Collected Works of H. S. Tsien (1938-1956)

Lifting-Line Theory for a Wing in Non-uniform Flow*

Theodore von Kármán and Hsue-shen Tsien

(California Institute of Technology)

Prandtl’s theory of the lifting line gave the answer to most of the questions in the aerodynamic design of airplane wings. Thus the three-dimensional wing theory became a standard tool of airplane designers. One restriction involved in the conventional wing theory is the uniformity of the undisturbed flow in which the wing is placed. Now there are many important cases which do not satisfy this condition. For instance, in the case of a wing spanning an open jet wind tunnel, the velocity of the air stream has a maximum at the center of the jet and drops to zero outside of the jet. Another example is the problem of ...