Airplane physics question

The thrust of plane's engines DOES indeed have opposition.

The opposition is the friction force created by the motorized, backward-accelerating conveyor. It's this FORCE that accelerates the plane backwards, if the plane engine are turned off.

Now that we recognize the presence of the rearward force (from the motorized, backward-accelerating conveyor), we can turn on the plane engines ... and recognize the two forces now in opposition that keep the planes wings stationary relative to the surrounding stationary air.

 

We only turned the plane engines off for a moment, to recognize the separate forces acting on our plane.

Keep the engines off, just for a moment. Accelerate the conveyor backwards ... the plane also accelerates backwards. Interim conclusion : the motorized, backward-accelerating conveyor must be exerting a rear-ward FORCE on the plane, in order to accelerate its mass backward.

NOW we can turn on the plane's engines. Forward thrust is provided. If this forward thrust of the plane engines matches the rearward thrust of the motorized, backward-accelerating conveyor ... the plane no longer moves backwards, or forwards, and wings stay stationary relative to surrounding air.

 

Cannot believe this is still being discussed.

The conveyor situation is no different to a hydroplane and they happily take off.

Anyway keep discussing ...
Pete

 

PSK, exactly.

werewolf...there is friction between the wheels and the conveyor belt, but the axle bearings have zero friction. As the belt accelerates, it accelerates the wheels. But that does not result in any acceleration of the plane, because the wheel bearings, having zero friction (ok, there is a minuscule amount there, but it's negligible), do not impart any linear force on the plane. Instead, the wheels just spin faster and faster, as fast as they need to go to maintain contact with the conveyor belt service.

Now along comes the thrust. NOTHING opposes it. So plane moves forward. With predictable results of airflow, lift, takeoff, and flight.

 

Incorrect. It' already been discussed.

It matters not that the wheel bearings have zero friction. The plane will still accelerate backwards, on a backward-accelerating conveyor.

One way to understand why, is to place a single tire on a conveyor belt. Turn on the conveyor. Does the tire move laterally, or just spin? The answer is that tire moves laterally, as well as spins. The force that acts on the surface of the tire can be decomposed into two forces : an identical, lateral force acting on the center of mass of the tire, and a rotating torque that will rotate the tire. It's the lateral force that moves the center of mass of the tire in the direction of the conveyor.

(The other way to argue the same point is that a tire which experiences one half the force on the top, with an opposing half force ... in the other direction ... on the bottom, will NOT move laterally. It will just spin. Surely, the situation where the full force is only applied to one side of the tire must have a different result. And indeed it does ... with an "unbalanced" force acting on just one side of the lone tire, the tire will move laterally as well as spin.)

This is the same force that will absolutely accelerate the plane backwards, with engines off, if the plane is placed on a backward-accelerating conveyor ... even with zero friction bearing at the tire's axle. And this is the same force that can oppose the plane engine's forward thrust.

Already been discussed.

 

Lol! It's already been discussed? I don't think any science debate has ever been settled with that argument before. Sorry, but you can have it as "settled" as you want in your mind. That won't change the (very) basic physics involved here. You are confusing yourself. That's cool Just don't try to confuse others.

Plane takes off. No matter how much you have "already decided" it won't.

 

Fixed

 

well that's an equally valid rebuttal !!!

Well done

My argument stands. A plane, with engines off, placed on a moving conveyor WILL move in the direction of the conveyor ... even with zero friction between the wheel (inside the tire) and its axle. The PHYSICS behind this conclusion is that the friction force acting on the bottom of the tire (instead of equally distributed between the bottom in one direction, and the top in the other) can be decomposed into two forces : a net lateral force acting on the center of mass of the wheel ... aka the axle ... and a rotating torque acting on the edge of the tire.

The backward accelerating conveyor therefore presents a rearward lateral force to the plane. If the acceleration is correctly chosen, the backward force created can BALANCE the forward thrust of the plane's engines (when they are turned on). Therefore it IS possible for the plane's wings to remain stationary, relative to stationary air. Zero lift on the wings.

