Can the Plane Take-Off?

[Morgan Gillespie]

The answer is yes; the belt tracks and recreates the planes speed in the opposing direction, yet if the plane isn't moving and just standing still, then neither is the belt. The problem never states it is moving in such a speed that it would cause the plane to not move forward, it only says it would go in the opposite direction at the same speed of the airplane.
Under experiment conditions... it works perfectly fine, even at take off the belt is only moving as fast as the plane is forward, this just means the wheels are rotating at twice their normal take off speed...

[Molten]

The reason I did not source the formula is because it has been around for long enough that it does not need a source. It is common knowledge. Also, the wheels can still be used to measure speed despite the fact that they are not used for propulsion. Furthermore, I am not discussing this anymore until I have seen Mythbusters. I hope that I did a reasonable job explaining some of the misinterpretations of my words. Until then, Good day.

[EricH]

Originally Posted by Molten

The reason I did not source the formula is because it has been around for long enough that it does not need a source. It is common knowledge. Also, the wheels can still be used to measure speed despite the fact that they are not used for propulsion. Furthermore, I am not discussing this anymore until I have seen Mythbusters. I hope that I did a reasonable job explaining some of the misinterpretations of my words. Until then, Good day.

I didn't ask for the source, I asked for a proof. Also, how does it tie in? You did not explain that part. The equation is there with no tie-in.

I don't disagree that the wheels can be used to measure speed, but there is a chance (I've done it in a simulator) that one or more wheels will be off the ground at any given instant, so which wheel do you measure? How do you determine which wheel's data is correct, if you do all of them?

And the conditions are clearly stated in the problem. What conditions did you have in mind? For anyone to analyze your conditions, you have to state them. You don't. Therefore, I cannot fully answer you because my mind-reader is on the blink (and has been for 19 years at this time). If I know what conditions you use, I can either agree or disagree with the conditions. I may or may not agree with you, but not knowing what conditions you have in mind prevents my doing either. I disagree based on the given conditions. You have other conditions. Very well, let's hear them.

[Pat McCarthy]

The Mythbusters have conclusively proven that a plane on a treadmill can take off! (When comparing airspeed vs. conveyor speed)

Warning! Science Content!
This can be explained by comparing the means of propulsion of a plane vs. a car. A car uses the powered spin of its wheels to propel it forward.

Now a plane uses it's propeller to push against the air, while the wheels are left to free spin. And a plane depends on the speed of the air passing over its wings to generate lift to take off. With enough headwind, a plane can take off while not moving relative to the ground. Thus, a plane will pull itself through the air, no matter if it's wheels are spinning (or how fast they are spinning) or even if they are not spinning at all.

There is a corollary to this.
And I'm not sure if I will be explaining it right.
You have to be measuring the plane's airspeed for the experiment to work. If the speed of the wheels was monitored, and you were only trying to match the speed of the conveyor belt to the rotation of the wheels, assuming no friction in the system other than that between the wheels and the conveyor, the plane wouldn't have to exert any propulsion of any kind to remain stationary (Newton's First Law of Motion). However, in real life, the plane would be pulled backwards along with the conveyor, relative to the ground due to the friction of the wheels and their bearings. So to counter this, the plane would have to be pushing some air with its propeller to remain stationary to the ground for the wheels to match the speed of the conveyor.
In this case, the plane would not take off, as the speed being measured was the speed of the wheels matching speed of the conveyor, not the airspeed vs speed of the conveyor. To sum it up, the plane would remain stationary to the ground and thus have zero airspeed (assuming no wind) and not be able to take off.