Let’s consider the case of a plane flying s/l in a headwind with a positive gradient. A wing produces lift by inducing a bound vortex superimposed on the relative wind., and in the particular case of flying in a positive gradient, one can imagine an extra pseudo-vortex associated with the gradient itself, that re-inforces the bound vortex producing additional lift.
The question is now how to quantify that additional lift. From the variables that enter in the circulation theory of lift, one can guess that the variables involved are the density of the air rho, the airspeed v, the wing area A, the chord c and of course the wind gradient ß.
From dimensional analysis, it results that the extra lift L is:
L = k · rho · v · A · c · ß
where k is a constant to be determined. It can be probably done with a ‘material experiment’, but my question here is whether it can be derived from already known data or from a ‘mental experiment’.