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Old 03-04-2006, 09:01 PM
zut zut is offline
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Join Date: Apr 2000
Location: Detroit, MI
Posts: 3,725
Originally Posted by enipla
No. Itís nearly a perfect analogy.
No it's not, really. Changing the treadmill from one that reacts to the plane wheel speed to a simple constant-speed treadmill is changing the meaning of the question.
Originally Posted by enipla
Does any one believe that ANY airplane could not take off because of the effect that the landing gear is spinning twice as fast as normal?

IT WONíT MATTER. It would be a ***** to steer before transition, but the plane would take off. It has ground speed. Air over the wings. Thatís all that matters.
I already explained in my previous post about the two different interpretations of the question. As did flight. As did timmerov2.

As far as I can tell, there isn't anyone in this thread who disputes the fact that, if you interpret the question as meaning that the plane fuselage moves forward and the wheels spin at double speed, the plane will take off. There's nothing wrong with that interpretation, and nothing wrong with that answer.

However, much of the rest of the discussion in this thread centers around the alternate interpretation. There's nothing wrong with this alternate interpretation, either, but it does lead to different conclusions.

Originally Posted by Paradoxic
The answer is not intuitive, and this fails as a thought problem unless you actually do the math.
  • Force generated by the engines directed in one direction.
  • Force generated by the treadmill in the opposite direction (how about a treadmill driven by the same engines as the plane uses?)
  • The forces meet and cancel out, at the wheel assembly (w/hot tires) and ground friction.
I'm still not sure if I agree with you, or you agree with me. Agreed that the plane requires airspeed, and the answer is not intuitive. However, you keep mentioning a treadmill "driven by the same engines as the plane uses," which makes no sense to me. It makes no difference what the power source driving the treadmill is, as long as it's large enough to provide the power necessary for accelerating the belt.

If you assume a treadmill capable of large velocities and accelerations, and assume that it tracks the wheel speed of the plane, the belt will supply a force to the plane to counteract the engine thrust. However, this requires some coupling through the wheels--the wheel inertia, for example. The scenario you're giving is a bit oversimplified because it skips the step describing the coupling mechanism.