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A theoretical approach is developed and a computational procedure adaptable to a high-speed digital computer is established for the evaluation of the blade pressure distribution of a marine propeller due to thickness and loading effects. The dual role of the blade thickness is considered. The contribution of the "non-planar thickness" to the propeller loading and pressure distribution and the effect of the "flow distortion thickness" are studied by means of the "thin body" approximation. The surface integral equation which relates the unknown loading to the known velocity distribution on the blades is solved by the mode approach in conjunction with the "lift operator" technique. The analysis treats both design and off-design conditions in steady-state and unsteady flows, and the proper chordwise modes are selected for each condition. The numerical solution yields the blade loading and resulting hydrodynamic forces and moments and blade bending moments, and, in addition, the blade pressure distributions on each blade face due to both loading and thickness effects, thus providing information necessary for the prediction of cavitation inception. Calculations have been performed for a set of three 3-bladed propellers of different EAR operating in a screen-generated wake, for comparison with experimental data.

The previous analysis of the propeller-rudder interaction problem by means of the lifting-surface theory has been modified to include the effects of thickness of both surfaces. The effect of propeller blade thickness and rudder thickness on the "flow displacement" in the field is taken into account by the "thin body" approach. The blade thickness effect on the loading of the propeller blade due to its nonplanar form, being small, is neglected. The resulting onset velocities on both lifting surfaces due to the thickness effects on the flow field are incorporated, together with the onset velocities due to hull wake and camber and incident angle of the surfaces, into the existing iterative procedure. The numerical procedure, which has been adapted to the CDC 6600 high speed digital computer, furnishes the steady and time-dependent pressure distributions on both lifting surfaces and the resulting hydrodynamic forces and moments. From the limited number of calculations, it is seen that the thickness effect does not change the general conclusions reached in the previous study of the interaction problem. The interaction apparently is governed principally by the loading effects. The mean and blade-frequency thrust and torque and the mean rudder force and moment are very little affected by the inclusion of thickness even at the smallest possible axial clearance between propeller and rudder. The influence of thickness is greater on the propeller bearing forces and bending moments, on the steady-state values more than on the unsteady, and decreases with increase in axial clearance. The thickness effect is most pronounced in the case of unsteady rudder forces and moments at certain axial clearances, varying cyclically with clearance.

The mathematical model used in previous Davidson Laboratory adaptations of linearized unsteady lifting surface theory to marine propellers has been revised by removing the so-called "staircase" approximation of the blade wake and replacing it by an "exact" helicoidal blade wake. A new numerical procedure and program based on the present model have been developed to evaluate the steady and unsteady blade loading distributions, which are used to determine the bearing forces and moments. Systematic calculations of these forces and moments for a series of propellers show better agreement on the whole with experimental measurements than did the earlier calculations for the same series. In addition, the chordwise loading distributions are much smoother than obtained previously. However, the quantitative improvement must be weighed against the considerable increase in computer time over the old method.

The propeller-rudder interaction problem is studied by means of the unsteady-lifting- surface theory. Both surfaces of arbitrary geometry are immersed in a non-uniform flow- field (i.e., hull wake) of an ideal incompressible fluid. The boundary-value problem yields a pair of surface integral equations, the inversion of which is achieved by the so- called "generalized lift operator" technique, a new approach developed by the authors, in conjunction with the presently used "mode-collocation" method. The analysis demonstrates the mechanism of the interaction phenomenon by exhibiting the filtering effects of the propeller on the harmonic constituents of the wake which allow the rudder to be exposed only to the blade harmonic and multiples thereof. A numerical procedure adaptable to the CDC 6600 computer has been developed which furnishes information about (i) the steady and time-dependent pressure distribution on both lifting surfaces, and (ii) the resultant hydrodynamic forces and moments. A limited number of calculations exhibit the importance of some parameters such as axial clearance, number of blades, and harmonic components of the hull wake.