Calhoun: The NPS Institutional Archive

Theses and Dissertations Thesis Collection

1950-08

Investigation of rudder characteristics with variation

of rudder position in a propeller race

Downs, Benjamin H.

Massachusetts Institute of Technology

http://hdl.handle.net/10945/24758

INVESTtGATFON OF RUDDER

-SS3 CHARACTERfSTfCS WITHi VARIATION OF RUDDER POSITION

iiiti#]fiiisinflfiicvs

BENJAMIN H. DOWNSCHARLES B, SWAYNE

ANDRICHARD E. HENNINQ

ThesisD71

^iOtUly

^cijj i

Ca.!nbrld>2e, Maasachuretts?^ay 19/1950

Professor J. B. •^e''*fell

Secretary of the FacultyMasfiiohuBetts Institute of TechnologyCambrlOge, KaesL.chuB'jtts

iKixT Sir:

In accordance vith the reouirsments for the

Degr«p of Naval Fn^lneer, ve eu))nit herev^lth a thesis

entitled, "InveEtigation of RiJiddPr Characteristics

with Vari£itlon of Rudder Position in a Propeller Race."

PLeEpectfully

,

Benj£i.T>in H. DownsLieutenant Coni-vinderU. S. Hy-vy

Ch&rl^8 B . ^vayneLieutenant Com;-nanderU. S. Navy

Rich;:..rd E. Henn i ngLieutenantU. S. Navy

Library

U. S. Naval Postgraduate School

Annapolis, Md.

'*

INVESTIGATION OF HUDD?:R CHARACT^RIPTICS ^^ITH VARIATIUN

OF RUDDER POSITION III A PROPFLL^R RACE .

By

Fenjamln H. Dovne Charles B. SwayneLlp»ut. Com-nunder, U. S. Navy Lieut. Cominander, U. 3. MavyB.C., Webb Institute ofNaval A^rchltecture, 19^1

Richard E. HenningLieutenant, U. B. MavyB.B., ?J!&8eachusettsInstitute of Technology

19^3

Sul)fflitted in Partial Fulf lllrap>nt of the

Requireaientfl for the Degree of

NAVAL SUGIKKFR

at the

KAS8ACHUSFTTS IKSTITUTTn OF "^ZCmOhOO-X

1950

Signature of AuthorsLieutenant Commander, USK

Liputenant Gomr:k:^n<Jier, USU

Lieutenant. , USN

Department of Niival Architecture and Marine Kngineering

May 19, 1950

Signature of Tneeie Supervisor

Signature of Chairman of Depart-ment Coms;iittee on Graduatefntuc'ents

AGKNOTfL ^1DONEHTB

v;e wish to expree? our apprt^ctation to Kr. S. C.

(soyer of thfi David Taylor Woc^el Basin for suggesting thfi

subject matter of this Inveetieatlon.

ue are further lnc3ebted to Professor F. H. Levis

of the Department of Naval A.i»chltecture and Marine Knglneer-

Ing, V. I. T. , for the use of the H. I. T. Propeller Tunnel

and. for hie valuable advice in the deterralnatlon and evalua-

tion of the experimental data.

In addition ve uish to thank Mr. Ray Johnson for

his assistance and cooperation during the laboratory phase

of the Investigation.

12870

TArsL^-: OF C-NT?^Ii'S

I . nUKT'ARY 1

II . lUTHO. UCTIOIJ 3

III . ?rv)CFr<uns 5

IV. H?;>ULTS 15

V. Dir CUS'^IOH OF H^>ULrS 35

VI . CONCLUSIOf:S ko

VII . RirCOKKS^NDATlOK? h2

VIII . APPK :DIX -'43

A. Guppleni^ntary Introduotlon. . .

.

43

B. Details of Procedure ^3

C. T&bleB of Data and Calculated

Coefrioients ^44

D. Sample Calculations 59

E. Bibliography * 66

I. 5T.(H>-[ABY

ThlB thesis was undertaken In order to lnvestlgat<9

the effect on rudder force charaoterlE tlcB of variation of

ru<5dffr position in a pi^speller race. It was thought thtxt the

results vrould contribute to the general fund of information

about rudders since, to the knowlec-ge of the authore , such

an Investigation had never before been carried out.

Utilizing the MaesAChueettB Inetltute of Technology

propeller tunnel, the experimental data "'as obtained vith a

e train gauge type dynamometer vhich measured forces on a rudder

in a propeller race. The rudder T.'as raounted in the dynamometer

T/hioh in turn was mounted in the tunnel in such a manner that

the rudder could be moved transversely in emsill increments

across the race of f^ right-hand propeller. At each such posi-

tion, lift and drag readings ^^ere taken for rudder angles

varying from 30^ left to 30° right rudder in 5^ increments.

The speeds of both tunnel and propeller xmre maintained con-

stant throughout all runs. In order to establish the average

velocity of the race, a trav rse xiras made usin^ a pi tot tube

which gave only the conoonent of velocity parallel to the tun-

nel axis. This neoennitated thf=> aesuniption that anj'le of at-

tack tras the same afl inidder angle.

The results indicate that lift and drag vajpy -widely

depending upon the position of th»» ruuder in the propeller race.

A glance at Figures IB and I9, ^-hioh best suniaariae the results,

indicates that the location of the rudder at either extreme of

- 1 -

I

the race apT'Parfl to result In an apprecialiLr' loei of lift

although thlB la aocompanied by a r**duc!9d arag. The loss

of lift v'ould appear to make such a looatlc.i undesirable f c r

a wa 7-6hip.

With the rudder located betvei^n on^t sixth and one

third of the propeller radiuB to the port clrie of the propeller

oenteriine, vp>ry g-^iod lift oharactprlftics were found, but

again thiG x-;&q a region of high di'tig. On the basin of this

experinent alone, using a single rigiit-hand propeller, a

eingle rudder, and constant spf'Pd, It app^arB that a na.rrow

range say exist at about one elxth of the piMDpeller radiue

to the starboard elc'^e of the propeller centerline where a high

lift-drag ratio tor.ether vXth high lift occurs. It is be-

lieved that this cannot be stated concluBlvely until further

intenBive investigations ar^ raade , but the authors recomnend

that the region betveen one third of the radiue to port and

one third of the radiue to Btarboard be thoroughly searched

in small Incremf^nta of transverse poeition uBin^ various? com-

binations of rud'Jers and propellers, and furth'^r that the

tunnel and propeller be operated at various speeds. The uce

of a spherical or univerfial pitot tube vould obviate the

neoeeeity for the aspumxition that an :le of attack equals rudcer

anjJle.

'Phe variations found in lift and drag vith transverse

rudder positlon,aaountinr to as nuch as 22.^, point to an optimum

rudder position, not n**oesBarily on the propell<"r centerline,

and it i? strongly reconnended that further lnve8tl,;iations be

made to cetermlne and d*»fine such a location.

II. ITITRJPUCTIOW

The probleiRB of turning and steering ahlpe are as

old ae nuirlne transportation itself, and in the present day

of high speed surface and undersea warships are hot! vital

and acute. Froifi the time of the earliest truly solentlfio

Invftstigations to the present, extensive research and energy

have been directed tovarde the develo^xaent of the sofit effective

and efficient means of maneuvering ehlpe and tovarde methode of

predicting reliably the performance of a particular design.

Beyond this, sffort haa been expended in all siaritirae natione,

to^mrdfl isolating the effects of ship forr", rudder shape, size,

bal&nce, and location on saneyverabtllty and turning oharaoter-

istica^^^

^.ssentlally all investlgatione of rudders are ooo-

cerned i^lth lift, drag, norsial force, tangential force and

torque on the rudder, and the reduction of these forces, where

poaBible, to dlsienslottleBs ooeffioients of raaxlfioum utility.

The Investl^iation of the eff-ct on rudder force oharaoteristics,

as measured by these coeffiolento, of varying the transverse

position of a rudder In a propeller race vas suggested by Mr.

S. C. Gover of the David v;. Taylor Model Basin. To the knovl-

edge of the authors and after a survey of the literature, such

an investigation has n^-ver been oonducted. On the other hand.

Investigations of the optlraujs r^idder location on a self-propelled

model have been oonducted. These concerned themselves priiaarlly

vith optimuiTi maneinferablllty of a particul:Ar hull form consider-

ing all elements, form, propeller location, and rudder location

(9)acting to.aether^ '.

- 3 -

It iB therefore the Intention of thiP th^nis to

Inv -^Ptl'.ate the ffffeot :^n rudder forc^ char^,cterlc tics of

varylnp th^ : r^xneversf; position of a ru<:''.;:f^r In a propeller

rac^ , ano. thue to attempt to isolate one of the nany varla.bles

ai'fectint-. turninr i'^-ri^- L'tperlng' chai^aotf?risiilcs of shipG.

« /+ -

III. Pl^Cv:i>tJRE

Initially It v:.-s app?irent that In or<1er to obtain

the npcecfiary data for this thesis, ra*=an8 nuot be tound to

TMPiiQVLie flo^r velooltlps and propeller r*=»volutionB. Tbf»«e

vpre requlr*»ci to defin?* the oharact«»rl8 tlos of flov past the

ruc^flei^ Kith aufflci<=5nt aocui^acy to evaluate the coefricients

by t^hich the performance of the ruic^er coiild b© neaeure^.

Further It vas neoecsary to develop a method of counting a

ruiifier in a propeller race in such a vay that transversa posi-

tion a.nc rudder an(:lf> could b@ varlpc" at will, and that at

l«ast t^'o components of thf!^ force acting on the rudder could

be detemin*™d.

The K. I. T. propeller tunnel, dosiprned by ProfesBor

F. v., Le^'^is , appeajp^d to b« suited ld<^ally to the measurenent

of flc ctn<3 propeller r'^volutione vlth accurate control of

eciCh, ami further afforfied an excellent raeans of mountin,^ the

rudder and siaXlng observations^-''^. Thf» rudoer dynamonetftr

developed by ^pp and Kissinger proved to b^ '-f^ell adapted to

transveree poeition variations as well as to tt» neaeureni'^-nt

of forces acting on thp rudder for varloug rudder angleg^ '.

