Can the Plane Take-Off?

[EricH]

Originally Posted by Pat McCarthy

Isn't Mythbusters usually on at 9 PM Eastern? I saw the ad, and thought of this thread, but I didn't notice the different time.

Yeah, I got Mythbusters confused with Smash Lab, so 9 EST/Pacific.

[fishgurl]

Yes.

[RP Robotics]

The plane could take off. Planes do not put any force into the wheels when it taxis. It moves the same way it does in the air, prop or jet. Due to inertia you could say the plane would stay in the same position relative a third stationary observer. the conveyer belt could move back and forth rapidly and the plane would still stay still. All the wheels do is just keep the plane from falling and give it support when it has 0 lift. If you turn on the prop the plane would move foward, it doesnt matter at all what the conveyer belt does, the only force it can put on the plane is up. If you had a converyer belt long enought he plane would take off for it would be moving compared to the 3rd stationary oberserver. The only way it would not work is if the conveyer belt was not long enough or there was a strong tail wind. but a plane can not take off without a conveyer belt in thos conditions.

[DonRotolo]

"A plane is standing on a runway that can move (some sort of band conveyer). The plane moves in one direction, while the conveyer moves in the opposite direction. This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in the opposite direction).

The question is:

Will the plane take off or not? Will it be able to run up and take off?"

Originally Posted by RP Robotics

The plane could take off.

The only way it would not work is if the conveyer belt was not long enough or there was a strong tail wind. but a plane can not take off without a conveyer belt in thos conditions.

Here we go again.
The key to this puzzle is the statement in the initial conditions "This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in the opposite direction)."
As soon as the thrust of the engine pushes the plane forward some small distance (thus it has some speed), the conveyer moves at whatever speed necessary to counteract that speed. It can move at any speed!

So, the force on the plane from the belt is limited by the friction of the wheel bearings. Move that belt at a high enough speed (a fraction of lightspeed, for example) and the force transmitted to the aircraft through the freely rolling wheels will be enough to counteract the force of the engine.

By definition, the plane cannot move because the belt is free to move at any speed, and while the rolling wheels don't transmit a lot of force to the airframe, the force is nonzero and therefore you must account for it.

Oh, in a real, practical world, you are correct: The plane will move before the belt can reach 0.1c. But, that wasn't the puzzle question...

Don

[vivek16]

Originally Posted by KenWittlief

Ok, I gotta fess up here and admit that when I took physics 101 in college I had to first unlearn 'roadrunner physics'

our thinking gets so ingrained to the things we experience personally, like driving a car or running on a treadmill, that we have a hard time doing thought experiments on things we are not familiar with (like flying a jet plane).

The question here makes you think the plane will not move at all, because our minds jump to something familiar - like a car on a dyno, or a person running on a treadmill.

Go back to the initial conditions: the plane is at rest, the runway is not moving.

The pilot hits the throttle and the plane has 30,000 pounds of thrust on its airframe. How on earth is the runway going to apply 30,000 pounds of thrust in the opposite direction to STOP the plane from moving? Through 3 wheels with greased roller bearings?

Lets say the plane gets up to 10mph like I said before. The runway is only allowed to move backwards at 10mph - to match the forward speed of the plane. There is no way the wheel bearings are going to have 30,000 pounds of friction while spinning at 20mph net speed! the wheels will have a few pounds of friction at the most, and the plane will continue to accelerate

and take off, pretty much like normal.

Picture the tablecloth trick, you yank the tablecloth out from under the dishes, and there is not enough force to pull them off the table.

'yanking the runway' out from under the plane is not going to have enough friction to overcome 30,000 pounds of thrust from the jet engines.

ok, before I read ken's post, I assumed that if they went canceling speeds then (like running on a treadmill) then the plane would stand still and Bernoulli's principle would have no effect. Now I see that the run way moving would have no effect whatsoever on the plane except making its wheels spin faster.

Cool, this would make for a very fun team debate

thanks, Vivek

[EricH]

Originally Posted by Don Rotolo

Here we go again.
The key to this puzzle is the statement in the initial conditions "This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in the opposite direction)."
As soon as the thrust of the engine pushes the plane forward some small distance (thus it has some speed), the conveyer moves at whatever speed necessary to counteract that speed. It can move at any speed!

Ummm... Don, I don't see how you can say that the belt can move at any speed.
The condition says that the speed of the conveyor is (effectively) the negative of the speed of the airplane. It does not say that the conveyor goes fast enough to stop the plane with friction. It does not say that the conveyor is attached to the wings or tail (which would be necessary to stop the plane from taking off unless the brakes were on).

All it says is that the conveyor moves at the same speed as the plane in the opposite direction.

That said, guess who's going to be watching Mythbusters next Wednesday if at all possible?

[Taylor]

Originally Posted by KenWittlief

its really a trick question. If you think the airplane will stay in one place, because the treadmill is 'matching its speed' - thats impossble.

