Can the Plane Take-Off?

[greencactus3]

"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?"

there's a 988 post arguement going on in this other forum... im pretty positive about the answer... (there is technically no true answer till someone experiments... and many people will argue that they need proof. only proof possible would be by experiment... and so far i know of noone who has done an experiment)
and please dont turn this into a flame war.... as has happened in the other forum. i mean for this to be amusing. ill post what i think a bit later after a couple posts have been made so i wont give any ideas from the 988 post wisdom i have lol. or you can pm me and ill answer what i think.

have fun!

[KenWittlief]

The answer most certainly can be determined by the laws of physics.

All planes move by reacting with the air, either through propellers or jet engines. The speed of the ground under the wheels has almost nothing to do with the speed of the plane down the runway.

In this case, the plane would accelerate down the runway, and the 'runway' would accelerate in the other direction. The plane would still take off more or less normally, the only effect being the wheels will be spinning twice as fast as they normally would when it leaves the ground.

Hey that was easy, we settled the argument on CD in one post! :^)

[Pat Fairbank]

As Ken said, whether a plane can take off or not depends only on how fast the air is moving in relation to the plane's wings.

It's for this reason that airplanes take off facing into the wind whenever possible: the plane's ground speed at takeoff is not as high as it would be if there were no wind, so a smaller length of runway is needed.

[greencactus3]

Originally Posted by KenWittlief

The answer most certainly can be determined by the laws of physics.

All planes move by reacting with the air, either trough propellers or jet engines. The speed of the ground under the wheels has almost nothing to do with the speed of the plane down the runway.

In this case, the plane would accelerate down the runway, and the 'runway' would accelerate in the other direction. The plane would still take off more or less normally, the only effect being the wheels will be spinning twice as fast as they normally would when it leaves the ground.

Hey that was easy, we settled the argument on CD in one post! :^)

yes.... except one thing.
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).

so. laws of wear and tear and motor output of either engine(plane or conveyor) ignored, but friction not ignored, the conveyor belt spins fast enough that the friction of the wheel bearings keep the plane from accelerating. so if the conveyor really can turn exactly the same speed(but in the opposite direction) of the plane, the plane would not be accelerating. relative to the conveyor belt it may as well be going almost the speed of light but since the conveyor belt is going the opposite way at almst the speed of light, the plane doesnt move.... im redundant arent i?
well anyways. so the plane wont fly then? i unno
but my thoughts are that a conveyor belt would fail before an airplane engine or landing gear so the plane would fly... eventually... but only after the conveyor belt fails.


-edit- addition-..... oh. and i should just say this.. you both completely ignored the way the conveyor belt works. its not a normal treadmill you see...

[KenWittlief]

you are adding conditions to the question that are not in the question.

The runway moves in the opposite direction of the plane, at the same speed. Nowhere does it say the runway moves to keep the plane in the exact same spot. That is your mistaken conclusion of what will happen.

A jet plane is able to produce thousands of pounds of thrust. Lets say its an F15, able to generate 30,000 lbs of thrust.

The wheels, with the brakes off, will have a very low coeffecient of friction. So lets start at zero mph.

The plane speeds up to 10mph, putting out 30,000 lbs of thrust. The runway matches this speed in the opposite direction. The wheels are putting maybe 5 or 10 POUNDS of force in the reverse direction due to the runways backward movement.

The resulting net force on the plane is 30,000 pounds forward minus 10 pounds backwards = 29,990 pounds of thrust (force) in the forward direction

and the plane is moving forward with a 10mph airspeed and its wheels are spinning at 20mph. The runway is moving backwards at 10mph (ground speed)

as the plane continues to accelerate (due to the thrust from its engines) the runway speeds up, but the force the spinning wheels apply to the airframe will never match the force of the engines, unless the pilot does something stupid like stand on the brakes.

[greencactus3]

Originally Posted by KenWittlief

you are adding conditions to the question that are not in the question.

nuhhuh.. its been there all along. you say it yourself.

Originally Posted by KenWittlief

The runway moves in the opposite direction of the plane, at the same speed.

same speed as in...... ZERO mph? which means its not moving?

Originally Posted by KenWittlief

...and the plane is moving forward with a 10mph airspeed ...

wait a second.... the plane does not get to 10 mph.... it does not move

Originally Posted by KenWittlief

...as the plane continues to accelerate

again, IT DOESNT!




yes,, arguements are finally starting.. i have succeeded in starting a big arguement! yay!!


ps. please rememebr to be nice to everyone. even i get excited and then agitated by seemingly nonunderstanding members of the opposing group.. but then again the other side thinks the same about me.

