Airplane physics question

This is actually a good response, and to top it off , this all happens instantly! And you as a passenger still get no frequent flyer miles added to your account.

Also, once again guys: Within the constraints of the original question, the situation is untenable.
Of course the realative motion of the wheels has nothing to do with whether the plane can takeoff or not.
However in this question, the conveyor and the wheels must reach an infinite speed instantly, which puts us into the realm
of what good old Kram is saying.

To pose an easier to argue question:
A plane can take off at 200 mph.
It has wheels, tires and bearings rated to 500 mph.
It is sitting on a conveyor that runs opposite the direction the plane will be traveling to take off.
As the plane begins it's take off role down the conveyor, the conveyor speeds up to 250 mph in two seconds.
Can the plane still take off?

(Hint: the answer is yes)

 

Not even close to grasping the question and the constraints implied.

 

Thanks, Erich. Your explanation helps me get closer to understanding.

 

Well at last we are getting to the real consequences of the question asked at the beginning of this thread (if teh belt tries to match the speed of the WHEELS....) The belt, trying to keep up with the wheels, very quickly goes, uh, very quickly....

FTR, I was in the "of course the plane takes off" camp at first, as I said in my inital post 'way back when. It was only when I looked at the consequences of the belt trying to keep up with the WHEELS (not the plane's forward speed) that I saw the problem.

And I will go back to my initial analysis: tha belt doesn't get to light speed because the friction between the belt and the tires limits the force the belt can apply to the plane. Bearing friction is small, but it increases roughly linearly with speed, and at some finite speed will exceed the ability of the tires to transmit the belt force to the plane.

So the belt is spinning at whatever speed it can, which causes the tires to skid on the belt, causing the maximum friction force to be applied to the plane. If the plane has enough thrust to overcome this retarding friction force it takes off, in a cloud of tire smoke. Cool.

Am I explaining this clearly? Shall I drag up the pics again?

 

PS, those who say the system will fly apart at some pont before equilibrium is reached are pessimistic. I have a single-cylinder engine sitting in my garage that turns 19,000 rpm on roller bearings. Translate that to a 6 foot diameter wheel and you get 4,000+ miles per hour. Making the belt go that fast is much easier, it just has to have big enough pulleys. Sixty feet in diameter translates to only 1900 rpm. Easy!

Yes the plane wheel bearings would be highly stressed, but I bet i could find an off-the-shelf bearing to handle it. Have you seen the size of some bearings? The tires would have to be specially designed, but even there, I don't see real problems.

A physicist asks: Why does it work?
An engineer asks: how does it work?
An accountant asks: how much will it cost?
A liberal arts graduate asks: You want fries with that?

 

I guess I still don't grasp this.

I asked a friend who is an engineer:

"Your non-engineering analysis is correct from a practical stand point, i.e. "then why hasn't this been put into practice, considering there are methods, such as wheel rollers, DYNOS, etc, that are more feasible than overgrown treadmills, yet still no application" of this....theory of flight."

No matter what, I can't get over the fact that with ZERO forward movement, the plane still has lift under the wings. I think somewhere in the "it will fly camp" is the implied explanation that there is SOME forward movement just prior to take off. If so, then I think that is not what the original hypothetical was stating. That is, it was leading us to believe that the plane would not have any forward movement prior to vertical lift.

 

sjmist You undestand the gist of the question: the problem impies that the belt can keep the plane stationary. The objection is that the belt CAN'T keep the plane stationary. A plane pulls against the air, not the belt.

The "of course it will fly" argument is that the belt can impart no (or at least no significant) force on the plane by spinning the wheels backwards. The wheels are "freewheeling." Spin them as fast as you want, they just spin freely. Meanwhile the plane is pushing against the air, and DOES move forward, despite the attempt of the belt to push backward. The plane does not take off at zero airspeed, it just ignores the belt spinning the wheels and moves forward, gains airspeed as normal, and takes off. Practically speaking, this is what would happen, if the question is "if the belt moves backward at the same speed the PLANE moves forward..." In that case the wheels just spin twice as fast as they normally would and the plane takes a little longer to take off due to the slight increase in drag caused by the bearings spinning twice as fast. That assumes the tires can stand spinning twice as fast too.

THAT is the problem being bounced around the net if I understand correctly, and the answer to "if the belt moves back at the same speed as the PLANE moves forward, will the plane take off" is YES.

The problem of "if the belt moves backward at the same speed as the WHEELS spin forward" is more complicated. Only geeks like me know or care why.

