Airplane on a converter belt question.

[Kevin J]

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Friction between the car’s wheels and the conveyor belt would only become a factor at very high rpm.

A belt sander might be more like it.

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Even so. Picture running a hot wheel car over a belt sander. No matter how fast the sander goes in the opposite direction of the car's wheels, you will be able to move the car forward, because the car's wheels are not what's generating the forward torque. Why wouldn't thrust work the same way?

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The belt sander is 5 feet wide and you’re pushing a refrigerator.

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I think you might have countered yourself here. Why would it be more difficult for the refrigerator to overcome the belt sander? Not because of it's wheel's speed, but because of it's weight! IOW- Gravity, not wheel speed.

[Nottom]

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Shouldn't this question be phrased. Can a helicopter take off?

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Helicopters don't have wheels so the belt wouldn't move. Even if it did a helicopter creates its own lift by spinning the rotor. There is really no arguement for it not to take off.

An somewhat equivalent question for a helicopter would be that it was sitting on a giant spinning circle that spun at the same speed as the rotor. Would the helicopter take off?

(I would think no)

[DougShrapnel]

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Helicopters don't have wheels so the belt wouldn't move. Even if it did a helicopter creates its own lift by spinning the rotor. There is really no arguement for it not to take off.

[/ QUOTE ] Right, essentialy you are turning an airplane into a helicopter. If the engine is powerfull enough to create enough lift, the plane will take off. I have no idea if a standard commercial engine is powerful enough, but my guess is that it is. The fluid speed, in this case airspeed, is what matters. Forward motion in realtion to a marble gound, a grass gound, or a converyor belt is not the only cause of lift. Forward motion in relation to the air is the cause of lift.

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An somewhat equivalent question for a helicopter would be that it was sitting on a giant spinning circle that spun at the same speed as the rotor. Would the helicopter take off?


[/ QUOTE ] I think this one is no. The fluid speed would be dictated by the helicopter it self. I don't think a helicopters engine is srong enough to create enough lift from the body of the helicopter instead of the rotor.

[TomTom]

Rather then considering belt speed locked to wheel speed, I first back off and think HOW they would be locked. Being an engineer, I would do this by measuring the position of the wheels. Say the plane points to the left, and the belt revolves to the right. If my control system saw the wheel move to the left, the belt would speed up. If the wheel moves to the right, the belt slows down. A classic single loop control feedback loop.

Thus a plane just beginning to move (to the left) would cause the belt to speed up (to the right) to return to the equilibrium state of wheel at the starting point.

Now wheels are by design low friction bearings, not the best (meaning the worst) way to impart a force is by spinning the wheels. If we let this friction go to zero we quickly reach the point where the slightest movement of the plane will require an infinite belt speed to overcome.

This infinite speed is the given of the thought experiment (the “converter belt which is rigged to move/spin in the opposite direction” part). So by the very definition of this problem, the plane sits exactly where it is on the ground, it has no air speed, it does not take off.

And of course, this assumes the belt itself doesn’t generate a back wind to raise the plane. But since the plane never moves, the belt can be as small as the contact area of each individual wheel, so this isn’t a limiting assumption. Either use multiple small belts, or one large one with wheel cut outs. No movement, no wind, no rise.

If we let this friction go above zero as we transition from pure thought to some kind of physical experiment, the wheel bearings become the critical item. The belt now need to turn fast enough (but now finitely so) to keep the plane in place by using this friction as a brake. The wheel bearings would need to absorb whatever force the engines are imparting to the entire plane.

I don’t see why this would be a problem at all. After all, I seem to be able to drive my car to and from work every day, and those bearings seem to handle the load acceptably well.

Here’s another way to look at the whole thing: Don’t think of belt/plane relative motion, be the guy standing next to the belt on the runway doing this experiment. Since he knows he wouldn’t see the plane move relative to him, instead of buying an expensive high speed conveyer belt, he buys a couple of bottle of crazy glue, and sticks the plane to the runway via the wheels.

De plane don’t move. De plane don’t take off.

[Sharkey]

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Shouldn't this question be phrased. Can a helicopter take off?

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The question really boils down to the following:

Can the plane acquire the minimum speed necessary for takeoff when, with every increase in plane speed, there follows an increase in belt speed by however much is necessary to increase the backward frictional force on the plane by however much is necessary to stop the plane?

Given that the answer is “no”, the plane will not move forward. Lift is not a factor.

[Kevin J]

Hopefully, you are an engineer who is not employed in the aerodynamic or jet propulsion fields. [img]/images/graemlins/laugh.gif[/img]

Everything you say is absolutely correct IF.... The wheels were what propelled the plane forward. However, thrust is what propells a plane, not it's wheels. The wheels only facillitate forward movement, they are not the cause of forward movement.

The plane's forward progress is hampered by the loss of surface to wheel friction, but it is not arrested altogether. Thrust force, which operates independent of wheel rotation (or any part of the plane for that matter), will eventually supercede this loss of friction and the plane WILL take off I assure you.

[Sharkey]

Incorrect.

The wheels may not be causing the forward motion, but they are the source of an arbitrarily great backward force which will be raised by way of an increase in belt speed whenever the plane begins to move foreward.

[madnak]

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Incorrect.

The wheels may not be causing the forward motion, but they are the source of an arbitrarily great backward force which will be raised by way of an increase in belt speed whenever the plane begins to move foreward.

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There is no backward force. The bearings prevent any force from being exerted.

[Sharkey]

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Incorrect.

The wheels may not be causing the forward motion, but they are the source of an arbitrarily great backward force which will be raised by way of an increase in belt speed whenever the plane begins to move foreward.

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There is no backward force. The bearings prevent any force from being exerted.

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No plane has ever been invented that would not coast to a stop on a long enough runway, air drag discounted.

[Sharkey]

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The wheel bearings would need to absorb whatever force the engines are imparting to the entire plane.

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Some good points in your post, except be advised that the tires on the runway are also a significant source of friction.