Airplane physics question

[Duke]

If the conveyor belt forward speed matched the forward rotation of the airplane wheels, then yes, the plane would take off. The belt is moving the plane, thus moving air over and undrer the wing creating lift.

If the conveyor belt is moving in the opposite direction of the wheels, then no, the plane would therefore be standing still relative to the Earth, and therefore no wind is flowing over and under the wings whcih means no lift.

But the forward motion is NOT generated by the wheels. The rolling wheels are a byproduct of the propellor pulling the plane through the air.

If the treadmill can only run opposite the forward direction of the plane, then the treadmill will remain effectively stopped and the wheels will roll down it like any runway. If the treadmill can run WITH the plane, the wheels will not rotate, and the whole assembly will move forward until the plane takes off (reference "World's Smallest Airport" above).

 

[Carlos_23]

Duke's post got me thinking.
We see this example every single day in gyms, houses, etc. When you run on a treadmill, do you move from the spot? Now take this and apply it at the aircraft problem. Since the aircraft is not moving (assuming the wheels move in the opposite direction as the belt does, at the same speed) the wings wouldn't generate enough lift for the aircraft to take off, assuming, once again, that is it a fixed-wing aircraft.

In the "World's Smallest Airport" example, the plane's wheels do not need to move at all, because the car's wheels are doing so for them, [edit] therefore moving the whole plane and generating air flow, so the wings can generate enough lift. Basically, the aircraft is not the one "making" the thrust needed for subsequent lift; the car is.

Also, about the planes, I think they are Piper J-3 Cubs (standard aircraft in FS9 ), couldn't tell you about the cars, though. Sorry...

 

[Zardoz]

...Bonus points for whoever can tell me what the aircraft and the cars are.

Piper Cub

1948 Ford Tudor Sedan

1969 Pontiac Bonneville 4-door hardtop

 

[Solid Lifters]

But the forward motion is NOT generated by the wheels. The rolling wheels are a byproduct of the propellor pulling the plane through the air.

If the treadmill can only run opposite the forward direction of the plane, then the treadmill will remain effectively stopped and the wheels will roll down it like any runway. If the treadmill can run WITH the plane, the wheels will not rotate, and the whole assembly will move forward until the plane takes off (reference "World's Smallest Airport" above).

OK, this is weird stuff.

If the treadmill can only run opposite the forward direction of the plane, then the treadmill will remain effectively stopped and the wheels will roll down it like any runway.

OK, I understand it's the thrust of the jet, or whatever, that pulls the plane and the wheels movement are a byproduct of that thrust pulling the airplane. But, again, why would the treadmill remain effectively stopped? I don't get that part.

So, let's say this. If a jet is at the front end of a treadmill runway. The teadmill starts to move the plane backwards at the planes top speed of let's say 700mph. Now, the plane starts to thrust forward, and hence move forward. But, since it's moving backwards on the treadmill at 700mph, it's not really moving forward, but backwards at a slower pace from the full 700mph of the treadmill. So, when the plane hits full throttle and full speed at 700mph, wont the plane just stand still? Because the treadmill is moving at that speed. Since the plane can't physically move forward, it can't fly. Isn't this the same thing as the treadmill matching the movment of the plane if both the plane and treadmill start off standing still, but the treadmill matches the forward movement of the wheels?

 

[Kylehnat]

It's a chicken/egg question, unfortunately. We can't agree on whether the plane moves the wheels, or the wheels allow the plane to move. In fact, we don't know the specifics of the conveyor belt, so the question is really unanswerable. It's one of those lame "theoretical" questions that physics profs like to ask, but has no basis in reality.

 

[Zardoz]

...the question is really unanswerable. It's one of those lame "theoretical" questions that physics profs like to ask, but has no basis in reality.

Bingo!

Give the man the prize, and we'll all go home and do something more worthwhile, like watching cartoons or reading tabloid newspapers...

 

[ExigeEvan]

Question :

Imagine a plane is sat on the beginning of a massive conveyor belt/travelator type arrangement, as wide and as long as a runway, and intends to take off. The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation.There is no wind.

Can the plane take off?

Okay, I've reposted this because so many people are saying how it will take off if the conveyer belt is moving the plane forward. We know that, or at the least I do. That idea is no different to the Steam catapults on aircraft carriers.

Now the original question was that, but in a slightly befuddled way, is what if the conveyer belt was moving in teh same effect as someone on a tread mill. So that the plane wouldn't actually move relative to the earth.

 

[Duke]

In fact, we don't know the specifics of the conveyor belt, so the question is really unanswerable. It's one of those lame "theoretical" questions that physics profs like to ask, but has no basis in reality.

No, it's not. You guys are all hung up on the movement of the treadmill, and that's irrelevant to the issue. The plane takes off no matter how the treadmill works or doesn't work, because the plane moves itself through the air. The important part is the movement of the plane through the air - the movement of the treadmill relative to the plane cannot affect the movement of the plane relative to the air.

