Why Do Airplane Routes Appear Curved?
Have you ever noticed that airplane routes on a map often appear curved? This isn’t an illusion, nor is it due to artistic liberty in map-making. These curves are the result of a fundamental mathematical concept: the geodesic. In this article, we’ll explore what geodesics are, why they are important, and how they affect our everyday lives—from planning airplane routes to understanding the universe itself.
WHAT IS A GEODESIC?
A geodesic is the shortest path between two points on a curved surface. While on a flat plane the geodesic is simply a straight line, things become more complex when the surface is curved. On a sphere, such as the Earth, a geodesic is represented by an arc of a great circle. A great circle is any circle that divides a sphere into two equal halves, such as the equator or the meridians passing through the poles.
For example, consider traveling between New York and London. On a flat map, the shortest route seems to be a straight line across the Atlantic. However, because the Earth is spherical, the true shortest path—the geodesic—is an arc that curves northward, often passing near Greenland. This is why airplane routes between distant cities can appear curved on a two-dimensional map.
WHY ARE THE IMPORTANT?
Geodesics are essential in various fields, including:
Navigation:
Ships, airplanes, and even satellites rely on geodesics to determine the most efficient routes. By following geodesics, these vehicles minimize distance traveled, saving time, fuel, and resources.Physics:
In Einstein’s theory of general relativity, geodesics describe how objects move through the curved fabric of spacetime. For instance, planets orbiting the Sun are actually following geodesic paths in the Sun’s gravitational field.Architecture and Engineering:
Geodesics are used to design efficient structures and paths on curved surfaces. From geodesic domes to optimal pipeline layouts, this concept has practical applications in many industries.Geodesy:
The science of measuring and representing the Earth’s surface relies heavily on geodesics to ensure accuracy in mapping, land surveying, and GPS technology.
EXAMPLE
A Practical Example: Flying from New York to London
Let’s consider a transatlantic flight from New York to London. On a standard two-dimensional map, the shortest route seems to be a straight line directly across the Atlantic. However, if pilots were to follow that straight line, they would actually be flying a longer route due to the Earth’s curvature.
Instead, airplanes follow a geodesic: an arc that curves toward the north, often passing near Canada and Greenland. This path is shorter in three-dimensional space, even though it looks curved when projected onto a flat map.
Why does this happen? The Earth’s spherical shape means distances behave differently than they do on a flat plane. A straight line on a map is rarely the shortest path in reality. Great circle routes, or geodesics, take into account the curvature of the Earth, allowing airlines to save precious time and fuel.
conclusion
Geodesics teach us to think beyond flat, two-dimensional perspectives. They reveal the beauty of curved surfaces and their implications for navigation, science, and everyday life. So, the next time you see an airplane route curving on a map, remember that you’re witnessing the magic of geodesics—the shortest path on a curved surface.
Want to dive deeper into the science behind geodesics and how they shape our world? Check out my video on YouTube here: LINK
