# Airplane travel questions

musicgold
Hi,

Can someone please help me understand these two situations?

1. When an airplane is flying from point A to point B, is Earth stationary from the point of view of the plane? While I am not sure, I think the answer to this question is yes, because a plane flies within the atmosphere of Earth and these atmospheric layers must be rotating at the same speed as Earth. Is that correct?

2. Is it possible to take advantage of Earth's rotation (about 1000 miles per hour) to travel from point A to point B? Why can't we create a rocketship that launches from point A on Earth, goes into the outer space in a straight line, stays there until point B is underneath it (due to Earth's rotation) and then comes down?

Thanks.

## Answers and Replies

tfr000
1. When an airplane is flying from point A to point B, is Earth stationary from the point of view of the plane?
Yes, for the reasons you stated.
2. Is it possible to take advantage of Earth's rotation (about 1000 miles per hour) to travel from point A to point B? Why can't we create a rocketship that launches from point A on Earth, goes into the outer space in a straight line, stays there until point B is underneath it (due to Earth's rotation) and then comes down?
We cannot, because the rocket will have the motion of the Earth as you launch it. In fact, this is used to advantage in getting payloads into orbit - they are usually launched to the east, so that the velocity of Earth's rotation adds to the velocity produced by the rocket.

Feinman
Answer may apply to older problem. Heavy planes (like the raid on Tokyo WWII) could take off from aircraft carriers because the speed of the ship was added to the speed of the plane. I think that's similar.

Mentor
1. When an airplane is flying from point A to point B, is Earth stationary from the point of view of the plane?
"Stationary" is a pretty arbitrary concept; We get to decide what we want to call "stationary". For simplicity, when we are sitting on Earth we call that "stationary". When we leave Earth in a plane, we change our frame of reference, but the earth-centered frame we leave is still "stationary".

Science Advisor
Homework Helper
If you want to navigate to a specific destination point, the easiest way to do that is work relative to the earth, which is the same as pretending the Earth is "stationary".

Since the atmosphere rotates at approximately the same speed as the Earth (apart from the wind speed which is usually much less than 1000 mph), and the aerodynamics of the plane is relative to the air it is flying through, again that gives no reason NOT to measure things relative to the earth. Of course that does not apply to space travel outside the atmosphere.

Heavy planes (like the raid on Tokyo WWII) could take off from aircraft carriers because the speed of the ship was added to the speed of the plane.
That's not quite right. You sail the carrier into the wind, to maximize the wind speed over the flight deck and therefore create the lowest takeoff speed and landing speed relative to the ship, not relative to the Earth (or sea).

musicgold
We cannot, because the rocket will have the motion of the Earth as you launch it. In fact, this is used to advantage in getting payloads into orbit - they are usually launched to the east, so that the velocity of Earth's rotation adds to the velocity produced by the rocket.

Okay. Is the direction in which the rocket goes that important? As long as we are able to get out of Earth's atmosphere and hover at one point for some time and come back in when the specific point on Earth is nearby, it should work, right?

Staff Emeritus
Science Advisor
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Okay. Is the direction in which the rocket goes that important? As long as we are able to get out of Earth's atmosphere and hover at one point for some time and come back in when the specific point on Earth is nearby, it should work, right?

Yes, it's vitally important. Rockets are launched in an easterly direction, since that is the direction in which the Earth rotates. As a result, the velocity the rocket requires to achieve orbit is reduced somewhat. If rockets were launched in a westerly direction, this velocity reduction would not be available, and the rocket would in fact have to achieve a greater velocity to enter orbit.

1 person
Gold Member
the velocity the rocket requires to achieve orbit is reduced somewhat.
No.It is not.The velocity required is same but the velocity WE give to the rocket is reduced somewhat.

Gold Member
Why can't we create a rocketship that launches from point A on Earth, goes into the outer space in a straight line, stays there until point B is underneath it (due to Earth's rotation) and then comes down?

Okay. Is the direction in which the rocket goes that important?

It would be, if you have a definite destination in mind. (point B)

Yes, it's vitally important. Rockets are launched in an easterly direction, since that is the direction in which the Earth rotates. As a result, the velocity the rocket requires to achieve orbit is reduced somewhat. If rockets were launched in a westerly direction, this velocity reduction would not be available, and the rocket would in fact have to achieve a greater velocity to enter orbit.

But OP isn't about orbit. Question was about going in a straight line and coming down at point B. Everything except the "stays there until point B" part is reasonably accomplished. Launching to the east is only beneficial for reaching latitudinal orbit. Here in the U.S., all polar orbit launches originate at Vandenberg AFB (California) and launched westerly.

So a rocket can benefit from 'least distance' flight path just as well as airplanes benefit from flying polar routes. This may not be exactly what the OP was expecting, but keeps in the spirit of the exercise.

