# Phunny Physics

#### Steve Shannon

##### Well-Known Member
TRF Supporter
I still say it can't move if the speed of the belt "exactly" matches the speed of the wheels.

For the plane to move relative to the ground the wheels would have to move at a higher speed than the (seemingly magical) belt. If the speed of the belt is infinite, no amount of thrust will overcome the friction of the wheels turning.

You're looking at it wrong. The speed of the wheels has absolutely nothing to do with the speed of the air passing over and under the wings. In fact, regardless of the airspeed of the plane, unless the brakes are locked up on the wheels, the wheels and the conveyor belt will always be going the same speed as each other. The conveyor belt will drive the wheels at its speed unless the wheels are prevented from turning.

Steve Shannon

#### Zeus-cat

##### Well-Known Member
I still say it can't move if the speed of the belt "exactly" matches the speed of the wheels.

For the plane to move relative to the ground the wheels would have to move at a higher speed than the (seemingly magical) belt. If the speed of the belt is infinite, no amount of thrust will overcome the friction of the wheels turning.

Why? Planes take off on skis and pontoons. The plane could just drag the wheels across the belt if the wheels can't turn fast enough.

#### RocketFeller

##### Well-Known Member
Okay, I fully understand that in real life the plane could take off, but how could the plane be moving forward if the belt exactly matches the wheel speed?

I must be missing something, but this seems like a purely esoteric question.

##### Well-Known Member
If my plane is on a treadmill the thrust would keep me at pace with the speed of the treadmill. Even at full speed I would never have airflow over the wings to generate lift. So the plane would never fly. If I turn my plane around so that I am going the same direction as the treadmill then it would fly as long as I can generate enough thrust to gain lift.

#### Steve Shannon

##### Well-Known Member
TRF Supporter
The wheels spin freely. The motion of the plane relative to the air is controlled by the plane's thrust alone. The rotation of the wheels is a completely different frame of reference. The wheels rotate so that at the point of contact the wheels and the belt, regardless of the belts speed, are not sliding against each other.
If you lock the wheels by applying the brakes, and lock the conveyor so it's not moving and if the engines are not strong enough to overcome the friction between the wheels and the conveyor then it's possible to hold the plane so there's no air motion over the wings, but that's the only way the conveyor can prevent air from passing over the wings.
It's also possible to launch the plane by turning the conveyor to drive the plane forward as if launched from a catapult on a carrier.

Steve Shannon

#### OverTheTop

##### Well-Known Member
TRF Supporter
Do they have any more difficult questions?

##### Well-Known Member
It's also possible to launch the plane by turning the conveyor to drive the plane forward as if launched from a catapult on a carrier.
If the wheels are on frictionless mounts on the aircraft then the exact opposite of the original question would happen. The conveyor would move the wheels, but with no friction transferring that movement to the aircraft, the aircraft wouldn't go anywhere.

As to the original problem: next time you're in a supermarket and the conveyor is moving your stuff towards the checkout, see if you can push your stuff against the conveyor. You can, because you're not on the conveyor yourself. It's even easier if you put a toy car on that conveyor and try to push it against the movement of the conveyor because its wheels provide less friction than sliding a loaf of bread along the conveyor, for example.

And so it is with the aircraft. The engines are not attached to the conveyor and push the aircraft forwards regardless of what the conveyor is doing.

#### dave carver

##### ....what hump?
The plane needs to be moving forward to fly and that's all there is to that. Plus if the wheels aren't turning then the plane isn't going anywhere and there's no lift without moving. So even if you could get a belt to move at 300 MPH the relative speed of the airframe is zero thus no lift.

Throttle back there, buddy. You're going nowhere fast

Actually the "what if" question renders this as academic. The wheels simply hold the airframe off the ground with the engines providing the motive power. You get a long enough runway and it's going to take off with the wheels freewheeling like mad. In this case the wheel speed is irrelevant to the speed of the airframe.

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#### Steve Shannon

##### Well-Known Member
TRF Supporter
If the wheels are on frictionless mounts on the aircraft then the exact opposite of the original question would happen. The conveyor would move the wheels, but with no friction transferring that movement to the aircraft, the aircraft wouldn't go anywhere.

