I’m with the New York Times on this. Cecil’s explanation is wrong. Here’s why: The wheels on a plane are there to reduce friction. It therefore seems accepted that a certain amount of friction will stop the plane from taking off. But a treadmill beneath the plane, increasing the speed at which the wheels are turning, also increases the friction that they feel: they are the equivalent of a drag on the plane. If that drag is great enough, the plane cannot take off. Since there will always be a coefficient of friction, the drag will become great enough at some speed.
The example Cecil gives of the rollerblades doesn’t account for the ever-increasing speed of the treadmill. The treadmill will knock you over, even with rollerblades on, at a certain speed. You won’t necessarily be able to pull yourself forward without falling.
Airplanes pull themselves through the air using the motor, yes the wheels aer only there to provide less friction for take off.
Planes can only become airborn at a certain speed. air has to be moving over their wings. for this a plane needs foreward movement.
If the pull of the planes engines can beat the friction caused by the turning wheel, then it would be able to pull itself foreward and thus take off.
the question is “is the planes thrust greater then the energy required to ocmbat the friction caused by the conveyer and the wheels?”
In many cases yes, the power of the engines would beat the friction caused by the turning wheel.
If the plane rolls foreward on its wheels until sufficient airflow over the wings provides lift-off, with the ‘ground’ moving backwards in a 1:1 ratio with the plane’s ‘foreward impetus’, the plane must remain motionless. The more force exerted, the faster the ‘ground’ will move backwards, with motionlessness (in relation to the ground) maintained.
(Ok, further thought produces my post below, and the solution to today’s problem.)
A big part of it is in the wording of the question, but I think the view that the plane doesn’t move is still rejected as illegitimate too readily. The general breakdown is that the plane either takes off because the wheels do not move fast enough to prevent the plane from moving forward; or that the phrasing of the question calls for the wheels to spin infinitely fast, because by ‘the treadmill matches the speed of the wheels’, it is intended that the speed of the treadmill equals the rotational speed of the wheel plus the speed the planeactually moves (which is the same as saying the speed of the treadmill equals the speed of the treadmill plus the speed of the plane).
The way I think about the problem, the treadmill is supposed to be analogous to a treadmill that would keep a car still. The reason the car is kept still is because the treadmill moves at the same speed as the rotational speed. Thus, the treadmill moves relative to the ‘foreward impetus’. In that case, as Nameless says, the plane’s treadmill should move relative to the plane’s ‘foreward impetus’, i.e. the air through the engines.
Now, in that case, does the plane take off? I guess so. The force on the wings is probably greater than the force on the wheels. You have to figure that the force on the wheels is negligible compared to the thrust of the engines.
Alright, I contradict myself: the plane does take off.
Mythbusters did it.
The plane takes off because of airspeed. The wheels must rotate as the plane gains sufficient airspeed. If the wheels do not allow the plane to move, as in the ground below them cancelling any foreward motion, sufficient airspeed cannot be achieved. If the wheels did not spin at all, they would be dragged, but as they spin…
wait a minute!
If they didnt spin at all, the plane would still, with sufficient energy applied, drag itself foreward, until an equilibrium of airspeed and ‘applied energy’ are in balance.
SO if no wheels, nor square wheels will not stop it from launch, nor draggy ungreased wheels, nor… why would it not launch with ‘spinning wheels’ if it launchs in all other conditions. Perhaps we are approaching the question from the wrong end? It pulls itself foreware relative to the ‘air’ in which it moves. There could be perfectly teflon coated greased buttered sharpened frictionless blades below that plane (equivalent to those ‘spinning wheels’) and the plade still achieves launch. The ‘movement’ of the ground (or the wheels, it seems) is irrelevent.
Thats my new story and I’m sticking to it, for the moment!
All roads lead to Rome, eh? *__-
Now, how does friction work in this situation?
Suppose there’s a maximum amount of thrust the plane can generate, because any more and it will tear itself to shreds or rip a hole in space and time or whatever. If that’s the case, there’s an amount of friction that would stop the plane from taking off. So my question is, is the force of friction constant on the wheels, assuming they don’t melt or otherwise fail structurally? I don’t remember how dynamic friction works as speed increases. If it’s constant or decreases, the plane takes off. If it increases, the friction might be able to defeat the thrust from the engines.
Who knows about this stuff? I’m too drunk to do research.
the engine thrust is with the air not the ground right? doesn’t that pretty much solve it? i don’t understand whats unclear about cecil’s explanation.
jets push the plane forwards. not upwards. The air pushes the plane upwards when the plane goes a certain speed, and so it doesn’t matter how much thrust the plane has. As long as it stands still and the air underneath it moves at a steady pace, the plane will stand grounded.
Right? Or are we talking about those new planes that can take off from downwards thrust?
