In this chapter the pressure fields induced by the loading and thickness distributions on a single blade will be derived. They are found to be composed of pressure dipoles (for the loading) distributed with axes normal to the fluid helical reference surface in way of the blade and tangentially directed dipoles along this surface for the thickness. The expressions are then expanded in exponential Fourier series to facilitate determination of the total contributions from Z blades. This reveals that the pressure “signature” contains only components at integer multiples of blade number. The behaviour at large axial distances at blade frequency is examined analytically and the variation of the weighting functions in the integrals for small axial distance is displayed graphically via computer evaluation. The chapter concludes with comparisons with measurements and with various approximate evaluations of the integrals involved made in the past.

PRESSURE RELATIVE TO FIXED AXES

We shall derive the induced pressures in a fixed coordinate system. In this system the propeller sees an axial inflow (in the negative direction) while it rotates about the x-axis. The pressure is derived at a fixed point so this situation corresponds to finding the pressure induced by the propeller at a point which travels along with the ship and is fixed, for example on the ship surface. Note however that neither the varying wake, mirror effects of the ship surface nor the influence of the free surface will be considered at present as they will be dealt with later (in Chapters 15, 21 and 22).