SUPERYACHT #509
September 2004
Article selected from our quarterly magazine dedicated to the largest
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Article by
Angelo Sinisi
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THE RUDDER
In the previous article on maneuverability, I pointed out
to the fact that the maneuvering qualities of a ship, as
well as her various characteristics, depend mostly on the
rudder's type and size.
For that reason, starting from the requirements supplied
by the customer, the designer must obtain the rudder's
characteristics that satisfy such requirements.
Subsequently, from such characteristics he must define
the dimensions that affect, on one hand, the structural
size of the rudder and, on the other hand, the power of
the system that will drive it. The two problems related
to rudder design involve a quite ample field of ship
hydrodynamics, which could be briefly synthesized with
the expression "the rudder hydrodynamic design". The
precise definition and the subsequent analysis of the
factors that have to be considered require quite an
exhaustive study thus, for a magazine article, a
synthesis is necessary.
The problems concerning rudder design have been treated
simultaneously by experts in aerodynamics and experts in
hydrodynamics. Therefore, the naval architect may use
such research studies to develop a good design. One of
the major and most useful data for rudder design is the
radius of evolution of the ship, which influences the
rudder area on the basis of the ship's hull
characteristics. After defining the rudder area to be
used, shape, size, dimensions and suitable location must
be fixed in order to obtain the most acceptable
hydrodynamic compromise. Rudder area means the area of
the symmetry plane of just one of its sides. Even though
it is very difficult to relate the forces and the moments
generated by the rudder to the ship's maneuverability
characteristics, the knowledge of such data is essential
for design, because the rudder thickness, the rudder
shaft diameter and the steering gear size - the system
needed to move it - depend on them.
Figure 1
Figure 1 shows the
involved forces that must be taken into consideration for
rudder design. Among the most widely known profiles, the
most suitable for rudder construction are the so-called
wing profiles with the rudder shaft in the symmetry
plaque. A profile of this type, immersed in a fluid
having speed U and angle of attack ???as shown in Figure
1, creates dissymmetry as for speed: speed on the
rudder's left side (passive surface) increases and on the
rudder's right side (active surface) decreases. According
to Bernoulli's Law, this generates a pressure decrease on
the left side and an increase on the right side. The
resulting pressure difference is the rudder force that,
in this case, is directed from right to left. Usually
such force is resolved into two components: force FL
perpendicular to the direction of speed U, and force D,
having the same direction as U (see Figure 1).
The creation of the perpendicular component FL is, in
fact, the only purpose of the rudder's existence. The
product of force P by distance cCP (see Figure 1)
between its point of application and the rudder shaft
generates a twisting moment, while the product of such
force P for the vertical distance between its point of
application and the load-carrying bearing, generates a
bending moment. As is well known, the two above-mentioned
moments are the main elements for calculating the
dimensions of the rudder shaft and of the hydraulic
steering system.
Figure 2
The maximum lift that may be generated by a rudder, as a
function of its angle of attack ?? is limited by a series
of events that cause the rudder to stall. When a rudder
stalls, lift suddenly falls to very low or null values,
therefore, in the design phase this possibility must be
carefully studied and avoided. Stall occurs when the flow
separates from the rudder low-pressure area and envelops
an area of vortical flow. As previously mentioned, this
separation generates an abrupt decrease in lift. The
point at which the flow changes from laminar to turbulent
is mainly a function of the Reynolds number, that is, a
function of chord, relative speed and angle of attack.
Three are the events related to stall: separation of the
laminar flow, cavitation and ventilation. The most
detrimental of them, that is, the one that by itself may
generate stall, is the separation of the laminar flow,
followed by ventilation and, lastly, cavitation.
Cavitation, even if in a minor way, may reduce rudder
thrust. The effect of cavitation is not as harmful, for
it results in the reduction in inclination of the lift
curve, compared to speed, rather than in a real decrease
in thrust (see Figure 2).
Figure 3
Ventilation, like cavitation, is a consequence of the
low-pressure values occurring in the flow adjacent to the
rudder's passive surface. Ventilation, in this case, is
the air suction appearing between the atmosphere and the
low-pressure area occurring on the rudder's passive
surface. Generally, this phenomenon happens only when the
rudder is too near the water surface and when the
pressure difference, between the atmosphere and the
rudder's passive surface (see Figure 1), overcomes the
resistance to the air passing through the interposed
water. In practice, as everybody knows, this problem is
solved by fitting a plate (see Figure 7) between the
rudder's top and the water level. In many cases this
plate is represented by the hull itself.
Figure 4
Another important factor to be considered before starting
the design of a rudder is to establish the number of
rudders to be used and their location. The hull wake
diminishes the speed of the laminar flow that hits the
rudder, while the propeller produces the opposite effect.
In single-screw ships and narrow stern the two effects
mostly cancel each other, while in twin-screw ships with
rudders behind the propellers the effect of the slipping
wake is considerable. The propeller not only modifies the
speed of the water outflow going to the rudder but it
also substantially slows the stall, thus remarkably
improving the rudder performance for angles of attack
greater than the angle of stall.
