DAVID W. TAYLOR NAVAL SHIP

RESEARCH AND DEVELOPMENT CENTERBethesda* Maryland 20084

AN INVESTIGATION OF APPENDAGE DRAG

SE

. AI P. LASKY•

L. r'2

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[. SPD-4 58-014 TITLE (and Subtitle) 5. TYPE OF REPORT & PERIOD COVERED

AN INVESTIGATION OF APPENDAGE DRAGA- SPD Report

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7. AUTHOR(,s ". CONTRACT OR GRANT NUMBER(&)

Marc P./Lasky / i9. PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT, PROJECT. TASK

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I8. SUPPLEMENTARY NOTES

Uk. KEY WORDS (Continue on reverie side li neceeoas ' and Identity by block number)

Appendage Drag; Resistance, Interaction and Scaling of Appendages; Reynoldsnumber

20. ,4STRtACT (Continue on rev.,,. side if necesgary and Identify by block numb*?)

The purpose of this report is to provide information about the resistance,interaction and scaling of appendages. A calculation procedure is developedthat can be used to compute the Reynolds number dependent components of

appendage drag. A correlation is made between the calculated values of drag

and data obtained from bare hull and appended ship-model resistance rests.This correlation indicates that t'he mathematical model is an effective means of

predicting the viscous drag of appendages and that the added drag due to pres-

.are as well as interaction between appendages and the hull form is of a smallFORM .DD ,•AN 7, 73 17 EDITION OF I NOV 6S IS OBSOLETE INtASSIFI•D - -,

!SN 0102-LF-014-6601

SECURITY CLASSIFICATION OF THIS PAGE (I&hIon Data Entered)

_ • ° o"

-. ?A&BLE OF CONTENTS(Page

AIDI..-STF7A-TtIE INFORŽ!TIO:N. .. * .... aaa *a*aa

I £NT?101.CT ION. & .aaa.2

VJiE!TcLEXPRESSIO'NS OF APEN.DAGE DRAG.. . .. . .. . .. *. . . . 4

M- APPDENDA,.GE MCO-PNENTS . . .a. .. . .. .. . . . . te .a 4

MIOCITY - AGNITUM XIDDIRECILtON. . .. ........ . ..*.*.* 4

I UDRSRTSADSAIIE FIN .o. . . . . . o .7

Reynolds Number Used to Obtaiu Cy. o . 0 . 0 . 0

flat Placre Friction R~esistance. ......... a..a*.8

S esl~stance. Due to Velocity Augmentation o . . 0 . . a a

1tess'jre or Separation Resistance .- . . . a * 0 * * . *

Add~d "Resistance fLue to Intersection with Hull or StrutB3arrel. . .. . . .. a*.aaa*.aa. **...-ts Drag Deo luntness of Trailing Edge .a*.***

GWLUP 1 -- Sa&--TiZG.. STIE!CTUBE BOSS INGS . AND. INTERMEDIATES7RUT. DARPRELS . . a . . . *.aa.a a a a 0 0 * a 0 a a a a .a

frIctic-a Resisraace and Reyrioles Number . . . . . . . . . 10

Pressure PFesistra-ce Corrected for Crossflo-w . . . . . . . .* 10(

Base Drag Due to Bluntness of 7airwater-Ending. .. aa*aa12

GMUP TV - BILGE KEELS AIM) SKEGS .a aaa apaa a13

~APP~D'A COfIMUVE-11 PROGRA,'t OF TH{E JNAThEF!ATtCAXL MlODEL .. a*aa. .14

CORPELAtION OF THE 11AT1lE-?*;7ICAL MODEL W1ITH !5.ODEL TESTS. .aaa aaa14

4 &3rJEF DESCRIPTION 0-7 THE SHlP-1.:ODELS &. & . .. a. 14

]?ALSENTATION OrFIPEL DATA ... * .aa.aa . *. ... ..

DISCUSSIONOF COME-SLATON. .o .a a .a.. .. .a .a .al

TErACTEON BEV.-EEN] APPENDAGES AID IHULLJ. aaaa aO ~

M~CLUS 'ZNS . . . a . .a .a .a a . . 20

. . a . . a 0 a . a a. 21

a2P~r;ED!X I -LISTING OF CO::PbTE-cR PUGýWtI . . . a . . . . . a a . . . . 27

"~PEN:DIX 11 - IN Fr OXM!T E0~CO.-PUTEP. Pr.OGI021 ,WPEN9l. . * 41 .A

APPEN:DIX:II - otrPr aW*00 90 0

R~EVERENCES . . . . . . . a . a a . . * aa*a*

C _ J

0 >"4.. -- 4 r

to Lk1w ~ ,.-4 ... mom"

"2 LIST OF FIGUpRS

Figure I - Graphical Representation of the Reynolds Number Page"Formula as a Function of Velocity. Length, andTemperature. . . . . , , . . . . a * . e . 0 . a * . 22

Figure 2 - Curves of Laminar, Transition and Turbulent FlatPlate Friction Coefficient as a Function of ReynoldsNumber * * * . e. . * . . . .. . v a 0 * a., •* * .23"Figure 3 - Comparison of Values of Appendage Drag Obtained fromthe Mathematical Model with those Deduced from CenterBare Hull and Appended Ship-Model Resistance Tests . . 24Figure 4 - Model Scale Differences Between Center Tests and the"1 athematical Model . .....

