# So, you have a plane on a conveyor belt...

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What if we mount the engines in reverse?

Since the magical treadmill, for some reason, needs to keep the wheels spinning, will the plane start moving forwards?

What if we put a giant anvil on the treadmill in front of the plane? Does that count as brakes?

Can't believe this thread is still going on.

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6 hours ago, DAL59 said:

The treadmill is equivilent to brakes.

If that were so, then you couldn't drive a car on a treadmill.

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10 hours ago, Shpaget said:

Can't believe this thread is still going on.

Can't agree more.

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12 hours ago, DAL59 said:

No, because the plane is held in place by the belt.  In either interpretation it doesn't take off.

I was like... oh oh oh... I think he may come around here.....

11 hours ago, DAL59 said:

But, the plane's wheels need to spin in order for the plane to move forward.

Oh yeah, he's almost there!!!  We'll see the light bulb click on any second now....

11 hours ago, DAL59 said:

The treadmill is equivilent to brakes.

Nope... we've lost him.

(All in good fun Dal!)

Meanwhile:

But this is so enjoyable....

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Now watch me confuse the issue.

All previous discussion has assumed that the wheels are massless/inertialess and the wheel hub is frictionless. When this is the case any forces on the wheels are infinitesimal.

It takes no force from the belt to rotate the wheels freely or to speed them up or slow them down and there is no resistance from the wheel hub. The wheels spin freely to match whatever speed the belt is moving completely decoupled from the plane. The plane doesn't care what the wheels are doing it sees no force through the wheel hub.

Now add wheel mass/inertia. The force of the belt on the wheels is not a couple, or pure torque. It exerts a moment so that when the belt is accelerating it spins up the wheels. But the force at the rim must be matched by a force at the hub in order to hold the wheel stationary relative to the plane (Resolving forces). This force does act as a drag on the plane, but it's tiny relative to the forces the plane's engines are capable of exerting because it takes very little force to spin a wheel compared to moving a plane, so inertialess is a good first approximation. And this force only acts whilst the belt is accelerating relative to the plane. At constant speed no force is required to change the wheels' velocity.

Now add wheel hub friction. A resistive torque at the wheel hub is opposed by a force from the belt creating a torque that holds the wheel to the speed of the belt. But as we've previously established, force from the belt is not a pure torque. So the force of the belt on the wheel rim is reacted at the wheel hub. It acts as a constant drag on the plane. But wheel hubs are built to have very low coefficients of friction. This rolling resistance is tiny compared to the force required to accelerate a whole plane. Therefore frictionless wheel hubs are a very good first approximation.

The belt is capable of exerting tiny drag forces on the plane. The plane's engines are massively more capable of exerting force on the plane. Therefore for any reasonable speed of belt it doesn't matter what the belt is doing. The plane can just apply thrust to overcome it.

Edited by RCgothic

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12 hours ago, DAL59 said:

But﻿, the plane's wheels need to spin in order for the plane to move forward.  ﻿

A Paddle Steamer can get up to the river head against the river current and the paddle is still spinning.

And that's something that powers the "wheel" directly. An airplane doesn't power the wheel, it just powers the entire craft. It can skid as much as it wants.

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40 minutes ago, RCgothic said:

Now watch me confuse the issue. ﻿

Also consider pontoons.

Same idea, but on water.   Think a long flat, but moving, river.

The water creates drag on the pontoons, but the engines have enough power to overcome that drag, accelerate to take off speed, and lift off.

This is identical to a plane on a treadmill, but with more drag applied.

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8 hours ago, cubinator said:

If that were so, then you couldn't drive a car on a treadmill.

You can, but it won't get anywhere.

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1 hour ago, DAL59 said:

You can, but it won't get anywhere.

True - for a car, the treadmill can prevent it from moving because the rotation of the wheels is a determinant of how fast the car can go. For a plane, however, the wheels have nothing to do with how it accelerates.

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Car has powered wheels.

Planes has unpowered wheels.

There's a difference.

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4 hours ago, YNM said:

A Paddle Steamer can get up to the river head against the river current and the paddle is still spinning.

And that's something that powers the "wheel" directly.

Which is why it doesn't fit the analogy. A paddle steamer is more like a car. Both get their propulsion by pushing against the surface. An airplane gets its propulsion by pushing against the air.

A closer analogy would be a sailboat. A sailboat can move against the current with a wind, because the air is pushing on it.

4 hours ago, YNM said:

An airplane doesn't power the wheel, it just powers the entire craft. It can skid as much as it wants.

Not necessarily. If a Boeing 747 goes to full throttle and then applies the brakes, it will not take off. A 747's TWR is around 0.3; the coefficient of sliding friction between rubber tires and asphalt is around 0.8.

3 hours ago, Gargamel said:

Also consider pontoons.

Same idea, but on water.   Think a long flat, but moving, river.

The water creates drag on the pontoons, but the engines have enough power to overcome that drag, accelerate to take off speed, and lift off.

This is identical to a plane on a treadmill, but with more drag applied.

No, because fluid drag is proportional to the square of velocity.

In practice, seaplanes typically take off pointing upstream, because the downstream flow of water creates a headwind. But imagine that the air at the water surface is stationary with respect to the bank. In order to accelerate to takeoff speed, your engine needs to overcome the fluid drag on your pontoons produced when you move through the water. Suppose that a plane typically takes off at 40 knots. If the water is moving downstream at 10 knots, then it will need to accelerate to 50 knots relative to the water surface, and the drag produced on the pontoons just before liftoff will actually be 156% of normal drag. If the water is moving downstream at 20 knots, the plane will need to accelerate to 60 knots relative to the water, and the drag will go up to 225%. If the water is moving at 40 knots, then drag will go up to 400%.

