dempsey - static stability characteristics of systematics series of stern control surfaces

8/2/2019 Dempsey - Static Stability Characteristics of Systematics Series of Stern Control Surfaces

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CD DAVID W. TAYLOR NAVAL SHIPRESEARCH AND DEVELOPMENT CENTERBethesda, Md. 20084CA.

STATIC STABILITY CHARACTERISTICS OF A SYSTEMATICSERIES OF STERN CONTROL SURFACES ON A

BODY OF REVOLUTION

byO Elizabeth M.DempseyI-0

,cr.LL>uJ

000> APPROVED FO R PUBLIC RELEASE: DISTRIBUTION UNLIMITED F

- C.C /I- ' SHIP PERFORMANCE DEPARTMENT

-.

S , 1T

t .AuqoSt 1977 Report 77-00O5


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MAJOR DTNSRDC ORGANIZATIONAL COMPONENTS

I OTNSROCCOMMANDER 00

TECHNICAL DIRECTORS...._ 0 1

OFFICERIN.CHARGE FOFFICERAINCHARGEI E I I I

iSYSTEMSDEVELOPMENTDEPARTMENT

I AVIAHION ANDSHIP PERFORMANCE _SURFACE EFFECTSDEPARTMENT 15 DEPARTMENT 16

( COMPUTATION, 'ESTRUCTURESN MATHEMATICS ANDDEPARTMENT LOGISTICS DEPARTMENT

_____ ____ ________18 jPROPULSION AND

-HIP ACOUSTICSDEPARTMENT AUXILIARY SYSTEMS19 DEPARTMENT 27

MATERIALS CENTRALDEPARTMENT INSTRUMENTATION28 DEPARTMENT 29


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UNCLASSIFIED%IECuMITY CLASSIFICATION OF TNIS PAGE (WtPn Data Entered)REPORT DOCUMENTATION PAGE READ INSTRUCTIONS

BEFORE COM(PLETIN(G FORM. REPORT mUMBR--" .. QOVT A I;ESSION NO . 3. RECIPIENT'S CATALOG NUMBER77_0085, ;. . .. .

------------------------------------............. S. ,P o" REPORT I PERIOD COVERED( STATIC STABILITY JHARACTERISTICS OF A,,.SYSTEMATIC,' 1FiaSERIES OF TERN CONTROL SURFACES ON A BODY OF -,REVOLUTIONt S...... ....- - S. PERFORMING ORG. REPORT NUMSER

7.-A JTN_. S. CONTRACT OR GRANT NUMIER(s)Elizabeth M Dempsey .

P:ERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT. PROJECT, TASKDavid W. Taylor Naval Ship AREA & WORK UNIT NJMERSResearch and Development Center 6..53_ .Bethesda, Maryland 20084 SRR2 3010/' .

I CONTROLLING OFFICE NAME AND ADDRESSNaval Sea Systems Command Au"91ugusTA.977jMaterials and Mechanics Division 13. NUMSER OF PAGESWashington, D.C. 20362 81

iA MONITORING AGENZI Y NAME & ADDRESS(If different front Conrrolitn# Office) IS. SECURITY CLASS. (of hie report)

IS*. DECL ASSI FICATION/ DOWNGRADINGSCHEDULE16 DISTRIBUTION STATEMENT (of thli Report)

APPROVED FO R PUBLIC RELEASE: DISTRIBUTION UNLIMITED-- , )

III. DISTRIBUTION STATEMENT (of the abestract etnterd In Block 20, If dlfferent from Report)

1' SUPPLEMENTARY NOTES

19 E Y WORDS (Continue on reverse side If ecessary an~d Identity by block numiber)Hydrodynamic Forces and MomentsStern Control SurfacesSubmarine Stability and Control

20 ABSTRACT (Continue on reverse eade It necmesary and Identitf' by block number)Experiments were conducted to determine the forces and moments due to

angle of attack on a representative streamlined body of revolution alter-nately appended with members of a systematic series of stern control surfacesThe data from these experiments are presented in the report in the form ofgraphs and tabulations of th e nondimensional force and moment coefficientsand static stability derivatives. Based on these data empirical mathemati-ca l expreqnions have been developed to predict the contribution of stern-

DD 1jAN 1473 EDITION Oi NOVAS s OBSOLETE UNCLASSIFIED,S IN0102.L 1 .014 .,601

IECURITY CLASSIFICATION OF THIS PAOER ("*n DVote ntsere)I .' ,


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TABLE OF CONTENTS

PageABSTRACT ................................ ............................. 1ADMINISTRATIVE INFORMATION .................... ...................... 1INTRODUCTION ............................ ............................ 1CENERAL CONSIDERATIONS ........................ ...................... 2DESCRIPTION OF BODY AND STER1N CONTROL SURFACES .......... ............ 3TEST APPARA'TUS AND PROCEDURE. ................... ..................... 6REDUCTION A)ND PRESENTATION OF DATA .......... .................. 17DISCUSSION OF RESULTS ................. ......................... 18CONCLUSIONS ....................... .............................. 24ACKNO.LtEDG(,',ENTS..................... ............................ ... 26APPENTDIX A - DERIVATION OF AN EQUATION FOR REPRESENTING THE RATIO

-Za AS A FUNCTION OF "lHE SPAN PARAMETER l-- 27CLt d2APPENDIX B - GRAPHICAL PRESENTATION OF LONGITUDINAL. ANI) NORMAL FORCE

AND PITCHING :fOMENT COEFFICIENTS AS FUNCTIONS OF ANGLEOF ATTACK . ........................... ................. 31

APPENDIX C - TABULATION OF LONGITI'DINAL AND NORMAL FORCE AND PITCHINGMOMENT COEFFICIENTS DUE TO ANGLE OF ATTACK ........... .. 53

APPENDI)X D - STATIC STABILITY DERIVATIVES, INCRFYMFNTAL DERIVATIVESANT) FREE-STRFAM LIFT-CURVE SLOPES FOR STERN CONFIGUPA-TION SERIES. ............... ....................... 65

REFERENCkES ........................ .............................. 68

" ~Ii'


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LIST OF FIGURES

PageFigure 1 - Sketch o0 Representative Control Surface ............ 7Figure 2 - Sketch of Model 4621 with Contri l Surfaces ........... 8Figure 3 - Variation of C and C with Eftective Aspect Ratio

fo r Various Span Parameters .......................... 20Figure 4 - Variation of the Ratio CZa with Span Parameter ..... 21

Cl-a

Figure 5 - Variation of Center-of-Pressure Location withEffective Aspect Ratio for Various Span Parameters .... 25

Figure 6 - Variation of Longitudinal and Normal Force and Pitch-ing Moment Coefficients with Angle of Attack fo r BareBody .................................................. 32

