Can the plane take off?

km1125 said:
"The conveyor belt is designed to exactly match the speed of the wheels". If the treadmill can't keep up with the speed of the wheel motion, then you've "broken" the problem and that statement above can no longer be true.

Let's take this example. Let's say someone left the "parking brakes" on in the plane and fired up the four jet engines. If the "The conveyor belt is designed to exactly match the speed of the wheels" and the wheels were to try to move AT ALL because of the thrust of the engines, then the conveyor would counteract that movement, resulting in the plane being stationary, even though the engines are at full thrust.

You can also think of the feedback loop if the treadmill anticipates the speed of the wheel, rather than having to respond to it.


This is certainly one of those problems where you'd need to "show your work" to get credit for the right answer. If this was a question in Physics101 or Mechanical Engineering101, then the correct answer would probably be "yes, it will fly" based on the earlier discussions about the engines pushing on air.

In any more advanced class, then the answer is "definitely not" but you'd have to explain why in order to get any credit. You might get some credit for an "it will fly" answer though.
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There is no case where “definitely not” would be the answer. The wording of the problem places no limitations on the theoretical maximum speed of the conveyor belt. Or it’s ability to match the wheel speed.
 
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km1125 said:
It's not very advanced math. The instant the plane moves then the wheels are exceeding the speed of the treadmill and therefore violates the "The conveyor belt is designed to exactly match the speed of the wheels" statement, because the treadmill just can't do that.

Q.E.D.

:)
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The statement you quoted clearly says the conveyor belt is designed to do that.
 
Riddle me this. If the answer were yes, wouldn't our airport runways be a hellofalot shorter?
 
ASH said:
Have you considered the landing?

I am getting a good chuckle from this entire post.
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That depends on the direction the conveyor belt is moving. Go the wrong way and then you overshoot the runway.
 
bajturner said:
The crux of the question is will the plane move forward through the air if the treadmill runs in the opposite direction in exact proportion to the planes forward movement (which, in turn, causes the wheels to rotate)?

Given the engines push against the air, and are not affected by a moving treadmill under the plane except for some added tire and wheel resistance, the treadmill is essentially a red herring. The treadmill has no fundamental impact on the engine performance for the aircraft, and limited impact to the overall forces.

So the answer is yes, it will move forward, it will gain airspeed, there will be lift, and it will take off. The added rolling resistance would add some distance to the ground-run. Certainly aerodynamics, Bernoulli's Principle specifically!
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Respectfully, I don't think you are getting this....
Assuming the conveyor is completely drag free and offers no resistance the plane's wheels.... if the thrust of the engines was increased to the point that resistance (gravity and drag) was overcome enough to move the aircraft, the aircraft would not move off the conveyor because as the plane began moving forward on the landing gear the conveyor would begin moving and match the speed of the wheels therefore keeping the plane in a static position. So your statement above is incorrect. Unless the plane/wheels began moving faster than the conveyor speed, at which point the plane will leave the conveyor, begin to increase speed through the air while still on the ground and then, if a speed is met that generates enough lift to make the plane fly, it will take off.

As I said before, it doesn't make any difference if the engines are running full thrust and the wheels turning faster than the speed of sound....if there isn't enough air moving over the wing surface fast enough to generate lift, the plane stays on the ground....period.

Consider a full power stall. A plane's engines can be running at full power but if the angle of attack of the wing surface in relation to the air moving over it becomes too great the wing will lose lift and the plane falls from the sky. Aircraft stalls are one of the first things you learn in pilot training.
 
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Dilemma/root cause averted.
 
All that matters is airflow over the wing. That what creates lift. If it’s not moving then there’s no lift. It can sit there all day. A Cessna 172 taking off in a headwind of 50 mph has a air speed of 50 but can have a ground speed of 0 and still fly. Air speed over the wing is what counts.
 
ASH said:
Have you considered the landing?

I am getting a good chuckle from this entire post.
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Yep it's great fun. I suppose for landing they'd have to spin up the trolly real fast and the pilot would have to be really good at hitting the mark. :D
 
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