EXPERIMENTAL UNSTEADY AND TIME AVERAGE LOADS ON THE BLADES OF THE CP REPORT 77-0110 PROPELLER ON A MODEL OF THE DD-963 CLASS DESTROYER FOR SIMULATED MODES OF OPERATION DAVID W. TAYLOR NAVAL SHIP RESEARCH AND DEVELOPMENT CENTER Bethesda, Md. 20084 EXPERIMENTAL UNSTEADY AND TIME AVERAGE LOADS ON THE BLADES OF THE CP PROPELLER ON A MODEL OF THE DD-963 CLASS DESTROYER FOR SIMULATED MODES OF OPERATION by Stuart D. Jessup Robert J. Boswell John J. Nelka APPROVED FOR PUBLIC RELEASE: DISTRIBUTION UNLIMITED SHIP PERFORMANCE DEPARTMENT RESEARCH AND DEVELOPMENT REPORT December 1977 Report 77-0110 MAJOR DTNSRDC ORGANIZATIONAL COMPONENTS DTNSRDC COMMANDER TECHNICAL DIRECTOR 01 OFFICER-IN-CHARGE OFFICER-IN-CHARGE CARDEROCK SYSTEMS DEVELOPMENT DEPARTMENT 1 SHIP PERFORMANCE DEPARTMENT ats STRUCTURES DEPARTMENT ie SHIP ACOUSTICS DEPARTMENT a SHIP MATERIALS ENGINEERING DEPARTMENT 9g ANNAPOLIS AVIATION AND SURFACE EFFECTS DEPARTMENT 4¢ COMPUTATION, MATHEMATICS AND LOGISTICS DEPARTMENT 18 PROPULSION AND AUXILIARY SYSTEMS DEPARTMENT 47 CENTRAL INSTRUMENTATION DEPARTMENT 49 L/WHoI MB mn IM INK NN 0 0301 ‘00324 UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAGE (When Data Entered) READ INSTRUCTIONS | REPORT DOCUMENTATION PAGE HERORPICGHEDETINGIGODM | 1. REPORT NUMBER 2. GOVT ACCESSION NO.| 3. RECIPIENT'S CATALOG NUMBER 77-0110 4. TITLE (and Subtitle) ‘ 5. TYPE OF REPORT & PERIOD COVERED Experimental Unsteady and Time Average Loads of the CP Propeller on a Model of the DD963 Class Destroyer for Simulated Modes of Operation Final 6. PERFORMING ORG. REPORT NUMBER 77-0110 8. CONTRACT OR GRANT NUMBER(a@) 7. AUTHOR(s) Stuart D. Jessup Robert J. Boswell John J. Nelka 9. PERFORMING ORGANIZATION NAME AND ADDRESS David W. Taylor Naval Ship Research and Development Center Bethesda, Maryland 20084 11, CONTROLLING OFFICE NAME AND ADDRESS Naval Sea Systems Command (0331G) Energy Conversion & Explosive Devices Division TaaINUMBERIORIDAGES Washington, D.C. 20362 310 14. MONITORING AGENCY NAME & ADDRESS(if different from Controlling Office) 15. SECURITY CLASS. (of thia report) Naval Ship Engineering Center (6148) Propeller, Shafting & Bearing Branch Unclassified Washington, D.C. 20362 1Sa. DECL ASSIFICATION/ DOWNGRADING SCHEDULE 10. PROGRAM ELE AREA & WORK Task Area SO Task 19977 Work Unit No. 12. REPORT DATE December 1977 ME UN 37 1544-296 16. DISTRIBUTION STATEMENT (of this Report) Approved for public release: Distribution Unlimited 17. DISTRIBUTION STATEMENT (of the abstract entered in Block 20, if different from Report) 18. SUPPLEMENTARY NOTES 19. KEY WORDS (Continue on reverse side if necessary and identify by block number) Marine Propeller Propeller Research Controllable-Pitch Propeller Unsteady Loads Loads DD963 Class Destroyer Propulsion Model Experiments 20. ABSTRACT (Continue on reverse side if necessary and identify by block number) Experiments are described in which the mean and unsteady loads were measured on a single blade of a model of the controllable-pitch propeller on the DD-963 Class Destroyer. The experiments were conducted behind a model of the DD-963 hull under steady ahead operation, hull pitching motions, and simulated acceleration maneuvers. The experimental techniques are outlined j and the dynamometer and data analysis system described. The results show that all significant loads except radial force are pre- dominantly of hydrodynamic origin. The circumferential variation of all FORM DD ; jan 73 1473 = EDITION OF 1 Nov 65 Is OBSOLETE UNCLASSIFIED S/N 0102-014- 6601 SECURITY CLASSIFICATION OF THIS PAGE (When Data Entered) UNCLASSIFIED LULCURITY CLASSIFICATION OF THIS PAGE(When Data Entered) measured components of blade loading is primarily a once-per-revolution | variation, with the variation following approximately the variation of the tangential wake velocity. For sinusoidal pitching of the hull with maximum pitch angle of 1.85 degrees and a simulated full scale frequency of 0.16 hertz, the peak-to-peak cir- cumferential variation of measured forces and moments increased by approxi- mately 50 percent over the values without hull pitching. For simulated operation during an acceleration maneuver, the circumferential variation of measured forces and moments varied approximately as the product of ship speed and propeller rotational speed. At no time during the simulated acceleration maneuvers were the circumferential variations of loads as large as during full power steady ahead operation. For steady ahead operation, circumferential variation of loading determined from the model experiments agreed fairly well with full-scale data, but was substantially larger than the theoretically calculated values. For all conditions evaluated, the results follow close to previously reported results of similar experiments on a model of the FF-1088. UNCLASSIFIED SECURITY CLASSIFICATION OF THIS PAGE(When Data Entered) TABLE OF CONTENTS Page IAB SHEA CMasenin ce ier ease eorunmaun adr aNNophitel Welty rail setVemines*\eli Kelton elie ohiilreitize 1 IAD MEN PES HE RAVINE ENE ORMAM ON isronavouiiel i loitoi ror ioit voli ciible Maniile/s elllroh! Nolte! lilsiitell i esiite aL TNA ROWUWGIBICON, 6 NB WGNol ao Nala Mo kor oi a Toi alo Valo joy aio) .6) ONG) oo. sd NG. 2 BACGRO UID, BS) Guy) BS Pee G So So Monin oso Moa 8! OS) oe al ouenio a 3 EXPERIMENTAL sPECHNIQUE) ee sn te et 9 TAGIOLIEING ANNOY ID ONVNG COMMING OGG alo 6 6 6 Oo ouo Oo OO) G65 9 CAIDA NITIOM Ga 6 eka! G Yo ro Oe oO 6 oub a volo roe o.i6e oO oo oN 12 EXPERIMENTAL CONDITIONS AND PROCEDURES ....-..+ +--+. = 14 DATA ACQUISITION AND ANALYSIS . . .... + © «© © © © © © © © © 17 IACCURAGYG siecle oe Loa (ettRon No cel mehite) Levelt) nou NeMien\Mell(tefuile tenimeanvoluielitis 21 CUA RIGVIAVONL, TIANA BG oy 6 Gal o6 0 66 19'S 686) boo 00 0 23 HOADIEN GH COMBONEN DS) 0 Wen (el) teietlrat vol roi roi Meyi ited Noll) oh 7oi/l0)) i olnite)" cen iitelliel i oll alfolhys 23) CENTRIFUGAL AND GRAVITATIONAL LOADS . .... +. + 26 «© » «= «© « « 26 INFLUENCE OF DYNAMOMETER BOAT . .... ++ + © © © © © © © © « 29 SEEADYOAH EAD ORE RAMMON (Eiri veda iicisiiitoil Collin) /ale\iale|t ele), o/hcellhteiuilte) uel Mie luieliiiis 31 EL WTAE ATED CHUN een sai icea rat uyou ail sole Nell Vall MeiNvoy) oll tenures laiellicel Pte li celiniemmieielnelli ken te 34 ACCHIE RATT ON ciiteu moniter tera renyronireMmiieliie. Veil ol it elntehitei uel vei eieMolMed voneielulte 38 CORRELATION WITH FULL-SCALE DATA AND THEORY ..... ++ +s - 42 SUMMARY WAND CONCLUSMONS ier lene teev iron Toye) ce) ve) Vey io) ho) 0) oles te) Wen Vol leNiuies ie 48 ANCRANO MMA DCONIONIES 6 966 656 0.566 G0 Oo GB 0 10 000 100 6 oO ool 50 APPENDIX A - DETAILS OF WAKES ..... 6 © © © © © © © © © «© «© « 51 APPENDIX B - DETAILED EXPERIMENTAL RESULTS . ..- - «© «© » «© © © « 58} RICMERIEN GE Swat alps Geniman iia bakiieillrs pith ites Monies verse iuenAver Mieiigeli fen (leila ipeitinelire tiFea serie 285 iii NM 10 11 12 13) 14 i5) 16 iL7/ LIST OF FIGURES Page Components Of IBladeMioadtiing aren ticy asian cimetciae ie -teronat tee tenn marr a) Schematic Drawing of CP Propellers on DD-963 Class Destroyer; DTNSRDC Model Propellers 4660 and 4661 ........ «56 Ship wand Model, Partdiculllarst solr ic.) sm 5) ene oben eh fe) een aren a OD Experimental Arrangement of Hull and Dynamometer Boat ...... 98 TypicalsySitrain, Caged! prillexunesy scl, «vs icetticuy oatcn mehr oy verte) ee OL Ry picalsyArcrangenentuor @hillexunes|s mH bs semee sell len lle oie iene) acm OLE Experimental Acceleration Conds tions. mie ame mucin micas annem OZ Experimental Data Showing Plus and Minus Two Standard Deviations on Measured Values of Fee MSM NS Peo OS Correlation of Theory and Experiment for Time Average (Gentrikugale Spandilie: Ronquecy siie) clurciacicy Lelia iron-on in mnt Distribution jor Wakesine Propeller) Daisies weawenmeiateeiop de) mich mith ht mt neOS) Open-Water Characteristics of DTNSRDC Model Dae pellilercs, AGO, eral AGO, 6 6 6 oso 6.66 610 56 6-0 605.0006 0 Influence of Extraneous Signals on Measured Loads ........ J/1 Experimental Data Showing Extraneous Higher Harmonics ...... 7/7 Variation of Experimental Hydrodynamic Loads with Angular Position for Steady-Ahead Operation ........... 83 Variation in Radial Center of Thrust F,,, and Transverse Hydrodynamic Force Fy with Sade Angular Position for SteadysAhead Open 6 566.6 0 6 00 a 5 0 A Variation of Experimental Total Loads with Angular Position for Steady—Ahead| Operation.) ys) se) 0) econ tein ete Harmonic Content of Experimental Hydrodynamic Loads for Stead=Ahead! Operatdion yo. 5mm ly ction besitos aici outed act nou ant TCL Harmonic Content of Experimental Total Loads for Steady—AheadwOperartslonsmeiaemeeiamremCnnt rn aicnateritch (oil -tar-Tn ie itn In ee OLS) iv 19 20 Dall 22 23 24 D5) 26 27 28 29 30 Variation of Components of Total Blade Loading with Fehoul: Ieskeein AMIE «6 6 G 5 0 9 © Variation of Experimental Hydrodynamic Loads with Angular Position for Quasi-Steady Acceleration . Variation in Radial Center of Thrust F,, and Transverse Hydrodynamic Force Fy, with Biade Angular Position for Quasi-Steady Acceleration . Variation of Experimental Total Loads with Angular Position for Quasi-Stead Acceleration. Harmonic Content of Experimental Hydrodynamic Loads for Quasi-Steady Acceleration. Harmonic Content of Experimental Total Loads for Quasi-Steady Acceleration. .. Taylor Wake Fractions During Simulated Acceleration MEINOUWEIES 5 6 5 6 516 5 00 6 Variation of First Harmonic of Experimental Hydrodynamic Loads with nV for Quasi-Steady MOECSILETEEVEOMY G=0' 15 6 6 60.00. 