection options available, they are the basic foundations of many methods and projection variations you may encounter. 

Cylindrical Projection

The very common World Mercator projection is an example of a cylindrical projection. This type of projection is conceptualized by wrapping a flat surface around the ellipsoidal Earth to form a cylinder, and shining an imaginary light from the center of the earth to project the shapes and locations onto the sheet.

Cylindrical can be transverse and oblique depending on how the cylinder intersects with the surface. (Image: “Mercator Projection”)

Cylindrical projections have high levels of distortion further from the standard parallel, where the projection sheet touches the Earth’s shape. In a World Mercator projection, this means increased distortion at the higher and lower latitudes with the most accurately depicted areas along the equator. While the World Mercator map is conformal, and conveniently uses parallel and perpendicular lines to represent all lines of latitude and longitude, it greatly distorts the size of features further from the equator. Other versions of cylindrical projections are equal-area, which distorts the shape of features toward the poles in order to maintain the relative size of features throughout the map.

Three different cylindrical projections are shown with circular area features to illustrate the shape and scale distortion created by the projection type.

The Transverse Mercator projection, a variation on Mercator, uses a standard meridian, or a line of longitude instead of latitude. This cylindrical projection type is commonly used and the basis for smaller area projections like many State Plane Systems in the US and the Universal Transverse Mercator projections that split the Earth into sixty vertically oriented zones.

Conic Projection

A conic projection is created by placing a cone shape over the ellipsoid model of Earth with tangent or secant intersection between the cone and the surface. The lines of latitude where the cone intersects the earth are the standard parallels for the projection. As you might infer, like the cylindrical projection, distortion is lowest around the standard parallels where the projection shape, the cone, touches the Earth’s surface. With the imaginary light source inside Earth again, the features are projected onto the cone shape.

A conic projection can have one or two standard parallels depending on how the cone intersects the model surface. (Image: “Conic Projection: Lambert, Albers and Polyconic”)

Similar to cylindrical projections, conic projections can be conformal or equal-area depending on the details of the projection method and how it is implanted. For example, the Albers Conic is an equal-area projection while the Lambert Conformal Conic is conformal.

Two conic projections are compared. From the reference, circles demonstrate the conformal and equal-area properties of each.

Azimuthal Projection

An azimuthal or planar map projection is created by placing a plane against the model of Earth that it contacts at one single point. A simulated light source from within, behind or represented by Earth as a while, projects the graticule and features onto the map plane. Azimuthal projections vary greatly depending on the position of the imaginary light source but they all retain the direction from the origin point to any location on the map.

Derived from projecting the graticule onto a plane, an azimuthal projection is centered on a single origin point. (Image: Albrecht)

Wide-ranging in shape and size, maps using azimuthal projection can display large or small areas of the earth. In addition to being azimuthal, these projections can also be conformal and equal-area. 

Azimuthal projections are centered on an origin point and maintain the relative direction from the origin to any point on the map.

While the projection types discussed here are the basic implementations of these concepts, many different map projection methods are used to depict the world and features around us. Considered in the context of a world map, any of the demonstrated projections can be scaled down and centered on a local area for a more accurate depiction of a particular study area. Global Mapper alone supports many different projections with methods to reproject data easily through the workspace configuration dialog, but if geodetic accuracy and fine control over the transformations used to change map view is important in your work, consider incorporating Geographic Calculator into your workflow. 

Check out how your data looks in Global Mapper, and how it can be transformed with Geographic Calculator by downloading a 14-day free trial of either program today. If this blog has piqued your interest in geodesy and you would like to learn more, sign up for Blue Marble’s upcoming Applied Geodesy and Geographic Calculator hands-on training class. 

 

Resources: 

Albrecht, Jochen. The Effect of the Light Source on the Projection Plane, City University of New York, http://www.geo.hunter.cuny.edu/~jochen/gtech201/lectures/lec6concepts/Map%20coordinate%20systems/Perspective.htm. 

“Conic Projection: Lambert, Albers and Polyconic.” GIS Geography, GIS Geography, 29 Oct. 2021, https://gisgeography.com/conic-projection-lambert-albers-polyconic/. 

“Mercator Projection.” Encyclopædia Britannica, Encyclopædia Britannica, Inc., 11 Sept. 2018, https://www.britannica.com/science/Mercator-projection. 

 

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