Further experiments on the rotating cylinder rudder

Technische

FURTHER EXPERIMJTS ON THE ROTATING CYLINDER RUDDER

Liu Youhua* and Xu Hanzhen**

Û2Ct

This aoer depicts the experiments that have been carried out in

s towing ank to see the effects of the cylinder speed ratio, thE Reynolds nu:nher, the cylinder diameter and the cylinder roughness on the lift, the drag and position of the ressure center of the rotating cjlinder rudder. It is pointed ou-c that ii' the cylinder sceca ratio surpasses ;.O, ne soot where it hcc ceen saic to ce the optimum for the lift, and increases to _{5, 10 or even larger,}

the lift will still rise, though relatively slow. Some special

phenomena of the rotating cylinder rudder are mentioned and

inter-preted.

Tests made to learn the performance of the rotating cylinder rudder in backward velocity showed that the rudder could afford

a ship in astern rnanoeuvring with rapid response and large controlling

force.

*)Fostgraduate in Depart:ent 0± Marine and Ocean igineering,

HuazhongUniversity of

.1.

I. Introduction

A rudder with increased lift coefficient is called high-lift rudder. Increasing the lift coefficient is essential to make improveñent on those conventional streamlined rudders which have

so much application in all kinds of ships, for any other ways to enhance the lift of a conventional rudder, such s increasing the controlling area, s.nd olacing the rucder in the ropeller race

for a larger relative velocity, :niht not be available in real

conditions, and these can also be used on the high-lift rudders.

The rotating cylinder rudder is a high-lift rudder with very high lift coe±'fi.cient but not very complicated :rechanis:n. It is formed by fixing a rotatable cylinder into the leading edge of

a conventional rudder, being confirmed that the cross section oÍ'

the rudder is still roushly streamlined. Rot.ting the cylinder in a proper direction can make the lift ascend, which may be reasoned in two aspec: first, from the Magnus Effect, the rotating cylinder itself can produce lift force; second, the stream oroected by the rotating cylinder will reform the ootential flow around the rudder and control the boundary layer, so the lift generated by the main body of rudder will be greatly enhanced, especially when the rudder

angle is a little large.

Since the National Physical Laboratroy (N.P.L.) in England published some exoerimental data of the rotating cylinder rudder in l97O, there have not been much research work known in this

subject. Although there have been some successful at'plications

(e.g., Jastram rudder-rotors in four large ro-ro ships in Germsny in the middle seventies) and the lab research has gòne deep into observing the effects of cavitation, the cylinder roughness and

the rudder-cylinder gap on the rudder performance2'3, there is

still much work to be done to make the rotating cylinder rudder

impressive and trustworthy among designers and users. In other words, there are still sorne problems to be researched, and work to be done ¿core comprehensively on domains that have once been

explored.

Almost all the capers published on the rotating cylinder rudder have corne to the conclusion that, when k, ratio of thE cylinder circu:nferential steed to the free stream speed, arives 5.0, the lift of the ro-tating cylinder rudder will be the meximurn. The euthors of this paper reckon this conclusion as reasoneble and

useful, but not exact. See APpendix I. It is the lift coefficient

curve of a single rotating cylinder from speed ratio k=C -co k=17 given ir reference 4. From this graph, it can 'be seen that near

k=3 the slope of CL vs. k curve of the rotating cylinder drope

sharply (from about 5.1 to 0.48). The lift coefficient of e rotating

cylinder is proportional to the circulation or average velocity

along a round path near the c:jlinder surface where the flow has become potential. From k=3 to k=17 the CL value still rises,

whichthat the circulation of the potential flow around the

cylinder atco increases, or

to project fluid particles to the around flow fiíld increases.

Hence, back to the case of the rotating cylinder rudder, we could excect that es k exceeds 3.0 end continues to increas, the lift of the rotating cylinder rudder will still ascend. Despite the certainly srndl sloce of increase, the mnner of variation of 0L when k increases to _5, 10 or even 2C would be of great significance

.3.

The conventional rudder can give a cruising ship enough

manceu-vring force, but it will likely lose its efficiency when the ship

is manceuvrin astern or in low velocity. To confirm shios with

enough controlling forces when they are rnanoeuvring astern or in

low velocity is the :nain task of developing special :flanOeuvrirìg

devices which include the high-lift rudders. Low-velocity perform-ance of the rotatin. cylinder rucder can be defined as its per-formance when k is very high and its critical Reynolds liu:uber. The performance o± the rotating cylinder rudder in backward veloc-ity is a topic the published papers left untouched, _{and which the} authors will uake efforts on.

