Uluru / Ayers Rock. In Oz. 1,100 feet (335 metres) high 2.2 miles (3.6 km) long 1.5 miles (2 km) wide http://maps.google.com/maps?ll=-25.344722,131.0325&spn=0.1,0.1&t=h&q=-25.344722,131.0325 It won't fly, either.
Anything will fly with sufficient thrust. Maybe not far, or in a controllable fashion, but it -WILL- fly. Just like the airplane on the treadmill.
The treadmill cannot prevent the plane from moving forward. The engines propel the plane forward, the wheels are free spinning. The idea that the treadmill can "match" the speed of the plane is impossible, as the engines WILL be moving forward as they generate thrust.
It's a dumb question, with inherent conflicts. You can make one of two arguments: The treadmill matches the speed of the wheels. That means the wheels stay stationary on the treadmill, relative to the ground. Anything attached to the wheels, therefore, will also be stationary relative to the ground. That would be the whole airplane. That means there is no airflow over the wings, so there is no lift. The plane does not take off. On the other hand, the thrust of the engines cannot be negated by the treadmill, no matter how fast it goes. Nor is there anything to stop the forward motion of anything attached to the engines. There is no opposing force to the thrust of the engines, so the plane moves forward relative to the ground and the wings therefore have airflow over them and can therefore provide lift. The plane takes off. So, what happens? Both. Neither. D'uh. In reality, the plane would move but that would violate the rule of the wheels matching the treadmill speed. As it would move forward, it would take off. So, it takes off, but only after violating the premise of the question. As stated, the conditions of the question cannot happen. A plane cannot sit on a treadmill and have its wheel speeds matched by the treadmill belt speed as the engines spool up and provide increasing levels of thrust. The conditions of the question will be broken and the plane will move forward. You can focus on the plane moving forward. Or you can focus on the question's conditions being broken.
I haven't read any responses. Yes the plane will fly. Wheels are not the driving force and their speed have nothing to do with actual aircraft movement. The plane will move forward in relation to the Earth. There is nothing to stop that from happening. GT
So, here is the next step in the answer. The wheels stand still, and the treadmill runs faster BACKWARDS as the takeoff speed increases. The wheels therefor stay stationary, as is the treadmill relative to the wheels. They match speed. The answer is: Yes.
Apart from the pilots hand ... the pilot who is trying to follow the premiss of the question, i.e. match wheel speed to belt speed.
After five years of this thread, the physics majors and engineers say it will fly. The lawyers on the other hand are still arguing what the the question really states as a premise and asks for as an answer.
Treadmill speed matches wheel speed in opposite direction of rotation. End result is, treadmill is irrelevant. The plane will take off exactly as it normally would except with double the wheel speed, which effects nothing. Couldn't be simpler.
Won't fly. Wheels cannot "move" forward to allow airflow over wings. They "roll" faster and faster but so does the tarmac. Same afffect as a 747 sitting with brakes on and full power on all 4 engines....It doesn't move forward...just blows anything that passes behind it into oblivion. Many videos of this around. Mythbusters did it with a 747 and blew cars passing behind to bits.
It is not the same effect as the wheels are free to spin, brakes are not on. The -thrust- driven plane would accelerate and fly just as if there was no treadmill under it at all.
Good catch. I re-read it and it says "exactly match the speed of the wheels at any given time, moving in the opposite direction of rotation" I misread that initially, thinking it meant the treadmill rotated reverse of the wheels (meaning if wheel was going clockwise, treadmill was going counter-clockwise). But, if it's moving in the opposite -direction- of rotation than I agree it would allow no wheel movement. Therefore if the plane usually leaves the tarmac at 200mph air speed and 200mph wheel speed, with the treadmill matching wheel speed but in the opposite direction of rotation it would allow for no wheel movement but would have to match the planes air speed to do so. That means it would leave the conveyor at 200mph air speed, zero wheel speed and 200mph treadmill speed. Same thing as if you pushed a shopping cart down a conveyor as you were walking on the ground beside the conveyor. If the conveyor matches your speed as you walk forward the shopping cart will also move forward because of the thrust of your hand on the handle but the wheels on the cart would not be spinning.
It will fly. The thrust from the engine goes thru the aircraft CG and is reacted by the atmosphere. The plane doesn't "know" anything about tires and the ground. All that happens when on the treadmill is that the relative rotational velocity of the tires will be higher on the treadmill than if they were on the "ground". But remember-the tires are not exerting any thrust loads to the ground or the treadmill. It is not like a car. Replace the tires with some "frictionless" skis and you can see that the treadmill is irrelevant. Look at a seaplane with floats. The plane can fly off the water whether the plane is going with the current or against the current. The flow of water past the floats has no influence on the plane taking off. (Yes-there is some drag affects from the water/float interface-but that simply increases the takeoff run.) Replace the water/floats with tires/treadmill and you will see the treadmill is irrelevant.