The normal direction of flov in the propeller tunnel

l£ one in "hich the w^ater flovrs in such a direction that the

e-hafting and supporting fltruts are on the do^/nntream side of the

propeller. For the purix>se of this invest! atlon it T^ras neoee-

sary to operate the tunnel vith reverse flo^r In order thrit the

shaft im- and struts v-:>uld be on the upe'rean side of the pro-

peller ^fith the rudder In the propeller rs-ce. Since the no?.zle,

- 5 -

dlffuser, £ind stralghtentn.; vanes of the tv.nrel vere not de-

signed for this direction of flov, the poeslblllty exietecJ that

the flo>' night be unsatisfactory. "I'hlle it If highly probable

that flov conditions in this reverse direction vera not as unl-

foiTOi as those of the de8lgnf='d floi^ direction It wae believed

that they would be sufficiently uniform to provide, at the least,

good comparative data osong tho various tranGTeree rud'rer posi-

tions. All phases of the Investl'-^atlon therefore vere baaed upon

this aaeuiaption. In operating the tunnel in reverse, hovever,

the venturi sieter by vhlch water velocity le rieaBured ^rlth the

tunnel operating in the designed direction, ^ras found to be lo-

catea in a region of unstable flow. It became neoeerary, there-

fore, to Install a pltot tube v/hloh could measure the average

velocity of flo^rr to the propeller. This pltot tube was placed

about six inches forr/ariS and five Inches outboard of the pro-

peller tip and w&fi left In place throughout all runs.

The rudder dynamometer employs SR-'i- strain ga.\ip:^e to

give a aeaeure of lift, drag and toiv.ue on th^-* rudder^ ^', The

dynamometer >'ae regauged iaraedlateiy prior to Its use and all

strain gauges vere tested prior to aseerably of the dynajnometer

components. Certain ralnor modificationf- were raacle to improve

its characlerlstioB and to alli^viate difficulties experlf»nced

In calibration. The dynaisoneter vas bolted to Z-bars fitted at

the top of the tunnel t-et section ar E:hovn in Plate I. The

upper flanf^e of these Z-bara had holee drilled on one-inch centers

so thL^.t a complete traverse of the propeller race could be niade in

one- inch incrementf?.

- 6 --

lirfore anci aitpr toF-ts, thf* dynarjoa-oter was call-

brat -cI by rount.ing it in :•. yrT-'.ocen tfB% stan<^ and applying

knovn horizontal lOv^ido In the tr"i?iavr?ree and longlt\K':inal

direction?' to a t«»2t '/uoc': inserted in thf* dyna'iiompt^r. This

vas aoc "»n'>iir>he-! by r';'-^vi;if: ^. •'Ir'^ fron the leat i-: cccV , over t.

i>ijllf=!y to a >• eight j)an and placing knotm veightE on the oeni,

StKiin readln^B for eaoh. longitudinal and trtmsvprse load thuB

appllftc? uere read on a Baicwin-Southvark strain Indicator which

vafl oonneote^d through a cwiiSchinp- box to th^ r train gaii?;'e6 on

the dynaniatn'=:>uer. Tti^'i Cixlibrai'.inn cvr^rf^& obtain'O'ci froB the-vn

readin^;6 shovinv etz^-in r*^adinf:>r- v^rfius applle'.. force cir? shovrn

in Figures 1, 2 c^n^- 23* l^if^rt tailing c'3ta durin^i: tents the re-

verse prooevlure ".vus ueed; thj.t Ip- strain readiiK n ^'erf^ taken for

longituciinal and ti'Cs.nBverse force ixTic these were convei'teti

through the use of the Oiilibration curves Into lift btii' da^ag.

In ari^iving at th«! flo'- velocity to be used during

the teetr- the force a,ctin,; upon the r^udder was taken to be a

function of ceversil variabl^^ji

:

F « f(^, V,// , L, e, e. or, r-^, r^, —)

where ^ = mass density of vater

V ' Average axlfeil velocity of the propeller

race In way of the rudder in ft./seo.

M ^ vteoosity of the fluid

L - a characteristic If^ngth of th^ body

c i speed of eound in ^ ater

g r acceleration of gravity

o< z. anf.le of attack

^1' ^2*""" for«i factors

- 7 -

-- r\ WH iTP" :"':}

V S\

1\ 2\

\,

\ In

k,

1 •,1

rl

\ t\ h

\s, 1 •

if

\^ 1 i/i

\

\, 1^\

CJ

^:

r

—UJ

^

L ^C

1;-

=> \ ^J 1 o

SB \s, I

,

i Jj'' ^ ni

'

\ ki2 8 1 I

• ih

ift

b:

i\\O i

> Sb

\ z c% 1

\ F ci f_ 5

•-

\^a

nZ i J

\

\

-

— \ o\

\\ -

1

\,A

\\

\

\\

O

\ §;

'

,

'

\ oN

I n 3

\, 8:^

\,

Ul

\\

A1 \

'.[I \

\'

\,i

V

N,

\ t

\1-

\

\s

\

'

\' '.

i:-'i i-:

\

\\

:--[

\,\

L-. .

—— \.

>9 < 4 * ^

. 'Ar -

{ 1

4

C i'

_^i

ON av 121 \MHM xa SN

,

_J

"

—— -—I~^—

.,.,..,

'• 1 ;;ii: : n ;:

' T. nr^TH'

' '

1

-i

'.'••

':'l

'

'

i-ii

.

<0;

1

t-

;1 C

— — — 1

'

' 1 I

61

, !1

i;

! J" .'; J

'N-

iii> 11'

'!'ri

;

! 1 J

ilf

,

, :l

'

1

,

: .

i; In''

|!! ; J 'I.

' h

in'

,

.

;

Nf' Ia

i,

ii'i 'vf

\N 1 1 {:

\s

:

J1

t J ^[

\ in \^9

j-

\fli

iUj

u^

;t

\,LU

1\ i

44> M S ^ 1 '[

\

\ lOQ >

ill J^

\N

'<*'

> ?K

b: \.y--

— --

-

\ 9 B.

^57

(A

2 1 j|__ 1

. 1

I 5 :

K, in;-|

V

\, 111-ii

^\

s

It

'

h:

g\V o :::

MI

\i<^

,-l|

X K'

'

\':U

D*T \,

:'.

>v

\,'-'-.

\'

Vl '

\.

!

'\

s

\ 'r\

— i

>

><? } i c

[

V 1

t )\ < <

\ [ ( \<

a \1

r!

N^ i

1,

>

!

i

<t

111

9N<aw i-a AMSM raj SNI \i- '";4

' \

N.':i1

\\

i N;.,'

' \ '

' '

1

\ Z

— ' i

\ --1— — — i . .L

;

os

N, I'f

( \V'- %

b\ 1-

'lit

\ u

_—, — -

—

,—

-

— __ .

—

__ jft- ,.,, — •^-T ——xs"

— __——

h

_l:

Hi:

- — — — '—— — ~~ —

.

Az

—'r-^-

'f'y

\

'

-a\V- -^:

\ Ht;

\ ^. \ 'f

^-—— -.——

^

,-4^ .^ __— ^_ 1

—

—

,

-r-* -«^ — — -^— -—— ..._

\

- — -\ —!+

— LI'

II __ ._ :: __ _ ;: „..-

~

_— -. ^ -_Z~z z N

1

'f-

Tt-f

— ^——

"

——~— —

n

——— -

—

— — — —m

i^l-h:

-———— . —— —

-

— -^— _—•

^— ——

-

— --,"It

_. -^^—I^ ^ " '

z ,, ^z ^__^

——

-

—-- —

—

.^-^

' ~

^ Z z-^

z ,,, _- ,.,- •1

k— T^—

^

— ———— "1# hti-msm IT"M— —"— ^

—

—A \'f^m ^^11^S i^s1

since the rucU'fir can be aseumpd to b« <»xpaivled geometrically

to full Gt.T.e for ahip uce, the f^rra factore r^ , r.^, are

taken as constant. Hence, by dlnenslonal analysis It can be

shown tbi^t:

j. = i vVf(«.|. EJ?. I?^)

P

VThe term - , comrsonly )cno'^"-ii as th^ Mach NU:'ai;fr, can

c

be conelderad to have negligible effoct slnc««* It is of iraport-

Hnce only "^here it approaches or exceede one, in ^'hich ca8«r

ahoc)c effects may be nf conseauence. Since V is very sraall in

comparison vlth c, no shock eff-^iots are to be expected.

The auantity -y , Icnovri as the Heynolde Number, should

b« kept constant in pre'dictlng full-scale performance fron^ raoclel

tfsts. %t was not po><?cibl?> to operate at the saioe Reynolds Kura-

ber in the tunnel ae. "^/'tuld be encountered, in full-ncale opera-

tion, but this T/ae not conelderefi serious 8lnoe flov In the

tunnel is turbulent at lov water velocities. In the turbulent

range of flow the effect of the Reynolde Mumber decreaetSf? as

the Reynolds Kiyaber Increaoes, apnroachli^- zero asymptotically.

It hae been shown in previous aoflel tests in the li, I. T. Vro-

,;ell^r Tunnel that the effective Yieynry'\A& Ilussber is in that por-»

tion of the turbul:»nt range >rhere ItB influence niay be disre-

gaivied ,,

- 10 ~

Thf Froude i^umber *»j la of Iraportance only vhftre

surface effects are enoountered, arui it haB bersn shovn in the

past thiit geoaetrlo^lly slmil.ir ships operating at thf) earae

:• roude Muaber will genpratfl georaetrloa ly sirailiir surface

i/avee. The de^p submergence of th<^ rudder durln; there testa

yuB thought to be oufflcient to eliminate surfaoe effecte

entirely- Hevertheless the ship on which such a full-scale

rudder would noriDally be nounted vould be subject to this

limitation and for this reafion it vae conFidered appropriate

to operate the tests at such a velocity that the Froude Number

would be that of ij. typical destiroypr rudder -^'ith the ship oper-

ating at maxiraura speed* The speed thus selected res-.ilted in a

flov velocity which fell vithin the favorable op^^rating range

of the tunnel and dynanoaeter.

VHien the foregoing analysis is employed for the c^««

of a ^^^d<le^ in a free stream, o* is usually taken as the rudder

anpv;le. \Oiile it wae recognized that thiB uae of «* might not

be rigorously oorreot for a rudder behind a propeller with the

flow unevenly distributed by the propeller, an exact determina-

tion of angle of attack vras beyond the Units of the equipment

available. For this reafion '^ , the angle of attack, vas

aaaura<=!d to be identloal with ru; der angle.

The rudder fozt>e can be e^x^re&B^d then as

F « ipV^AfCoC )

2

and if by definition

C.,. = f(ot)

- 11 -

then

This force can be resolved into lift and drag conponents

vhence L = Cl'^PV^A

an<3 traneforr-iing

This Is the form in which the results are presented. A saniple

calculation is shown in the Appendix.

