Practical Ship Hydrodynamics

202 Practical Ship Hydrodynamics
Except for 3, details of the rudder shape in side view (e.g. rectangular or
trapezoidal) have hardly any influence on dCL/d˛. However, the profile thickness
and shape have some influence. Computations and measurements of the
lift coefficient corrected for infinite aspect ratio by the formula above yield
the following conclusions:
ž All values differ from the theoretical value 2 by less than š17%.
ž For the same profile, measurements and computations by any method differ
generally by only a few per cent, except for NACA profiles with thickness
ratio greater than 25%.
ž Two-dimensional and three-dimensional RANSE computations hardly differ
from each other except for thick NACA profiles.
ž The Reynolds number based on axial inflow velocity and mean rudder chord
length has relatively little effect on the lift gradient.
ž The BEM fails to predict the low lift gradient of profiles with large opening
angle of the trailing edge. For such profiles, the Kutta condition used in
potential flow is a poor approximation.
ž Substantial thickness at the trailing edge increases the lift slope.
Further detailed investigations based on RANSE computations produced the
following insight into the effect of profile thickness:
ž Thick profiles produce more lift than thinner ones if they have a sharp end
(concave sides), and a lower lift if they end in a larger angle (convex or flat
sides).
ž The mostly used NACA00 profiles are worse than the other profiles investigated,
both with respect to lift slope and to the ratio between lift and
drag.
ž For all profiles, the lift/drag ratio decreases with increasing thickness. Therefore,
for a good propulsive efficiency, one should use the thinnest possible
profile.
ž The IFS profile generates the largest lift. However, when compared to the
HSVA MP73-25 profile the difference is small and the lift/drag ratio is worse
than for the HSVA profile. The IFS profile is also more liable to suffer from
cavitation due to its very uneven pressure distribution on the suction side.
BEM is not capable of predicting the stall angle because stall is inherently a
viscous phenomenon. For hard-over manoeuvres, the stall angle and its associated
maximum lift may be more important than dCL/d˛. RANSE computations
show that higher Reynolds numbers produce larger maximum CL. Thus experimental
values without extrapolation to actual Reynolds numbers are misleading
with respect to maximum lift forces. Other conclusions for the maximum lift
at stall angle from RANSE computations are:
ž The maximum CL ranges between 1.2 and more than 2. This upper limit is
substantially larger than assumed in classification rules.
ž The aspect ratio 3 is of minor influence only. Larger aspect ratio produces
somewhat smaller CL,max.
ž Small 3 yield large stall angles. (They also yield small dCL/d˛, hence little
change in the maximum CL.)
ž The taper ratio of the rudder has practically no influence on the
maximum CL.