This document summarizes key aspects of rudder theory and design. It discusses how rudders generate force through pressure differences on each side, and how this force has both lift and drag components. It describes different types of rudders based on the position of the center of effort relative to the axis of rotation, including balanced, semi-balanced, and unbalanced rudders. It also discusses rudder construction materials, pintle bearings, and considerations for rudder stock sizing based on the type of rudder.

1. RUDDER THEORY
Mohd. Hanif Dewan, Chief Engineer and
Maritime Lecturer and Trainer, Bangladesh

2. When a rudder is turned to some angle (α), a force (F) is produced due to the high and low
pressure regions generated by the water flow. On one side of the rudder the flow reduces in
speed whilst on the other it increases. By Bernoulli, lower velocities are associated with higher
pressure, whilst higher velocities give lower pressure so that a rudder force is produced as
shown in the sketch.
 WATER
FLOW
+
-

3. The total force generated can be assumed to act as a
single force at the centre of pressure of the rudder, more
often referred to as the `centre of effort'.
The force F has two components:
 a `lift component' which is the transverse
component of the rudder force, causing the
ship to turn;
 a `drag component' which is the longitudinal
component of the rudder force.
+
F
-
DRAG
LIFT
CENTRE OF EFFORT
b
The torque imposed by the water flow (which
needs to be overcome by the steering gear)
is the force on the rudder multiplied by the
distance from the centre of effort to the axis of
rotation. If the rudder were assumed to rotate
about its leading edge and the distance to the
centre of effort was `b' as in the sketch, the
torque would
e F x b.
0.4
0.2
10 20 30 40
Rudder Angle
Centre of Effort as a
Fraction of Rudder Area
The position of the centre of effort from the leading edge varies with rudder angle (α) as shown in
the graph. Therefore, if the rudder has between 20% and 40% of the rudder area forward of its
axis of rotation, then at some rudder angle, the axis of rotation and the centre of effort will
coincide and the torque on the rudder will be zero. At this angle the rudder is said to be `fully
balanced'

4. Lift to Drag Ratio of Rudder:

5. STALL ANGLE
There is a maximum angle at which a
conventional rudder is effective. This is
due to the stalling effect. At stall, the flow
of water around the rudder becomes very
turbulent, with eddying on the aft side. At
this point the lift force drops sharply
whilst the drag increases greatly. The
rudder is then acting as a brake rather
than a turning device. Hydrodynamic
work has shown this to be at
approximately 350 for an aerofoil shaped
rudder.
= 10
0
= 20
0
= 30
0
= 40
0

6.  Rudder angle normally does not exceed 35 degrees. Why?
a. avoid stalling of rudder
b. avoid flow separation on low pressure side
c. avoid reduction of effectiveness of control surface
d. avoid sudden discontinuity of lift force on downstream surface of rudder OR increase in
drag force
RUDDER SHAPE
Although there are different types of rudder, their
section, in plan view, is usually of hollow, aerofoil
shape.

7. Compared to an equivalent mass, single plate rudder, the hollow aerofoil shape offers the
following benefits:
 Greater buoyancy, therefore less weight acting down on the
steering gear, carrier bearing etc.
 More streamlined shape since all of the stiffening required can
be fitted inside the rudder;
 Higher stall angle than a single plate rudder.
• Size and shape of rudder is governed by:
a. shape and type of stern
b. area of rudder deemed necessary
c. capacity of steering gear
d. service condition of ship

8. RUDDER CLASSIFICATION
Rudders are classified as one of three types:
 Unbalanced;
 Semi-balanced;
 Balanced.
An unbalanced rudder has all of its area aft of its axis of
rotation, resulting in a high torque on steering gear, rudder
stock and pintles.
CENTRE OF EFFORT
+
AXIS OF
ROTATION

9. +
AXIS OF
ROTATION
CE
A semi-balanced rudder has up to 20% of its area forward of its axis of rotation. This results in
a lower torque on steering gear, rudder stock and pintles than the unbalanced
.

