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Author Topic: Why doesn't a glass of water in an aeroplane spill when the airplane turns?  (Read 9849 times)

Konstantin Tretjakov

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Konstantin Tretjakov  asked the Naked Scientists:
   
Dear Chris,

First of all, thanks a lot for your great shows, especially the naked scientists podcast. I'm a reverent fan of it.

In a discussion on an internet forum I've accidentally made a remark regarding the physics inside of an aeroplane, which was met with such violent resistance by nearly all of the other members, that I started doubting my own opinions, despite the fact that the whole thing seemed a rather straightforward matter to me before. Now I really need an authoritative opinion on this question to sleep normally, and your email seemed to be the most authoritative source I could turn to. Even googling did not help!

The problem is the following. Anyone who flies reasonably often can easily observe that no matter how steep the roll angle of an aeroplane is, the tea in your glass always stays parallel to the floor, which seems quite amazing. The question is, how can that be. Is it due to the skill of the (auto-)pilot that must always perform a perfectly banked turn to balance all forces and thus keep the water parallel, or is it a more trivial consequence of aeroplane physics and the only thing the pilot needs to do is not to screw things up by, say, wobbling the tail too much.

My opinion was the latter one, and I attempted two explanations, which were both rejected.

The first explanation referred to the fact, that the only force that can act on the aeroplane, but not on the glass is the lift of the wings. And as this force is always perpendicular to the floor, the glass inside an aeroplane must always have its "weight" vector pointing towards the floor. Basically, for the water to spill, something must push on the side of the aircraft, but there is no source capable of doing that, except perhaps for the air resistance of the fuselage, which I think can be ignored, because it is way smaller than the resistance of the wings. I also assume the pilot avoids abrupt movements of the rudder (which would also push the plane on the sides).

The second attempt to explain the same thing is by referring to a picture, which demonstrates that there are three forces acting on an aeroplane (gravity, centrifugal force due to the turn, lift) and two forces acting on the cup of tea (gravity, centrifugal force). I assume the cup is currently unsupported and ready to fall somewhere. Therefore, the force that will move the cup with respect to the plane is (gravity
centrifugal)-(gravity centrifugal lift) = -lift, which is directed towards the
floor of the plane, not the earth or anywhere else.

It is especially important to note, that the magnitude of the centrifugal force makes no difference, and therefore even if the pilot screws up the turn and makes it with a larger/smaller radius than appropriate, the water will stay parallel to the floor.

Now quite a number of opponents in the discussion stated that both proofs are flawed and it is strictly due to the choice of the proper turn radius and other pilotage skills that the water does not go towards the side of an aeroplane. If it is indeed the case, could you pinpoint the flaw in my train of thoughts? Or maybe you know of an authoritative aeronautics specialists capable of helping?

Hoping for an answer,
Konstantin.

Tartu, Estonia.

What do you think?

Vern

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As a pilot, I can tell you that the skill of the pilot is not a great part of the water remaining parallel to the floor. You can screw up the entry into a turn by improper use of the rudder and ailerons, but once in the turn the aeroplane quite happily keeps the sense of down pointing towards the bottom of the aeroplane.

Physicists will tell you that the sense of down is the result of the forces operating on the aeroplane. Thrust, lift, and drag balance out to keep everything normal. These forces work so well that a pilot cannot determine whether an aeroplane is turning without reference to the world outside or to instruments inside.
« Last Edit: 12/02/2009 13:37:16 by Vern »

yor_on

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Do you mean that if i was standing the airplane on the side, one wing pointing down at Earth, doing a bank the water and its surface would still be parallel directed at the airplanes floor?
I don't think so, the water would be spilled at some point.

You would have to do a very steep bang letting angular movement take over from Earths gravity to succeed I think?
You can treat all things inside and defining your airplane as one 'system', but that system will be relative outer forces like air pressure and Earths gravity playing on it.
« Last Edit: 12/02/2009 15:09:44 by yor_on »

dentstudent

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If you were banking and the plane was following an arc, then the centripetal force would be pushing effectively vertically downwards through you and the glass, and so the water wouldn't spill. If the plane was traveling at that angle, but in a straight line, then there would be no centripetal force, and so the water would indeed spill out.

Vern

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Quote from: yor_on
Do you mean that if i was standing the airplane on the side, one wing pointing down at Earth, doing a bank the water and its surface would still be parallel directed at the airplanes floor?
I don't think so, the water would be spilled at some point.
You can do a complete loop without spilling the cup. :) If you turn so tightly that one wing points straight down, the g forces would be very uncomfortable, but the water wouldn't spill.

yor_on

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Yep, thanks for that one Vern:)
But Dent, there will be some point in that curve where the centripetal force ain't enough.
You don't need a 'straight line' for that water spilling out.
To me it seems that to have a 'stable' water surface, not spilling,  your bank need to 'overcome' that one G directed relative Earth?

