Review of previously published rudder studies

Experimental Towing Tank

Stevens Institute of Technology

Hoboken, New Jersey

REVIEW OP PREVIOUSLY PUBLISHED RUDDER STUDIES

by

Karl De Larsen

Prepared for

the

David Taylor Model Basin

-

Navy Department

Washington. D.C.

under Bureau of Ships Contract NObs-22087

Job Order No. 5

1

July 1946

_{Technical Memorandum NO. 79}

TABLE OF CONTENTS

Page

SUMMARY 1

PURPOSE 2

SCOPE 2

PRESENTATION AND DISCUSSION OF RESULTS

Part

I, The Rudder in 4 Free Stream

Rudder Size

Aspect Ratio Thickness Ratio Rudder Shape

Balanced

or

Unbalanced

Presence of a Fin Forward of the

Leading

Edge

Location with Respect to a Hull

The

Rudder as an Appendage to a

Hull CONCLUSION ,REFERENCES Co P. 'ae?

Part II

4 8 11 11 13 23 24. 5 15

-17

TM - 7 9

. Variation of Lift Rate, dCL ay. Maximum Lift Coefficient, C, - (max)

,

Critical Angle of Attack for "Burbling" Leaation and Displacement of Center of Pressure Torque Coeffi-oient of Rudder (Stock at Lead-Lng Edge except where noted) Initial Turning Moment of Hull

Aspect Ratio Increases with

increasing as-pect ratio, R. Closely approxi-mated by: dCL 0.01746 Appears to have an effect but relationship is unoertain Deoreases markedly with increasing as-pact ratio No noticeable

effect Increases near-ly linearly

with increasing aspect ratio No experimental data available Trc ' b.ias + 1 ffir Thickness

Ratio Very small de-crease with

in-creasing

thick-nees ratio

Varies in ac-cordanoe with some law which

appears to

pro-ride an optimum

thickness for

maximum CL

Small effect. Trend not

deft-nits

Very slight

tendency to move

forward with in-, creasing thick-nese ratio Moment ooeffi-client decreases slowly with in -creasing thick-ness ratio No experimental data available

Rudder Shape No appreciable

effect Shape has sec-ondary effect,

Small increase

when broad part

of rudder is near surface

No noticeable

effect

Moved aft a i

small amount

when trailing edge of rudder is raked Small increase when trailing edge is raked

Shape has sec-andary effect.

Moment is less when major part of area is near surface. Balancied or Unbalanced Rudder No effect on dCL Effective only insofar as a gap is created between rudder and fin Effective only insofar as gap ie created be-tween rudder and fin Position of rudder stook has no effeot unless preceded by a fin or dead-wood Torque Coeffi-cient depends on the position of the rudder stock

I

No effect ex -oept where a gap is created behind rudder and hull or fin da. Fin with Na Gap between Fin and Rudder Rae negligible effect on dCL a-,-,--c. Approximately doubles value for rudder in free stream Delayed to much

greater angles Movesto or beyond \forward/Essentially the leading

edge but never

goes far aft of hinge zero. Rudder overbalanced if stock is at quarter chord point Turning Moment greatly in -creased

Fin with Gap between Fin and Rudder Has negligible effect on dC, r-,-, Only slightly greater than for rudder in free stream Only slightly greater than for rudder in free stream Moves forward i to or beyond \f leading edge

for small angle.,

Moves slowly aft

at angles above 100 Torque ooeffi-oient very small up to about 100. In-creases slowly at greater angles Moment much

less than with

fin. Propeller

hole decreases

moment.

Widen-ing gap

de-creases moment

Covering Hull For small Aspect

Ratios increaees to values given by twice the

As-peat Ratio. In-cretise less for

larger Aspect Ratios Decreases slightly for small Aspect Ratios .Increases for larger

val-us. Decreased one to six degrees, Maximum effect at small aspect ratios No noticeable

effect Moment Coeffi-cient greater

when rudder is

close to hull.

Data not con-elusive No experimental data available I ,

/

-I - --I

TM79

-1-SUMMARY

The

results of experimental studies on rudders published to data

have been surveyed rather completely in an attempt to

establiSh working

laws governing their performance both in a free stream and when rigged

an a hull.

Unfortunately, the results are contained in a large number

of isolated papers published by

individual workers

who have generally

selected the geometry of their rudders with solo specific objective or

test in mind.

