Page 236 - Introduction to Naval Architecture

PROPULSION 221

actuator disc used in that theory must now be replaced by a screw with
a large number of blades.

Blade element theory
This theory considers the forces on a radial section of a propeller
blade. It takes account of the axial and rotational velocities at the blade
as deduced from the momentum theory. The flow conditions can be
represented diagrammatically as in Figure 9.12.

Figure 9.12 Forces on blade element

Consider a radial section at r from the axis. If the revolutions are N
per unit time the rotational velocity is fyiNr. If the blade was a screw
rotating in a solid it would advance axially at a speed NP, where P is the
pitch of the blade. As water is not solid the screw actually advances at a
lesser speed, V z. The ratio VJND is termed the advance coefficient, and
is denoted by/. Alternatively the propeller can be considered as having
'slipped' by an amount NP - \£. The slip or slip ratio is:

where p is the pitch ratio = P/D
In Figure 9.12 the line OB represents the direction of motion of the
blade relative to still water. Allowing for the axial and rotational inflow