Practical Design of Control Surface(1)

8/10/2019 Practical Design of Control Surface(1)

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PRACTICAL DESIGN OF

CONTROL SURFACES

Om Prakash Sha

Department of Ocean Engineering and Naval Architecture

Indian Institute of Technology Kharagpur, 721 302


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1. INTRODUCTION

Rudder and other control surfaces such as bow thrusters are crucial in achieving the

controllability objectives. Different control devices can help in achieving the desired

controllability characteristics of a vessel, but the rudder is the most simple and popular

control device and hence this section will look into the design process of a rudder.

During the concept and preliminary design stage, a naval architect has little information on

which to base decision. Nevertheless he has to decide at this early stage, the hull form in

terms of the shape of the underwater body, distribution of buoyancy, the shapes of sections

and underwater profile. He then has to take decisions regarding the location and sizes of

propeller, rudder and thrusters. All these decisions, which are interrelated, will affect

controllability of the vessel. It is, therefore, important for the naval architect to evaluate at

the preliminary design stage the type of rudder, its hydrodynamic efficiency, its structural

supports, and clearances between propeller and rudder. The following are the four major

constraints that limit the design of a rudder and any other control surface.

(a) In profile, the rudder should fit within the dimensions dictated by the shape of the hull.

Its maximum span should fit within the vertical distance measured from the bottom of

the deepest projection below the baseline of the ship permitted by draught or docking

restrictions upward to the bottom of the hull immediately over the rudder or to the

minimum prescribed depth below the water surface, whichever is lower. If the rudder

is abaft the propeller, its chord should fit within the horizontal distance from the

extremity of the ship to a line corresponding to a prescribed clearance from the

propeller. (Control surfaces that extend significantly beyond the block dimensions of a

ship, such as fin stabilizers, or the bow planes on some submarines, are almost always

designed to the retractable).

(b) The rudders, in maintaining a straight course, should minimise speed loss at every

level of ship power plant output.

(c) The rudder, the rudder stock, the rudder support, and the steering engine, considered

together, should be of minimum size, weight, complexity, and initial cost, consistent

with required effectiveness and acceptable standards of reliability and low upkeep

costs.


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(d) Undesirable effects of the rudder on the ship such as rudder-induced vibration should

be kept to a tolerable level.

Violation of any of the four listed constraints constitutes a misjudgement in rudder design.

Because of the influence of the rudder on ship power [constraint (b)], adherence to aminimum total ship cost [constraint (c)] requires consideration of the entire ship design

process.

2. HYDRODYNAMIC CONSIDERATIONS FOR RUDDER DESIGN

The considerations for rudder design from hydrodynamic point of view are summarised as

follows:

(a) Type of rudder and location

The type of rudder, its location and relative placement have significant influence on rudder

effectiveness and ship controllability. Ideally, rudders should be located near the stern and

should be located in the propeller stream for good controllability. Theoretically and from

experience it can be shown that for dynamically stable forward moving ship at all speeds

except dead slow, lateral control forces should be exerted at the stern and not at the bow.

The formula for a ships dimensionless turning rate as derived from linear equation of

motion for dynamically stable ships is

Turning rate

rr

RYNNY

YNNY

R

L

where = ship lengthL

R = turning radius

R = rudder angle.

With conventional rudder location at the stern, the dimensionless turning rate is proportional

to the sum of the magnitudes of the two numerator terms. But if the rudder is located at the

bow, the sign of the factor is reversed, and the turning rate is then proportional to the

difference in magnitudes of the two terms.

N


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The physical effect of locating the rudder at stern and bow for ahead motion is illustrated in

Fig 1.

Fig. 1 Effect of location of steering force [1]

When combined with forward ship motion these actions generate drift angle in the same

direction, and drift angle brings into play the large hydrodynamic side force and consequent

yaw moment that actually causes the turning. If, instead, the lateral control force acts at the

bow, the contributions to drift angle due to yaw rotation and lateral translation are in


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opposite directions and tend to cancel each other. Because both contributions are large, their

difference is small, and turning rate is much smaller than in the rudder-aft case.

