Memorandum examining the phenomenon of airfoil drag, which is related almost exclusively to skin friction at high speed flight conditions. The primary way to reduce drag is to delay the transition from laminar to turbulent flow in the boundary layer along the surface. A particular airflow design that may delay transition and therefore have fewer problems related to drag are provided.

Consideration is given to the techniques used in telecommunication where a nonlinear system (the modulator) results in a linear transposition of a signal. It is then shown that a similar method permits linearization of electromechanical devices or nonlinear mechanical devices. A sweep function plays the same role as the carrier wave in radio-electricity. The linearizations of certain nonlinear functionals are presented.

"A general method concerning optimum problems in nonstationary flight is developed and discussed. Best flight techniques are determined for the following conditions: climb with minimum time, climb with minimum fuel consumption, steepest climb, descending and gliding flight with maximum time or with maximum distance. Optimum distributions of speed with altitude are derived assuming constant airplane weight and neglecting curvatures and squares of path inclination in the projection of the equation of motion on the normal to the flight path" (p. 1).

With applications to meteorology in view, the method of small oscillations is used to investigate the stability of a plane laminar boundary layer in which the density depends in a special way on the distance from the plate. It is found that for a constant Froude number the flow becomes more stable as the Richardson number increases until, at a critical value of the Richardson number that depends on the Froude number, the flow is stable for all disturbance wave lengths and Reynolds numbers. The calculated results are verified by experiment.

Through the work of V. Z. Vlasov a theory of thin-walled rods has been established that is widely applicable in practice. This theory was extended by A. A. Umanski to thin-walled rods of closed profile section. This report attempts to construct a theory of thin-walled rods, including the classical theory of deformation of thin rods, by making use of a kinematic assumption.

"The study of the hydrodynamic properties of planing bottom of flying boats and seaplane floats is at the present time based exclusively on the curves of towing tests conducted in tanks. In order to provide a rational basis for the test procedure in tanks and practical design data, a theoretical study must be made of the flow at the step and relations derived that show not only qualitatively but quantitatively the inter-relations of the various factors involved. The general solution of the problem of the development of hydrodynamic forces during the motion of the seaplane float or flying boat is very difficult for it is necessary to give a three-dimensional solution, which does not always permit reducing the analysis to the form of workable computation formulas" (p. 1).

"The influence of thickness and length of a hub projecting from an inlet opening was investigated on one of the two new classes of circular cowls reported in NACA TM 1360" (p. 1).

"For application in practice for annular radiator fairings and similar arrangements, two new classes of circular cowls are developed by theoretical method, and investigated in a systematic test series regarding their behavior under various working conditions" (p. 1).

Starting with the Love equations for bending of extensible shells, "principal stress states" are sought for a thin-walled rod of arbitrary but open cross section. Principal stress states exclude those local states arising from end conditions which damp out with distance from the ends. It is found that for rods of intermediate length, long enough to avoid local bending at a support, and short enough that elementary torsion and bending are not the most significant stress states, four principal states exist.

The displacement effect of the boundary layer on the outer frictionless flow is discussed for both steady and unsteady flows. The analysis is restricted to cases in which the potential flow pressure distribution remains valid for the boundary-layer calculation. Formulas are given for the dependence of the pressure drag, friction drag, and total drag of circular cylinders on the time from the start of motion for cases in which the velocity varies as a power of the time. Formulas for the locations and for the time for the appearance of the separation point are given for two dimensional bodies of arbitrary shape.

Among the information presented are included displacement, momentum, and kinetic energy thicknesses, shearing stress distributions across boundary layer, and surface friction coefficients. The Gruschwitz method and its modifications are examined and tested. An energy theorem for the turbulent boundary layer is introduced and discussed but does not lead to a method for the prediction of the behavior of the turbulent boundary layer because relations for the shearing stress and the surface friction are lacking.

"The theory of turbulence reached its full growth at the end of the 19th century as a result of the work by Boussinesq and Reynolds. It then underwent a long period of stagnation which ended under the impulse given to it by the development of wind tunnels caused by the needs of aviation. Numerous researchers, attempted to put Reynolds' elementary statistical theory into a more precise form. During the war, some isolated scientists - von Weizsacker and Heisenberg in Germany, Kolmogoroff in Russia, Onsager in the U.S.A. - started a program of research. By a system of assumptions which make it possible to approach the structure of turbulence in well-defined limiting conditions quantitatively, they obtained a certain number of laws on the correlations and the spectrum. Since the late reports have improved the mathematical language of turbulence, it was deemed advisable to start with a detailed account of the mathematical methods applicable to turbulence, inspired at first by the work of the French school, above all for the basic principles, then the work of the foreigners, above all for the theory of the spectrum" (p. 1).

"Model tests on the "running belt" and tests with a full-scale tail wheel were made on a rotating drum as well as on a runway in order to investigate the causes of the undesirable shimmy phenomena frequently occurring on airplane tail wheels, and the means of avoiding them. The small model (scale 1:10) permitted simulation of the mass, moments of inertia, and fuselage stiffness of the airplane and determination of their influence on the shimmy, whereas by means of the larger model with pneumatic tires (scale 1:2) more accurate investigations were made on the tail wheel itself. The results of drum and road tests show good agreement with one another and with model values" (p. 1).