. 25Figure 4a - Comparison of Values of Appendage Drag-as a Percentageof Bare Hull Drag Deduced from Center Bare Hull and

Appended Ship-'!odel Resistance Tests . . . ...i

.. - . . . 26Figure 4b. - Com'qparison of Values of Appendage Drag as a Percentageo: of Bare -Hull Drag Deduced from Center Bare Hull andAppended Ship-Model Resistance Zests . o • , . • * * . . 27Figure 4c - Comparison of Values of Appendage Drag as a Percentage.of Bare Hull Drag Deduced from Center Bare Hull andAppended Ship-Model Resistance Tests 2 8 , . •.,.,2* .

LIS. OF TABLESTABLE I The Hull Forms . . . . .

16TABLE II -. The Appendage Suits.

" iii iI:

-

U'* .MDZNCLATI;RE

I*chord length

-S Coefficient of flat plate friction

Spressure drag Coe fficient

diameter

L 1en4th of a•pendase

base resistance due to bluntness of trailing edge"3. flatpltae frictonal resistance

"added resistance due to intersection

pressure or separition resistance%A Velocity augmented resistance

"planforn area of one side of appeadage

"projected area of base or trailin edge* thickness

* -, S thickness of base or trailing ecge (V valocity I

cross flow angle (angle between hull and appendage)S::neiatic viscosity

'C mass density

tI

•.5.

* - . . -i ii i

•

-, -

ABSTRACr

The purpose of this report io to provide information

about the resistance, interaction and scaling of appendages.

A calculation procedure is. developel that can be used to

compute the Reynolds number dependent components of appendage

drag. A correlation is made between the calculated values

of drag and data obtained ftom bare hull and & •ended

-ahip-model resistance tests. This correlation indicates

tbat the mathematical model is an effective means of

predicting the viscous drag of app ndages and that the added

'drag due to jressure as well as interaction between appendages

and the hull form is of a small order of magnitude.

AD.U41NISTRATIVE INFORflATION

This study was authorized under the Naval Ship Systems Co•and --

Exploratory Development Program in lHydrodynamdcst Budget Project 32, and

was funded under Subproject SF 35421, Task 1713.

Ai.

I -a - a

ýY,

I DRODUCTMO k

I

Ship appendages refer usually to element:- outside the main hull, such

as shafting, shaft supporting struts and bossings, power transmission pods

and struts, bilge keels and control surfaces. It has been common practice

to measure the drag of these a pendages as the difference In drag w -conducting resistance tests with a ship-model in the bare hull and the

appeuded cond•tlion. These measurements provide a gross assessment of the

total drag of appendages plus interaction effects for a particular design,.

but they do not give detailed drag data- for eachi appendage, nor inter-

t actions between hull and appendages.. The designer does not'have sufficient

Information to improve designs where the, combined drag is unduly high.

Furthermore the extrapolation, from model to Sull-scale,, of appendage drag

±s-questionable at best:.

"A procedure for designing appendages was presented in 1953 by Philip

-Handel * In his summary, Mandel states that scale effects of appendage--

=ea-ist•cnce ... are Lmportant not only in accounting for part of any discreq-

tanciez: between model power predictions and full-scale results but also ia

:establishiug the validity of comparative model testing conducted for the

purpose of evaluating competitive appendages-• Fundamental studies and tests

of individual appendages over a large range ofRey'nolds nuwbers are needed

for this purpose." In 1957, E. P. Clement conducted such'a study. using

-appendages from a planning boat Clement concluded that the resistarce

redictions based oa previous model. tests'were'.too high-by-about 2.9% when

they were compared with his tests. He-further- concluded that this error .Ya"

a scale effect due to the fact that below a Reynolds number of 106 the extrap-

olator used with the Schoenherr friction line was not steep enough. , In

.1.966, Hadler 3 developed mathematical ex.ressions for" predicting the drag of

planing boat appendage- and used Clement's work to determine the accuracy oE

his rmechod.

1 References are listed on page 55.

2

0 *i

0 The present task would appear to be to verify if the-works by Clement

and Hadler can be applied to displace'ment type surface-ships. The major

problem encountered in this area is in predicting the flow- In way of -the

appendages. l1hereas in a planing boat; it may be assumed-that the flow is

parallel to the bottom of the hull and has the some mag~aitude as the boat

speed, this is not necessarily the case for displacecneut ships.

This report.vwill. discuss -ways of eitimating the magnitude" and direction

of. the velocity in way of the appendages. Thenw amathematical model will

be developed for estimp-ing the.Reynolds number dependent drag of the

following.appendage components: *

-1. Rudders,

2. Shaft support struts,

3. Stabilizer fins,

-' 4. intermediate and main shafts,

5.. Sterntube bossings,

6.. Intermediate and main strut barrels,

7. Bilge Keels, and

8. Skegs.I

The results obtained from the mathematical modeL are then- correlated with

uodel.rest.data and there.is a.discussion.of the-induced'forces and the

interaction between the appendages and the'hull; --

-. S

.--

.I-

* It should be noted that although this report- does not., cover such appendagesas power transmission pods or right angle dr.;ve.units, information regaidingthese appendages may be found in References'4"and-5;*It*is hoped, that at alater date expressions will be developed for these appendages-as there would

appear to be quite a demand for this information- in the future.