Locating rudders at the stern in the propeller race takes advantage of the added velocity of

the race both at normal ahead speeds and at zero ship speed. This advantage is significant

and may not require any increase in propulsion power over what would be required if the

rudder were not in the race. The reason for this fortunate circumstance is that a properly

shaped rudder in the race can recover some of the rotating energy of the race, which would

otherwise be lost. There are, however, some negative aspects associated with locating a

rudder in the propeller race. One is the possibility of rudder-induced ship vibration. For this

reason, clearances of one propeller radius or more are common between the propellers and

rudders of high-powered ships.

Submarines have horizontal bow planes and stern planes to control their motion in the

vertical plane. Bow planes are moderately effective in this case because they either extend

beyond the hull lines or are located on a superstructure above the main hull and hence do not

interact too unfavourably with the hull. Bow planes extending beyond the hull lines are

usually made retractable. The primary function of bow planes is to improve control at low

speed at periscope depth under a rough sea. In the case of submarines that are very

unsymmetrical about the xy -plane, bow planes are also useful to control depth at very low

speeds deeply submerged; in this case the stern planes can cause ambiguous effects for

reasons associated with the existence of the hydrostatic moment, .M .

Fig. 2 shows some of the major rudder type available to the designer. These are

All movable rudder

Horn rudder Balanced rudder with fixed structure

All moveable rudder with tail flap

Each of these types has been used as single or multiple rudders or single and multiple screw

ships.


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Fig. 2 Various rudder arrangements [1]

All movable rudders are d e turning forces for their

ize. With the possible exception of large fast ships, the all-moveable rudder is preferred for

all-moveable rudder is from structural considerations. Unless

tructural support is provided to the bottom of the rudder, the rudder stock of an all-

moveable rudder has to withstand large bending moment as well as torque moment. The

esirable for their ability to produce larg

s

ships that possess control fixed stability without a rudder. For ships that are unstable without

a rudder, the rudder area needed to achieve control-fixed stability may be larger than that

necessary to provide the specified course-changing ability. In such cases, the horn rudder or

balanced-with-fixed structure rudder is an attractive alternative to the all-moveable rudder.

This is because the total (fixed plus moveable) rudder area of either of these rudders can be

adjusted independently to provide the necessary controls-fixed stability. On the other hand,

the moveable area can be adjusted independently to provide the required manoeuvring

characteristics. The minimum total area generally satisfies the constraint (b) but not

necessarily the constraint (c) of Section 1. The minimum moveable area should satisfy the

constraint (c) of Section 1.

The main drawback of the

s


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bottom-supported type of rudder was common on slow and medium speed single-screw

merchant vessels. But its use is avoided on high-speed ships as the cantilevered support is a

potential source of vibration and its contribution to the support of the rudder may be

structurally complicated.

The rudder stock size tends to become excessive on large fast ships. On these ships, a

reduction in required rudder stock size can be achieved by extending the lower support

earing down into the rudder as far as practicable, or by the use of horn rudder or balancedb

rudder with fixed structure. The bending moment on the stock for these rudders is

considerable reduced because bearing support is provided close to the span-wise location of

the centre of pressure of the rudder. The horn rudder is also favoured for operation in ice.

Table 1 gives a rough first guide in selecting the balance ratio based on the block coefficient

(CB) of the ship.

The balance ratio is defined asarearuddertotal

krudderstoctheofforwardrudderofArea

Table 1 Balance ratio

CB Balance ratio

0.6 0.250 0.255

0.7 0.256 0.260

0.8 0.265 0.270

The preferred location of the rudder should aft of the propeller at the stern. Unless

necessary, combinations such as single rudder with twin screws or single screw with twin

dder should be avoid as per as possible. At zero or low speed the propeller slip-streamru

increases the effectiveness of the rudder. The stern rudder is also more effective than a

rudder placed at bow for manoeuvring ahead where as the bow rudder will be more effective

in astern manoeuvring. The reason for this is the direction of drift angle which makes

substantial contribution to the turning of the ship when the rudder is located aft.


