1.  12/06/2006, 11:23 PM Every time I've seen this problem on message boards, it's triggered heated debates. And so I figured this would be great for TC. Both sides are always absolutely certain they are correct and that the others are complete idiots. Here it is: A plane equipped with fixed horizontal engines and wheel landing gear is placed on a huge treadmill runway. The treadmill has a clever design and always matches the speed of the plane, but runs in the opposite direction. Will the plane take off and fly or not?
2.  12/07/2006, 12:50 AM Hmmm... if the plane is on a treadmill that's matching its speed in the opposite direction, is the plane standing still? It would be standing still if the wheels of the plane were providing the forward thrust, but they're not... It's the jet engines providing the forward thrust, not the wheels, so the jet would take off... As a test, put your roller blades on and stand on a treadmill. Using a 20 foot rope stretched out and tied to the wall in front of you, turn on the treadmill and immediately start pulling your self forward using the rope. Does the treadmill matching the speed of the wheels on your blades stop you from pulling yourself forward and off the treadmill? I say the jet plane moves forward and takes off.
3.  12/07/2006, 01:14 AM If the plane does not move, no lift would be provided by the wings. Even with the jet engine involved, the force required to lift is dependent on the wings, at least for planes.
4.  12/07/2006, 02:12 AM Plane stays grounded. Wind needs to pass over the wings to provide lift. The design of the wings make the air above the wings travel faster then the air below the wings. This difference in airspeed caused an upward pressure or "lift". No fast wind, plane no go up. Palm IIIe -> Visor Deluxe -> Palm 505 -> Clie tj37 -> Treo 600 -> Treo 700P
5.  12/07/2006, 06:36 AM This problem was posted on airliners.net and got well over 200 responses. Debate was lively. Turns out the question was worded wrong and implied that the conveyor belt matched the speed of the -wheels- but in the opposite direction. (If that was the case, the plane could never even begin to move.) Once the wording was corrected, consensus was reached very quickly. The original question as posted elsewhere has the conveyor matching the speed of the -airplane- but in the opposite direction, which would only mean the tires of the plane would be spinning at twice their normal speed during the takeoff run. In that case, as long as the airplane doesn't exceed the tires' speed rating, the plane would be able to take off normally. The engines don't power the wheels; they push the airframe. As long as the brakes aren't applied, the plane will accelerate and take off. "Yeah, he can talk. It's gettin' him to shut up that's the trick!" -Shrek
6.  12/07/2006, 07:06 AM Originally Posted by Tom LaPrise The original question as posted elsewhere has the conveyor matching the speed of the -airplane- but in the opposite direction, which would only mean the tires of the plane would be spinning at twice their normal speed during the takeoff run. In that case, as long as the airplane doesn't exceed the tires' speed rating, the plane would be able to take off normally. The engines don't power the wheels; they push the airframe. As long as the brakes aren't applied, the plane will accelerate and take off. That's not true IMHO. Speeds are always relative. What does "the treadmill matches the speed of the airplane" mean? In the case of a car, I guess the meaning would be that the treadmill goes in the opposite direction of the car, at the speed the car WOULD make on normal ground. So at a speed of 60 mph the car would drive 60 mph relative to the surface of the treadmill but 0 mph relative to the ground around the treadmill. The case of the plane seems different at first glance because there the jets push the plane forward, not the wheels. However, this is not really relevant in my view. The airplane could just as well roll forward like a car by moving the wheels/using a motor. For the speed of the wheels or the speed of the airplane relative to the ground, this makes no difference. Therefore, when the plane starts moving on the runway, the airplane is basically identical to a car: the wheels roll forward, but the treadmill compensates that movement relative to the surrounding ground, and - more importantly - relative to the surrounding air. Suppose the pilot increases forward thrust - the treadmill will just go faster as well, the plane still stands still relative to the air. Because of this, no air flows over the wings, no upward lift is produced, the plane remains on the ground and continues to behaves just like a car would - it stands still relative to the ground/air and does NOT take off. I know that there are lots of wrong solutions to this problem to be found on the Internet, but I am quite confident that the above is correct. If you disagree, please state which part of my reasoning does not work. I guess the misunderstanding stems from the fact that the situation of a plane in the air is different. After takeoff, the movement of the plane is independent of the movement of the wheels. But this is not the case as long as the airplane is rolling on the ground. There, it cannot gain speed relative to the air because of the speed-compensating treadmill and stays grounded. “Reality is that which, when you stop believing in it, doesn't go away.” (Philip K. ****)
7.  12/07/2006, 09:00 AM I guess the plane could fly, if the the treadmill produced enough drag to move the air above it (the treadmill) to a point (i.e. sufficient air velocity) where this movement (of the air, across the wing) would produce lift. Since we are talking hypothetically, I guess this is as hypothetical as it gets.
9.  12/07/2006, 12:55 PM Originally Posted by meyerweb Sigh. A knowledge of physics is a good thing, but clearly not something widely held. I was aware of the things you wrote. I think it all depends on what "the treadmill matches the speed of the airplane" means. As I wrote above, my understanding is that the treadmill goes in the opposite direction of the plane, at the speed the plane WOULD make on normal ground. So suppose the airplane is in a state in which it would - under normal conditions - roll on the runway at a speed of 275 km/h or 170 mph (takeoff speed of an A320). Due to the conditons given in the original question (according to my understanding), this means that the treadmill rolls at 275 km/h into the other direction, resulting at speed zero relative to the air. No? The more thrust you give, the faster the treadmill goes into the other direction... or doesn't it? “Reality is that which, when you stop believing in it, doesn't go away.” (Philip K. ****)
10.  12/07/2006, 03:00 PM Sod that, get yourself a Harrier jump jet. End of problem. Next! Animo et Fide