What is an example of a curved flight path being shorter than a straight line?

Question

I need to know a flight that is curved, say so it goes around the north pole, to be quicker than a "straight line".

Answer 1

I guess the confusion arises because of maps used. The map's map the 3D structure of the earth to a 2D flat sheet and it would appear that the straight line is the obvious answer.

You can verify it yourself. Take a soccer ball and mark two points anywhere on its surface. Try connecting these two points and you will find that the shortest path is the curved line called the great circle (the plane of the great circle passes through the center of the sphere, here it is earth). Now if you are mathematically curious, try mapping these points using some cordinate system, from 3D to 2D and you will see that the shortest distance between two points on the surface of the earth is a curve. Intrestingly, if you draw a straight line between these two points in the above mentioned 2D coordinates and map them accordingly in a 3D sphere, you will find that the "straight line" is actually longer!

Answer 2

Technically all flights are curved since the Earth is curved. But what I think you are asking is that, for example, on a flight from San Francisco to Tokyo, why do they fly so far North instead of going due West? The answer is that that is the shortest distance. You can see this for yourself with a globe and a piece of string. Hold the string tight against the globe with one finger on San Francisco, and one finger on Tokyo and you will see that the shortest route goes up over the Aleutian islands in Alaska. The string shows you what is called the "Great Circle" route between those points.

Answer 3

Here's a good example of a "polar route" between two distant points lying at roughly the same latitude. Find a globe and stretch a string from San Francisco, California, USA, to Athens, Greece. Surprisingly, you will see that near the mid-point of the flight, the string will pass over Greenland above the Arctic Circle! Notice also that your initial heading upon departing San Francisco will be north of northeast!

If you were to fly between these two cities by flying straight east on about the 38th parallel, your trip would cover a much greater distance.

Answer 4

A straight flight is always shorter than a curved flight because of simple logic.

However, a straight line between two destinations on the earth cannot be achieved by a constant heading unless it is along the equator or directly north or south. This is why on maps flight paths appear curved, even though in reality they are straight. These are called great circle routes.

If you fly a constant heading, your flight path will be curved and a longer distance to the destination.

Try connecting Los Angeles to London with the ruler on Google Earth. Looking from above the mid-point of the ruler line it will be straight, but you will see that it will go north from LA and then turn south as it approaches London.

Answer 5

The path you are thinking of is called a "great circle" it is the shortest distance between two points on a sphere. It is hard to describe how it is generated in this small a space. You should be able to get more detail from Googling "great circle or maybe navigation.
Cheers

Answer 6

Not possible.... shortest distance between two points is a straight line unless you're talking about warping space travel. Quicker may be achieved if you don't encounter headwinds on some course versus headwinds on another but that would be the exception, timewise.

Answer 7

when you fly from the USA to japan. you don't fly straight to japan. you fly the global arc. you fly up and over is shorter than flying straight.