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(b) Area, Size and Height of rudder

A suitable rudder area for a given hull form is to be selected so as to satisfy the desired level

f dynamic stability and manoeuvring performance in calm water. Ships having higher block

e require larger rudder area for meeting stability

o

coefficient are less stable and thereforrequirements. It may also be noted that larger rudder areas have better performance under

adverse conditions of wind and wave.

The rudder area should be calculated and verified during the initial design stage. The

proposed DnV formula for calculating the minimum rudder area is given as:

251100 L

AR BTL

2

8515

43

toB

Lfor

L

BTL

where

= rudder area

T = draught

L = length between perpendicular

B ip

RA

= breadth of the sh

The above formula is to be used for aspect ratio ( AR ) of rudder around 1.6. If the aspect

area is increased by a factor given byratio of rudder is less than 1.6, the rudder

21

31

6.16.1 ARAR

to

The DnV formula applies only to rudder arrangement in which then rudder is located the

irectly behind the propeller. For any other arrangement the DnV suggests an increase the

dder area of at least 30 per cent. The value of rudder should be compared with existing

d

ru

rudder areas for similar ship type and size. A table giving rudder area coefficients for

different vessels is given.


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Table 2 : Rudder area coefficients

Sl. No. Vessel Type Rudder area as a

percentage of TL

1 Single screw vess 1.9els 1.6

2 Twin screw vessel 1.s 5 2.1

3 Twin screw vessels with two rudders (total area) 2.1

4 Tankers 1.3 1.9

5 Fast passenger ferries 1.8 2.0

6 Coastal vessels 2.3 3.3

7 Vessels with increased manoeuvrability 2.0 4.0

8 Fishing vessels 2.5 5.5

9 Sea-going vessels 3.0 6.0

10 Sailing vessels 2.0 3.0

A rge numb oeuvring troubles can be avoided by providing a margin of

extra rudder area at the preliminary design stage. For some ve enefit of larger

dder area will diminish after the rudder area becomes greater than The

fit mos

rease the height as much as possible so as to obtain a more

fficient high aspect ratio for a given rudder area. The bottom of the rudder is kept just

la er of potential man

ssels the b

ru TL2.0 .

effectiveness of larger rudder area is directly dependent on the inherent dynamic course

stability of the vessel. A vessel with positive inherent dynamic course stability will benefit

least with increase of rudder area whereas vessel with instability will bene t from

increased rudder area.

The rudder height is usually constraint by the stern shape and draught of the vessel.

However it is desirable to inc

e

above the keel for protection. A higher value of the bottom clearance is preferred for vesselshaving frequent operations with trim by stern. Recommended propeller, hull and rudder

clearances as given by LRS are shown in Fig 3.


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Fig. 3 Propeller clearances [3]

(c) Section Shape

For a given rudder location an e chord wise section shape is

overned by the following considerations:

maximum lift

o section shapes like NACA0018 and NACA0021

se these sections have a relatively constant centre of pressure.

hicker sections offer reasonable drag characteristics and are also preferred from structural

ruggedness of construction and is also beneficial for astern operations.

d rudder area, the choice of th

g

Highest possible

Maximum slope of the lift curve with respect to the angle of attack

Maximum resistance to cavitation

Minimum drag and shaft power

Favourable torque characteristics

Ease of fabrication.

A relatively higher thickness to chord rati

are preferred. This is becau

T

considerations.

The trailing edge of rudder has a noticeable thickness rather than taper to a knife-edge. This

allows increased

NACA section having any desired maximum thickness t, can be obtained multiplying the

basic ordinates by the proper factor as follows:


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432 1015.02843.03516.0126.02969.020.0

t

where

xxxxxt

y

x is the chord length expressed in fraction of chord length along x -axis from 0 to 1.

s the basic rudder foil chord wise cross-section with a table of ordinates for a

rudder having a thickness of 20% of the chord.

Fig. 4 show

Fig. 4 Basic ordinates of NACA family airfoils

(d) Rudder deflection rate

The classification soci m rate ofeties and regulatory agencies prescribe a minimu 312 deg/sec

nd this value is independent of ship parameters. Whereas the design rudder deflection angle

d turning characteristics, the transient manoeuvres (those

a

deci es the desired steady

manoeuvres in which the period of time the rudder is in motion is relatively long compared

to the total manoeuvre time) determine the rudder deflection rate. The quickness of response

in yaw and overshoot improve at increased rudder deflection rates. However, beyond a

certain rate further improvements in transient manoeuvres are insignificant. The effect of an

increase over the prescribed minimum of 312 deg/sec is the greatest on fast and response

vessels. Large full-form ships benefit more from having large rudder areas than from an

increase in rate of swing.

