disciple wrote:No it doesn't, read it again.
...because you're assuming something from an ambiguous statement (and one that is utterly irrelevant to the problem, as has been covered, but let's not get back into that).
Let's look at the various definitions of "speed" for the wheels that might be useful to us.
1: Linear speed of the whole wheel assembly relative to the ground
2: Linear speed of the whole wheel assembly relative to the aircraft
3: Linear speed of the contact patch, relative to the ground
4: Linear speed of the contact patch, relative to the aircraft
5: Angular speed of the wheel relative to its axle.
The first is fairly sensible, and we can see that a magical tardmill in this case would operate by moving its carpet at -V where V is the velocity of the aircraft, there's no impossibility here.
The second is very easy. The wheel does not move in a linear fashion relative to the aircraft, so the treadmill is always stationary. Saves on motor controllers, at least.
The third is identical to the second if we assume zero slippage, the rubber in the contact patch is not moving thus the treadmill is stationary. If we allow for slippage (nothing mentions perfect tyres that never skid) this also works, the treadmill will roll very gently backwards and probably reach equilibrium.
The fourth is impossible except at rest in a zero-slippage situation, with skidding allowed it may reach equilibrium.
The fifth is, largely speaking, absurd, and the results depend on the size of the treadmill itself. As we have been told it is the size of a normal" runway , we may reasonably assume that matching angular velocities of the treadmill and the wheel will result in skidding except at rest; thus it's impossible in the 'zero slippage' case except at rest, and would result in almost instant burn-off of the aircraft's tyres in a "slippage allowed" case.
I contend that the only case that actually makes any sense given the problem as stated is the first. But even so, the definition of the magical treadmill is largely irrelevant; the only thing that's going to stop the plane moving forward through the air is that cursed handrail.
[edit]
I might also add that the only thing that actually makes sense is to take the linear speed of the wheels as a whole; nothing guarantees that "the wheels" of the aircraft are the same size, so angular speed would be different resulting in an impossibility for cases 4 and 5 (and probably case 3, when allowing for slippage)
[editedit]
Hah, I pismelled "treadmill" as "tardmill". I think I prefer that.
Simon
