Plane On Treadmill Problem
Sun, 12/03/2006 - 09:57 — me
A plane equipped with fixed horizontal engines and wheel landing gear is placed on a huge treadmill runway. The treadmill has a clever design and always matches the speed of the plane, but runs in the opposite direction. Will the plane take off and fly or not?
Comments
Of course it will fly
Of course it will fly because the plane is pushing air below its wings. It's simple high school physics!
Will it fly?
No, it won't. A plane does not fly because of thrust, it flys due to the lift produced by airflow over its wings as thrust moves it through the air. In your model only the wheels would spin. Sure there is thrust, but in this problem, it serve only to move the plane over the belt, so the plane never achieves lift, and will never fly.
Will it or won't it fly.
The confusion for this problem and thus the inability to reach consensus is obvious. No where in the problem does the situation state with the plane is doing in relation to the REAL ground and thus the air. The problem could be read that the plane is stationary to the air and ground (thus it won't fly) or is moving in the air, but stationary to the treadmill (will fly). The problem here is in the author's inability to make clear the problem.
The problem is not unclear.
The problem is not unclear. The movement of the plane in relation to the air IS the problem. Most of the solutions are ignoring the real problem. They simply ASSUME that: A) the treadmill makes the plane stationary (no fly) or B) the thrust of the jet makes the treadmill irrelevant. Neither assumption is correct.
The posts discussing the friction of the wheels are getting the closest. The key is the force balance between the thrust and the friction of the wheels. As the treadmill speeds up the wheels, the friction of the wheels acts as a brake against the thrust of the airplane engines. If the thrust exceeds the friction forces, the plane will gain airspeed and fly, if not it won't. (I think we can neglect drag since the plane will need airspeed for there to be any drag) The real question is: will the thrust of the plane's engines enable it to attain any airspeed against the frictional forces of the wheels?
Clearly in a frictionless system, the airplane would take off, as the action of the treadmill would always produce zero frictional forces.
However, this appears to be one of those theoretical real world problems, where we have friction, but also have a treadmill with perfect controls and infinite speed. I guess we could have an infinitely powerful engine as well. In this problem, the treadmill would always be able to match the speed of the wheels. So the idea that the thrust of the engines causes the airplane wheels to move twice as fast as the treadmill is impossible. As soon as the engines engage, the treadmill begins to speed up such that the friction of the wheels matches the engine thrust. Since the frictional force is very small, the treadmill gets to extremely high speeds very quickly. If nothing fails, the jet should stay in it's place with balanced forces.
Of course the heat generated by the frictional forces in real life would cause something to fail. If the conveyor locks up, the jet would take off, but if the wheel or converor fell apart, the airplane would crash.
I believe that a system constructed in today's world would take off, though, because I don't think we can design a treadmill to speed up as quickly as it would need to do to counteract the thrust of the engines. Also I don't think we can generate enough speed from the treadmill to counteract the thrust. As the engine engages, the plane would begin to move, which would cause the treadmill to turn the wheels, and an increase in the friction. But the thrust from the jet engine would be much great than the force of friction, and the airplane would begin to move farther forward. The treadmill would try to speed up to compensate, but I think it the airplane would accelarate more quickly than the treadmill could match the speed of the wheels. Once the plane begins to move, it will take off.
That's just a guess, though. I remain unconvinced without some math to back it up or a working model to prove it.
Yes, it will fly.
Yes, it will fly.
This is due to the fact that a plane is propelled by thrust and not through friction of the wheels as is the case for automobiles. There is nothing to counteract the thrust except some negligible rotational friction in the axle. The plane would fly at near regular speed, yet the tires would spin twice as fast.
If you want to experiment in real life to prove this, you can try one of the following exercises:
Get a treadmill and attach a rope to the front end of treadmill or a wall in front of you. Now stand on rollerblades or a skateboard and turn the treadmill on. Now start to pull yourself forward. As long as the wheels are greased enough (as they would be on a plane) you should have no problem. The only hard part might be at the beginning when the treadmill is moving and you are not. This would not happen in the theoretical plane problem as the treadmill matches its speed from the beginning.
Go to an airport or any other place that has a long moving walkway. Put a stroller or a luggage cart or even a piece of rolling luggage on the moving platform and walk along side it pulling it. Once again, the only thing that will make it any more difficult than walking normally would be the rotational friction of the wheel on the axle. A little wd40 will show this to be true.
Therefore, assuming you can overcome the rotational friction caused by the spinning wheel on the axle (which should be done easily on any well kept aircraft) the plane will propel itself forward at a normal speed and take off.