(e) Maximum rudder deflection angle

The maximum rudder deflection angle could be

The maximum angle to which the steering gear can turn the rudder, i.e. the design

maximum rudder angle


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be used for a particular manoeuvre, i.e. the

aracteristics of the manoeuvre, i.e. maximum useful rudder

udders experience a loss of lift at stall angles. Therefore, the maximum useful rudder angle

an that of the stall angle.

The maximum angle specified to

manoeuvre maximum rudder angle

The maximum rudder deflection angle which when exceeded yields no significant

improvements in the ch

deflection angle.

The maximum useful rudder deflection angle will decide the design maximum rudder angle

and the manoeuvre maximum rudder angle.

R

will likely be just lower than the stall angle. However, the maximum useful rudder

deflection may exist at angles of attack less th

Fig. 5 Orientation of ship and rudder in a steady turn to starboard


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The possibility of the rudder achieving an angle of attack exceeding the stall angle is most

likely during transient manoeuvres such as overshoot manoeuvre rather than during a steady

turn. For example when a rudder is laid over in the opposite direction to check overshoot

manoeuvre the angle of attack on the rudder may be larger than the deflection angle if the

rudder deflection rate is very fast. On the other hand, during a steady turn the angle of attack

on the rudder is far less than the deflection angle. Thus the useful maximum rudder

deflection angle is likely to be far greater in steady turn than that of overshoot manoeuvre.

The magnitude of the maximum rudder deflection angle will in almost all cases be

determined by steady turn considerations. The angle of attack at the rudder during steady

turn is (see Fig. 5)

RR

where

R = rudder deflection angle

R = actual drift angle at the rudder.

The geometric drift angle at the rudder is given by

R

= flow to theangle due to straightening influence of hull and propeller on thewhere

rudder.

The geometric drift angle is a function of the radius of turning circle. For a rudder located at

a distance 2L aft of the origin, R is related to the drift angle at the origin of the ship,

, by

cos2

1tantan

RR

where L is the length of the ship and

R is the turning circle radius

Measurements of made during the turning experiments of single-screw merchant ships

reported indicatemodels


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RL5. (where22 is in degrees)

he straightening effect of the hull and propellers on the rudder is approximately a linear

.e.

T

function of the geometric drift angle in the rudder, i

10 jforj R

Rj

j

1

Combining the preceding equations the following expression of angle of attack on rudder

during steady turn is obtained.

jR

LR

L

RL

R

15.22cos2

5.22tantan 1

In most cases the steering gear capabilities tend to impose an upper limit on the rudder

ing considerations. Certain types of steering

s and Great Lakes ships are built with design maximum rudder

o parts:

Selection of the geometric parameters and tur te necessary to develop the

desired ship characteristics, and

Calculations of torque loadings on the arrangement including the steering gear that

must control the rudder movements

namic forces and torque on the rudder as the hull turns

requires an accurate assessment of:

Hull wake

deflection angle, which is independent of turn

gears may not be suitable for mechanical reasons for deflection angles larger than 35

degrees. Most naval shipangles up to 45 degrees.

3. RUDDER DESIGN

The process of rudder design is usually conducted in tw

ning ra

Determination of the hydrody


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Hull drift angle

Change in the rudder angle of attack as the hull turns

In addition we need to know

The frictional losses in the rudder stock bearings

span-wise centre of pressure corresponding to the maximum

resultant force

r bearings

Steering gear drive mechanism

The computation of rudder-stock size requires knowledge of:

(a) The maximum design value of the resultant force on the rudder

(b) The location of the

(c) The location of the rudde

The computation of the rudder-stock location and steering-gear torque for all the rudder

requires knowledge of:

(d) The rudder normal force Fand the location chord-wise centre of pressurec

CP)( as a

function of rudder angle of attack at the maximum ship speed.