3

* S *A

" .... ".MATHEMATICAL EXPRISSIO,•'S OF. APPENDAGE DAG

.In.the development.of mathematical expiessions-that cea predict the, drag

of the aforementioned appendages.it was necessary- to*rmake-assuxnptions so

that the calculations. could be made'.with :relative .ease and still, be

applicable.,..The first .major.assumptio-.is-.that- the-appendages can be

divided into their, component .parts,' the drag-of-each" component being

calculated separately and .therefore. the:total-appendage-drag is equal to'

the sum of the drag.of each appendage; -The'second-majora-ssumption is

that the drag.of.the znpendages is considered-:to-be-viscou: in nature.,

(These assumptions AlI be discussed:In- further- detail'later, in the tex't.).

Other assumptions will be discussed:for-each- case and-specific references

are-noted next to.each expression. '

THE APPEIDAGE COMOPONENTS -. -.

The appendages. considered. herein are brqken- down into the followLig

.groiups: - - ("Group I Rudders, struts, and stabilizer fins;

Group II Steratube bossings, intermediate shafts, main shbf:s,.tand intermediate strut barrels;.

Group III Main strut barrels;

Group- IV - Bilge keels and skegs.

-Groups I and II are treated as tw-io-dimensiornal'sufaces'C-roup•lII jis treated

like a body of revolution and Group IV is treated similar to a flat plate

friction plane..

VELOCITY - MAGNITUDE A;ND DIPECTION

In the preliminary design stage, more often- than-not;" the designer can

only apyroximate the velocity at the'stern. -At-presentthere-are no simple -

4

* . - I -" - -"" -'' o

:. -.., . , .-. - • • . :

.- -. . - -. - - -

methods for predicting the flow in way of'a ship's appendages. The Douglass

S•Aircraft Company, Inc. has developed* a* computer'programufor calculating

potential flow about arbitrary three-dimensional-bodies* (Reference 6).

" •The Douglass program has been used successfully- in several'cases to predict

the flow about ship hulls. There has'been, some-success-in-predicting the

pressure distributionover a bow-mountedHsonarwome. "owever. in the

early"stages'of this project, an attempt-was'made-to-predict the flow at

the stern of a ship, a-id it,.was concluce" - that- this-method-was too expensive,

time consuming, and necessitated- information- which- might- not necessarily.

be available to-tbe"user during, the* prellmln7r" design- stage of the hull.

For simplicity, if we restrict'this'investigdtion-to ships with

multiscrew" propulsion systems that have some-type-of transom, stern with a

relatively flat bottom, we may thenassume- that-the-wake-fraction, for this

type of ship; will normally range from-zero-to-eight-percent. Therefore.

we may use as the loc~l velocity in way'of-the appendage) the freestrean

velocity or modify it bya wake fraction" (based' on data for- a similar ship

which has-previously been tested); *It is felt-thatiin'terms-of percentages.

the error due to'this assumptionwouldbe-approximately'O'to 8 percent

(at most) of the velocity as measured from-a'wake survey.

As for the direction of the local velocity; it -is assumed that the struts,

skegs, bilge keels, stabilizer-fins and- rudders- align-with the flow. Further.

the direction of flow past cylindrical bodies-such'as-shafts, sterntube

bossings, strut barrels, and fairwaters is assumed- to -be parallel to the

hull and thet there is no transverse crossflow;" Therefcres the dirertion

of the flow over these appendages can be estimated-to'be the angle they

make (locally) with the hull.

- This assumes that the velocity error will bero greater than the wakefraction for the hull form.

-ii 5,

i~ii " :e

I-

THE FRICTION F%ýAULATION

The Schoenherr friction line, (Reference 8), has been used for all

friction calculations on the appendages. The numerical valuts of

derived from the Schoenherr formula apply to the viscous component cf

flat surfaces whereas other friction lines commonly used by naval

architects in determiuing the frictional resistance of ships might

Incorporate various degrees of a form factor.

Therefore, since the Schoenherr formulation is considered to be a

baseline, the expressions used to calculate appendage drag will relate the

geometric parameters of the appendage to the corresponding flat plate

friction coefficient.

The Schoenherr friction formula may be simplified by the following

vxpression:

Cp - 1/(3.46 log1 o(Rn) - 2 (1)

.- ,;a

This approximation is considered to be within + 2 percent of the standard

Schoenherr formulation.

The formulations are for turbulent flow. However, a correction shculd

be made to account for the fact that the appendages experience a local

flow which may be laminar up to a point and then becomes turbulent

afterward. The following are the expressions which have been used to

obtain the coefficient of friction for all work discussed in this report:

1.327/'-- (2a)

Laminar

CPubulent 0.242 + loglo(Rn CF), (2b)

F

n 10T| O

C A (cT':ransition " CF - 'ule " (2c)F .snTurbulent an a

where A ( Turbulent CVLaminar)f

(eall taken at the chosenReynolds" numberrat transition)

It will be shown later that forthe'present'work-on- appendages, an

appropriate Reynolds number'for transition- s' approximately 5 x 104.

Figures 1 and 2 are provided to facilitate, the- user in- obtaining Reynolds

numbers and friction coefficients;''Figure'1"presents a graphical

solution for obtaining Reynolds 'numbers;- a* sample- problem- is* shown by the

indicated arrows; Figure 2 presents'curves'of"the'friction coefficient

previously discussed. Transition-curves- from-laminar to'turbulent flow

are given for RnTransition = 5 x 104; 1 x 105. and5 x"10 5 . Conditions

where "forced turbuience" would-be used correspond to-the'case where the

turbulent curve is used for all Reynolds-numbers'and-would be generated by

using Rniransition 0.0.