Won't fly
I think you are misunderstanding the problem. The statement:
"The treadmill has a clever design and always matches the speed of the plane, but runs in the opposite direction"
This would imply that the plane would have no forward motion. The plane needs forward motion to generate lift from air passing under the wings. No forward motion -> no flight.
One other experiment I
One other experiment I forgot to add:
Take a yo-yo and set it on a piece of paper. Using the string, pull the yo-yo in one direction while you pull the paper in the other direction. You will see the results. Note: the string should not be wound around the yo-yo lest you add an extra components into the problem.
It will fly, the plane
It will fly, the plane pushes off of the air, not the ground. It won't matter if its velocity relative to the ground is zero: as soon as it generates enough lift, its outta there. Tis a classic physics problem.
It won't, the plane stays at
It won't, the plane stays at one spot, it doesn't make any sense if it would take off, the only thing that's diffrent when a plane is standing still on the ground are the wheels that are running.
It's all relative
This is a great problem.
The tricky part is: what's moving relative to what
If you put a car on the treadmill, and put the car in gear and stepped on the gas, the car's engine would be turning the car's wheels, which would move the car forward relative to the treadmill. If, at the same time you were moving the treadmill backward relative to the ground at the same speed, then the car's movement relative to the treadmill and the treadmill's movement relative to the ground, and the car would stay in one place relative to the ground.
Airplanes work differently than cars. Assuming the wheels are rolling freely, once the engines start running the airplane begins accelerating relative to the air. At that point there is nothing you could do with the treadmill to change the airplane's speed by more than a tiny bit (due to the effect of friction in the wheels.)
Let's say you're standing on the ground watching, and the airplane is moving at 100 MPH from your left towards your right. If ran the treadmill at 100 MPH from left to right, then the airplane's wheels would not be turning, but the airplane would still be moving at 100 MPH from your left to your right. If, on the other hand, you ran the treadmill at 100 MPH from your right to your left, then the airplane's wheels would be spinning against the treadmill at 200 MPH, but the airplane would still be moving from your left to your right at 100 MPH.
The treadmill has no significant effect; the airplane takes off normally.
How can it generate lift if
How can it generate lift if its standing still? It generates life by passing through the air, at first it does so on the ground until it takes off and then it does it in the air. It its standing still it can´t do that so it won´t take off.
Imagine you park your plane somewhere (do you "park" planes?) and the next day its gone because it decided to fly away because it doesn´t need the ground but only air...
Yes planes are parked..
Yes planes are parked.. IMHO it would not fly as it could never move forward and gain any lift under the wings.
Of course it won't fly. The
Of course it won't fly. The plane needs to be moving forward to push air downwards with its wings, or it won't take off. Simple.
Yes it will. The friction
Yes it will. The friction generated by the ball bearings (I suppose the wheels have ball bearings) is so small that the the push force generated by the turbines greatly exceeds the speed of the threadmill.
you don't understand, the
you don't understand, the wheels don't do anything.
All the wheels do is reduce friction with the ground, the plane is pushed by the engines. NOT BY THE WHEELS
everyone who said no is a f****** Cage Monkey!
Yes, but to what end are the
Yes, but to what end are the engines pushing the plane? As I understand it, to produce speed, to produce airflow under the wings, to produce lift. The treadmill counteracts the work done by the engines, resulting in no speed in relation to the surrounding air being gained, and thus no lift is generated? Am I wrong, and if I am, how and why?
Furthermore, when you declare that people thinking otherwise than you on an issue that has been the subject of debate all over the internet and elsewhere for years and years without a definate answer showing up, you are the effing whatever.
Not when I debunk truthiness
Not when I debunk truthiness with fact.
What people don't understand that the treadmill isn't acting against the force of the plane's forward motion.
It's not like drag with acts against thrust, pushing against the body of the plane. The treadmill is acting on the wheels, which roll freely from the plane
.
You are imagining this problem like a car.
A car pushes against the ground to push itself forward. A plane pushes against the air to push itself forward. So the treadmill does nothing to the thrust.
You are a f****** Cage Monkey for refusing the accept fact and science over the faith you have in your own uninformed and confused ideas of physics and aviation.
Why would it fly? The plane
Why would it fly? The plane in this scenario is essentially the same as a plane that's sitting still: There's no relative motion.
Of course it won't fly! Air
Of course it won't fly! Air passing over and under the wings is required to generate lift so the plane can get off the ground. The plane is only moving relative to the treadmill not to the air around it, so there is no airflow over the wings (well, there actually would be some generated by the jets "sucking" air around the wings, but not enough to generate the required lift), therefore no lift, therefore it can scream its little jets off but it still won't fly...