10. A balanced rudder has between 20% and 40% of its area
forward of its axis of rotation. This not only results in a
lower torque than the semi-balanced rudder, but also
means that at some rudder angle, the axis of rotation and
centre of effort coincide. At this angle the torque is zero
and the rudder is said to be `fully balanced'. This will
usually occur at a rudder angle of approximately 1
50.
+
CE
AXIS OF
ROTATION

12. BALANCED RUDDER
The sketch shows the after end of a vessel having
a `simplex' balanced rudder. The rudder has an
axle passing through it to take up thrusts
perpendicular to the stock.
The rudder will have a filling hole and drain hole
and air hole for testing. A lifting tube is fitted to
allow unshipping of the rudder.
A detail of the rudder shows a hollow aerofoil
section being stiffened internally by horizontal and
vertical webs.
The tail of the rudder is finished with a solid round
bar to facilitate a better welded joint.
There is a problem fitting the closing plate of the
rudder since it cannot be welded from the inside.
STOCK
HORZ WEB
AXLE
HORZ WEB
HORZ WEB
AXLE
SECTION
THROUGH
VERTICAL
WEB
HORIZONTAL WEB
STERNFRAME

13. Slots are cut in the closing plate and these align with flat bars welded to the vertical and
horizontal webs. The closing plate is then securely attached to webs by `plug welding' onto the
flat bars.
The connections at the top and bottom of the
rudder axle are shown in the following sketches.
The top connection shows the `jumping clearance' (see later note)

14. TOP CONNECTION BOTTOM CONNECTION
BRONZE LINER TUFNOL STAVES
BRONZE CAGE
HARD STEEL UPPER
BEARING RING
MILD STEEL LOWER
BEARING RING
BRONZE LINER
TUFNOL STAVES
BRONZE CAGE
CASTING
PALM COUPLING
AND BEARING TUBE 
Another type of balanced rudder, generally fitted with multiple screw vessels, is the spade
rudder. The rudder is entirely supported by the stock. Thus it must be of sufficient strength to
take the tensile stress due to the rudder weight, as well as the twisting and bending moments.
This can be achieved because the rudder is of the balanced type and thus has a very low torque,
nevertheless it has a very large diameter stock.

15. .
PORTABLE PLATE
40mm BEARING PLATE
22mm PHOSPHOR BRONZE BEARING
20mm GUNMETAL BUSH
TILLER LINKS
STEERING GEAR FLAT
20mm GUNMETAL BUSH
OIL TUBE
25mm STUDS GUNMETAL GLAND
CAST STEEL BEARING
DECK
PACKING

16. SEMI-BALANCED RUDDER
The rudder shown in the sketch is very popular nowadays. It is a semi-balanced rudder (also
referred to as a semi-spade rudder) generally fitted with a single pintle.
PLATE RUDDER TRUNK FLOORS ON EACH FRAME STATION
S G FLAT
STOCK
INTERCOSTAL GIRDER
OPEN WATER STERNFRAME
MAINPIECE
PINTLE

17. The pintle fitted in the semi-balanced rudder is shown in
detail. The pintle takes up the bending moment that would
otherwise be applied to the stock and thus allows a
smaller diameter stock than the spade rudder. If the pintle
clearances were allowed to become too large, then
bending stresses would be incurred in the stock, which it
was not designed to accommodate.
Also, vibration would increase, and since the stock is
generally a forged (rough) surface with a large change of
section at the palm coupling, the result could be stock
fracture.
BRONZE CAGE
TUFNOL STAVES
BRONZE LINER
RUDDER MAINPIECE
3 - 6mm
JUMPER BAR
The palm coupling must be very secure due to the effects of vibration and stress. Surveys have
revealed that nuts have loosened, or are missing and fretting is a problem. To overcome these
problems, palms are sometimes `stepped', or have keys fitted, and fitted bolts are used for the
connection.