As to the original problem: next time you're in a supermarket and the conveyor is moving your stuff towards the checkout, see if you can push your stuff against the conveyor. You can, because you're not on the conveyor yourself. It's even easier if you put a toy car on that conveyor and try to push it against the movement of the conveyor because its wheels provide less friction than sliding a loaf of bread along the conveyor, for example.

And so it is with the aircraft. The engines are not attached to the conveyor and push the aircraft forwards regardless of what the conveyor is doing.

I'm sorry I didn't make it clear. My third paragraph was meant with the wheels locked as in my second paragraph. If the wheels are locked so the conveyor is moving the plane, and the conveyor is spinning fast enough, it could launch the plane. Of course without the engines it would just glide to a stop.

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#### ThirstyBarbarian

##### Well-Known Member
It seems like with this problem, you are just spinning your wheels.

If you put a car on the magic treadmill, it would never get moving at all, because it's the car's drive wheels that push the car down the road. If the treadmill matches the speed of the wheels, the car doesn't move.

A plane is not pushed down the runway by the wheels. The wheels turn freely, and the plane is pushed by the thrust of the jet engines. It doesn't matter what the wheels are doing, the plane will still move forward under the thrust of the engines and will take off.

I'm actually having trouble visualizing how the magic treadmill would work with the plane. What does it mean to say the treadmill exactly matches the speed of the wheels, moving in the opposite direction? As long as the wheels are not sliding against the treadmill, doesn't the treadmill always match the speed of the wheels? The problem doesn't really define a frame of reference for measuring the speed of the wheels.

With the car, it's seems obvious, the car's motor drives the wheels at a certain rate, and the treadmill will turn at that rate. As soon as the car applies torque to the wheels, the car's momentum keeps the car in place, and the treadmill begins to spin at the rate of the wheels, leaving the car stationary.

The plane doesn't move by applying torque to the wheels. So when the plane fires up its engines, right before it starts to move, the wheels' rotation is zero, and the wheel has an angular momentum that will resist it beginning to turn. So when the plane starts to move, could the treadmill just move with it, matching the wheels' angular speed of zero?

Or or does the problem mean that the treadmill matches the movement of the hub of the wheel, but in the opposite direction, like in the earlier free body diagram? The diagram shows how that would work very well.

Or is there a way of looking at it more like the car problem, and before the plane can even move the tiniest fraction of an inch, the wheels and treadmill spin up "to infinity, and beyond!"

#### Steve Shannon

##### Well-Known Member
TRF Supporter
It seems like with this problem, you are just spinning your wheels.

If you put a car on the magic treadmill, it would never get moving at all, because it's the car's drive wheels that push the car down the road. If the treadmill matches the speed of the wheels, the car doesn't move.

A plane is not pushed down the runway by the wheels. The wheels turn freely, and the plane is pushed by the thrust of the jet engines. It doesn't matter what the wheels are doing, the plane will still move forward under the thrust of the engines and will take off.

I'm actually having trouble visualizing how the magic treadmill would work with the plane. What does it mean to say the treadmill exactly matches the speed of the wheels, moving in the opposite direction? As long as the wheels are not sliding against the treadmill, doesn't the treadmill always match the speed of the wheels? The problem doesn't really define a frame of reference for measuring the speed of the wheels.

With the car, it's seems obvious, the car's motor drives the wheels at a certain rate, and the treadmill will turn at that rate. As soon as the car applies torque to the wheels, the car's momentum keeps the car in place, and the treadmill begins to spin at the rate of the wheels, leaving the car stationary.

The plane doesn't move by applying torque to the wheels. So when the plane fires up its engines, right before it starts to move, the wheels' rotation is zero, and the wheel has an angular momentum that will resist it beginning to turn. So when the plane starts to move, could the treadmill just move with it, matching the wheels' angular speed of zero?

Or or does the problem mean that the treadmill matches the movement of the hub of the wheel, but in the opposite direction, like in the earlier free body diagram? The diagram shows how that would work very well.

Or is there a way of looking at it more like the car problem, and before the plane can even move the tiniest fraction of an inch, the wheels and treadmill spin up "to infinity, and beyond!"

You're exactly right.

#### Incongruent

##### Well-Known Member
I'm sorry I didn't make it clear. My third paragraph was meant with the wheels locked as in my second paragraph. If the wheels are locked so the conveyor is moving the plane, and the conveyor is spinning fast enough, it could launch the plane. Of course without the engines it would just glide to a stop.