[sciguy125]

Think of it this way:
If I have a balsa glider in my hand and I run down the sidewalk, there will be lift on the glider due to the moving air. If I run on a tredmill, the glider doesn't have any lift.

The situation at hand is the same. The airplane is on a tredmill, so it can't go anywhere.

[Elgin Clock]

Yeah.. so most people know that I am a student who absloutely hates the book work of physics, but gets what is going on in the experiements.

I'm gonna switch to common sense, or lack their of in this analogy, and say that since Plane (A) is "accelerating" in a positive direction, and Conveyer belt (B) is "accelerating" in a negative direction based on Plane (A) then in all essence the plane is not moving (linearly) at all on this conveyer belt and the plane will not take off.

A = +X speed
B = -X speed

They cancel each other out, and there is no linear displacement.

And my physics training will say that distance (or the X amount of miles the plane is racking up spinning it's wheels on the conveyor belt, does not equal the displacement required to take off.

For example:
What would happen if you put a car on a dyno machine.. It accelerates, and adds up milage, but it's not going anywhere.. (as long as your dyno doesn't fail and freeze up) lol

And yes, I know cars and airplanes are not created equally, but I'm just sayin' - It's the same kind of setup.

[ahecht]

Originally Posted by greencactus3

yes.... except one thing.
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).

so. laws of wear and tear and motor output of either engine(plane or conveyor) ignored, but friction not ignored, the conveyor belt spins fast enough that the friction of the wheel bearings keep the plane from accelerating. so if the conveyor really can turn exactly the same speed(but in the opposite direction) of the plane, the plane would not be accelerating. relative to the conveyor belt it may as well be going almost the speed of light but since the conveyor belt is going the opposite way at almst the speed of light, the plane doesnt move....

Ahh, I see where the confusion is here. The problem states that the speed of the conveyor is exactly the same as the speed of the plane. If this is the case, the plane will take off with no problems. However, you are interpreting the problem as saying that the conveyor is moving at exactly the same speed as the surface of the wheels (relative to the plane).

In a car, where the interaction between the wheels and the road provide the forward motion, these two are equal. However, in the case of an airplane, these aren't necessarily the same.

If the conveyor moved as the same speed as the surface of the wheels, the plane would probably not take off because as soon as the plane started moving, the speed of the wheels would always be larger than speed of the conveyor, and you would get the belt up to an infinite speed, and the friction would be providing an infinite force backwards (this is all assuming, of course, that the wheels don't slip at all, which they would far before the force equalled infinity ).

However, since the problem clearly states that the speed of the plane is being matched, Ken (and the others on that side) are correct.

[artdutra04]

Ken and all the others are correct. If you want proof, see this video clip. They mounted a fan on top of a skateboard, and as the skateboard began to gain velocity, the paper underneath the skateboard was pulled backwards at the same velocity in the other direction. The skateboard continued to accelerate, just as normal.

Here is another good way to think of this problem, as it was posted by an unregistered user on another forum:

If you still don't get it - imagine you are wearing a pair or rollerskates and you're standing still on a conveyer belt which isn't moving and you are holding a rope tied to a distant tree. You start to pull on the rope with sufficient force to pull you forward at 5mph. The conveyer belt instantly moves at 5mph in the opposite direction. Does that stop you moving closer to the tree? NO. You continue to move at 5mph and the wheels rotate at the equivalent of 10mph.

[greencactus3]

Originally Posted by artdutra04

Ken and all the others are correct. If you want proof, see this video clip. They mounted a fan on top of a skateboard, and as the skateboard began to gain velocity, the paper underneath the skateboard was pulled backwards at the same velocity in the other direction. The skateboard continued to accelerate, just as normal.