Gold Member
It would be, if you have a definite destination in mind. (point B)

But OP isn't about orbit. Question was about going in a straight line and coming down at point B. Everything except the "stays there until point B" part is reasonably accomplished. Launching to the east is only beneficial for reaching latitudinal orbit. Here in the U.S., all polar orbit launches originate at Vandenberg AFB (California) and launched westerly.

So a rocket can benefit from 'least distance' flight path just as well as airplanes benefit from flying polar routes. This may not be exactly what the OP was expecting, but keeps in the spirit of the exercise.
The OP was talking about launching a rocket up at point B and stay there until Earth rotates and B is below the rocket.I think this is more expensive and risky than just an aeroplane travelling.

1 person
Gold Member
The OP was talking about launching a rocket up at point B and stay there until Earth rotates and B is below the rocket.I think this is more expensive and risky than just an aeroplane travelling.

I think expense and risk are eclipsed by the "how" are you going to "stay there". That's why I mentioned that as the exception. However the rocket can be launched in a straight line, and it does have a 'zero moment' at the peak of its trajectory, and it can leverage the Coriolis effect to take advantage of Earth's rotational speed.

Any advantage, of course, would depend on points A and B. E.g., you could never get rotational advantage traveling from the north pole to the south pole.

1 person
Science Advisor
When an airplane is flying from point A to point B, is Earth stationary from the point of view of the plane?
Of course not. How would the plane get from A to B, if there was no relative movement between plane and Earth?

Is it possible to take advantage of Earth's rotation (about 1000 miles per hour) to travel from point A to point B?
Yes, if you travel fast enough relative to Earth, there is a apparent weight reduction, so you save some fuel. But the effect is negligible and when you fly back the same way, it is reversed. See Fig. 5 of this paper:
http://naca.central.cranfield.ac.uk/reports/arc/rm/3680.pdf

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1 person
Science Advisor
Gold Member
Okay. Is the direction in which the rocket goes that important? As long as we are able to get out of Earth's atmosphere and hover at one point for some time and come back in when the specific point on Earth is nearby, it should work, right?

How did you envisage doing that? To stay up there you need to be in an orbit or use an unthinkable amount of energy. To 'hover' over a particular spot (over the equator, only) you would need a geostationary orbit which is 30,000+km.

1 person
musicgold
Thanks folks.
How did you envisage doing that? To stay up there you need to be in an orbit or use an unthinkable amount of energy. To 'hover' over a particular spot (over the equator, only) you would need a geostationary orbit which is 30,000+km.

Hmm...I didn't think about this. Now it is clear to me. Thanks a lot folks.

voko
2. Is it possible to take advantage of Earth's rotation (about 1000 miles per hour) to travel from point A to point B?

Yes, and this has been done for centuries, if not millennia. Google "trade winds".

Today, this is seen in airline timetables: flights from North America to Europe are about one hour shorter than the other way around.

Science Advisor
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Everyone who sails a boat is making use of the Earth's rotation, too. It's the Coriolis force that provides the high speed winds in the vortices we call depressions and cyclones.

Science Advisor
Everyone who sails a boat is making use of the Earth's rotation, too. It's the Coriolis force that provides the high speed winds in the vortices we call depressions and cyclones.
It's not like there would be less wind, if the Earth didn't rotate. At high altitudes it would probably be even faster.

dauto
Everyone who sails a boat is making use of the Earth's rotation, too. It's the Coriolis force that provides the high speed winds in the vortices we call depressions and cyclones.

The Coriolis doesn't produce any winds. The Coriolis force is always perpendicular to the direction of motion of the wind so it does no work. It's the pressure gradient force that does the work on the atmosphere that produces the winds.

voko
It's not like there would be less wind, if the Earth didn't rotate. At high altitudes it would probably be even faster.

Would they still have a longitudinal component?

The Coriolis doesn't produce any winds. The Coriolis force is always perpendicular to the direction of motion of the wind so it does no work. It's the pressure gradient force that does the work on the atmosphere that produces the winds.

Explain how the pressure gradient makes the Clipper Route possible.

Science Advisor
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The Coriolis doesn't produce any winds. The Coriolis force is always perpendicular to the direction of motion of the wind so it does no work. It's the pressure gradient force that does the work on the atmosphere that produces the winds.

You didn't read what I wrote. The coriolis force introduces vortices into what would be smoother flowing convection currents. Depressions are there because of the coriolis force. When vortices are introduced into a smooth flowing fluid, we find regions of higher (and regions of lower) speeds. That's why designers of planes, boats, cars and turbines try to suppress the formation of vortices.

Aamof, I am pretty sure that a spinning planet with an atmosphere but no source of radiation (a nonsense scenario, I know, as any fluid would freeze) would still have circulating currents and shear movements in its upper atmosphere. These would end up affecting the whole atmosphere and the combination of centrifugal and coriolis forces would be producing winds.

