The theoretical maximum lift of a cylinder is 4π. At that point the forward and rear stagnation points coalesce on the bottom of the cylinder. Practical solutions use rotating cylinders (Flettner rotor) but will not reach this theoretical limit.
This should illustrate that 6.5 is not outright impossible but the distance between a cylinder and an airfoil is ...
One place where a reversible aerofoil is used is on the daggerboard of Proas - boats that can be sailed in either direction. They have fixed windward and leeward sides, rather that forward and aft ends, so the foil is always required to generate lift in the same direction, but the flow is reversed.
Their shape is very like that in Peter Kämpf's answer.
Either of the wings in the diagram will produce lift in both directions. The one on the right is the shape of a boomerang wing, so it works, but there would be less loss if the air at the tip is separated both up & down.
It all boils down to physics. What we are looking at here should be a helicopter.
Yes, absolutely, with contra-rotating rotors it would fly.
But now we must look at the demands of flight, how much force is needed to overcome
gravity and how much is needed to overcome drag while producing velocity. It becomes
clear the design is backwards, with tiny wings ...
That formula describes the "lift-induced drag" for a planar wing. Lift-induced drag
As the definition implies, this drag is induced by the generated lift, the effect of stall (flow separation) is not contributing to this drag component.
Therefore, there is no other formula for the stalled regime.
Typically in numerical simulations, instead of an ideal(inviscid) vortex, a viscous vortex with a finite core is used to avoid the singularity at the centre. In these viscous vortices, the swirl velocity inside the core is assumed to be linearly increasing from zero at the centre. While outside the core, the induced velocity remains the same as that of the ...
There are better physicists than I at this site, but seem to remember a solution proposed in a wind tunnel test with load cells as follows: Do the measurements separately.
Lift could be measured at the center of lift using only support 1. C lift could vary with AOA (data points are generated one at a time from C lift at a given AOA).
Pitching moments ...
A classic comparison would be boat props vs aircraft at various RPM. A higher density (viscosity) fluid would put more stress on the blade tips, hence shorter and more robustly built blades. The amount of twist would depend on loading of props and would include chord length. A tapered prop may have a different twist from an untapered or reverse tapered. ...
If we interpret induced drag as the backward component of the lift vector (explained here and here), post stall is not much different from pre-stall.
It is simply the vector decomposition of the lift, so if we rotate the wing more, the induced angle of attack increases and induced drag increases.
However, with stall, when we rotate the wing more, we ...
Beyond the stall, the wing profile is governed by flat plate aerodynamics. The airfoil does still have lift and drag, and one could express one as a function of the other, but I have not seen a useful application of it.
Flat plate drag is a function of Reynolds number. The picture is from this document, and shows $C_D$ as function of $Re$ and AoA.
I very much like @Gerry's answer. It illustrates the principle of lift through potential theory very well.
I would like to add that circulation doesn't mean that fluid particles are rotating around the airfoil. In fact, even a simple rotating cylinder in an inviscid/irrotational flow would have well-defined streamlines flowing from upstream to downstream.
You ask "What I can't understand is, what makes the aircraft pitch up when both the wing force and tail force increased by the same factor, due to increase of airspeed."
It is critical to understand that an imbalance in pitch moment-arm between the wing and the tail is only required to cause a CHANGE in the rate of pitch rotation, not to cause a pitch ...
Somewhere on the rcgroups.com website I once saw a post describing where someone took the wing of an rc model airplane and flipped it around so that the trailing edge was in front and attached it to the fuselage with rubber bands. Flight was possible.