The rudder used hcid an aspect ratio of one vith an

area of 12.03 square Inches, a thickneec ratio of 0.18? and

30;< balance.

A conventional four^blade right-hand propeller ^rlth

a six-inch diameter and a constant pitch ratio of one wac used.

It wae operated at suoh a speed as to give a slip representative

of thsit for full-Bcale operation under the stated aseumption

that reasonable flo-"/ characterietiee at the propeller woiAld be

resilized. In order to ascertain this flo^-: and to get an average

flOH velocity at the rudder, a complete pitot traverse vas pvade

acrors the propeller ruoe. The reeults of this traverse are

shovm in Figiur'e 3-

In taking experimental data, the dynamojneter was lo-

cated at a speoifio transverse position and readings -''ere taken

for rudder angles varying fron 30° left to 30^ right rudder in

- 12 -

riOUBI 3

i«o

VUft or TSLOCITIlt ( ft./««e. ) ACROSS HtomiXR BACl

Tiinn«l T«loolt7 - 11.22 ft./«M.Prop«ll«y Sp«td * 1500 RHI

5^ inoreiaents. This pi\)oedure vae repeated for each of the

transveree ruc.oer pocitlons. Propeller and tunnel speeda

T'ere iTmlntalned constant thro>j^hout the procedure.

Plateo II through V show the rwSder located at two

different transveree poBitions for each of T-^loh two rudder

angles are sho^n. Tunnel speed at the time of the photographs

vas 11.22 feet per second and propeller spt^.f^d v^ae I50O P.. P.M.

- 14 -

.jtik.'

I/. RESULTS

Results are shovm ffntlrr»ly in graphical form

In FlgiiTpe k to 22.

5

- 15 -

H:H4--

.'"t;

V-\

±t-r

i-rr

JiiM PI

vxm-m^vi

n^v^y<?fyy;<;^jMta Ys ^(^ F r^yf^

A^KEiB

i--

r-1-

20« 2603J)0

3ijO 4pO

0F ATTACKI

i

-.:-4-^|-T

M.^._4...:.__K-

j;. J

i--h-H

V-r:

mm

^^

-.^0^

A P-

POm'^ OFlA^TAd^

m

'S'^A

10^ »•• si^ i^ieJji^ ^$^ ii^

\'\xvr^

it-r^

^H¥'"TitmMim

r-rr

Jpii±.i^-:^-q4t

tr.

fg1

-T—7---—-J-

!7IGUBE! I

^1!

i! i yiGUHE 13

:i-_.

iK2E2F4

! Rtmr^iiposrtiowfi i« ^ort-—

:

1

RIGHT Rtn4JER

I

TiKyT|RW3TffIR-^ -:ri»

•T"

FI(ȣ^ 14

i

'J' ••f- ITGD^ 15"

PLOT OF JRPBPy 90BPgIC]pliT8 .78 A«(g^ (|g ATlgABK

t RirrapBR PcjsiTICmV ij" fTillBOAIiD"^^

TTiaUBB"Ij5~

t-"-f

—

u

-CQEPi

'"JRUDUam P0$ITI0tfr 2f STjOtBOARl)

I

RKjHT RUDMllI

LEyr Ru:?>i®R'

.._J,1 i

1 •

:

+—t-

.:-.-4-

_^—

_

^

, , .

^^— ,—^JQ^J^_ .J^,^.

RUDDlER P^ITidN: ij" ^T/lRBOAHD

T"^""

- -'•

' ^.:

'

'

"

'^l M'' 1 ; TT

1

' TT'--

': •

'

','

\'1

1: i

::

,

1:;

1 ; I'tj--

;

,1 :,

; i,.|, ;L:-;

j

:

1

r, n Z'' '''}.

' 1

1.1, :

--«- _a._— +^ V- —-^ .

-— -•- ^ ^—

H

7, ;

-

/ /' r 1 V * z 1 |"1

'":

/ / '

/ /

Iv|

t

/ / /

":

/ ,

; r

a., „ ,.

/

1

t

4--* T-_(„ / 1_,

,, :,i, ,- lii ,, T-^ 4- : 1

—

i;|

u-a

— - — —t- \

f—

-

flzf- -i^ --] T—---- ^^~- ~j-^ ^-'-

u „ —_—

-e^^ ^-«hr-4 ^^- »-ji „^__

/

—4- ,i!

-J --+*H r^:+.

:

I -.*^-I 1;

,\ ^ '

, "V--1—f T- ,, ,

,

H4__ _ . J - ,1 11

1

'

. -4 z—

-

u_ 4^ ~ Jt—

/

s/ i

:, ''^

/(

i r

I J41

1

'

Lr4

— —

e

— — 4—

"

I- -+--->>-4~ ^ «^ •1- U--^r'——t'*—

» 2

"—

*

% z,

I tz , , ; , T-^ +— --** ^-4

—— (1—

c

c t—— —

+

—']

-4- — - —-^ ^^— — ' ''"

i^ -—

1

~ ~^ i«r-||}:|—

e

t-

— )- —-—

.

—— -s—"T^

___^ 1

, —

^

^I

-11

; !'

t

( If

,.^1 '

!-

——— ,

a4

, t

4 I" '« -

Y^

":

s^

:: A M—

h

— \

\ 1' __1

"5)

c

5

5v7 •c> N/ ^ / i v7 ,

'

^ 1• E

( oo

X5r'V J

,

^^,1 ^

\, N- (k

* ^ - T ';:«=^a

|.

'

. —

-

——

-

_.— _-. .—\

—t~

._. -wV ~t- "4 .„.. A ^~——^ —1-

--:-i» -^g —— -

—

—i A

-

—

4— -•

—

-

—

t— -

1^

\ \

'

:

'

,

'1, t

—__ ——— —

h

——

^

V^ — -i—— ^.^4—

^

_..,^„ ___

— ——_

_.

~-

_

«^

^—

f

:^ --«-—-^

t"1—

u

I— H

p- 1!1cM

~z

—_ ,_ „— __^ ^ u \

k V' \'\

r--^tv:~1

1:'.^_ r—"+ -—

r

^— 1:

z__- -,- —

'

— , -^r*-

.5r" y\~'Xn H ^ V

-, _ —

, , I^^ ~

z'

^„_ ^^ ^^^—

-

^ T s—r—

,

— ^_ X.-. -*t-~~ -_.

-,

——cL i » ^ >

'

1 » •>5 < B If i__ __; >. _ji—^ t>,

* ^ti

—,

L

U—

fltt fiu-

——

-

-'-^

—"^

••j in;

1

00

MeZP iiiiffiHIZ tri

,

"V^ '—^

-'

.. " r"^ ''' "17

1 !;

:

I

i'

1

,!

\

'

"t : -

i

, ^ ___—+— +«-+ (-*-—^ t— -tr-* .,—

-

7; „^ a7.

jlll

.,

—:•— \,,\ ^i- i

'

i

"

'; — — —tfk<

'

—'A I .. L 1 t1 * '"'

ar.

— —7 -

1

i

T Ti

''

'

~1. ^

'. 1

,

j -;.1

'

/1

• • 1;

/,i-

i

i

'"

'

1

:l

< J1 i 1

.:

,1 ''.''

1

'

, i i .i

;

.

'

'

J t '

J:

-Mr7

—

.

! _

£I

f5>>

'9-^ ~"*

11 ^ V

,L,^r f

—

i

t 1.

^^^ ,_,

i

-.-_'•'

1

——1

)4 ^j ,.v'),.,.~t—

-

— — ,

_1 -_1r— ——f

- 2i — — [

' '

'

'1 \:

. ,

^

\— /vT :

-*-_ ^ 11

'

\ /\ \ TT -

— — — -— '

! — J*—-—]

L -.

\| \11

a—

i'

]- -'1

,

-^ —i

+ T~^B ~^ ^ T^r V- -r——— A i

—

—

r

f -^ ——p. 1

.

—__i

— / 1 )f

__j:

— —n

« k. —T""^—

7

ID

-1

" ^ —

^

—/

'

V y /,

Ul —i

i 1 —— —5) Ic

— — "" — —,— / i LjU 7v'-4a. —— i

n~ —7-^— :

^^

1

—-a

s^——~ !

. --9

——7- i7 ^'r77"ii^-

©-La

-0r

jH/

r- —— 15

\

:

-r

''

'

M 1

V'

^ '+

-/-iU- u.

— —i

i !

:

f i1 7 i^ i..i ^1 .: M

1

: i Tir t1

/.en

09

4f

(AJ

a.

1:

,

:;,

;>

'

_t z t

— -^

—

— -_- M .— —— -^ —

H

— 4 10 — _—

-~ ~~ iliL

«c— —— —

1

—1

11

'^

rr-r

i-

r— —r -*-t -—ec_

i-

^— __- — ,

—

*-T- '

'

i...

.

L 4 __ — --

_

—4:

^— -^^t , 1

9-— — 7-— __J — r^ \- \- \ r — —; 1 __

: , 1

, \ _j^ \ ]

'i —

+

^ ^ V? ri~

'-;

*.^_n '—^—^—^—— -^ P

\it'\\- CI

_— ~-

I-.T—

^-.— *——--

,—

.

— u- -*--]~---— "--^

— ~""

\

1

I1-4-——

"

—— t

jL: '

•

1 t—^:

^ !:--: r

'

i ""~—

-

— .1 X

I7~ \:7+-4i—

————\-

''

z.

' L

.*-r^ +**T

^.4-1-

--T~ _^

^ ^

-,—

^T— T-f—

<

^ V

- /

z^-ft-t,t nr--^

'~ *~*

-i — —— — — — — —~—

i ill-1 i-iii

. li-L

-^^- Tr*^ ff ^~~--+^^

———

i-<

—__

_* 1

—

m

——

«

Tt3

<

liiiM Tit m1

,-:— -r-

I '

"; T-f^'

-

'

11

!^:

''[ ' (:^

:

^

I-

;\_

,' ^ iiii

['

''

i-'

;

i: 1

.

'

':1

-i 1.

i-, M. — — — __

—

n^—

-

_ — ^ i|j;

rT^4+if-i-pJ4i+^- 4+41

ftV rt*—

^'t

-4 —^—f—^

—

-^T-^ ' ^^rfir 1.1 i

i

''i ! \

'

i

-n r-1

n-*-

il4

:;;;,;.{.: 1 [ 1;

j

: -1:,|

|,, r" .

