Is the Betz limit really a law?

I have written a preprint on the calculation of a wind turbine power. Betz’s theory is correct, it is made from the calculation of the kinetic energy of the fluid. This calculation does not take into account the constraints on the structure of the wind turbine. The hydrofoils on the sailboats allow to lift the sailboat and to reduce the forward forces. The wind allows the sailboat to move forward but also allows it to be lifted and yet the wind has not been doubled. Instead of creating stress on a keel, we create a flow around a profile to make the sailboat lift. This is potential energy that is transformed into kinetic energy. For a wind turbine, we can eventually transform stresses into additional energy production. My preprint deals with this subject and I would like to have your opinion. A paper similar to my preprint is being submitted.
Before giving your opinion, I let you read my preprint

Hi Pierre,

The Lanchester–Betz–Joukowsky Limit is not worthy to be called a Law, or even the “Betz Limit”. A proper physical Law should hold in all basic cases.

The Limit is an approximation based on an unphysical idealized assumption of a 2-dimensional rotor disc. While many turbine rotors indeed sweep a disc-like area, others do not. The reductio ad absurdum gedanken is to consider an original Archimedes Screw turbine of indefinite length able to eventually entrain far more power from its mean wind field than 100% of what a given frontal disc area can pass.

Furthermore, Betz was a Nazi who was not even the originator of the “Law” attributed to him. Lanchester is more properly credited with first having developed the Limit principle [Gijs A. M. van Kuik, The Lanchester–Betz–Joukowsky Limit, Wind Energ. 2007; 10:289–291]

Good luck with your paper, there is nothing wrong with continuing to explore VAWT concepts. My own contribution to the VAWT concept-space is that the Great Triangle Routes of the Atlantic and Pacific, during the Golden Age of Sail, comprised the largest two wind turbines ever, from a systems engineering perspective, that no modern turbine even comes close to rivalling :stuck_out_tongue:

Dear Dave,

Thank you for this information.
I did not know that Albert Betz was a Nazi.[1]
I knew that Lanchester was a precursor.
All the books, the websites present Betz’s limit, that’s why I presented this limit.
Now with the information you gave me about Betz’s past, if I can edit the article, I will.

Epple, Moritz, Andreas Karachalios, and Volker R. Remmert. “Aerodynamics and Mathematics in National Socialist Germany and Fascist Italy: A Comparison of Research Institutes.” Osiris, 2nd Series, 20 (2005): 131-58. Accessed September 3, 2021.

Take a look better on

Lanchester was certainly one of the precursors to define the coefficient of Limit power. Betz and Joukowsky have concretized the definition of this coefficient. In my article, I do not try to define who is the author of the definition of this coefficient. But I notice that the potential energy was not taken into account and that allows to define a new power coefficient.

I have modified the preprint
I think that it can make you think about Betz’s theory which is exact but which did not take into account the potential energy

link for the preprint … 9/document

I have posted a new version of the working paper (prepublication). I would like to have your comments. Betz’ theory does not take into account the potential energy for fast moving wind turbines. If we take into account the variations of kinetic and potential energy, it is not in phase with the conservation of energy. I have tried to present a new formulation to respect the conservation of energy. I would like to have your opinion

I am asking you again for comments on my preprint.
The Betz limit is defined from this figure.
There is no justification for using this figure.