A jet plane on a large treadmill

[PNWbrit]

If a powered treadmill exactly matches the accelration and speed of the jets rotating wheels the plane stands still - it will not fly.

It would push itself off of an unpowered freely rotating treadmill or conveyor then given enough room to attain take off speed would fly.

[DJSapp]

If a powered treadmill exactly matches the accelration and speed of the jets rotating wheels the plane stands still - it will not fly.

It would push itself off of an unpowered freely rotating treadmill or conveyor then given enough room to attain take off speed would fly.

[PNWbrit]

It doesn't matter that the plane is propelled by a jet, it's forward movement while on the ground is governed by the rotating speed of the wheels relative to the ground.

[DJSapp]

It doesn't matter that the plane is propelled by a jet, it's forward movement while on the ground is governed by the rotating speed of the wheels relative to the ground.

I'll write the proof tonight. I'm done until then.

The wheels do not matter.

[PNWbrit]

The jet does not matter - The wheels do matter.

The plane can only travel over ground at the rate it's wheels rotate. It does not make any difference that it is being pushed by a jet and not being driven by it's wheels.

The speed matching powered treadmill negates any rotation of the wheels - the plane doesn't move.

[dubu]

this thread is funny now..

and people are dumb.
the plane is not a car.


in a car:

engine accelerates car by spinning wheels,
treadmill spins wheels,

therefore the two cancel

car does not move

in a plane

engine accelerates plane by pushing air.
treadmill still spins the wheels, which have nothing to do with the speed of the plane.

therefore wheels spin, and the jet body moves. plane takes off.

[Ubersheist]

The jet does not matter - The wheels do matter.

The plane can only travel over ground at the rate it's wheels rotate. It does not make any difference that it is being pushed by a jet and not being driven by it's wheels.

The speed matching powered treadmill negates any rotation of the wheels - the plane doesn't move.

Here's a couple of ways that you could be mistaken:

1. What you're not understanding is that this is a hypothetical situation. The "lift off" people are assuming that there is no resistance in the wheels of the plane and that the the planes wheels can spin at infinity rpms. Given this situation, as soon as the jet fires up, the treadmill and the wheels would speed towards infinity instantly, and there would be no possible way for the treadmill to stop the forward movement of the plane.

Remember, the jets are pushing air, not the ground. As such, the wheels and the treadmill would be spinning at infinity, but there would be no way to stop the jet from moving forward relative to the assumed still air and the stable ground away from the tread mill.

2. Conversely - assuming that there IS friction in the wheels, even if you have no wheels at all but are grounded on some two-by-fours on the non-treadmill tarmac, but that you have impossibly powerful jets on your plane... The jets are pulling and/or pushing air. The jets are therefore going to move air and create it's own wind over the wings. Therefore, if you gave the jet enough juice, it would take off vertically relative to the ground because it would be creating it's own windspeed over it's wings. As soon as it left the ground, the windspeed would die down, and the jet would move forward.

Hypothetically, in either scenario, the jet takes off.

Also, the whole scenario is an impossibilty. Something would realistically burn out, break or melt. Whether or not the jet would really takes off depends on what your weakest link would be.

[f2f]

beaver said it 5 pages ago:

the jet takes off while moving forward (forces not related to the threadmill are pushing it), its wheels will rotate twice as fast, however, forced to do so by the friction with the threadmill.

if, instead of a threadmill, you had a huge fan blowing air at the plane at exactly the same speed as it accelerates at it will take off stationary (that's the principle of wind tunnels and those little toy planes at calgary airport's spaceport)

/former physicist

[Dr. Send]

2. Conversely - assuming that there IS friction in the wheels, even if you have no wheels at all but are grounded on some two-by-fours on the non-treadmill tarmac, but that you have impossibly powerful jets on your plane... The jets are pulling and/or pushing air. The jets are therefore going to move air and create it's own wind over the wings. Therefore, if you gave the jet enough juice, it would take off vertically relative to the ground because it would be creating it's own windspeed over it's wings. As soon as it left the ground, the windspeed would die down, and the jet would move forward.

And maybe if you had an impossibly massive car with a powerful engine, the inertia of the car would cause the whole earth to rotate backwards under the car's wheels, until the speed of the earth relative to the stationary atmosphere would be enough to allow planes to take off vertically relative to the earth, because the airspeed of a plane stationary relative to the earth will be equivalent to the speed of the earth relative to the car.