18. UNBALANCED RUDDER
The `unbalanced' rudder illustrated is an older type of rudder requiring a `rudder post' on the
sternframe for attachment of pintle connections.
LOCKING PINTLE
BEARING PINTLE
At the top is a locking pintle whilst at the bottom is a bearing pintle.
Intermediate pintles may also be fitted.

19.  Effect on rudder stock of different rudder configuration
a. balanced rudder….centre of pressure on turning axis, no torque on rudder stock
b. unbalance rudder..centre of pressure is furthest from turning axis, high torque on rudder
stock
RUDDER CONSTRUCTION:
Modern rudders are of streamlined form except those on small vessels, and are
fabricated from steel plate, the plate sides being stiffened by internal webs. Where the
rudder is fully fabricated, one side plate is prepared and the vertical and horizontal
stiffening webs are welded to this plate. The other plate, often called the ‘closing
plate’, is then welded to the internal framing from the exterior only. This may be
achieved by welding flat bars to the webs prior to fitting the closing plate, and then slot
welding the plate as shown in Figure 21.4. Other rudders may have a cast frame and
webs with welded side and closing plates which are also shown in Figure 21.4.
Minor features of the rudders are the provision of a drain hole at the bottom with a
plug, and a lifting hole which can take the form of a short piece of tube welded
through the rudder with doubling at the side and closing plates. To prevent internal
corrosion the interior surfaces are suit- ably coated, and in some cases the rudder
may be filled with an inert plastic foam. The rudder is tested when complete under
a head of water 2.45 m above the top of the rudder.

20. RUDDER PINTLES:
Pintles on which the rudder turns in the gudgeons have a taper on the radius, and
a bearing length which exceeds the diameter. Older ships may have a brass or bronze
liner shrunk on the pintles which turn in lignum vitae (hardwood) bearings fitted in the
gudgeons. Modern practice is to use synthetic materials like ‘Tufnol’ for the bearings,
and in some cases stainless steels for the liners. In either case lubrication of the
bearing is provided by the water in which it is immersed. Until recently it has not been
found practicable to provide oil-lubricated metal bearings for the pintles, but Queen
Elizabeth 2 has this innovation.
RUDDER STOCK:
A rudder stock may be of cast or forged steel, and its diameter is determined in
accordance with the torque and any bending moment it is to withstand. At its lower
end it is connected to the rudder by a horizontal or vertical bolted coupling, the bolts
having a cross-sectional area which is adequate to withstand the torque applied to
the stock. This coupling enables the rudder to be lifted from the pintles for inspection
and service.

21. Rudder stock
SECTION A–A
Horizontal web Welded tube
Rudder stock
Bolted coupling
Vertical web
Cast frame
Slot weld
Lifting hole
Bolted palm
Bolted
palm
Upper
bearing
Side plates
welded to cast
frame
Side plate
Slot weld
DETAIL OF
SLOT WELD
Lifting tube welded
through rudder
Vertical
web
A A
Horizontal web
RUDDER WITH
CAST FRAME
Side plates
are slot
welded to
tube
Drain plug
Lower bearing
FIGURE 21.4 Rudders