This has resulted in a great amount of unrelated data

from which it is impossible to isolate the precise effect of varying

any one factor.

Certain relationships, such as the variation of lift rate

dCL

with aspectaspect ratio, can be definitely established, but others, such as

the effect of rudder thickness on the lift rata, can be only inferred

from incomplete data. Most of the "laws" which might have been form..

lated from this study fall into the second category and cannot be stated

precisely until a series of carefully selected experiments are completed.

The chart on the opposite page summarizes the first order

TM-79

2

-PURPOSE

The purpose of this report Is to assemble

_{and review published}

information on rudders, in order to evaluate

_{and suagrarize the}

col-lected results. _{Should it be found that}

_{information is not available}

to show the effect of geonetrical changes of the rudder on its

hydro-dynamic characteristics, a _{new test program can be planned more}

_ins.

telligent/y after correlating the _{existing results.}

The presentation and discussion of the available information on

rudders, as culled from the work of _{various investigators, fall natur}

ly into two major parts:

The rudder (with and without

_{a fin or dead-wood) in a free}

stream,

The rudder as an appendage to a hull.

The factors which can

_{influence the performance of a rudder}

_are

limited in number by its very simplicity,

since a rudder is, after all,

nothing more than a refined form of

flat plate.

_{These factors- are:}

Size,

Aspect ratio, Thickness ratio, Shape,

Balance or unbalance,

Presence of a fin or dead-,wood immediately forward of the leading edge,

Location with respect to a hull,

Location

with respect to i propeller or propellors.

The variation of each factor will be discussed

_{In terns of its}

resulting effect on the following hydrodynamic characteristics of the rudder:

dC

19

Variation of the lift rate,

----dck

a1-D.

Maximum value of the lift coefficient, CL

Critical angle of attack, i.e., the point at which "burbling"

or breakdown occurs,

Location of the center of pressure,

Torque coefficient about the leading edge,

Initial turning moment when the rudder is laid.

Itens 1, 2, and 3 contribute to the effectiveness of a ship's steering

and turning ability, while items 4 and 5 are primarily of importance in

the design of the ship's steering engine and rudder stock. Since factor

H and item 6 are definitely dependent upon the geometry of the hull, in

addition to that of the rudder itself, they will be considered only in

Part II.

When reviewing the available papers and reports, it becomes

immedi-ately apparent

that the great amount of data on rudders has been obtained

through

experiments designed to achieve some specific objective of a

spe-cialized nature. It is almost impossible to establish fundamental laws describing the performance of rudders, since practically none of the

re-suits of any one set of experiments is suitable for comparison and

corm

relation with that of

any other. A translation of Dr. Fischerle work at

Gatingen (1) is the only reviewed report in which a logical series of

controlled experiments isolate the effects

of various changes in the

geo-metry of the rudder. Unfortunately, the details of Fischer's experimental

method are missing. A large amount of the information for this report is

drawn from material written by Darnell (2), Baker and Bottomley (3),

and

Bottomley (4).

These references deal with particular hydrofoils whose

shapes prevent clean-cut isolation of the effect of changing their

vari-ous geometric dimensions.

TM-'79

m 3 m

TM-79

PRESENTATION AND DISCUSSION OF RESULTS

Part I - The Rudder in a Free Stream

A. Rudder Size

When studying haw the hydrodynamic

characteristics of rudders

are affected by variation of their geometry, it is convenient to

eli-minate the effect of rudder size by the use of dimensionless coefft.,

cients, defined as follows:

Force

Force Coefficient

A

72.

Moment

Moment Coefficient

V2 *

From each of the above general equations, a particular coefficient may

be defined in

terms

of the actual force or moment used.

For example,

the lift coefficient

CL

would be:

CL

i7A V2

while the pressure coefficient Cp would be:

Force Normal to Rudder

C

P

E

A

V2

2

Moment coefficients may be defined similarly.

Actually, the size of the rudder is

important when considering

particular full scale ships since the magnitude of the forces or

moments acting on a ship is proportional to the rudder area.

This

is not true, however, when scale effect is

taken

into consideration

as the value of the various coefficients increases slightly when

geo-metrically similar

rudders of

increasing size are compared.

Scale

effect is displayed most noticeably by the behavior of the rudder

near breakdown.

