Airplane physics question

Given that the conveyor belt will match the rotation of the tires, and that the plane is trying to move forward, the tires will immediately overspeed. How fast? Right up to the bump stops. See post #368 on page 19 for what will happen then.

 

Murcielago, I apprectiate your honest inquiry. However, I am not in the position to type a written response in the depth necessary to describe all the physics involved with this scenario. I will say that simply speaking, based upon how I am interpretting your question; yes, the plane will lift off with the wheels at the origingal start position in relation to the conveyor belt, and that this issue is irrelevant to the flight of the plane. If you are implying that the aircraft will flip over (?), then that will not happen based upon the flight controls of the aircraft (i.e. aerodynamic physics, which have nothing to do with the conveyor belt/wheel issues).

 

Hi RichRowe,
I believe that acehole is depicting the tire in his diagrams and not the conveyor belt roller.

 

Yep you answered the question I was looking for. Which I guess could have reworded as "Where is the rear wheel of the plane relative to the start point at the moment of lift off?"

Thanks. And thanks to everyone else who gave some input.

 

Hi MHWCS,

Yes, I too believe the circle is the wheel of the plane and not the conveyor roller.

My explanation from a few posts up still stands, though.

Look at the red side again, if you would. The circle is the plane's wheel and the line is the belt of the conveyor. The roller driving the conveyor would be underneath the line. Imagine the roller turning as the conveyor moves in the direction of the arrows and the wheel turns as indicated.

The wheel is turning counter-clockwise - can you see that the roller of the conveyor would be turning *clockwise*. This is the opposite direction, and that's what the question states, yet he has labelled this side as wrong when in fact it is right.

You could do a similar exercise with the green side to show that that side is not labelled correctly also.

I hope that makes my thinking more clear.

Best Regards,

Rich.

 

The example of the person on the treadmill is the closest we have to this question. But it's missing one important factor--the treadmill speeds up to make sure the rollerskates don't move forward or backwards. Now what?? Teh person moves forward but their legs don't. They stay in the same place. The person will lean forward more and more until he falls flat on his face. At that point, he will either be swept backwards on the treadmill, or, if you push him hard enough, he will go forwards (losing a serious amount of skin).

Same thing with the airplane--the landing gear will look like Segways gone bad until each one breaks. Once the landing gear breaks, it's a test of strength between the treadmill, fuselage, and engines.

 

RichRowe,
I believe I now understand how you are interpreting acehole's diagram.
This is where we differ. I am interpreting and assuming that the direction of the conveyor belt as compared to the direction of tire/wheel rotation is made at the contact point between the tire and the belt (not depicting the wheel rotation as it is at the top of the tire).
Does this make a difference?

 

RichRowe,
I looked at your position more closely, and now further understand what you are interpretting (i.e. counter clockwise, clockwise rotations of the wheels and conveyor belt vs. same or opposite rotation).
I interpret the original question to indicate that the belt is moving such as to counteract the rotation of the wheel/tire.
However, I think we both agree that the wheel rotation is irrelevant to this hypothetical question.

 

Hi MHWC4S,

Aha! I read your first post and was thinking of an answer, but then your second post said pretty much exactly what I was thinking!!

I'm glad you get where I'm coming from now.

Basically, i'm the camp that says if the wheels rotate clockwise, the conveyor's rollers rotate counter clockwise. The effect this has on the plane's wheel rotation is that they spin faster, clockwise.

And yes, because the wheels are freely spinning, they don't allow the conveyor to impede the forward motion of the plane (just a more extreme example of the fixed face of a normal runway doesn't impede the forward motion of the plane, because it has free turning wheels then, too).

I'll have to hit the sack again soon, unless I find another song I want to re-write!

Best regards,

Rich.

Edit: MHWC4S, just re-read your posts again - I think I get where you're coming from a bit better now. Yet I think the stipulation that 'the conveyor moves such that it tries to stop the wheels rotating (counteract the rotation)' and 'the conveyor moves to match the speed of the wheels, only in the opposite direction of rotation' are actually the two different rotation directions we've been debating. The latter is what the question states, and is how I've been looking at the conveyor belt. It's good to have that 'Aha!' moment when you at least understand the other person's argument, even if you don't agree with it.

 

I was bored.
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I've been imagining this as the correct scenario too. However, I now realize it is wrong, further proving the original question poses a conundrum.
The wheels don't drive the conveyor and the conveyor doesn't drive the wheels. The conveyor only MATCHES the speed of the wheels, therefore the wheels must accelerate to infinity, and do it instantly, without a power source. Since there is no forward motion of the plane in this scenario, there is NO motivation to the wheel.
The fact is the wheels will only turn if the plane moves forward, and in this assumption the plane NEVER actually moves forward, and even if it did there is not enough power to instantly accelerate ANYTHING instantly to infinity, let alone the wheels.
This solution doesn't work.

 

I believe the question in this thread was posed improperly. I have read the question many times, on different forums, and it has usually had the conveyer matching the speed of the aircraft, not the wheels. That does away with this infinite speed crux people are running into. That is really beyond what the question is intended to make people think about.

 

Hi Folks,

shiggins - many thanks for the diagram (post 460, bottom of previous page)! - now hopefully it will be easier to see what I mean.

teak - yup - no super forces at work, just plane forwards at 10, conveyor backwards at 10, and so on until plane gets fast enough to take off.

2000YELLOW360 (nice motor, by the way )
The force the treadmill/conveyor is exerting is applied to the surface of the roller skates' wheels/plane's wheels. What this force does is make the wheels turn but does not move the wheel (or the thing on it) bodily backwards. Yes, in the real world you'd need to hold a person on roller skates on a treadmill because the wheel bearings wouldn't be perfect, but imagine holding someone still if they had running shoes on instead - you'd have to be Hulk Hogan to keep them in place either by causing their shoes to skid or stopping the whole treadmill.