) Bearing radii and coefficients of friction.

the use of rudder in going astern, items (a), (b) and (d)

for both maximum ahead and maximum astern speeds. On recent naval

s and hence are capable of

stern speeds.

re large, heavy steering gear.

of full astern power for crash stops, but there is no

need to go astern at high speed after stopping.d the sustained astern shaft

ithin the ahead limits.

(e

On ships that have no restrictions on

have to be known

ships, there has been recognition of the following:

Typical combatant ships have large astern power

correspondingly high a

Adequate design for that astern speed would requi

It seems reasonable to allow use

Accordingly, instruction plates are provided limite

rotational speed to that which permits steering gear operation w

The acceptance trials include demonstration of the workability of the Instruction

Plate limit.


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Thus, design practice for naval combatant ships bases the calculation of rudder-stock size,

cation, and steering gear torque on the ahead conditions.

d experimental data are used for estimating rudder forces and

am data to compute the

tions have been made concerning:

The maximum angle of attack the rudder is likely to encounter,

lo

Empirical formulas an

moments. Details for computation of rudder forces and torque for spade and horn rudders

have been given Harrington [2]. However, in order to use free stre

maximum design value of normal force, assump

max .

The maximum flow velocity averaged over the rudder, . max)( RV

Rudder effective aspect ratio, a .

3.1 Rudder Torque Calculations for a Spade Rudder Ahead Condition

Number of rudders =

Length on waterline (L) = m

Draught (mean) (T) = m

Max. Design Speed Ahead (V) = knots

Froude Number

V

Fn5144.0

=

=

ake fraction ( ) =

L81.9

Thrust deduction fraction (t)

wW

Total appendaged resistance at V (RT) = Newtons

Density of water = kg/m3

Propeller Diameter (D) = m

Maximum Astern Speed (Vastern) = knots

Design speed ahead knotsVV 5144.0 = m/s

Speed of Advance AV = wV 1 = m/s

Propeller Thrust (T) =t1

= NewtonsRT


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Dynamic Pressure ( p ) =2

2 41v

2 D

TA

= N/m

2

Rudder angle of deflection = degrees

Rudder angle of attack M = degrees, where

35

35

7

2

7

5 M

Variation of to be cons ed = 7o, 14 21ider

o,

o, 28

o, 35

o

Variation of to be considered = 5o, 10

o, 15

o, 20

o, 25

o

Fig. 6 Stern arrangement and support details of spade rudder

The stern contour and propeller position must be available. Rudder shape, rudder stock

ft of stock centreline must

ared similar to Fig.

6. Once the rudder geometry is known the following quantities must be noted in meters: ,

and T and upper stock bear

st also be noted from g. 6.

Taper Ratio :

centre line location and distribution of rudder area forward and a

be determined as has been discussed before and the rudder diagram prep

1X

ings2

1d

X , X , X X , X , X , X X he diameter of lower3 4 ,

2

5 6 7 8 9 .

and d in meters and type of bearing mu Fi

215

XX

X


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Mean chord : )(5.0 521 XXXc

Sweep angle :

3

422151 25.0tanX

XXXXX

Rudder deflection angle in degrees :

where,

35

35

7

2

7

5 M Rudder angle of attack in degrees : .M

5.1225625.375125.61 Rudder deflection angle in degrees :

Effective aspect ratio :

7523

C

Xa

Data for uncorrected taper ratio :

Lift coefficient (see Figs 7 and 8) :

Drag coeffic

Centre of pressure (see Figs 11 and 12) :

1LC

ient (see Figs 9 and 10) :1D

C

1CCP

Lift coefficient1L

C , drag coefficient1D

C and centre of pressure1C

CP can now be

determined for various values and the effective aspect ratio a for sweep angle 0 and

11 degrees from the graphs given in Figs. 7, 8, 9, 10, 11 and 12.