As the size

of the rudder Is increased, with a

°or-Lift Force

respondinely greater velocity and Reynolds Number, the character of

the breakdown appears to shift from a short, well-defined break in the

lift curve for model rudders to a very gradual transition observed in

the curve for full scale rudders.

The break occurs at essentially the

same angle of attack for all sizes of rudders.

A, study of the phen-.

omenon of breakdown as effected by size is made by Wood

(5).

For the purpose of this discussion, however, all hydrodynamics

characteristics

will be studies in coefficient form.

Therefore, the

size of the rudder can be disregarded.

B.

Aspect Ratio

The aspect ratio of a rudder is undoubtedly the dominant factor

governing its hydrodynamic characteristics. Variation of this factor

has the following results:

dO

le

The effect of aspect ratio on the mi511.92.21.11fLEEI2,

L

has been derived theoretically

by Jacobs and Anderson (6). Their

doc

results have been simplified by Darnell (2) to the follow.. ing approximations:

dC

0.01745

17

3l85+ 1

erR

wtore R is the aspect ratio.

A curve of the slope,

calcu-lated by using this

theoreti-cal formula, is plotted on

Figure 1 for comparison with

the experimental points by

Fischer (1),

Darnell (2),

Jacobs and Anderson (6),

Cowley (7), and Munk (8).

From the close agreement of the curve predicted by the

formula with the experimental

.06

FICiURE 1

Fischer pernell

Jaco%s & Anderson x Munk Flachsbart Cowley, Simmons and Coales Aspect Ratio 20 . 4 0 I ,L 6f0

TM-79

-5-t

T14-79

-6-0

2.0

1.5

1.0

0.5

0

FIGURE 3

Aspect Ratio

1

Z.0

Darnell

Fischer

Flachsbart

--o

S.

--o-o

-o

FIGURE 2

Darnell

Fischer

Flachsbart

Carney

Munk

4.0

6.0

C.)

Darnell

4.3

Flachsbai

_0 C aw ley

_e

Munk

FIGURE 4

Aspect Ratio

_.0

-a

80

60 ft 40 _ \0\B o

\

a

\

,

2 0-4 ,r)

Aspect Ratio

2.0

-,-4.0

6.0

0

dCL

points, it is evident that the theoretical values of /-0--c

are

accur-ate to within a few percent over the normal range of values of R

se-lected.

It is apparent that the

V2

law is followed quite closely,

since aswide range of speeds are represented, ranging from Darnell'e

value of 2.5 knots up to the wind tunnel speeds of Jacobs and Anderson.

2.. A conclusive statement regarding the effect of aspect ratio

on the maximum value of CL cannot be made on the basis or the

informa-tion at hand.

Experimental points by Fischer (1), Darnell (2), Cowley

(7),

Week

(8), aneFlachsbart (9

are plotted on Figure 2.

_Although

the work of Fischer (1) is suitable for establishing a relationship,

lack of information concerning his experimental

procedure makes his

re-sults less convincing. The rere-sults of

Dee-malts experiments are fully

described in his

report.

However, he uses

hydrofoils whose thickness

ratio changes from top to bottom so that a new variable may be intro-duced when determining the effect of aspect ratio on the maximum value

of CL. Although Cowley (7), Munk (8), and Flachsbart (9) all used flat

rectangular plates of constant thickness ratios, their results show

no

agreement.

It is therefore

apparent that

a generalization an the

be-havior

of maximum

CL cannot be established without more extensive

ex-perimentalwerk.

The value of the critical angle of attack (burble point) show-s a marked dependence on aspect ratio. The general shape of the curves on Figure 3, drawn through points obtained by Fischer (1), Darnell (2), and Flachsbart (9), are essentially

the same -- all showing a

_marked delay of the burble point as the aspect ratio is decreased. (Only those

results of Darnell which were obtained by using rectangular rudders

with identical thickness ratios are included.)

The displacement of the center of .ressure with increasing

as-pect ratio is shown on Figure 4. The values, which are compared at a rudder angle of 100, are from the data of Darnell (2), Cowley (7), Munk

(8), and Flachsbart (9). Darnell's points are

for a rectangular rudder

with a thickness coefficient of .096, while those of all the others

are

TM-79

-7-TM-79

-for thin rectangular platen. In general, it appears that asoect rat

has very little effect on the location of the center of pressure and

that for a given hydrofoil its position remains essentially fixed un

til the critical angle of attack is reached.