Figure 7 - Variation of Longitudinal and Normal Force and Pitch-ing Moment Coefficients with Angle of Attack fo r Bodywith 3A Srernplane ..................................... 33

Figure 8 - Variation of Longitudinal and Normal Force and Pitch-ing Moment Coefficients with Angle of Attack fo r Bodywith 5A Sternplanes .................................... 34

:igure 9 - Variation of Longitudinal and Normal Force and Pitch-ing Moment Coefficients with Angle of Attack fo r Bodywith 7A Sternplanes .................................... 35

Figure 10 - Variation of Longitudinal and Normal Force and PitchingMoment Coefficients with Angle of Attack fo r Body with9A Sternplanes .......................................... 36

Figure 11 - Variation of Longitudinal and Normal Force and PitchingMoment Coefficients with Angle of Attack fo r Body11A Sternplanec ......................................... 37

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LIST OF FIGURES (continued)Page

Figure 12 - Variation of Longitudinal and Normal Force and PitchingMomnt Coefficients with Angle of Attack fo r Body with3B Sternplanes . ......................................... 38

Figure 13 - Variation of Longitudinal and Normal Fcrce and PitchingMoment Coefficients with Angle of Attack fo r Body with5B Sternplancs ......................................... 39

Figure 14 - Variation of Longitudinal and Normal Force and PitchingMoment Coefficients with Angle of Attack fo r Body with7B Sternplanes ......................................... 40

Figure 15 - Variation of Longitudinal and Normal Force and PitchingMoment Coefficients with Angle of Attack for Body with9B Sternp .,anes.......................................... 41

Figure 16 - Variation of LonKitudi;nal and Normal Force and PitchingMoment Coefficients with Angle of %\tackor Body with11B Sternplanes ........................................ 42

Figure 17 - Variation of Longitudinal and Normal Force and PitchingMoment Coefficients with Angle of Attack for Body with3C Sternplanes ......................................... 43

Figure 18 - Variation of Longitudinal and Normal Force and !'itchingMoment Coeot ictents with Angle of Attack fo r Body with5C Sternplanes ......................................... 44

Figure 19 - Variation of Longitudinal and Normal Force and PitchingMoment Coefficients with Angle of Attack fo r Body with7C Sternplanes .......................................... 45

Figure 20 - Variation of Longitudinal and Normal Furze and PitchingMoment Coefficients with Angle of Attack fo r Body with9C Sternplanes ............................................. 46

Iitv


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LIST OF FIGURES (continued)PaRe

Figure 21 - Variation of Longitudinal and Normal Force and PitchingMoment Cojfficients with Angle of Attack fo r Body withlIC Sternplanes ........................................ 47

Figure 22 - Variation of Longitudinal and Normal Force and PitchingMoment Coefficients with Angle of Attack fo r Body with3D Sternplanes .......................................... 48

Figure 23 - Variation of Longitudinal and Normal Force and PitchingMoment Coefficients with Angle of Attack fo r Body with5D Sternplane ........................................... 49

Figure 24 - Variation of Longitudinal and Normal Force and PitchingMoment Coefficients with Angle of Attack for Body with7D Sternplanes .......................................... 50

Figure 25 - Variation of Longitudinal and Normal Force and PitchingMoment Coefficients with Angle of Attack for Body with9D Sternplanes .......................................... 51

Figure 26 - Variation of Lougitudinal and Normal Force and PitchingMoment Coefficients with Angle of Attack for Body withlid Sternplanes ......................................... 52

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LIST OF TABLES

PageTable la - Geometric Characteristics of Bare Hull Expressed in

U.S. Customary Units .................. ................... 4Table lb - Geometric Characteristics of Bare Hull Expressed in

S. I. Units ................... ........................ 5Table 2a - Geometric Characteristics of Sternplanes Expressed in

U.S. Customary Units ................ ................... 9Table 2b - Geometric Characteristics of Sternplanea Expressed in

S. I. Units................. ........................ 13Table 3 - Tabulat ion of Longitudinal and Normal Force and Pitching

Moment Coefficients Due to Angle of Attack .... ........ .. 54Table 4 - Static Stability Derivatives, Incremental Derivatives

and Free-Stream l ift-Curve Slopes for Stern Configura-tiCn I .. .............. ........................ 66

V j


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NOTATIONA Projected area ef one sternplane extended

to hull centerline (leading edge contin-ued at same angle)AP Aft perpendicular (end of afterbody)

2b 2a Effective aspect ratio, 2b2

b Distance between sternplane tip chord andhull centerline2b Span parameterdCL Lift coefficient, L

c Mean chord of sternplane, average of tipchord and root chord

d Maximum diameter of hullL 11ydrodynanic lilt force, positive upward

Length of hullM M'1 M Hydrodynamic mroment about y-axis10 3 U2MMM - w Derivative of moment component with respectw w OL3U to velocity component w

AMw., , . - Contribution of sternplanes to Mw w 3U

U Velocity of origin of body axes relativeto fluidw w' w Componen. of U along z-axis

Xx' X Hydrodynamic longitudinal force, positiveio 2 U7 forward

zZ' - Z IHydrodynamic normal force, positive downward

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ZZ Z ' - Derivative of normal force component withW w p 2 U respect to velocity component w

LZLZ AZ ' w Contribution of sternplanes to Zw w ne 2 U wCx Angle of attack

Mass density of water

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ABSTRACTExperiments were conducted to determine the forces and moments due

to angle of attack on a representative streamlined body of revolutionalternately appended with members of a systematic series of stern controlsurfaces. The data from these experiments are presented in the report inthe form of graphs and tabulations of the nondimensional force and momentcoefficients and static stability derivatives. Based on these dataempirical mathematical expressions have been developed to predict thecontribution of sternplanes to the static stability derivative Z ' whenwthe sternplanes are appended to a submarine whose basic hull is a stream-lined body of revolution. A graph Is presented for estimating the locationof the center of pressure of the forces due to the presence of sternplanes.

ADMINISTRATIVE INFORMATIUNThis project was performed under the sponsorship of the General

Hydrodynamic Research Program.

INTRODUCTIONAn experimental investigation was made of the static stability

characteristics of a streamlined body of revolution alternately appendedwith each se t of a family of low-aspect-ratio stern control surfaces.The purpose of the investigation was to determine the contributions ofthe control surfaces to the forces and moments on the total fin-bodycombinations and to present the results in a form that would be useful

in the preliminary design of submarines from a stability point of view.In the past extensive experimental work was carried out at the

David W. Taylor Naval Ship R&D Center to determine the tree-stream


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1, ' ,aracteristics of a family of low-aspect-ratio control surfaces. Thiseffort provided comprehensive information more directly applicable tosubmarine appendage design than had been available In the aerodynamicl i terature. As a next step, the work presented in this report was per-formed to provide fundamental data on the characteristics of controlsurfaces when fin-body interaction factors are present.

