OK. sooooo wrong… or at least not nearly specific enough.
Since Gustave Whitehead flew the first recorded powered western civilization flight in 1901 (two years before the plagiarizing thieving war profiteering Wright brothers stole his idea and plans for flight and then later forced the Smithsonian to lie to us all for a hundred years or so about the validity of Kitty Hawk) aircraft engineers have been attempting to get more thrust out of tiny plane engines because of one very important reason. Thrust does not a flight make.
As planes got bigger, they realized they needed “more” from their or just more engines, ramjets, or rockets, but each time they improved their designs, there was one thing they always relied upon…Lift. Lift is the essential reason aircraft are shaped the way they are. If we could rely on just a prop, then all we would need is another prop to counter the torque and a steering platform. Sure, there are flying vessels that need no lift but they are rare (see NASA’s space program or the U.S. Navy), and your proposal of a treadmill under a plane is flawed and entirely too general. Which plane? Where’s the wind coming from? Indoors or out? Big fans in front of this hovering plane? Motorized or powered landing gear? Come on…
Planes don’t fly (generally) due to their thrust, they fly due to several factors, but chiefly -and this is key- LIFT. regardless of what the ground is doing, unless it is a fighter jet or rocket assisted craft, most aircraft in general require a negative pressure on the wing surface to obtain lift, or to be more precise, air flowing over the wings…the whole wingspan, not just the small surface area affected by the prop. The prop on any aircraft “generally” does not supply enough airflow to achieve this process. NO.
Take a Seawind 300 and place it on a roaring river heading aft. Aint goin nowhere unless there is a breeze heading in the same direction as the water (headwind). Enough headwind and you don’t even need the prop. LIFT will yank the plane right off the ground. Try blowing on a paper airplane sitting on your desk. Same idea.
Take any average plane and place it at very high altitude (I wont quote a height)…it drops like a brick. Why? “Air” molecules too far apart to create lift, not enough pressure to create lift, not enough O2 for the engine intake to move the plane forward to create sufficient lift, lots of factors, but chiefly? LIFT.
In fact, there are very few aircraft that have enough thrust/lift ratio to do so…well there is one I know of…the Balsa Flyer found for $1.95 at your local grocery store. But a Cessna, Piper, or Beech Craft single engine? NO WAY. A Learjet 60XR? NO…WAY…In fact, any large commercial multi-engine sky whale like a 767 drops like a stone the moment it has ill efficient lift across the foils (see wind sheer, flap errors, air stalls, take off, flight, and landing minimum speeds etc.). there certainly are exceptions to this idea, the Harrier and others like it have specialized thrust vectors under the craft or vertical props causing “artificial” lift, but unless this hypothetical airplane treadmill is inside a fully operating -up to sufficient wind speed- wind tunnel, you can forget this idea…and while you’re at it, forget this idea. Why even postulate this? I know…for those that do not understand how airplanes work. So, “But believe this: The plane takes off” sentence? Cecil, bubby, which plane? The Rubber powered Balsa Flyer? Not much else.
A rocket Scientist.