When

burbling

occurs

it is indicated that the shift aft is greatest for the larger aspect

ratios.

5.

Since the

s?_ar_fa_zttheldi/toruecoefficientaleaied, Cm, is

a function of both lift coefficient and position of the center, of

pressure and since both of these are functions of aspect ratio, it

is to be expected that the torque coefficient will also be a function

of the aspect ratio.

The location of the center of pressure renains

essentially fixed up to the burble point so that the curve on Figure 5

of the torque coefficient about the leading edge followe the trend of

the lift coefficient.

0,3

0.2

0

FIG7RE 5

cC = 10

Aspect Ratio

jarnell

Flachsbart

4.0

C..)

C.

Thickness Ratio

Very little information is available to show the effect of

varying thickness ratio. Fischer (1) used a logical approach to the

problem by measuring the lift force at various angles of attack,

us-ing a constant length and an aspect ratio of 5.

Darnell's hydro

io

foils (2) are all tapered in section from top to bottom so that they

can be represented only by using average values of thickness

ratio,

which may or may not be accurate for present purposee.

Sone wind

tunnel data on airfoils obtained by Jacobs and Anderson (6) are

ire-eluded.

1.

The trep-dimeneional airfoil theory predicts that the slope

of the CL vs.oc curve should be unaffected by the value of the

thiek-ness ratio.

Fischer's results, as plotted on Figure 6, are in

agree-ment with the theory.

Darnell, and Jacobs and Anderson observe a

slight decrease in the slope of the lift curve with increasing

thick-ness.

The theory, however, may be somewhat in error since it neglects

the effect of viscosity.

In any event, changing the thickness

ratio

has a relatively small effect on the lift rate.

1.5

-0,5

0

FIGURE 7

Darnell

Fischer

Jacobs and

Anderson

Thickness Ratio

O2

0r1

2.

The effect of varying the thickness ratio on the MAXiMUU

value of CL has been investigated by Fischer

(1), Darnell (2), and

Jacobs and Anderson (6)0

Their test results are shown on Figure 7.

For a hydrofoil of any given profile, there appears to be an opti

man thickness for a maximum CL.

TM-79

FIGURD 6

-0.15

_Darnell

Fischer

-

Jae obs and

Andersom

.10

-0- --

--

0

-0.05

Thickness Ratio

0

0 1

_0/2

TM-79

10

-3.

It seems fairly evident that thickness ratio has a small

ef-feet on the size of the critical angle of attack, as shown on Figure 5.

Darnell (2) and Jacobs and Anderson (6) show that the magni

tude of the thickness ratio has a negligible effect on the location of

the center of pressure.

The displacement aft of

the center of

pres-sure after the rudder reaches the burble point appears

to

be greatest

for the smaller values of the thickness ratio.

Since the center of pressure remains essentially fixed as

the

thickness ratio is changed, the torque coefficient about the leading edge varies in the sane

manner as the lift coefficient.

The curves on

Figure 9 above, from data

obtained by Darnell (2) and Jacobs and

Anderson (6), show the expected small decrease in moment coefficient as the thickness ratio

increases.

FIGURE S FIGURE 9 40 0,20 _

30

9.15

a

0

20

P4 r-i

-

--0.10

0

-

0-0 Darnell 10 Fischer Jacobs and 0.05 Darnell acobs and Anderson Anderson Thickness Ratio 1

Thickness Ratio

1 1

0

0.1

0.2

0.3

0

0.1

0.2

0.:

-a

Rudder Shape

Since it is rather meaningless to set up

_{a numerical factor}

de-scribing the shape eta rudder, the effect of

changing its outline

will be discussed only

_{qualitatively by summarizing the results of}

Darnell (2). Although

the five shapes tested do not cover an extreme

range, the results indicate that shape has no appreciable effect

_on

the value of the lift coefficient _{or its variation with angle of at..}

tack.

_{The position of the center of pressure seems to be affected}

slightly by the outline, chiefly when the departure from a

rectangu-lar shape is at the trailing edge. _{The maximum lift coefficient also} appears to

be somewhat greater under

_{the same conditions, although}

the angle of attack at which the maximum lift

_{occurs appears to be}

unchanged by the raking of either the leading or

trailing edge. It

may thus

be generally concluded that the

outline of the rudder has

only a second order effect on the hydrodynamic properties of _{a rudder} when it

is tested in a free

stream. This conclusion is confirmed by

Baker and Bottomley (3), Bottomley (4), and King (10), who determined

from tests of rudders on models that the shape of the rudder is rola..

tively unimportant, except for triangular shapes with the broad part

near the surface. Such rudders display a smaller lift coefficient

and a law slope when

CL

is plotted against the angle of attack.

