Practical Ship Hydrodynamics

184 Practical Ship Hydrodynamics
TheformulaeforCL, CD, andCQN do not take into account the profile
shape. The profile shape affects mainly the stall angle ˛s, the maximum lift
and the cavitation properties of the rudder, but hardly the lift at a given angle
of attack below ˛s. Table 5.5 shows that, compared to the ‘standard’ NACA
profiles, concave profiles with thickness maximum in front of the standard
value of 30% of the chord length (measured from the leading edge) produce
larger maximum lift and less change of the centre of effort of the rudder
force. The latter fact allows a smaller steering gear if the rudder is properly
balanced. On the other hand, these profiles have higher drag coefficients, thus
requiring more propulsive power for the same ship speed. (For a rudder behind
a propeller, the slipstream rotation causes angles of attack of typically 10° to
15°. A 10% increase of the rudder resistance in this angle-of-attack range
accounts for approximately 1% increase in the necessary propulsion power).
For ship speeds exceeding 22 knots and the rudder in the propeller slipstream,
profiles with the opposite tendency (backward-shifted maximum thickness) are
preferred because they are less prone to cavitation.
Greater profile thickness produces greater maximum lift at the (correspondingly
greater) stall angle ˛s, but it increases the rudder drag, and in most
cases the danger of cavitation in high-speed ships. Thus, the smallest thickness
possible to accommodate the rudder post and bearing is normally used.
For rudders of small aspect ratio, the greater maximum lift of thick rudders
is realized only in yaw checking, but not at all if the steering gear allows the
normal υ D 35° rudder angle only (Fig. 5.14). A trailing edge of substantial
thickness decreases the change of the centre of effort cs with angle of attack ˛,
but it causes substantially increased drag; thus, because of too large drag, the
application of these profiles should be avoided at least in long-range vessels.
The approximate formulae for the force coefficients are only valid for angles
of attack ˛