Ecaides, this pafler will also discuss the effects of varying the cylinder dia:ieter end the cylinder roughness or. the performance cf the rotrting cylinder rudder.

II. Exoeri:ients

1. The Facilities and Model Rudders

The experiments were carried out in th _{RUST Towing Tank, whose} length is 175m, width 6m, depth 4m, and towing velocity can be

adjusted to from 0.2 to 8.Om/s.

The model rudders are all of a. chord length of' '200mm, and an aspect ratio of 1.267, the sauìe as that in reference 2 and 3. The rotating cylinders were connected through _{flexible axles to the}

shaft of the motor, whose rotation _{rate could be chosen in any} values within 3000rpm. The rudder bodies were connected through

rudder shafts to a strain gauge, and the strain gauge was combined

with an apparatus for changing the rudder angle, which was fixed onto the structure of the towing carriage. Shown in Photo.1 is the mechaniam. The rudders were dipped in water, with their tops

Photo.1 The mechanism

/

N

Fig.2 The roughed cylinder

in the depth of' 10cm.

One of the cross sections of the rudders is shown in Fig.í. Five model rudders were used in the experiments (see Photo.j,

with varying cylinder di2meters end roughness, 'but a fixed crlinder

gaD o± 0.5% the chord length. The cylinder roughness ws developed

'by grooving rarellelly and symmetrically to the cylinder sxis on

the otherwise smooth surface, as shown in Fig.2. The following

ta'cle dispisys some other pare.meters of the rudders.

Na:1e _{Qlinder diameter (mm) (1inder surfce}

DO

D40 40 _smooth

D50 50 _smooth

Rl 40 rough, =t

R2 40 _{rough, 2.*t,--sZ}

The model rudders Photo . 2

.5.

For the sake of compariso't, a conventional rudder with chord

length of 215mm, span of 216.5mm, and with NACAOO20 cross section

was taken into use. Experiment States

ery rudder had towing velocities of 0.8, 1.0 and 1.25m/s, and backward velocity of 1.0m/s. Under each velocity, there ere six cylinder rotation rates, correspondent with k=0,1,2,3,4 and 5

resoectively. The rudder angles had 12 values, varying from O

to 8G.

After that, low-velocity experiments were carried out with towing

velocities, forward and backward, of 0.6, 0.4, 0.3 and 0.::n/s,

and cylinder rotation rates corresondent with k=O,5,5,10 and

n=3000rpm.

Exneri:nent Procedures

In an experiment first read the strain values representing

respectively tne normal orce, th tangential force anc tne moment

concerning the whole system of rudder, rudder shaft _{Ld the} flexi-ble axle, then take off the rudder tody (with the cylinder) and read the three strain values repreEenting the forces and moment

mounted on the parts left. From calculation _{can get the coefficients}

of

forces and

mounted on the rudder, and

tr-is-fori-qa-tjor of the coordinates the lift coefficient _CL, the drag

coefficient Qy and the non-dimensionel distance from _{the pressure}

center to the leading edge i? can be got.

III. An Expression to the Experiment Resulte

Fart of the exacriment output is shown in _{Append!:< II. iHere is}

an expression to the results.

1 T

-'4-.

Li

(i) The Effect of Seed Ratio k

to i is the most significant to the rise of CL; and wheno25 the

region of i to 2 is the most significant.

When k=23, the slope of the C vs. k curve drops shsrpl;. When k=3-5, the CL vs. k curve is rather even, but still has a not-zero

slope (e.g., it is about 0.04 when

_o&=50').

reveal that even when k ascends to 20, the Ct_ vs. k curve still has

a not-zero slope, which may be even larger than that when I=35(e.g., when d=50°it is about 0.08), though one can wonder whether it is

still so at larger Reynolds numbers. So we see that the speed ratio

of 3.0 is not the optimum point where the maximum lift occurs as it had been pointed out, since the lift coefficient of th _rotating

cylinder rudder shall rise slowly but also steadily after that;

end if the word optimum is interpreted as that corresponding no

further rapid rise to the lift coefficient, the optimum point should

be about 2.0, and not 3.0.

The effect of k to CL varies es changes. The larger

i, the

When

k<2,

angle, which is the so-called stall. If k2, there would be no stall.

In conducting the experiments of rudder Rl and R2, which have roughed

cylinders, there had occured civittion, and

the pethline of

the cavitation, it was obeerved clearly that the flow along the suction side of the rudder was smooth and without separation, even

when - reached 80.