Balanced or Unbalanced

There is no experimental data available for

this report on the

ef-fect of changing a given

rudder from an

unbalanced to a balanced, or

partially balanced, condition. Cowley (7) has verified the

expecta-tion that

the hydrodynamic

_{characteristics of the}

_{rudder should}

_remain

the same, except for

the torque

or torque coefficient about

the rudder

stock.

The obvious

decrease

in the torque on the rudder stock as the

stock moves closer to the center of pressure is well established. It

is known from

the

data collected for this report that the location of

the center of pressure is not stationary so it

is therefore impossible

to

balance the rudder for all angles of attack.

_{Furthermore, when the}

ship is backing the center of pressure moves to a point approximately

TM-79 .

-TM-79

-12-20

le,

1.0e

05

FIGURE 10

COWLEY

Rudder Hinged at Fin

Rudder Hinged at Quarter

Chord Point

Rudder without Fin

10

20

Angle of Attack, Deg.

30

40

0

10

20

30

2.0

FIGURE 11

MUNE

Rudder Hinged at Fin

--- Rudder without Fin

1,3

1.0

0.5

25

of the

chord length

forward of the aft end of the rudder.

Con-sideration of this condition must therefore partially govern

selec-tion of the posiselec-tion of the stock.

In those cases where a fin or dead-wood

precedes

the

rudder, the

variation of the space between them, caused by

changing

the angle of

attack, has a major effect upon

the

flow around the rudder, as dis-cussed on page 15. The location of the rudder stock then becomes

portant for reasons other than the size of

the steering engine.

F. Presence of a Fin Forward of

1,,LLIe12121:21121

Although this part of the report is

concerned with the isolated rudder in a free stream, it

is appropriate to consider here the

out-come of placing a fin or

dead-wood immediately forward

of

the rudder.

This has a marked effect which is

primarily dependeet on

the size of

the gap ferried between the fin and rudder as the rudder angle is changed. In his investigation, Cowley (7) included three cases: a

flat plate rudder, of aspect ratio 1.5, hinged at the trailing edge

of a fin;

the sane rudder hinged at

_{approximately}

the quarter-chord

point and with no gap between it

and

the fin

when the rudder was set

amidships; end the sane rudder without a fin. The

other investigator,

Munk (8), tested two cases:

a plate rudder, of aspect ratio 5,

hinged at the trailing edge of a fin; and the sane rudder in a free

stream with no fin.

Their results, which are shown on Figures 10 and 11, indicate

that, for small angles of attack, the presence of the sires has little

effect on the lift coefficient and its variation with rudder angle.

If the rudder is

hinged directly to the aft edge of the fin,

break-down is delayed until the rudder angle is greater than 400,

thus

mak-ing possible extremely large maximum lift forces. If circulation

around the leading edge

is permitted by

leaving a gap befeieen rudder

and skeg, the maximum lift coefficient and the critical angle

are

only slightly

greater

than for a simple flat plate rudder in open

water,.

The most noticeable effect of a fin on a rudder is the location

T11-79

-14

0.4

0

00- "I-,

1.00

0.75

0.50

0.25

0

_

-FIGURE 12

COWLEY,

Rudder Hinged at Fin

Rudder Hinged at

Quarter Chord Point

--- Rudder without Fin

0.5

Holm Angle,

1 1

10

20

30

1.0

-

43 r-1

FIGURE 13

Gap Width/Chord

1 KEIT2F DC=

_10°

20

50

P.

40

1.5

g

4,

40

Deg.

0

f it carter of pressure. At small angles, this point appears to be on the seng, since for all practical purposes, as shown experimentally by Cowley (7), the torque on the rudder stock is essentially zero up

to angles near 100. At greater angles, the behavior of the center of

pressure depends upon the formation of e

gap

betreen rudder and skeg.