.

:'. ^ :

,

;

'

1 !1

i

''1 ii '

1

1 1 1

\"\i

' <1

''1 ',';

1:' ~* ^

'

M. l"!|«erl+^t ^r

1

trht '

.

!."t:

t4+ •4j'

W'^'''o1-

-! '1

-1

; ^1 r~ .11 :;..

'

1 , :

'S4 — —^ 1

—

, ,

_.., ,*_ _— _ .,1 .^

—

,-—

,

.^

—

\ ^— 4^^—

.

-+-* —

^

— ~-e—^——

1

—

^

; !

"

:i

1'

1

^T*

_i.

'(

, ^

^-4 - T—

^

,

—;

!

1

|t4

-t 44 *-

.1.1

——— -^

t—

iff

i

—-— —— -t^ l~- 4^ 4^^ -i-U|t^ i— .u-— -+-4

•^-^N1

'

1 1 ^ T-r

, I

1

1— ^

44-

e""'

r-n--^

^

-.i II, [.. 1., t~ -*~- r —1

-r—

*

-T+— \ \

',

-t • r+^ ,.|. ^ -t- 44-— rt- "^~~r^t— —a. ..u

1^^.—.— i_

— It.

o-

o— ^'-

. :

'!:

-I — - 1^ — -—»_^—li

r

Y'1

-4--

1

F5 ^

4--

,4

P

__— ^+4+

-p++

n ,!

(—-h-

,,. , (

1

'

:

7-I:

1'

!

:

*1

'

_^,-

t

J-

1

• ,,

1

'

—iJ

J

p"^— 4": ;44

T- ' ^ —* +'^- tc —|-n- 1-^^

~-~)

y J. At t+J^

«

< H t4-

:li'

'

,

¥t

^rr -r-

•

—

^

-1Tfp

-+*•—*~»k -T T++T 1^*n i*

«

*

c!

r 41

1-

t

1^

_—_———

K

— r--^'^—

T 4 - ! ,; ,~^

^"5 :«

',,

M_

—

^

t—

T

r

liir^T^ -*-' 1

'

I'J

-4t

r- -t- -<-—,

1—.»

' 111

4j1

i4f

-^ — 1

—

<

E—

-^ i-f-U. -4

llP^^~r^^T

1r-hr

'.!.^-i-

''1 1 ^ V.I.. ^

'*t-, ,{ '

•' :

—T—Bt.

--^

rt—*-

-- — ._.^~ f —

—

I^Ll-^L;

i

,

!

,-;1

i1 ^ I

'

— — — I"'-"

: 1 f:

*t4ij]^-ij, '-

1

; ±^' — -

' '1

[; \

1

.__1 —

-

, J1-

_, -*

u — __. -_,-^-

4-^^—-—^ '- —

„

—1— — ^--^ r-

'

- '

"*~rTr — (5. ——

^

. 1J» "

'

1

d-'.i.i-

445Tt'

1

,

, 1

: 4 ' 7j'

rt;

|i ." -'

: I

r*r^"T"1 ^\ 1 4'

' t ;

t^f^r .^ ' : -^ -^-^

'

'

!

-t-^

1 ——

-

-"H

'

'

' f

47^r —--—— -+— ————— ^- —

n

: " —^ft~ \~] :

,

'! ; ^

•

'

—<-r-*—1

' —^"<t--^

L.^r

~-

1--^

—— --

-

;jiib iJTfEm iiL^' ^

UiiJ^li

4_J C4 ^T+

19! _

iti

j

1

i

1'!

—

i<.

;l

—J

n|

1 — — —.-

™.

1

^ ;

I

'

. 1-

G^' '4

l''-^

Ua J

lO\

. :j:

C •i 1

i; *^

1''l^-

u •

N,K ^

-

1

,

i:

:

,

c\ 3

\ ac 1

I

=

Iko \ \t

1 "V^

I S\

' 1 K2

:j

'

,

\I :^ ^ ._ _. ^ _^ .

fe;: 0- ;;

1

I \ \ a

3-" bl1

\ \i•

. \ d aJ

a:III

(

11

1 c 1

mi_

! >11 1

(0 c

:;-,z< s \ s 2

»- e:'"-

1^^

-

!.

/4

iH—

f

< >1

'

'} / /'

/:u

M -) j

/ // «

r.--

l\ /__- _L

1 1

1-7_ -^ __f f*r

—^— —

T

—— 1-

n- -^ -T-1 I"

^- -h __L.

*— -^ i^^ ^_ -T-— 5e^— -'— —^ ^ hi ^

4

—. 1

c

1;

— —_t

i-'i K it~1

f C

-iUJ io

n0^

g

^i

Z ^J

i+^

—_

--

^— 1

-T-^ ,

—i: ,

\ ., t ,;

-[—:: _.

—I— —

I^

— —— trt-

O

—— —

h

:—— — -— -^- — — — — —~—

^

IT^—

—rr

—— ————;"l

; ^

— H—

-

e-^——

>—L_— -f—

___

—1

,

rr^-+- _ f^

-" ^— ——

—

i

^

1.

*--- —

;

T~

r~^

:;—-T- —

'%— —

r

—

r

-+-*—t ". f

—-^t

^— -'-

I-_

':

-•ai-— i^ i --^

—

H

—

^

-«

— — —3^

r^ "H':

t+-^ -•—;

'^ -^n!t

f— -^^j

, r- -7'— --^ U^ —-^t-

1^ ,..

. ... z „ ^ __r I"^

__ ,

^T —1,1,^.

——— j^.B—

I

— ——.l--'^

1 , : .

^ WJ-^:}j^1 U

,,

.

——1

J-

1

—'~ "-.!'

1 i^;

'

' T^"n^ ,

'

: i

,'J if-, i;

,

II l[-

•:

1i

:

'

' i ,!

;

il'

'

!

i

.

"j' illj"

'

i

''

! ^nr" '

.1 1 1

M-1

1 i

'

„ I

1 M:

.1

!

^

"',:

/i :J

!

Ti?

/:

M!

,M m! Pi M '

;f

/ / //

1 /

F/ /.

/ / //

1 /...1

'

, b

CvlJ /

//

1

'

//

vu'

^

/ /: 1

'' F i

at1

/(i ,

'

3 1 1 j i''[

I /'[

*

r :i_^^

J

'/ '

fri ""^ ^,

,

"t.

\ /1

\ /

;i

[ •

1

\//

A1

1

. 1

.

,j

//

N1

CM /» '

.f, •

cll

1

/

' < ^

I)/ to >

3,

/

*'

<^: \. i-

1..1

/

6—it1

1

i

3 o/

, !

/ i,

\ ll:

J::-[

/ oi ll

(r / ;

1

/''a\-

— — S

— t- --— Ulo->

— — — -^- —~t

-—4 4- —-H--^ 1-

"*(

XH^_L__

~J

1-

___ ^ ~~— .1

^'

r ^

h ^^TF

31

\-

H ' ' M ' +'

5

ST7/

/ /

' ^' i [

j;

. —

_

._^_ - f

^.1 ^__ /., MM

' :':

'

_»* ~ -nt

"f—— ——— "" —/

—-f:- f~ t' ;-

; ir »/-If

1

—ft

'/' i I

i

^^ i-'*

T!: :^

/

"

1"'~

xJ- 1

> t

- /' ' r

i:J^'

~' :-f

ij

J )—

-

—

e

— 1- -—

c

1

^1—-1lO 3

1^Tr)4i_

Z 1'

\\ •'

ff

1-;!^

11

. 3

1

\

\

\

\<> 1

iM*

^

\\ \

''.:•. \,[• t\ jnj

^-^-— — E — T-^-^ -^^^ H—\_ _.. A.

1L. •! ^^^ '

' [.-^ 1^

M

-f4f:

'—— — —

-

—— -^ -\— \— ——-^

^t-^-^'^^ ^-^—

'H\

\T"^ ;

,

'

-1

1-1

1

-,!-

^ \ \ 4- H— ^ .__ ^— -

—

EE3

<£*~— ~^. J^.- V1--_._\

ItL— 1

_

t- f 1 !-M-

—

—;\

\\ V

— -\-^h f— a

'iii

__ ^_ ^ __. __ — ^_^_--V

__ ^\

: ^; I

:

, ; , ! I:: M1

M1 _^

,,'\j

,

ill \ \1

'

1

V\''' 1

1

[

'

'

, V'- !

"^ ll; M V I \ h 'ji' :

i-.r1

;.

1 \;.i -^

\,

;\ ,1

1

1

Xi^ ^ r—^_ ^aV > .:

1

\'

, \ " \ '

' :, '

'''f-i

,:

\ %' : \-i

1! r

V v r -

V-^-^ N \h^-^ \ n -, —— .

<K—

1

i:

-!J

M i

' M '

Mi

'

±:

;

'";

^1. ;?:

i ^ '

j <; «'

:

!''

j

'

;n ;m

:

i L— L_-J V , i=u - -^l—--i

__t

——'-- — — ---—-^ —-T-r—-^-^^^

T-'

;i i^:

1

Wl«&—tH I'm r-^ 'T, h

1lt^'M m. hffli ^i^f ^i! '-I

'-

TfiT m n^m Sirms 1liiiM Itif 1

From th« IndlvldUiil curves of Ol and Cq versus

angle of attack, Figures 4 to I7, it fi^ppei^rc that the values

of the coefflolftnte at th« various anglee of L^tt.^ick are In

the right order of magnitudft aa ooraparecl %rlth values ob-

tained from previous Invectlgatlons for a clmllsr rudder

In a free ctreaja^ '. Further the general characteristics

of the ouirveB appear to be reasonable by the sane standard.

There is apparently eorae tendency towards higher copfflclents

vhen the riir^cer le in certain poeltione over oorreepontilng

free etreaa values. A direct comparison may be obtained by

comparing these curves with those of Gogen and Tara -^. It

should be noted, hw-rever, that the investigation of the latter

thesis was oondiKSted with the tunnel operating in Its denip^ned

direction. For this reason It le probable that flo^r conditlone

varied between the two theses, ami direct oomparlBons might b«

aialeading. The Intent of the present lnvestlPi;ition, ae stated

previously, has been Itialted deliberately to comparisons of

relative oharaoterlstlcs among the various transverse positionf.

,

ancJ- assuming that angle of attack and rudder an\le are the eame.

It is recoiE-^ended that a spherical or universal pitot tube be

used In future Investlratlone in order to obtain three coripon-

ents of velocity. This Kould eliminate the necessity for the

assumption concerning angle of attack.