This report describes the model and stern control surfaces; out-lines the procedures used in the experiments; presents graphs and tablesof ,he experimental results; and present empirical methods fo r estimat-ing the contributions of sternplhnes to the static stability derivativesfo r submarines whose basic hulls are streamlined bodies of revolution.

NEtIERAL CONSIDERATIONSI'he hulls of most modern submarines are basically bodies of revolu-

tion with afterbodies (the portion of the body aft ef the maximum diameter)such that the ratio uf the length of the tail (or afterbody) to the maximumdiameter falls somewhere between 4.2 and 4.6. This chara.reristic is aroigh indication chat the fullness of the tails and the nondimensionalthickness of the buundaty luyer in the vicinity of the stern control sur-faces do not vary markedly from submarine to submarine.

Fo r this reason th e assumption was made that an experimental studyof fi'-body combinations composed of stern control surfaces mounted on abody of revolution having a fairly representative tail section would yieldfin-body interaction effects that could be applied to other bodies havinggenerally similar afterbodies regardless of the shape of the forebodies.111icker, I.,Folger and Leo F. Fehlner, "Free-Stream Characteristics of aFamily of Low-Aspect-Ratio, All-Movable Control Surfaces fo r Applicationto Ship Design," DT>M Report 933 Revised Edition (December 1958).


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An existing streamlined body of revolution having an afterbody fine-ness ratio of 4.4 was chosen as the test vehicle. A family of 20 sets(4 identical stern control surfaces per set) was selected which covered arange of sizes, relative to the hull, that could reasonably be expectedto be of interest for submarine design. No propeller was used,

The planform of the planes was such that the trailing edges werenormal to the tip chords. The sweep angle and section shape were thesame fo r all. The spana and tip chords were varied in a systematic wa yso that for each of four outreaches from the centerline of the modelthere were five sets of planes with different tip chords.

The vehicle wa s tested with each of the 20 sets of planes orientedon the hull in the cruciform arrangement with trailing edges normal to0l1 lungiLtudial axis of the hull. 'le rudders were located slightlyforward of the sternplanes and the longitudinal positions of the trail-ing edges of both sternplanes and rudders with respect to the AP of themodel remained the same fo r all configurations.

DESCRIPTION OF BODY AND STERN CONTROL SURFACES1:Teody was Model 4621, a 180-inch (4.572-metre) strearlined body of

revolution with a 24.52-inch (0.623-metre) maximum diameter. The hullwas fiberglass with a mahogany tail cone. The offsets of the model andother pertinent characteristics are given in Tables la and lb.

The control surfaces were constructed of mahogany and consisted ofa family of 20 sets of 4 identical square-tipped planes. The trailingedge uf each of the planes was normal to the tip chord. Each had aquarter-chord sweep angle of 15.25 degrees and a NACA 0015 section shape."lhe bases of the planes were cu t on a 12-degree slant to fit the average

r3


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TABLE 1A - GEOMETRIC CHARACTERISTICS OF BARE HULL EXPRESSEDIN U.S. CUSTOMARY UNITS

Length, ft. 15.0Maximum diameter, ft. 2.044Wetted surface area, sq. ft. 70.55Volume, cu. ft. 29.53Longitudinal center of buoyancy, ft. 6.684

Hull Offsets

X in inches Y in inches X in inches Y in inches

0.0 0.000 93.6 11.823.6 3.500 97.2 11.667.2 4.977 100.8 11.4910.8 6.108 104.4 11.2914.4 7.047 108.0 11.0718.0 7.850 111.6 10.8321.6 8.549 115.2 10.5625.2 9.160 118.8 10.2728.8 9.697 122.4 9.95432.4 10.17 126.0 9.61336.0 10.58 129.6 9.24339.6 10.93 133.2 8.84343.2 11.24 136.8 8.41146.8 11.50 140.4 7.94550.4 11.71 144.0 7.44754.0 11.89 147.6 6.91057.6 12.03 151.2 6.33461.2 12.13 154.8 5.71564.8 12.21 158.4 5.05368.4 12.25 162.0 4.34472.0 12.26 165.6 3.58475.6 12.25 169.2 2.77479.2 12.21 172.8 1.90882.8 12.15 176.4 0.98486.4 12.06 180.0 0.00090.0 11.97

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TABLE IB - GEOMETRIC CHARACTERISTICS OF BARE HULLEXPRESSED IN S. 1. UNITS

Length, m 4.5720Maximum diameter, m 0.6228Wetted surface area, m2 6.55453Volume, m 0.8362Longitudinal center of buoyancy, m 2.0373

Hull OffsetsX In Metres Y in fietres X in netres Y in T-tres

0.0 0.0 2.3774 0.30020.0914 0.0889 2.4689 0.29620.1829 0.1264 2.5603 0.29180.2743 0.1551 2.6518 0.28b80.3658 0.1790 2.7432 0.28120.4572 0.1994 2.8346 0.27510.5486 0.2171 2.9261 0.26820.6400 0.2327 3.0175 0.26080.7315 0.2463 3.1090 0.25280.8230 0.2583 3.2004 0.24420.9144 0.2687 3.2918 0.23481.0058 0.2776 3.3833 0.22461.0973 0.2855 3.4747 0.21361.1887 0.2921 3.5662 0.20181.2802 0.2974 3.6576 0.18921.3716 0.3020 3.7490 0.17551.4630 0.3056 3.8405 0.16091.5545 0.3081 3.9319 0.14521.6459 0.3101 4.0234 0.12831.7374 0.3112 4.1148 0.11031.8288 0.3114 4.2062 0.09101.9202 0.3112 4.2977 0.07042.0117 0.3101 4.3891 0.04852.1031 0.3086 4.4806 0.02502.1946 0.3063 4.5720 0.02.2860 0.3040

5


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ilope of the hull at the mounting points. A sketch of the general planformand the dimensions coanon to a ll of the planes are presented in Figure 1.

When the planes were mounted on the tail cone of the model, thetrailing edges were normal to the longitudinal axis of the body. Theposition of the trailing edges of the sternplanes was maintained at 7.9inches (0.201 metres) forward of the AP. The rudders were 2.25 inches(0.057 metres) forward of the sternplanes. The spans and ti p chordswere varied in a systematic way so that the sternplanes had four differ-en t outreaches from the centerline of the model, and fo r each outreachthere were five sets of planes with different tip chords. The outreachesof the sternplanes were 9, 12 , 14.5, and 17.5 inches (0.228, 0.3048,0.3683 and 0.4445 metres). The ti p chords were 3, 5, 7, 9, and 11 inches(0.0762, 0.1270, 0.1778, 0.2286, and 0.2794 metres). Because of thelongitudinal offset between the rudders and sternplanes, the outreachof the rudders was, in each case, 0.48 inches (1.22 centimetres) greaterthan their matchlng sternplanes.

