Is it straight or arched?

Question

In a long-haul, non-stop flight across the globe and with its altitude kept constant, is the plane's trajectory straight or curved, geometrically speaking?

Answer 1

altitude above land or sea level?

If you're talking about keeping your altitude above sea level constant, your path is neither straight nor arched.

but otherwise, why are you asking? how could it be straight?

Answer 2

I think any flight which is oriented by altitude would necessarily be a curved path.
I know of no method of orientation which would result in a straight line, in either the 2 dimensional or 3 dimensional sense. In the 2 dimensions, wind and correction for wind would keep the line from being perfectly straight, though GPS Global Positioning comes as close as possible. GPS could have made it possible for straight line in the 3 dimensional way, but those units designed for pilots which give an altitude readout have been designed to make it a curved path, because that is what the pilots want and need. Their concern is with terrain clearance and air traffic clearance. Planes flying on headings of 0 to 179 degrees fly at an odd altitude (3, 5, 7, 9, 11, or 13,000 feet if on Instruments and plus 500 feet if on Visual References) this is for traffic separation. Above a certain altitude all the flights are Instrument and the altitudes are assign by Air Traffic control.

Answer 3

If you're maintaining a constant altitude above a curved surface (the globe) you will definitely be flying an arced path.
Most flight routes tend to curve to keep the planes within a reasonable distance from airfields along the course in case of emergency.
When flying point-to-point, it is typically best to maintain a straight course, lineally speaking, but in terms of trajectory, yes, it's arced

Answer 4

The path is curved (or arched) as viewed on a 2-dimensional map. This is called great-circle distance. Because the earth is curved, the shortest distance between two points is not a straight line, it is a curved path called a great-circle route.

The longer the flight, or greater the distance, the more pronounced this curve becomes. This is very apparent in modern times as direct flight is possible over large distances due to GPS and other advanced forms of navigation.

Answer 5

In mathematical terms the flight is always curved. Even a mile of absolutely flat road or runway has a small curvature. The only way you can take a straight route between two points on the earth's surface is if they are both close together and on elevated land with no obstructions between, or by digging a tunnel.

Answer 6

Curved to take a short cut over the globe a straight line is always longer on a globe. Measure it out with a string and see what happens.

Answer 7

In a long distance flight, the route is never a straight line on a 2D plot. If we assume that the Earth is a perfect sphere, the shortest route between two points would be an arch with the same centre as the one of that sphere. If you plot that route on a 2D map it won't be a straing line, but a curve.

Answer 8

If it's relative to the earth's surface (in a 2D system of axis, where the earth is the Ox axis) the plane's trajectory is straight. Otherwise, in a 3D system of axis, where the center of the earth is on the origin of the system, the plane's trajectory is an arch.

This is a longer discussion actually, it really depends on who is its relative and what is the distance traveled. In real life, there's no such thing as a straight trajectory. We only have values that tend to be straight.

Answer 9

generally, the flight path is the shortest possible route, often the "great circle route is the most direct route because it takes into account the curvature of the earth. The further apart the departure and dstination points, the more "curved" the flight path will be

Answer 10

Its curved along with the earth's surface due to projectile motion (i know it starts with a p) or the fact that gravity holds them in its "orbit"