Here is another good way to think of this problem, as it was posted by an unregistered user on another forum:

hmm.. well although this wont mean anything, there is no proof that the paper was moving at the same speed... actually, it wasnt.

i have no idea how i should word this, but well...
you are all saying that the belt is moving at the same speed as the plane but the plane moves forwards. wheels or not, if Vplane=-Vground(in this case belt), Vplane+Vground=0. which means the plane does not move. ignore the wheels completely. the plane is on blocks attached to the plane.. the plane has unlimited thrutst so this does not affect anything.. (the belt also has unlimited thrust... or torque, if its a conventional conveyorbelt. so that also doesnt change anything)
so at first the plane is standing still. so Vplane=0.... which means Vbelt=0 also

now the throttle is pushed on the plane.
so Vplane relative to the air = 1
except since Vplane =1, Vbelt=-1... except the blocks and belt have enough friction ............................
or waaaaaaaaaait a second...... Friction is changed only by normal force...(since the coefficients dont change)....
Crap.. a BIG point everyone including me has failed to point out.... Force of Kinetic friction is always constant no matter how fast the two planes are rubbing right?darn.... so basically the wheel's bearings.... no matter if they are spinning at 1rpm or 287346821736498723649876rpm, the force of friction is the same right?... so the conveyor belt... no matter how fast it spins, it can not stop the plane...
aha. and no, noone mentioned that before, yes people have said that the friction was negligible but noone backed that up. i think im not the only one that was under the impression that the faster you......
or.... darn it. lost it.... anyone continue on that proof?
till then..

but yea. well i guess this shouldnt be called a physics problem cuz so much is ignored.... and yea. the plane does go up i guess. or does it..
all these people have examples of experiments.... even the video.. but noone has created a "true" conveyor belt... so those experiments are flawed. SO confusing... but this problem is a neverending pit of trying to prove the other wrong.

[ahecht]

Originally Posted by greencactus3

you are all saying that the belt is moving at the same speed as the plane but the plane moves forwards. wheels or not, if Vplane=-Vground(in this case belt), Vplane+Vground=0. which means the plane does not move.

Woah, I just realized that this problem is a whole lot more interesting than I originally thought.

We can all agree that the real question here is "does the plane move forwards?". There is a lot of talk about how planes are different from cars, but let's look closely at what would happen if we put a car on the conveyor. I will restate the problem thusly:

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

The question is:

Will the car move or not?

I am going to argue that it does!

Imagine that you are in the car on the conveyor. You start the car moving forwards at 1mph, and the belt begins to move backwards at 1mph. However, when the belt reaches 1mph, your car is now essentially going at zero speed, so the belt stops. With the belt stopped, you are now going at 1mph, so the belt goes to 1mph, and so on. If you take the average speed of the belt and your car, you will see that each is half the time going 1mph and half the time stopped, so the average of each is .5mph.

Of course, you have to take acceleration into account here, since the belt cannot start and stop instantly. If you do, you will see that between the belt speeding up and the car slowing down as a result, you will soon reach the point where, as stated above, the belt's speed is 0.5mph and your car's speed is 1mph-0.5mph=0.5mph. That means that with everything working, you will always move forward at half the speed showing on your spedometer.

Therefore, my conclusion is that this is a poorly worded question since it fails to identify how speed is measured (speed of the wheel's rotation, speed of the plane relative to the ground, or speed of the plane relative to the belt).

Originally Posted by greencactus3

now the throttle is pushed on the plane.
so Vplane relative to the air = 1
except since Vplane =1, Vbelt=-1... except the blocks and belt have enough friction ............................
or waaaaaaaaaait a second...... Friction is changed only by normal force...(since the coefficients dont change)....
Crap.. a BIG point everyone including me has failed to point out.... Force of Kinetic friction is always constant no matter how fast the two planes are rubbing right?darn.... so basically the wheel's bearings.... no matter if they are spinning at 1rpm or 287346821736498723649876rpm, the force of friction is the same right?... so the conveyor belt... no matter how fast it spins, it can not stop the plane...

One of my pet peeves about physics education is that teachers make sweeping generalizations about things like friction, which people (myself included) take to be fact.

What you said about friction is only true for dry friction. However, when you have lubricated bearings, you must take viscosity into account. When you have "friction" against a fluid, the resisting force is actually a function of the speed you are moving through that fluid. This is why falling objects reach a terminal velocity: as the speed increases, the resisting force increases until it is equal to the force of gravity, and which point the object stops accelerating since the net force on it is zero. However, as Ken below me pointed out, this effect is very small compared to the rolling friction in the wheel itself.