00 O00 0 Comparison of Time-Average Values Per Revolution and Peak Values of Various Components of Experimental Total Blade Loading for Quasi-Steady and Unsteady SamulatedgAcceilleraltelonueue mci n en ieniecn laley oii eu ite Variation of Hydrodynamic Bending Moment at 30 Percent and 40 percent Radii with Blade Angular Position, Theoretical Prediction With and Without DMEM MVIESTS IIOENE g 8S) old 40 6) 6 o. Givo 70, a 6 6 Variation of Hydrodynamic Bending Moment at 30 Percent and 40 Percent Radii with Blade Angular Position, Comparison of Model Data with Theory... Harmonic Content of Hydrodynamic Bending Moment at 30 Percent and 40 Percent Radii, Comparison of Model Data and Theory. ... Page 90 96 104 109 IE) 133 149 150 153 9 161 162 10 12 ibs) 14 15 LIST OF TABLES Characteristics of Propellers on DD-963 Class Destroyer; DTINSRDC Model Propellers 4660 and 4661 Calibration Matrix . Model Experimental Conditions. Full-Scale Conditions Simulated by Model Experiment. Repeat Runs for F. for Steady-Ahead Operation. Centrifugal and Gravitational Loads. Summary of Circumferential Variation of Loads at the Self Propulsion. Condition; V=6.52 knots, n=14.08 revolutions/second . Time-Average Loads for Steady-Ahead Operation at the Self Propulsion Condition; V=6.52 knots, n=14.08 HEVolUMtLOms SECO dM sini eay sm Ween ctins Mole e Maa oi Mireden ane Wake Without Dynamometer Boat. Wake Waltth) Dynamome ter sBoae ee vais) ie) elie elise ie isi area tel Ke Experimental Loads for Steady-Ahead Operation at V=6.52 knots, n=14.08 revolutions/second . Experimental Loads During Quasi-Steady Acceleration at V=2.65 knots, n=10.21 revolutions/second. Experimental Loads During Quasi-Steady Acceleration at V=3.55 knots, n=10.96 revolutions/second. Experimental Loads During Quasi-Steady Acceleration at V=5.36 knots, n=12.70 revolutions/second. Experimental Loads During Quasi-Steady Acceleration at V=6.26 knots, n=13.78 revolutions/second. Page 164 165 166 166 167 168 169 170 171 206 240 258 261 269 Zieh XsVoZ NOTATION Expanded area, ZS cdr ah Propeller disk area, nD=/4 Fourier cosine coefficient of radial component of wake velocity Velocity cosine coefficient of tangential component of wake velocity Fourier cosine coefficient of longitudinal component of wake velocity Fourier sine coefficient of radial component of wake velocity Fourier sine coefficient of tangential component of wake velocity Fourier sine coefficient of longitudinal component of wake velocity Correlation allowance Elements of calibration matrix Thrust loading coefficient, T/((p/2)V,",)) Blade section chord length Propeller diameter Froude number nth harmonic amplitude of F Force components on blade in x,y,z directions Camber of propeller blade section Advance coefficient, J=V ,/nD Effective advance coefficient based on thrust identity Effective advance coefficient based on torque identity Ship speed advance coefficient, J=V/nD 2 th * ae orce coefficient, Bee se all Won Di) XsV5Z Moment coefficient, M Imm) X5,V5Z Torque coefficient, O/oneDe) Centrifugal blade spindle torque coefficient, My /(opn°D”) Ded & Thrust coefficient, T/(on D ) Moment components about x,y,z axes from loading on one blade nth harmonic amplitude of M Propeller revolutions per unit time Propeller blade section pitch Time average propeller torque arising from loading on all blades, ~2M,, Radius of propeller Reynolds number, Co 7VR*/Y Radial coordinate from propeller axis Radial center of hydrodynamic component of axial force, M/A CEs ay) Ya He Radial center of hydrodynamic component of transverse force, M /(F_ ) HOH Skew back of propeller blade section measured from the spindle axis to the midchord point of the blade section, positive towards trailing edge Time average thrust of propeller, positive foward, ZF Maximum thickness of propeller blade section Model speed Propeller speed of advance Vector sum of speed of advance and rotational velocity at the 0.7 sadius, Wie + (0.7mnD)2)1/2 Radial component of wake velocity, positive towards hub nth harmonic amplitude of es viii Rx Tangential component of wake velocity, positive clockwise looking upstream for starboard propeller (left hand rotation), positive counterclockwise looking upstream for port propeller (right hand rotation) nth harmonic amplitude of Wes Longitudinal component of wake velocity, positive forward nth harmonic amplitude of Vie Volume mean longitudinal velocity through propeller disk determined from wake survey Taylor wake fraction determined from torque identity Taylor wake fraction determined from thrust identity Wake fraction determined from volume mean longitudinal velocity through propeller disk determined from a wake survey, VV) /V Coordinate axes Number of blades Rake of propeller blade section measured from the pro- peller plane to the generator line, positive aft Advance angle at 0.7 radius, eer lv, (r=0.07)/(0.71n v)| Blade strain Angular coordinate used to define location of blade and variation of loads, from vertical upward positive counter- clockwise looking upstream for starboard propeller (left hand rotation), positive clockwise looking upstream for port propeller (right hand rotation), O=-6,, Skew angle measured from spindle axis to projection of blade section midchord into propeller plane, positive toward trailing edge Angular coordinate of wake velocity, from upward vertical, positive clockwise looking upstream for starboard pro- peller (left hand rotation), positive counterclockwise looking upstream for port propeller (right hand rotation), 6..=-6 W alr Subscripts: A CW MIN Ship to model linear scale ratio Kinematic viscosity of water Mass density of water Mass density of propeller blade Pitch angle of propeller blade section, eens (P/ (2tr)) nth harmonic phase angles of F,M based on a cosine series (F,M)=(F,M) + bs (FM) cos os (OFM nth harmonic phase angles of We based on a sine series, ewe) i 2y Cn ooo (n6,, Bi Cpe ee nth harmonic phase angles of V.. based on a sine series, v.=@,) + 2) (,), sin (ne, + (6y,*)_) nth harmonic phase angles of Vee based on a sine series, WW )=@,) + 2) (V,), sin (ne, + (by, *),) Pitch angle of hull Applied values of loads Arising from centrifugal loading Value in calm water Arising from gravitational loading Arising from hydrodynamic loading Value of hub radius Indicated values of loads before calibration matrix is applied Model value Maximum value at any blade angular position Minimum value at any blade angular position PEAK SP XYZ Superscripts: Value of nth harmonic Port propeller Peak value including variation of both time-average value per revolution and variation with blade angular position Ship value Value at self-propulsion point Starboard propeller Total loading from hydrodynamic, centrifugal, and gravitational components Component in x,y,z direction Value at r=0.3R Value at r=0.4R Value at r=0.7R Time average value per revolution Unsteady value Rate of change with time xi enue Beek co ABSTRACT Experiments are described in which the mean and unsteady loads were measured on a single blade of a model of the controllable-pitch propeller on the DD-963 Class Destroyer. The experiments were conducted behind a model of the DD-963 hull under steady ahead operation, hull pitching motions, and simulated acceleration maneuvers. The experimental tech- niques are outlined and the dynamometer and data analysis sys- tem described. The results show that all significant loads except radial force are predominantly of hydrodynamic origin. The circum- ferential variation of all measured components of blade load- ing is primarily a once-per-revolution variation, with the variation following approximately the variation of the tan- gential wake velocity. For sinusoidal pitching of the hull with maximum pitch angle of 1.85 degrees and a simulated full scale frequency of 0.16 hertz, the peak-to-peak circumferential variation of measured forces and moments increased by approximately 50 per- cent over the values without hull pitching. For simulated operation during an acceleration maneuver, the circumferential variation of measured forces and moments varied approximately as the product of ship speed and propeller rotational speed. At no time during the simulated acceleration maneuvers were the circumferential variations of loads as large as during full power steady ahead operation. For steady ahead operation, circumferential variation of loading determined from the model experiments agreed fairly well with full-scale data, but was substantially larger than the theoretically calculated values. For all conditions evaluated, the results follow close to previously reported results of similar experiments on a model of the FF-1088. ADMINISTRATIVE INFORMATION The work reported herein was funded by the Naval Sea Systems Command (NAVSEA 033), Task Area S0379-SLOO1, Task 19977. The work was performed under David W. Taylor Naval Ship Research and Development Center (DINSRDC) Work Unit No. 1544-296. The English system of units was used in the original calculations presented in this report. Therefore, all data are presented in the English units. However, the International System (SI) of metric units are shown in the text in parentheses following the English units. INTRODUCTION Major naval ships powered with marine gas turbines and using controllable-pitch (CP) propellers for thrust reversal are currently being added to the Fleet. Ships with CP propellers include the DD-963 Class, the FFG-7 Class, and the DDG-47 Class. Accordingly, the Navy has been conducting a research and development (R&D) program to establish the technology for producing reliable CP pro- pellers with delivered power in the range of 35,000 to 40,000 horsepower (26,000 to 30,000 Wee As part of this program, CP propellers were installed on the U.S.S. PATTERSON (FF-1061) and U.S.S. BARBEY (FF-1088) with delivered power of 35,000 horsepower (26,100 kW). These installations were intended to demonstrate that CP propellers in this range of power had adequate reliability for application to ships with gas turbine prime movers. Because of the structural failure of the crank rings to which the blades of the CP propeller on the FF-1088 were bolted, R&D efforts were intensified. The program undertaken at DINSRDC included: 1. Blade Loading of CP Propellers a. Model measurement and theoretical prediction of blade load- ing on CP propellers. b. Model and full-scale wake measurements and theoretical pre- dictions of wake. c. Full-scale measurements of forces, pressures, and strains in CP propeller components. 2. Structural Design of CP Propeller Blade Attachments. 