When such a gap is formed, the center of pressure is diepleced eft

with increasing rudder anele. When no opening occurs, however, the

center of pressure appears aft of the stock at about

100

rudder angle

and gradually

moves toward the trailing edge with increasing rudder angle to a point roughly 55 of the rudder chord. As the helel angle

is further increased, the motion of the'center of pressure tends to reverse its direction of displacement until it again falls near the

hinges. This is shown by the curves en Figure 12.

In general, the

presence

of a fin just forward of a rudder

greatly reduces the torque coefficient by shifting the center of

pressure

close to the leading edge of the rudder.

Kempf (11) measured the effect of a gap between, the rudder and

dead-wood on the initial turning moment of a self...propelled model.

He considered three cases:

an unbalanced rudder at the trailing edge

of the fin; the same rudder separated from the tin by a distance of

half the chord lengeh;and finally the rudder moved aft a distance

equal to its own chord.

As shown by the curves on Figure 13, the

turning =pent decreased considerably as the gap was widened,

C.

Locetion with Res ect_to a Hull

The influence of a "covering" hull has been studied by Darnell

(2) who neunted a hydrofoil very close to the flat bottom of a boat.

He rode corrections for the wake of the boat by measurine the

vorti-cal velocity distribution set up by the hull and averaging this over

the ruder surface,

His tests indicate that the proximity of the hull modifies the

flow to such an eeeent that the effective aspect ratio of the rudder

is doubled. A Curlie of dCLAICC, calculated by using the theoretical

formula on pace 5 , is plotted on Figure 14 against the geometric

TM-79

-16-0.08

0.06

0.04

0.02

FIGURE 14

1

2.0

4.0

A DARKELL

peat ratio.

Darnell's experimental points show good agreenent with

the theoretical curve at the smaller values of aspect ratio.

For

as-pect ratios above unity, there is a trend toward the values of

dCildcc-observed for the rudder clear of the hull.

A study of the behavior

of the burble point also indicates an increase in the effective as

-pe ct ratio which approaches twice the geometric value at the smile]

magnitudes.

0

1 2 3

4

Scale, in. for model

LWL

Part II

The Rudder as an AlopdacaFto_a Lull

The data derived from a

_{survey of studies made with a rudder rigged}

on a hull are inadequate to establish fundamental

_{relationshipe.}

_{It 1,2}

possible only at the instant that the

_{rudder is laid to isolate its}

in-fluente - that is

_{before an appreciable yaw angle has}

_developed.

_When

the 'ship attains 4 large yaw angle, it

_{becomes virtually impossible to}

separate the farces set up by the rudder

_{alone from those due to the}

as>nnetry of flaw about the rest

of the hull.

The work of 3aker and Bottonley (3) and

_{Dottemley (44 124 13) on}

the rudder as an appendage to

a

FIGURE 15

OUTLINE OF MODEL RUDDERS

hull encompasses the work of othor

in-vestigators to such aneç

tent that the information

fer the remainder of thia

,report will be drawn only

from these sources., .Their

results are shown in

Graph-ical form on following

pages

in Figures 180 17. 18 Whore

coefficients of pressure and

initial ship turning moment

are given as functions of

the rudder angle.

Tests were run on the vari

cus rudder shapes shown in

Figure 15., Since they

are

all flat plates of &nal/

thickness ratios and nearly

equal aszeot ratios, it is

impossible to establish the

influences .,,t1 these factors

on the test results.

The

figures shoW quite clearly,,

however, that the shaoe of

the rudder has little

_effect

T}s1470

FIGURE 16_ rCURVES OF APvz 2.0 1.5i WITH VARIOUS ' 1, SCREW

SHAPES BEHIND SOLID FIN PLATE

SPEED 8 KNOTS FOR 400 SHIP 1°-.411-1.

1

SPEED 12 KNOTS FOR 400 SHIP

A PORT HELM -40° 200 0 WITH SCREW

> 1.0

20 WITHOUT SCREW B& D A 20° 40° -I 0 STARB0ARD IHELM

PROPELLER WORKING COUNTER CLOCKWISE IN SCREW APERTURE WITH PROPS NOT WORKING PRESSURES ARE SAME FOR _{PORT AND STARBOARD HELM}

FIGURE 17

CURVES OF

9

VARIOUS

SHAPES BEHIND MODEL

SPEED 8 KNOTS FOR 400'SHIP

SPEED 12 KNOTS FOR 400' SHIP .6 4Q.°

.?0° AT 8 & 12 KNOTS D AT 8 & 12 KNOTS PORT HELM le 0.8 0.4 Q. 1.4' ₁₁₂

1.0

WITH SCREW

1,2

1.4 D WITHOUT SCREW AT 8 & 12 KNOTS 20° 40° 1 1 1 STARBOARD HELM -1.5 B a.

_-

_0.2

_-0.6

A -0.8 I TH SCREW

1.0-on its hydrodynamic characteristics. Rudder C may be an exception

since

this form differs

from types A, B, and

D because of the larger fraction of its area near and

above the

waterline.