22. RUDDER BEARING:
The weight of the rudder may be carried partly by the lower pintle and partly by a
rudder bearer within the hull. In some rudder types, for example, the spade type which is
only supported within the hull, the full weight is borne by the bearer. A rudder bearer may
incorporate the watertight gland fitted at the upper end of the rudder trunk as shown in
Figure 21.5. Most of the rudder’s weight may come onto the bearer if excessive wear
down of the lower pintle occurs, and the bearers illustrated have cast iron cones which limit
their wear down.
RUDDER TRUNK
Rudder stocks are carried in the rudder trunk, which as a rule is not made watertight at
its lower end, but a watertight gland is fitted at the top of the trunk where the stock enters
the intact hull (Figure 21.5). This trunk is kept reasonably short so that the stock has a
minimum unsupported length, and may be constructed of plates welded in a box form with
the transom floor forming its forward end. A small opening with water- tight cover may be
provided in one side of the trunk which allows inspection of the stock from inside the hull in an
emergency.
RUDDER LIFTING
During pitching, the after end suffers `slamming' impact and the rudder may also experience this
impact force, as well as a sudden increase of buoyancy as the rudder is alternatively immersed and
emerged. The tendency is for the rudder to lift, forcing the rudder stock up through the steering gear.
This is resisted by having a small jumping clearance (3 - 6mm) by welding a doubler onto the top of
the balanced and semi balanced rudders. The unbalanced rudder has a shoulder machined on the
bottom of the locking pintle to restricted upward movement.
JUMPER BAR
3 - 6mm
JUMPER BAR
3 - 6mm
Construction of Rudder
• Inside of the rudder is coated with bitumastic preservative or filled with inert foam
• Vent plugs are provided for venting and draining
• The rudder stock is connected to the rudder by vertical or horizontal coupling with fitted bolts
and are locked by pins
SHOULDER
3 - 6mm

23. Advantages of a Double Plate Rudder
• Lighter , stronger
• Reduce appendages resistance because of its streamlined , smooth surface/shape
• Greater lift force produce due to aerofoil cross-section
• Buoyancy reduced carrier bearing and coupling load
• Perforation of one side due to corrosion/damage does not reduce its effective area.
Special Rudders
• In addition to the conventional types of rudder, there are some special types of rudder in use
depending on the service condition of the ships.
Spade Rudders
• Also known as ‘skeg rudder’, it is a free hanging fully balanced rudder in the shape of a spade.
• It has no external supports in the form of pintles and is entirely supported by its
stock…purpose of this design?
• The stock is 30% heavier; shape tends to shift the C.P to turning axis and reduce B.M on
stock; no pintles benefits
• Rudder Theory

24. Flettner/Becker Rudders
• Flap or flaps of small area are hinged to the trailing edge of the rudder
• These flaps are independently controlled and can improve steering capability when activated
without increasing its drag force at large angle
• The flap having a high aspect ratio gives a high lift to drag ratio which improves steering
capability.
Borg Rudders
• It is a rotary unit that provide maximum manoeuvrability while operating at low speeds and
while carrying heavy load
• It uses the magnus effect to steer the ship..a cylindrical body, rotating in a fluid develops a high
lifting force at right angles to the flow on the side of the rotor turning in accord with the fluid
flow.
• Lift force increases rapidly as the surface speed of the cylinder increases

25. Pleuger Active Rudders
• It is an active rudder that does not depend on the speed of the ship to be effective
• It has a stremlined body mounted on it that houses an electric motor coupled to a ducted
propeller
This arrangement can actually turn the ship around its own length even when she is at rest
Rudder Pintles and Carriers
• A head is fitted to the upper pintle to prevent undue vertical movement of the rudder – locking
pintle
• The bottom pintle is known as a bearing pintle since it rests on a hardened steel pad
• Bearing pintles are only required to support the weight of the rudder in the event of the rudder
carrier failing
• It is essential that the centreline of stock and pintles are in the same line, otherwise the rudder
will not turn
• Appreciable wear of bearing generally is due to the misalignment of the rudder stock
• The major part of the rudder’s weight is carried by the rudder carrier

26. Watertight Gland for Rudder Stock
• A separate watertight gland is often fitted where the stock enters the rudder trunk.
• A small opening with watertight cover may be provided in one side of the trunk, which allows
access to a greater length of the rudder stock
• It also removes the need for a watertight construction of the carrier bearing and reduces the
unsupported length of the stion.

27. Inspection of Rudder in Dry-Dock
• Watertightness (Air tested to a pressure equivalent to a head of 2.45m above the top of the
rudder)
• Dent
• Crack
• Holed
• Wastage
• Corrosion
Any Question? Thank you!