:

2

3.5773.063.1

CL Lift coefficient correction

a

Corrected life coefficient : LLL CCC 12

a

CCC

LL

D38.2

22

22

Drag coefficient correction :

DDD CCC 12 Corrected drag coefficient :

Uncorrected normal hydro-

dynamic coefficient : sincos 111 DLN CCC Corrected normal hydro-

dynamic coefficient : sincos 222 DLN CCC

LNCCM CCCPC 21

25.0 14 2


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2

4

2

2

25.0

N

CM

C C

CCP

Corrected centre of pressure :

23 ... NCXcpF Normal hydrodynamic force :

Hydrodynamic torque :

2

. 422

XXCPcFQCH

Rudder stock bearing friction : FQ

8

9822

911 .

2..

2. F

XFQF

Rudder torque (displacing) : FD QQ

3

8

3 42.042.0

X

XXXdXXd

HQ

HFR QQQ Rudder torque (restoring) :

The coefficient of friction is given as

= 0.05 to 0.1 for bronze bearing

= 0.01 for roller bearing

= 0.1 to 0.2 for phenolic bearing

Thus, F , HQ , FQ , DQ and can be calculated and tabulated for various angles of attack

dynamic torque acting on the

s follows

RQ

a

The maximum bending moment max)( BMQ and hydro max)( HQ

rudder can be computed a

: cH

CPdFQ max)(

: bCPDLQsBM

21

22

max)(

where ,F L , D ,c

CP ands

CP are determined at max and maximum speed and is

to the centre of the lower bearings supporting

he rudder.

ed in a fixed location as the angle of

attack on the rudder increased, it would be desirable to locate the rudder stock just forward

would insure low maxi um torque value and in the event

b

the distance from the root chord of the rudder

If the chordwise centre pressure on a rudder remain

of the centre of pressure. This a m


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that the rudder were inadvertently freed, the rudder would tend to trail at 0R deg as long

as 0 deg. Unfortunately, on most rudders the centre of pressure moves as the angle of

. Therefore, in order to reduce the maximum torque valu st ship rudders

ru ders. The practice is to determinam o at an angle of attack of about 10 to 15

su ttack curve takes the form as s g. 13.

er angle of attack, the m m torque at

aft

e, mo

e the location of the stock on

hown in Fi

aximu

attack increases

are not designed as trailing dthe basis that the hydrodyn ic torque should be zer

deg. A typical torque ver s angle of a

Therefore, if the zero point were taken at a larg

max co ld be 5-deg zero poin is used to

inimi ourse keeping, which on most ships

requires more than 10 to

u significantly reduced. The 10 to 1 t torque

m se the power required for routine steering and c

seldom 15 degrees of rudder angle.

It can be seen from Fig. 13 that such a rudder is unstable at 0 deg. If the rudder was free

at this point it would flip over to either 15 deg port or starboard. This instability may

produce rattling, shock and excessive wear in gear mechanis . Some designers thereforems

0recommend that the rudder stock should be located at ( deg) position of centre of

to a requirement for a larger capacity

g r.

pressure. However, this recommendation will lead

steering ea


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Fig. 7 Lift coefficient, sweep angle 0 deg [2]


22/40

Fig. 8 Lift coefficient, sweep angle +11 deg [2]


23/40

Fig. 9 Drag coefficient, sweep angle 0 deg [2]


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Fig. 10 Drag coefficient, ]sweep angle +11 deg [2


25/40

Fig. 11 Chordwise centre of pressure, sweep angle 0 deg [2]


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Fig. 12 Chordwise centre of pressure, sweep angle +11 deg [2]


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Fig. 13 Typical torque versus angle of attack relationship

3.2 Rudder Torque Calculations for a Horn Rudder Ahead Condition

Number of rudders =

Length on waterline (L) = m

Draught (mean

ax. Design Speed Ahead (V) = knots

roude Number

) (T) = m

M

L

VFn

81.9

5144.0F =


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Thrust deduction fraction (t) =

ake fraction ) =

Total appendaged resistance at V (RT) = Newtons

Density of water

( wW

= kg/m3

Propeller Diameter (D) = m

Maximum Astern Speed (Vastern) = knots

Design speed ahead knotsVV 5144.0 = m/s

Speed of Advance = = m/s

Propeller Thrust (T) =

AV wV 1

t

RT

1 = Newtons

Dynamic Pressure (p) = 22 4

2

1

D

TvA = N/m

2

Rudder angle of deflection = degrees

Rudder angle of attack M = degrees, where

35

35

7

2

7

5 M


o, 21

o, 28

o, 35

o


o, 15

o, 20

o, 25

o

The stern contour and propeller position must be available. Rudder shape, rudder stock

centre line location and distribution of rudder area (fixed and moveable) forward and aft of

stock centreline must be determined as has been discussed before and the rudder diagram

prepared similar to Fig. 14. Once the rudde etry is known the following quantities

ust be noted in

r geom

meters: X , X , X , X , X , X , X , X , X and X .m 1 2 3 4 5 6 7 8 9 10


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30/40


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23 ... Nl CXcpF Normal hydrodynamic force :

2. 42

2

XXCPcFHydrodynamic torque : Q

CH l

lFQ Rudder stock bearing friction :

91198221110

123

81110

1233 .42

1. Xd

Q

3 .42.0

2

.0.

2XdXXd

XX

XX

X

F

XX

XF llF l

Upper Rudder Section

:2

61 XXcu

Mean chord

NuC Normal force coefficient (see Fig. 15) :

Hinge moment coefficient (see Fig. 15) : HMC

Nuuu CXcpF ... 7 Normal hydrodynamic force :

Hydrodynamic torque : HMuH CXcpQ u 72

Bearing friction :uF

Q

91198221110

127

81110

12733 ..

42.042.0 XXFXXd

21.. XdXXd

XXXXXFQ uuF

Tot

2u

al Rudder Section

Hydrodynamic torque :ul HHH

QQQ

Bearing friction :ul FFF

QQQ

R

dr

2

cos11 Single ram correction :

HFHFD QQrQQQ Rudder torque (displacing) :

HFHFR QQrQQQ Rudder torque (restoring) :


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Fig. 15 Hinge moment and normal force coefficients of rudder area abaft horn [2]

Fig. 16 shows a graph of the torque elements ( and ) during a simple

anoeuvre. As can be seen, the frictional torque t. The curve represents the

drodynamic components. centreline

is d at Point . The

rudder is then held in position by the hydraulic ram and small moveme

ss , caus g mov e

to the centreline, the pro e from the

HQ ,

is sign

Movem

der

nt to Point

FQ ,

ifica

e

ed a

pressure,

HQ

DQ

n

ngle

c

RQ

D

nt of the rudder from

he

on the

Q

re

m

sum of frictional and hy

a

nts tend to

curve. A drift

would entail torques following the curve until the or ac

dissipate the effects of friction in making the transition to Point b HQ

. If the rudder is then orderedangle is assumed by the ve el in em

cess works in revers curve moving to the RQ curve.


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Fig. 16 Rudder torque elements during a simp manoeuvre

3.3 Astern Torque Calculations Joessel Method

Based on experiments conducted in the Loire river (having a maximum current of 1.3 m/s)

with rectangular plate of span 30 cm and chord 40 cm, Joessel ved empirical

relationships for the variation of torque and variation of centre of pressure with the angle of

attack. These relationships, when corrected for larger dens are as follows:

le

deri

ity of sea water,

nd

sin122.418 2 wvAQ

sin305.0195.0 w

xa


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where,

= rudder torque about leading edge of the plate inQ mN

A = area of the plate in

= velocity of water in

2m

v sec

2

m = width of the plate inw m

= angle of attack in deg

x = distance of centre of pressure from leading edge in

By combining the above two equations, the resultant force on the plate is determined to be:

m

sin305.0195.0

sin122.418 2

vA

x

QF

The horn type rudder shown in Fig. 17 can be transformed into two rectangles as shown by

the dashed lines. By applying the foregoing equations along with an inclusion of a Joessel

coefficient, expressions for ahead and astern torque become as follows:

2

2

21112

sin305.0195.0

)sin305.0195.0(sin122.418)( hwhw

bwvKQ

aheadaheadH

)sin0305805.0())sin305.0195.0((sin305.0195.0

sin122.418)( 2

2

2111

2

hwhwwa

vKQ

asternasternH

where aheadK and asternK are the Joessel coefficients or the experience factors

Compute the hydrodynamic torque in astern condition using the above Joessels formula for

different rudder angles of attack .