I don't see why the plane
I don't see why the plane would actually take off. Unless the fact that planes take off is directly related to how fast that turbine is spinning, the wings aren't slicing through any air to even become airborn are they? The plane is stationary. :[
The plane isn't pushing off
The plane isn't pushing off the treadmill to push itself forward like a car does; so it isn't fighting against the force of the treadmill at all, all the treadmill would do is roll the wheels and double the speed.
Plane Problem explained by Moz.
Flash video: Plane Problem (explained by Moz)
No matter how much logic or
No matter how much logic or rational thinking is involved, i will stay undecieded untill a fullscale treadmill/testing facility is built.
If there was a blimp above a
If there was a blimp above a treadmill, and I was on the treadmill holding a rope tied to the blimp, and the blimp decided to continually apply thrust, I would get dragged along and scream and cry right off the treadmill, possibly even make a poopie.
I didn't grab it either at first, but it'll click. Coming from a fellow 'no fly' this might help ;)
Get a skateboard, and stand up next to a wall. Push yourself away from the wall, just using your hands with both feet on the skateboard (or your butt, if you can't stand on a board). Got the feel for how that works? You are not involving the ground in anything other than holding you up.
Now lets get on a treadmill with the skateboard, with a wall behind you. Get up to a nice speed. Now push yourself forward off the wall. You still moved forward. Why? Because again, just like when the ground wasn't moving, the ground didn't do anything other than hold you up. The only difference is the skateboard wheels are moving super fast.
Now in all likelyhood, if you turned the treadmill up too fast, you'll just hurt yourself, because I imagine the average human can only push themselves so far with one good shove.
But imagine if you were Mr Stretchy Arms Guy, and your arm continued to press forward at the same rate, or even faster. Even with the treadmill trying to continually match your speed, you'd just keep moving forward until you die, or in the case of the airplane, take off.
It completely goes against the 'gut feeling', and I completely agree that it *shouldn't* work. And in the real world we couldn't GET it to work just because of the expense and the phucking uber wheels it would take.
Fellow "no-flyers", it's ok. I was one once too. The flying side cares and loves all! And...well, makes you feel like a dunce for not seeing it once it finally clicks :)
re: If there was a blimp above
I guess it still hasn't clicked for me yet. You aren't accounting for friction. Friction is a force; and we know that whenever we exert a force against something, that object exerts an equal and opposite force against us (or the thing applying the force). That's why cars are able to drive on a clear road, but have problems with ice. If there were no friction (in the skateboard analogy), we wouldn't be able to move. Another problem with that analogy is that when you talk about "pushing yourself forward off the wall," that implies a speed greater than the speed of the treadmill. The only way the plane would fly is if it were able to travel faster than the treadmill.
This has had me scratching
This has had me scratching my head a bit but i've come to this conclusion in the end (that video helped Moz ). Now is this the final answer or am I still wrong? OK now i've thought about it some more..would the wheels not just spin on the spot if the conveyor is always moving at the same speed as the plane? Bah i'm not so sure now.
okay...the simplest way to
okay...the simplest way to give an analogy...
im sure weve all had our arm out of a car window when its moving, and if you angle your hand correctly, the wind will push it up....now imagine putting that car on a stationary treadmill, hitting the gas on the car to about 30mph, and then have the treadmill spinning in the opposite direction 30mph...so the car is not moving relative to the grond the treadmill is on....would your arm still go upwards? no...because theres no wind caused by movement in relation to the ground (or air to me more technical)...only movement in relation to the treadmill
Seeing as how the treadmill
Seeing as how the treadmill will keep increasing its speed - the amount of thrust you would need is more than you can imagine. I guess if reality isnt a factor then a jet engine with with no thrust peak could theoretically outrun the treadmill - but outrunning it to the point of takeoff would take a miracle.
Just a quick update on my
Just a quick update on my thoughts on this - my picture sucks and needs updating! The wheels don't really have an effect on the forward speed - they just roll at the speed of the treadmill (assuming we can forget friction in this hypothesis). without thrust the plane would stay still (not perfectly but enough for this). Adding the force of the thrust removes the equalibrium provided by the wheels and the plane moves forward. As long as we can assume its possible for the plane to move forward then its possible for it to take off in this example.
YES it would take off .. The
YES it would take off ..
The plane is not propelled by its wheels, they simply keep the body of the plan off the ground and let it move freely.
The plane moves using thrust from the air it draws through its engines.
As thrust builds the plane will move, building to lift off speed in the same distance it would on a normal runway.
The treadmill running in the oppisite direction simply makes the wheels turn faster, and has no effect on the actual speed of the plane.
For example ..
On a normal runway, the wheels would be spinning at 200km hour when the plane lifts off.
On the treadmill, the wheels would be spinning at 400km hour at point of lift off.
There is NO force preventing the plane from actualy moving.