If the plane is staying in one place then its speed is zero. If the planes speed is zero then the treadmill speed is zero. So whats stopping the plane from taking off? where does the force come from?

The only way the treadmill CAN move is if the plane is moving - and if the plane IS moving the treadmill is not holding it in one place.

This argument reminds me of that trouble-making ancient Greek philosopher, Zeno. To paraphrase him tremendously, he argued that motion is impossible.
Take the example (as he did) of an arrow shot from a bow. It is understood that the arrow exists, and takes up space, and at every infinitessimal instant, has a known position. Since positions are absolute and immobile (as measured from your frame of reference, i.e. the earth's rotation), the arrow does not move because at any given freeze-frame moment it is in a given position & orientation and therefore it is still.
We all know this is not true, otherwise Robin Hood would have been out of a job. But, as Zeno endeavored to prove, it does show the fallability of human logic. There are many more instances that recall this notion (Heraclitus saying one can never step in the same river twice, and the completely ridiculous "if a tree falls...." nonargument) that show that logic can be used to prove (or disprove) nearly anything.

To discuss the notion of a giant fan producing lift (or "suck") to the plane, this would be a colossal mistake. As soon as the plane leaves the wind chute provided by the fan, it would enter the (relatively) still airmass and fall back down, either tilting back each time and eventually reaching a stall or resulting in a nosedive.

[ALIBI]

The plane can take off. The thrust is not relative to the speed of the wheels turning. The plane will move forward regardless of how fast its wheels are turning, the thrust is not going into the wheels. The question is basically flawed in making you think that because the conveyor belt is moving at the same speed as the wheels that the conveyor could hold back the thrust/forward movement of the plane. To believe that the plane can not take off, you would also have to believe that if the conveyor belt was moving the wheels at the same speed the plane needs for take off, the plane would fly without its engine on. In order for the conveyor belt to stay under the plane once the thrust is enough for take off, the conveyor had better be moving pretty fast in relation to the ground if it wants to stay underneath the plane. The conveyor can not put enough force into free spining wheels to hold back the thrust of the planes engine.

EDIT: The plane does not move forward and take off because the wheels are turning, the wheels turn because the plane is moving and the wheels turning do not make the plane take off. The question is flawed.

[Clinton Bolinger]

I love this question.

See attached Image.

-Oris-

[Molten]

I see that both sides have good reasons, however in theory I believe that it would not take off. IF the conditions were exactly as stated, then it would be impossible for the plane to move relative to the air. And that relativity is the important part. Oh well, I guess we will all see come Wednesday. However, I guarantee you that no matter how MythBusters recreates this somebody will not agree with their conditions and will therefore claim the results void.

[EricH]

Originally Posted by Molten

I see that both sides have good reasons, however in theory I believe that it would not take off. IF the conditions were exactly as stated, then it would be impossible for the plane to move relative to the air. And that relativity is the important part.

I ask how would it be impossible?

For the record, if I had a long enough conveyor belt, I would probably be able to test it. The rig would be the problem, but I can almost guarantee you I could get a plane off the ground under the experiment conditions.

[Molten]

Originally Posted by EricH

but I can almost guarantee you I could get a plane off the ground under the experiment conditions.

Don't you see the problem in this debate? It is the "experiment conditions". The way many of you are reading it, it suggests that the plane can move just because the wheels don't give any propulsion. The way that I am reading it, the plane can't move(relative to the air) period. That is what is critical here. It is not that they can't take off if the plane can move relative to the air. In fact, with the conditions that you specify I agree, It could take off. The point I disagree with you is the conditions that you interpret from the original statement.

The original post:
"A plane is standing on a runway that can move (some sort of band conveyer). The plane moves in one direction, while the conveyer moves in the opposite direction. This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in the opposite direction).

The question is:

Will the plane take off or not? Will it be able to run up and take off?"

The formula:

The vest way to track the speed of the plane would be to find the
C=circumference of the wheels
R=# of rotations of the wheel
T=time the wheel takes to rotate that # of times
S=Speed of plane=Speed of conveyer belt

S=(C X R)/T

Now, let's take this one step at a time. The plane is stopped. The conveyer belt is stopped. The plane starts to move and the conveyer belt INSTANTANEOUSLY starts to move in the opposite direction. (remember this is all in theory with ideal conditions) As the plane speeds up to the speed necessary to take off, the conveyer belt does the same in the opposite direction. Now, with these conditions, it is impossible.

To truly put this to rest, the conditions would have to be more clearly stated in the question. For instance, how does it track the planes speed? That is rather critical. Do we ignore friction? As some have posted in the past, what about wear and tear? I think that interpretation is the true decider on this one. I am positive that with the conditions in my mind, I am right. I am positive that with the conditions in your head, you are right. The thing is that the conditions were not clearly stated to the original post and thus we have no choice to say that either outcome is possible depending on how it is interpreted.

P.S. I hope that if you do not understand my statement on the interpretation of the problem, then we can just agree to disagree.

Also, sorry for the long post.