In evaluating the results of this theslP, all informa-

tion must be examined in the light of the fact that a rirht-hand

propeller v^s used, and that the same infox^a.tion for a l»ft-hand

- 35 -

propeller a^ifst te worked to the opposite hand. A rlght-h^nd

propeller Ifi deflri'^d as one turnlag oloolcwifie when viewed

from astern.

From the plot of lift coefficient versus transverse

rudder position as a fraotion of the propeller radius » Figure 18,

it is Immediately apparent th&t the lift coefflolent falls off

sharply for both left and ri^rht nidder for all rudder positions

on the starboard side of the propeller a.xl«. Sirailarly it is

apparent that for rudder positions further outboard than two

thirds of the propeller radius on the port side of the axis

the lift coefficient decreased rapidly. The optimum position

for Biazimuia C|^, therefore, narrotrs to the range between the

propeller axis and two thirds of the radius to port. Further

it is apparent as the rudder position is varle*^ fron one third

to tvo thirds of the radius to port, that while C^ for left

rudder is higher than that for the oenterline position, Cj^ for

right rudder is dropping sharply. Since it is patent that a

ship vhioh will turn well in one dlri^otion only is undesirable,

the optimum range is further narroved to the range between the

propeller axis and one third of the radius t^^ port, 's^ithin this

range ther^foa^e a close scrutiny of results is required.

For left rudder vlthln this range the rudder position

at one third of the radius to port is quite obviously the posi-

tion of maximum CV ^or all rudder angles. For right rudder,

aaximura values of Cj^ occur progressively closer to the propeller

axis as the angle of attack dporeases, vith the best value ap-

pearing at about one fourth of the radius to port for an angle

• 36-

of attach of 25^. Taking rlgbi and I'-ft rudder 'iogeiiher to

obtain an optlmurn value of C^ for the cunablnat*.:>n, It would

appear that so far ae Cj^ alone le conoem«d the beet rudder

position would be bett^een one Blxth to one third, of thp radius

to port depending upon the particul».r rudder angle for vhioh

optimum turning Qharacterieticfl are desired. It will be noted

that the points for an angle of attack tor 30*^ are plotted but

are not oroae faired. These curves ^ere omitted delibelately

sinoe it was found that rudd»=!r breakdovn vae beginning at or

near the 30*^ positions and any curves plotted through theee

pointB eould only be mieleading. llhls appllee to all of the

cross curves of ooeffloient v*^reus transverse poeltion.

From the plot of drag coefficient ver«uo transverse

rudder position. Figure 19» a clearly defined ainiraufa value of

C;p iB Been for all left midder angles at about on© sixth of

the propeller radius to starboard. Further, the value of Cj^

for all left rudder anglee 1b seen to have tvo maximua values,

the greater of which occurs at a nidder position of approxi-

mately one half the propeller radius on the port side, and the

lesser at a rudder position of approximately one half the radius

on the BtarboaiHi side. As the rudder moves outboard of either of

these tvo positions of ssaixlrauiB value » the coefficient decreases

with increasing distance from the centerline.

For right rudder values of Cp, a minimum value is ap-

parent for all rudder angles at about five sixths of the pro-

peller radius on the port eide» and a maximiiia value is noted at

rudd*>r positions varying from about one sixth of the radius on

-- 37 -

the port side to about one half the radiuf? on the T>ort elde.

Conslciprlng right and left ru-r^uer to ether to ob-

tain an optlmura value of C^j for the comblncition, there is a

minlnuni value at approxiri.\tely one-Blxth radius on the st.ai>-

board aide i^nd lov valuec at both extremeB of the propeller

race. In view of the preo€M3.1ng anal^/eif* of C^* i^ vould ap-

pear that the position for alnimum Cp nearest the oenterllne

Is of the raoet interest.

The curves of C^j and C^, Figures 20, 21, oind 22, shotf

the sane trends as those of Cr and C^ ae irould be expected.

They are included since these coefficients are not infrequently

us ed

.

The results would appear to Indicate that the optijaum

location for a rudder behind a right-hand propeller may not be

on the conventional oenterllne position but posolbly at a loca-

tion near one sixth of the propeller radiua to starboard.

Further intensive investigation would, of course, be required

to coni'irm this observation. It ie recommended that future in-

veetlgations be along the llnee indicated belov':

1. A further investigation of lift and drag, employ-

ing eraaller increments of tnineverce position, in

the range from one- third radius port to one-t lird

radiuc starboard.

2. A further invest igatlon employing various combinations

of tunnel and propeller epeeds.

3. A further Investigation ©aploylni varioun combinations

of rudoera ana propellere.

- 36 -

^-. A complete Investlpal-lon of flo»' conrlltlonG a.cr-ofi6

the oropeller raci» using a s y.T^rlca' or •imiv?=»i'>':al

pi tot t;ub». This vjuld elinina.tie t^w n<=o^;"'nity

for as'-'urDim', that un.'-l*^: of attac' »^oua.lG iry'd^.r

»

J

./>

For a inidder of the type used In theBe experiments,

operating behind a right-hand propeller th*^ follovlng oonolu-

Blonfi may be stated:

A. Lift Coefficient

1. For right rudder, ruoder position for

rnaxlraura Cj_^ varieB frora one third of th« propeller

radius to the port Bi^e of the propeller center-

line at an anr:?le of attacli of 25° to one third, of

the radius on the starboard side for an angle of

0®. A reasonable meyun position for optlmiua C, at

all angles of attack could be taken at the center-

line.

2. For left rudder, raaj:inium C, for all angles

of attack occurs at a rudder position approximately

one third of the propeller radius to the port side

of the propell<^r centerllne.

3. An average of right and left rudder value?-

for optimum C, indloatee that this will occur at a

rudder position between one sixth and one third of

the propeller radius to the port side of the pro-

peller centerline.

B. Prag Coefficient

1. For rioht rudder, the rufider position for

miniinun C-^ occurs at about five sixths of the pro-

peller radius to the port side of the propeller

oenterline. A position of high C-q occurs between

- 40 -

one elxth and on© lialf of the propeller rfiulluc

on the port side.

Z, For left irudlder, a rudder position of

approxliaatdly on© sixth of the propeller radius

on the ctarboai^l elde of the propeller centerllne

g^ves mlnlraijirQ Cp. Kaxiratn valued of Cp occur at

about one half of the propeller r&dlup on both

sideB of the centerllne and deoi^ease vlth further

movement towards both extremee of the raoe»

C. Qptlaum Rudder Looatlon

On the basic of this Investigation alone, using

a single right-hand turning propeller, a single

inidder and constant speed, there is evidence to

Indicate that an optlcaum rudder location, not

neoesearily on the centerllne, does exist vrhere

high lift-drag ratio and high Cj^ ooour simultane-

ously.

- 41 -

It Ir. reco'-mended that future Investigations be

alon^': thp llnefi Indicated belo^'':

1. A furth*«5r InvpBtlgatlon of lift and drag, employing

siaallrr Inorenents of transverse poeltlon, In thp ran^ie from

on**- third port to on©- third starboard.

2. A further Investl ..citlon employing varloue combinations

of tunnel and propf^ller speeds.

3. A further Inveetl^atlon employing various combinations

of rvidcf^rs and propellers.

4. A complete Investigation of flov conditions acroer the

propellf*r race uslnp a spherical or universal pltot tube. This

would eliminate the necessity for assuming that an-Qle of attack

equals rudfi.er angle.

- 4? -

t m

VIII. AP--^FDiy

A

.

3up;:)leta8ntary Introcluotion

Certain phases of th? InveatLation not Included in

the ns-in body of the report are present ed here for the b'-neflt

of those Interested. In the technical aepeots of the problem eo

that the mfthoda used and results obtained may be independently

eviiluated.

B. Details of Procedure

1. Propeller speed - The propeller revolutions were deter-

mined by an electric clock counter mechanism which au~

tonuitically counts the revolutions over intervals of

one tenth of a ralnute .

2. Tunnel apeed - For the purpose of setting tunnel speed,

a magneto vas attached to the tuanel Impeller shaft and

the voltage gen?^ rated was read on a copper oxide recti-

fier type voltmeter. This arrangenjent was used for the

coarse adjustrment; the fine velocity reading being given

by 1ihf» fixed pltot tube deBoribed in the body of this

reoort.

3. Modification to propeller tunnel - Heversing th^ flovr

in the tunnel \;as uocompliahed by a svitching arrange-

;nent vhloh revelled the polarity of the impeller motor.

It vfas necessary, ho^^ever, to provide an additional

thrust bf^iiring on the impeller shaft, since the exist-

ing b'taring vas cajxibl'= of reslstlnfi thrust in the

ahead direction only.

- 43 -

I

4. Dym.noffleter cs.llbral *.on ourvee ~ It shoulr; bf^ noted

th-jtt the calll lotion curvfts sho^m In Figure 23 are

not constc.erec rRllablp for tba ipper tr6«.nsv«rBe,

upper lon^vltTKilnal, and toraue ^bl\x^:(^b, Ihxrinp- thf»

calibrations it wus found that f^p curvftB for the

lov-er tiTinsvprse and lo^.'er longitudinal gaugf^e

could be repeated at will, but that th(» curves for

thp uppp:r gauges were sojopwhat erratic, ifhlle those

for fhe torciue gaugeo e?e.*affcl to df»ppnd Bolely upon

the tension in the machine screws vhich Beoured the

linkages to the strain gauge ItB^lf. Since the

tension in thf»Be eorevs varied widely frora one cali-

bration ran t ) another (although it could bF held

constant during any eine^le run) and further since

during* the t?:s?t runs^ the tension in these screvrs

changed due to the vibration in the dynaiaometer,

the use of the torque gauge v.'a.B abandoned. On the

other hand, both calibration and test readin.os could

be rep<=ated eagily for th?^ tuo lover gaugee and this

thesis relies upon the readings of these t^ro gauges,

G. Tables of data and calculated coefficients - TABLE. I

through XIV.

Original data is sbo"!m in the tables includec: in the

follovlng pa- 68 under thp columns nar'-ced LO*'ER LO:iGITU~

DIM/iL OA'-JC'-" R"A!)im> and L0'"^:H TH/V^IoV^.RS^ GAUGE RKAOIHG-.