Hope this helps

 

It would ntfly beacause the engines could not be up to thrust or the plane would roll even if the belt was moving the plane is sitting still on the belt and if the engines were on it would fly but would move on the belt.

 

Yes, thanks for your explanation, in that it clarifies an important premise for me: That the plane DOES move forward prior to take off. i.e., Even though the treadmill moves backward at the same speed as the plane's wheels, somehow, the plane defeats that and goes forward THEN takes off.

I found this on the net, whuch must not be correct:


“The plane will not take off. PERIOD.
Taking off requires an upward net force. This is caused by LIFT. So, with Newton helping us out a bit here, we will prove that the plane cannot take off. The following that
Starting out, at v=0, the plane is not moving through the air, hence the total net force is still a vector pointing DOWNWARD (this is the airplane's weight). When the airplane starts moving (by providing forward thrust) the conveyor belt reacts and does not let the plane roll forward RELATIVE TO THE AIR. Velocity relative to air is STILL zero.
Key point here: if the airplane does not move THROUGH THE AIR, the lifting force is NOT generated.
And thus the airplane does not take off. "

 

Hi Folks,

Me again.

First up, many thanks to Auraraptor/Omar for taking the time to carefully re-assess the problem and his view of it.

sjmst, the plane doesn't lift off 'in place' - the plane is able to drive down the conveyor belt and get lots of air going over its wings, and the airflow over the wings produces lift, just as it does when a plane propels itself down a normal runway. So there's no practical application of a conveyor being used in the way posed by the question.

The crux of the problem is in the understanding of the 'role' (no pun intended) of the conveyor in the taking off of a plane.

If we start with the normal situation of an ordinary plane at the beginning of an ordinary fixed runway, what forces allow the plane to gather speed and ultimately lift off?

1) The plane's weight is pushing down on the runway and the runway is in turn holding up the plane. These forces are equal and opposite so the plane isn't going to accelerate in the up and down sense. At this point the plane is stationary and there is no wind, so the wings aren't contributing any upwards force to lift the plane.

2) Now, the pilot throttle's up the engines and what happens is this (I'll just stick to jets but it's very similar with propellor driven planes). The jet engine sucks air in through the front (via that massive fan you can see), mixes it with aviation fuel, combusts the mixture and directs the hot gases out of the back. The jet of hot gases pushes the jet engine (and the plane connected to it) forwards as it itself rushes backwards. These forces too, are equal and opposite.

3) If we examine the forces on the plane now, the *net* force on the plane in the horizontal sense is a forwards force - it is pushing itself forwards against its exhaust gases. So, the plane starts to accelerate forwards, building up speed in relation to the Earth and the still air.

4) What about the wheels? Well, they are free-wheeling, not being driven by or connected to the engine power of the plane. Their job is to keep the belly of the plane off the deck and to give it a means to roll along with as little drag as is possible (no point holding it back when the intention is to go forwards).

5) The plane weighs quite a bit, so it needs quite some time and distance to get enough speed up for the air over the wings to become a significant force. It blasts down the runway getting ever faster, and even though the air is 'still' in relation to an observer by the runway, the air and the plane's wings are moving in relation to each other. Thus the wings, when they have enough airflow over them, generate the lift that allows the weight to be lifted off the wheels. The plane's weight is still pulling it downwards, but as the wings generate more and more lift, the wings lift the weight off the wheels, and ultimately the whole plane gets lifted off the ground. Remember that all the wheels are doing is keeping the plane's belly off the deck and giving it a really low friction way to move down the runway while it gathers speed.

Right - now for the special situation posed by this problem. If you put a conveyor under the plane and have the conveyor going backwards, does it stop the plane moving forwards and getting up the speed it needs in relation to the air, and so taking off?

I beleive it cannot 'grab' the plane and drag it backwards - the wheels of the plane are freely spinning.

The problem states that the conveyor is going backwards at the same speed as the wheels. So, when the plane gets to, say, 10mph in relation to the Earth/Air, the conveyor is doing 10mph backwards in relation to the Earth/Air. The plane's wheels, having the surface of the tyres squished onto the belt of the conveyor, 'see' a surface that appears to be doing 20mph in relation to them. This is just like watching traffic on the opposite carriageway of the road - you do 50mph one way, they do 50mph the other way (both in relation to a static observer) yet to the driver of each car the closing speed is 100mph.

This is why I believe the wheels rotate at twice the speed that they would do if the plane was taking off from a normal runway.

