ARGH.
Here is what happens, folks. Assumptions made in the following:
- The treadmill is automatically controlled to operate against the plane's speed, and is perfect in said control.
- Friction can be ignored.
Case #1: plane's speed defined by body and wings of plane with respect to undisturbed surrounding air.
The plane is started up, and as it increases power, it moves forward as the treadmill rolls backward. The plane takes off when it reaches flying speed; as it takes off, the wheels are spinning at the equivalent of double takeoff speed.
Case #2: plane's speed defined by body and wings of plane with respect to ground.
The plane is started up, and as it increases power, it moves forward as the treadmill rolls backward. The plane takes off when it reaches flying speed; as it takes off, the wheels are spinning at the equivalent of double takeoff speed.
Case #3: plane's speed defined by rotational speed of wheels.
The plane is started up, and as it begins rolling, positive feedback causes the treadmill to immediately begin to approach infinite velocity. Meanwhile, the body and wings of the plane are moving through the air, and pretty soon, it's passing through the air fast enough to take off. The wheels are at this point spinning an infinite number of times per second, but the plane still takes off.
In the real world, if you can make a Case #3 treadmill, the plane may not take off, because you have a chance to burn out the wheel bearings before it reaches flying speed. However, while wheel rotation is a suitable measure of speed for a car, it makes no sense whatsoever for an aeroplane, because what matters for an aeroplane is not how fast the wheels turn (unless they're going fast enough to cook the bearings) but how fast it's travelling with respect to the air around it (for lift) and how fast it's travelling with respect to the ground (for navigation).
The bottom line: THE PLANE TAKES OFF.
Now can we PLEASE go back to finding a '67 Chevy that we can put huge amounts of rocket power in and hope it doesn't blow up this time?
One can ask the question another way.
ReplyDeleteDoes a treadmill stop a hovercraft?
It then becomes obvious.
The trouble is, people still start thinking about it by thinking of a car. The relevant question for a car is, if you put it in a wind tunnel, will the wind make it impossible to drive forward?
ReplyDeleteI'm still a little bit confused: How do the wings actually start moving relative to the undisturbed surrounding air?
ReplyDeleteSpencer: the engines of the plane produce a net thrust by throwing large quantities of air backwards. That's how the plane moves at all, whther it's powered by a piston engine with a propellor, jet engines, rockets... it's all done by throwing gas backwards, which invokes Newton's third law and produces a reaction pushing the plane forwards. The wings being part of the plane, they move forwards and start to produce lift.
ReplyDelete