If the plane could take of without wheels, as Nameless says, then the treadmill probably couldn’t move fast enough to stop the plane from taking off. It wouldn’t provide enough resistance to keep it still, and it would pull forward anyway. But if there’s a fairly low minimum friction, and rotational friction functions a certain way, the plane is probably held back by its wheels.
Maybe we can construct the full equation.
Say the engine thrust is Fe. The rotational speed of the wheels is Vw, the wheel has radius R, and the coefficient of friction between the wheel and the axle is C (assume there is no slippage between the tire and the runway).
Depending on how friction works, an equilibrium state exists when
Fe=f(R,C)
where ‘f(R,C)’ is some equation that determines the constant resistance of a wheel of radius R and coefficient of friction C in the case that friction is not speed dependent; or
Fe=f(R,C,Vw)
where ‘Fe=f(R,C,Vw)’ is the more complex equation where the friction is speed dependent.
So, we need to find f(R,C) or f(R,C,Vw). I tried to find it, but instead I found that a plane travels at 550 mph. That doesn’t help.
When going on the freeway in your car just stick your hand outside the window and tilt the pinkey side down. Notice that your hand will move upwards. That’s because you create drag for the air, and the air pushes upwards. Move the thumb side of your hand down and your hand goes down. same principle here. If the plane stands still, and the air surrounding it stands still, the plane will not fly. It doesn’t matter how much thrust forwards it has.
ps. do the jets push air towards the parts of the wings which flap up and down? Cause if they do, then the plane could take off.
There is no friction. the wheels turn, the ground turns 1:1 reverse ratio, it would be like the plane were on slick skates, no friction. the plane moves pulling/pushing air against air. Wheels are just to keep it ‘comfortable’.
The friction is negligible. The wheels dont push the treadmill, the tread runs independent and in synch. The friction would be that inherent in the system; wheel bearings, etc… There would be no more friction than an ice skate on wet ice (I think). The launch is relatively independent of wheels. Square wheels would little hinder a launch, and thats lots of friction.
Remember tha the wheels can turn pretty much as fast as they need to, with very little friction.
Like a takeoff on iceskates! Sweet! Woosh! Into the wild blue yonderrrr…
Oh sure, everyone just ignore that crazy bastard Anthem.
youtube.com/watch?v=YORCk1BN7QY
The only way to keep the airplane stationary would be to govern the wheels to the takeoff speed of the aircraft (which is the speed of the treadmill in the problem). As it is, the wheels spin twice as fast as the takeoff speed dictates.
Whatever you find on ‘youtube’, the only way that the wheels become relevent at all is if the wheels had their own motive power, and were themselves responsible for gaining appropriate speed for lift-off. Then the ‘ground’ moving in the opposite direction would cancel foreward motion.
With the motive power being irrelevent to the ground (it is an air vs air thing) the wheels can be safely eliminated from the equation, and the plane still takes off…
This is different from what I said how?
You said;
“The only way to keep the airplane stationary would be to govern the wheels…”
And I responded that the wheels made not a whit of difference; whether they were going forewward, backward, are square or punctured, they are irrelevent to the question. The ‘only way to keep the plane stationary’ is to anchor it beyond the power curve of the engines to overcome (big chain), or insufficient engines, but the question did not limit the engine power.
Therein lies the difference, as I see it.
Peace
Therein lies your ignorance.
If the wheels were governed to the takeoff speed of the aircraft and they didn’t slip on the treadmill, the plane wouldn’t take off. Yes, you can take off on most any type of contact with enough power because the force would overcome the friction, but now we’re getting into silly alterations of the experiment like sticking a rocket engine on a Cessna. I don’t think a normal plane would be able to take off sliding on its wheels, but I guess I shouldn’t have said ‘the only way’. Sure, you could dismantle the airplane and it wouldn’t take off, or you could tie a tank to it and it wouldn’t take off, but I was making the smallest silly alteration I could think of that would match how those who are mistaken about the experiment might think the airplane should behave.
Ignoring your stupid and juvenile comment, I’ll go this one last time;
There IS NO FRICTION when the wheels and the ground have a 1:1 inverse ratio. Need i explain this? Can you understand? Without the ground moving equally backward, there would be more friction than otherwise. As the OP has stated, the plane can thrust foreward. If you knew anything about the physics involved, many, if not most, modern planes and most if not all jets can take off sitting belly on the tarmac with no landing gear at all. Once the initial friction is cracked, it just takes a bit more power, and the fusilage is tobogganing down the runway. There was no power limit in the OP, and I do not refer to any out of the ordinary power gradient.
And what do you know of a Cesna? Ever pilot one? Know the stats re; thrust and lift? Relative to airspeed or groundspeed?
Yes, you are entitled to your ‘thoughts’, ill informed as they might be, regarding “normal planes” (…those that fly around in your egoic fantasies of knowledge), wheatever thay might be.
I’m done, believe what you must.
nameless out