The geometric characteristics of the sternplanes are given in Tables2a and 2b . Figure 2 is a sketch of the modcl with control surfaces.

TEST APPARATUS AND PROCEDUREThe experimental work was conducted in the deep-water basin on

2Towing Carriage 2 using the DTNSRIDC Planar-Motion-Mechanism System.The model was supported by two struts in tandem, 6 feet (1.829

metres) apart. The reference point was the center of buoyancy of thebare hull and was located midway between the gimbal-centers associated2 Gertler, Morton, "The DTNB Planar-Hotion-Mechanism System," NSRDC

Report 2523 (July 1967).

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Sweep Anwie of Qu&rter Chord = 15.25 degrees

_____Tip Chord- ---

I NACA Section IX:IL

0at to Chord Line

Figure 1 - Sketch of Representative Control Surface

'*1 7.-


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TABLE 2A - GEOMETRIC CHARACTERISTICS OF STERNPLANES EXPRESSEDIN U.S. CUSTOMARY UNITS

Span A

(Values are fo r I sternplane)

Sternplanes 3A SA 7A 9A Il.A

Span from CL of hull, in. 9.0 9.0 9.0 9.0 9.0Tip chord, in. 3.0 5.0 7.0 9.0 11.0Root chord, in. 5.24 7.17 9.10 11.03 12.96Taper ratio 0.57 0.70 0.77 0.82 0.85Span, distance from root 6.16 5.96 5.77 5.57 5.37

chord to tip chord, in.Projected area, sq. in. 25.4 36.2 46.3 55.6 64.0Aspect ratio 1.50 0.98 0.72 0.56 0.45Projected area of I plane 41.75 59.75 77.75 95.75 113.75

extended to hull center-line, sq. in.

Aspect ratio of I plane 1.94 1.36 1.04 0.85 0.71extended to hull center-line

I9---


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TABLE 2a (continued)

Span B(Values are fo r I sternplane)

Sternplanes 3B 5B 7B 9B 11B

Span from cL of hull, in. 12.0 12.0 12.0 12.0 12.0Tip chord, in. 3.0 5.0 7.0 9.0 11.0Root chord, in. 6.30 8.22 10.14 12.08 14.01Taper ratio 0.48 0.61 0.69 0.75 0.79Span, distance from root 9.06 8.86 8.66 8.46 8.26

chord to tip chord, in.Projected area, sq. in. 42.0 58.4 74.1 8R.9 103.0Aspect ratio 1.95 1.34 1.01 0.81 0.66Projected area of I plane 62.2 86.2 110.2 134.2 158.2extended to hull center-line, sq. in.

Aspect ratio of 1 plane 2.32 1.67 1.31 1.07 0.91extended to hull center-line

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TABLE 2f (continued)Span C

(Values are fo r I sternplane)

Sternplanes 3C 5C 7C 9C LIC

Span from C of hull, in. 14.5 14.5 14.5 14.5 14.5Tip chord, in. 3.0 5.0 7.0 9.0 11.0

Root chord, in. 7.18 9.11 11.04 12.97 14.88Taper ratio 0.42 0.55 0.63 0.69 0.74Span, distance from root 11.46 11.27 11.07 10.87 10.68

chord to tip chord, in.Projected area, sq. in. 58.2 79.3 99.6 119.1 137.8Aspect ratio 2.26 1.60 1.23 0.99 0.83Projected area of 1 plane 81.75 11C.75 139.75 168.75 197.75extended to hull center-line, sq. in.


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TABLE 2a (continued)Span D

(Values are fo r 1 sternplane)

Sternplanes 3D 5D 7D 9D li D

Span from cL of hull, in. 17.5 17.5 17.5 17.5 17.5Tip chord, In. 3.0 5.0 ..0 9.0 11.0Root chord, in. 8.22 10.16 12.09 14.02 15.94Taper ratio 0.37 6.49 0.58 0.64 0.69Span, distance from root 14.36 14.16 13.96 13.76 13.57

chord to tip chord, in.Projected area, sq. in. 80.5 107.1 132.9 158.0 182.3Aspect ratio 2.56 1.87 1.47 1.20 1.01Frojected area of I plane 108.2 143.2 178.2 213.2 248.2extended to hull center-line, sq. in.


12


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with the two struts. The longitudinal and normal force components withrespect to the body axes were measured by means of internal force balanceslocated at each strut. All of the tests were run at a depth of 10 feet(3.048 metres) to the centerline and at a speed of 6 knots which corre-sponds to a Reynolds number of 1.4 x 107 based on model length.

The experimental program consisted of static stability tests onthe bare hull and on the hull appended with each of the 20 sets ofcontrol surfaces. Th e forces and moments were measured over a rangeof angles of attack from -6 to 18 degrees. The control surface anglesettings were zero at all times. To stimulate turbulence a sandstripwas installed on the hull 9 inches (0.229 metres) aft of the nose.

REDUCTON AND PRESENTATION OF DATAThe data obtained from the captive-model experiments are presented

in nondimensional form in the appendixes. The organization of theappendixes is as follows:

Appendix A contains a derivation of an equation for representingthe ratio CZ /CLa as a function of the parameter 2b/d. Appendix Bcontains plots of the nondimensional hydrodynamic coefficients X' , Z',and M' as functions of angle of attack. Data for the bare body as wellas for the body appended with each of the twenty sternplane configura-tions are presented. Appendix C presents tabulations of data shown inthe plots in Appendix B. Appendix D contains tabulations of the deriva-tives Zw M t, AM ,Z, CLu which apply to each configuration.

Summary figures based on the data obtained from the experimentsare given in the body of the report.

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DISCUSSION OF RESULTSAs mentioned in an earlier section, the major objective of this

investigation was to determine the contributions of control surfacesto the forces and moments on the total fin-body combinations in orderto obtain information that would be useful in the preliminary designof submarines from a stability point of view.

