Airplane - Treadmill Conundrum

The Airplane - Treadmill Conundrum is thought experiment concerning the possibility of an airplane taking off from a treadmill. The experiment is often posed as simple as, "Can an airplane take off from a treadmill?" In longer explanations, it is explicitly stated that the treadmill is of infinite length and moves at a constant speed against the airplane. Alternately, it is described as a treadmill of some arbitrary length that always moves opposite of the airplane, ensuring that the airplane does not move forwards or backwards relative to the ground below the treadmill.

This issue has gained notoriety on the internet and caused significant debate.cite web |url=http://www.airplaneonatreadmill.com |title=Airplane on a Treadmill |accessdate=2008-09-08] There is an episode of the television show MythBusters which investigates this exact question.cite web |url=http://www.youtube.com/watch?v=KSBFQOfas60 |title=Mythbusters on youtube |accessdate=2008-09-08] In it, they designed a large treadmill (a tarp pulled by a pickup truck), and to the surprise of their pilot, the plane took off easily. [cite web |url=http://www.youtube.com/watch?v=YORCk1BN7QY&NR=1 |title=MythBusters clip of episode end on youtube |accessdate=2008-09-08]

olution

The experiment has been described as a litmus test of the individual's understanding of aerodynamics and aeronautics. An aircraft takes off by gaining lift under the wings. Lift is achieved by moving air past the wings. The movement of air is achieved by moving the aircraft forward (no common aircraft uses vertical takeoff or jet exhaust in front of the main wings). In order to take off, an airplane must be able to move forward. Were the treadmill able to keep the airplane still, it would not take off. A key to understanding may be that the treadmill matches the airplane's forward "speed" and not the engine's forward "force."

However, unlike the wheels of an automobile, an airplane's wheels do not propel the plane, they are there simply to reduce friction. An airplane's forward momentum is generated solely by the push of the engines against the air. A treadmill therefore would have minimal effect on an airplane, as the force from the treadmill would not be transferred to the airplane itself, except for the small amount of force which would be caused by friction from the rotating wheels.cite web |url=http://www.straightdope.com/columns/read/2638/an-airplane-taxies-in-one-direction-on-a-moving-conveyor-belt-going-the-opposite-direction-can-the-plane-take-off |title=the straight dope |accessdate=2008-09-08]

If the airplane engines only produce enough forward momentum to keep the airplane still relative to the ground, then the airplane would be unable to take off. However, if the engine were run at regular take-off throttle, the speed of the treadmill would be irrelevant — the wheels would just rotate faster and the airplane would get enough speed to takeoff assuming the bearings could handle the higher rolling speeds.

References

External links

* [http://www.airplaneonatreadmill.com/ airplane on a treadmill]
* [http://www.straightdope.com/columns/read/2638/an-airplane-taxies-in-one-direction-on-a-moving-conveyor-belt-going-the-opposite-direction-can-the-plane-take-off the straight dope]
* [http://blag.xkcd.com/2008/09/09/the-goddamn-airplane-on-the-goddamn-treadmill/ xkcd blag]