The effect of Earth's Roatation on Flight

[alon]

I was wondering what the effect of the Earth's rotation is on the time of long flights.

most people I've talked to claim that the Earth's rotation has no effect at all and that the most important thing is the winds.

However, let me ask this question:

suppose we floating in the air somehow. the only force acting upon us is that of the air around us, which do to friction is rotating with earth. It is well known that by applying a small force (by using a small fan, for example), I can resist that force at the very least and even produce a greater force.

My question: taking all of the above into consideration and assuming my fan is applying an equal and opposite force to the force applied by the air, will I be on the other side of the Earth is I maintain my status for 12 hours?

Thanks,
Alon

 

[KingNothing]

It definitely has an effect! In flight school, you do learn about it. It is called the Coriolis effect. If you look at international flight paths, most of them are parabolic rather than direct to the destination. This is because they take into account the rotation of the earth.

I don't quite understand your question about the fan.

 

[alon]

Thanks for your answer.

Let me clarify my question. Is it possible for me, assuming I can somehow float in the air, without moving, to travel around the earth, simply by waiting for the Earth to rotate?

 

[KingNothing]

Without moving relative to the air - yes. The air doesn't rotate as fast as the earth.

If you could float within a single air pocket and stick with it for a day or two, sure. But the wind patterns may take you places you don't expect!

 

[Filip Larsen]

It definitely has an effect! In flight school, you do learn about it. It is called the Coriolis effect. If you look at international flight paths, most of them are parabolic rather than direct to the destination. This is because they take into account the rotation of the earth.

I think you have gotten things mixed up a bit.

First, the Coriolis effect on an airplane does not have any significant effect on normal subsonic flights and is not something the crew would care about - the Coriolis effect is by far overshadowed by local wind effects. However, the Coriolis effect is significant when you want to understand the principles of weather systems in general or if you, as an aerospace engineer, want to calculate trajectories for (long range) ballistic missiles.

Secondly, "international flight paths" are not parabolic. I guess you are referring to flight paths when viewed on a flat map often seem to go in a curve from A to B instead of a straight line. This curve is really (as far as airspace structure allows) the shortest distance between A and B as viewed on a globe and using such paths for navigation is generally called Great Circle Navigation since the plane would follow a great circle.

 

[alon]

KingNothing:

So let's assume that I am in air pocket. When no winds are present, it should take me 12 hours to reach the other side of the planet. Why then is the flight time of planes, which are moving extremely fast, is also about 12-14 hours when traveling such a distance?

 

[Filip Larsen]

Let me clarify my question. Is it possible for me, assuming I can somehow float in the air, without moving, to travel around the earth, simply by waiting for the Earth to rotate?

The rotation of Earth indirectly makes the air mass circulate of most of the Earths surface, so if you are prepared to wait for a potentially very long time, then, yes, you should be able to "travel" anywhere you like. If you are able to change height you could even utilize that the air mass in different heights are going in (slightly) different directions to more actively control where you go. This is how long range balloons controls their flight path.

 

[Filip Larsen]

So let's assume that I am in air pocket. When no winds are present, it should take me 12 hours to reach the other side of the planet.

No, wind is defined as having the air move relative to the ground (surface of Earth), so if there is no wind the air just rotates along with the surface and you would not leave the spot you hoover above.

And even if there is wind, its has nothing to do with the air "trying to stop rotating". A particle that moves (slowly) near the surface of the Earth will only feel very small effects from the fictitious forces and none of these will try to "stop" or "brake" the particle as viewed from a non-rotating system.

 

[Lsos]

suppose we floating in the air somehow. the only force acting upon us is that of the air around us, which do to friction is rotating with earth. It is well known that by applying a small force (by using a small fan, for example), I can resist that force at the very least and even produce a greater force.

I understand that you want to use a "fan" to resist the force of the air and kind of hover in place while the Earth rotates underneath you.

No.

It takes a small force to resist slow air movement, but the force rises exponentially with speed. At the equator, you would need to resist air moving at about 1000mph in order to "sit still" above the earth. Resisting the force of a 1000mph wind while hovering takes the same amount of power as flying at 1000mph. Just for reference, a 747 jet uses something like 80,000 horsepower to perform this task, but at only around half the speed. The power required rises as a cubed function of speed.

So, perhaps yes you could use a fan to do what you mentioned, but it would not be a "small fan", and it would probably need hundreds of thousands of horsepower.

But my understanding is that even that would probably not work, as the physics of aerodynamics at supersonic speeds are somewhat different.

 

[alon]

Thanks guys.

Filip: if the air moves with the surface, then why should I move with it? I would not move with the surface and therefore be able to travel utilizing the Earth's rotation.


Lsos: Good comment. Indeed the friction will increase with speed. Thanks.

 

[cjl]

Filip: if the air moves with the surface, then why should I move with it?

You move with the air because the air pushes on you. There's no real fundamental difference between moving air over a stationary object and a moving object through stationary air, and in both cases, the object will feel a force which will try to slow down the object's relative speed through the air. You can push back of course, but as has been pointed out, that's effectively what airplanes are already doing, and it's far from trivial. In addition, there's nothing inherent about flying against the Earth's rotation - it's exactly as easy to fly in either direction with the same speed relative to the air. All that matters from the airplane's perspective is how fast the air is moving relative to the plane, not how fast (or in which direction) the Earth is spinning.

 

[alon]

You are right. But for the same conditions and speed of flight, moving against the direction of the Earth's rotation will result in a larger distance traveled.

 

[Janus]

Thanks guys.

Filip: if the air moves with the surface, then why should I move with it? I would not move with the surface and therefore be able to travel utilizing the Earth's rotation.