3. Development of Materials for CP Propeller Systems. The current report presents the results of work conducted under Sec- tion la of the CP Propeller Research and Development Program, i.e., model Theses silie J.J. et al, "U.S. Navy Controllable Pitch Propeller Programs," presented at a Joint Session of the Chesapeake Section of the Society of Naval Architects and Marine Engineers and the Flagship Section of the American Society of Naval Engineers, Bethesda, Maryland (19 April 1977). measurement and theoretical prediction of blade loading of CP propellers. Work under the other sections of this program will be reported separately. The present report presents experimental results obtained on a model of the CP propeller on the DD-963 Class Destroyer. The results of similar experiments on a model of the FF-1088 were reported in Reference 2. BACKGROUND Extreme care must be taken to design the blades and pitch-changing mechanisms of high power CP propellers so that they possess adequate strength including consideration of yield and fatigue stresses. This requires an accurate estimate of the maximum time-average and alternating loads under all operating conditions. High time-average and alternating loads occur at steady full-power ahead conditions and during high-speed maneuvers including full-power crash astern, full-power crash ahead, and full-power turns. In addition, the influence of the seaway may substan- tially increase the time-average and alternating loads. At present there appears to be no confirmed technique whereby the pertinent loads can be predicted to the desired accuracy. Schwanecke and Weeeldeneae reviewed the factors affecting blade loading for propellers in general, and Rurseesiieey and Hawdon et ee discussed some of the factors peculiar to blade loading of CP propellers. Sogetaiil, R.J. et al, “Experimental Determination of Mean and Unsteady Loads on a Model CP Propeller Blade for Various Simulated Modes of Ship Operation," The Eleventh Symposium on Naval Hydrodynamics sponsored Jointly by the Office of Naval Research and University College London, Mechanical Engineering Publications Limited, London and New York, pp 789-823, 832-834, (April 1976); also "Experimental Unsteady and Mean Loads on a CP Propeller Blade of the FF-1088 for Simulated Modes of Operation," David Taylor Naval Ship Research and Development Center Report 76-0125, October 1976. Scehmemcekes H. and R. Wereldsma, "Strength of Propellers Considering Steady and Unsteady Shaft and Blade Forces, Stationary and Nonstationary Environmental Conditions," Proceedings of the Thirteenth International Towing Tank Conference, Report of the Propeller Committee, Appendix 2b, Vol. 2, pp 495-526 (1972). sRucetelinn A.A., "Hydrodynamics of Controllable Pitch Propellers," Shipbuilding Publishing House, Leningrad (1968). 5 Hawdon, L. et al, "The Analysis of Controllable-Pitch Propeller Char- acteristics at Off-Design Conditions," Transactions of the Institute of Marine Engineers, Vol. 88, Series A, Part 4, pp 162-184 (1976). 3 Near the self-propulsion point in calm water, the time-average loads can probably be calculated with reasonable accuracy. However, even at these conditions, the variation of loads with blade angular position ap- parently cannot be calculated with high accuracy. Various techniques, including quasi-steady procedures, stripwise unstead procedures, and methods based on unsteady lifting surface theory, have been proposed for calculating the unsteady loading arising from the circumferential varia- tion in the inflow and Flexure 3 measured components Ee and M, (Figures 1, 5, and 6). An arrangement of three separate flexures rather than one to measure all components of blade loading was adopted Because it appeared to result in higher natural fre- quencies (Criterion 1), higher sensitivities (Criterion 3), and lower interactions (Criterion 4), than would have resulted had a single flexure been used. The flexures were mounted inside a propeller hub which was specifi- cally designed for these experiments (Figure 6). Only one flexure could be mounted at a time, because of space limitations, and this necessitated duplicate runs, as discussed later in the section on experimental condi- tions and procedures. The strain-gage bridges were excited by a common d.c. voltage source, transmitted through the sliprings on the propeller shaft. The constant-current excitation used by DObayae was not employed in the pre- sent experiment because it appeared to be too sensitive to temperature. The voltage output from the flexures (due to blade loading) was transmitted through the sliprings to individual amplifiers (NEFF 119-121). These amplifiers utilized field effect transistors to produce an extremely high input-impedance (100 megohms, minimum). This high impedance essen- tially eliminated slipring noise to the amplifier. The voltage signals were transferred across the sliprings in the presence of only a small amount of noise-producing current. The amplifiers used here had zero- phase shift qualities in the d.c. to 20 kilohertz range. They were chopper- stabilized to enable both the steady and unsteady signals to be recorded simultaneously. This signal-conditioning system was essentially the same as that used by Dope. iil The signals were then digitized and analyzed by using a Model 70 Interdata Digital Computer, and then stored in digital form on a nine- track magnetic tape. The on-line analysis of the data is discussed in the section on data acquisition and analysis. CALIBRATION Prior to the experiment, each flexure was statically calibrated in air to establish flexure sensitivities, interactions, and linearity over the loading range of interest. These calibrations were conducted with the flexures mounted in a calibration stand, with the flexure electrical ca- bles connected through the flywheel and drive assembly as in the experi- ment. Each flexure was subjected to independently controlled forces in the axial, transverse, and radial directions (i.e., Flo ee and Fo re- spectively) and to independently controlled moments about the axial, transverse, and radial directions (i.e., M, Bye and M,> respectively); see Figure l. The static calibration showed that all flexures had a linear re- sponse over the load range of interest. Table 2 shows the interaction matrix. These calibrations indicated that all flexures had good sensi- tivity except Be whose sensitivity was slightly lower than desirable. The interactions were small except for the effect of M, on ae The infe- rior characteristics of the ER flexure is not considered a serious short- coming since Ek arises primarily from centrifugal loading and can be analytically calculated. In addition, no significant variation of ES with blade angular position was anticipated. Flexure 3, which measured F. and M,> was further evaluated by correlation of air-spin experiments with analytically calculated results, as discussed later. The interac-— tions were taken into consideration during data analysis. The flexures used in this experiment had been dynamically cali- brated by easy” to determine the frequency range over which unsteady forces and moments could be reliably measured. In this procedure, an electromagnetic shaker in air was used to apply a relatively constant, maximum amplitude, variable-frequency force or moment-excitation in all six-component directions to all six flexure elements. The force or mo- ment amplitude imposed by the shaker was monitored through an extremely 12, light-weight, strain-gaged single flexure element. The measured lowest. natural frequencies of the three flexures in air were as follows: Frequency (hertz) Mode Flexure 1 550 M, Flexure 2 450 MO Flexure 3 282 M, The measured amplification factor (ratio of output amplitude to in- put amplitude) and phase shift for all three flexures was as follows: Frequency Range (hertz) 0 to 60 60 to 120 Phase Shift (degrees) 0 to 0.05 0.05 to 0.15 Amplification Factor 1.00 1.00 to 1.05 In the previous eeperimentd the natural frequency of the flexures was found to be reduced by 55 percent when submerged with blades attached. As a result, it was concluded that the flexures had a "true" dynamic re- sponse up to at least the third harmonic and no greater than a five per- cent amplification up to the sixth harmonic. Because the blades used on the present experiment were lighter and smaller than those used on the previous experiment, it was assumed that the natural frequency of the flexures would be reduced to a lesser extent when submerged with blades, so that the dynamic amplification would be less. This assumption was supported by the increase in frequency of the extraneous signals appearing in the unfiltered experimental data as discussed in the experimental re- sults section. The propeller shaft drive and soft-mount support system were dynam- namically loaded in the vertical, longitudinal, and transverse directions to obtain the lowest natural frequencies of the system. The natural fre- quencies of the system in air were found to be: Mode Natural Frequency (hertz) Vertical bending W252 Horizontal bending 6.0 Axial 4.6 The support system had a low resonant range; however, the soft- mount system was specifically designed to prevent towing-carriage 13 oscillation (with the resonance at 100 to 200 hertz) from being trans- mitted to the blade flexures. Based on the measured resonance, it is concluded that the soft-mount system should successfully meet this ob- jective. Although some resonances were close to the propeller rotational speed for some experimental conditions, it was considered more desirable to isolate the system from towing-carriage vibration. EXPERIMENTAL CONDITIONS AND PROCEDURES Experiments were conducted at several conditions including steady- ahead operation, simulated pitching of the hull, and simulated accelera- tion. All conditions were run with the model hull rigidly attached to its support, with no freedom to sink or trim, and with essentially equal rota- tional speed on the port and starboard propellers. The steady-ahead condition is defined