To see someone way ahead of me in terms of forward thinking about Betz limit in awe look to
An engineering model for the induction of crosswind kite power systems by Gaunaa et al
Abstract. The present paper introduces a new, physically consistent definition of effective induction that should be used in engineering models for power kite performance that use aerodynamic coefficients for the wing. It is argued that in such cases it is physically inconsistent to use disc-based induction models – like momentum models – and thus a new, physically consistent induction model using vortex theory methodology is derived. Simulation results using the new induction model are compared to the previously often used momentum method and Actuator Line (AL) CFD simulations. The comparison shows that the new vortex based model is in much better agreement with the AL results than the momentum method. The new model is as computationally light as the momentum induction method.
And
… , where the tip speed ratios are not too low (usually TSR>6) and where the aerodynamically effective part of the blades extend almost to the rotation axis. For the kite case, there is (usually) only one “blade” circling in the “rotor-plane”, and the effective “root” (inner kite tip) of the blade is often at 80%-90% of the radius of the “tip” (outer kite tip). In this case the Goldstein function would be immensely different from Prandtl’s tip correction, and it would be an extremely large correction to the raw momentum results. This case is very far from the comfort zone of the methods used in the wind turbine community.