WhenoL=Cand k1, there will exist a lift, which is a phenom-enon the oublislied work had not reported. When k changes from i to

5, the coefficient of this lift will _{vary in the region of 0.05 to}

0.15, which is the level of' the conventional rudder at rudder anale '

.7.

(2) Comparison with the Conventional Rudder

When the cylinder is not rotating (i.e. k=0), the performance of the rudder is bad comparing with that of the conventional rudder due to the not-streamlined cross section: the maximum lift before stall would be only one fourth to one half of that 0±' the conven-tional rudder, and the stall an,le is between lOand 15

When k=1 , the stall :-ngle has risen to 2030 and the lift before

stall has also reached the level of the conventional rudder. It is

clear that k=1 has cancelled the disadvantage on the lift due to bac cross section.

when k2, there would be generally no stall at all; the slope 0±' the t vs.o curve t oL=040 which is nearly a straight line,

\..ill be shout 20% to 40% greater than that of the conventional rudder; and the maximum lift will t'e :nuch greater than that of the

conven-tional rudder: when Re=(1.42.2)

(fand

ma _{lift of' the rotating cylinder rudder to that of the}

conven-tional rudder would be î.82.2; i± k=3, the ratio would 'be 2.0'2.3;

if k=4, it would be 2.02.4, and if' k=5 the ratio be _{2.i2.4; when}

Re1.0xlC and k rises to 10, 20 and even 30, the ratio would soar

to 5.3, 5 and even 10.

(3) The Effect of Cylinder Roughness

The cylinder roughness makes the lift curve of k=1 closer to those

of k2

30even earlier; it also makes the stall angle increase (e.g., when k=1, rudder D40, with smooth cylinder, stalls at rudder _ansie 0f 20-30, while the stall angles of Rl and R2, with roughed _cylinders, are 3C4O°and 4050°respectivelj). The cylinder roughness also

raises the max lift.

cavitation might be generated. Although the cavitation seems have no significant effect on the rudder performance, it is harmful fro:n other points of view, and must be avoided. It was observed

that st n=2300rpm Rl began to generate cavitation, while R2 began

at n=l800rpm.

The Effect of Cylinder Dismeter

when the cylinder is not rotating, the lift cf D50 st small rudder i _{obviously lower th..n those of B3C and D4C), while the}

latter two do not have significant difference. When k2, _{the lift}

of L30 i _{obviously not so great as those of D40 and B50, while}

tb latter two do not differ much. Besides, sometimes there sre

stalls occured to D30 when k=2, while to D40 nd D50 there are

none.

So it could he concluded that D40 is the best of the three in

lift performance.

The Effect of Reynolds Number

rhen Re=(î.O-2.2)iO _{the lift curves of the rotating cylinder}

rudder are generally not affected by the Reynolds number. _{But when} Re=(O.51.0)xlO the decrease of the Reynolds number makes the

lift coeffiç\ient increase, as shown in _Eig.3.

\30

2.0

(.0 ).o _Reu/Ot) 2.5

.Fïg.3 The effect of the Reynolds number on

the max lift coefficient and the lift

.9.

Tests were done with the rudders in backward velocity to find

out their performance when ships move aft, a topic on which no

one has covered from the knowledge of the authors. Comparison was made between this and that of the conventional rudder. Below is

the conclusions.

(i) The effect of k on the backward lift is the most signiuicsnt

st =G sa growing, the effect is weakened, and when 09LC the

C vs. k curve is elmost s. horizontal straight line. This is tust

oonosite to the case of forward velocity, which might be becsuse in forward velocity the cylinder is the leading edge, while in

'osckwsd velocit..r it is the tr.iling edge. The CL vs. k curve of o=O°is very conspicuous for its s-ceeoness. when k=4 it hs.s risen

to about three cuartera the max backward lift coefficient, or about the same value of the backward lift coefficient of the

conventional rudder at =3O'. This imlies that without turning

the rudder, only rotating the cylinder of the rudder can s great

ms.noeuvring force be produced. This means the rudder response

could be cuickened, and the astern manoeuvr&bility of ships

could be improved.

The cylinder roughness makes the CL vs. k curve of o(=G more steso. Eut 2 seems to be no better than Ri.

Increasing the cylinder diameter steepens the _{CL vs. k curve}

of o=C though before k=5 the siope has lessened and the lift

at k=5 does not increase.

when Re=(1.ü-2.2)X1C the backward lift does not change

fol-lowing the Reynolds number; when Re=(O.5'1.0)x1ü the backward

lift would increase with the Reynolds number decreasing. But when

ward Jif-t; might be in the opoosite direction as expected (onlj in a very narrow region from =O'is it not so).