In accordance with this objective, the stability derivatives Zwtand M ' were determined fo r a ll configurations by taking the slopes,at the origin, of the curves shown in Appendix B of Z' and M' versusangle cf attack and converting them to "per radian" measure. The valuesof Z ' and M ' fo r the bare hull were then subtracted from the covre-w wsponding derivatives fo r the body with control surfaces to obtain theincremental effects which are referred to in this report as Zw' and

W

In order to divorce the incremental effects of the control surfacesfrom the length of the particular body on which they were tested, thevalues of (-Z ') were re-nondimensionalized using the projected area,2A. of the two sternplanes extended through the body. since for smallangles L : -Z and a - w', this procedure in effect converted the incre-ments into lift-curve slopes, GZa, which could be compared with free-stream results.

The work done by Whicker and Fehlner (Reference 1) has shown thatgood correlation exists between experimentally-obtained lift-curve

18

" '""' " I....... ' 'y IF ... .. ...


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slopes fo r low-aspect-ratio control surfaces in the free stream and thefollowing semi-empirical expression fo r l ift-curve slope

1. wa1.8 + cos. co-A- + 4)(1coo (1)

whereC slope of lift coefficient with respect to angle of attack ain radians at i - 0

a - effective aspect ratioA - sweep angle of quarter chord lineValues of CL a fo r various effective aspect ratios and a sweep angle

of 15.25 degrees were computed from this equation and were plotted as afunction of effective aspect ratio in Figure 3. The derivatives CZafrom the sternplane series were also plotted in Figure 3 as functionsof their respective effective aspect ratios (aspect ratios of the stern-planes through the body). It can be seen from the figure that the experi-mental values of CZo (indicated by the symbols) are functions of outreacha. well as of aspect ratio.

The solid lines drawn through the data points were determined in thefollowing manner: For each span parameter. d-, the ratios of the experi-mental values of C to the corresponding values of CL a from Equation (1)were computed. Then the average of these ratios was computed and a curvewas constructed by multiplying the values of CL cby this average ratio.ZL

Figure 4 is a plot of the average ratios, --- , as a function of theCLa2bLcspan parameter, 2-- The curve joining the symbols is the following

19


32/84

4.0. . - ~ -j-TC Uf un , Equation (1)

0 CZ from Experiments I -3.6,. I-*... ..... ... .. .... . .~' I _

I... : .. . . . t. . . ... . .. ... . . . . . . . . . .. . ., I I

I,8I .. . .... _

SI I / l i Span Parameter.N i] . .. .. . . *I 1.427

2.4" : ' I1.183U .0 2.4S I

41.

I / . I

1.2I . II,

010

O

* I - I-

0 1.0 2.0 3.0 4.0 5.0 6.0 7.0

Effective Aspect Ratio, aFigure 3 - Variation of C and C with Effective Aspect RatioZa Lufa r Various Span Parameters

20


33/84

a

0.8 10.7 1 t0.6---

I I!7

L ,I I N I I .o. I________ _ _,_ _- _ _

0I !

* I I0.4 i i

Span Parameter, 2b

Figure 4 -Variation of the Ratio C c/Ca with Span Parame~ter21ei Li


34/84

least-squares fit of the points:C-- 0.3644 + 1.2380 2b -003728 ())2CLa (2)

fo r th e range 0.734 2b/d " 1.426.Combining Equations (1) and (2),

- 1.8-aa1- [0.3644 - 1.2380 (2b) + 0.3728 2 2 (3) 1.8 + Cos A(lo-n--A + 4) d+032 - 3

Equation (3) may be used to compute th e contribution to Z ' of agiven set of sternplanes on a given streamline body as follows:since C 6

za w 2Aand th e effective aspect ratio of th e sternplanes extended through th ebody is 2b 2a-- A

then

w . . 8 2 0.3644- 1.2380 2b + 0.3728 (.Lb2 (4)w 1.8 + cos A(-~3 d (4)-)[-34

fo r the range 0.734 : 2b/d - 1.426.

While Equation (2) gives a very good representat ion of th e ratiofo r values of a in th e range between 0.734 and 1.426, extrapolations

CL2

22


35/84

beyond this range cannot be relied upon. As the span of the sternplanesapproaches infinity the ratio - should approach unity. Equation (2)

CLadoes not satisfy this condition since it reaches a maximum value of

2b 2b0.663 at -- 1.6604 and becomes zero at - 2.994.C

An alternate equation for representing the ratio - is derived inCLaAppendix A. This equation fits the experimental data slightly less well

2bthan Equation (2) but has the advantage of becoming unity at -d-For this reason it is recommended that this alternate equation which is

__ 0.56inb 1(0~.4015CZA 0.2556b) db) 0.1612] - 0.6366 sin 2b/d (5)

2b 2bbe used for 0.4015 0.734 and 1.426 e .d dThe use of Equation (5) then gives the tollowing equation fo r LZ w

,z _ 1. na 2.b,)0.2556w 1.8 + Cos. + 4) ( - 1 (.2b.6

(6).2b.2 0.4015.}- 0.161211- 0.6366 sind si 2b/d~

23


36/84

2b 2hf or 0.4015 .- L- -0.,34 and I.416 - d

The longitudinal positions of the center of pressure of the forcesdue to the sternplanes with respect to the hull LCB were determined by

AM Ithe ratios z--r . These center-of-pressure locations were then referred

wto the trailing edge of the sterrplanes and the resulting distances werenondimensionalized by the mean chords c.

Figure 5 shows a plot of the center of pressure locations as func-tions of effective aspect ratio. Although there is considerable scatterin the data, particularly for the A sternplane series, it can be seenthat for a given aspect ratio the center of pressure in general movesforward as the span parameter -L. ncreases and, in some cases, Is actu-ally forward of the planes.

CONCLUSIOISFrom the experimental results of this investigation empirical

mathematical expressions have been developed to predict the contribu-tion of sternplanes to the static stability derivative Z ' when thesternplanes are appended to a submarine design whose basic hull is astreamlined body of re,olutian. A graphical method is provided toestimate the location of the center of pressure with respect to thetrailing edge of the sternplanes.

24


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*N

S-d

10) 4I.I0. CLi

>0* 0

0~ 08

*

Jo 02P3 -'II3J 3VSUl~~nTur

25*4


38/84

ACKNOWLEDGMENTSThe author wishes to express her appreciation to Messrs. A. Goodman

and M. Gertler formerly of DTNSRDC who initiated this experimental pro-gram; to B. Carson, R. S. Dart, E. H. Dittrich, Dr. E. C. James, N. King,and 1. Mahoney who participated in the experimental work; and to Dr.J. P. Feldman fo r his contributions and guidance.