- ^2^ -

.-jaftPiL

ZIBLI I

TABLE or DATA AND CALCULATED COlDTICIiaiTS

BIGHT BUDDZR

HUDDEE POSITION: 3» TO POBT OP CENMELUn)

ZERO GAVQE BEADINGSt

LOVZB LONGITUDINAL 5835LOWER TBANSVERSE 6005

H6LI orATTACK

LOVIBLOHO'LGAUGE

READING

LOVIBTBANS 7ERSIGAUGE

READING

Lirrcoir.

DBAGcoir.

NORMALPOBCIcoir.

TANGENT.-rOBCEcoir.

5730 5875 -.0662 .0604 -.0661 .0604

5 5740 6130 .0644 .0546 .0698 .0487

10 5706 6400 .2060 .0761 .2155 .0390

15 5625 6710 .3676 .1231 .387 .0239

so 5530 7000 .619 .1786 .549 -.0095

25 5400 7320 .686 .2550 .731 -.0590

30 5230 7660 .864 .3540 .926 -.1239

35 5050 7890 .984 .4600 1.070 -.1880

TIMPIRATUBI T 4d

^ AYq^ = 11.565

TA£LE II

TABLE OP BATA AND CALCULATED COETPICIENTS

LEFT RUDDER

RUDDER POSITION: S" TO PORT OF PROPELLER SHAIT

ZERO OAUOS READINGS

:

LOVER LONGITUDIKAL 5810LOWER TRANSVERSE 5970

AN(aE OFATTACK

LOVERLONGaGAUGE

RTJLDING

LOWERTRANS V1?;RSE

GAUGEREADING

LIFTCOEF.

DRAGCOEF.

NORMALFORCECOEF.

TANGENT.FORCECOEF.

—.- —

^

—.— - . .._ .i—

.

5 5750 5680 .1472 .0344 .1499 .0214

10 5690 5420 .2793 .0690 .2864 .0193

15 5630 &L10 .4365 .1032 .4489 -.0133

20 5545 4825 .5910 .1521 .5985 -.0557

25 5400 4510 .7435 .2355 .7745 -.1008

30 5245 4240 .8580 .3242 .9050 -.1481

TEMPERATURE oF 61

%kl^ s 11.544

TABLI III

TABLE OF DATA AND CALCULATED COEFFICIENTS

RIGHT RUDDER

RUDDER POSITION I 2" TO PORT OF PROPELLER SHAFT

ZERO GAUGE READINGS

f

LOWER LONGITUDINAL 5835LOWER TRANSVERSE 6005

ANGLE OFATTACK

LOWERLONG'LGAUGE

READING

LOWERTRANSVERSE

GAUGEREADING

LIFTCOEF

IRAGCOEF.

.0604

NORMALFORCECOEF.

TANGENT

.

FORCECOEF.

5730 5880 -.0636 -.0636 .0604

5 5720 6155 .0781 .0662 .0836 .0591

10 5695 6470 .2425 .6806 .252 .0«15

15 5620 6790 • 409 .1240 .427 .0028

20 5520 7120 .582 .1815 .609 -.0286

25 5410 7450 .755 .2445 .786 -.0970

30 5190 7780 .928 .3720 .991 -.1411

35 5010 8100 1.093 .4750 1.066 -.2370

TEMPEEATUEE ^I 47

%AVo^ = 11-655

/

TABLE 17

TABLI 0? DATA AKD CALCULATED COHTICIEMTS

LIFT HUDDIR

BUDDIE POSITION: 2" TO POBT OT PfiOPILL]i£ SHiLIT

ZIRO QAUGI BUlDIKOS:

LOWIB LONGITUDINAL 5810LOtnSB TBANSVIRSl 5970

ANGLE 07ATTACK

LOVSBLONG'LGAUGE

BEADING

LOVERTBANSVEBSSOAUGS

BEADING

LinCOBf,

DBAGCOET.

NOBMAL70BCEC0E7.

TANGENT.FOfiCS

COET.

—6 5725 5570 .2038 .0489 .2065 .0266

10 5655 5205 .3890 .0890 .3980 .0199

15 5596 4930 .5295 .1233 ^5430 -.0175

20 5470 4565 .7150 .1954 .7375 -.0609

25 5310 4220 .8905 .2869 .9300 -.1168

30 5080 3850 .9345 .4195 1.1420 -.1769

TEMPSBATUBE ^7

^A^'fJ^ = 11.646

60

TABLE OF DATA AND CALCULATED COEFi'ICIENTS

RIGHT RUDDER

RUDDER POSITIONS 1" TO PORT OF PROPELLER SHAFT

T^BLI 7

ZERO GAUGE READINGS

x

LOWER LONGITUDINALLOWER TRANSVERSE

58356005

ANGT.E OFATTACK

LOWERLONG'LGAUGE

READING

LOWERTRANSVERSE

GAUGEREADING

LIFTCOEF.

IBAGCOEF.

NORMALFORCECOEF.

TANGENT.FORCECOEP.

.06615720 5950 -•0281 .0660 -.0281

5 5710 6240 •1:^26 .0719 .1286 .0609

10 5670 6570 .295 .0950 .3065 .0422

15 5590 6915 .475 .1410 .495 .0135

20 5460 7250 • 649 .216 .685 -.0193

25 53S0 7620 •843 .296 .764 -.0876

30 5100 8000 1.041 .423 .889 -.1548

35 4910 8300 1.199 .532 •985 -•2555

TSMPEEATOHS ® ? 46

^A7o^ = 11.566

TABLE VI

TABLE OF DATA AND CALCULATED COEmCIENTS

LEFT HUDDER

EUDDER POSITION: l" TO POBT OF PBOPBLLER SHAFT

ZEBO GAUGE READINGS:

LOWER LONGITUDINAL 5810LOWER TRANSVERSE 5970

ANGLE OFTTACI

LOWERLONGaGAUGE

READING

LOWERTRANSVmSE

GAUGEREADING

LIFTCOEF.

DRAGCOEF.

NORMALFORCECOEF.

TANGENT.FORCECOEF.

— — — — — —

6 5720 5560 .2085 .0517 .2120 .0334

10 5650 5230 .3763 .0919 .3863 .0263

16

20 5460 4530 .733 .2009 .758 -.0614

25 5290 4170 .9166 .2992 .9568 -.1164

30 5100 3820 1 .0945 .4005 1.1484 -.2004

TEMPERATURE F

/'^AV^ ^ 1L546

59.5

TABLX VII

TABLE OP DATA AND CALCULATED COEFFICIEBTS

RIGHT RUDDER

RUDDER POSITION I ON CENTIKLINE OF PROPELLER SHAFT

ZERO GAUGE READINGS!

LOWER LONGITUDINALLOWER TRANSVERSE

58356005

ANGT.E OPAl'TACK

LOWERLONG'LGAUfiB

READING

LOWERTRANSVERSEGAUGE

READING

LIFTCOEF.

IXUGCOEP.

NORMALFORCECOEi'.

TANGENT.FORCECOEP,

5790 5950 -.0280 .0259 -.0280 .0259

5 5765 6245 .1251 .0402 .1285 .0292

10 5710 6600 .3105 .0737 .3180 .0186i

15 5630 6920 .4780 .1180 .4920 -.0098

20 5530 7270 •6600 .1842 .6820 -.0525

25 5380 7610 ,8370 .2620 .8650 -.1165

30 5180 7900 .9880 .3770 1.043 -.1676

35 4990 5030 1.147 .4860 1.217 -.2585

TlMPEBilTUSS 'T 44

^/Zkl^ r 11.666

TABLE VmTABII 07 DATA ASD CALCULATED COUTICISNTS

LXTT BUDDIR

EUDDSR POSITIOH: OH CENTIBLIltE 07 PBOPXLLSR SHAJTT

ZXBO OAUai ESADI5GS:

LOVIR LONOITUDIfiAL 5810LOVIB TBAHS7XBSI 5970

AHOLX 07ATTACK

LOVIBLOHO'LGAUOI

BEADING

LOVIBTBASSTIBSI

GJLUOI

BEADING

LI7TC0E7.

DBAGC0E7.

NOBMALFOfiCE

C0I7.

TANGENT.70BCEC0S7.

6

10 5730 5250 .3582 .0459 .3609 -.0170

15 5640 4950 .5195 .0978 .5275 -.0403

20 5536 4610 .6908 .1579 .7028 -.0878

25 5380 4280 .8609 .2474 .8858 -.1395

30 5190 4005 1.0018 .3559 1.0439 -.1929

TEHPEBATUBI 7 58.5

A7o** = 11.547

TABLI IX

TABLE OF DATA AHL CALCULATISD COEFPICIINTS

HIOHT fiUDCXR

BUDDIB POSITION: 1" TO STAHBQAKD OF PROPELLIE SHAIT

ZIBO QAUOI BXADINGS:

LOVIE LONGITIXDINAL 5810LOVIR TBANSITCRSX 6010

ANGLI OFATTACK

LOVISLOHG*!aAuai

BEADING

LOVnCR

TBANSVIBSSQAUGI

RIADING

LIFTCOIF.

DBAGCOXF.

NOBMALFOBCXCOXF.

TANGSNT.FOBCICOIF.

5760 5975 -.0178 .0287 -.0178 .0287

5 5750 6250 .1251 .0345 .1278 .0235

10 5725 6535 .2735 .0489 .2777 .0005

16 5675 6845 .4356 .0778 .4412 -.0372

20 5500 7060 .5480 .1782 .5753 -.0190

25 5400 7400 .7254 .2357 .7656 -.0943

30 5200 7700 .8815 13504 .9386 -.1378

TIMPIPATUBI ^I 54

%AV^^ =11.550

TABU I

TABLE OF DATA AND CALCULATED COSITIC IlDTTS

LUT RUDDER

RUDDER POSITION: !•• TO STARBOARD 07 PROPELLER SHAIT

ZERO GAUGE RBADIE08:

LOVER LONOITUDISAL 5810LOVER TRANSVERSE 5970

ANGLE 07ATTACK

LOVERLONG'LOAU^

READING

LOVERTRANSVERSE

GAUGEREADING

LI7TC0E7.

DRAGC0S7.

NORMALFORCEC0E7

TANGENT.70RCEC0E7.

