The original question where it matches the wheels. The answer is its impossible so why are we arguing.

If you think of the wheels as a sprocket and the treadmill as a chain and assume the “sprocket-tire” can never jump out of the chain then you increase the force of the plane’s forward thrust on the treadmill-chain. But then you really don’t have an airplane on a treadmill, you have an airplane engine driving a sprocket-chain assembly. Not the same thing.

Real-world example with existing items, the plane takes off. Fantasy land where you can introduce some way to anchor the plane to the treadmill (sprocket-chain), the thrust is diverted towards driving the treadmill instead of pulling the plane forward.

Resolved: The plane will NOT take off.

(See also here,

How about a treadmill moving the same direction as the plane. The wheels couldn’t be free spinning. If this was the case the treamill would have little effect. The wheels would have to move only in the forward direction. This reminds me of a conveyor in an airport that people walk on. You move twice as fast. Of course this wouldn’t make the plane take off while standing still, but it should cut the runway length drastically. Sort of like the sling shot device used on carriers.

All that matters is the wind speed relative to the airplane (and, more specifically, the airplane’s wings). Hypothetically, if you pointed a really powerful fan at an airplane, coming from directly in front, you wouldn’t even need the engines to generate the thrust (which, in turn, would increase the wind speed over the wings and therefore generate lift). This is what happens inside a wind tunnel during testing. On the other hand, since in the example the plane is not moving, there is no positive airflow past the wings and thus no lift is generated.

The plane does not take off.

I’m shocked by the comments here, but even more so that Cecil was actually wrong about something. I was expecting some ingenious explanation of why this example is counter-intuitive (like the Door-Picking exercise in “Let’s make a deal” that Cecil mentions in the article), but instead, this…?!?!!?

As I made explicitly clear in my last post, all my answers assume a frictionless/low friction environment. Hence, it’s NOT like a plane sitting on the ground, doing an engine run with the brakes on and the chalks in place. In that scenario, the friction of the rubber on the ground (held motionless), the grip of the groundbrakes, and the force of the chalks against the tires is enough to hold the plane in place.

In the treadmill conundrum, it’s absurd to take friction into account; if we do, the whole exercise is useless as the friction of the wheels spinning at 2X ground speed would quickly destroy the entire undercarriage.

So…assuming no friction, nothing would hold the plane in place, the wheels would spin at a rotational velocity that corresponds to twice the airplane’s ground speed, and the engines would act on the air surrounding the plane to create thrust and push the plane forward. See JustinD’s explanation for a practical exercise you can do to prove this correct.

If this is the case, the plane won’t ever reach the end of the runway, because all of it’s forward energy will be cancelled out by the magical frictionless treadmill.

Grab a glider at Toys ‘R’ Us (or make a paper airplane), hop on your treadmill, and crank it up to as fast as you can run. You’re the jet engine, you’re the wheels. Hold the glider over your head and let it go. If it’s heavy, you should wear a helmet or be prepared to dodge, because it’s going to fall straight down.

You’re right–in a practical application that’s what would happen, and you’d have a fiery, terrific crash.

However, assuming a frictionless/extremely-low-friction environment (as one often does when attempting to divine the physics behind a practical experiment), my previous statement still stands.

And, uh, Andy? The thrust doesn’t turn the wheels. The thrust pushes the plane forward, and the forward motion of the airplane turns the wheels. They’re just there to reduce friction.

Assuming the treadmill effectively increases speed to an indefinite number or at least very high, the friction of the rubber on the treadmill will be so high that the tires will burst. The tires will have exceeded the maximum tire speed (published for transport category aircraft). At that point the plane will be resting on metal stumps, on a stationary treadmill. Given that the thrust rarely exceeds the breakaway force required from the metal on treadmill combo, the plane will not lift off.

sop if the plane is not moving, you will not creat any lift, and inturn the plane will not leave the ground. and as someone stated your engines do not create any life is entirely correct, a plane is pretty much a rock that you threw a rocket on and hope for the best.

but since the aircraft is not moving the slats and flaps will not do their job of making an air bubble under the wing that lifts the wings and in turn lift the plane, positive airflow over the wings is what creates this pressure difference that lifts the wings. so you need enough forward movement to create this differenc to lift the plane.

thank you i was great

On a treadmill that is long enough for the plane to achieve V2 (safe rotation speed) while still on the treadmill, the plane will accelerate and lift off normally.

On a treadmill of shorter length, the plane will reach the end of the treadmill at ground speed X with its tires rotating at whatever rotational velocity that would correlate with ground speed 2X. Hence, when the plane reached the end of the treadmill, you would see a large cloud of tire smoke as the wheels immediately decelerated to half their rotational velocity, but the plane would continue as normal, reaching v2 and rotating (assuming 1) no mechanical failure due to the rapid deceleration of the wheels and 2) sufficent space AFTER the treadmill for the plane to achieve sufficient velocity.)

