The Theory of Propellers III : the Slipstream Contraction with Numerical Values for Two-Blade and Four-Blade Propellers

As the conditions of the ultimate wake are concerned both theoretically and practically, the magnitude of the slipstream contraction has been calculated. It will be noted that the contraction in a representative case is of the order of only 1 percent of the propeller diameter. In consequence, all calculations need involve only first-order effects. Curves and tables are given for the contraction coefficient of two-blade and four-blade propellers for various values of the advance ratio; the contraction coefficient is defined as the contraction in the diameter of the wake helix in terms of the wake diameter at infinity. The contour lines of the wake helix are also shown at four values of the advance ratio in comparison with the contour lines for an infinite number of blades

Note on the theorems of Bjerknes and Crocco

The theorems of Bjerknes and Crocco are of great interest in the theory of flow around airfoils at Mach numbers near and above unity. A brief note shows how both theorems are developed by short vector transformations

On the theory of wing sections with particular reference to the lift distribution

This report gives a simple and exact method of calculating the lift distribution on thin wing sections. The most essential feature of the new theory is the introduction of an "ideal angle of attack," this angle being defined as that at which the flow enters the leading edge smoothly or, more precisely, as the angle of attack at which the lift at the leading edge equals zero. The lift distribution at this particular angle is shown to be a characteristic property of the section and has been termed the "basic distribution." it is shown that the lift of a wing section may always be considered to consist of (a) the basic distribution and (b) the additional distribution, where the latter is independent of the mean camber line and thus identical for all thin sections. The specific reason for the poor aerodynamic qualities of thin wing sections is pointed out as being due to the fact that the additional lift in potential flow becomes infinite at the leading edge. It is established that the essential parameter occurring in this analysis is the radius of curvature at the leading edge. It is further established that the actual slope of the lift curve is dependent on this parameter. The theoretical lift distribution is compared with the distribution obtained by direct measurement on a number of the more conventional wing sections. The new theory is of value in calculating the strength of wing sections

A New Principle of Sound Frequency Analysis

In connection with the study of aircraft and propeller noises, the National Advisory Committee for Aeronautics has developed an instrument for sound-frequency analysis which differs fundamentally from previous types, and which, owing to its simplicity of principle, construction, and operation, has proved to be of value in this investigation. The method is based on the well-known fact that the Ohmic loss in an electrical resistance is equal to the sum of the losses of the harmonic components of a complex wave, except for the case in which any two components approach or attain vectorial identity, in which case the Ohmic loss is increased by a definite amount. The principle of frequency analysis has been presented mathematically and a number of distinct advantages relative to previous methods have been pointed out. An automatic recording instrument embodying this principle is described in detail. It employs a beat-frequency oscillator as a source of variable frequency. A large number of experiments have verified the predicted superiority of the method. A number of representative records are presented