If the wheels are locked the conveyer belt doesn't move.

TRF Supporter

#### boomtube-mk2

##### Well-Known Member
Years ago a group of friends and i hiked to the top of Mount San Antonio aka Mt Baldy in the San Gabriel Mountains in SoCal a tad over 10,000 feet. On the western slope was a small single engine aircraft in perfect condition. The story was simple if harrowing. The pilot was attempting to fly over the mountains when he encounter a storm. The headwinds were so severe that while his airspeed was ample enough to keep the plane in the sky his speed over ground was slowly dropping to zero. And then the mountain got in his way and for all intents and purposes he parked it on the ridge.

Apparently he kept the motor running to provide heat and waited out the storm and then hiked down. The he had to charter a helicopter and crew to go and and haul his plane down.

#### Lowpuller

##### Well-Known Member

I believe your thrust is used up in turning the conveyor.

If understand the described scenario, any applied energy would move the conveyor, negating forward movement.

The Myth Busters scenario is not accurate. The plane is moving forward because other forces are moving the conveyor.

If the energy generated by the plane causes the plane "to move" this will cause the wheels to turn which will then drive the conveyor, meaning no forward motion, no lift, no fly...................

#### watheyak

##### Barnstormer
TRF Supporter
Nothing from the plane could cause the conveyor to move!

#### dhbarr

##### Amateur Professional
TRF Supporter
I can't tell who's trolling in this thread; it's glorious.

#### Steve Shannon

##### Well-Known Member
TRF Supporter

I believe your thrust is used up in turning the conveyor.

If understand the described scenario, any applied energy would move the conveyor, negating forward movement.

The Myth Busters scenario is not accurate. The plane is moving forward because other forces are moving the conveyor.

If the energy generated by the plane causes the plane "to move" this will cause the wheels to turn which will then drive the conveyor, meaning no forward motion, no lift, no fly...................

Thrust does not drive the wheels. It simply forces the plane in the opposite direction from the thrust: Newton's Third Law.

#### BuiltFromTrash

##### Well-Known Member
But LOWPULLER your saying that the conveyor is somehow powered by the airplane, when it clearly is not in the original diagram provided by the OP.

Say you have a cart on wheels. Drag it across the ground. Observe the wheels turning and the cart makes progress over the ground. Put said cart on conveyor and turn it on. Observe the cart moving on the conveyor. Grab the cart while maintaining contact with the conveyor and walk against the conveyor. Observe the cart's wheels turning. Now they are turning faster and the cart still makes the same progress over the ground as in the earlier demonstration.

The carts wheels have friction, therefore the conveyor will move the cart. (In a world without friction, It would stay in place. Remember Newtons 2nd law.)
Your feet have friction with the ground to the side of the conveyor. You are providing a second motive force to the cart, one that overcomes the friction of the wheels.
All the conveyor has to overcome to move the cart is the cart's inertial mass. You overcome both the inertial mass and the friction of the wheels to move the cart.

TL;DR If you pull the launch rod through the rocket's LL rather than have it stationary, the rocket will still takeoff. (LL is the wheels, Launch rod is the conveyor, Rocket is the plane.)

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#### Steve Shannon

##### Well-Known Member
TRF Supporter
But your saying that the conveyor is somehow powered by the airplane, when it clearly is not in the original diagram provided by the OP.

Say you have a cart on wheels. Drag it across the ground. Observe the wheels turning and the cart makes progress over the ground. Put said cart on conveyor and turn it on. Observe the cart moving on the conveyor. Grab the cart while maintaining contact with the conveyor and walk against the conveyor. Observe the cart's wheels turning. Now they are turning faster and the cart still makes the same progress over the ground as in the earlier demonstration.

The carts wheels have friction, therefore the conveyor will move the cart. (In a world without friction, It would stay in place. Remember Newtons 2nd law.)
Your feet have friction with the ground to the side of the conveyor. You are providing a second motive force to the cart, one that overcomes the friction of the wheels.
All the conveyor has to overcome to move the cart is the cart's inertial mass. You overcome both the inertial mass and the friction of the wheels to move the cart.

TL;DR If you pull the launch rod through the rocket's LL rather than have it stationary, the rocket will still takeoff. (LL is the wheels, Launch rod is the conveyor, Rocket is the plane.)

#### BuiltFromTrash

##### Well-Known Member
Lol I know you aren't. I typed it up when Lowpullers post was the latest one. I will correct the post.

