Where has this propulsion been tried?

Take a tennis racket and lay strips of paper across it with the tops of the paper attached to the strings by the top by tape and allowed free movement in one direction. The strips of paper are reminiscent of Venetian blinds. With the paper facing down towards the earth stroking the tennis racket towards the earth makes the blinds fully closed and it acts upon the air. When stroking upwards there is nearly no resistance. So it acts a bit like a valve. If you hold the racket parallel to the earth and drop it, the racket will deflect as it falls depending on it's orientation. You can feel the wind in one stroke pattern vs 180 degrees. Rapid motion up and down would give you a basic ornithopter configuration. Has anyone done this before?

Powered flight using gas could be as simple as a double ended piston that runs a 2 stroke cycle. The linkages are simply attached to the cylinder through a fulcrum. The engine power strokes whenever the piston reaches near the ends. The thrust stroke would need to be many times more violent than the return stroke thanks to the valve nature of the wing. Turbo chargers can be used to increase air intake pressure. The wings sweep 20 degrees yaw and roll giving pilots fine grained control on thrust from the four wings.

Estimating the lift force:

If the wing has a fan at the ends that has a 1 meter arc and an overall area of 4.5 square meters if the wings beat at a rate of 30 down strokes per second we can know the force developed with:

1/2 * 30x1 (speed and stroke) * 30x1 (speed and stroke) * 4.5 (wing area) * 1.2 (kg/m3) = 2430 newtons x 0.101972 kilos per newton = 248 kilograms x 4 wings = 992 kg or 2186.99 pounds.

I'm not sure if this scheme is better in anyway than helicoptors for fuel or any other practical matter.

https://www.youtube.com/watch?v=_3R8xsFSUrs