Comment on "Shaping of Axisymmetric Bodies for Minimum Drag in Incompressible Flow"

Abstract

R 1 is something of a milestone in hydrodynamics; the first publication in the open literature of a complete method for calculating the resistance of a body of revolution, so that the drag minimization problem is taken away from the empiricism of the test tank and put on the computer. It is not a new concept in aerodynamics, of course, tbut in hydrodynamics it was not attempted until 1969, principally because: a) it was generally felt that a laminar boundary layer could not be maintained at large Reynolds numbers (Re), (despite CarmichaePs 3 clear proof to the contrary); and b) no one seemed willing to fund the rather considerable effort of constructing a computer program, and then comparing its output with experiment. In 1969, it became possible for us to break through this log jam, to model the problem, and to build and test a full-scale semioptimized low drag body. In their preoccupation with sophisticated methods of optimizing the mathematical model, the authors of Ref. 1 have understandably forgotten to give a little credit to this earlier work. Yet the story is interesting, and is offered as a footnote to a truly excellent paper. In 1967, in connection with a study of high-speed (200 knot) airships, the writer concluded, from the literature available at that time, that extensive laminar flow was possible at large Reynolds numbers. A typical two-dimensional result for a linear velocity gradient