[cj001f]

therefore wheels spin, and the jet body moves

The wheels are always spinning at same speed as treadmill by definition. If the wheels are always spinning at the same speed as the treasmill - the jet can't move forward relative to the ground unless it seperates itself from it's wheels or the wheels no longer spin perfectly on the treadmill (the reverse of locked brakes). It's constrained by the motion of the wheels by defintion; you can't ignore the boundary value and assume no force from the treadmill acts on the plane: If the treadmill is constantly accelerating and opposing the motion of the airplane there is some force acting on the treadmill and therefore on the airplane. Classical mechanics people, change in velocity over time = acceleration = force/mass dv/dt = a = F/m. A force equal in magnitude and opposite in direction to the force (thrust) from the jet engines.

It may not be physical it is how the problem is constrained.

[f2f]

cj001f,

what you're describing is called, in high school physics, "rolling friction". rolling friction forces are much, much lower than sliding friction (which is two bodies against each other, directly).

because friction in wheels is so low you would need, as uberscheist put it, almost infinite speed on the threadmill to be able to counter the much stronger jet propulsion forces exerted by the plane's engines. it is almost certain that the plane wheel's bearing will melt down before you can spin the threadmill fast enough to slow it down or halt its progress.

as a real-life example, compare how the wheel that was stuck sideways on the landing of that jet in california burst in flames almost immediately on touchdown (sliding force) vs how they never do when aligned properly (rolling force).

i was looking for an example and think this one explains it quite well:



it has to do with building pyramids, but with the plane it's the same -- jet engine force >> rolling friction force. the amount of spin you need to exert on the wheels to keep the plane in static position is disproportionately large compared with what the engine pulls out.

ultimately, it may turn out that the wheels should cover more ground than the speed of light

i doubt we can be bothered with the equations

[smmokan]

So now that we have the airplane problem solved, will someone please answer the question about KITT pulling onto the moving trailer? I'd like to hear that one.

[Tippster]

I get it CJ's point. In the original post the wheels are artificially constrained to equal the speed of the treadmill (X) so there will never be X+thrust. A retarted question then.

[cj001f]

Problem definition:

Velocity plane = Velocity treadmill

and d(Velocity plane) = d (Velocity treadmill) - the treadmill always accelerates to match the plane, instantaneously.

If both of these are true the plane can't take off - it's air speed will always be zero unless there is some wind. The problem artificially and unphysically says both are true so some force from the treadmill has to act on the plane (no, no not possible, but thats how the professor defined the problem....) to keep the accelerations equal

edit: beaten by tip by a few.

[iceman]

Yeah I thought Beaver was right but cj has (at least for now) convinced me otherwise. If the speed of the wheel remains identical to the speed of the treadmill, the wheels can't advance. And the plane can't leave its wheels behind.

In Bircheater's wheelchair/treadmill example the speed of the treadmill is constant so the chair is able to move over the treadmill as it's wheel goes faster than the treadmill.

The speed of the wheel and treadmill would approach infinity but the plane won't move.

[Telenater]

I guess I'll still my oar in.

The plane will take off assuming that nothing untward happens to the wheels and that there isn't an inauspicious end to the tread mill.

Others have analized the forces quite accurately. DJSapp, doing so quite eloquently at one point.

The fact that the airplane does not use the ground for the reaction force to its engines is absolutely key. The plane is not pushing on the ground in anyway other than straight down. The treadmill on the otherhand only provides as much force as the friction in the landing gear transmits on the air plane.

To go back to the treadmill and and wheel chair analogy....

Consider your arms to be the engines, the air to be a railing alongside the treadmill and the treadmill to be the treadmill.If you are merely holding place using the handrail with a moving treadmill you'll have to provide some small force to hold yourself stationary. And, by the definition of the situation at hand if you're stationary, the so is the treadmill. now consider that you're moving forward at 1m/s using the handrail to pull yourself. The treadmill will now be moving 1m/s backwards giving you a speed relative to the treadmill of 2m/s and 1m/s to the ground. Accelerate using your hands on the rail to 2m/s and you're now moving forward at 2m/s and 4m/s relative to the treadmill. Assuming that the forces of friction from the treadmill to the body are negligible (which compared to a jet's thrust isn't far off), your acceleration relative to the ground is not constrained by the treadmill. you'll merely have twice the relative velocity with the ground relative to the treadmill. Assuming that the hand rails are stationary (or that the air around the jet is stationary) all that matters is your velocity relative to the medium providing your propulsion (rails or air) which is essentially relative to the ground speed.