GROUP I - RUDDEPS, STRUTS AND STABILIZER FINS

Group I appenda-es, as considered herein, are'assumed-to have stream-

line sections with a maximum thickness located at' 30-to 50 percent of the

chord length.. They are treated as two-dimensional'surfaces which forappendages aligned with the flow appears'to be acceptable; '"his is becauseexperimental work for rudders, for example; reference-lO,'has shown that

the effects of aspect ratio, sweepangle; and tip'ending'are small for zero

-angle of attack. Furthermore, it is also assumed that there' is no venti-r!

lation or cavitation. With all of these simplifying assumptions taken into

consideration the total drag can be derived'as'the'sum'of the .various

components usually considered in two-dimensional-foil prediction.

Expressions for these components such'as flat'plate friction resistance -(RP&

7

• o -

• - - ,--'.•-- ,~ - , ~

resistance due to velocicy augnentatIonr (R..d),'pressare-or separation

resistance added resistance due- to an Intersection-with the hull

or a strut barrel (R.) and the base drag, due- to- a, bluntness of the

trailing edge ( -)are presented below.

Reynolds Number" Used to Obt aia Cy

The Reynolds nunber used for Group-Iappendages-is-a function of

-'velocity, kinematic, viscosit" and* chord length or,

-,4

71st Plate Friction Resistance ' -

"- -he expression useA to obtain the flat elate friction resistaace

U as follows:,

l 1./3,.2 •SV2 (2C.)

Resistance Due to Velocity Augtzentation

* 2he mean average velocity around-a syzmetrical" foil- sectioa Is hig/her

"than that- of- the- audisturbed" flow.- The'added- resistance due to this

va.locity augrentation is given by: .....

eA pl/2 SV2 (2Cy) (2t/c);": (5)

F cessure or Separation Resistance - ""

The pressure or separation resistance'is s'component originating due to

Ohe lack of pressure recovery* associated.,withboundary-layer- thickness andj

F -or the work presented in this report; the maximum chord length was

.used -AAea the drag of tapered appendaga'was to'bk; calculated.

." - • Roo

k-I

-, or separation along the afterbody of"foil'and'strut'sections. The

expression for approximating the pressure- drag'is-given as follows:

R 1/2 pSV2 (2C,) 60 (t/c)4 - (6)IipAdded Resistance Due to Intersection with'iull-or'Strut Barrel

The added resistance due to-an intersection-of any-of- these appendagesJ with another surface will be'treated as'Ifit-were-an intersection with

"a flat wall. It is speculated that, "when a*wing or*strut- adjoins a wall

(or an end plate), the boundary layers of-both; the wind-and the wall,

Join each other. Subjected to the pressure- gradient* along the rear of

the foil, section* the -boundary -layer is- further retarded;- and additional

pressure drag (i.e., interference drag) arises."1 1 It-should be noted

that for very thin sections (t/c <.081 this interference* drag might become

- -,negative. The expression for estimating-this-drag' component is given

below:

R= 1/2 pV2t2 .75(tic)'- 0.0003/(t/c (7)RLO L

Base Drag Due to Bluntness of Trailing EdgeI r-

The base drag of foil section with blunt trailing'edges may be

approximated with- the following expression.

Ra 1/2p 1J 0.13513 c Ad c(8)

GROUP II - SHAFTING, STEWITUBE BOSSINGS AND INTE1-1EDIATE STMUT BARRELS

In Order to estimate the drag of the shafting, it-was necessary to

divide this appendage into the following sections:" (I)" Intermediate

shaft (between the sterntube bossing and the intermediate strut barrel),

and (2) main shaft (between the intermediate strut barrel and the main

9

4: ". .. - --

- - --.---.--- "-- -.. " "

Strut barrel). The resistance components of Croup- 11" appendages are thefricticn?• resistance (R. and the pressure resistance corrected for

Crosstow (1y).

fricticn Resistance and Reynolds Number

The Reynolds number. used .in estitading the frictional dra3 is basedon th.e a2pendage length along the 1ongitudinal-axfs; Therefore.,

(9 .

where -"

Z le.ength of appendaga along the longitudiual:axis-(for ster9tubebossings, the length is taken'to'the'intersection-with the hullalong -he" shaft ceaterline),

The fricti6n resistance =aW be determined-byt the-follow-n& e-xpression.

o 3js/ pLDV'wS

* (10) (

!Pressure Resistance Corrected for Crossflow

The expresslon used to estimate the pressure"drag has been taken froma derivation proposed by Roarner (reference 11), The*general form of theequation is:

23Y. 1/2 pLDV C Sin a'.)

The pressure drag coefficient CC.) may be further defined for non-cavdtating-d ca'rI-tating flows. The proposed definition of C follows fron work

presented In reference 1l. page 10-8, Figure 15a; This figure presentsdrag coefficients as a function of cavitationnumber- for flows that are

10

-.....

"above and below the critical Reynolds number for separation. The

parameters used to describe the flow are Reynolds number (Rn) and

cavitation number (a).

Rn - D (12)V

S- 2D.(13)

S(P ambi - P ap)/(1/2 p V2) (13)

where

Pa--i. - ambient pressure acting at the centroid of theappendage,

- vapor pressure of the surrounding fluid.yap

The expressions for the pressure drag coefficient represent the afore-

mentioned curves in reference 1i in polynomial form and are given below

for various flow conditions.

kn < 5 X 10 anr1 u>2.5,C1 - 1. 17Rn > 5 x 105 and 0>2.5, Non-Cavitating Flows

S- 0.50

RM <5 x 105 and cr <2.5,

C" -. 5 + .5a - .052 a2 + .046 C -3.061 a4 + .014 C 5 ,

ft >5 x 10 and 2.1<0 < 2.5,

S-6.125 - 2.25 a, Cavitatiing Flows5

Rn >5 x 10 and < 2.1,

C" -. 5 + .5a- .039 a2 + .006 .