So, basically, the wheels have nothing to do with the drive of the plane forwards, and the conveyor can't grab the plane, so it moves forwards in relation to the earth and air and takes off.

Hope that helps!

Rich.

 

RichRowe is 100% correct on this!

No, the plane's position and velocity relative to the conveyor belt IS changing as it accelerates. It moves along the conveyor belt, and this results in air passing over and under the wings, creating lift. The tires are neither accelerating, nor decelerating the plane. The tires and the conveyor belt are simply acting as passive bearings on which the plane "slides" as it is "pushed" by the engine.

The engine provides the thrust that pushes the plane and accelerates it.

Because the plane is accelerating, so is the air over its wings, but in the opposite direction. Since there is airflow over the wings, lift is generated. How much lift the plane experiences at a given moment depends on the plane's velocity at that moment in time.

 

Hi Rich, good to see you again.

As you may note from my answer above, I can argue the "of course the plane can move forward and take off" argument as well. Maybe I am answering the question nobody asked, but in giving fair credence to the question, I had to look at the situation of the belt trying to keep the plane stationary, as that is the gist of the "it won't fly" argument.

My contention is simply that no matter how hard the belt tries to keep the plane from moving, it can only try so hard, limited by the friction force available through the tires. No matter how fast it spins the tire backward, the max force is the wieght of the plane times the friction coefficient of the tires.

Neglecting friction is all very well, but in the real world friction is not negligible.

 

Rich, what you are not seeing here is the fact that the question states that at ALL times the conveyor EXACTLY matches the speed of the wheels. Given this important point, you can then see that in order for the plane itself to be going 10 mph, on a conveyor going the opposite direction of the plane, then the wheels MUST be rotating at greater than 10mph. They are, in fact, turning at 10 mph PLUS whatever the speed the converyor is going.
In your example above, if the plane is going 10mph and the conveyor is going backward at 10 mph, then the wheels are turning at 20 mph.
This is not the within the constraints of the original question.
It doesn't work.

That means the wheels are turning at 20 mph, which is twice as fast as the conveyor.

I don't think the original intent of the question was for the wheel speed to be translational, but rather for it to be rotational. (In which case tire would have been a better term to use than wheel)

 

Hi Dubai/Scot,

Good to have you back - no pictures this time?

Yep, I've been open all along to the purely hypothetical/real world question, i.e. can we say that wheel bearing friction is non-existent or must we accept some friction because no real wheel bearing is perfect.

In the real world I think the plane would be given a *tiny* bit of drag as a result of the wheel bearings not being perfect, but I think the question is really getting to the crux of the how a plane produces its forward movement, and the fact that it doesn't rely on its wheels for the motion.

Like anything, though, I guess it can be as involved & deep as much you care to indulge in the minutae or just paint in broad brush strokes.

Good debate, though, but I think a few people still believe the belt instantly whizzes up the infinity.

Keep well!

Rich.

If you ever get to have lunch the Burj al-Arab, a rather choosy friend of mine really recommends it!!

 

Runway conveyor belts are not real-world either. This is a thought experiment and friction is regularly ingnored in thought experiments of this nature as it is not really relevant to the basic question being put forth. (even though the original question is not very well written in this thread).

 

Hi Teak,

With greatest respect, I must disagree with your argument.

Lets look at the situation of the plane moving forwards at 10mph in relation to the earth and the conveyor belt moving 10mph backwards.

The speed of the wheels, in the rotational sense, is 20mph - I agree with you there.

I also agree that the conveyor belt is moving at 10mph backwards in relation to the earth.

So I seem to be owning up to having broken the constraint... But I'm not:

The plane is moving forwards in relation to the *earth* at 10mph (and likewise the conveyor is doing 10mph backwards in relation to the same earth)That means the plane is moving forwards in relation to the *conveyor* at 20mph. That 20mph is exactly equal and opposite the 20mph speed of the wheels in relation to the conveyor.

I'm not saying you have to agree, but I hope you see where I'm coming from.

Cheers!

Rich.

 

I just saw you're last post and you are saying you think that wheel speed as defined in this question is translational and not rotational.
That's another debate I guess. I think the intent is clearly that it is rotational.

Anyway, all this talk makes me wish I had a jet. (And the fuel to go with it of course!)

 

Oh my friggin lord,

This is really absurd. First, I'm going to post what was posted on page 2 of this thread again:

http://www.avweb.com/news/columns/191034-1.html

Please EVERYONE take the time to read that article. The whole idea behind this "test" if you will, was to see which of those people would forget that a plane does not accelerate like a car does.