Or think of it this way. You're back in your wheel chair on the treadmill with a hand rail. Set the tread mill to accelerate indefinitely. Can you pull yourself forward using the hand rail? Yes, you can because the speed of the treadmill is immaterial to your acceleration if you're not using the treadmill to accelerate yourself.

One absolutely critical assumption is that the plane is not in someway fixed in place. If it were, the problem would be easy. Both plane and conveyor would have velocities of zero. However, the problem states that the conveyor matches the plane's speed (ie the planes' speed can be nonzero) but in the opposite direction. Given that the only interface between the plane and conveyor is the wheels and they're essentially freely rotating there is no reason that the plane cannot accelerate to take off speed while it's wheels turn at twice that speed.

This is a question that would show up on a high school ap physics test as a frame of reference problem. Because the wheels are considered to be freely rotating and are the only interface between the plane and treadmill the treadmill's speed does not matter because the frame of reference governing the plane's ability to take off doesn't care how fast the treadmill is going with respect to the airplane's speed relative to the air (again, assuming that the landing gear can take the heat/speed of rotation without failure).

[iceman]

We just answered different questions, nate. If the speed of the plane and the belt are at issue you are correct, the plane will take off.

But if it's the WHEEL, and not the plane, that is going the same speed as the treadmill, the plane cannot move forward and will not take off.

[Telenater]

We just answered different questions, nate. If the speed of the plane and the belt are at issue you are correct, the plane will take off.

But if it's the WHEEL, and not the plane, that is going the same speed as the treadmill, the plane cannot move forward and will not take off.

A plane (747 passenger jet) is sitting on a runway that can move (some sort of band conveyor). The plane moves in one direction, while the conveyor moves in the opposite direction. This conveyor has a control system that tracks the planes speed and tunes the speed of the conveyor to be exactly the same (but in the opposite direction).

Fine, but the question didn't involve the wheels at all. the plane is accelerating based on the force applied to the air and relative to the air. The speed of the wheels and conveyor don't matter unless the friction from the wheels rotating at twice the plane's speed relative to the ground (or assuming a calm day the air) can privide a force equal to the thrust of the plane.

edit: and now back to writing my statement of purpose for grad school.

[cj001f]

there is no reason that the plane cannot accelerate to take off speed

except that the problem statement says it's impossible. As soon as it's accelerating relative to the treadmill vplane > -vtreadmill a solution not allowed by the constraints of the problem, because the problem defines there velocity relative to each other as 0. The only way for the plane to acheive takeoff speed would be for it to accelerate the plane & treadmill system to takeoff speed or some wind or for it to move relative to the treadmill

[belgian]

I wasn't quite sure if I thought you guys were geniuses or just complete morons, but I think I get it now.

in THEORY (which you guys should drop, it makes the explanation far more confusing) the plane will take off if the wheels have absolutely no friction with the airplane itself. i.e. almost as if the wheels weren't even a part of the aircraft itself but just rollin' along, correct?

in REALITY, the wheels DO have friction with the airplane. i.e. if you put the plane on the treadmill and fired up the treadmill w/out the engines on, the plane would slide off off the end of the mill. The friction which it does create would prevent the plane from taking off up to a certain speed, after which the forward thrust of the jets would overcome the friction of the wheels, thus the airplane would take off. The only problem with this is how much friction there is with the wheels vs. how much thrust the engine can create.

just trying to clarify. am I correct?

If so, I get it, the plane would take off and I was wrong. If not, my hate for physics just got bigger.

[Telenater]

except that the problem statement says it's impossible. As soon as it's accelerating relative to the treadmill vplane > -vtreadmill a solution not allowed by the constraints of the problem. The only way for the plane to acheive takeoff speed would be for it to accelerate the plane & treadmill system to takeoff speed.

No, that just it. the plane is not fixed in position on the treadmill. If it were, none of this would be an issue.

The only constraint is that the speed of the airplane is exactly equal to the -speed of the treadmill(unvoiced assumption that it is the surface of the treadmill, but that doesn't really matter either). By stating this, the following must be true.

Vplane = -Vtreadmill ie plane at 1m/s treadmill at -1m/s
dVplane = -dVtreadmill ie plane acclerates 1/ms^2 Treadmill at -1m/s^2

This in no way prevents the air plane from accelerating relative to the air which is all that matters when asking if the plane will take off.