We're assuming a treadmill runway, sitting on the ground, in stationary air. That last part is the important part.

OK, I understand it's the thrust of the jet, or whatever, that pulls the plane and the wheels movement are a byproduct of that thrust pulling the airplane. But, again, why would the treadmill remain effectively stopped? I don't get that part.

Here's the deal: the propellor of our J3 Cub is what's pulling it through the stationary air mass. The air mass does not move realtive to the ground the treadmill is mounted on.

So, Pilot Pete gooses the throttle, and the propellor bites into the air and pulls the plane forward. The treadmill senses rotation, and starts moving backward. If it was B-spec Bob in his Trueno, he'd sit fixed in the same spot, going 40 mph relative to the treadmill and zero relative to the ground and air. But the airplane doesn't care what the treadmill does, because the airplane is driven by force against the stationary air mass, and is moving forward. So the propellor pulls the plane forward regardless of the motion of the treadmill, to a J3's takeoff speed of 40 mph. Now the treadmill is trying to counteract the rolling wheels, but because the plane is moving relative to the fixed ground and air mass, the tread mill sits still and the wheels roll forward over it, because the reference point of the axle is moving forward at 40 mph, rather than the car example, where the reference point of the axle sits still and therefore the treadmill must move 40 mph backwards to accomodate it.

It's all in the relativity - a car would move relative to the treadmill but NOT the ground/air. Since the plane IS moving relative to the ground/air, assuming the treadmill can't move backwards, then the treadmill stays stopped relative to the ground and the plane moves relative to the treadmill.

Now, if the treadmill is designed to run both ways, then the wheel'd don't roll and the plane takes off anyway. Pilot Pete gives her the gun and the Cub pulls itself forward, but the treadmill senses the motion and starts up immediately under the wheels, moving to cancel their rotation. So the plane moves itself forward at 40 mph and the treadmill moves itself under it at 40 mph, so the wheels don't roll. But again, the plane is moving itself through the air to takeoff speed, so as soon as it hits 40 mph relative to the air, it lifts off.

So, let's say this. If a jet is at the front end of a treadmill runway. The teadmill starts to move the plane backwards at the planes top speed of let's say 700mph. Now, the plane starts to thrust forward, and hence move forward. But, since it's moving backwards on the treadmill at 700mph, it's not really moving forward, but backwards at a slower pace from the full 700mph of the treadmill. So, when the plane hits full throttle and full speed at 700mph, wont the plane just stand still? Because the treadmill is moving at that speed. Since the plane can't physically move forward, it can't fly. Isn't this the same thing as the treadmill matching the movment of the plane if both the plane and treadmill start off standing still, but the treadmill matches the forward movement of the wheels?

This example misses the point that the plane pushes on the air, so the plane can move itself forward regardless of the wheels. That's what I'm trying to explain above.

Let's modify the original example a little. In the original example, there's some kind of feedback loop so that the treadmill can accelerate. This might lead to the uncontrolled overacceleration of the treadmill and wheels that Der Alta theorized. But in our new example, let's assume that the treadmill is speed limited to the takeoff speed of our J3 Cub, 40 mph.

Park the Cub at the end of the treadmill, with the tailwheel sitting up on a jackstand that is anchored to the ground. Fire up the engine and go to full throttle. The plane is pushing air backwards at 40 mph, because the anchor is preventing the plane from pulling itself forward at 40 mph. The treadmill is not moving because the wheels are not rolling.

Now shut the plane down and start the treadmill, backwards at 40 mph. The wheels now roll forward at 40 mph, because of the treadmill, but neither the plane nor the air are moving.

Now start both up. Air is being forced backwards by the propellor at 40 mph. The wheels are rolling forward at 40 mph, driven by the treadmill. The plane is still anchored at not moving relative to the ground.

Release the tailwheel and what happens? Instantly, the plane stops moving air backwards and starts moving itself forwards. So the plane accelerates up to 40 mph relative to the fixed air/ground, 80 mph relative to the treadmill, and takes off.

 

[Small_Fryz]

the thing wrong with this statement is that it doesnt matter how fast the wheels go, the plane will still go forwards.

The wheels dont have to turn for the plane to take off. so it doesnt matter if the wheels arnt moving as long asthe plane goes forwards. The plane will end up taking off on the treadmill as the wheels wont be moving, but the treadmill will be.

Anyway i think the plane will take off.

Edit im with Duke 100%

What he said ^^^^

 

[Carl.]

Indeed. Wouldn't the only force you can apply to the plane through the wheels - assuming no is brake applied - be the friction of the wheel bearings? I think a threadmill would have to go awfully fast for that force to counter the thrust of a jet engine...