11

CGROUP 1IlT -AIN STRL-C BARRLS (

The co!ponents of a main strut barrel are:

(a) strut barrel,

(b) propeller hub,

W(c) fairwater.

These ce-poaants together are considered one unit.

The components of re-A-stance for these appendiges are friction

resistance (.±, pressure resistance. corrected for crossflow and tihe

base drag due to the bluntness of the* fairwater trailing tip.- (R&). Theapresslons used to estImate the resistance-due. to friction and pressure

are the same as the one-; for Group II appendages-Ecquations (9) through.

(13)).

Base Drag Wue to Bluntness of Fairwater-Ending

Accordlng to Roerner, the base drag of three- dimensional bodies very,similar to the fairwater (projectiles- fuselages-and.. elipsoids- for example)

S' found to depend largely on the- length- of- the- forebody, its surface

*6ndtions., and the ratio of ba3e to body diameter; -The expression used

Mo..estluate the resistance due to the bluntness- of, the- fairwater-endiu. Is:

RI _V2 12 3 ___S 4" [V.029. (/B/D) /(2ACE(L/D)) 1 (14) "

4 I'.-.tere

D - caxim-um diameter of appendage,

D - diameter of base (gee above),

L = Jlength of appendage along the longitudinal axis if blunt orroun.ded trailing end, use the- extended- length- i;e. * the length

the appendage would be If it were not blunt.

12 -(

.--- -

I - in

"- C@ROUP IV - BILGE KEELS AXID SKEGS

The resistance of bilge keels and skegs is" treated"similar to theI

drag of a flat plate. This assumes that these appendages are alignied

with the flow.'- It should be noted that, generally" skegs are considered

as an Integral part of the bare hull form and not'as a separate appendage.

The e~xression for estimating the resistance'of'this group-of appendages

S 2/2 SV2 C(15)

where

S wetted surface area of the appendageminus'the'wetted surfacearea of that part of the hull that has been" covered up by theappendage. By tak•-ng the wetted-surface-in this manner, theloss of bare hull friction drag due- to a net- loss of wetted""siurface on the bare hull can be compensated for.

I

*he Reynolds ntmber to be used to obtain the-flat plate friction

• coefficient is a function of the velocity,'length-of appendage, and kine-

Smatic viscosity, as follows: "

VL. - (16) -

'1p

!I

"APPENDU A CONfPUTER PROGIRA1• OF THE N-ITiEU!TICAL M4ODEL

The expressions derived in the previous' section" for calculating the

drag of various appendages have been used as: the'basis for a computer

routine named APPEND. Details of the computer program are presented iii

Appendices I through III wit.h the routine/algorithm" ±_Fortraýn presented

In Appendix i; input format andoutput-format' inAppendices XI.and III

respectively.

"CORRELA&TION OF THz MLAIHEŽ!ATICAL WDEL"WITH MODEL TESTS

In the presentation of any calculation method, itfwould be'most

-desirable if the expressions could be--prove." out'by- experimental data.

F oar the case of appendages•, this would- involve the- testing of various

"--sizes- (scale- effect)-" shapes, and comblnations-with one another (inter-

i ctIcns). "" However," it was not possIble to conduct* such- aa• experimat•-al

Vrcgrxa= for this study. It was necessary; therefore; to'simulate a data

"-"base which could substitute for the test program.

The decision was made to make use of-the results of'previous model

tests conducted by the :'aval Ship Research' and Development" Center. This

-methud" involved the- selection of, fourteen shipý-models- that'had been tasted

In the bare hull and appended modes'for resistance; The drag of the

ppendeaes'as a group was then obtained from the difference in resitantce

"of the two modes and compared to the'results obtained by'using' the eynress-

tons presented herein.- A f airing of'the" data-has been made in order to

facilitate'general comparisons.

P. BRIEF DESCRIPTION'OF TiE SUIP-MODELS

In general, the fourteen ship-models chosen for-ths sttdy were of the

twin screw prop Uslion'type and represent'three'basic-bhall forms wih

1IV

transom type sterns. Tables I and II present, a-more-detailed description" of the hull forms and their appendages.

PRESENTATION OF MODEL DATA

"As stated previously, it Is-most desirable'to'present-some experi-mental data In'order-to verify-a mathematical'model;-'Keeping in mind

"* *"that the mathematicalrmodel presented-herc.in- is supposed- to"represent the" - ~- Reynolds number- dependent components-of"the"appendage-drag, then the

data should be presented in such a'manner-soas to"describe'visually tht- 'answers to-the"following questions. "First-s"and'most"important, are the

expressions able-to predict within a"reasonable-tolerance the Reynoldsnumber dependent drag-of the various appendages- and second, what arethe pcssible sources of error inherent-to-thprmathematical-model and howcan they be compensated for? The data-are-presented,-therefore, in twoways in order to determine if the-answers to'the-above-questions are just"a function of'the-individual appendage suit in question-or if there are

t general trends which- can be- applied to-any- appendage suit.