In order to refute this argument, you have to argue that even a single tire placed on a conveyor will NOT move LATERALLY in the direction of the moving conveyor. I'll even offer a simple experiment : place something that easily rolls ... a small model car tire, a roll of quarters, a thread spool ... on a piece of paper on a flat surface. Pull the paper in one direction, and see if the rolling item moves, laterally, in the direction that the paper moves (as well as spinning). Only constraint : no slippage at the interface between the rolling item and the paper.

How's that? Get back to me on the single tire experiment ... or, refute the kinematics (physics) that i've presented.

 

I don't know if it's "twice as fast" or not, but a moving runway should have an effect on wheel speed.

The prop and wings don't care what the ground is doing. They are independent of the ground. Their only function is to create airspeed and lift (not caring a hoot whether the ground is moving or not).

But wheels are not independent of the ground.

Say an airplane takes off at 100 Kts airspeed on a non-moving runway. Now look at that same take-off roll as that same aipplane is accerating through 50kts on that same stationary runway. The wheels are now moving at a certain rpm on the stationary runway to keep the airpeed at 50kts.


Now flip the switch on that starts the conveyor belt. The converyor belt is going to start moving at what ever rpm the wheels are moving. There is now a difference in the speeed of the runway, and the wheels will have to adjust their rpm's to whatever rpms are required to keep the airspeed at 50 kts.

Like I said, I don't know enough math to do the calculations, but shouldn't there be an effect on the speed the wheels are turning in order to maintain a constant airspeed?

 

Airspeed trumps groundspeed as far as flying is concerned. That's what wheels are for. To adjust to make sure the airspeed is not influenced by "groundspeed". Because, in truth, the airplane IS still on the ground. Whatever it is that particular piece of real estate may be doing...ie...moving or not moving, the airspeed must remain at 50 kts and it's the wheels' job to make sure it stays at 50kts should the ground start to move..

 

Yes, it will affect the wheelspeed, but not the take-off speed of the airplane. I agree with you that the wheel speed is affected, but I don't agree that it will result in the wheels moving twice as fast as they normally would be at the point that the plane takes off.

 

No, the wheel's job is to support the plane in a stable position at all times that it is on the ground. You can have sticks, skids, skis, pontoons, wheels, etc. They all do the same job. Some devices do it better than others, depending on the circumstance. For hard, smooth surfaces, wheels are good because they can roll along easily, while the axles don't move, and anything attached to the axle also stays in the same relative position. When you attach an airframe to the axle at a specific position, it stays in the same relative position as long as the wheels are on the ground.

The question is an impossibility. Either one condition or the other has to hold. Both cannot be true.

First condition: conveyor belt matches wheel speed. IF you accept this, fine, but then plane cannot be moving forward. Therefore its propellor or jets are not producing thrust. Because if they were, the plane would absolutely move forward since there is nothing producing any force to oppose their thrust. So you won't be simulating the question at that point.

Second condition: plane's propellor or jet engine is producing thrust. If this happens, then the plane moves forward, since nothing is opposing the thrust vector. The moment the plane moves forward on the belt, first condition is broken. The plane (and its wheels) cannot be moving forward on the belt if the belt speed is matching the wheel speed. That can only be true if the plane is stationary on the belt.

Question is invalid.

In the real world, you can of course put a plane on a conveyor belt and fire up its engines and try to match the belt speed to the wheel speed and see if the plane moves, or if some magical, previously undiscovered force will keep it still. Note that the moment the plane moves over the belt, the belt speed cannot possibly be matching the wheel speed.

 

That is is correct, Sir.

The question itself is flawed.

 

The original question is vague, but certainly not impossible!

A motorized, rearward-accelerating conveyor belt generates a friction force that tends to accelerate the plane backward. The plane's engines generate a forward thrust that tends to accelerate the plane forward. If these forces ... and therefore, accelerations ... are in balance, then the plane remains stationary relative to surrounding air. Zero lift on wings.

Perhaps nobody yet believes the kinematics i've presented (single, off-center lateral force resolved into a lateral force on center of mass, plus a rotating torque) which demonstrates that a motorized, backward-accelerating conveyor will indeed accelerate a plane backward (even with zero friction at the axle). So ... has anyone attempted my simple experiment yet, to verify that an accelerating conveyor will indeed move a rolling item LATERALLY, in the direction of conveyor movement? Where does that lateral movement come from?

Note, once again : a conveyor moving at a constant velocity is a very, VERY different thing than an accelerating conveyor. Shame on mythbusters, for not recognizing this most basic principle.