 

[Zardoz]

...Let's modify the original example a little. In the original example, there's some kind of feedback loop so that the treadmill can accelerate. This might lead to the uncontrolled overacceleration of the treadmill and wheels that Der Alta theorized. But in our new example, let's assume that the treadmill is speed limited to the takeoff speed of our J3 Cub, 40 mph...

That's the problem with the whole exercise, isn't it? As worded, it simply doesn't make any sense. You have to "modify" it.

(BTW, am I right about the cars?)

 

[Carl.]

An analogy:

Think of a skateboard you're moving with your hands over a threadmill. No matter what speed or direction the threadmill is going, you can push it forward or backward, as long as the friction in the wheel bearings isn't too high.

 

[Duke]

(BTW, am I right about the cars?)

Yep! A little hard to tell if it's a Catalina or a Bonneville, but it's definitely a 1969, and probably a Bonny. And you're right on the Ford, too.
👍

An analogy:

Think of a skateboard you're moving with your hands over a threadmill. No matter what speed or direction the threadmill is going, you can push it forward or backward, as long as the friction in the wheel bearings isn't too high.

An excellent analogy! 👍 👍 I should have thought of that.

 

[Sharky.]

I agree with Duke.

More food for thought:

If a plane is travelling down a runway at 80km/h, and it has a(n) 80km/h tailwind, can it take off?

 

[Duke]

I agree with Duke.

More food for thought:

If a plane is travelling down a runway at 80km/h, and it has a(n) 80km/h tailwind, can it take off?

Nope. But if you turn around, and the stall speed is less than 80km/h, it will fly without moving over the ground. In fact, it may even fly backwards relative to the ground, assuming you can hold it stable.

 

[Danoff]

This is a dynmaics problem and should be treated as such. Let's look at the forces acting on the aircraft. Let's assume that the wheels are frictionless.

Force 1: Thrust (applied by the engine) acting in the forward direction with a force F.

There are no other forces acting on the aircraft (neglecting drag). If the aircraft is translating on the conveyer at a velocity S, the aircraft will speed up with respect to S with acceleration F/M. If the conveyer is turned on at the same moment the thrust is applied, the aircraft will speed up with respect to zero with acceleration F/M.

The conveyer does nothing due to the movement of the wheels.

To see this, all you have to do is remember that the earth rotates and that therefore the runway is moving (much like the conveyer)... this does not stop the aircraft from speeding up.

The problem is poorly posed because it is impossible for the conveyer to keep up with the wheels after the engines are turned on. The more the conveyor speeds up, the more the wheels will speed up. The aircraft will accelerate regardless. The treadmill is simply rolling the wheels - not forcing the aircraft.

 

[daggoth]

Someone should submit this to mythbusters

 

[Zardoz]

...The problem is poorly posed because it is impossible for the conveyer to keep up with the wheels after the engines are turned on. The more the conveyor speeds up, the more the wheels will speed up...

...and, in fact, accelerate to an "infinite speed", right?

"Poorly posed", indeed...

 

[Azuremen]

This is a dynmaics problem and should be treated as such. Let's look at the forces acting on the aircraft. Let's assume that the wheels are frictionless.

Force 1: Thrust (applied by the engine) acting in the forward direction with a force F.

There are no other forces acting on the aircraft (neglecting drag). If the aircraft is translating on the conveyer at a velocity S, the aircraft will speed up with respect to S with acceleration F/M. If the conveyer is turned on at the same moment the thrust is applied, the aircraft will speed up with respect to zero with acceleration F/M.

The conveyer does nothing due to the movement of the wheels.

To see this, all you have to do is remember that the earth rotates and that therefore the runway is moving (much like the conveyer)... this does not stop the aircraft from speeding up.

The problem is poorly posed because it is impossible for the conveyer to keep up with the wheels after the engines are turned on. The more the conveyor speeds up, the more the wheels will speed up. The aircraft will accelerate regardless. The treadmill is simply rolling the wheels - not forcing the aircraft.

Beat me to it, but I was thinking of maybe doing a free body diagram

The only force the wheels exert on the aircraft is the normal force caused by the earth pushing up, assuming the bearings in the wheels are perfect. All we are concerned about is the Sum of the horizontal (x) forces acting on the plane, which are drag and the prop.

Drag is a function of area and velocity. So the plane must be moving relative to the air in order for drag to be an issue.

Thus, drag is not regarded at this point, as we are just debating in the plane will move.

So, the only x force on the plane frame is the force of the prop.

From that, it is clear the net force along the x axis must have a magnitude. So the plane must move.

The wheels themselves would be a completely different system, aside from the y forces as a result of the normal force and the plane's weight.

 

[Danoff]

Beat me to it, but I was thinking of maybe doing a free body diagram

The only force the wheels exert on the aircraft is the normal force caused by the earth pushing up, assuming the bearings in the wheels are perfect. All we are concerned about is the Sum of the horizontal (x) forces acting on the plane, which are drag and the prop.