Edit: Fixed

#### Incongruent

##### Well-Known Member
Or is there a way of looking at it more like the car problem, and before the plane can even move the tiniest fraction of an inch, the wheels and treadmill spin up "to infinity, and beyond!"

Yes. It might not instantly speed up to infinity, though. Check my thoughts. The speed of the conveyer belt is equal to the speed of the wheels. (C = W) The speed of the wheels is equal to the speed of the plane (think wheels on a normal runway) plus the speed that the conveyer belt imparts to it by spinning. (W = C + S(speed of the plane)). By substitution, you get C = C + S.

If the plane isn't moving, you get C=C+0, or in other words, the wheels and conveyer belt will maintain a constant speed. (Not necessarily 0) If the wheel is spinning, (and the conveyer belt) friction will try and brake the plane and drive it in the opposite direction that the wheels are spinning, along the conveyer belt. This results in the wheel spinning slower (because the plane is moving with the conveyer belt) and the system will slow to 0.

Now if the the plane is moving, the equation becomes C = C + 1 (depending on the interval of time used, 1 will fit. The point is that the plane is moving in relation to the ground) and you get a positive feedback loop. I (currently) think that this will result in the conveyer belt accelerating backwards at the speed of the plane, (every second the speed of the conveyer belt backwards in m/s increases by the numbers of meters the plane moved forwards) or it could just accelerate to infinity. I used to think it was the latter, but after reconsidering I believe the former will happen. In context, let's assume the plane moves at 1 m/s. (Time graduated to 1 second increments) The first second, the plane moves forward 1 meter and the wheels equally as much. The second second, the plane moves another meter and the wheels turn 1 meter plus the meter they're already turning, which makes them (and the conveyer belt) turn at 2m/s. The next, 3 m/S and so on. In other words, the speed that the plane moves is the rate that the wheels and conveyer belt accelerate. This is why when the plane moved with the conveyer belt because of friction in the plane not moving example, the conveyer belt decelerated to 0.

Ok, never mind (maybe). I consulted the calculator and they told me that y = y + x (which may not be the right equation, because X means the plane's speed is increasing, while the model has the plane at a constant speed, which is true but what am I even talking about now?) creates a vertical line (which means instant acceleration to infinity) Now I'm really confused. Help!

#### BuiltFromTrash

##### Well-Known Member
We ALL need help in this thread. (Seriously, no HS physics classes were taken?) XD

Reminds me of: Rocket engines are a hoax. They have nothing to push against in space.

#### EXPjawa

##### Well-Known Member
Think of it this way: you're at the airport. You're running late, so you drag your carry-on wheeled bag down as many of the moving walkways as possible to save time. In this example, the bag represents the plane and you are the plane's engines, providing the thrust. The walkway is independently powered, doing its own thing whether you're on it or not.

As you pull the bag down the walkway, the wheels on your bag turn. They're rolling over the walkway, at a speed relative to the walkway surface the same as if on flat ground, but the speed of the bag's progress is increased in relation to the hallway outside the belt (assuming you're walking with the belt). So, for the sake of argument, lets say that the belt allows the bag to progress along at twice the speed it would on flat ground, with the wheels rolling at normal speed. So, the wheels are rolling at half the rate otherwise required for that rate of progress. Now, if you walk against the belt - thereby slowing your forward progress down and pissing off other airport visitors that are coming at you head-on - your bag's wheels are still rolling at the same rate in relation to the belt surface. But your pace of progress is cut in half. If you had enough "thrust" to get back up to your walking speed against the belt (relative to the outside world), your bag's wheels now spin at 2X the RPM as they would on flat ground for that speed. But you still make progress - you still achieve your goal of walking to the end of the belt. If you happen to have wings, and in the process of getting to the end of the belt happen to go fast enough to achieve sufficient lift, you take off.

Its a matter of relative motion and speed. And, with the assumption of an independent belt system (I read nothing to indicate that it is somehow driven by the plane itself), the wheels react to that. But that isn't part of the closed-loop that thrusts the plane forward and up to speed. If the belt is at a fixed speed, assuming the wheel hub friction is less than the belt drive mechanism, as the plane speeds up, the wheels' speeds are only offset somewhat from their normal rate of rotation at take-off. The wheels roll down the moving belt, just like the bag at the airport that's trying to get to the plane. Now, if the belt is jiggered so that it speeds up in proportion to the plane's acceleration, the wheels will continue to roll at a rate 2X (or whatever) their normal rate, increasing in speed as they do. But the plane is thrust along and, as a system, doesn't care what the wheels are doing. There's nothing in the plane-belt system that causes the plane to drive the belt as described in the problem.