Simply put, as long as there were freely rolling wheels underneath the plane, those wheels could do anything they wanted, it wouldn't change a thing. The jets would push the plane forward by pushing through the air ... wheel speed has absolutely NOTHING to do with a planes ability to move forward.

For the person who was writing about a boat's movement through water ... the key here is that the boat accelerates by pushing on the water. If the boat accelerated by pushing on the air, like an air boat or hovercraft, it would be completely irrelevant how fast the current was moving (with the exception of a little more friction on the bottom of the craft). Ever see video of a hovercraft in action ... ever notice how it doesn't slow down if it "jumps" a wave like a boat does when it jumps and catches air. That's because the hovercraft continues to maintain its speed because its still pushing on the air ... just like a plane does.

This "test" never had anything to do with bearing friction, or wheel friction, or anything else. It was a joke to see who would jump the gun and forget that planes don't accelerate by their wheels, the wheels are there just as freely moving objects to help the plane roll around.

Another example ... 8-second drag will light-up street tires at full throttle. An 8-second jet powered car runs skinnies on all 4 corners and could never, in its life, spin its tires. A jet car doesn't apply power through its wheels, it accelerates by pushing on the air, so as long as the air isn't moving ... there's nothing to prevent the drag car from moving forward, no matter what brand treadmill you put it on.

Bill in Brooklyn

 

Hi Teak,

I'm saying that it works with both translational speed (centre of wheel moves forwards at some speed in relation to a reference point) AND rotational speed (face of tyres on wheel moves around to match the surface it is moving in relation to).

It really is enough to say that the conveyor belt matches 'the speed of the wheels' without specifying translational or rotational.

I wrote that one up in an earlier posting - I might dig it out but not right now!

IF (and this is a big IF, because it *isn't* a constraint mentioned in the problem) the wheel's rotational speed was stated as having to be the same thing as it would be *if* the wheel was down on the ground, that would be another story. But a pretty boring one, because for the plane to do 10mph, the wheels' rotation would have to be the same as you get on a normal runway at 10mph, and of course that would mean that the conveyor belt wouldn't be allowed to move. So it is not possible to pose the question with the constraint of the conveyor belt going backwards AND the wheel's speed being related to the ground - it would just make the question implausible.

Best,

Rich.

 

Hi Bill,

Well put!

But see how easy it is to get drawn into providing your own explanation and analogies (even very good ones like yours)?

The motivation of the question may be to see who jumps the gun (as you say) but MY motivation is to debate and de-bunk the wrong Physics and misunderstanding of the question that we've had here on this thread.

So far I'm having a good and respectful debate with a whole host of folk - but I was happy with my understanding of the problem *ages* ago.

Plus I'm (slowly) learning how to summarise to get my point across.

Cheers!

Rich.

 

Actually, wheel speed has everything to do with it, if you take the question at face value.

IF the threadmill matches speed exactly to the planes wheels, then the plane by definition cannot have forward movement. End of story.

No forward movement - no take-off.

Engine thrust has zilch to do with this. For the plane to generate wind speed, the plane has to move. Period. For the plane to move the wheels have to ALLOW IT. They have to spin faster than the threadmill for this to occur, which the puzzle doesn't allow for.

Basically, if you think in terms of infinity and real physics, and hypothetical math - the plane won't fly.

If you assume the threadmill can only go so fast, and thrust overcomes friction, etc. Then you believe the plane will fly. BUT, to assume any of this you have to allow that the plane will move, which isn't possible if the wheels spin at the same speed as the threadmill and have to remain in contact with it...

 

OK, I read this again.

http://www.avweb.com/news/columns/191034-1.html

I then pictured the plane dangled from a crane, its wheels not even touching the ground. Of course it will start to move and fly.
I guess the damn thing will fly!

 

Bpu699/bo,

Nope, sorry, check out a few posts up on wheel speed and relative speeds etc. There's plenty in there that says the plane can move forward, and thus generate lift.

sjmst,

YES! I'm so glad you get it!! Thanks for perservering!

Regards,

Rich

P.S. we got to 20 pages without anyone threatening violence on anyone - does that make us better than BMW drivers??

 

That was NEVER the point of the original post. As the article I just posted mentions, the wording was off.

Bill in Brooklyn

 

Agreed. I don't think anyone was being argumentative; we all just wanted to figure it out!