-....... .. Figure 3 presents the values of'appendage-drag-(injcoefficient form)as calculated-from the mathematical model using'both"arfriction linebased on forced-turbulence at tl-e lower-Reynolds numbers and on a"transition-Reynolds nu..ber equal to5 xu10 .(these-friction-lines may be --

"-• - seen in Figure 2)., Also presented-in*Figure 3"are-the-appendage drag data-... .. obtained from model tests as previously described;---The differences in

model appendage-drag coefficient for various-hull'forms of the samedesignation, e.g. three 3-D forms,-are-due-to differences in the models -not readily apparent- from the descriptive-parameters-listed in Tables Iaad 11. The predicted values of Reynolds number-dependent appendageresistance appear to be in close-agreement with'the'model data exceptwhere "humps" appear. To further investigate- this-phenomena, Figure 4 hasbeen prepared. It presents the difference between the-calculated values

15

A .. ".1ti lII,

I:l il "

S..

TABLE I

The Hull Forms

Hull Name of Coefficient* TYPE !** -TYPE 2 TYPECoefficient

CB Block Coefficient A6 - .66 .48

Longitudinal PrismatI•c. .63 -. 67 .59Coefficient

CX Maximum Section Coefficient 0.97 '.99 o81

CT Waterplane Coefficient .78 -" .84 073

Forebody Prismatic .60 -. 67 .56Coefficient

""A Afterbody Prismatic .67 .67 .62'Coefficient

:CPE Entrance Prismatic .60 .65 .58Coefficient

CPR Run Pr'ismatic Coefficient .66 .67 .59

CvT Vertical Prismatic .78 .79 .65Coefficient

"CvpA Afterbody Vertical .72 .69 .62Prismatic Coefficient

-C Forebody Vertical .88 .93 .78Prismatic Coefficient

Forebody Waterplane .66 .72 .58Coeffirtent

%PA Afterbody Waterplane .90 .96 .96Coefficient

• Formulae f~r the hull coeffIcients may be found in Reference 12.

I- The numerIcal values for the hull coefficients for each hull type arethe average values for all the designs used.

16-

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(using the transition Reynolds number 5 x 104) and the model data in the

form of percent dlfjerence and the actual magnitude in pounds. These

absolute and relative differences are presented as a function of the model

speed non-dimensionalized by the design speed value-"

Values of appendage resistance as a percentage of bare hull resistance

for the fourteen selected models are presented versus speed-length ratio

in Figures 4a, 4b, and 4c.

DISCUSSION OF CORRELATION

In order tJ discuss the correlation of the results obtained from the

mathematical mi-del to the model data, the speed. range will be broken down

into two components. The first speed-range will be defined to be below

design speed and the second will be above design" speed. ,The design speed

forr hull forms 1 and 2 is approximately equal to a speed-length ratio of

J8 and for hull form 3 the design speed-length-ratio-is about 1.2. It Is

.assuzed that the aipendage drag below design speed is for the most part:

dependent-on Reynolds nautber and that the- coatribution of the Fr..'de depend-

ent resistance becomes'a factor slightly-below and about- design speed.

Pigure 4 indicates that the agreement between the mathematical model

-and the model data below design speed is very good. For example, the

-.average magnitude of this difference at 80 percent design speed is less than

0.2 pomuds. Vle may, therefore, deduce that the mathematical model.is valid

In-this speed range. The deviation from the mean maybe caused by..a

misalignment of such appendages as struts, stabilizer fins, bilge keels,

etc., to the flow and will be discussed later in the'text. For now, it will

be called an induced drag (PR) that is, in nature, independent of Reynolds

number. - ,

The case for the differences between the results from the mathematical

rmodel and the model data is similar for the higher speed range. However,

.. "8•- . .8

4- . - ..-

- '• " -" .' "' " .-.' :-.. . ... " -.. . "

the magni.tude is larger, which would tend to confirm the second part of our

assumption, I.e., that the Froude number dependent resistance-has an effect

at the higher speed-values. The shape of the curve through the data is still

more evidence indicating the Froude nuTber dependence of this component of

the appendage drag.

INTERACTION BETWEEN APPENDAGES AND HULL

If it is assu.med that part of the difference between the calculated

values and those data deduced from the model resistance tests is due to

the previously mentioned induced resistance caused by misalignment to the

flow, then the question arises as to what causes the -est of the difference?

This may be answered by using some deductive reasoning.

It is a well known phenomenon that an appended model will not necessar-

ily have the same trim clharacteristics as a bare hull model. It is also

known that the tr.-'= of a model has an effect on its wave making resistance.

Now, it will be recalled that the model data used for the verification of

"the mathematical madel were obtained by subtracting- the bare hull model

resistance from the appended hull model resistance. Furthermcre, since

we were able to predict all but 0.2 pounds of the appendage drag up to 80

percent of design speed (this being almost ttally dependent on Reynolds

number) there is no reason to believe that we do not have the same relative

accuracy for predicting Reynolds number dependent drag above the design

speed. It appears to be reasonable, therefore,'to deduce that the remainde'--of the difference between the values obtained from the calculation procedure

and the model data is caused by the interaction-of the-appendages On the hull

form and that this interaction is a resistance- that is'Froude number

dependent and wave making In nature.

19

U r

CONCLUSIONS

Sulmariz±ng what has been accomplished in* thepreceding chapterss the

follo•ing conclusions nay be drawn.

1. A mathemnatical model has been developed for the predictioa

of the viscous components for appendage drag.

2. The predictions obtained from .the mathematical model have

been correlated with nodel appendage 'reslstance'dataobtained from the

results of fourteen ship-nodel resistaace tests'and'the mathematical model

was found to be an effective means of predicting- appendge drag.