26


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APPENDIX ADERIVATION OF AN EQUATION FOR REPRESENTING THE RATIO

cZ-- AS A FUNCTION OF THE SPAN PARAMETER -bSLot d

C2

g 27


40/84

APPEND)IX ADerivation of an Equation fo r Representing the Ratio

CZ a 2h- as a Function of the Span Parameter-C ct dIf the lift distribution on a control surface in the freestream

is assumed to be elliptical, the lift,( 1 .i, is proportional to

2b b-o ' (b, x-) dx ---

If the lift due to sternplanes on a streamlined body of revolutionis assumed to be proportional tc the shaded area in the sketch

Iree-ptre-'lift

/

bb

b

C7 1 proport ional to

2: W - x) dx - 7b[: - )- sin- 1K]

2M


41/84

The ratio C is thenCLx

Czr -K(1- K,)!, 2- sin K (7)

C~aC?

A value of K fo r the average experimental value of C--- fo r eachC7-span was determined from Equation (7) and listed in Tabulation 1 togetherC 2bwith ' -4'2 and th e product K(d).

TA.BULATION IC2b KZ()

-4- KK(I--)d C L,1 d0.734 0.3436 0.542 0.39780.978 0.4868 0.415 0.40591.182 (".5810 0.335 0.39601./,?0 0.6420 0.285 0.4064

It can be seen from Tabulation 1 that the values of K(-) arecs9entially constant, giving an average value such that K( - 0.4015

0.4015or K - L ,b

This indicates that the "defect" in the effective span of the wingthrough the body is 2 x Kb - 0.4015d.

Substituting 0.4015 fo r K in Iquation (7) gives2b

(7)4


42/84

CZ a I 0.2556 [(d2b)- 0.16122 0.6366 sin- 0.40151 ( b)"" - 2b/d

Tabulation 2 compares the values of CZ'- from the experiments withCLathose computed from Equations (2) and (8).

TAB'LATIoN 2

2b C (CZ. CZ_d CL i C " CL 1

Experimental rquation (2) Equation (8)0.734 0.3436 0.3434 0.3-000.978 0.4868 0.4898 0.49241.182 0.5810 0.5781 0.57601.426 0.6420 0.6420 0,6463

It can be seen that Equation (2) gives slightly better agreementCZ'with the experimental values of - than does Equation (8).CL,

30


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APPENDIX BGRAPHICAL PRESENTATION OF LONGITUDINAL AND NORMAL

FORCE AN PITCHING MOMENT COEFFICIENTSAS FUNCTIONS OF ANGLE OF ATTACK

31


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14--".. .- , -----. m-, r.. . . __..3= .

"k-.-- x0 -I. i

140 s..- 28I I-i [ I / -I 'i' I

' I 'H.8

- I '81 I I __ _

14

I I.,I

..- LP.......... - - .- - - *---- Iz1 0 0: I

- T-- /-I,4

. ,i , , 6

-. 4., - , I, 4

I_-_-- I: 4--

-.4 z

FIgure 6 -Variation of Longitudinal autd Normal1 Force and Pitching MomentCoefficients with Angle of Attack for Bare Body

*'A


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1'04 2- 24 x10-4

0C- - r -- - 20

I t

41.... . . .

O 0S .

S.. 0 4 8 1 .---- 4-Si 4

Angl of Atac a indgre

i' I'* i-

I I

4 I \_-*0- -4 I L 6Z

F1g~7Anglle of.til 0in de~re

Fisuee 7 -Variation of Longitudinal and Normal Force and Pitching MomentCoefficients with Angle of Attack fo r Body with 3A Sternplanes

33


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I0i 100 2010-4

so - - 166111111426o U;, 4o

U4

0

0 - , 0

0 T "a

- i ,4 0 4 8 i 1fA.l . 1 Atta.. a n i" "

Figure 8 -Variation of Longi tudinal an d Normal Force an d Pitching MomentI Coefficients with Angle of Attack for Body with 5A Sternplanes34


47/84

I0** -- I0 2-4 10

60 .. . - - - A,

,,,

N 40.-

1 1

,,.1I I -

I.

S. .4:.2

kI - 4 0 4 8 12 16-Z 3

AngIe of Uttack 0 in degrees

Figure 9 - Variation of Longitudinal and Normal Force and Pitching MomentCoefficients with Angle of Attack fo r Body with 7A sternplanes

35


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10 -, o00 T 7 T , F - 20 . 10 -I I II 1I i M

60r 12Ia I I

20 4- t -. . .. . . !.. -- I- , T)

4 T (40i

ZI II

'1 .4 ( ... -4 Z- " "

-

-16

I, ,

-. -4 4 " 16 20\II. K'

Figure 10 - Variation of Longitudinal and Normal Force and Pitching MomentCoefficients with Angle of Attack for Body with 9A Sternplanes

3b


49/84

t o

In x IfO- -- 10t

- '+ ':ff74

x OC

'4I

" bi .4 ! .. .. ....

Ang: ,f Attack C in d-gr..ci"

Figure 11 Variation of Longitudinal and Normal Force and Pitching MomentCoefficients with Angle of Attack for Body with 11A Sternplanes

.,.


50/84

IC'" 'Oi I1 I2! I 0ii

~ I 4 ,

"I - -- 4

- 1 I

AII

7 !~' -,\ I.QI I

Figure 12 -Variation of L.ongitudinal and Normal Force and Pitching MomentCoefficients with Angle of Attack for Body with 3B Sternplanes

3A_


51/84

o 0 I I8 16 ,o',

20 4 I Z

Ui0 0

L..xU

S-40

I I I

- i1 I '8o .16

-* .4 0 4 16 102

Angle of Atlat Ik in d e\s

Figure 13 Variation of Longitudinal and Normal Force and Pitching MomentCoefficients with Angle of Attack for Body with 5B Sternplanes

39


52/84

I(- ~x 0 112 1 0-'M

0 0.

220 -24

0 t811 120

Angle of Atta, k 0i in aegr~ee

Figure 14 -Variation of Longitudinal and Normal Force and Pitching MomentCoefficients with Angle of Attack for Body with 7B Sternplanes


53/84

10 x 60 ] i 10I M'

40 8

to 4

0 0

'Io -b4

CE

E -40 -a4 ! lb -8

\iigi 't' ' n i r

Fiue1 Vraino Lniuia andNo,,a Frc anJicigMmn

-80 " _-16

-100 ,I S -zo

-b -4 0 4 8 It if, 10"\Figlv vf Atta, P a in dekrpee

Figure 15 -Variation of Longitudinal and Normal Force and Pitching Moment.Coefficients with Angle of Attack fo r Body with 9B Sternplanes

SI: ./4l


54/84

40 M

101 -4- I"

-F 1Coefficient. A1 .....

S: II _ _ _i* I

-100 2-0iI __ ___-12O0 _____ ______ -24

-8 -4 0 12 16 2O

Figure 16 - Variation of Lonigitudinal and Nor'mal Force and Pitching MomentCoefficients with Angle of Attack fo r Body with lIB Sternplanea

4'-


55/84

40 -

4i

EE

I I C.