6 5765 5660 .1575 .0317 .1596 .0177

10 5690 5290 .3458 .0690 .3526 .0079

15 5640 5060 .4665 .0976 .4685 -.0268

20 5520 4665 .6630 .1665 .6880 -.0706

25 5360 4320 .8398 .2582 .8700 -.1202

20 5160 3930 1.0380 .3730 1.085 -.1969

TEMPERATURE ®7 62

%A7o^ = 11.543

TABLI XI

lAHLI OF DlIA AND CALCULATED C013TICIENTS

BIOHT BUDDSE

BUDDIR POSITIONt 2>« TO STABKIASD OF PBOPMXSB SHAFT

ZIBO GAUCa BSADIHOS:

LOVIB LONOITUDJKAL 5810LOVXR TBANSVIESI 6010

AHGLI OFATTACK

LOVSBLONO'LOAUOS

BXADINO

LOVnCB

TBANS7fS8XOAUOS

BIADINO

LIFTCOUP.

DBAQCOIF.

NORMALFOBCICOSF.

TANGENT.FOBCSCOSF.

57'X) 6980 -.0155 .0230 -.0155 .0230

5 5780 6260 .1302 .0172 .1315 .0058

10 57» 6520 .2658 .0469 .2690 -.0010

15 5670 6780 .4010 .0805 .4083 -.0260

20 5550 7100 .5684 .1495 .5839 -.0645

25 5445 7450 .7513 .2094 .7683 -.1272

30 5280 7780 .9222 .3045 .9525 -.1972•

TIMPIEATURS " F 56

% A7o^ r 11.549

2A£LI III

TABLB or DATA AND CALCULAT3Q) COSTPICIENTS

LSFT EUDDSR

EUDDKE POSITION: 2" TO STABBOABD Of PEOPTBLLlffi SHAJT

ZEBO OAUQE BXADINQS:

LOWKE LONGITUDINAL 5810LOVIH TBANSVTCRSI 5970

ANGLE OJATTACK

LOVIHLONGaQAUG3

RTCADING

LOVBRTBANS7IRSI

GAUGEHEADING

LITTCOET

DBAGCOIF.

NORMALFOSCECOEF

TANGENT.FOSCECOEF.

5 5740 5700 .1371 .0402 .1401 .0283

10 5690 5390 .2945 .0690 .3022 .0167

15 563» 5100 .4416 .1091 .4665 -.0089

20 5510 4745 .6235 .1723 .6450 -.0513

25 5360 43ao .ti098 .2640 .8450 -.1027

30 5160 4055 .9740 .3670 1.0300 -.1641

TEMPERATURE °F 62

%kl^ = 11.543

TABLS XIII

TABLB OF MTA AND CALCULATSD COBFFICIINTS

RiaHT fiUDDIB

RUDDICE POSITION: 3" TO STAfiBOAfiD OF PEOPISLLSR SHAFT

Z5B0 GAJJQl HSADINGS:

LOVER LONGITUDINAL 5810LOVER TRANSVERSE 6010

ANSLI OFATTACK

LOVERLONG'LGAUGE

RXADING

LOVERTRANS VKHSE

GAUGEREADING

LIFTCOEF.

DRAGCOIF.

N0R14AL

FORCECOEF.

TANGENT.FORCECOEF.

SVTO 5920 -.0458 .0230 -.0458 .0230

5 5765 6180 .0884 .0259 .0908 .0181

10 5745 6430 .2132 .0374 .2163 -.0002

15 5690 6690 .3643 .0690 .360 -.0261

20 5600 6970 .5000 .1208 .5104 -.0578

25 5480 7225 .6328 .1896 .6540 -.0951

30 5310 7390 .7189 .2872 .7665 -.1099

TEMPERATURE " F 57

Vz^'^o' « 11.548

TABLE XIV

TABLE OF DATA AND CALCULATED COEFFICIENTS

LEFT fiUDDEB

fiUDDBB POSITION; 3" TO STABBOABD OF PBOPILLEB SHAFT

ZEBO OAUOE BEADIN&S:

LOVEB LONGITUDINAL 5810LOWEB TBANSVEESE 5970

ANGLE OFATTACK

LOWEBLONG'LGAUGE

BEADING

LOVEBTBANSVSBSE

GAU(^BEADING

LIFTCOEF.

DBAGCOEF.

NOBMALFOBCECOEF

TANGENT.FOBCECOEF.

5 5750 5715 .1298 .0345 .1320 .0230

10 5700 5440 .2697 .0632 .2682 .0154

15 5640 5150 .4160 .0891 .4270 -.0152

20 5540 4830 .5800 .1551 .5985 -.0530

25 5430 4555 .7200 .2180 .7450 -.1068

30 5250 4260 .8695 .3219 .9145 -.1561

TEMPEBATUBS °F

2^/Z ^\

62

r 11.543

VIII. A?'".HniX (Continued)

D. SaoDle Caloulationfi

Caftffiolpnt. oa l oia-i.i:ions Refpr to '"'able III

Data:rransverse poBitlon 2 Inches portPropeller speed 15no R.?.>!,Averac>f» speed of rfice

at^rudaer (V^) 11.9^ ft./s^o. (from Fig. 3)Rudder angle 20*^ righty-uter tempc'*rature ^i'7'^F.

Rudder area .O836 sq, ft.LL (Lovrer longltucllnal ) 5620 iiicro unitsLT (Lower transverse) ^^790 micro units .

Kase dpriP.lty of vater {P) 1.939'^ lb. secVft.^LL LT

Dynamometer - zero reading 5335 ^u 6CO5 aiuj

Dynamometer - 20*^ right rudder reading 5520 mu 7j',^9 '^^^

Difference 3^5 t^iu 1115 f^u

(decreasing) (increasing)Slope of calibration C)rve 150 '5 :nu/lb. IG6 rau/lb.

Drag » 2iL.EH . 2.095 lbs.150.5 Wll).

Lift . -.^iii5-!?B- = 6.620 lbs.166 au/lb.

sin 20° - .3^20 eo0 20° = .9397Drag X eln 20° t .716 lbs. Drag x cos 20^ = l.S^65 Ibe.Lift X Bin 20° = 2.295 lh«. Lift x coo 20<^ - 6. 31 Ibc.

F^ 2 Lift cos« -w Drag Ein<e 3 6.3I lbs. -»• .716 Ibe. = 7.03 IbP

.

B'.y s Drag oos« - Lift ain<^ = 1.965 Ibe,- 2.295 lbe.= -.y^Q lbs. I

k . ^^i . ii232L5-i2§3LL.lik2iii: ,11.55 lbs.j

n . Lift _ 6.72 l^QO"L - -Y- nT55 ^ •

^®^

c^ -. Prss -- ^^i'ii -- .1815C k 11.55

^^^ '-T -11:55"'^^^

C -. El . I:l303 ,_ ..0286T

>. 11.55

- 59 ~

Slio caloulation

Propeller R.P.K. r 1500R.P.S. - 25

Rudder d • .5 ft.p/4 = 1.0

p X as 25 X .5 = 12.5 ft./seo.

Tmmel V z 11.22 ft- /sec.

Slip z lZ^^9^Z^lliii X 100 10. 2^^;:^

12.50

- 60 -

-

PUATC>

11

1

4* J

1

POS%TIO»4 '. <^

%

0( s o*

\

k

•

PLATE. IV

1

1

( *s2^mI^^^^^^H

1

1 ^^^H

I1

N PPOSiriOH

:

a* sr'B'o W 0** V

VII:-I>i (ConUinueci)

1. '

. ?>. h. rJuvic^f^on - "On t>i- rurnib. ,;,nd Zt^-f^vliw of

oQips'' ;.^;.,-.' .". ?rans:«.otir>!iB , '-oiume 5~» i9''>*-^'

2. C. R. Hagen - ";yarodynamlc Clic.ructpris tlci:! of Ti?ln

Rudders Loc^ited at Four AtJtr.'artRhlp i-ofltionG De^pr^

mined frc^m Tests on a I'ioclel of t-nf* U.S. 3. iinmerman,

»D 828" David Taylor ).Uocp1 Baeln P-eport C-60.

3. j*', H. Le^-rlE - 'Propeller Testing Tuna«?l at the

F.aesaohusette Institute of technology' :i. i.A.L. :..

Transaotiona , Volune 4?, 1939.

h-, R. K IE ginger &nd L. A. Rjpp - •'Oeveloprarnt of d.

?^,odel ftudaer Dyna-no'neter'* M. I. T. MaKter's

ThesiB, 19^-3.

5. K. I. Gogen and Vi, A, lara - "The Effect: of Aspect

Ratio am^ Thlolcnecs Katio on RuvJcer Jorque, Lift,

Sine. Drag Coefficients" K. I. T. Master' 6 Theals,

19^.

6, H. E. RoGsell and Chapman - 'Principles of Haval

Architecture'* Volume II.

-^ 66 -^

%

¥

»

12870Downs

Investigation of rudde:characteristics withvariation of rudderposition in a propellerrace.

L

ThesisD71 Downs

12870

Investigation of rudder

characteristics, withvariation of rudderposition in a propellerrace.

':t^->^

^d'^f'n

1

— ?- - - --tf-L..u

;1

1 ; „

; -i—.

-:

1 v^; 4 ."pi ;

^i" \^

. i . --

... J...; , ^

p.1

-' '

i i

"']"~ ""j—

;

•

i

JZMi t^- ;^

. i

---i~

.

—-1 1:-

—

t

i.

-1 !n.

pnH^HSHpMKiflHpipinMni1!

i -1

- .

:

-', : .!:

. - 1

j

--!..

. -i.-'

I i f—

^

1 - ~~~^'"1 r

.--,-. ._-i—.j- B^E -.

4»

^ac^ZJBHL^flfcQ^SLf - »jp. *»»•• - r^ >iV^ t'

-^I—;——r-

!-A - 1 \

1 : !

__; .-.1 -ill i

'

1

i

i

,1

. 1 M1

!

;1 ',

i

! r i

^i.;_ '. i ^jLL-i-l1

- J "T i i 1

.XT T'V '\

- _^ -,

"J_ 1 1

'

r

i

,

-,—' 'VI i -1 -r

t' ;

: T r 1 T_']_ZZa

; r --;- -1j

\ T* ' M f '~[„L..LLl ^i— '

i;

1. '

'

f

- -

J

_

L' _

']

.

.^ „^

__.,

^.

^

,

^ MM i

,^ ,. i

;

,

J ~^l^.^ : i

' f

'"i

! 1 i ; •-

! .

''

i' '

;

.:,., ...J

""

' T ;

" r^\'

! t

t.J.

i ^ .'

{"'" '".'":

1j

___,_._!__^--ijji ; i -1 MJ 1.'

.

'

\; ! 1

t 1 M • i ii

'

- ; -j —r— -j1

1

'

i 1

^-'-"-'

" '' '

'.;

i : j ; i : i . 1 .