The differences bet-4een the results from the mathematical model and

the model data appear to be due to two basik resistance components. i.e.,

Induced drag due to misalignZent of an appendage to the flow and a Froude

S humber dependent drag due to the interaction-between theappendagr.c and

-the hull form. These effects will be considered at greater length as""

'bis, study progresses. ".

3,. A Fortran IV comipter program, refer to Appendix I1 to be

used on the Center's CDC 6700 .comquter has-been* developed using the

Ssathenatical expressions presý-nted herein. The computer program as presented

herein utilizes excessive core space and is presently-being modified. The

modified version will be available by 1 karchl1972; The program also contains

en error ln the base drag formulation;-howevert this'error is being corrected

In the modified version. The present form will provide correct drag values

&s long as base drag terns are not needed.

-WO-

I . . "

_. -......-..-. " . ,;,, --

RECOMENDATIONS

A procedure for calculating the vector lift and-drag- components of the

"appendages could be developed, 'and their- effect -on- the- change- in trim angle

correlated to the added appendage drag'due to-change-in-underway trim.

This could be done by assurning that the forces-acting-on-the appendages

are located at the centroid of the appendages;*then-by taking the sum of

the moments about the center of flotation-,the'chanie-in-trim due to the

addition of appendages could be calculated;,-These- developments would be

very helpful to the designer.

Art experimental study should be conducted"on-a-set'of carefully

selected geosims to verify the scaling'techntque;.--This- study should also

Indicate if a correlation allowance for appendages-Is necessary. Since ft

may be difficult to conduct some phases'of such-an-experimental program Ir

a towing tank due to the size of some of-the-larger-geoslm" appendages, the

use of a subsonic wind tunnel may be cons dered'as-complcmenting the work

done In a towing tank.

21

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0 EAA IkDUCED FROM EL RES•ISTAXCS TESTS

. ANALYIICAL PiRDIZCTOz1 USING; FORCFD jtUpuZ6-;CE

J- ZALY1ICAL PR-DICTIOC USING R OF 5 X 104,__ ._____ __ '-Tr'_._',!. _L L_ _LoL

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- Sf-F1ED - LENGT 111 RTIO (/lFPiure 3 - Comparison of Values of Appendage Drag Obtailned from

.the Mathematical MIodel with those Deduced from,Cent.er Bare 1•ulL and App.-n'ed Ship-&-odel

Resistance Tests 24

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APPENDIX I -LISTING OF~ COMPUTER PROGRM1

APPEND is a Fortran computer prograin which may'be used to calculate

the Reynolds nuo.ber dependent resistance of the-appendages previously

mentioned in this text. The program, which-hasbeen-writtea for- the center's

CDC 6700 computer, will calculate appendage- drag- for any'size appendage,

I.e., model-scale or full-scale. APPEND consists of" the following sub-

routines: RUDDER, STRUT, FIN, SHAFT, BOSS, MAIN, BILGE, SKEG, and FRICE6

and the function PRESUR. In general, .the first eight subroutines are used

to calculate the various viscous drag components-of the appendage indicated

by the title. Subroutines FRICT is used"to" calculate the frictioa coefficient4

(CF), based on a Reynilds. number of transition of 5 x 10 Function

PRESUR is used to calculate the basic pressure coefficient described in

equation (11).

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S( *APPENDIX II - INP'r FORKI•AT FOR COINPUTER PROGRAM APPenD

CARD ENTRY FOnMIAT FIELD RDEMARKS

SNCASE 15 1-5 . Number of cases to-be calculated

2 TITLE 13A5 1-65 Used to identify the case

3 ISPOT 15 1-5 Number of speeds'to be calculated

SF10.5 6-15. Wetted surface of appeadages, ft2

Sao F10.5 16-25 'Model water density, slugslft 3

=U F10.5 26-35 Model water kinematic viscosity x 10%ft 2 /sec

-BROS P10.5 36-4z Ship'water density, slugs/ft 3

X4US F10.5 46-55 Ship-water kinematic viscosity x 10g.ft 2 /sec

ZO.A! F10.5 56-65 Ship-model linear ratio

NLSHIP F10.5 66-75 Ship length, ft

hIRUD i5 1-5 Number of rudders - 0 to 4-

NSTRUr 15 6-10 Number of struts - 0-16

ZSRAFr 15 11-15 Number of shafts - 0 to 8

XBOSS 15 16-20 Number of sterntube boss.ngs andIntermediate strut barrels - 0 to 8

.WAIN 15 21-25 Number of main strut barrels - 0 to 4

UBILGE 15 26-30 Number- of bilgekeels - 0 to 4 -

NSKEG 15 31-35 Number of skegs - 0 to 4

UFIN I$ 36-40 Number of stabilizer fins - 0 to 4

IUE NEXTISPOT CARDS VS F10.5 1-10 Ship speed in knots

.. 3-WT F10. F 11-20 Wake fraction

"*0 O 0

* "-. E N E X T

* URUD CARDS SRUD F10.5 1-10 Rudder planform area for-one side. ft2

TRUD F10.5 11-20 Rudder maximum thickncss, ft

o.-

;.1.,t.

•" 0-• • " •'• .oO .