Some of you have been distracted by the red herring of “a jet engine does not produce airflow over the wing”, using that statement to discount arguments that suggest take-off is possible. While it is true that jet engines do not produce airflow over the wing, they do provide forward thrust to the airplane, which enables the movement that, in turn, creates airflow over the wing, an area of low pressure above the wing, Bernoulli’s principle, magic flying pixie dust, et. al. (Although, technically, Bernoulli’s principle does not thoroughly explain the lift created by an airplane’s wing–it’s an easy (for the layman) to understand explanation that comes close but relies on the fallacy of equal transit times…wings actually create lift because they force air downwards. For more info, check this out: http://home.comcast.net/%7Eclipper-108/lift.htm) The forward thrust that the engines create is INDEPENDENT OF THE WHEELS, THE GROUND, AND ANYTHING OTHER THAN THE AIR SURROUNDING THE AIRCRAFT, any way you slice it. The airplane does take off–not because of jet engines creating airflow over the wings, but because of the ground-independant forward thrust they provide.

It’s pretty simple actually, no need for physics unless you really really want to get into it.

An airplane’s wheel are free-rolling - that is, they are not like the wheels on a car. They’re like the wheels on a… stroller. They just roll free.

The conveyer and the airplane wheels are red herrings, because an airplane does not rely on it’s wheels at all to take off - the wheel are just there, in a simple sense, to allow the plane easy movement relative to the surface it is sitting on. That is, an airplane does NOT rely on the speed of its wheels to take off (that implies it’s acting like a car, using an engine to drive it’s wheels) - it relies on the speed produced by its engines. The engines push the plane through the air.

Best way to demo this for yourself is with a toy car - I sent my folks this question and it had them arguing. =) So here’s what I showed them:

A Matchbox car, a long strip of paper, and your fingers. First, hold the car steady between your fingers, and pull the paper out from under the car. The car’s wheel are free spinning, so the paper slides easily out from underneath. This is somewhat representative if a REAL car was in this conveyer situation - it would stand still because it’s engines will propel it forward relative to the ground (moving or not!)

Now, do the same thing, but instead of holding the car steady with your fingers, push the car forward as you pull the paper out from under it. The car moved forward relative to its surroundings, right? This is because your fingers are now acting as the JET’S ENGINES. A jet’s engines work by moving air, NOT by acting upon the ground. That’s how a plane moves along the ground. The plane’s wheel dont have little engines in them - the plane’s big turbine engines suck in air, push it out the back and propel the plane forward.

Hell, if holding the toy car with your fingers doesn’t do it for you, attach the car to a string. As you pull out the paper, pull the car forward - you pulling the string represents the jet’s engines, because the jet’s engine produces forward thrust completely independently of whatEVER the hell the ground is “doing” - whether it’s a conveyer belt, ice, frictionless magic surface, etc.

I used to be on the “no take-off” side, for precisely that (incorrect) reason. But he doesn’t even get it quite right; the conveyor CAN keep the plane stationary if it moves fast enough, but it doesn’t; it only moves as fast, backwards, as the plane moves, forwards.

My scenario: airplane with engines running, low-friction wheels. Conveyor matches ground speed of plane (in reverse). What happens? Regardless of the situation with the wheels/conveyor/air resistance system, the engines produce forward thrust, moving the aircraft forward faster until it attains lift-off. Throughout the take-off process, the conveyor matches the ground speed of the airplane (but in reverse), thus when the airplane is moving forward at 5mph, the conveyor is moving backwards at 5mph and the wheels spin at 10mph. The plane still moves forward. At take off, the wheels spin twice as fast as the take-off speed, but the plane is still moving at take-off speed and still lifts off.

UNLESS: If you take the question a little differently (the way I used to), the conveyor can move infinitely fast, and it will always attempt to _keep the airplane stationary_ (that’s the difference).

Imagine scenario 1: airplane with engines off, frictionless wheels. Conveyor starts moving at an arbitrary speed. What happens? Due to the inertia of the plane, it stays stationary and the wheels/treadmill can spin as fast as they want.

Scenario 2: airplane with engines running, frictionless wheels. Conveyor starts running at an arbitrary speed. What happens? Due to the forward thrust of the engines, the plane moves forward and gathers speed with respect to surrounding environment until it lifts off. The wheels/treadmill can spin as fast as they want without affecting this.

Scenario 3: airplane with engines off, low-friction wheels. Conveyor starts running at an arbitrary speed. what happens? Initially, the plane’s inertia will resist moving with the conveyor, but slowly the friction from the wheels will cause the plane to move in the direction of the conveyor. The backwards speed of the plane will continue to increase until the wheels/conveyor/air resistance system is in equilibrium (in an airless environment, equilibrium would obtain when the wheels became motionless with respect to the conveyor surface).

Scenario 4: airplane with engines running, low-friction wheels. Conveyor starts running at an arbitrary speed. What happens? Because the wheels are NOT 100% frictionless, the friction from the wheel/conveyor system will overcome the forward thrust from the engines at a given speed. The conveyor will have to move really, really, really fast to cause the wheels’ friction to overcome the thrust of the jet engine, but in a theoretical sense, it happens. Thus, no forward motion for the plane, no lift, no take-off. That used to be my answer, until I read the question correctly.

Especially Murph. Murph apparently thinks the point of jet engines is to proivde downforce like a giant finger.

And especially Clay. Clay apparently believes that a light breeze that could fly a kite can also lift an airplane.

And most especially me for posting this and not just pointing and laughing.

If you can fly it running at your fastest, then the answer is yes. The plane will take off.

If you cannot fly it running at your fastest, then the answer is no.