Vern

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The problem is that to maintain a wing down attitude the plane must slip sidways. Then the side of the airplane becomes the wing- so to speak. In that case it is not really a turn.

 

LeeE

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I'm a bit short of time right now, but look through youtube for some videos of Bob Hoover doing chandelles while pouring water from a jug in to a cup while upside down.

yor_on

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http://www.youtube.com/watch?hl=en&v=TUVWHUR5OEI&gl=US

I will need to get this explained :)
--
Does that roll negate one G?
How?

---

Thanks for that one LeeE, I just love airplanes, Zeppelin's, everything that can fly in fact.
He must be one heck of a pilot.

---
And yes, I do even include helicopters:)

Btw: for those of you into that kind of 'romantics', read Gavin Lyall.
He loved planes, and wrote some of the best action I've read.
--
The Wrong Side Of The Sky
The Most Dangerous Game
Shooting Script
Judas Country
-----
« Last Edit: 12/02/2009 20:03:21 by yor_on »

LeeE

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The Chandelle, if correctly performed is a constant G maneuver, and that's why it's possible to pour the water from the jug in to the cup while upside down.

In that video clip you're actually seeing two types of different 'rolls'.  There's the one where the aircraft rolls about the axis running through the aircraft - in the video BH briefly holds the aircraft at each point in the roll - and the other type of roll where the aircraft is flown along helix around a central axis.  In the first type of roll, where the aircraft rotates around it's longitudinal axis, any drink in your cup would pour out as soon as it had tipped over enough.  In the second type of roll though, the Chandelle, it is like flying around the inside of a tube and if you get everything right you can maintain a steady G-force, which effectively acts down through the floor of the aircraft regardless of it's orientation, throughout the maneuver.  If you were inside and there were no windows you might not even realise that you were, for a while, upside down.

Of course, it's much easier said than done.

John Chapman

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I know the answer to this as a few years ago I learned to fly ultralight (3 axis) airplanes.

A car travels in one plane only and steering one is simple. You turn the steering wheel clockwise, the car turns to the right and all the passengers get squashed against the windows on the left hand side. At least they do when my son is driving.  If you had a cup of tea in my son's car it would end up all over the left window. If you steered an airplane the same way, by using the tail rudder, then the plane would point it's nose in the direction you wanted but it would continue to travel in the same direction slipping sideways because of it's inertia (momentum). This is dangerous because the airfoil shape of the wings mean they only provide lift when air is passing over them in the right direction. In a really bad slip the wing can stall (ie stop lifting) and the plane will begin to fall. Because the plane is moving sideways the control surfaces (ie the parts of the plane that it uses to steer, such as ailerons, elevators and rudder) will not work and the pilot may not be able to regain control without putting the plane into a dive to force the air to travel over it in the right direction. If you had a cup of tea in that aircraft you would probably end up wearing it! :o

Pilots take great pride in the quality of their turns. To counteract slip they do two things:

Firstly he will roll the airplane slightly using it's ailerons (one of the flaps on the trailing edge of the wing) so that it banks into the curve of the turn. This means it is tilting sideways and so gravity will make it want to 'slip' sideways the other way. If the pilot judges it right the slip caused by the turn will exactly balance the opposite slip caused by gravity and your tea will stay in the cup.

Secondly, an aircraft's lift is always perpendicular to it's wings so if the airplane is not level it's lift force will not be pointing directly upwards and the plane will begin to descend. To counteract this the pilot will throttle up (accelerate) and point the plane's nose up using the elevators (the flaps on the tail's mini wings). If he does this well and makes what's called a 'balanced' turn his passengers should not even notice the plane is turning unless they look out of the window. And neither will your tea.

When I was having lessons my little aircraft had a slip meter. This was basically a concave bowl with concentric stripes printed on the inside (so that it looked like a target if you looked down on it) and a small ball sitting in the bottom, resting on the 'bullseye'. I spent hours practising turns without letting the ball roll up the sides and eventually I could make tight turns and keep the ball on the bullseye. And so your cuppa would also have been safe with me!

Another thing we did was attach a length of red wool to the nose in front of the 'windscreen'. As long as the wool fluttered directly back along the centre-line of the nose everything was fine. If it ever fluttered to one side I was letting the plane slip. With thousands of hours flying under his belt your pilot would have instinctively known if his aircraft was slipping and would have corrected it automatically and without even consciously thinking about it. Aerobatic pilots could loop the loop without spilling your tea.
« Last Edit: 13/02/2009 13:31:27 by John Chapman »

Chemistry4me

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Wow, that is neat :)
Nicely explained.

konstantin

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Hello. I'm the author of the original question and I'm having a deja vu now.
But I hope it will be easier for me to explain my position here, because I guess the readers of this forum have a better understanding of physics, because I have made my best to understand the problem, and because I have some experience explaining it now already.

