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This report gives a summary of the work done in Russia from 1911 to 1914, by Professor Joukowski and his pupils. This summary will show that these men were the true originators of the theory, which combines the theory of the wing element and of the slipstream.
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A theoretical analysis is presented for obtaining, by use of Theodorsen's propeller theory, the load distribution along a propeller radius to give the optimum propeller efficiency for any design condition. The efficiencies realized by designing for the optimum load distribution are given in graphs, and the optimum efficiency for any design condition may be read directly from the graph without any laborious calculations. Examples are included to illustrate the method of obtaining the optimum load distributions for both single-rotating and dual-rotating propellers.
A theoretical analysis is presented for obtaining by use of Theodorsen's propeller theory the load distribution along a propeller radius to give the optimum propeller efficiency for any design condition.The efficiencies realized by designing for the optimum load distribution are given in graphs, and the optimum efficiency for any design condition may be read directly from the graph without any laborious calculations. Examples are included to illustrate the method of obtaining the optimum load distributions for both single-rotating and dual-rotating propellers.
Values of the circulation function have been obtained for dual-rotating propellers. Numerical values are given for four, eight, and twelve-blade dual-rotating propellers and for advance ratios from 2 to about 6. In addition, the circulation function has been determine for single-rotating propellers for the higher values of the advance ratio. The mass coefficient, another quantity of significance in propeller theory, has been introduced.
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The various theories concerning propeller design are discussed. The use of digital computers to obtain specific blade shapes to meet appropriate flow conditions is emphasized. The development of lifting-line and lifting surface configurations is analyzed. Ship propulsive performance and basic propeller design considerations are investigated. The characteristics of supercavitating propellers are compared with those of subcavitating propellers.
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Development of a theory for determining the aerodynamic forces for unsteady, compressible subsonic flow on a propeller in forward flight. The acceleration potential method is used in developing the basic downwash integral equation which governs the flow. This integral equation is solved by the doublet-lattice method, which consists of placing 'load' lines at certain locations on the chord and satisfying the downwash condition at other selected positions. The examples presented include the spanwise and chordwise loading on a rotating propeller for incompressible flow, an example of compressible flow calculations, and, finally, a calculation illustrating the loss of aerodynamic damping of a propeller blade due to the passage of the blade over its own wake.
The noise of three supersonic helical tip speed propellers was compared with the noise predicted by an existing noise theory. Comparisons of the peak blade passage tones showed fairly good agreement beween theory and experiment at the lowest helical tip Mach numbers tested, 0.86 and 1.00, while at higher numbers, the theory predicted higher noise levels than measured. When the differences among the propellers were considered the theory and measurement showed fairly good agreement. Directivity measurements in general showed that the measured blade passage tone data peaked further downstream than the theory predicted. At the cruise design condition the harmonics appeared to fall off faster in the data than the theory indicated.
A theory for predicting the noise field of a propeller with a realistic blade geometry is presented. The theory, which utilizes a large blade count approximation, provides an efficient formula for predicting the radiation of sound from all three sources of propeller noise. Comparisons with full numerical integration indicate that the noise levels predicted by this formula are quite accurate. Calculations based on this method also show that the radiation from the Lighthill quadrupole source is rather substantial when compared with thickness and loading noise for high speed propellers. A preliminary application of the theory to the problem of the sensitivity of the peak noise levels generated by a supersonic propeller to the variations in its tip helical Mach number has produced a trend that is in qualitative agreement with the experimental observations.
A theory for predicting the noise field of supersonic propellers with realistic blade geometries is presented. The theory, which utilizes a large-blade-count approximation, provides an efficient formula for predicting the radiation of sound from all three sources of propeller noise. Comparisons with a full numerical integration indicate that the levels predicted by this formula are quite accurate. Calculations also show that, for high speed propellers, the noise radiated by the Lighthill quadrupole source is rather substantial when compared with the noise radiated by the blade thickness and loading sources. Results from a preliminary application of the theory indicate that the peak noise level generated by a supersonic propeller initially increases with increasing tip helical Mach number, but is eventually reaches a plateau and does not increase further. The predicted trend shows qualitative agreement with the experimental observations.
This report presents a calculation of the torsional frequencies of revolving bars with allowance for the air forces. Calculation of the flexural or bonding frequencies of revolving straight or tapered bars in terms of the angular velocity of revolution. Calculation on the basis of Rayleigh's principle of variation. There is also a discussion of error estimation and the accuracy of results. The author then provides an application of the theory to screw propellers for airplanes and the discusses the liability of propellers to damage through vibrations due to lack of uniform loading.
Liquid propellant slosh control - design application of linearized theory