An azimuthal projection is a way to draw Earth on a flat circular map from the viewpoint of one chosen point. Imagine a flat sheet touching a globe at the North Pole, South Pole, or any other location, then projecting the globe onto that sheet. This idea matters because every flat map distorts Earth, and azimuthal maps make some directions or distances especially useful from the center point.
They are common in polar maps, airline route planning, radio communication maps, and world maps centered on a city or pole.
The point where the plane touches the globe is called the point of tangency, and it is the place where distortion is usually smallest. As locations get farther from that point, shapes, areas, distances, or directions become more distorted depending on the exact type of azimuthal projection. In an azimuthal equidistant projection, distances from the center are shown correctly, which makes it useful for measuring how far places are from one central location.
In a stereographic or orthographic azimuthal projection, the map may better show appearance or geometry, but it still cannot preserve everything at once.
Key Facts
- Azimuthal projections map Earth onto a flat plane that touches or cuts through the globe at a chosen center point.
- The center point has the least distortion, and distortion generally increases with distance from the center.
- On all azimuthal projections, directions from the center point to other locations are shown correctly.
- Azimuthal equidistant projection: distance from the center to any point on the map is correct.
- Great-circle routes appear as straight lines only in some projection cases, not in all azimuthal maps.
- No flat map can preserve area, shape, distance, and direction everywhere at the same time.
Vocabulary
- Azimuth
- An azimuth is a direction measured as an angle clockwise from north, such as 90 degrees for east.
- Azimuthal projection
- An azimuthal projection is a map projection that shows the globe on a flat plane centered on one point.
- Point of tangency
- The point of tangency is the location where the projection plane touches the globe.
- Distortion
- Distortion is the change in size, shape, distance, direction, or area that happens when Earth is drawn on a flat map.
- Great circle
- A great circle is the largest possible circle around a sphere and represents the shortest route between two points on Earth.
Common Mistakes to Avoid
- Assuming an azimuthal map is accurate everywhere is wrong because accuracy is greatest near the center and usually decreases outward.
- Reading every straight line as the shortest path is wrong because straight lines do not always represent great-circle routes on every azimuthal projection.
- Using a polar azimuthal map to compare land area near the edge is wrong because outer regions can be strongly stretched or compressed.
- Forgetting to identify the center point is wrong because the projection's useful directions and distances depend on where the map is centered.
Practice Questions
- 1 A polar azimuthal equidistant map is centered on the North Pole. If a city is 3,200 km from the North Pole, how far from the center should it be shown on the map using a scale of 1 cm = 800 km?
- 2 An azimuthal equidistant map is centered on Chicago. City A is 1,500 km from Chicago and City B is 4,500 km from Chicago. Using a scale of 1 cm = 500 km, how far from the map center should each city be plotted?
- 3 A student wants a map that shows accurate directions from Tokyo to many cities around the world. Explain why an azimuthal projection centered on Tokyo would be a good choice, and describe one kind of distortion the student should expect far from Tokyo.