INPUT F0on.RA FOR APPEND (CONT)

CARD ENTRY FORMiAT FIELD PJI2ARKS

CRUD no.5 21-30 Rbidder maximum chord, ft

TBRUD F10.5 31-40 Thickness of trailing edge ofrudder$ ft

SBRUB 110.5 41-50 Projected area of blunt edge* of rudder, ft 2

* *

THE NEXT

NSTRUT CARDS SSTRUr F10.5 1-19 Strut planform area for one side, ft2

TSTRuT fI0.5 11-20 Strut maxiimun thickneos, ft

CSTRUT F10.5 21-30 Strut maximum chord, ft

TBSTPTt. F10.5 .-i1-0 Tnhickness of trailing edge of strutft

SBSTRUJT Fo.5 41-50 Prolectrd area of blunt edge ofOtrut, f02

0 -.

• .-

"THE'NEXT

-FIN CARDS SFIN FI0.5 1-10 Fin planform area for one side, ft

TFIN F10.5 11-20 Fin maximum thlckness, ft

CFIN F10.5 21-30 Fin maximv-n chord, ft

TBFIN F10.5 31-40 ,Thicknes .of trailing edge of fin, ft

SBFIN F1C.5 41-'0 Projected area of blunt edge of strut,• ft 2

42

INPUr FORM1AT FOR APP.END (CONT'D)

CARD ENTRY FORIAT FIELD REMARKS

* THE NEXT"NSHAFT CARDS XLSIIAFT Fl0.5 1-10 Shaft length, ft

RSHIAFT F1O.5 11-20 Shaft diameter, ft

ASHAFT F10.5 21-30 Angle of flow, degrees

HSHAFT F10.5 31-40 Depth below waterline to shaft, ft

THE NEXTNBOSS CARDS XLBOSS F10.5 1-10 Bossing and/or intermediate strut

barrel length, ft

RBOSS F10.5 11-20 Bossing and/cr Intermediate strutbarrel diameter

"ABOSS F10.5 21-30 Angle of flow, degrees

HBOSS P1O.5 31-40 Depth below waterline to bossing and/or intermediate strut barrel, ft

THE NEXT

NALZIN CARDS XLNAIN F10.5 1-10 Main strut barrel length, ft

RMAIN F10.5 11-20 Main strut barrel diamerer, ft

AMAIN F10.5 21-30 Angle of flow, degrees

R?1AIN F10.5 31-40 Depth below-water to m;iaLn strut b arrel,ft

RBIAIN F10.5 41-50 Diameter of fairwater ending, ft.

"43

"-

.................... . ......

* -

INPUT FO.IL\T FOR APPEND (CONT'D) (CARD ENTRY FOMMAT FIELD * RENAP5KS

THE NEXTNBILGE CARDS LBILGE F10.5 1-10 Bilge keel length, ft

SBILGE F10.5 11-20 Bilge keel wetted surface ft2

(as described in text)

"THE £EXTNSKEG CARDS LSKEG F10.5 .1-10 Skeg length,, ft

SSKEG F10.5 11-20 Skeg wetted surface, ft 2

.(as described in text)

_ (iL .

START THE NEXT CASE BEGINNING WITH CARD #2

4

i.

°"Ii " Q

449I g 0 "

APPENDIX III - OUTPUT

The output formats of "Append" have been written so as to give the

user detailed information about the drag 'of his appendages. First, the

drag cozponents of each individual appendage are printed out, this includes

the speed-length ratio based on the length of the hull and the local

Reynolds number. Next,.the total calculated frictional resistance components

are printed and finally, the total.calculated viscous resistance is printed.

The program will output the above information for both the model and the

full-scale appendages.

f -

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REFERENCESU

1. Mandel, P., "Some Hydrodynamic Aspects of Appendage Drag," Transactions,Society of Naval Architects and Marine Engineers, Volume 61 (1953).

2. Clement, E.P., "Scale Effect on the Drag of a Typical Set of Planing_Boat Appendages," David Taylor Model Basin Report 1165 (Aug 1957).

3. Radler, J.B., "The Prediction of Power Performance on Planing Craft,"Transactions, Society of Naval Architects and Marine Engineers, Volume 74(1966).

S4. Moore, W.L., "Some Theoretical and Experimental Results on PressureInteraction of Hydrofoil Boat Components," David Taylor Model Basin Report2131 (Nov 1965).

5. Cheng, H.M., et al., "Analysis of Right-Angle Drive Propulsion System,"

Paper No. 20, Society of Naval Architects and Marine Engineers DiamondJubilee International Meeting, New York (Jun 1968).

6. Smith, A.M.O., and Hess, J.L., "Calculations of Non-Lifting PotentialFlow about Arbitrary Three Dimensional Bodies," Journal of Ship Research,Volume 8, Number 20 (Sep 1964).

7. Denny, S.B., "Applicability of the Douglass Computer Program to Hull

Pressure Problems," David Taylor Model Basin Report 1786 (Oct 1963).

8. Schoenherr, K.E., "Resistance of Flat Plates Moving Through a Fluid,"

Transactions, Society of Naval Architects and Marine Engineers, Volume 40(1932).

9. Hama, F. R., "Boundary-Layer Cbaracteristcs for Smooth and Rough Surfaces,"Transactions, Society of Naval Architects and Marine Engineers, Volume 62(1954).

10. Whicker, L.F., and Fehlner, L.F., "Free-Stream Characteristics of a'Family of Low-Aspect-Ratio, All Movable Control Surfaces for Applicationto Ship Design," David Taylor Model Basin Report 933 (Dec 1958).

U. Hoerner, S.F., "Fluid Dynamic Drag," Published by the Author (1964).

12. "Explanatory Notes for Resistance and Propulsion Data Sheets,"

Society of Naval Architects and Marine Engineers Technical and Research BulletinNumber 1-13 (July 1953).

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