 

It is impossible. A wheel cannot move forward on a treadmill without exceeding the speed of the belt in the opposite direction. So, if it is just sitting there, matching the speed, then there is no airflow past the wing and the plane does not take off. This can only happen when the propellor or jet is not producing thrust. Since it does take off, then it must be experiencing thrust and moving forward relative to the belt. If it is moving forward, then wheel speed is greater than belt speed in which case you are breaking. one of the original conditions. Both conditions cannot exist simultaneously.

 

The original question is vague, but does not describe an impossible condition.

It's vague, because it describes a "wheel speed" that matches a "conveyor speed". A wheel has translational speed as well as rotational speed. Which one does the original question refer to? Maybe a combination of both? Does it refer to the lateral speed of the center of the wheel, or the lateral speed of a point on its circumference?

My interpretation of the condition is this :

Experiment one : Plane on solid ground, engines on, accelerating to take off. We'll assume constant thrust, therefore constant acceleration: 0sec 0mph, 1sec +40mph, 2sec +80mph, 3sec +120mph, etc.

Experiment two : Plane on backwards-accelerating conveyor, engines off. Friction force moves plane laterally backward (as well as rotating tires). Adjust conveyor acceleration so that plane experiences : 0sec 0mph, 1sec -40mph, 2sec -80mph, 3sec -120mph, etc. (i've offered the "resolution of forces" from kinematics to justify this, as well as simple experiment that can be done on a kitchen table)

Now combine two experiments. Forces balanced, speeds balanced at each point in time, plane never moves relative to still air.

It should be pretty obvious that the conditions i've described certainly can't be met by a conveyor moving at a constant speed. Forces tend to be proportional to accelerations, not velocities (shame on mythbusters). To match the forward acceleration of a plane under engine thrust, requires a rearward acceleration from the conveyor. Alternately, to create a rearward force, to balance the forward thrust of the engines, requires friction from an accelerating conveyor.

Honestly, with engines off for a moment (just to analyze the forces involved) ... is there any question that an accelerating conveyor will accelerate the entire plane in the direction of conveyance? Alternately, is there any question that an accelerating conveyor will create a friction force that causes lateral movement of the entire plane? Once we get past this, it's trivial to see how it's indeed possible (although perhaps not practical!) to keep the plane stationary relative to surrounding air, when the engines are turned-on to create forward thrust.

 

Werewolf is doing a great, in depth job of explaining exactly why the plane will not take off and the rest of you are doing a great job of saying "Not-uh".

 

I have a headache!

 

It is obvious which speed the question is referring to because it says the plane is sitting on the treadmill. In order to do that, it is not moving forward. In order to not move forward, it's wheels are rotating forwards so that the tangential, circumferential speed is matched to the belt speed. That is the only way the plane can sit still on the treadmill.

If it sits still (and the question says that it does), then the only way it can continue to do so is if there is zero thrust. The moment there is any thrust when all else is in equilibrium, an equal and opposite force to the thrust must be introduced, or the plane will move forward due to the unopposed thrusting force. The instant it does so,
1. the wheel speeds no longer match the belt speed.
2. there is airflow past the wings, resulting in lift, resulting in takeoff.

 

The equal and opposite force is the treadmill. It is required by the question to match the wheelspeed.

 

incorrect.

The forward thrust of the engines is matched by the rearward friction of the backward-accelerating conveyor, which exerts a rearward force on the plane. Forward & rearward forces in balance, plane does not move relative to still air. Wheels rotating (faster & faster!) as plane stays stationary (relative to air) on motorized, rearward-accelerating conveyor. No slippage at tire/conveyor interface. All conditions of original question met, plane is stationary relative to surrounding air.

You must understand that plane on solid ground accelerates forward when engines are on, AND that plane accelerates rearward on motorized, rearward-accelerating conveyor when engines are off. When BOTH engines and accelerating conveyor are ON, plane stays stationary relative to surrounding air. Conveyor moving faster & faster, wheels rotating faster & faster, plane stays stationary (relative to surround air). All conditions met, zero lift on wings.

Can't be done with a constant-speed conveyor.

 

Werewolf, I just read your post. You are confusing yourself. You are right about the plane being moved backwards when the engine is off. But your reasoning goes terribly wrong once the engines are started.