I IZ,-Z --1

SI iI

An~le of Attack a in degreesa

Figure 17 -VariatIon of Longitudinal and Normal rce and Pitching MomentCoefficients with Angle of Attack for Body with 3C Sternplanes

4


56/84

I0Q 1 40 - M'i x|0.M

:0 4

'40. U I

* 100 z

.140 LJ~L _4 I z 1

Figure 18 -Variation of Longitudinal and Normal Force and Pitching MomentCoefficients with Angle of Attack for Body with 5C Ste:nplanes

4 4


57/84

IO'x 40 8 K 10"

zo L ... 4-

0 X,-"xL- - 40-

0E7

VK

-O 0 U

II II .

-100--~

.8 -4 0 4 8 1 ~ 16 z0Angle vi Atta k a in degrees

Figure 19 -Variation of Longitudinal and Normal Force and Pitching flomentCoefficients with Angle of Attack for Body with 7C Sternplanes


58/84

--- -- ] ... .. . .. .

0 0

x -2c -4-40

I.z

zC

"-40 - - C

-10Anl oft~ ' i n dere

I

- g -420 -24

ArKle uf Attack. 0 in deKfe~el

Figure 20 - Variation of Longitudinal and Normal Force and Pitching MomentCoefficients with Angle of Attack fo r Body with 9C Sternplanes

46.


59/84

10 40 8 10____

0 0II C

I!f tI

I I*I "- .. ..-'- U

- .

-

--

"4-- ' 1 _ _"I

z

IbO 3 -- i- -.----

--

44 . I 4RI.l

Figure 21 -Variation of Longitudinal and Normal Force and Pitching MomentCoefficients with Akigle of Attack for Body with 11C Sternplanes

47

5


60/84

Iox 4

0 0I--

- -0-- - -4 -

-~-40 - -4i 4 _zE -40 i I -- i' \ i -s -ECI

.60 z

-80 I z 16

I, """-j-- 4i II

-100 -- 0

r . . .. . . . . . . . . . . . . . . . . . .. _ __..... - - -'"

.8 -4 4 8 1 lb2Ang-l of Atta .k !n degree@

Figure 22 -Variation of Longitudinal and Normal Force and Pitching Moment,oef I Ienw th Angle of Attack for Body with 3D Sternplanes

48

I- : '


61/84

10 ~40 --- 0',- -. --.-- - , -. ,-

M,

"C-

UU

-60 ,-Iz :

-164

.40

2 .4-M -4 4 Z~ I

Figure 23 Variation of Longitudinal and Normal Force and Pitching MomentCoefficients with Angle of Attack for Body with 5D Sternplanes

IIgr 3-Vraino o~tdn] n o oc n tetgH~nC&ef et*wt1n )takfr nywt D trpae


62/84

104x 40 8 0'

0 4

I. 0 ,

- o,

2 0 --- 4_

1..4 0,-60

C -100o -i- i

.140 2

. -8 -4 U , 4 . M Izj '3

Angle of Attack a in drfgrr~e

Figure 24 -Variation of Longitudinal and Normal Force and Pitching MomentCoefficients with Angle of Attack for Body with 7D Sternplanes

50

, i tA


63/84

4.

.40 h- I12

I16

CL

.14

Anxi ,I %Il,__ain ___~r

Figure 25 -Variation of Longitudinal and Normal Force and Pitching MomentCoefficients with Angle of Attack for Body with 9D Sternplanes


64/84

10 4R 10ZC - -4 x 10Nx- 0 -4

SI I -'-60- , i \ !

S!I __ Mc o"I Ii -- -'-I If

""U 0 -,

4 4 1 z 16 z(

Figure 26 -Variation of Longitudinal and Normal Force and Pitching MomentCoefficients with Angle of Attack fo r Body with 11t) Sternplanes

')2


65/84

APPENDIX CTABULATION OF LONGITUDINAL AND NORMAL FORCE AND

PITCHING MOMENT COEFFICIENTS DUE TOANGLE OF ATTACK

53


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TABLE 3 - TABULATION OF LONGITUDINAL AND NORMAL FORCE ANDPITCHING MOMENT COEFFICIENTS DUE TO ANGLE OF ATTACK

Bare RodyVALUE! OJr ALL C IFFICIENTS MUST 01 MULTIPLIED BY 10 "1

Degeg X) Z' Ilvi

-6 -10. 9 10.7 -12. 29-4 -10.7 6.5 -8.84-3 -10.7 4.4 --6.62-Z -10.7 2.6 -4. 42-1 -10.5 1. 3 -2.23

0 -10.6 0 01 -10.8 -1. 3 2. 222 -10.7 -2.8 4. 423 -10.7 -4.7 6.644 -10.6 -5.8 8.496 -10.6 -10. 5 12.698 -10.5 -16. 3 16. 31

10 -10.6 -24. 1 19.2812 -10.4 -33.8 21.8614 -10.0 -45.6 24. 2716 -9.6 -58.4 26.4Z18 -8.5 -73. 1 28. 55

54


67/84

r-p

-Cl

0.r -

co IQ N -

x~ .0.

z '1

-X-

0! z

'i-i,

s-.f ,,


68/84

Gr- ~ .o1 t- NJ r-0(] L(n t- oo 00 'o - O ~ 4 r

14i

r-N r'0 0 L

-O CO O r- rn 00 m

0

(-I,,

-3-

C-t4


69/84

- - 1 1-4 N

ON

0 N N Q W N r- . - O'0 0 0' 1* Nr- if N N if NO N . 0o - '1 -4 t I - - rJ 'ONU I I I I I i

___ -fj. U Z - - t 1 -r -r '0 '0 1 - NO

- - 0 0 0 0' (0 t- X -* I I I I I I I I I I I I I

- ;'oE - '..O a *1* '.0 -3 *1*

__ ;ur:LI:i: -C0U

I- I--- - - - - - - - - - - --- L1 0"I ".- ' 0 'J t '0 r--- N NI -

I--- Ia N ' r - 0' . '0(0 '0E 1 0 0 t i -i *P '3(0 - -I- N N '01

I I - -J ' **1 -.3 NI I

.I, a C. 2-0 C - -'2 -'- - - N 0' a -t -t

'-I I I I I I I I I I I I I

*0 -0 -.