So let me start.
First of all, in order to approach the problem clear-minded and without the need to fight your intuition, we start with two simple examples.

Example 1.
Take a bucket with water (or a plastic bottle) on a string (it is important, don't just hold it in your hand!), and start swinging the bucket. You may try swinging, rotating, performing curves by letting the rope go and pulling the rope towards you, making full turns around you and around your head. You will note that the water in the bucket will stay, amazingly, quite strictly parallel to the bottom. The explanation is simple (link), but I dare you to do the experiment to destroy some of your intuition that hinders the understanding of the airplane case.

Example 2.
You probably have seen paragliders in the air. If you haven't, just go to youtube and type "extreme paragliding". Note that no matter what the roll angle of the paraglider is, it is always hanging straight perpendicularly to the parachute. If you would give a cup of tea to a paraglider, which way, do you think, the tea would orient itself? Of course it will be parallel to the floor.

Now the main thing you need to understand, is that if gravity can act freely both on the container (i.e. an airplane, a bucket, a seat of the paragliderist) and the object inside it, the object "can not detect gravity", if the only thing it can observe is the container. In other words, it is not gravity that plays a role in water orientation. And this is a crucial a-ha-revelation moment.

With this being clear and gravity out of the way, the intuitive question becomes different: how can water be not parallel to the floor. In order for that to happen, there must be some force pushing "on the side" of the airplane. What could be the source of this force?

Although I have only flown a plane on a simulator, I've done some background studies and have some understanding of this point.

Reason number one - the rudder. Rudder can be used to change the yaw of an airplane, i.e. rotate it around its vertical axis. In physical terms this results in a side-force being applied to the hull, but interestingly, this force acts on one side in the front of the aircraft (before its center of mass) and in an opposite direction in the back. Therefore, when you turn the rudder to the left, say, the water will incline slightly to the right in the cabin of the airplane (similarly to the "ball" mentioned in the previous comment). However, in the back of the airplane the water will incline to the different side, and in the center of mass it will not incline (just rotate around its axis).
However, the rudder is a very sensitive way to control an aircraft, and is thus never used at the speed the commercial passenger airliners travel.

Reason number two - adverse yaw. This is a weird effect related to the imperfect construction of the ailerons. That is, when an aircraft is turning using the ailerons, a momentarily rotating force is applied and this basically acts in the same way as the rudder. This is the force that must be counterbalanced during the turn via the rudder by "watching the ball" (mentioned above). The resulting turn is called "coordinated".
However, firstly, the side push of the adverse yaw only exists when the ailerons are not straight, that is, during the time when the airplane is rotating itself around its main axis, and this force is approximately proportional to the rate of rotation. Therefore, even if an uncoordinated turn is made, you could see water incline slightly in the period when the plane is going into the turn, but once the roll angle of the plane is established and the ailerons are straight again, adverse yaw disappears.
And when the turn is performed slowly, smoothly, without abrupt movements, adverse yaw is quite small and the water won't incline much, even if the airplane itself "slips".

Third reason - body lift. It is normal to assume that lift force is only applicable to the wings, not to the body of the airplane, and in most cases, when the airplane hull is oriented approximately along the path of its movement it is indeed the case. It is always the case for passenger flights and I guess the pilot must be a skilled aerobat or a suicidal to achieve significant body lift.
So how do you achieve it? Well, one way is to incline the airplane while avoiding the turn, i.e. keeping the orientation of the fuselage straight (I guess this can be done using tail ailerons).
As a result the airplane will start gliding downwards along the slope of its wings, with its falling speed increasing linearly at first. However, at some point the air resistance will prevail and the falling speed will become constant. The same effect happens to a human in free fall. If I'm not mistaken the free fall speed is about 60m/s, and I guess it must be even larger for an airplane. Clearly, most pilots will avoid letting the plane descend with such velocity.
Secondly, they say it is possible to modify the "falling" situation above slightly, by heading the nose slightly upwards. An airplane fly nearly on the side as long as it can keep the orientation of the hull inclined slightly upwards with respect to its travel direction and earth. The angle of attack of the body will then produce lift capable of holding the airplane in that position for some time.
However, clearly this kind of aerobatics is never performed on commercial airliners.

Therefore the answer to my question is rather 1 - the physics of the airplane, than 2 - the skill of the pilot.
And I'm happy that the first comment of a pilot confirms that.

yor_on

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This Chandelle should be the quest for all airline pilots.
To entertain your fellow passengers.
No discomfort, no lost G:s, just a new angle..

LeeE

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Bob Hoover did a Chandelle in the Boeing 707 prototype; he was the test-pilot, but although the Chandelle is regarded as a 1G maneuver it still imparts a centripetal force on anything away from the center axis.  With aircraft having their engines slung outboard, under the wings in nacelles, there's an appreciable side-ways force on the nacelle mounts; once the aircraft reaches a certain size you're likely to damage or lose them.

 

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