2. Dra,

çi) hen the cylinder is not rottin (k=O), the drag i a little iarF,er ttin tbrt of the conventional rudcer st rudder anale of

nd the vs aL curve is not smooth et these rudd-r angles.

'vhen k=1, at ° the drag curve is

s.00th End

is about the sme s that cf the conventional rudder; at >)O' the

drsa curve would fluctuate, but svereely it is of the same level

s that of the conventional rudder.

hen k?2, at o40 the drag is a little larger then that of the conventional rudder 'cut tf:e- drag curves are rather smooth, and k does not have obvious effect on C; at _{>4c; th} drag is

gen-erally much larger than tht of ti-ia conventionai rudder, and _with

k increasing the dreg, would also increase. Eut if k reaches IC or more, the drag would be negative at smell rudder angles.

In backward velocity the larger k becomes, the greater the difference between the drag of the rottting cylinder rudder and that of the conventional rudder would be. The increase of k

Sig-nificantly enlarges the drag at =0'-30 and makes the 0D vs.°t- curve

sharply fluctuate.

Increasing the cylinder diameter slightly increases the drag, for the feiring of the rudder is being worseried.

The cylinder roughness slightly decrease the dreg, for it

increases the turbulence of the flow. Eut there is rìot obvious difference between Rl and R2.

In air tunnel or towing tank rudder tests, s critical Reynolds number should be defined, above which the curve of drag coefficient, the slope of the lift curve etc. will not be affected by the

vari-tion the _{Reynolds number. From the}

for the conventional rudder the critical Reynolds number is in

the region of (1.5'1.9)x10 while for the rotating cylinder rudder

it is about 0.7X10

3. Position of the Pressure Center

(i) Except for the csse of k=0 where the pressure center varies nosition sharply due to the early stall caused by bad streamline,

the lo vs. o curves almost coincide with es.ch other in a slowly rising curve, especially when k?2.

Compared with the conventional rudder, the shift of the pressure center following the rudder angle of the rotating cylinder rudder is very small. E.g., when tue conventional rudder changes rudder

angle froLn 5°to 30; lo would increase from 0.15 to 0.35, with .

change amount of 0.2, while correspondingly the change of the rotating cylinder rudder is only C.050.1.

In backward velocity th& oressure center is close to the point of lp=O.3 at small rudder angles, while correspondingly Ip of the conventional rudder would he as high as 0.60.7. As the backward lift of the rotating cylinder rudder would reach the maximum at o(=10°when k3, the rudder angle should be rather small in the

case. This means the moment on the rotating cylinder rudder in

the case is much smaller than that of the conventional rudder,

for the position of rudder shaft, depending on the performance

in forward velocity, would be near lp=C.3.

When the Reynolds number is very small ('0.7X1C ₎ and the

rudder is in backward velocity, the flow around the rudder would be very turtul-nt nd unstrble, and the position of the pressure

center would change rapidly. luckily in th _{time the magnitude} of the moment is iot great.

IV. Some Special Phenomena Discovered and Their Interpretation

From the experiments sorne phenomena have 'been noticed. Although

some of them could occur only in special conditions, to recognize and understand them should be important to a more comprehensive knowledge of the rotating cylinder rudder, and should also be

useful to designers and users.

The authors try to interpret these phenomena. _{As the flow field} around the rudder is very compil ex and because of the _serious

ia-volvement off' viscosity, the explanation might be somewhat farfetched. Any more reasonable answers to the phenomena will be welcome.

1. AT ZERO RTJDDER ANGLE, THE RISE OF CL FOLLOWING k IS VERY SLOW

IN FCR'RD VTThCCITY, WHILE I

REACHING ITS NAXINtJI'. VlUE (OF ABOUT 1 .25) .kT ABOlIT k=4 BUT

DROPPING IF k CONTINU7S

_T:

since the 110w rounci the cylincer is strongly influenced by the main 'body of the rudder, the rotating cylinder cannot gene-rate _{lift as high as it is set alone in the incident stream,} and its lift is difficult to estimate. _{For this reason, except}

considering its influential velocity field, its contribution to

the lift will be neglected.