..._ - ... .J. --L.^ :. i'

! :

: ; t

':''

: :

j

i

:

:

1 1

p^""

j

..H-J-^;.|.-.-

i . !'

:

ji . i

; 1

'! ."1

t

..; . - —

^

J

i 1 1 "' '<

1 r1

1

: 1

i

I

!

' r, ,

i- n :

-r ->

.'""V

I

j -!

i i Ml J M..:.'

_.L ! !. i — -

1

IJZT._x_.[T i

1

! ; !i.

- rI '

;

""";

\

"

'

.

1 -1 4-i:d:

:;

j

i t-I i : —-j

i

1, ^'TT ri

1

1

! . .1, I, .

r

t

-

,^ . .-1—J...

.

i i'j

III i L ;

1

t i1 1 -

i i'-

1

1

II

r'

t

!

; ^^^^""^"r"v^ I- '

.

'i '

.i

1i

i

t

1

M : 1

; I :•

i•

-•.

tJ I

-i-U-1'.

! 1

4 -i- [

;! •

'"

-

1 1'

;1

i

i .

1

j Tf-^ - • 1

j

t

-

'

i

\! i

r !

1 1 i-t/i-

1

t i :

_ .{. .^

:

1

i\ i

i ! i

i t- ! f r- ; . : !

-

.! ' I ,- 1

!__ _.

.

; [•

14 i

L.

.

'._lJ

,

i1

_ .1

,

"""[. p-rr

i.

•

'

~"','

i „_":.

__ .

~ "'"'

' f 1: .

'

j-

i~ 1 ~' ,

,

"~ 1^ L4

"- ] r -f :_"'-

- M:

j -i

L L t —

i

J

i

'" ^ - ^

: .

_„. j

4 '

- i- -

•T . •! w

.

i-- -k- mmMHWM^^B^^B "17"

__L.|-^-'^\-

—'" "

7.-

."-"'

._!.

.-

__i_ _.

^~~

r r:i ""

".~~

ll'

"_ ;

. ..

(

1 ^ '1 .:M..bmhi 1:---

__ zl;

^^^IV^B^^^^^H

MM^H^B^B^SWmIS

WMH|HIBiHHHIHKppHi1HHBJ^_»»BHUBIwbui

i^Biy HR«i^HB H91SiraHPifliI^9H^Bm ^M1^B 95^^S ^BBBi^BuS 1^B^H| BBBBSKi ^BmM ^1Wl 1HP8 Ih BBJmjm ^Swm ^M

-+'-.—^ h~

ni^iB

mm^^—^--r--'^ ^

, : i : 1 : j ! i ! • i 1 !,

4M^^ ,: :

1 '

i i- ' ^

•

i

j M ' ^-.

; i i

^: 1 '

i

; M :^

1 :

'•

;

i

1 ; ; 4 ;

i--- -H~ -| --;;-• T T "^"^''-^"T'lt

-.L. l±X i4_l .1-;-. .J-.iH .h 4.,. ^i__Li_i

'' ;' ' i ! ; 1 , 1 !

111.I '. i i • : ! 1 - ' !

't '

..[...74 i_JX!M:,

• ; ! M 1 :l^ [ .J |._.L I.'

! 1 1 1 |._LL:4. ill ,!:!'!' = !' : !'

i 7i..: 1.7'! [ MJ. ,

!

: '

i! ' , ^

i i • 'i :

.;

':

1 1 i

;

1

—\1 . :

:,

:

'

'

1i !

: r,. ! - . ..

^ L-J. ' -i. -r-H---- ---1—^L^""~ !"'' ' '-'': ~- - - ["i

ij ;

1 ' i

i! • j

. ,,:-"-i^-rH

H...L.: -LI.: .jJ., . 1 MJ. LJJ '\

'

1M 1 M 1 ! .i 1 M j

1: :^ ; ;

i- 1 [ j | | i ' j- }';

r i: !

• 1 ; ' :i

;'

! lit 1 '1 ;

-.._.7 7.-7l4J __....- :

/ .-.-^-l:: iiziU! M : 1 : ! ' M -•

i! . i

' i

i! i 'Hi M '

;

*"; ^i

" t T M r M '

i

[r - i

!

,

I i 1 M J '

; :• T '

'; .

i

:1

: ! ^ 7 i .: i - ;• ' i

• ' ' '1

!'

''; i '

!

'

:

1'

;.

I .,

i

—

]

ji

;

' :— '.

1;

1

—h--:—-i--- ! T -[ -1—;—

j

: ; : 1 ' 'i ' ', 1 '

: ' ! '

, j i : ! ,i

' : 1

,t - I ^1 i ! .i i- ,! .1 1 I : T

1 i .: ! ! . 1 ' ! 1 i 1 . ; ,

: r 1 1 ^i

: j • : ,1 t : . .

1 ' 1 , 1 ! ; , i : '

i'

' M .M ..1 j

-

... .L _|. ...4 ..|.. 1 l.-j.. ^-.|...L. . . _ .,

_^_.. 7"', ;'"[ '~' 1^7"^

; 1i

! 1 . ! 'j ! : . ^ i '

i: i

'

i i

i

: ' '\

''

\ '

1-

. ' 1 ! ' " : ; 1 ! ':

; 1' :. i : r ; 1.

;>"'-'!^

.7 : :rt_.7..[.!.i.i.i

-'.'. r

i

1

i

u i ! 1 I j i , ; ;M

111 : ! ; . ; !i

: ! -j "

i M : 1 - • Ml';.1 . - ' i 1 ; I . ; ,

-i i

.' : i ^ 1 ; i

i ! i1 . ! i nnBMni^H

1 , ! . ' : . J ..' 1 ! : '

: 1

;

!

—

T

:

'

i1 1

1-

—

^~-^-^—^- T—

[

1 !

i-- - - ,--,

- ' - \ ' 1.

.[-- -i 1

i

.1

: : M !

'

i.

. 4 ^" ''

\ \

-!-r 1

7-',

f-l J ' ' Ml J ^ L4 ---i",.

i

1- i-71|M i i

--:-h-i-4-^ H-^

:1 ! : 1 r—-* r-—

;

! —

H

i'

|

'

—

ir—

^

i

' •

; Li'!' ' I''

—^""1~l

!

' M i i

1

'— j—r—1

—

ir— -

-

\ 'i \

-i ^! t ! !! -i-L '

^' "Tt^n MM.- 1

_!jg--t-j_7 '_

j7 M M

; i • ' ^-\ ! —r—r—!

! •—;

- - - - f

i1

. : : . !

j!

1 1

,

:

; i

j

i:

1

1

r[

1— j—

T

'

'

\

!

-

! , ! ., [ I^ Li J

!'—

r

'

i r-f—s———f—t—i—1

—

'--i

—

:

———1—1 ' i^< 7':—rM T—Mi—1—r-

.y ,4- ^.. _ -^..-._

-- i -. ^. ; 7: : .1. , ] . !

' ! • •. it

^- I I

^ :

'i 1 . I- -1 !

'] '[ BMMBBH^mBBmBmIB^mBihhi i

'

i. ^ : ; j Hi::11-1-!- ! 1 ,

; !

f -. M' i H ji

i ii

'' '

'.

'

H^HHf*BwBWBlUMtfWWBKiWBlBBHftK

- i.

1

1 ;

L '1 j—

' .j 1 :-!

—

—\-~—j—!i

i

__L

—

]1 1 :

1 T-i Mi

—

r-^-j-j-

1 1 1 :' 1.7J.

} 1 !/' ; .t 1

i

~!i—M—1—^ '/^"'

1

•'1

—^"'' '"fflfflBBSHHSSSS^ni

4-i-a -, 11j i

L'

.' ^_.L_.. 4.. ...... j '

.4|4_;_^4-4.xi, i

-1- I- . i . r

!

1-^—

r

T "^'' ~]^1 i

--;--:-- - iM1 : j 7 |.>r;. t ,

^; . ;

•

.1 bn^" Y '"r7 i Ti-Tf-r:j7 p:--|-^

-1- 1-

f' - 1 1 f i

i1

..i.,.i _ ...i .j..+..i.-i..44_;-..-U ' '[

Hi^HI^^^HIHHHBHBHVSMNlHHI^^^^^HHfl^^^HlHI^H^HI

.MK7t7iM7fi#+fitJMM-7-( --4-—-4 .L^- -4

-t-UM-i M^M4M-iw^^^m^^^^W^^WB^tJ.i-|.[..j-,-L.l.-i:i^47|---i

— ^

:

j

'

i

K-i p—

'

1'

' t-. Li ;

..7J4M:"^TT:.7:.

r \

..__L: .:i

il TTll •Tl...>T^-'4-7M ;

__.14.-44, -4- -M .-.^|.-.m4-.^M-

!• ' M i . M-

i

.

i

4.. ^ t. I-' :4.'i M 7 i

._'-iri,Gui^c^a|3 .

„ 4-4 -4-^ J

__L4_4-1_4_.. -J -^,

f -i- i:

, j

i

'•' ' r •

i

i

!

1 1

i

,-.-.-.. ,..

r- !,_ L"L-,

:

;!

1

J''

•

i'

i 1'--J

1.1j

i i

1

! \

'i

1

[--j—i

i F"^"' !

^ , , ,

j

!r •

1 1

_.-|.-..-

i-,-^-_-i....ju.-t-l

i

; i

.

j_

1 i j1

'

:

j_ i.J__..;.....__I...i_t4-i-!- ^^S-'^^

1 i ' '1

l'"^'^"],

. 1i

\ \Mi'.

i !

i i

\'\ '

4 ; •f

—1

—t

;

' i;

i

-..-J...J

1

'

I f

,! ;

'' 1

r~l"'

1 T-—

—

"\'

;

»i

L:LiJ„!i-: j- -i T t ,

\

"'; -

i__J_-j1

i

L L.^ i

! 4

!' . I 1 '1 ... —

]

j j

'

'• 4 1!._4-_J.. .'....J.^,

1

: i

'

: , i-1 .- I ; ) 1

i ^ i

; • 1 » 1 ; . -) .

t_

\

•

11 1 ' ' '

I _......:

1

' 1.

.

: 1 t I j ;1

1 : ; 1

1 : ' 1

L_i i--:__

1

9S00 .J

i , 1

_ I

!

i

I

i

t

(0500

-"floss SECTION M.iiMtTCf

thesD71

Investigation of rudder characteristics

3 2768 002 00643 9DUDLEY KNOX LIBRARY