If we assume that the friction force acting on the plane as transmitted through its wheels is negligible compared to the force of the jet's thrust then then we can essentially ignore the force provided to the plane by the treadmill. All of the remaining force from the plane's engines then goes into accelerating the plane relative to the air that it's pushing against. The previously stated equations are not violated. The retarding force imparted by the treadmill is merely inconsequential with regards to the airplane's acceleration relative to the air.

just trying to clarify. am I correct?

You are. Unless the friction from the wheels rotation on the surface of the treadmill provides a force equal to or greater than the force provided by the plane's thrust, the plane will acelerate relative to the ground/air.

[MeatPuppet]

what are the JET engines pushing against?

that is the treadmill pushing against?, no its not the plane.

In the end, they are both pushing against the friction in the wheel bearings of the landing gear. That's about it.


This thread has become almost unreadable...

[cj001f]

No, that just it. the plane is not fixed in position on the treadmill. If it were, none of this would be an issue.

The only constraint is that the speed of the airplane is exactly equal to the -speed of the treadmill(unvoiced assumption that it is the surface of the treadmill, but that doesn't really matter either). By stating this, the following must be true.

Vplane = -Vtreadmill ie plane at 1m/s treadmill at -1m/s
dVplane = -dVtreadmill ie plane acclerates 1/ms^2 Treadmill at -1m/s^2

Nater-
If the velocity vector and acceleration are always equal in magnitude and opposite in direction the sum of each respectively is always zero

Vplane + Vtreadmill = Vplane - Vplane = 0

dVplane + dVtreadmill = dVplane - dVplane = 0

therefore the position is fixed relative to each other, if the plane were moving relative to the treadmill the some of the velocities wouldn't be 0. Assuming the treadmill is fixed the plane has to be moving relative to the treadmill to takeoff, it can't be and keep those statements true. 0 = a = dv/dt no change in velocity with time and 0 = v = dx/dt = no change in position with time. There is nothing physically fixing their position relative to each other; the problem has defined their position to be fixed relative to one another. It's the retarded phrasing of the question that has tripped people up.

[PulverSchwein]

The wheels are always spinning at same speed as treadmill by definition. If the wheels are always spinning at the same speed as the treasmill - the jet can't move forward relative to the ground unless it seperates itself from it's wheels or the wheels no longer spin perfectly on the treadmill (the reverse of locked brakes). It's constrained by the motion of the wheels by defintion; you can't ignore the boundary value and assume no force from the treadmill acts on the plane: If the treadmill is constantly accelerating and opposing the motion of the airplane there is some force acting on the treadmill and therefore on the airplane. Classical mechanics people, change in velocity over time = acceleration = force/mass dv/dt = a = F/m. A force equal in magnitude and opposite in direction to the force (thrust) from the jet engines.

It may not be physical it is how the problem is constrained.

Your first statment above is where i think you are making an error in defining the problem cj. The problem doesn't say the wheel speed matches the conveyor, it says the plane speed in one direction is always matched by the conveyor speed in opposite direction, no mention of wheels

A plane (747 passenger jet) is sitting on a runway that can move (some sort of band conveyor). The plane moves in one direction, while the conveyor moves in the opposite direction. This conveyor has a control system that tracks the planes speed and tunes the speed of the conveyor to be exactly the same (but in the opposite direction).

Broken down, the problem says "the plane starts out stationary on a runway that can move", then it says "the plane moves", and that "the conveyor moves in opposite direction", and finally that "the conveyor speed always matches the planes speed". I don't see anything that constrains wheel speed to match conveyor speed. If it did you'd be right and the definition of conditions would gaurantee zero speed and no take off.

Picture yourself on a airport conveyor wearing rollerblades with a bigass metal plate on your chest. At the end of the conveyor dude throws a switch on a well focussed motherfucker magnet. Exactly the same situation as above. A force that has nothing to do with the treadmill acts on you. Nothing stops you from accelerating (wheel friction is neglible). As you accelerate to the right, the treadmill accelerates to the left. Wheel speed = relative speed between their moving axis of rotation and the moving treadmill = 2x your speed relative to ground = 2x treadmills speed relative to ground. Am I still wrong?

[PulverSchwein]

Now that I see the next reply, I counter with this cuz I know you still don't agree with me.

All the velocity and acceleration vector balance stuff you are talking about only works when it is ground contact that provides both forces. Any force the conveyor applies to the wheel spins off freely without acting on the plane itself, while the force causing the plane to move definitely acts on the plane. That puts only the jet propulsion force acting on the plane and it moves.