Science Advisor
It's not like there would be less wind, if the Earth didn't rotate. At high altitudes it would probably be even faster.
Would they still have a longitudinal component?
Define "longitudinal" for a non spinning planet.

Science Advisor
I am pretty sure that a spinning planet with an atmosphere but no source of radiation (a nonsense scenario, I know, as any fluid would freeze) would still have circulating currents and shear movements in its upper atmosphere. These would end up affecting the whole atmosphere and the combination of centrifugal and coriolis forces would be producing winds.
What would drive those circulating currents and shear movements in its upper atmosphere?

voko
Define "longitudinal" for a non spinning planet.

If the planet has no spin "about itself", it is still revolving about its Sun. So the straight line through the center of the planet orthogonal to the orbital plane can be considered the North-South line, and everything else follows.

But that answers my question, I think. The part of the planet facing the Sun would be hottest at the spot closest to the Sun, which should generate an upward stream there, with colder air drawn from all the directions radial to that spot, so, yes, that would have "longitudinal" components except at the poles. But the pattern of prevailing winds will be markedly different, and, locally, it would change significantly in the course of the year.

Science Advisor
Gold Member
It's not like there would be less wind, if the Earth didn't rotate. At high altitudes it would probably be even faster.

Not a lot of help for sailors lol.

Science Advisor
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This thread has done an interesting morph from the OP content.

But for the rotation of the planet, the weather would be pretty much predictable with massive extremes of temperature (viz Mercury) and, with a 365 (366?) day 'day', evolution would have taken us down a very different route. There would, of course, have to be no moon or that would have got us spinning, albeit rather slowly.

Science Advisor
Not a lot of help for sailors lol.
There would still be wind at the surface without rotation, just different patterns. Saying that using wind power (e.g. sailing) is "using the Earth's rotation" is IMHO misleading.

What is even more puzzling to me is your claim, that there would be wind without the sun, purely due to rotation. How would the combination of centrifugal and Coriolis forces produce winds?

Gold Member
To 'hover' over a particular spot (over the equator, only) you would need a geostationary orbit which is 30,000+km.

That's not what the OP is about. It's about traveling from point A to point B. A geostationary orbit would go nowhere. OTOH, hovering while the Earth rotates below (what the OP asked about) is a relative view from the rocket's perspective. From the Earth POV, the rocket is traveling. So there's no need to 'hover' to gain advantage of Coriolis on a rocket path when the route provides for that. Just plot a straight line trajectory to where point B will have rotated to at end of flight.

Science Advisor
Gold Member
There would still be wind at the surface without rotation, just different patterns. Saying that using wind power (e.g. sailing) is "using the Earth's rotation" is IMHO misleading.

What is even more puzzling to me is your claim, that there would be wind without the sun, purely due to rotation. How would the combination of centrifugal and Coriolis forces produce winds?

A fair question but my reasoning is to do with what goes on at extreme distances where 'orbital' forces start to be relevant. An object that's not going round above and parallel the equator will take up an orbit in a plane that's inclined to the equatorial plane. At an altitude well below the geostationary orbit, this would be a subtle effect as the g attraction is way more than the necessary centripetal force for a 24 hour orbit at a few hundred miles but there is still a finite effect. The same could reasonably be assumed to apply to air molecules. Doesn't this provide a reason for shear movements in the very low density layers? The orbital forces are not 'stratified' the same as the gravitational forces / air pressure. I might be convinced that some equilibrium situation could obtain but it looks to me that it is not an equilibrium situation.

Also, I was not implying (and definitely did not write) that sailing is using the Earth's rotation alone, just that the rotation / coriolis effect modifies the normal convectional (N-S) winds in a useful way. It increases the maximum wind speed and, usefully, causes the direction to vary so that you have a chance of going in any direction (as long as you are prepared to wait for a depression to shift.

voko
Saying that using wind power (e.g. sailing) is "using the Earth's rotation" is IMHO misleading.

That was not said here. The question was "Is it possible to take advantage of Earth's rotation (about 1000 miles per hour) to travel from point A to point B?"

And the answer is definitely yes. Our aerial and sea routes do just that.

Science Advisor
A fair question but my reasoning is to do with what goes on at extreme distances where 'orbital' forces start to be relevant.
What are "orbital forces"? In the rotating rest frame of the planet there are:
Gravity + Centrifugal : a conservative field that adds no energy to the atmosphere
Coriolis : acts perpendicular to movement, so also adds no energy to the atmosphere

I see nothing in here that would prevent a static pressure distribution, with the atmosphere at rest w.r.t the planet.

Science Advisor
Gold Member
So it would be sufficient for the atmosphere just to have an equatorial bulge? I guess I could buy that. I imagined that some other factor must be there. But the reference frame argument sort of clinches it.