in Tables 3 and 4. The simu- lated full scale ship speed and propeller rotational speed for this condi- tion were determined from model self-propulsion data* at simulated dis- placement of 7,800 tons (7,920 tonnes) including corrections for wind drag at zero true wind and a three-percent margin on effective power with Cy = 0.0005. The trim and draft at this speed were obtained from Reference 28. These had been determined by setting the specified still water trim (even keel) and draft (19.5 feet (6.40 m) full-scale equivalent), attaching the model to the carriage so that it was free to trim and sink, running at the specified speed, and locking the model at this equilibrium trim and draft. The equilibrium sinkage was 0.5 feet (15.4 cm) at the bow and 3.0 feet (98.4 cm) at the stern. Runs simulating hull pitching were conducted at the same conditions as the steady-ahead run, except that the hull pitch was varied. Two types of runs were conducted: (1) quasi-steady simulation in which the hull pitch angle ~ was set at various fixed positions, and (2) unsteady *DTNSRDC experiments 21 and 22 on Model 5265-1B. eve W.G., "The Effect of Speed on the Wake in Way of the Propeller Plane for the DD-963 Class Destroyer Represented by Model 5265-1B," David Taylor Naval Ship Research and Development Center Report SPD-311-37 (July UGS) ¢ 14 simulation in which was varied sinusoidally with time. For the quasi- steady simulation, runs were conducted at five different values of yw, from 1.85 degrees bow up from the calm water equilibrium VW=V ou) to 1.85 de- grees, bow down from vow (Tables 3 and 4). For the unsteady pitch simu- lation, the value of ~ was varied sinusoidally about vow with an ampli- tude of 1.85 degrees and a frequency of 0.8 hertz.* The selected scaled amplitude and frequency were within the predicted response characteristics of the DD-963. All runs were conducted in calm water; therefore, the re- sponse of the hull to the seaway was simulated but the seaway was not simulated. Acceleration runs were conducted based on analytical dynamic simu- lation studies of the DD-963.-> The experimental conditions followed run 7501061 of Reference 29, which was an acceleration from 8.7 knots to full power (see Tables 3 and 4 and Figure 7). Trim and displacement were fixed at the values corresponding to the self-propulsion condition (Condition 1 of Table 3). Two types of runs were conducted: (1) quasi-steady runs in which all quantities including model speed V, rotational speed n, and pro- peller pitch P were held constant (V=n=P=0), and (2) unsteady runs in which V was varied with time but n and P were held constant (V>0, n=P=0). For the quasi-steady simulation, runs were conducted at five different combinations of V, n, and P. The conditions for each run represent the conditions at one instant of time during a "true'' acceleration in which V, n, and P vary with time. Thus, one "true" acceleration run is repre- sented by five steady runs which do not simulate the time rate of change of V, n, and P. For the unsteady simulation, runs were conducted at the same five combinations of fixed n and P as used for the quasi-steady simu- lation, and V was varied with time (the same variation was used for each run) representing an acceleration of the model hull (Figure 7). For each of these runs, data are of interest only near that value of V which oc- curred concurrently with the fixed values of n and P during the "true" x Full scale equivalent frequency is 0.16 hertz. Cea C.J. and T.R. Harper, "Propulsion Dynamics Simulation of the DD-963 Class Destroyer," Propulsion Dynamics, Inc., Report 74R1B (January OID) he 15 acceleration (V>0, n#0, P#0). Thus, one "true" acceleration run is rep- resented by five runs which simulate the proper time rate of change of V but not the proper time rate of change of n and P. The quasi-steady and unsteady acceleration simulations were for the same conditions, the only difference being that V=0 for the quasi-steady simulation whereas V>0 for the unsteady simulation. In general, P varies with time during a "true" acceleration run; however, for the acceleration run under simulation here, P was constant throughout the portion of the run simulated. For the unsteady acceleration runs, the carriage speed was manually varied with time in a carefully controlled manner. This was achieved with the aid of an inked pen on a two-dimensional Cartesian plotter. In one direction, the pen was controlled so that it moved linearly with time, and in the orthogonal direction, it was controlled so that it varied with the instantaneous carriage speed. When an acceleration maneuver was to be executed, the switch moving the pen with time was turned on and the car- riage operator manually varied the carriage speed so that the inked pen followed a prescribed velocity versus time curve. As discussed earlier, each of the three load-sensing flexures measured only two components of blade loading. Therefore, each of the experimental conditions described in Table 3 was run with each of the three blade loading flexures. The blade pitch was set by using a Sheffield Cordax 300 measuring machine. In order to change either the blade pitch or the flexure, the propeller had to be removed from the drive system. Air-spin experiments were conducted with all three flexures over a range of rotational speeds in order to isolate the effects of centrifugal and gravitational loading from hydrodynamic loading. Supplemental experi- ments were conducted to assess the influence of the downstream dynamo- meter boat on the flow in the propeller plane. These supplemental exper- iments consisted of wake surveys in the propeller plane at the self- propulsion point (Condition 1 in Table 3) with and without the downstream body, but without the propeller. These wake surveys yielded a direct measure of the change in the velocity distribution through the propeller 16 disk attributable to the downstream body. The details of these wake sur- veys will be reported in a future DINSRDC report.* DATA ACQUISITION AND ANALYSIS Data were collected, stored, and analyzed on-line by using a Model 70 Interdata Digital Computer. A special-purpose computer program was written with options for analyzing each of the three basic types of runs: (1) steady ahead, (2) dynamic hull pitching, and (3) unsteady acceleration. These types of runs have already been discussed in detail. The program allowed the propeller blade force and moment data to be sampled and stored on magnetic tape as a function of shaft position. Sampling was triggered by external pulses generated by a Baldwin Digital Encoder mounted on the propeller shaft, as discussed earlier. Pulses were generated as a function of shaft angular position; hence, the sampling of blade force and moment data was related to shaft position. There were two outputs from the shaft encoder; a single pulse per revolution and multi- ile (OO pulses per revolution for the current experiments). When the experimental condition was achieved, the computer operator initiated the data collection cycle. The program "waited" until the sin- gle pulse occurred; when the single pulse occurred, the computer again "waited" for the occurrence of the first following pulse of the 90 pulses; data were then sampled for all channels through an analog-to-digital con- verter and stored in computer memory. This process was repeated for 180 pulses, or two shaft revolutions. At the same time, the program "read" two frequency counters into core memory which measured model velocity V and propeller rotational speed n. The values of V and n were measured by counting the pulses from geared wheels attached to the towing carriage drive system and to the propeller shaft, respectively. The values of V and n were averaged over two shaft revolutions. Thus, there was an average V and n corresponding to each pair of two consecutive revolutions. After two revolutions of data were sampled and stored in core memory, the data were transmitted from core to a nine-track digital tape recorder. The transfer time was small and no pulses were missed during the transfer. * These wake surveys were conducted by R.F. Roddy, DINSRDC Code 1524. 107/ The data collection cycle proceeded continuously until the operator dis-— engaged the computer. The sampling procedure was the same for all types of experimental conditions, and at the completion of an experimental run, all data were stored on magnetic tape and were available for analysis im- mediately or at any later time. For the analysis, the computer operator selected the appropriate option of the program depending on the type of run, i.e., (1) steady ahead, (2) dynamic hull pitching, or (3) unsteady acceleration. The appropriate calibration factors were stored in the computer and considered in the analysis. However, since only two of the six components of blade loading were measured during a given run, the interactions between the various loading components could not be considered during the on-line analysis. The interactions were taken into account later after measure- ments were completed with all three flexures for a given condition. For the steady ahead condition, blade force and moment data at each 4-degree increment of blade angular position were averaged over the number of cycles recorded (usually over more than 200 cycles). Spurious data not related to shaft position are averaged out by this method. An harmonic analysis was then performed on the average wave forms of the blade loading components. This gave the amplitude and phase of the first 16 harmonics. For the dynamic pitch runs, the hull pitch angle varied sinusoidally with a frequency of 0.8 hertz. A position potentiometer translated bow vertical displacement into hull pitch angle, and this was read into the computer in the same manner as blade loading components. During dynamic pitching, the shaft rotated independent of the pitch oscillator. During a single propeller revolution, 90 pitch positions were measured. Thus, to correlate pitch angle position and revolution, an average