L -.0 .t '' N - -J ' '0 (0 0 N 1' '0(0I I I I I - - - -


70/84

C- M 01 V I -M W

r.; -o 0r1 0* C), C) 0

aa

N N rn''C ~

U L- -~ -~ - - ~- ~ N -- N

'.4~0 r- 0 7

CO 0 a, IIr

4.04lj C j 't 0 c ) t c


71/84

- 0 7 c w t- N-0

N-N

I V~ .D o

cJcc

etaj-D t-

S-r -c cc o r- t-. -- I

77r 11 'or '0 N-" D3


72/84

-r -n-- -

00, 00ck

'r - 0o

U,

r- .I NJ

14

'~ >00 4) >

ID LI


73/84

LA t-o - -

MJ It j --,

N -j mi rI -,j NJ "i cN: a:~ ~ t

c, ID o

-A

.~ ;'

0

4.40


74/84

r- ~ ~ cofl N N Or3,- UN r I

go

r- in 0 LnU . '0 0- -r t- C 0' rn -4'oCO 1, 1*1 CO 0 0 ' V oNo ~ I I .- q- 4 " 4~U r-4

I~a,

X o -P -y -1 co r.:I S-D t. 0,

jo .1coL 0, -t -D c0v

U6


75/84

N N

-Jw-

'r 0 0, C) -v - :

r- 30 -VD 0 XoS.. .. - I - . '~1~ . ~ 0 . 7-

CD j "r 4I-

U~~~~~~ -. . . . . .. . . . .


76/84

-- a- n - - - - ---. co 71 'D IvA'1 N N .- D VAL 0 n N u' fv -- -.0

- ~0 00o t~..- a- ~ Or

a..

W W 'D 00 '00 .

) f- (1 n I a, U-*01E N O* co '.0 00 r1'.

IV -- z- -r 'o c


77/84

APPENDIX DSTATIC STABILITY DERIVATIVES, INCREMENTAL DERIVATIVES AND

FREE-STREAM LIFT-CURVE SLOPES FO R STERNCONFIGURATION SERIES

. 65


78/84

TABLE. 4 - STATIC STABILITY DERIVATIVES, INCRFMENTAL DERIVATIVES,AND FREE-STREAM LIFT-CURVE SLOPES FOR

STERN CONFIGURAT1ON SERIES

Se1neZ' M ' Z M' Cz aS te mr l a ne zw mw L w a w C lC

Configuration

3A -0.01117 0.01117 -0.00315 -0.00145 1.223 3.5025A -0.01189 0.01072 -0.00387 -0.00190 1.049 2.9447A -0.01218 0.01060 -0.00416 -0.00202 0.866 2.509

9A -0.01239 0.01061 -0.00437 -0.00201 0.739 2.169IIA -0.01239 0.01061 -0.00437 -0.00201 0.622 1.9033B -0.01499 0.00906 -0.00697 -0.00356 1.815 3.7545B -0.01662 0.00825 -0.00860 -0.00437 1.616 3.2777B -0.01776 0.00770 -0.00974 -0.00492 1.432 2.8839B -0.01833 0.00759 -0.01031 -0.00503 1.244 2.55811B -0.01862 0.00768 -0.01060 -0.00494 1.085 2.287

66


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TABLE 4 (continued)

Ste rnp lane Z' Hw ' .Z ' tMw C CConfiguration

3C -0.01933 0.00716 -0.01131 -0,00546 2.241 3.8935C -0.02199 0.00586 -0.01397 -0.00676 2.043 3.4727C -0.02396 0.00526 -0.01594 -0.00736 1.848 3.1119C -0.02500 0.00469 -0.01698 -0.00793 1.630 2.804lic -0.02sbc 0.00468 -0.0175.8 -0.0079q 1.440 2.5423D -0.02498 0.00496 -0.0169r' -0.007,66 2.539 4.0135D -0.02840 0.00359 -0.02038 -0.0C,904 2. 305 3.6457D -0.0 1137 0.00229 -0.02 335 -0.01033 2.122 3.3219D -0.03438 0.00162 -0.02636 -0.01100 2.003 3.037lID -0.03572 0.00073 -0.02770 -0.01189 1.808 2.791

Notes: 1. Z and M fo r the bare body are -0.00802 and 0.01262 respec-w wtively.2. CLA is computed from Equation (1) using the effective aspectratio of the planes extended through the body.3. C. * -AZ 2A

[7


80/84

REFERENCES1. Whicker, L. Folger and Leo F. Fehlner, "Free-Stream Characteristics

of a Family of Low-Aspect-Ratio, All-Movable Control Surfaces fo rApplication to Ship Design," DTMB Report 933 Revised Edition(December 1958).Gertler, MorLon, "The DTMB Planar-Motion Mechanism System," NSR.DCReport 2523 (July 1967).

68OH~~ OOFPwwa n HJt iN - .. '.... .. H D |'~l ilN | |


81/84

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2 U. of Notre Dame 1 E. Miller1 En bib I A. GoodmanI Strandhagen I V. JohnsonI C. C. 11su

III Penn State/Arl/B. Parkin Lockheed, Sunnyvale/WaidI Princeton U./Mellor

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Copies2 McDonnell Douglas, Long BeachI J. Hess

1 T. Cebeci1 Newport News Shipbuilding/Lib1 Nielsen Eng & Res1 Oceanics1 Rockwell International/B. Ujihara1 Sperry Rand/Tech LibI Sun Shipbuilding/ChiefNaval Arch1 Robert Taggart1 Tracor

CENTER DISTRIBUTIONCopies Code

1 1500 W.E. Cummins1 1504 V.J. Monacella1 1520 R. Wermter1 1521 P. Pien1 1524 W.C. Lin1 1540 W.B. Morgan1 1552 J. McCarthy1 1560 G. Hagen1 1561 C. Lee1 1564 J. Feldman

10 1564 E. Dempsey1 1568 G. Cox1 1572 M.D. Ochi1 1576 W.E. Smith

30 5214.1 Reports Distribution1 522.1 LI.b (C)

522.2 Lib (A)

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DTNSRDC ISSUES THREE TYPES OF REPORTS(1) DTNSRDC REPORTS, A FORMAL SERIES PUBLISHING INFORMATION OF

PERMANENT T-CHNICAL VALUE, DESIGNATED BY A SERIAL REPORT NUMBER.(2) DEPARTMENTAL REPORTS. A SEMIFORMAL SERIES. RECORDING INFORMA-

TION Or A PRELIMINARY OR TEMPORARY NATURE. OR OF LIMITED INTEREST ORSIGNIFICANCE, CARRYING A DEPARTMENTAL ALPHANUMERIC IDENTIFICATION

(3) TECHNICAL MEMORANDA, AN INFORMAL SERIES, USUALLY INTERNALWORKING PAPERS OR DIRECT REPORTS TO SPONSORS. NUMBERED AS TM SERIESREPORTS; NO T FO R GENERAL DISTRIBUTION.

dempsey - static stability characteristics of systematics series of stern control surfaces

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