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#### Steve Shannon

##### Well-Known Member
TRF Supporter
Lol I know you aren't. I typed it up when Lowpullers post was the latest one. I will correct the post.

Edit: Fixed

Thanks! I'm babysitting my 17 mo. Granddaughter so my thoughts and posts are disjointed anyway, but I didn't think I was that bad!

#### ThirstyBarbarian

##### Well-Known Member
Yes. It might not instantly speed up to infinity, though. Check my thoughts. The speed of the conveyer belt is equal to the speed of the wheels. (C = W) The speed of the wheels is equal to the speed of the plane (think wheels on a normal runway) plus the speed that the conveyer belt imparts to it by spinning. (W = C + S(speed of the plane)). By substitution, you get C = C + S.

If the plane isn't moving, you get C=C+0, or in other words, the wheels and conveyer belt will maintain a constant speed. (Not necessarily 0) If the wheel is spinning, (and the conveyer belt) friction will try and brake the plane and drive it in the opposite direction that the wheels are spinning, along the conveyer belt. This results in the wheel spinning slower (because the plane is moving with the conveyer belt) and the system will slow to 0.

Now if the the plane is moving, the equation becomes C = C + 1 (depending on the interval of time used, 1 will fit. The point is that the plane is moving in relation to the ground) and you get a positive feedback loop. I (currently) think that this will result in the conveyer belt accelerating backwards at the speed of the plane, (every second the speed of the conveyer belt backwards in m/s increases by the numbers of meters the plane moved forwards) or it could just accelerate to infinity. I used to think it was the latter, but after reconsidering I believe the former will happen. In context, let's assume the plane moves at 1 m/s. (Time graduated to 1 second increments) The first second, the plane moves forward 1 meter and the wheels equally as much. The second second, the plane moves another meter and the wheels turn 1 meter plus the meter they're already turning, which makes them (and the conveyer belt) turn at 2m/s. The next, 3 m/S and so on. In other words, the speed that the plane moves is the rate that the wheels and conveyer belt accelerate. This is why when the plane moved with the conveyer belt because of friction in the plane not moving example, the conveyer belt decelerated to 0.

Ok, never mind (maybe). I consulted the calculator and they told me that y = y + x (which may not be the right equation, because X means the plane's speed is increasing, while the model has the plane at a constant speed, which is true but what am I even talking about now?) creates a vertical line (which means instant acceleration to infinity) Now I'm really confused. Help!

Yep. This is the most confusing one. I don't really know how the math should be set up, but it's basically self referential --- some kind of feedback loop where the speed of the conveyor is equal to the speed of the wheels, but if the plane is moving even a little bit, the speed of the wheels is greater than the conveyor, and the conveyor accelerates to infinity to catch up.

It a "division by zero" kind of situation that will result in the entire universe callopsing in on itself, forming an infinitely hot and dense singularity! Real wrath of God type stuff! Fire and brimstone coming down from the skies! Rivers and seas boiling! Forty years of darkness! Earthquakes, volcanoes! The dead rising from the grave! Human sacrifice! Dogs and cats living together! Mass hysteria!

#### BuiltFromTrash

##### Well-Known Member
And a world without ThirstyBarbarian!

#### RocketFeller

##### Well-Known Member
This is how I imagine it:

Plane is sitting on treadmill, nothing is moving.
Plane applies a teensy bit of thrust. Wheels try to roll forward , but magical treadmill instantly speeds up to match their speed.
At this point the plane is not moving forward and friction in the hubs are equal to the small amount of thrust.
Plane increases thrust, and the speed of wheels increases, quickly leaving the realm of real world velocity.

For the plane to be moving forward its wheel speed needs to be greater than the belt's speed. If they are exactly equal the plane isn't moving, assuming the treadmill itself is stationary.

Pretty silly, but fun to argue about!

#### RocketFeller

##### Well-Known Member
Also, now that I've read Thirsty Barbarian's last post I think that all that can be said has been said. He seems to know too much...

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