pitch must be taken over each revolution. Fourteen dynamic pitch angle positions were selected for analysis. These were characterized by pitch angle ) and the sign of the time rate of change of pitch angle j. The computer calculated the average ~ and sign of corresponding to each propeller revolution. Based on these calcu- lated average values of w and sign of }, each propeller revolution was either placed in a suitable hull-pitch angle category or discarded if its average ) fell outside the tolerance band of all the 14 specified values 18 of ~. Several passes down the towing tank were required in order to obtain a sufficient number of samples. After all the data had been sorted based on ~, sign of }, and tolerance, the cycles for each combination of jp, and sign of ~ were analyzed in exactly the same manner as the data for the steady-ahead condition at fixed jp. For unsteady-acceleration runs, the model speed V varied with time t. During an acceleration run, data, including a measure of V, were sam- pled and stored in the same manner as for the steady-ahead runs. Five values of V were specified for analysis. For each acceleration run and for each specified V, the computer selected the propeller revolu- tion which had the average value of measured V nearest to the specified V. However, because only one revolution at each specified velocity was ob- tained for a single acceleration run, each such run was repeated five times. This yielded five revolutions at each specified velocity. All the cycles for each specified V were then analyzed in exactly the same manner as the data for the steady-ahead conditions. Thus, the on-line analysis system yielded average wave forms and harmonic analyses of the average wave forms for steady-ahead conditions, for specified conditions of ~, sign of W during the dynamic pitch cycle, and for specified velocities V during the acceleration operation. However, these on-line results are preliminary because: 1. They do not consider the interactions between the various load components. These interactions were determined during the static cali- bration of the flexures. 2. They include the complete measured signals with no filtering. As discussed in the section on experimental results, some extraneous sig- nals near the natural frequency of the flexure being used appeared to be superimposed on the signals generated by blade loading. 3. They include the effect of centrifugal and gravitational load- ing on the aluminum model propeller. The centrifugal and gravitational components of loading were measured separately during air-spin experiments, as discussed earlier. 4. They do not have any corrections for the influence of the dyna- mometer boat. These corrections are discussed later. 19 5. The bending moments were calculated about the radial location of the strain gages on the flexures, rather than about the shaft axis or some desired radius on the blade. Final analyses were conducted after completion of the experiment to consider interactions, to filter out extraneous high frequency noise, to isolate hydrodynamic loading from centrifugal and gravitational loading, to correct for the dynamometer boat, and to resolve bending moments as desired. These analyses were conducted using a Control Data Corporation (CDC) 6700 Computer. For each condition, the average wave form for each of the six load- ing components was multiplied by the inverse of the calibration matrix given in Table 2. FAA ar Oo Bt Bon Mg FYI E IF Mn Mey oo FA z1 MA a This matrix multiplication was performed at 4-degree increments of blade angular position. An harmonic analysis was then performed on the signals corrected for the interactions. Based on an harmonic analysis of the wake in the pro- peller wile, it was judged that there should be no significant loading of hydrodynamic origin at frequencies above ten times shaft frequency. Therefore, the wave form was then reconstructed by using the first ten harmonics of shaft frequency. This reconstruction using only the first ten harmonics had the same effect as filtering out all frequencies above ten times shaft frequency. Cecmtincss D.E., "Numerical Prediction of Propeller Characteristics," Journal of Ship Research, Vol. 17, No. 1, pp 12+18 (March 1973) 20 Corrections were made to the mean values of the measured loading components to account for centrifugal loads and the influence of the dy- namometer boat, and to the first harmonic of the measured loading compo- nents to account for gravitational loads. The derivation of these correc- tions is discussed later. From the known values of the three measured force components and three measured moment components, the values of the bending moments about the shaft centerline and bending moments normal to the nose-tail line at the 0.3 and 0.4 radii were calculated. These bending moments were calcu- lated at every 4 degrees of blade angular position, and harmonically ana- lyzed. The wave form was reconstructed by using the first 10 harmonics of blade angular position, in exactly the same manner as was used for the other components of blade loading. Plots of the data were generated by the CDC computer system using a -Calcomp Plotter. ACCURACY During the experiments for steady operation, V=0, and dynamic pitching, W#0, where many revolutions of data were averaged during a sin- gle run, the standard deviations of speed V, rotational speed n, forces, and moments were computed, assuming the distribution in these variables at a given condition follows the normal probability distribution. For forces and moments, the standard deviation was calculated at every increment of blade angular position at which forces and moments were recorded. An error band around the data mean was then represented using the standard deviation multiplied by a factor dependent on the confidence level chosen. For the present analysis, the factor of 1.96 was selected which corre- sponds to a confidendence level of 95 percent. A confidence level of 95 percent indicates a confidence (or probability) that 95 percent of the data considered falls within the error band. For a given run the average error (95 percent confidence band) in model speed V was approximately +0.005 foot per second (1.6 mm/s), while the error in rotational speed n was less than 0.001 revolution per second. The very low error in n re- sulted from the use of a precision solid-state motor controller as dis- cussed in the section on facility and dynamometry. Za For a given steady run (vV=0, #0) the error (95 percent confidence band) in measured forces and moments, fluctuated from +5 to +10 percent of the mean signal, depending on the circumferential blade position. Figure 8 demonstrates the variation in error in one revolution of the uncorrected, raw Bas signal at the full power condition. This figure represents the general trend of all the force and moment components measured. Besides the fluctuation in signals occurring in a given run, the overall accuracy of the data is dependent on the repeatability from one run to the next. An effort was made to set experimental conditions iden- tically on repeat runs; however, the propeller rotational speed and model velocity were set by hand, so some variation was unavoidable. Table 5 demonstrates the variation in the measured experimental conditions and the raw data for the Ee component for 11 repeat runs. The variation in the mean force was +4 percent over all the runs, but on a given day the vari- ation averaged +2 percent. The same trend can be observed in rotational speed, model velocity and the harmonic force components. This day-to-day variation could be due to different operators setting the experimental conditions, slight variations in the draft of the model, and variations in the gain of the sensing electronics. The variations shown for a are typical of all the measured force and moment components. For all experimental conditions the rotational speed of the port and starboard propellers were intended to be equal. However, some exploratory runs were conducted to determine whether the mean or unsteady loads, which were measured on the starboard propeller, were influenced by the rotational speed of the port propeller. At a fixed value of rotational speed on the starboard propeller ne» the rotational speed on the port propeller n_ was varied. The results showed that there was no measurable effect of n_ on the mean or unsteady loads in the region 0.95 ne £8, < 1.05 no: For all runs for which data are presented, 0.99 n. 5 < 1.01 ns; therefore, the results presented are not measurably influenced by inaccuracies in aye For the unsteady acceleration (V>0), the average of the five values of V and n for which data are presented during the unsteady runs was generally within +0.2 foot per second (6.5 cm/s) and +0.2 revolution per second of the target values respectively. 22 For runs with fixed hull pitch angle w, (W=0), the value of p could be controlled to within +0.005 degree. For dynamic pitch runs +0, the selection of a propeller revolution at a specified ~ necessitated a toler- ance of 0.1 degree to ~; however, the average value of ~ for which data are presented during the unsteady runs was generally within 0.02 degree of the target }. Considering all sources of error including deviations during a run and inaccuracies in setting conditions, the model scale forces and moments presented in this report are generally considered to be accurate to within (plus or minus) the following variations: g Fax M MMAX 1b = «© (N) 1b (N) jin-1b (N-m)}jin-1lb (N-m) Steady ahead V=0,U=0 | 0.1 (0.4) | 0.2 (0.9)| 0.2 (0.02)| 0.4 (0.06) Dynamic pitch V=0,040| 0.2 (0.9) | 0.3 (1.3)| 0.4 (0.04)| 0.6 (0.07) Acceleration V>0,=0 ONSH Gl3))E ON aaa Glee) Om One (ORO) a Ole (0.09) The values are somewhat more accurate for the steady-ahead runs than for the time-dependent runs, because the experimental conditions could be controlled more precisely for the steady runs and the measured forces and moments were averaged over many more revolutions of the propeller. The time-average values per revolution (based on 90 samples per revelolution) are slightly more accurate than the maximum values (based on one sample per revolution) which took into account the variation with blade angular position. Further, the peak values may have been slightly influenced by the dynamic response of the flexures, as discussed in the section on cali- bration. EXPERIMENTAL RESULTS LOADING COMPONENTS The basic loading components are shown in Figure 1. For a right- hand propeller the sign convention follows the conventional right-hand rule with a right-hand Cartesian coordinate system. For a left-hand pro- peller all the loads are the same, but for this case the sign convention follows a left-hand rule with a left-hand Cartesian coordinate system. 