lördag 4 augusti 2012

Text Book: Theory of Flight by von Mises

The classic text book Theory of Flight by Richard von Mises, first published in 1945, was launched as a Dover reprint in 1959:
  • Perhaps the most balanced, well-written account of fundamental fluid dynamics ever published. Mises' classic avoids the formidable mathematical structure of fluid dynamics, while conveying — by often unorthodox methods — a full understanding of the physical phenomena and mathematical concepts of aeronautical engineering. "An outstanding textbook." 
The book presents the Kutta-Zhukovsky theory stating that the lift of an airfoil results from circulation around the airfoil section generated by a sharp trailing edge (p 179):
  • It had been known from the very beginning of flight that wings with a sharp trailing edge must be used in order to obtain a well-defined lift. 
This statement does not describe physical reality, since it has been known from the very beginning that a rounded trailing edge (of radius as large as 10% of the chord length) gives about the same lift as a sharp trailing edge (while the drag remains the same for radii smaller than 1%) and that wings with radii smaller than 0.5% are rarely manufactured and used.  

This was of course known to von Mises when he wrote his book, and so it is natural to ask about the meaning of his statement that a sharp trailing edge "must be used to obtain a well-defined lift". 

What von Mises is describing is not real physics, but instead fictional physics in the form of circulation theory stating that lift is proportional to circulation with lift thus determined by circulation, which in general can be of any magnitude, but for an airfoil with sharp trailing edge is determined by the Kutta condition of smooth flow off the trailing edge. Von Mises thus says that in the fictional physics of circulation theory, a sharp trailing edge "must be used" to obtain a well-defined circulation and lift.

Von Mises thus deliberate fools the reader and the world by giving the impression that his "theory of flight" describes real physics, while in fact it only describes mathematical peculiarities of non-real fictional physics. Von Mises thereby sets a standard of modern aerodynamics, which can now be questioned in the light of the New Theory of Flight.  

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