The Use of the Wind Tunnel in Connection With Aircraft-Design Problems
Authors: von Kármán Th. , Millikan Clark B. 
Published: February 2023

Abstract
The paper is divided into two parts, the first of which deals with the general problem of extrapolating wind-tunnel results to full-scale free-flight conditions in connection with the initial prediction of overall performance characteristics of airplanes. Using the notation of Oswald, it is found that the three parameters about which the designer would like information from the wind tunnel are: the “airplane efficiency factor” giving the variation in parasite drag with lift coefficient, the “equivalent parasite area” giving essentially the minimum parasite drag, and the maximum lift coefficient. If the tests are made at Reynolds’ numbers of the order of 1,500,000 or larger and on models of modern “clean” airplanes, the extrapolation of the first parameter to full scale is felt to be trustworthy for gliding flight. The need for further data on the influence of the change to power-on flight is mentioned. For the second parameter the effect of the change in Reynolds’ number involved in the extrapolation is shown to be important, and a method for carrying out the extrapolation is described. This method is based on the modern hydrodynamical theory of skin friction, and has already met with some success as developed and used at the Guggenheim Aeronautics Laboratory of the California Institute of Technology. In connection with the third parameter, it is shown that the influence of Reynolds’ number and turbulence on the value of the maximum-lift coefficient is very large. The importance and confusion attending this phenomenon led some time ago to its intensive investigation at the laboratory. The more important results of an experimental and a theoretical approach to the problem are discussed. The experimental researches involved the testing of a 6-ft-span N.A.C.A. 2412 airfoil at a series of Reynolds’ numbers and with various degrees of turbulence produced artificially in the wind tunnel through the introduction of grids or screens upstream from the model. The results furnish quantitative evidence of the considerable dependence of CLmax on Reynolds’ number and turbulence, and in particular demonstrate the fact that, even at fairly large Reynolds’ numbers, the value of CLmax may be increased by as much as 30 per cent by introducing artificial turbulence into a normally very smooth wind-tunnel flow. The theoretical investigation involves an analysis of the boundary-layer flow around an N.A.C.A. 2412 airfoil, and is particularly concerned with the transition from the laminar to the turbulent regime and with the separation of the laminar boundary layer from the upper surface of the airfoil. The second part of the paper gives illustrations of the diverse nature of the special aircraft-design problems for which the wind tunnel may give valuable information. The examples discussed are all chosen from investigations initially undertaken at our laboratory at the request of aircraft manufacturers and at their expense. Many of the problems so begun developed an independent scientific interest, so that the tests were subsequently amplified by the staff to a degree not at all contemplated when the work was started. A series of six distinct types of investigations is included in the samples considered.