3} The sign conventions for both right-hand and left-hand propellers are shown in Figure 1. In all pertinent figures and tables throughout this report the blade loading components are listed in the following order: 1. Components measured by Flexure 1: a. Ee - axial force, or thrust per blade. b. Me - bending moment about the axis normal to the shaft axis at r=0. This moment is generated primarily by the B component of force. 2. Components measured by Flexure 2: a. By - tangential force, or force normal to the propeller axis and the spindle axis. b. M — moment about the propeller axis, (r=0), or torque per blade. This moment is generated primarily by the By component of force. 3. Components measured by Flexure 3: a. Ee - radial force, or force parallel to the blade spindle axis. b. M, - moment about the spindle axis, or spindle torque. 4. Supplemental components which were derived from the components listed above (not derived for all conditions). ae My 3 = Fe Gn -0.3R) cos 0.3 + By (x — bending moment applied on the spindle axis about the axis inter- Fy -0.3R) sin $5.3 secting the spindle axis at r=0.3R and parallel to the expanded pitch line at r=0.3R. The My 3 vector as defined by the convention- al right-hand rule for a right-hand propeller (left-hand rule for left-hand propeller) intersects the plane normal to the propeller axis at the angle bo ane tan (P, 3/0-3 mD) and is directed so that a positive M 3 puts the face (pressure side) of the blade in 0 tension. be Ei SOSA EED -0.4R) cos do.4 4p a ee -0.4R) sin 5.4 — bending moment applied on the spindle axis about the axis inter- ONE secting the spindle axis at r=0.4R and parallel to the expanded pitch line at r=0.4R. The M vector as defined by the conven- 0.4 tional right-hand rule for a right-hand propeller (left-hand rule 24 for the left-hand propeller) intersects the plane normal to the pro- peller axis at the angle $6 Tia tan (Py ,/ (0.47D)) and is directed so that a positive M puts the face (pressure side) of the blade 0.4 in tension. In calculating M from the experimental values of the 0.4 three measured forces and three measured moments, an adjustment was necessary to allow for the contribution of loading in the region 0.4R>r>r, =0.3R where Th is the hub radius. It was estimated that for all harmonics including the time average values, 3 percent of M, and ah was contributed by the loading in the region 0.4R>r>r, These estimates were based on a refinement of the method of Cummings for the time-average values, and the method of Tsakonas et pile for the unsteady values. Hydrodynamic, centrifugal, and gravitational loads may contribute to each of these components of loading; however, for some components the centrifugal loads and/or gravitational loads are zero, as discussed in the section on centrifugal and gravitational loads. Each component of loading is generally presented as a variation of the instantaneous value with blade angular position ® and as a Fourier series in blade angular position in the following form: F,M(6) = (F,M) + ae (F,M) cos (né - ) (OF Mn where F,M = circumferential average value of F,M (F,M)_ = amplitude of the nth harmonic of F,M 6 = angular position about the propeller axis, positive counter- clockwise from the vertical upward looking upstream for starboard propeller (left-hand rotation) positive clockwise looking upstream for port propeller (right-hand rotation) (OF wn = phase angle of nth harmonic of F,M where the reference line of the blade is the spindle axis; see Figure 2 and Table 1. The components SS and M, are the most important for determination of the time-average and unsteady stresses in the hub mechanism of an actual BS) controllable pitch propeller. The components Mo 3 and My 4 are the most important for determination of the time-average and unsteady stresses in the blades of a propeller. CENTRIFUGAL AND GRAVITATIONAL LOADS The results of the air-spin experiments, corrected for interactions, are presented in Table 6. The time-average values arise from centrifugal force whereas the first harmonic arises from gravitational force. There- fore, the mean values should vary as ma where n is the propeller rotation- al speed, and the first harmonic should be independent of n. For the mean values, which arise from centrifugal force, signficant nonzero values were obtained only for the Hae Fo ee and M, components. Any realistic propeller would have nonzero values of centrifugal loading — — 31 components Go, and (Me: Nonzero values of oe and Coe are pro- duced by the nonzero values of skew and rake of the propeller evaluated. The components CO and mm), should be zero for any geometry, however, a small value of (Ey was measured. This small nonzero (Pade probably arises from inaccuracies in the air-spin experiment and interaction matrix. For all components the experimentally determined mean value varies essentially as i The experimental air-spin results were faired so that the values of the mean loading components used for separating hydrodynamic loads from total loads varied exactly as mee For the first harmonic loads, which arise from acceleration due to gravity, nonzero values were obtained only for the #09 M and Ee flexures. For Mie and Geile the phase angles are +96 degrees and -96 degrees, respectively; therefore the maximum and minimum values of these components occur when the blade is approximately horizontal. This would be expected from the geometry. The phase angle for ile is -159 degrees; therefore Ny seesTal R.J., "A Method of Calculating the Spindle Torque of a Controllable-Pitch Propeller at Design Conditions," David Taylor Model Basin Report 1529 (August 1961). 26 _ maximum value occurs when the blade is nearly vertical downward (6 o'clock position). This is again as would be expected from geometry. The phase angles would not be expected to be precisely +90 degrees or 180 degrees since the propeller has 22 degrees of skew. The amplitudes of Dig and Cag each should be equal to the combined weight of the blade and that portion of the appropriate flexure at radii greater than ‘the radius of the appropriate strain gage. The values of Oia and ete wei confirmed by weighing the blade and appropriate flexures. The values of CO ag and Cae are essentially zero because the blade is skewed and raked so that mass of the blade is balanced about the spindle axis in both the plane containing the spindle axis and the propeller axis, and the plane normal to the propeller axis which contains the spindle axis (see Figure 2 and Table 1). The value of Cis is nearly zero since lies is always in a nearly horizontal direction. For all components the experimentally determined amplitude and phase of the first harmonic were essentially independent of rotational speed n. The experimental air-spin results were faired so that values of the amplitude and phase of the first harmonic of the loading components used for separating hydrodynamic loads from total loads were constant, independent of n. Approximate scaling parameters for centrifugal loads are (F/ppn°D") and (M/o,n°D>), whereas appropriate scaling parameters for gravitational loads are (F/opgD°) and (M/0p8D"). The model experiments presented in this report were conducted at full scale values of Froude number FA = (V/VveL) and advance coefficient J = (V/nD). Constant Froude number implies that V~(gL) ?~(gb)? V-~eD Constant advance coefficient implies that V~nD vee nee Therefore, ened ppeD’~ppn-D* 5 ‘PpsD ~Ppn D 27 Thus, for the results presented in this report gravitational loads and centrifugal loads scale the same. Furthermore, if proper allowance is made for the difference in density between the model propeller and the full scale propeller,* the gravitational and centrifugal loads scale the same as the hydrodynamic loads. Therefore, in addition to the components of loading arising from hydrodynamic effects alone, for many experimental conditions the compo- nents of loading arising from the sum of hydrodynamic, centrifugal, and gravitational effects are presented. The components of loading arising from the sum of the hydrodynamic, centrifugal and gravitational effects are designated components of total loading. The centrifugal and gravi- tational loads presented are equivalent values for a nickel-aluminum- bronze propeller blade. These combined, or total, loading results are discussed in later sections. The time-average centrifugal spindle torque results, M, are com- c pared in Figure 9 with calculated values using the method of RELL Previous measurements of spindle torque by Boswell et anki and by Hawdon et ai have correlated well with values calculated by this procedure. The calculated value of M, is 33 percent lower than the experimental c value at design pitch (see Figure 9); however, this is within experimental accuracy. The largest measured value of M, is 0.5 inch-pounds (0.07 N-m) e as shown in Table 6 whereas the accuracy of this measurement is plus or minus 0.2 inch-pounds (0.02 N-m) as discussed in the section on accuracy. The large experimental inaccuracy as a percent of the measured M, value c results from a combination of (1) the small value of the measured M, ; c and (2) the inferior characteristics of flexure number 3, which measures *The model propeller used in these experiments was made of aluminum, den- sity pp=5.44 lbf-s2/£t4 (2.80 g/cm3). The full scale propeller on the DD-963 is made of nickel-aluminum-bronze, density Pp=14.48 lb£-s2/f£t4 (7.46 g/cm3). re crieilil, R.J. et al, "Experimental Spindle Torque and Open-Water Per- formance of Two Skewed Controllable-Pitch Propellers," David Taylor Naval Ship Research and Development Center Report 4753 (December 1975). 