Oase 0±' forward movement. As the fluid sucked then _rojected

has origins from various direction, _{as shown in Fig.4a, the flow}

/

.13.

along the lower side can be approximately considered to be not affected by the cylinder rotation, so its contribution to the lift can he neglected. Since work has been done by viscous force during the course of accelerating the fluid by the rotating

cylinder, the flow projected by the cylinder has a somewhat high pressure; adding the likely existence of flow rflectiori

(see 4h) the rea where the oroectec

flo'v

the rudder su:-í'ace, the contribution o the flow along the unper side to the lift is also very small. deolte the incrense of

flow velocity aion this alce.

Cese of 'ceckward movement. The rotation of the cylinder affects the pressure distribution in both sides of the rudder surface:

its suction lessens the presste on the un:er side, and ita. projection rises the pressure on the lower orle. ;hen k is small, its increase makes the lift ascend, sad et shout k=4 the lift has corne to the

peak. If k continues to increase and reaches a large number, e.g. 10, the nowerful cylinder projection would propulse the stagnation area on the lower side forward to a spot near the leading edge (which is the trailing edge in the case of forward movement), after which a large region of circling flow with low cressure would be formed. In the cnse the lift would drop, and the pressure center would move forward. If the rudder angle is not zero, because the suction of the _{cylinder cannot prevent}

the flow from separation on the upper side, the lift would drop

sharply and even come out to be negative as the rudder ang] e

increas es.

2. WJj k5 THE DRAG- _{T ZERO OR SNAIL RUDDER ANGLES DOES NOT}

CHANGE MUCH, AND WHF »5 THE DRAG MY BE NEGATIVE; BUT IN THE

ANGL INCREASES RAPIDLY FOLLOWING- k

It cari be interpreted as that, a propulsive force is produced

b the rotating cylinder as it projects fluid backward slang one

side of the rudder surface. For exararle, in the case of forward riovetent, when k5, rs the propuJsive force is small and almost

ence11ed b- the mora; sed tangential force on the main body due to the oroection, the resultant drag does not change much; but if k is veri lare, the oronuisive force will make the total tan-gential force negative, and as the tantan-gential force dominates the

drag: at snail rudder angles, the drag may be negative.

V. Conclusions

Through sets of exoeriments, a comparatively comprehensive knowledge of the rotating cylinder rudder have been got.

The rotating cylinder rudder has been proved to be a high-lift rudder with fine performance. Its maximum lift is as high as 2.0 to 2.4 times that of the conventional rudder, and the slope of

its lift curve s.t small or middle rudder angles is about 20% to 40% largei-. It can generata a certain lift at zero rudder angle.

In general when k=2.O its lift would have been the optimum. Eut with k continuing to increase, the lift coefficient will stili rise, though rather slow with k increasing 1, the increment of

C'id

low-velocity msnoeuvring ai' ships, for although when a ship

cruising k could hardly surpass 2.0 or 3.0 du to the limited rotation r;tes of the motor running. th cylinder, Lt CoUld likel-rise to 5.0, 10.0, or ever larger durii- the ship setting sail, docking or in other cases of S]OW manoeuvrirp.

The performance of the rotating cylinder rudder in backward

.15.

be of the same level as that of the conven-ional rudder when it is at 30°rudder angle. This means that the rotating cylinder

rudder could afford a ship with rapid response and good. msnoei-vra'oility in astern movement.

In general the rotating cy] inder rudder has a slightly larger

drag than the conventional rudder, out is pressure center

posi-tion changes significantly more gently following the rudder angle. It is proved that a cylinder with diameter of the rudder

thick-ness will be more advantageous thn that with diameter of 0.75 or 1.25 times the rudder thickness. The cylinder roughness can

improve the performance of rudder, out it is not that the rougher,

the better. When roughing the cylinder by grooving, one must

avoid sharpness lest there would 'se cavitation appearing at high cylinder rotation rate.

Some special phenomena at high cylinder rotation rate and low velocity have been noticed. It would be favorable if designers

and users should accuaint with these.

Tho ceriments would Leve Leen more detailed. The selection of N&CA foil as the main body, the values of the cylinder diameter and the method of increasing the cylinder roughness were not

chosen under much consideration. The authors believe that if

efforts are payed on these aspects, there should 'oc _{a big potential} of improving the perfoi:inance of the rotating _{cylinder rudder and} m:kin it more co:npetent.

VI. Acknowledrements

The authors will like to eoress their gratitude to Ms ¿bu Jianhua, for her ardent assistance in preparing and conduting the experiments. We also wish to thank Ássoc.Prof. Sun Yibin

and Eng. Xu Zhanchong for their instructions and helps in build-in the mechanism.