Contrast this with the airplane on the treadmill. Suppose the airplane's takeoff speed is 40 knots and normal rolling drag on a flat runway inhibits the airplane's progress by a force of 100 Arbitrary-Force-Units (AFU). If we move the airplane from the runway to a treadmill and do not turn the treadmill on, then rolling drag will still be 100 AFU. If we turn the treadmill on to operate at a constant 10 knots, rolling drag...will still be 100 AFU. If the treadmill is turned on to 50 knots, rolling drag will still be 100 AFU. If the treadmill runs at 100 knots or 200 knots or 500 knots, rolling drag will still be 100 AFU. The speed of the conveyor belt does not change the forces acting on the plane.

If you want the pontoon example to match,  you'd need to say that the pontoons are coated in some kind of nearly-frictionless oil that has a set amount of drag and doesn't get more draggy matter how fast it goes.

19 minutes ago, cubinator said:
1 hour ago, DAL59 said:
10 hours ago, cubinator said:
Quote

The treadmill is equivilent to brakes.

If that were so, then you couldn't drive a car on a treadmill.

You can, but it won't get anywhere.

True - for a car, the treadmill can prevent it from moving because the rotation of the wheels is a determinant of how fast the car can go. For a plane, however, the wheels have nothing to do with how it accelerates.

Maybe this will help.

Replace the airplane with a car.

Place the car in neutral.

Attach a winch to the front of the car, and secure the winch to a big rock way out in front of the treadmill.

Turn on the winch and the treadmill at the same time.

Does the car move?

Most importantly: Can the conveyor belt keep the car from moving?

Edited by sevenperforce

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What if its a tank, which has pre-installed wheel-speed-matching conveyors on both sides?

On a conveyor.

Going uphill.

Underwater.

At the North Pole.

Now where is your riddle god?

Edited by p1t1o

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Place a giant treadmill on a steep downward incline.

Place a car on the treadmill, in neutral, and set the brakes.

Turn on the treadmill (going uphill) and release the brakes.

Can the treadmill go fast enough to keep the car from rolling downhill and off the treadmill?

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If the plane does ever take off, does it sound more like someone saying "Yanny" or someone saying "Laurel"?

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4 hours ago, sevenperforce said:

If﻿ a Boeing 747 goes to full throttle and then applies the brakes, it will not take ﻿off.

In FSX, it will.

So it does in real life eventually, after burning the tyres off and tearing the runway away.

Edited by YNM

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Why don’t you just taxi the plane off the treadmill and take it off?

oh yeah right, it defeats the purpose of the challenge.

Duuuuuurrrr

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1 hour ago, p1t1o said:

If the plane does ever take off, does it sound more like someone saying "Yanny" or someone saying "Laurel"?

Is the plane painted blue and black, or white and gold?

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13 minutes ago, razark said:

Is the plane painted blue and black, or white and gold?

Its hard to say, whenever I look directly at it, it disappears.

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If a plane is on a conveyor belt in the forest and no one sees it, will the Yankees win the World Cup?

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7 hours ago, sevenperforce said:

Most importantly: Can the conveyor belt keep the car from moving?

Yes.

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6 minutes ago, DAL59 said:

Yes.

WRT the belt surface ?

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11 minutes ago, DAL59 said:
7 hours ago, sevenperforce said:

Replace the airplane with a car.

Place the car in neutral.

Attach a winch to the front of the car, and secure the winch to a big rock way out in front of the treadmill.

Turn on the winch and the treadmill at the same time.

Does the car move?

Most importantly: Can the conveyor belt keep the car from moving?

Yes.

How?

The car is in neutral. Nothing the conveyor belt does can possibly prevent the winch from pulling the car forward.

This is where my brain starts to melt. It's one thing to say, "The airplane on a treadmill problem is just a case of mistaken interpretation; one group is trying to show that planes don't use their wheels for propulsion while the other group is trying to insist that a stationary plane cannot take off." But....this?

Another example:

Put on roller skates.

You will now need to hold onto the grips more tightly, since the treadmill acting on the roller skate wheels is pulling you backward a little bit.

Does it get harder to hold on? No, because the rotation rate of the wheels does not alter the force acting on the skates.

Turn up the treadmill even more, faster and faster.

Does it ever become impossible for you to pull yourself forward against the direction of motion of the treadmill, using the grips?

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1 hour ago, sevenperforce said:

Nothing the conveyor belt does can possibly prevent the winch from pulling the car forward.

In order for the car to move, the wheels must spin.  The treadmill forces the wheels to not spin in the correct direction.  The winch is irrelevant.

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14 minutes ago, DAL59 said:

In order for the car to move, the wheels must spin.  The treadmill forces the wheels to not spin in the correct direction.  The winch is irrelevant.

Wait, what?!

A car can be winched in any conceivable direction without regard to whether or not the wheels spin, or what direction they spin in.

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2 hours ago, DAL59 said:

In order for the car to move, the wheels must spin.  The treadmill forces the wheels to not spin in the correct direction.  The winch is irrelevant.

But if the wheels are not exerting any force on the car, they can spin in place. It's as if the car (or plane for that matter) were sitting on near frictionless skids.

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