28 EN and M,> relative to the other two flexures as discussed in the section on calibration. INFLUENCE OF DYNAMOMETER BOAT The results of the wake surveys with and without the downstream body (dynamomemter boat) are presented in Figure 10, and in Appendix A. These data indicate that the downstream body had only a small effect on the circumferential and radial variation in the flow and only a small effect on the harmonic content of the flow. However, they also indicate that the downstream body reduced the volume mean velocity through the propeller disk by approximately 12 percent; i.e., without the downstream body the volume mean wake (1-w)=1.06 and with the downstream body (1- m7 0-93- W. These results are, of course, without the propeller in place. i The change in effective velocity through the propeller due to the downstream body was deducted from thrust and torque identities between the mean thrust and torque measured during the blade loading experiments at the self propulsion point (Condition 1 in Table 3), and mean thrust and torque measured during a previous self propulsion model experiment.* These results, which include the effect of the propeller, indicate that the downstream body reduced the effective velocity through the propeller disk by approximately 5 percent; i.e., without the body, (1-w,)J=1.02 and Caton men sou: whereas, with the body, (1-w,,)=0.97 and Cheat Ooe2 The difference between the effect of the downstream body on volume mean wake and effective wake is probably due to a combination of the following: 1. The effect of the propeller action; (1-w,) and Cy) include the effect of the propeller but (1-wyy) does not. 2. Experimental inaccuracies; both methods for calculating the change in velocity are based on a small difference of two much larger nearly equal experimental results. *DINSRDC experiments 21 and 22 on Model 5265-1B, in which the mean thrust and torque was measured using transmission dynamometers mounted inside the model hull. 29 It is judged that the dominant cause of the discrepancy is the effect of the propeller. Based on these results it was concluded that the downstream body reduced the mean velocity into the propeller by 5 percent at the self- propulsion condition. This is somewhat smaller than the 10 to 14 percent reduction in effective wake that was obtained in Reference 2 in which the same dynamometer boat was used behind a single screw model hull. It was assumed that the 5 percent reduction in the present experiment occurred at all conditions at which experiments were conducted. Therefore, after the effects of centrifugal force were subtracted from the measured loading components as discussed previously, the time-average value per revolution of each hydrodynamic loading component was corrected for the effect of the downstream body as follows: From the measured hydrodynamic blade thrust CE ) and hydrodynamic blade torque (M ), effective advance coefficients H based on thrust identity (Jp) and torque identity (J) were deduced from the open-water data (Figure 11). These values were multiplied by (1/0.95) to obtain corrected values of Jn and Jos i.e., without the downsteam body. The corrected values of La and M were then obtained from the open-water H data at the corrected advance coefficients Jr and Jae respectively. It was assumed that the downstream body did not affect the radial center of thrust F_ and tangential force F_. Therefore, Vy M corrected = (F_ corrected/F measured) (M_ measured) Vy aH Vy 2 -F corrected corrected/M measured) (F_ measured) Vy *y aH vy The spindle torque (M, ) was corrected by the same procedure as used for F_ and Gos using unpublished hydrodynamic spindle torque data for the DD-963 propeller. No corrections were made to Ee for the effect of H the downstream body; however, BD is very small for all experimental con- H ditions, as discussed later. No correction for the effect of the downstream dynamometer boat was made to the measured circumferential variation of the loading components. 30 Calculations made by the methods of Tsakonas et aie? and MeCArEnyaG indi- cated that the influence of the downstream body alters the peak-to-peak circumferential variation of the loads by no more than 2 percent. How- ever, these methods did not agree well with the experimental results, as discussed in the section on correlation with full-scale data and theory. STEADY-AHEAD OPERATION For operation near the self-propulsion point (Condition 1 in Table 3), Figure 12 presents the variation of the various components of total blade loading with blade angular position and Figure 13 presents the amplitude of the first 25 harmonics of the various components of total blade loading. Based on the dynamic. calibration, as discussed in the section on calibration, it was judged that for all loading components the data are valid for the first 10 harmonics. In addition, the wake data shows no significant amplitudes for harmonics greater than the tenth; see Appendix A. Therefore, all data and analysis except Figures 12 and 13 are based on reconstructed signals using the first 10 harmonics. The symbols shown in Figure 12 indicate unfiltered values determined from the experiment; each represents the average value at the indicated blade angular position for over 200 propeller revolutions. The variation in measured values at a given angular position is discussed in the section on accuracy; see Figure 8. The lines on Figure 12 are the signals reconstructed from the first 10 harmonics. Figure 12 indicates that the variation of the signals with blade angular position are adequately represented by the number of harmonics retained. Figure 13 shows that there are no significant resonances for any of the loading components below the 23rd harmonic, which corresponds to (23)x(14.08)=324 hertz. This is higher than the lowest frequency reson- ance obtained in the results presented in Reference 2; i.e., 247 hertz. As discussed in the section on calibration, the higher frequency of the fundamental significant resonance obtained in the present experiment was anticipated because smaller and lighter blades were used in this experi- ment than were used in Reference 2. Bilt The variation of all measured loading components with blade angular position for the self propulsion condition (Condition 1 in Table 3) is shown in Figures 14 and 15 for the hydrodynamic loads, and is shown in Figure 16 for the total (hydrodynamic, centrifugal and gravitational) loads. The amplitudes and phases of the harmonics of these loading compo- nents are presented in Figure 17 for the hydrodynamic loads and in Figure 18 for the total loads. Appendix B presents tabulated values of all the data in Figures 14 through 18, and Table 7 presents a summary showing the maximum value, minimum value and first harmonic of each loading component. The values for each loading component are presented as decimal fractions of the time-average value of the corresponding loading component. These time-average values for both hydrodynamic loads and total loads are pre- sented in Table 8. These data show that for hydrodynamic loading the variation of all loading components was predominantly a once-per-revolution variation. The extreme values for all loading components, except F, and My» occurred near the angular position of the spingle, axis, 0=124 ek degrees; i.e., 34 degrees beyond the horizontal. At these positions the blade tip is approximately 12 degrees beyond the horizontal. This suggests that the tangential component of the wake is the primary driving force; see Figure 10. The extreme values of Fy and M, occur at up to 120 degrees after the extreme values of the other components. The reason for this variation in location of extreme values is not clear; however, it may be partially due to experimental inaccuracy with the FO-M, flexure as discussed in the section on calibration. For total loading, the variation of all components with blade angular position follows basically the same pattern as for hydrodynamic loading. This occurs because the unsteady loading due to gravity, which is a pure first harmonic of blade angular position, is much smaller than that due to hydrodynamic force. Further for all components with a mea- surable gravitational load, except Fo» the maximum value occurs near the angular position at which the spindle axis is horizontal; i.e., the gravitational load is nearly in phase or 180 degrees out of phase with the hydrodynamic load. B2 For hydrodynamic loading, F, and M_ were the largest measured force H H and moment components; see Table 8. For these components the maximum values were approximately 1.43 times the time-average values, and the maximum value minus the minimum value (double amplitude) was approximately 0.91 times the time-average values; see Table 7. For F_ and|M |, the YH “A maximum values and range of values with blade angular position were slightly smaller fractions of the respective time-average values. For nae? the maximum value and range of values with blade angular position were much greater fractions of its time-average. This large fractional variation in F occurs because|F M Hee maximum Zz Zz Zz H H H value and range of values were 1.30 and 0.6/7, respectively, times the time- was very small. For average value. The radial point of application of FY varies from 0.68R H to 0.73R, and the radial point of application of Bo varies from 0.6/R to H O.79R. The maximum values of es and a were approximately 1.41 times the time-average values, and the range of values were approximately 0.88 times the time-average values for combined hydrodynamic, centrifugal and gravi- tational loading components, or total loading components. These results are nearly the same as the hydrodynamic results