VII. Notation

k: ratio of the c:/linder circumferential speed to the free

iritd

s resrn speeA,

6cV

ac: rudder angle

l: Reynolds number, Re=Vb/V

CL: lift coefficient, C=T./pSV =CNoO-Csin C»: dr _{coefficient, CP=D/PSV2=GN51+OTCCO}

lo: nori-di:nensional distance from the oressure center to the

ieadng edge of the rudder, lî=Kb+CM/CN Kc: talance area ratio of rudder

CM: o:ient coefficient, C=M/-pshv

coefficient of norml force, _CN=I/-9SV1

C,: coefficient of tngentii force, Cr=T/9SVt

d: cylinder diameter

b: chord lendth

S: rudder area

V: velocity of free stresm n: cylinder rotation rate, rpm

p : water density

Aendix I

2

L

56

89

k

1 11 12 13 14 15 16 17

Ct vs. k curve of two-dimensicn rotating cylinder

Appendix II Experiment Result

It should be pointed out that, the ip values of the rudders in backward velocity are correspondent with the leading edges

of the rudders when they are in forward velocity.

Following ere the Reynclds numbers corresonding

venous

velo citi es:

for tie rotating cylinder rudder: V=O.4m/s, Re=C.70x10'

V=O.Crn/s, Re=1 .05X V=O.8:n/s, Re=1.40X10' V=1.Om/s, Re=1.75x1O

V=1.25m/s, Re=2.18X105

for the conventional ruddr : V=1.On/s, Re=í.88X1C

V=.25m/s, Re=2.35K1C

C] ,Cd 2.0 1.5 1.0 0.5 Cl. Cci 2.8 1.5 1.0 0.5 L ..

!.

IAi?

-/

C. 7'

gr

-fr'

U

_{i. ,;ø}

'f

Fig. i

Vi.rn/s

Eig.2

0 10 20 30 40 50 60 70 80 RLF8(deg.

EIg.3

050

VH.Om/s

F19.4

D50 V1.@m/s(BR[WRf9)

4l

r

Il

IJ

¿4

mV/Fi

Cl Cd 2.0 LS 1.2 0.5 Cl , Cd 2.0 1.5 1.0 g. g ALFR(dg.

i

u.

-V,.

rA

_,.",,

'f

I

u-

I

u

' mii

P!"

WA

U

NUIRaI

Flg.5

Vø.8m/s

Flg.6

V1.øni/s

CI Cd 2.0 1.5

i.0

'p

AII

4---r

VA";

\

v'a

-.%

ri

-B

' a__suma

F1g8

040 V1.0m/s(ßRCWPR0)

Cl ,Cd 2.0 1.5 _{1.0 0.5} 1.5 1.0 0.5

i

rdìi

_,

-__VAk1U

V1

U

//

__VfdÒ

_{_VulU c,U}

_

v.Ò

__

FIg.9

V=.Bm/s

FIg.l

Vl.@m/s

O 10 20 30 40 50 60 70 80 ALFA I d.

Fig. 11

V=l.25m/s

VIA IUU

;;':' :U

V/A

'p

--u_

V

wwjv

2y

çv

,,< s

'I

,, u_s_

Flg.12

V=i.m/s(BACIWRfREJ)

3.0 2.5 CI Cd 1.5 1.0 0.5

iii!

_IIi

_'i-I'

_,

Uil

cAri_M

ii

s

"

-i.

_Iii

ni

i,_

will

VI

dV 555

i

fr.

F19.13

V=ø.6m/s

1.5 1.0 _0.5 0 10 20 30 40 50 Flg.15 R2

V1.rn/s

i

Lp_

_WA !_.

rl/A

-/IA

4'

í:4/

___

-

g'.

-

,--WA

j ::;'

_r

R2 V=1.m/s(BRCKWARO)

k

Flg.17

V1.øm/s

FIg.l8

C] 2.0 1.5 1.0 0.5

FIg.19

V=1.øm/s

Fig.2e

V=1.m/s

Cl 2.0 1.5 1.0 _0.5

FIg.21

FIg. 22

CONVENTIONAL RUDIJER Rl FORWARD AND BACKWARD SPEEDS

-' OMIS

PLP

-i,

rA

Appendix III References

"Application of rotating cylinders for ship mano euvrin", The Naval Architect, July 1972.

McGeough, F.G. arid Miliward, A., "The Effect 2 Cavitation

on the Rotating Cylinder Rudder", ISP.,Vol.28c.317,Jan.1981

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