Several conclusions may be drawn from tests made by Bottomley

(12, 13) on rudder D under a variety of conditions.

The wake due to the hull reduces the value of all rudder

coefficients for

a given hull speed.

If a rudder is in a

propeller race, its hydrodynamic coef-ficients tend to increase for a given hull speed.

The coefficients of

a single rudder between twin screw are

essentially the sere as when the propellers are not working, except

at those rudder angles

where

the rudder swings into

the

race of one

of

the propellers.

A screw

aperture in the skeg

or a gap between the rudder

and skeg diminishes the initial ship turning moment coefficient and

the torque coefficient about the leading edge.

This confirms the

work by Kempf (11) cited in Part A, page 15.

A given rudder on a single screw ship will have larger ini-tial ship turning moment and pressure (lift) coefficients in one di-rection than in the other. Bottonley (12) has compared

the

perform,-ance of several rudders of different shapes

in the race of a single

screw rotating in a

counterclockwise direction.

The profiles of the individual rudders

arc

shown on Figure 15 and the results of the

tests

are

shown by

the curves on Figures 16, 17, and 18. It appears, in

general, that a rudder of the shape C. with the greater portion of

its area near the surface, has larger force and moment coefficients

when the rudder blade is moved opposite to the direction

of motion

of the top blades of the screw. If a rudder is of the shape B, with

the majority of its area aft of the lower blades, then larger forces

and moments are set up when

the rudder is turned in the direction of

motion of the upper blades. A brief

consideration

of the flow

condi-tions indicates that this

behavior is

to be

expected. Forces and moments measured in corresponding right and left positions of a

near-ly rectangular rudder should yield equal forces and

Merents in

either

direction. An examination

of Bottonleyls results, plotted on Figures

5)

TM-79

19-TM- 7 9

PAGE-20-SHIP TURNING MOMENTS WITHOUT PROPELLER

AND

WITH PROPELLER WORKING

FIGURE 18

8 KNOTS I 2 KNOTS -A WITH 0 _SCREW

"/

-.00

WITHOUT SCREW AT AND 12 ENOTS 2'0° 40° STARBOARD HELM -0.50

WITHOUT PROPELLER THE SHIP TURNING MOMENTS WERE THE SAME FOR PORT AND STARBOARD

-100 HELMS -1.50 WITH SCREW -.50

7/

-0.50 //

//

40° PORT HELM 2'0° 8

---16, 17, and 18, essentially verify this conclusion.

When twin screws arc used, there is an appreciable effect

from the direction of rotation. In general, inboard rotation increases

the torque and forces upon the rudder by approximately 20

over the

values

for outboard

wheels.

The

initial ship turning moment is modified in the same may.

Inboard rotation causes an increase of about 5% over

the moment for

outboard rotation. When propellers are used with only a fin fitted with bosses, the

direction of

rotation makes practically no difference

in the

force and moments

The relative fore and aft positions of

the rudder and whether

twin or single screws

are

used has little or no effect on the forces and turning moment.

Increasing the diameter, pitch and

diameter-pitch ratio

pro-duces only slight increases in rudder force, torque and ship turning moment.

Bottomley tested

identical

rudders behind flat plates and

also behind models of different prismatic coefficients. The observed

rudder

forces and initial ship turning moments were somewhat less

when the rudder

was behind

the model than when it was behind a flat

plate. Variation in the fullness of form of the model did not appear

to have an appreciable

effect on the forward motion of water at the

stern.