[Taylor]

Originally Posted by Molten

The formula:

The vest way to track the speed of the plane would be to find the
C=circumference of the wheels
R=# of rotations of the wheel
T=time the wheel takes to rotate that # of times
S=Speed of plane=Speed of conveyer belt

S=(C X R)/T

The key to this problem, which has been established by some pretty intelligent aerospace engineers earlier in this thread, is that the wheels' rotation have ABSOLUTELY NOTHING to do with the speed of the plane.
It took me a while to get my head wrapped around that notion, but once I did, this problem became very simple.

[EricH]

Originally Posted by Molten

Don't you see the problem in this debate? It is the "experiment conditions". The way many of you are reading it, it suggests that the plane can move just because the wheels don't give any propulsion. The way that I am reading it, the plane can't move(relative to the air) period. That is what is critical here. It is not that they can't take off if the plane can move relative to the air. In fact, with the conditions that you specify I agree, It could take off. The point I disagree with you is the conditions that you interpret from the original statement.

The original post:
"A plane is standing on a runway that can move (some sort of band conveyer). The plane moves in one direction, while the conveyer moves in the opposite direction. This conveyer has a control system that tracks the plane speed and tunes the speed of the conveyer to be exactly the same (but in the opposite direction).

The question is:

Will the plane take off or not? Will it be able to run up and take off?"

The formula:

The vest way to track the speed of the plane would be to find the
C=circumference of the wheels
R=# of rotations of the wheel
T=time the wheel takes to rotate that # of times
S=Speed of plane=Speed of conveyer belt

S=(C X R)/T

Now, let's take this one step at a time. The plane is stopped. The conveyer belt is stopped. The plane starts to move and the conveyer belt INSTANTANEOUSLY starts to move in the opposite direction. (remember this is all in theory with ideal conditions) As the plane speeds up to the speed necessary to take off, the conveyer belt does the same in the opposite direction. Now, with these conditions, it is impossible.

To truly put this to rest, the conditions would have to be more clearly stated in the question. For instance, how does it track the planes speed? That is rather critical. Do we ignore friction? As some have posted in the past, what about wear and tear? I think that interpretation is the true decider on this one. I am positive that with the conditions in my mind, I am right. I am positive that with the conditions in your head, you are right. The thing is that the conditions were not clearly stated to the original post and thus we have no choice to say that either outcome is possible depending on how it is interpreted.

P.S. I hope that if you do not understand my statement on the interpretation of the problem, then we can just agree to disagree.

Also, sorry for the long post.

I'm sorry, but I still do not understand. You haven't done any work to prove the equation. Under the experiment conditions, I could probably get at least an R/C aircraft off the ground. The only condition is that the conveyor is moving at the airplane's speed in the other direction. And the fact of the matter is, an airplane's wheels give NO propulsion. (If you want to argue this point, come on over to SDSMT, and I will take you into the CAMP area to where the Aero Design team is and show you on R/C aircraft. Or, find your local model-aircraft store.) The only factors here are friction and thrust. Friction of the wheels--probably negligible. Thrust of the motor/engine--plenty to overcome friction.

[lemon1324]

Originally Posted by sanddrag

One thing you could do (theoretically) to shorten a takeoff or landing distance is to create a nice strong headwind along the runway. The airplane would maintain enough of a speed difference with relation to the air to maintain lift, but you could theoretically have it with zero speed in relation to the ground. You could takeoff and land while not moving in relation to the ground. You could even do it going backwards in relation to the ground. (I've done this on my RC flight simulator program and it is great fun).

However, flying a plane in any sort of strong wind is tricky and it would be difficult to construct an apparatus to move such a large volume of air at such a high velocity to create this artificial headwind.

If you theoretically create a huge fan at the end of a runway, that will shorten the ground roll of the aircraft. However, the aircraft will not have enough speed to fly if it immediately leaves this stream of moving air. Thus you can have a shorter runway but the aircraft will need to remain in the accelerated air for some time.

Again, not to beat a dead horse, but the fact that rolling frition and static friction both depend on normal force makes this question possible to answer. Regardless of the speed that the airplane moves [and thus the conveyor belt] the force exerted by the wheels on the aircraft is constant (Except that it will be marginally higher initially to go from static to kinetic friction). Unless this constant is so large that the aircraft cannot take off under normal circumstances, the aircraft will take off.

Now to argue the other extreme:

As mentioned earlier in this thread, assuming the experiment conditions make it such that the aircraft cannot move, due to viscosity effects in the air immediately above the treadmill, the treadmill drags some of the air along with it. This boundary layer increases in thickness with increasing velocity, and so at some speed of the treadmill, the wing will experience enough relative air velocity to produce lift. At this point, it will lift the aircraft off of the ground. Now it may be argued that the treadmill now stops, the aircraft drops to the gound, repeat ad infinitum, or that the aircraft will then gain enough airspeed to then transition to full forward flight. In either case, the airplane has lifted off the ground, technically a takeoff.

Thus the aircraft will lift off regardless of any of the conditions in the problem statement.