RUDDER THEORY

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

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.

WATERFLOW

+

-

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.

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.

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'

+

-DRAG

LIFT

CENTRE OF EFFORT

b

F

0.4

0.2

10 20 30 40

Rudder Angle

Ce

ntr

e o

f E

ffo

rt a

s a

Fra

ctio

n o

f R

ud

de

r A

rea

Lift to Drag Ratio of Rudder:

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.

= 100

= 200

= 300

= 400

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.

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

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

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 .

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AXIS OF

ROTATION

CE

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.

+

AXIS OF

ROTATION

CE

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.

HORZ WEB

AXLE

HORIZONTAL WEB

HORZ WEB

HORZ WEB

SECTION

THROUGH

WEBVERTICAL

AXLE

STOCK

STERNFRAME

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)

TOP CONNECTION BOTTOM CONNECTION

BRONZE CAGE

TUFNOL STAVESBRONZE LINER

HARD STEEL UPPERBEARING RING

MILD STEEL LOWERBEARING RING

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.

BRONZE CAGE

TUFNOL STAVES

BRONZE LINER

CASTING

PALM COUPLINGAND BEARING TUBE

.

PORTABLE PLATE

STEERING GEAR FLAT

TILLER LINKS

20mm GUNMETAL BUSH

40mm BEARING PLATE

22mm PHOSPHOR BRONZE BEARINGOIL TUBE

GUNMETAL GLAND25mm STUDS

CAST STEEL BEARING

DECK

PACKING

20mm GUNMETAL BUSH

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.

S G FLAT

PLATE FLOORS ON EACH FRAME STATIONRUDDER TRUNK

INTERCOSTAL GIRDER

OPEN WATER STERNFRAME

PINTLE

STOCK

MAINPIECE

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.

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.

BRONZE LINER

TUFNOL STAVES

BRONZE CAGE

RUDDER MAINPIECE

JUMPER BAR

3 - 6mm

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.

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.

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.

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

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

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

JUMPER BAR

3 - 6mm

SHOULDER

3 - 6mm

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

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

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

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.

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!