The pressure

on a rectangular rudder when deeply submerged

on a single screw ship followm closely the formula of Baker and Bottomley (3),

P

A

Vz,

where K is a coefficient depending

upon the

aspect ratio and rudder

angle. For rudders

of

any shape behind a single screw ship, the pressure is modified by Baker and Bottomley to the form

P K1 A1.04 V1.85

where Ki is now a function of rudder angle only. The V2 law does

not appear to be quite correct when the blade is near or partly

above the waterline. The relationship for partial submergence does

not seem to have been discussed in any of the reports available for

this

study.

n-7

21

CONCLUSION

The hydrodynamic coefficients governing

the behavior of rudders

of normal form and size appear to bear comparatively simple

relation-ships to the

geometry of the rudders. Experiments

performed in the

past scarcely permit the formulation of exact quantitative laws where.,

by the

effect of changing any one dimension

_{or ratio of}

_{dimensions can}

be determined. A series of integrated tests

_{might be performed to}

establish

these laws.

However,

the approximate qualitative laws shown in tabular form in the Sunnary are probably adequate for many

practi-cal purposes. This is especially true because the

interference

ef-fects

_which

_{appear when a rudder is fitted to a hull will always cause}

deviations from any quantitative law. In fact,

the increased accuracy

with which the basic laws for isolated

-rudders could be established by

more extensfve tests might well

_{be over-shadowed by the relatively}

-larger interference effects due to

the

_{hull, propellers and other}

ap-pendages when the

rudder is rigged in the conventional _manner. It is believed that

future

work should be

aimed at establishing the

_relative

importance of

_{the interference effects, so that there will he an}

ade-quate basis for decision as to whether it is _{more important to refine} available rudder data, or to further investigate

_{interference effects.}

-TM-79

TM-79

REFERENCES

Fiacher, "Calculation of Rudder

Force."

_{Volume 19,}

pp. 259261, September 1938. United States Experimental

Model Basin Translation No. 52, November 1938.

Darnell, R.C.: "Hydrodynamic Characteristics of Twelve

Sym-metrical Hydrofoils." United States Experimental Model

Basin Report Mc. 341, November, 1932.

Baker, 3.S., and Bottomley, G.H.:

"Maneuvering of Ships

--Part I -- Unbalanced Rudders of Single-Screw Shins."

In-stitution of Engineers and Shipbuilders in Scotland, p. 522, 1921-1922.

,(4)

Bottomley, G.E.:

"Maneuvering of Ships --

Part II --

Unbal-anced Rudders of Twin-Screw Ships." Institution of

Engi-neers and Shipbuilders in Scotland, p. 509, 1923-1924.

(5) _{Wood, D.h.: "Tests of Large}

Airfoils

_{in the Propeller Re..}

search Tunnel Including Two with Corrugated Surfaces." National Advisory Committee for Aeronautics Report No.

336, 1929.

(5) Jacobs,

E.N.a

and Anderson, P.E.: "Large Scale Character-istic of Airfoils as Tested in the Variable Density Wind Tunnel."

National Advisory

Committee for

Aeronautics,

Report No. 352, 1930.

Cowley, Simmons, L.F.C., and Coales, J.D.: "The

Ef-fect of Balancing a Rudder, by Placing the Rudder Axis

behind the Leading

Edge, upon the Controlling Moment of

the Motion." Technical Reports of the Advisory Comprittee

for Aeronautics, p. 154, 19161917.

Munk, Ms "Systematische Versuche and Leitwerkmodellen."

Technische Berichte der Flugzeugmeisterei, p. 168, 1917.

Flachsbart, O.: "Mcssungen and ebenen und gew61bten

Plat-ten." Ergebnisse der Aerodynamischen Versuchsanstalt

zu Ggttingen, Volume 4, P. 96.

Ting, J. Foster: "Rudders."

Institution

of Enginec,rs and

Shipbuilders in Scotland, Volume XLV.

I

-24-(1)

(g)

'Kempf, C.:

das Steuern ix

freien und in beyenzten

Wasser irch verschiedene Ausbildung der Schiffsforn be-einfluc,t ward." Worft,

Roederei*

Hafen, July, lc31. Bottonley, ":ianeuvering of Ships Part Ill

--Unbalanced Rudders behind Single-Screw Ships, Effect of

Varying fulness of Form."

Institution of Engineers and

Shipbuilders in

Scotland*

p. 455, 1926-1027.

Bottomloy, G.R.:

"Maneuvering of Ships Part IV

--Unbalanced Rudders behind Twin-Screw

Ships*

Effect of

Varying Fulness of Form,"

Institution of Engineers and

Shipbuilders in Scotland, p. 94* 1930-1051.

"Wie (12) -(1a) TM-7S