[KenWittlief]

Originally Posted by greencactus3

Friction is changed only by normal force...(since the coefficients dont change)....
Crap.. a BIG point everyone including me has failed to point out.... Force of Kinetic friction is always constant no matter how fast the two planes are rubbing right?

aha. and no, noone mentioned that before, yes people have said that the friction was negligible but noone backed that up.

um... no. Kinetic friction being a constant has been brought up - go back and read the thread again

FROM PAGE 3: the other thing that is counter-intuitive in this problem is this: the rolling friction of wheels is independant of the speed at which they are rolling

you simply ignored what we have been saying until now, because you jumped to your conclusion first, then tried to backfill your reasoning. *

This is a common debug problem that engineers face everyday: we think we know the answer, but then when things dont work out we cant figure out why. Its always something you assumed to be correct, and very often its stareing you right in the face.

This plus the logical error that planes spin their wheels the same way cars do. If the plane is not moving forward relative to the earth, then what is making the wheels rotate? Nothing. If the wheels are not spinning, and the conveyer is not moving, then what is stopping the plane from moving? Nothing!

and BTW, the rolling friction of a wheel is not fluid friction. The bearings are oiled or greased but they roll over the races, they do not slide through a pool of oil or grease. The major component of rolling friction on a tire is the compression of the rubber. This is what causes a tire to heat up on straight and level pavement, the rubber is constantly flexing. But this amount of energy dissapation is small.

I have to say, this problem does demonstrate how difficult it can be to convey the laws of physics into a frame of reference that the average person can grasp. I was so temped to draw detailed vector force diagrams, but keeping this discussion in text made it more challenging.

* wanted to add: this is human nature. When we get an idea in our heads it becomes 'our idea' and for some reason we feel the need to defend it. Part of it is ego and part is pride. Its something we have to deal with as engineers all the time: jumping to a conclusion, then feeling like you have to stand behind it, no matter what.

In fact, this is a very interesting aspect of engineering. A Jeckel and Hyde situation. In the early stages of the engineering design cycle we try to figure out everything, and avoid mistakes at all costs. We dont want to design something that will have bugs.

But when you reach the point where something is fabricated, or manufactured, or code is written, then you WANT to find the errors - then errors are golden, you have to discover your errors and embrace them, discover the root cause of every mistake in the design.

The reason is, if you dont find the errors in your system (through testing and debug) then your customers will! Once you start shipping product or delivering systems its very expensive to recall them and make updates or corrections.

So at first mistakes and errors are a bad thing and you shun them, then they are golden and you must embrace them and understand them. Engineers very often cant make the jump to the second part. When errors or bugs show up in a product, some want to sweep them under the rug, or patch them up as quickly as possible, instead of understanding how they happened, how to fix them correctly, and how to keep them from happening on your next project.

[greencactus3]

Originally Posted by KenWittlief

um... no. Kinetic friction being a constant has been brought up - go back and read the thread again

whoops. sorry. mustve missed that. posts pile up so fast i cant keep up.

Originally Posted by KenWittlief

you simply ignored what we have been saying until now, because you jumped to your conclusion first, then tried to backfill your reasoning. *

This is a common debug problem that engineers face everyday: we think we know the answer, but then when things dont work out we cant figure out why. Its always something you assumed to be correct, and very often its stareing you right in the face.

wait a second. from the moment i posted this problem up i said i agree with both sides. i just kept trying to find ways to unbalance the arguements. kinda ran out of ideas tho,..

Originally Posted by KenWittlief

and BTW, the rolling friction of a wheel is not fluid friction.

good point. didnt notice that detail.

Originally Posted by KenWittlief

* wanted to add: this is human nature. When we get an idea in our heads it becomes 'our idea' and for some reason we feel the need to defend it. Part of it is ego and part is pride. Its something we have to deal with as engineers all the time: jumping to a conclusion, then feeling like you have to stand behind it, no matter what.

i totally agree. i just hope you arent directing that towards me.

[Kit Gerhart]

Originally Posted by KenWittlief

The answer most certainly can be determined by the laws of physics.

All planes move by reacting with the air, either through propellers or jet engines. The speed of the ground under the wheels has almost nothing to do with the speed of the plane down the runway.

In this case, the plane would accelerate down the runway, and the 'runway' would accelerate in the other direction. The plane would still take off more or less normally, the only effect being the wheels will be spinning twice as fast as they normally would when it leaves the ground.

Hey that was easy, we settled the argument on CD in one post! :^)

There is a high probability, though, that the tires would fly apart before the airplane took off, and this could cause very bad consequences.