The Betz-Joukowsky limit: on the contribution to rotor aerodynamics by the British, German and Russian scientific schools

摘要

The derivation of the efficiency of an ideal wind turbine has been attributed to the three famous scientists of the three aerodynamic research schools in Europe during the first decades of the previous century: Lanchester, Betz and Joukowsky. However, detailed reading of their classical papers has shown that Lanchester did not accept Froude's result that the velocity through the disc is the average of the velocities far upstream and far downstream, by which his solution is not determined. Betz and Joukowsky used vortex theory to support Froude's result and derived the ideal efficiency of a wind turbine at the same time. This efficiency has been known as the Joukowsky limit in Russia and as the Betz limit everywhere else. Because of the contribution of both scientists, this result should be called the Betz-Joukowsky limit everywhere.