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Distance Formula

Using the Pythagorean Theorem to determine distances

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Going the Distance

Credit: Cristiano Betta
Source: http://www.flickr.com/photos/cristiano_betta/2870563171/

Have you ever looked at a map of flight routes? You’ll find that most flight paths are curved. Since the shortest distance between two points is a straight line, why don’t airplanes fly in a straight line to save time and fuel?

Planes and Spheres

The distance formula calculates the distance between two points on a plane—that is, on a flat surface. Maps depict the surface of the Earth as a plane. However, in real life, we live on the surface of a sphere. To find the shortest distance between two points on Earth, navigators must calculate distances along a great circle. A great circle on Earth has its center at the Earth’s core and its edge on the surface of the Earth. There are an infinite number of great circles on a sphere. The shortest distance between two points on Earth always falls along the edge of a great circle. This is why, for instance, the shortest route between Istanbul, Turkey and Los Angeles, California involves flying north over Greenland.

Credit: Pacific Marine Environmental Laboratory/NOAA
Source: http://commons.wikimedia.org/wiki/File:Noaa3-2006-0602-1206.jpg

For some airplane flights, the shortest distance between two cities lies over the North Pole. Flying directly over the pole cuts flight times and saves fuel. For instance, polar routes cut five hours from a flight from New York City to Hong Kong. However, these polar flights come with a risk. Radiation from space bombards the Earth every day. At the poles, the Earth’s magnetic field is weaker and does not offer protection from this radiation. On a typical polar flight, passengers receive 12% of the annual maximum radiation dose. While most people don’t fly frequently enough to experience adverse health effects from polar flights, pilots and flight crews face a serious risk. The average pilot on these flights encounters more radiation while working than an employee of a nuclear power plant.

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