Can the Plane Take-Off?

[lemon1324]

Originally Posted by sanddrag

One thing you could do (theoretically) to shorten a takeoff or landing distance is to create a nice strong headwind along the runway. The airplane would maintain enough of a speed difference with relation to the air to maintain lift, but you could theoretically have it with zero speed in relation to the ground. You could takeoff and land while not moving in relation to the ground. You could even do it going backwards in relation to the ground. (I've done this on my RC flight simulator program and it is great fun).

However, flying a plane in any sort of strong wind is tricky and it would be difficult to construct an apparatus to move such a large volume of air at such a high velocity to create this artificial headwind.

If you theoretically create a huge fan at the end of a runway, that will shorten the ground roll of the aircraft. However, the aircraft will not have enough speed to fly if it immediately leaves this stream of moving air. Thus you can have a shorter runway but the aircraft will need to remain in the accelerated air for some time.

Again, not to beat a dead horse, but the fact that rolling frition and static friction both depend on normal force makes this question possible to answer. Regardless of the speed that the airplane moves [and thus the conveyor belt] the force exerted by the wheels on the aircraft is constant (Except that it will be marginally higher initially to go from static to kinetic friction). Unless this constant is so large that the aircraft cannot take off under normal circumstances, the aircraft will take off.

Now to argue the other extreme:

As mentioned earlier in this thread, assuming the experiment conditions make it such that the aircraft cannot move, due to viscosity effects in the air immediately above the treadmill, the treadmill drags some of the air along with it. This boundary layer increases in thickness with increasing velocity, and so at some speed of the treadmill, the wing will experience enough relative air velocity to produce lift. At this point, it will lift the aircraft off of the ground. Now it may be argued that the treadmill now stops, the aircraft drops to the gound, repeat ad infinitum, or that the aircraft will then gain enough airspeed to then transition to full forward flight. In either case, the airplane has lifted off the ground, technically a takeoff.

Thus the aircraft will lift off regardless of any of the conditions in the problem statement.