At that point, the plane experiences forward acceleration. So do the axles. As a result, the wheels are accelerated forward. Because of their friction on the belt surface, as they move forward, the tangential linear velocity at the tread surface increases, ie. there is acceleration. The belt speed matches this, per the question. However, there is nothing to oppose the forward thrusting force of the engine. So the plane moves forward. Now, in real life, the two conditions are mutually exclusive:
- either the plane sits still and the wheel and belt speeds match, or
- the plane moves forward and the wheel and belt speeds do not match.

In real life, the only way this could manifest itself is if the wheels are dragged as they spin, allowing for belt speed to be matched to wheel speed while also allowing for the plane to move forward while keeping the belt and wheel speeds matched.

You are right about what happens at first. This is because of the mass resting on the wheels leading to a lot of rotational inertial. If the belt is accelerated at a slow enough rate so as to not overcome the rotational inertia of the wheels, the plane will indeed move backwards. The moment the slightest force is applied that results in the wheels spinning however, you can accelerate and decelerate the belt all day long, and it will not affect the plane. Conversely, you can accelerate the plane all day long, and no amount of belt acceleration or deceleration will affect the forward motion of the aircraft. In reality, the wheels, due to friction, will spin. For the sake of the question's condition, you can say they get dragged along, thereby meeting the condition that the speeds match.

Imagine a very, very slimy surface on the belt. Now accelerate it. Will the plane on top move? It won't.

Now fire up the plane's engines. Will any amount of belt acceleration prevent the plane from moving forward?

 

No. Conveyor cannot and does not exert any force on the plane once the wheels are turning. There is zero friction (for all intents and purposes) at the axle bearings. So, you can accelerate the belt all day long. It will angularly accelerate the wheels because of friction between the surfaces. Sure, the wheels will spin faster and faster. However, there is no friction at the wheel bearings. So the axle does not experience any linear force and the plane will not accelerate (or decelerate) linearly due to the belt acceleration--because no linear force from the conveyor will be imparted. This means that the thrust from the engines will be unopposed. That is a linear force. There is no opposing linear force being experienced. The conveyor is only imparting an angularly accelerating force on the wheels. They will spin faster, sure. But, that will not result in translational backwards force on the plane (and consequently, no opposing force to the thrust). That is why the plane will move. That is why it will take off. But in moving, it will break the condition of the question--that the wheel and belt speeds match.

That's why it's a flawed question. The only time the condition can hold true is when belt speed is zero and engines are off.

If just the belt is moving, then plane moves backwards. Wheels do not rotate. Therefore their speed does not match the belt speed.
If plane's engine is working, it moves forward because nothing opposes the thrust. Again, belt and wheel speed do not match. If they did, it could not move forward over the belt.

Stupid question.

 

exactly.

We REALLY must understand the answer to this question:

Plane engines off. Plane is place on rearward-accelerating conveyor. Wheels will spin. Will plane ALSO move backward, laterally?

You won't understand the rearward force that can (potentially) balance the forward thrust, until you're comfortable with this concept (don't feel bad, mythbusters didn't get it either).

I'll offer my simple experiment, once again. A rolling item (empty soda can?) on a piece of paper flat on a table. Slide the paper under the can. Try to steadily increase the sliding speed. What does the can do? Yes, it will rotate. Does it also move laterally, compared to it's original rest position? What FORCE caused this lateral movement?

(Kinematics tells us that even though the friction force of an accelerating conveyor ... the paper, in this experiment ... is NOT acting on the center of mass of the can, the off-center force can be "resolved" into two forces : a translational or lateral force of equal magnitude acting on the center of mass, and a rotating torque that will spin the can. It's the translational force that causes the lateral motion of the center of the can. And it's this same force that will accelerate the entire plane rearward, laterally, on a rearward-accelerating conveyor).

 

this is exactly & precisely where you are wrong.

I've offered several explanations, and a simple experiment you can perform at home in 5 minutes to prove my point.

The friction force between the tires & the accelerating conveyor absolutely DOES exert a lateral, or translational force on the plane ... even with zero-friction bearings at the axle of the wheels. The rules of kinematics dictate this to be true. And you can prove it to yourself with my simple experiment.