Page 239 - Introduction to Naval Architecture

224 PROPULSION

of the vortices varies with radius and the line in the radial
direction about which they act is called the lifting line.
(2) Lifting surface models. In these the aerofoil is represented by an
infinitely thin bound vortex sheet. The vortices in the sheet are
adjusted to give the lifting characteristics of the blade. That Is
they are such as to generate the required circulation at each
radial section. In some models the thickness of the sections is
represented by source-sink distributions to provide the pressure
distribution across the section. Pressures are needed for studying
cavitation.
(3) Surface vorticity models. In this case rather than being arranged
on a sheet the vortices are arranged around the section. Thus
they can represent the section thickness as well as the lift
characteristics.
(4) Vortex lattice models. In such models the surface of the blade and
its properties are represented by a system of vortex panels.

PRESENTATION OF PROPELLER DATA

Dimensional analysis was used in the last chapter to deduce meaningful
non-dimensional parameters for studying and presenting resistance.
The same process can be used for propulsion.

Thrust and torque
It is reasonable to expect the thrust, 7^ and the torque, Q, developed by
a propeller to depend upon:

(1) its size as represented by its diameter, D;
(2) its rate of revolutions, N;
(3) its speed of advance, V a\
(4) the viscosity and density of the fluid it is operating in;
(5) gravity.

The performance generally also depends upon the static pressure in
the fluid but this affects cavitation and will be discussed later. As with
resistance, the thrust and torque can be expressed in terms of the
above variables and the fundamental dimensions of time, length and
mass substituted in each. Equating the indices of the fundamental
dimensions leads to a relationship: