The design of spade rudders for yachts

16 NOV. 1976

RCH1EF

ADVISORY COMMITTEE FOR YACHT RESEARCH

Lab.

y.

Scheepsbouwkunde

Technische Hogescheol

Deift

ji"

s

UNIVERSITY

OF

SOUTHAMPI I

ON

department of

aeronautics

and astronautics

S.U.Y.R. Report No.28

THE DESIGN OF SPADE RUDDERS

FOR YACHTS

SOUYOR

Report No.28

THE DESIGN OF SPADE RUDDERS FOR YACHTS

Miliward.

December,

₁₉₆₉

1.. INTRODUCTION

In the last few years the advent of the popular bilge-keel cruisers and of modern ocean racers with short keeLs has ed to the adoption of the separate spade rudder hung under the huil. This. forms a sharp contrast to rudders hung on the after end of the keel which has been the usual

practice with a very few exceptions, back to the time when this arrangement replaced the steering oar.. This large change in design has brought problems

since the accepted rule of thumb procedures are not necessarily valid any more for this type of rudder.. This has sometimes led to bad handling characteristics, which seems a pity since there is enough data available

in the technical literature to make the design of spade rudders a fairly straightforward process.. 1-1owever the modern helmsman is perhaps not

entirely blameless when it comes to riti.cisin this new type of rudder since he very often abuses it in a way which can easily be avoided if the comments in this article are taken into account0

The first and most important stap is to understand that a rudder has to perform two different and not whofly compatible tasks. There can therefore be no ídeal rudder since each design will necessarily be a series of compromises.. Even so the.re are stili a number- of major factors which if properly considered can result in a rudder that is better than many now existing.. One task that a ru.dder must be able to do is the obvious one of steering the yacht satisfactorily but the second task is probably less commonly appreciated - that it can contribute to the hydrodynamic side force produced by the yacht hull and can therefore particularly affect the windward performance of the yacht.. Yachtsmen who have followed recent work on sailing, such as described in 1"1archajs Baiiing Theory and Practice

will be familiar with the diagrwn shown in Figi which illustrates the

horizontal forces produced by the sails and hull of a yacht which is sailing to windward. The sails produce a driving force to propel the yacht through the water but in addition there is a large side force which must be balanced by an equally large side force produced by the hull to prevent the yacht being driven sideways and to do this the hull moves at a small angle of leeway It can be appreciated that if the rudder is also kept at an angle

to the water flow then it can either contribute to or detract from the Bide force produced by the hull and keel depending on which way the rudder is turned. This is illustrated in Fig.2a where the rudder force is adding to the hull side force and in Fig2b it is opposing the hull force. It should perhaps be emphasised at this point that the rudder angle that is important is not that shown by the position of the tiller to the centreline of the boat but the angle of the rudder to the direction of water flow along the underside of the hull This may seem unnecessarily pedantic but it is important to realise that the rudder is working in the wake of the keel and hull which are deflecting the water in order to produce various forces and it is unlikely that the flow is along the centreline of the boat., Thus it is possible that what appears to be a positive rudder angle by the position of the tiller is in fact a negative and therefore inefficient angle when related to the flow direction. Unfortunately it is not yet possible to specify the likely angles between the flow direction and the centreline

of the yacht because no measurements have so far been made of them, though some representative answers could readily be obtained from towing tank tests of several model hulls

It is important to remember therefore when deciding on the design of a

particular spade rudder that it shotd.d normally be working at a small angle to the flow direction even under steady windward and reaching sailing

conditions Therefore the design which will be the most efficient may not be the one which would have the least drag if the rudder were not at an angle to the water

flow0

2 ASPECT RATIO

The most important point to consider when designing a rudder is to decide whether its shape, looked at from the side,, shall be long and thin or short and fata The term normally used to describe this is aspect ratio2 and for a rectangular shape where there is no gap between the rudder and the hull it is simply the ratio of twice the length to the width of the rudder0 Fig3 shows the side force produced at different angles by _{a series} of rudders which have the same area but where the aspect ratio is altered. It can be seen that for a given rudder angle the side force increases consìderably as the aspect ratio increases. For example at a rudder angle

o

-of 5 the side force changes from 18 lb. wÌen A i to 50 lb when A 8

as the rudder is made longer and narriwer. _{In addition the drag is reduced} from

35

1h.. to 3 lb, as shown ri Fig.ì A large side force is needed to assist the keel to provide side force and also to turn the boat when tacking or manoeuvring. As the ¿rap

drag penalty, indeed there is a small. drag decrease _{it is evident that a} long narrow rudder would be best fcxn the hydrodynamic point of' view, though the benefit gets Drogressively smaller above an aspect ratio of 4 or

_5,

that is when the rudder depth is roughly twice its chord0 In addition structural and practical sailing considerations must be taken into account too since an extremely long narrow rudder would be difficult to make strong _{enough not to}

h shows that this can be obtained for no extra

bend or even break and is also more prone to pi.ck up weed or mooring ropes0 A secondary and less desirable effect of making the rudder long and narrow is that the stall angle decreases. This is the angle., shown in

Fig0

3,

at which the side force reaches a maximum, after which the side force decreases as the rudder angle is increased At. the same time the drag becomes very much bigger. It is worth noting therefore that for an aspect ratio of about

4,

which could well be the size of a good rudder, the stall angle is about 16°. It is a point that helmsmen particularly should bear in mind and is discussed again later

3, PLANFORM

The results discussed in the previous section were for rudders where the planform is rectangular hut

will he

approximately true for other shapes even though the actual forces obtained will not he quite identical For non-rectangular shapes however it should be remembered that the width is not

constant and that the average value for the whole rudder should be used when calculating the aspect ratio.

Ideally, if there was no gap between the top of the rudder and the hull, then the best planform for a rudder would be the semi-elliptic shape shown

in Fig5. In practice however there is certain to he a small gap so that the benefits of this shape are mostly lost, in addition the semi-el1iptic

shape is a much more complicated one to produce than either a rectangular, straight tapered or triangular shape. The extra drag for various tapered rudder shapes is given in Fig-6 when compared with the semie11iptic shape and the results show that the least penalty occurs for a tapered rudder when the chord at the bottom tip is one third of the chord at the upper or root tip0

TIP SHAPE

The shape of the lower tip of the rudder can also have a small effect on the efficiency of a rudder and there have been some tests on a few of the possible shapes. The answers have been

expressed

in the fora of changes in the aspect ratio of the rudder that ìs an increase in aspect ratio means that the rudder-is effectively longer and hence more efficient than its actual length

would

suggest since it has already been shown earlier (Figs ₃ and ) that an increase in aspect raic beneficial0

Five possible tip shapes are shown in FigJ and. it can be seen that shape E has no disadvantages and the simplest shape of all (A), which is just the

straight

rectuangui.ar tip cut off square haß a small positive gaine The list is however by no means comprehensive and there may well be other tip shapes which have greater advantages.

These results

thoh do show several shapes to be avoided if possible,

SI4EEPBACK

The next point to consider is _{bether the rudder should be vertical or} raked either forward or bek as shown in F!g8a.. The drag for a rudder which is

producing a

constant amount of stheforce is given in Fig.8b for different angles of rake or sweepbank _{noting that the sweepback angle is the} angle between the verticai. arid a lìn.e drawn through points _{one quarter of} the chord from the leading edge of th.e rudder _{The reasons for choosing the} quarterchord

lines,

as it is known. to define the sweepback angle will be more easily understood after reading the later part of this artic1e _which deals with aerofoil section characteristics.

aft has a high drag and the best resuJt is obtained when the rudder is

raked 50 aft0 Thus although the very raked rudders seen on some yachts look

fast they are in fact less likely to be efficient than the not so spectacular looking rudder which is almost vertical0

6. kiULL GAP

It has been mentioned when discussing the shape of the rudder that the gap between the hull and the upper ti.p could play a noticeable part in

determining

the efficiency of the rudder0 The results shown in Fig.9a and 9b illustrate tne effect on the side force and drag of a rudder as the gap between the upper tip and the hull is altered. Although it is not

anticipated that any rudder 3 feet; long would be suspended as much as lO

in0

below the hull the curves show that a gap of about in. would have a

noticeable effect, decreasing the sidefore by about 10 per cent and increasing the drag by about per cent compared with the values if the rudder were

completely attached to the hull0 rn pre.ct ice however there must be a small gap to allow the rudder to turn f reey and. while for a. production cruising boat it may be acceptable to reduce the rudder efficiency slightly to permit

ease of assembly and hence lower costs Lt is evident that for a racing boat the gap between the hull and the rudder should be reduced to a minimum,

L SECTION SRPE

Most people already realise that a good rudder section is likely to resemble an aerofoil shape1 with a rounded leading edge and faîrly sharp trailing edge hut it' is more

difficult te

_{decide which of the many aerofoil}

shapes

is

most suItable, There ere basicakly two families of aerofoils which might be considered and these are shown in FìglO.. _{The normal aerofoil such}

as the NACA 00 series has its maximum th:ickness at about a third of the distance from the leading edge, and the laminar or low drag aerofoil such as the NACA 66 series has its maximum thickness halfway between the leading

and trailing edges The haracteristi of the low drag aerofoil section is that it has been designed to have a particularly 10W drag for a small range of side force values as shown in Figll. whih gives the values for a section taken out of the centre of a very long rudder and thus the values do not depend on aspect ratio It can be seen that there is a sort of bucket

shape in the curve0 Outside this range cf conditions however it has a

higher drag for a particular side force than a normal aerofoil which is also shown, The curve of s2de force against rudder angle for both aerofoïis is shown in Fig012 and it can be seen that the value of side force at which the low drag shape becomes less efficient 6

bs.i,,,

obtained from Figll occurs at a very small rudder angle. This shows quite clearly that even in ideal conditions the low drag shape is le,ss effi:ient, except in the unlikely case that the nodder anges can be rstrited to 30 _{In practice also if}

the surface of the rudder is marred by scratches pimples or any other imperfection then the adantages of e i'w drag design are lost even over that very small range of rudder ange

If therefore itis de'Lded that mre normal shape, which has its maximum thickness about a third of the distance from the leading edge is to be used it still remains to decide whet thickness the section should be.

Some results of the forces measured ca three sisilar shapes but with different thicknesses are gives in igs13 atd tt ac i can be seen that aLthough the

thinnest shape, which a" a hi'knes to chord ratio of 6 per cent has the lowest drag when it is not developing any side force it has a comparatively

high drag when the side _{force is fairly iarge. at a rudder angle of more}

o

o

than 4 _{It also has the disadvantage}

that it stalls at a small _angle

_{(9 ),}

that is, the side force

starts to decrease while the drag continues to increase, _{The thicker of the remaining two shapes has the}

disadvantage that it has a slightly higher _{drag for a particular side}

force than the ₉ per cent thick shape but has the _{advantage that it stalls}

at an angle of

o.

o

16 instead of 13

& BALANCE

Although the balance of a rudder itself is the last design _{point to} be discussed it is by _{no means the least important}

Indeed several otherwise good rudder designs have _{been spoiled by a}

poor choice of pivot line for the rudder _{Equally, nowever well designed and balanced the rudder}

itself may te it cannot compensate for _{poor design in the initial matching}

of the hull and sails which _{can also contribute to large rudder}

forces The most important point _{to grasp is that for}

most rudder section shapes the force _{on it appears to act at a quarter}

of the distance back from the leading edge _{as shown in Fig015,}

If therefore the pivot was put at this point then it would require _{rio effort to hold the rudder}

at any angle or to change the rudder ang1e.

The disadvantage here is that the helmsman would have no feel _{arid could make unnecessarily}

Large changes of rudder angle without realising it and then have t-o

reverse the rudder angle to correct his mistake,

The second possibility is

to pivot the rudder behind the quarter chord point as shown in Fig,16a, _{This is however}

a very unstable condition _since as soon as the rudder _{is moved it produees a force}

tending

to pull the tiller out of the helmsxnans hand If

the

_{ti1lr were released}

for even a

moment the rudder would immediately swing hard over - a disconcerting and dangerous experience particularly in confined waters, but fortunately not very common,

The third possibility is the one which is usually encountered when the rudder pivot is forward of the quarter chord point as shown in Fig.l6b so that the rudder tends to return to amidships0 If the pivot point is too far forward it requires a considerable force to move the rudder from

amidships and is very tiring for the helmsman0 A suitable compromise which allows the helmsman a reasonable amount of feel in the helm without being too tiring is to pivot the rudder about a fifth (20 per cent) of the

distance back from the leading edge of the rudder. It should be noted however that unless the rudder is a simple shape and the quarter chord line

is vertical the position of the total force is difficult to determine. This is because the distribution of force is not uniform over the length of the rudder with the result that,, although for each section of the rudder the force acts at the quarter chord points the total force does not act at the average quarter chord point0 If however the rudder shape is chosen so that the quarter chord line for the whole rudder is vertical then the actual position of the total force along the span is unimportant since it must lie on the quarter chord line as for the rudder shovn in Fig017. The position of the total force for a more complicated rudder shape, such as a well swept rudder or one with a skeg in front of it, is difficult to estimate and is best found either by calculation or by a towing tank test0

9 HANDLING

Even when the designer has made his choice and arrived at the final design of the rudder it still depends on the helmsman whether the rudder will

be allowed to

do its work

_{pr''per.ly since in some ways it must be handled} in a different manner from the ¡flore traditional _{rudder which is hinged on} the trailing edge of the kee _{It has been mentioned earlier that if the} rudder angle is too large then the side force decreases rapidly while the drag force continues to rise and this will slow the _{boat dovn It is} therefore important to realise that chasges in _{course, particularly when} tacking should not be made with a sudden large application _{of the rudder,} However as the boat starts to turn the water flow near the stern will change direction as the stern of the yacht swings round and it will therefore be possible to increase the rudder angle relative to the boat while the angle to the water is maintained _{This means that a small rudder angle is used} to start the turn and then the rudder is pushed steadily further over as

the yacht turns, _{if on the other hand the rudder is jerked}

hard over it will probably stall with the result that the yacht will turn slower _because the side force is small, and will slow down more because of the higher

rudder drago

A further point to remember is that the forces _{produced by the rudder} rise extremely rapidi.y with boat speed as shown in Fig,180 _{This means that} in light weather conditions the _{rudder cannot be expected to turn the boat} very quickly and it becomes particularly important to avoid stalling the rudder by pushing the helm over too rapidly but in stronger winds the rudder can be turned more speedily.

-Distance from leading

edge

*

The trailing edge will have to be made thicker than this to avoid breakage TABLE i

Table of Offsets for the Aerofoil Sections shown in Fig0lO

Thickness from centre line (per cent chord)

11

-(per cent chord) _{Norma t Aerofoil}

(9% thick)

Low Drag Aerofoil (9% thick) o

0.5

075

O o

o . 68ï

o824

L25

1.120

lO30

2.5

1.961

1.368

5

2,666

L880

lo

3.512

2.626

20 4

.303

3601

30 501

4173

4O

1,352

4.457

50

3,971

4 4 5

60

3,423

4 .204

70

2, 748

3, 428 80 i . 967

2263

90

1.006

096l

*

100

0,095

o

Figi

Sai'

side force

Hull centre of resistance

Hull drag

Le ew ay

Sail

thrust

_{Sail centre of effort}

Apparent wind

Hull side

Leeway

L

Fig 2b

Hufl and keel

side force

Direction of

water flow

Fig 2

Direction nf

water

flow

HutI and keel

side force

Hull and

Rudder

keel drag side force

Hull and

keel drag

Rudder

drag

Rudder

drag

Rudder

side force

80

260

u o -o I-D -o

c2O

20

Fig 3

Stall angle

I t t I I i

AL

A6

Speed

3 kn

_A8

15

_{Rudder area 4 sq. ft.}

-°

Aspect

ratio A

A=1

Speed

3 kn

Rudder area

/. sq. ft.

Aspect ratio A

A=2

A1

A3

2 4 6 8 10 12 14 16 18 20

Rudder angle

(deg)

Fig 4

L. ₆ 8 10 12 16 16 18 20

o

Fig

/y////////

Fig

5

t _{I I} 1.0 c.5

Jr a n g ut a r

C root

Rectangular

Spe2d

3 kn

Area

/ sq. ft.

Rudder angle 50

tip

0.2

_o.'

_0.6

_0.8

1.0

Cti

root

Fig7

A B C D E

C C

ç.

-0.18

-0.20

-0.19

0

6 3

Sweep

angle

\.

ì

Quarter

*4

chord Line

Fig Ba

Speed

3 kn

Area

4 sq. ft.

Rudder angle

50

1 i.

-90

-60

-30

0 30

60

90

Sweep angLe

Fig 8b

5

rU I--o

D4

D

I-Q _{. ç}

-Fig 9a

Fig SL

speed

3 kn

Rudcer area

I

q. ft.

Runder depth

3 ft

L

J

2 4 6 8 10

Gap beten rddr and huit

in

-D

Spd 3kn

o.

-t,

Rudder

Rudd2r

area

dpth

¿ sq. ft.

3ft

2 1. ₆ 8

lo

Gap btwn tp

f

rjdder and huit (in

3.0

Low drag shap2 -NACA 66010 section

Maximum thickn2ss

at

5Q0/

chord

NormaL shape

- NACI 0010 section

Maximum thickness

t

30°/o chord

-D 0.2

o

0.4 0.3 0.1 o 30 20 u

o

D

w

10

Fig 11

Low drag shape

Normal shape

Section area

1 sq. ft.

Speed

3kn

I t 10 20

30

40

Side frce (b)

Low drag shape

Section area

lsq. ft.

Speed 3kn

4 8 12 16

Rudder angLe (deg)

-û 140

30

Fig 14

Fg 13

tic

t/c z 6°/e

tic

1StaJl

- t,c

6/

/

/

//

_TiiçkrC

_{= /chrd}

_ratio

_t/c

Steed 3kn

Section

area

1

sq. ft.

L

¡ J L ₈

_'2

₁₆ 20

Rudder ang.e

( de

tic

9°/o

Thickness /chord

ratio

t/c

Speed 3kn

Section ared 1 sq.ft.

10

20

30

Side force

(

bi

tic z9°/

0.4

0.3

Q.2 o-1

o

0.1 O

Row direction

Flow

direction

Rudder angle

-7

Pivot point

Side

force

Drag

c/I.

3c/I.

Rudder angle

-i-Flow

-direction

Dr a g

Fig 15

Side force

Side force

Rudder angl2

Pivot pivot

Design pivot

irz

Quarter

Drectjon

of

water flow

300

-c

L-2 L-200

D D D

Fig 18

Rudder angle

50

Rudder area

h sq.ft.

I _1_ ______J____.__ I I I 3 5 6 7 8 g 10

Yachts speed

(kn)