Boards
Aeroplanes - treadmills etc...
End of the woolly thinking, I've done the maths.
The take-off velocity of an average airliner is about 250 km/h or 70 m/s.
This velocity is 'indicated airspeed' which means relative airspeed. This is the only important factor. if the plance has 70m/s or more indicated windspeed it can generate enough lift to fly... otherwise no flight will occur.
The wingspan of a boeing 747 is about 60m. therefore a frontal disc of aerodynamic influence (a reasonable approximation) has area 3000m2.
At 70 m/s that is 210,000 m3/s of air shifting through that disc. The only thing shifting this air is the thrust of the engines. Assuming that the ambient air is stationary, all this air must be accelerated by the engines.
Kinetic energy of the air is (mv^2)/2 210000 x 1.2 x (70^2) *0.5 = 617,400,000 Joules
meaning that the jet must do work at a rate of 620MW (the entire electrical power used by scotland. or if you prefer move 756000tonnes of air a second. It wouldn't happen.
I might have got my maths a bit wrong. but you get the idea.
The engines aren't designed to accelerate that much air. Accelerating air over a wing is less efficient than accelerating a wing over air (like in a helicopter).