Drag is a function of area and velocity. So the plane must be moving relative to the air in order for drag to be an issue.

Thus, drag is not regarded at this point, as we are just debating in the plane will move.

So, the only x force on the plane frame is the force of the prop.

From that, it is clear the net force along the x axis must have a magnitude. So the plane must move.

The wheels themselves would be a completely different system, aside from the y forces as a result of the normal force and the plane's weight.

Yup. Exactly what I was trying to say - of course I neglected the forces in the Y direction completely. It's certainly more thorough to show them cancelling out (until we get lift of course).

 

[Azuremen]

Yes, and then rolling resitence would change the normal force changed.

This would be an interesting problem over all for a dynamics class wtih friction and drag considered. Too bad I just got done with statics

Though it can be initially treated as a statics problem because the debate was mostly over whether or not the plane could even move.

 

[Solid Lifters]

OK, I'm starting to comprehend this stuff! Woo-hoo! Finally!

Sorry, Duke. I'm sure there were moments when you felt like you were trying to teach a chimp how to play a board game of chess, and I, the chimp, refused to stop chewing on the game pieces.

Yeah, I was thinking, "This could be submited to 'Mythbusters'." Though, they would, 'drop it on a dime.'

 

[Duke]

OK, I'm starting to comprehend this stuff! Woo-hoo! Finally!

Sorry, Duke. I'm sure there were moments when you felt like you were trying to teach a chimp how to play a board game of chess, and I, the chimp, refused to stop chewing on the game pieces.

Yeah, I was thinking, "This could be submited to 'Mythbusters'." Though, they would, 'drop it on a dime.'

👍
No need to apologize - I only throw the formatting tags into my longer posts to spice them up a little, not because I'm getting impatient!

 

[Sage]

… and a little over two years later, myth busted.

 

[SolidSnake15]

I stumbled upon this over another forum the other day, and apparently it's been making rounds over the internet but I haven't seen it posted here yet. If it's a repost, then mods please delete the thread!

Question :

Imagine a plane is sat on the beginning of a massive conveyor belt/travelator type arrangement, as wide and as long as a runway, and intends to take off. The conveyer belt is designed to exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation.There is no wind.

Can the plane take off?

Discuss.

...

There are 4 forces that act on an airplane during flight. Lift Gravity Thrust and Drag. Now since your asking about the wheels, this deals with thrust. The only thing that the wheels are good for, is keeping the underside of the plane off the ground, and stopping. That means they provide no source of thrust. The conveyor belt wouldn't be able to keep up with the wheels. The thrust from the plane would push the entire thing forward, the conveyor belt would have to be running at speeds way faster than the wheels are spinning to have any critical effect on it. Any man-made conveyor belt would burn to ashes before ever reaching these speeds. Also when the conveyor belt accelerates, the RPM's of the planes wheels increase.

All thanks to the Air Force Junior ROTC program at school for teaching us about avionics.

 

[Tornado]

I find it rather scary that the pilot of the full size plane they used didn't know enough about how planes work to realize how stupid the idea was.

 

[niky]

+1... now imagine how scary it is that people in a Physics forum couldn't figure it out...

… and a little over two years later, myth busted.

Why oh why did you ressurect this!?! OMG... newbies are coming... newbies are coming! It's gonna start all over again! Just like WTC, mannnn....

 

[Omnis]

The thing is, The Indigo One has got it wrong.

… and a little over two years later, myth busted.

Myth busted indeed.

 

[Alfaholic]

haha! I was wondering why this looked unfamiliar. Just to be difficult, I put my money on the following result:

1) conveyor moving in same direction to plane: Plane takes off, wheels aren't turning at time. Airline reports excellent tyre mileage.

2) conveyor moving in opposite direction to plane: Wheels are rotating twice as fast as expected for any particular airspeed and aircraft suffers wheel or tyre failure, possibly causing plane to fail to take off, or crash on landing, or in flight.

 

[Famine]

You know, it's funny. We were dicussing this on another forum a long time ago, and my position was exactly opposite to the one in this thread. I can't for the life of me explain why though...

Car: Engine transfers power by driving wheels, resulting in motion.
Plane: Engine transfers power by sucking air in one end and firing it out of the other, resulting in motion.

The wheels are irrelevant to a plane's motion.

Put it another way. Imagine a plane flying at 500mph at 5 feet off the ground, above the same conveyor belt. Without slowing, it lowers its landing gear so that they are now in contact with the conveyor belt - which starts moving. Does the plane's forward motion suddenly cease because some bits of circular rubber are touching some other bits of circular rubber? If the plane were to now retract the landing gear would it not be able to take off again?

Maybe I had a GTP-off-day.