  A classical derivation of Betz's law is first presented along with some
insights. The extended Betz's theory is deduced for a rotor with axis
orthogonal to the direction of an ideal fluid in uniform motion. The conceptual
design used to demonstrate the generality of the aerodynamic aspects of energy
conversion - starting from a suggestive approach to the classical theory and a
geometric explanation of Betz's law - is defined by imposing compliance with
the minimum requirements that a turbine must have to approximate the ideal
efficiency of 16/27. The discovery of the role of the Betz's angles has
permitted demonstrating the theory in a more general context, extending it from
a flat, two-dimensional, representation to a deeper, three-dimensional,
understanding of the problem. The ensuing result, in particular the possibility
of obtaining constant yield and maximum efficiency through a finite topology of
the actuator cylinder, implies in principle feasibility with a real turbine
with axis perpendicular to the wind direction.