Compute the normal hydrodynamic force on the lower and upper rudder sections in astern

tion.condition, i.e., asternlF )( and asternuF )( from the above equa


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Fig. 17 Model of a horn-type rudder used with Joessel method [2]

Steering Gear Torque and Power3.4

Total steering gear torque : AFHT QQQQ

where,

= hydrodynamicHQ torque

= error allowance =

FQ = bearing frictional torque

AQ cF 02.0max

The error allowance for both lower and upper rudder section to be calculated and summed

up.

Calculate and for all angles of attack.aheadTQ )( asternTQ )(


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Select the maximum torque = Maximum of { and

Rudder deflection rate ( ) in radians /sec is defined as

s

max)( TQ aheadTQ )( asternTQ )( }

s

=starboardhardovertoporthardoverfrommovetorequiredtime

starboardhardovertoporthardoverfromangledeflection

180

2 max t

=

where,

max = maximum rudder deflection on either port or starboard side

= time require in seconds

The regulatory class requirements for minimum deflection rate ( ) is

t

s 31

2 radians /sec.

Power required for steering gear :g

T sQP1000

)( max kW

where g is the steering gear efficiency 0.75 to 0.85 (see Fig. 18).

Fig. ciency of a Rapson-slide18 Effi steering engine


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38/40

Fig. 19 Rudder area distribution for stock diameter computation

.9 Estimation of Turning Circle Diameter [4]

ocedure

have been com ared w fiel

Wh a turn, the steady turning speed is less than the steady forward

speed at that engine power. For estim , the following

procedure is followed:

. Estimate he res nce all appendages withrudder held at ship centerline position over the desired speed range.

Estimate the drag of the rudder ( over the desired speed

range pe

Then, calculate the incr der drag at various angles of deflection (or attack)

at o ang

4. Augment the appendage craft resistance to account for added drag due to yaw and heel

of the cr n a urn ttack

3

The procedure described below is given in Ref [4]. The results obtained from this pr

p ith d trials of fast vessels of both displacement and planing type.

en a vessel takes CU

ating the reduced speedAU UC

1 t ista to forward motion of the craft including

2. s ) at various rudder angles

as r the procedure described earlier.

3. Estimate the rudder drag at zero angle using the ITTC friction line for frictional drag.

ement in rudover the drag zer le.

aft i t . Since the effective angle of a of a rudder during aeffcraft turn is less than the geometric angle due to yaw of the craft, the followingrelationship is assumed:

.Meff

where and are in degrees andeff


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35

35

7

2

7

5 M

Then craft angle of yaw, is given by

eff

The drag of the craft with appendages in yaw can be given by

5075.01 DD

where is the drag of the craft with appendages at no yaw condition.

ement of rudder drag to resistance of

yawed craft in turn to obtain the total resistance of craft in turn for that forward

D

5 For each rudder angle considered, add incr

speed AU and rudder angle .

6. Draw the new speed power curve EHP versus assuming the same engine power

esti

following relationship:

CU

for the corresponding speeds AU and CU .

Once has been estimated, the turning circle radius CR can be mated from theCU

2

2

22

CC

CACR

UK

UUL

1

where

in feet,

U = Vessel forward speed in ft/sec,

L = Craft length in feet,

RC = Steady turning radius

A UC = Vessel steady turning speed in ft./sec,

KC = an empirical constant which is

302 nC FK

where 2nF = Displacement Froude number, which is

2

1

3

1

g

UF An


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4. REFERENCES

V. (Ed), Principles of Naval Architecture Vol. III, Trans. SNAME

1990.

. H iction, Trans. SNAME 1981.

f Shipping Rules and Regulations

. Denny, S. B. and Hubble, E. N., Prediction of Craft Turning Characteristics,

M

1. Lewis, E.

2 arrington, R. L., Rudder Torque Pred

3. Lloyds Register o

4

arine Technology, Vol. 28, No. 1, Jan. 1991, pp. 1-13.

Practical Design of Control Surface(1)

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