You would move with it because you are already moving with it. Even if you remove the air from the equation, Lifting yourself from the surface of the Earth will not change your velocity with respect to the surface. If you are standing at the equator, the Earth is moving West to East at ~1000 mph So are you. Inertia will cause you to remain moving West to East at ~1000 mph even if you were to lift your feet off of the surface. To change this you would have to apply a force opposite to this velocity in order to stop your West-East motion. Only then would the Earth "turn beneath you".

 

[Cleonis]

I was wondering what the effect of the Earth's rotation is on the time of long flights.
[...]
suppose we floating in the air somehow. the only force acting upon us is that of the air around us, which due to friction is rotating with earth.
[...]

About the atmosphere:
The atmosphere as a whole has been co-rotating with the Earth ever since the Earth first formed. The reason the Earth's atmosphere hasn't stopped co-rotating with the Earth is that objects tend to keep their existing velocity (inertia).

If you circumnavigate the Earth (along the equator) in westward direction you are counter-circumnavigating. ('Counter-circumnavigating' in the sense that the westward journey proceeds in counter-direction to the Earth's rotation.)
Circumnavigating in eastward direction is then 'co-circumnavigating'.

Let's say an aircraft takes to the sky at noon, local time. So the sun is directly overhead. As you have pointed out, if the aircraft then starts a counter-circumnavigating journey that is fast enough to go around the Earth in 24 hours, then thoughout that journey the Sun will be directly overhead.

For simplicity we assume the atmosphere is motionless; we think of the atmosphere as perfectly co-rotating with the Earth.
Then for a counter-circumnavigating journey and a co-circumnavigating journey the same velocity relative to the atmosphere is required.

In that sense it won't make a difference whether it's counter-circumnavigating flight or co-circumnavigating flight; the amount of effort required to sustain velocity relative to the atmosphere will be the same.However, there is another thing that will be different.
Objects located on the equator (co-rotating with the Earth) weigh less than their weight at the poles. The reason for that is that for the equatorial co-rotating motion centripetal force is required. On the equator some of the Earth's gravity goes up in providing that required centripetal force. It's a very small difference, though; less than 1 percent.

An aircraft in counter-circumnavigating flight is in a sense "hovering" in the same position; an aircraft in counter-circumnavigating flight is in a sense "staying in one position", with the Earth rotating underneath it.
This means that an aircraft in counter-circumnavigating flight will weigh slightly more.
Conversely, the co-circumnavigating aircraft is going around the Earth twice as fast as co-rotating motion, so twice as much centripetal force is required. [Later edit: as willem2 has pointed out in post #15, it's actually 4 times as much centripetal force required.] Therefore an aircraft in co-circumnavigating motion will weigh slightly less.

As I said, it amounts to less than a percent, so under normal circumstances the difference is negligable
But if you ask specifically: the counter-circumnavigating aircraft will need slightly more lift force, because it has more weight. The co-circumnavigating aircraft will need slightly less lift force.

The more lift force you need to generate, the more fuel you will consume. So overall for the counter-circumnavigating aircraft a bit more effort will be needed than for the co-circumnavigating aircraft.

So there is a rotation-of-earth-Effect after all, and it's unfavorable to fly against the Earth's rotation direction.

 

[willem2]

Conversely, the co-circumnavigating aircraft is going around the Earth twice as fast as co-rotating motion, so twice as much centripetal force is required.

4 times as much actually.The centripetal acceleration $\Omega^2 r$

 

[sophiecentaur]

It definitely has an effect! In flight school, you do learn about it. It is called the Coriolis effect. If you look at international flight paths, most of them are parabolic rather than direct to the destination. This is because they take into account the rotation of the earth.

I don't quite understand your question about the fan.

Flight paths are normally Great Circle Paths because a great circle is the shortest distance between points on a sphere. OR were you referring to a modification of the Great Circle Paths to compensate for Coriolis? It is true that, on a long haul journey, the Earth will have rotated a fair way and a North - South course could be affected by Coriolis force if it weren't for the atmosphere, which will provide a much more dominant set of forces.

If you look at the path of a polar orbiting satellite over the Earth's surface, that can be interpreted as having a coriolis component (About 20minutes from equator to pole and the Earth would have rotated by around 5 degrees) but that shows that it's only Geometry at work, really.

 

[cjl]

It definitely has an effect! In flight school, you do learn about it. It is called the Coriolis effect. If you look at international flight paths, most of them are parabolic rather than direct to the destination. This is because they take into account the rotation of the earth.

I don't quite understand your question about the fan.

The reason the flights are curved (as shown on a standard map) has nothing to do with coriolis, and everything to do with the fact that the Earth isn't flat. This can be seen very quickly with a piece of string and a globe.

 

[sophiecentaur]

If you wanted your satellite to orbit exactly over the Greewich Meridian, you'd need to keep pushing it to the left all the time as you approached the North Pole and to the right as you left it down the 180 degree longitude line. That's what the Coriolis 'force' is all about. The value of it in the context of a flying aircraft will be small and anyone who wants to claim that it is significant would really have to calculate it and put it in the context of all the other forces at work. It's up to You, whoever it was who is saying it is significant. (It's very doable but I can't be naffed)

Edit: Correction about the actual direction of force needed: It is always to the left when in the northern hemisphere and to the right in the southern hemisphere.

Also see this link http://elibrary.unm.edu/sora/Auk/v097n01/p0099-p0117.pdf" which discusses the coriolis force and bird navigation - it calculates the force to be pretty small but measurable.

 

[Gaute Huus]

The fan needed would probably blow your face spacewards long before the Earth had made it's full rotation.

Maybe, however, you could sit within a capsule thick enough to withstand the air produced by the fan, so that you would not be "blown" to pieces. I'm not sure if this would work though - maybe someone else could make a comment on that.

- Gaute Huus