## söndag 15 juli 2012

### Making of the Prandtl Myth by Von Karman

Here is a continuation of the previous post analyzing the making of the myth of Prandtl as the Father of Modern Fluid mechanics, this time by his student Theodore von Karman in the book Aerodynamics: Selected Topics in the Light of their Historical Development from 1954:

Von Karman: At the time of the first human flight, no theory existed that would explain the sustenation obtained by means of a curved surface at zero angle of attack. It seemed that the mathematical theory of fluid motion was unable to explain the fundamental facts revealed by experimental aerodynamics.

Comment: This is correct.

Von Karman: The Kutta-Zhukovsky condition seems to be a reasonable hypothesis, both because it is indicated by visual observation and also because the lift calculated by means of this condition seems is in fair accordance with measurements. The usefulness of the theory is restricted to a limited range of angle of attack, comprising relatively small angles. Beyond this range the the measured lift falls far below the values predicted by the theory.

Comment: Von Karman here uses the logical fallacy of confirming an assumption by observing a consequence: If there is circulation then there is lift, and since lift is observed there must be circulation.
This makes the theory fool-proof, and as such pseudo-scientific.

Von Karman: The man who gave modern wing theory its practical mathematical form was one of the most prominent representatives of the science of mechanics, and especially fluid mechanics, Ludwig Prandtl. His creates contributions to fluid mechanics were in the field of wing theory and the theory of the boundary layer. His control of mathematical methods and tricks was limited: many of his collaborators and followers surpassed him in solving difficult mathematical problems. but his ability to establish systems of simplified equations which expressed the essential physical relations and dropped the non-essentials, was unique.

Comment: This is the Prandtl myth: Prandtl reveals the mathematical secrets of fluid mechanics without knowing much math.

Von Karman: To be sure, Prandtl's theory has limitations, as does every theory. Its first limitation is caused by the phenomenon of stall.

Comment: By admitting limitation the theory is strengthened. The fact that stall is not predicted, should alone be sufficient to eliminate the theory as unphysical, and thus very dangerous to use for the design of real airplanes.

Von Karman: Our knowledge of the reasons "why we can fly" and "how we fly" has increased both in scope and depth in a rather impressive way.

Comment: The qualification "rather" means that the knowledge is not convincing.

Von Karman: We aerodynamicists were always more modest (than physicists) and did not attempt to change basic beliefs of the human mind or to interfere with the business of the good Lord or divine Providence.

Comment: The theory is strengthened by showing a humble attitude, different from that of physicists.