So the wheels make it not possible for the conveyor to hold the plane in the same place. When the engines throttle up like they meant it to try to take off, the net force on the plane is a forwards one, so its blasts down the runway and takes off.

Speaking of taking off, I got to get some zzz's, I've had too many late nights on this!!

Best Regards,

Rich.

Edit: added reference to shiggins' diagram

 

My last response to Kram brings up this thought:

The original question (as I have stated before), is a conundrum that involves an impossible situation.

It asks that the wheel speed matches the conveyor speed, lets call this speed X.

Since (as anyone reading this thread realizes by now) the spinning of the wheels doesn't have anything to do with the planes accelerating to takeoff, we know the plane will takeoff. Lets call this takeoff speed Y.

Therefore the question is proposing a situation whereby the wheels must be going two speeds at the same time; X and X+Y ( and for all of you really thinking hard, all speeds between X and X+Y at some point during the takeoff roll)

Therefore the question is invalid as posed.

 

Art you got the idea. of corse I'm assuming the person in the skates is perfectly rigid and will not lean forward (or backwards). therefore the thrust of the person pushing the other person in the skates is what makes the skater acellerate forward.

 

I just discovered this Thread. 24 pages is quite a lot for such a question!

I haven`t had the time to read everything. Is anyone still interested in a mathematical solution? If so I`ll try to set up the equations at the weekend, if I`ve got enough time.

By the way, it will fly.

 

teak360 has it right. It's an invalid question.

The plane's body definitely accelerates due to the engines. But the wheels can't change their position relative to the conveyor if it keeps matching their speed in the opposite direction. Since the wheels can't change position, they will keep spinning faster and faster, but the landing gear cannot accelerate linearly with the rest of the plane, so it will eventually break. There are two mutually exclusive things happening simultaneously. The plane can't move and not move at the same time--something's gotta give. That would be the landing gear.

If the plane moves (velocity not zero) from a standstill (velocity zero), it changes velocity, ie. it accelerates. This means the plane moves forward--it changes its position on the conveyor belt.

The plane, via the landing gear, is attached to the wheels. The forward force (thrust) goes through the plane to the landing gear and translates into a rotational acceleration in the wheels. They spin faster. But the conveyor belt spins faster in the opposite direction, matching their speed at every instant. So the wheels won't change their position on the conveyor belt.
Starting landing gear velocity zero, no change in position, no acceleration, no forward movement. You can't have a rigid body and accelerate only a part of it without putting a force through it. When this force is great enough, the weakest point, probably the landing gear will break. It could also be the engine mounts that give first.

Taking the question literally, then, once the landing gear goes and the plane belly flops onto the conveyor belt, it will burn up or tear apart before it can get the speed to take off, even if the wings are intact and still have airflow over them. So it won't take off.

Really though, it's an impossible situation.

 

That is silly! THE CONVEYOR BELT is what moves in opposite, not the wheels powering the belt.

Get a soda can and a book. Then come back and argue.

 

Sorry mate. You're wrong.

 

Your telling me, that the question says "The wheels powering the conveyor belt are spinning in the opposite direction" ?

The conveyor belt moves in the opposite rotation.If you look at my diagram you will understand this. If you dont, then i give up!

 

Holy Crap,

24 pages of this?

So you people are telling me that the landing gear plays by all physical rules, but there's a magic conveyer that can go to infinite speeds no problem? And when that happens the wheels fail, so the airplane can't take off?

Well let me tell you, I saw the event leading up to this question. In reality the gear was designed much better than the magic belt, so the belt was destroyed first. When it failed, the plane was thrust forward by it's super spinning wheels, just like a catapult off an aircraft carrier, and the plane instantly jumped into the air and vanished, never to be seen again. And then all the elves that made the magic belt and sold it to the King were beheaded after they failed to return the king's money.

But the evil wizard who devised the scheme was on the plane! He took the riches to his favorite island hideaway, where he blew it all on whiskey and crack cocaine.

Last I heard he was tending bar at some beachside resort, amusing himself by asking silly questions to tourists with way too much time on their hands. I hear his favorite one begins "imagine you have a plane..."

 

Hi DesmoDog,

I think you're starting to take after your canine cousin, Triumph.

To paraphrase,

Does the plane take off?

YES! NO!

I'm so sorry - the correct answer is 'Who gives a (*&^!'

Cheers!

Rich

 

This is the wording from the question.

So, what does this mean. According to you, it means the conveyer belt moves in the opposite direction of the wheels tangential velocity at it's contact patch. Like Diagram A. Tell me though, in Diagram B, we have an infinite number of valid directions of tangential velocity, I only show 4, but you get the idea. So, why not pick one of them? Why not the one at the very top of the wheel? It's just as valid at any instant of time.

The opposite direction of rotation, as the question states, is as I have shown it. As I mentioned in an earlier post. This question is not worded as it originally was. It was originally said that the conveyer moved in the opposite direction of the planes motion. Which again, is shown by my picture. Same question, just without the infinite speed conveyer belt people are talking about.
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Okay, obviously the scenario people are trying to look at is one where the conveyor moves backwards at the forward speed of the aircraft.

If the aircraft is stationary with no wind over the wings, it won't fly.

But -- bzzt -- wrong again. The conveyor won't keep the airplane from moving.

Let's eliminate the confusion factor to zero: Wheel speed = conveyor speed = zero.

Just eliminate the conveyor and the wheels too. Sit that bird on it's belly on a strip of concrete.

When the throttle gets up high enough, that sucker will still move.

Ever see an aircraft in a static thrust test station? They don't just put a treadmill under the wheels.

Now, shall we debate the whichness of what for a while?