Figure 5
Consequently, the rudder
maximum efficacy occurs when it is hit by the propeller
race. Single-screw ships always have one rudder; twin-
screw ships may have one central rudder or two rudders
behind the propellers; generally, three-screw ships have
just one rudder behind the central propeller and often,
four-screw ships are steered by two rudders that are hit
by the stern-propellers race. In twin- or four-screw
ships, fitting two side rudders behind the propellers is
much more efficient than fitting just one central rudder,
even when the total surface is the same. This is true
because the feeding speed increases as a consequence of
the low coefficient of hull wake and of the effect of the
propeller race. Moreover, total area and rudder height
being equal, generally affected by the ship immersion,
the two side rudders have greater height and thus greater
lift coefficient, tiller angle being equal (see Figure 6).
Figure 6
As everybody knows, lift increases with the increase
of the angle of attack and with the square of the impact
speed. When fitting the rudder astern of the propeller,
one must verify that, even though it benefits from
greater speed, it is not hit by the propeller hub vortex
(see Figure 8), which not only has the effect of reducing
the lift, but also of causing erosions and eventually
annoying vibrations. For this reason, the rudder is often
installed slightly towards the inside compared to the
propeller center. If the above-mentioned conditions are
satisfied, the rudder shall be fitted the most astern as
possible, with the clear purpose of obtaining the maximum
arm K compared with the center of gravity of the ship
and, as a consequence, the best turning characteristics
(see Figure 1).
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Figure 7
Figure 8
Figure 9
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There are three main types of rudder: the
Flap, the Horn and the Spade types (see Figure 3). The
Flap and Horn rudders may be useful whenever, for reasons
of directional stability, an additional surface is needed
besides the existing one and when all of the above-
mentioned surfaces should not be mobile. Moreover, they
should be fitted when a fixed supporting structure is
preferable in order not to load excessively the rudder
shaft and its supports. If the turning qualities are to
be improved, the rudder surface compared to the lateral
ship surface is to be increased; yet, if both are
increased, the hull dynamic stability improves and, as a
consequence, also its straight line path stability.
Nevertheless, one must be careful in fitting the rudder
and the lateral ship surface because they may affect in a
negative way the ship's dynamic stability. In fact, as
explained in the previous article on maneuverability,
when the rudder is taken to tiller angle ? and the ship
starts turning, various forces are generated the moments
of which ( F * h ) make the ship list. If the rudder is
pushed to the right (see Figure 4) and the moment given
by FL * hL (the force generated by the rudder multiplied
by the vertical distance between the center of
application P of the total transversal resistance that
the ship encounters when turning) is greater than the
moment FC * hC (the centrifugal force of the ship
applied to the center of gravity G multiplied by the
vertical distance between G and P), the ship shall list
to the right. Vice versa, if the rudder moment is smaller
than the moment given by the centrifugal force, the ship
shall list to the left. Therefore, the rudder surface,
location and shape affect the listing moment during the
turn and, as a consequence, also the listing angle. In
following seas, even a prominent lateral ship surface
generates a transversal listing force that, if not
adequately countered by an efficient rudder, may cause
dangerous transversal listings, especially if the ship
has a low stability index. One of the rudder
characteristic data is the figure ratio a defined as the
ratio between rudder height b and its medium chord c
(see Figure 5).
In a Spade rudder (see Figures 5 and 9) with a high
figure ratio a = b/c there is:
- a greater vertical distance from the center of
pressure and, as a consequence, a greater bending
moment for calculating the rudder shaft,
- an increase in the lift coefficient (Figure 6),
- a low angle of attack ? at which stall occurs (Figure 6),
- a greater listing during the turn.
The area forward of the rudder shaft is called
compensation area (Figure 5). This area and thus the
compensation degree to be assigned to the rudder, i.e.
the ratio between the rudder surface forward of the shaft
and its total surface, must be such as to be able to
obtain a low torque both in forward as well as in reverse gears.
NACA sections are to be considered among the various
profile sections for rudder construction and NACA 0015
offers the best combination of hydrodynamic qualities and
construction possibilities for Spade rudders. Usually,
this type of rudder has a trapezoidal shape, which not
only increases the center of pressure by reducing arm hT,
but it also has an elliptical distribution of load along
its height. This distribution opposes minimum resistance
and improves the lift curve.
The bottom end of the rudder may be squared, that is with
a sharp edge, or rounded. Testing showed that rudders
with squared bottom have greater lift than rudders with
rounded bottom. Nevertheless, design practical conditions
such as resistance to progress, rudder weight, rudder
support weight and steering gear weight impose the
construction of a rudder with the smallest possible
surface. Therefore, the designer is faced with a problem
the solutions of which can only be a compromise and the
technical approach of which is complicated by the
influence of several factors which come into play in
addition to the rudder's main ones.
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