since the centrifugal and gravitational loads are small for these components; see Tables 6 and 8. The centrifugal and gravitational loads are a significant portion of the total loads for other loading components; for total loads F /EL=1.14 MAX whereas for hydrodynamic loads F /F_=1.40. This large difference YuMAx YH results from the combination of centrifugal force adding to the time- average hydrodynamic force and gravitational force substracting from the circumferential variation of hydrodynamic force. Similarly, for total loads M /M,. =1.26 whereas for hydrodynamic loads M, /M X H,MAX “H centrifugal loading Ey is two orders of magnitude larger than the time- average hydrodynamic loading, and for M R634, ava 7 the centrifugal loading is almost as large as the time-average hydrodynamic loading; see Table 8. The results presented here follow trends similar to those in Refer- ence 2 for the FF-1088 which is a single screw transom stern configura- tion. The component Oe which is the largest moment component for both cases, yields He ae =1.40 for the present configuration (DD-963 Class) MAX and M /M =1.38 for Reference 2 (FF-1088). The maximum and minimum YMAX yi) values occur at approximately the same angular position of the blade mid- chord at the 70 percent radius for the two configurations. HULL PITCH Figure 19 presents the variation of the peak values and time-average values per revolution of the various components of blade total (hydro- dynamic, centrifugal and gravitation) loading* with hull pitch angle yp for both quasi-steady simulation (time rate of change of hull pitch angle b=0) and unsteady simulation (W#0). These data show that for the quasi- steady simulation the time-average value per revolution of each loading component remains within 6 percent of its value corresponding to self- propulsion in calm water. The time-average value per revolution for the unsteady simulation, deviates by up to 12 percent from its value corre- sponding to self propulsion in calm water. Data at each specified value of hull pitch angle w for the quasi- steady runs were recorded and averaged for a minimum of 200 propeller revolutions whereas data for the dynamic pitching runs at each specified W represented an average of from 10 to 35 propeller revolutions. As dis- cussed earlier, the selection of a propeller revolution at a specified yp during the dynamic pitch runs necessitated a tolerance of only 0.05 degree to ~. Therefore, the differences between the results for the quasi-steady and unsteady simulations, including the time-average values per revolution, were Significantly larger than any errors which may have arisen from inac-— curacies in setting the experimental conditions. For quasi-steady simulation, the absolute value of the time-average value per revolution of all loading components, except spindle torque M,> + No results are ahown for F_ since the F_ loading arises primarily from centrifugal effects, as discussed previousl¥, which are independent of hull pitch. 34 were larger for the stern-up condition than for the stern-down condition; the largest value occurs at (UP yp =1-85 degrees or time=0.31 seconds in the reference of Figure 19. This suggests that the effective speed of advance of the propeller increases slightly for the stern-down condition and decreases slightly for the stern-up condition. This appears reason- able since for stern-up the propeller tends to be further into the bound- ary layer of the hull. However, the time-average value per revolution did not monotonically increase with increasing ~ for all components. For dynamic simulation the largest absolute value of the time- average value per revolution of all loading components, except spindle torque My» occurs at approximately 0.15 second after the condition WV oy) =0> W>0, which is the reference for time t=0 in Figure 19. This indicates that the maximum time-average value during dynamic simulation occurs at a value of hull pitch angle ~ which occurs 0.16 second or 0.1 cycle, before the » at which the maximum time-average value occurs during quasi-steady simulation. There was a significant difference between the peak values for the quasi-steady simulation and the unsteady simulation. For the quasi-steady simulation, the variation of the peak values with hull pitch angle yp followed approximately the same trends as the variation of time-average values per revolution. These quasi-steady results indicated that for V-Voy up to 1.85 degrees, the maximum increase in the peak value of any loading component above the corresponding value for vv oy was 5 percent. For the dynamic simulation, however, the maximum value of the peak loads increased as much as 23 percent above the corresponding value for steady ahead at a fixed hull pitch YVoye The dynamic simulation exhibited a dramatically different trend of peak load with ~ than was indicated by the quasi-steady simulation. For the dynamic simulation, the largest value of the peak loading, for all components except spindle torque My» occurred at approximately time t=0.8 second in the hull pitch cycle shown in Figure 19. This corresponds to w=1.5 degrees stern down during the portion of the cycle in which the stern is moving down; i.e., (-Voy=-1-5 degrees, t<0. For dynamic 35 simulation, the smallest value of peak loading occurred near VV ony as the hull passed from the stern-down to the stern-up portion of the cycle; i.e., (W-W ay )=0, ¥>0. This difference in the unsteady loading between the quasi-steady and unsteady simulations may be due to an additional relative velocity compo- nent arising from the motion of the hull during dynamic pitching. As the hull passes through p=) the vertical velocity of the hull (and propel- > ler) is a maximum. As a hull goes from stern up to stern down through YVoyp the upward velocity component relative to the propeller in the plane of the propeller tends to increase above the values at fixed hull pitch at v=Voye This tends to increase the amplitude of the first harmo- nic of the tangential velocity, and thereby increase the unsteady loading (and increase the peak loading). The maximum vertical velocity of the propeller for sinusoidal pitching with Cbuax Yew 7d: 85 degrees and fre- quency=0.8 hertz is approximately 1.47 feet per second (0.448 m/s). This is equivalent to an additional tangential velocity ratio OND) Ose, (05 a13}3}., For ~ fixed at v=Voy ((V,),/V)=0.130 (see Appendix A). Therefore, (VM ax, i40 = 0.130 + 0.133 = 2.02% ((V),/V) §-0,0-Voy 0.130 This maximum occurs at a model simulated time of approximately 0.2 second before the maximum measured loads. The measured increase in unsteady loads arising from dynamic pitching was somewhat smaller than this calculated increase in tangential velocity, for example: F = 10 . x ba MAX , 70 ca = LGD & i. /Mil : ay 0.4 *A numerical error was found in a similar calculation presented in Ref- erence 2, With the numerical error corrected the results in Reference 2 are substantially the same as those presented here. 36 On the basis of two-dimensional quasi-steady theory, the increase unsteady loading should be approximately proportional to the increase in tangential velocity.* The unsteady loading is important from consideration of fatigue of the propeller blades and hub mechanism. Since a ship may operate for an extended period in a seaway, the effect of the ship motions, such as dynamic hull pitching, on unsteady blade loads is significant. The differ- ence between the peak load and the time-average load per revolution is a measure of the unsteady loading. With this difference as a measure of the unsteady loading, the quasi-steady simulation indicates that for hull pitch angles b-Voy up to 1.85 degrees, the unsteady loading for Mo which is the largest moment component, increased by 8 percent above its corres- ponding value for v=Voye By contrast, the dynamic simulation showed the unsteady loading for the Mt component increased by 50 percent above its corresponding value for Vow without hull pitching. This indicates that the quasi-steady simulation is completely inadequate for estimating the effect of the seaway on unsteady loading. This also shows that the effect of the ship motions can dramatically increase the unsteady loading on the blades. Therefore, the effect of the ship motions due to operation in a seaway should be considered in any analysis of blade loading and in any fatigue analysis of the propeller blades or hub mechanism. The results presented here for hull pitching generally agree with the same type of results presented in Reference 2 for a model of the FF- 1088, which is a single screw transom stern configuration. For ae which is the largest measured moment component in both cases, the comparative results, presented as a fraction of the time-average value without hull pitching, are as follows: “Chis simple analysis provides an upper bound to the dynamic pitching load, since the hull boundary above the propeller would tend to reduce the dynamic pitching induced upward tangential velocity relative to the propeller. 37 DD-963 FF-1088 (Present (Reference Report) 2) Peak value, W#0 1.60 Lo S7 Peak value, =0 aS 1.40 Peak value without pitching v=0, v=Vow 1.40 1.36 Maximum time-average value, wW#0 EO) 1.03 Maximum time-average value, W=0 1.05 1.04 The variation of the loading components with simulated time during the pitch cycle are also somewhat similar for these two configurations. The comparative results for Ho presented as time in seconds following the point YY oy=O> W>0 are as follows: DD-963 FF-1088 (Present (Reference Report) 2) Peak value, W#0 0.77 0.62 Peak value, W=0 0.31 0.31 Maximum time-average values, #0 0.20 0.72 Maximum time-average value, W=0 0.31 0.31 ACCELERATION The variation of all measured loading components with blade angular position for the quasi-steady simulated acceleration condition Vv=P=n=0 (Conditions 7 through 11 in Table 3) is shown in Figures 20 and 21 for the hydrodynamic loads, and is shown in Figure 22 for the total (hydrodynamic, centrifugal, and gravitational) loads. The amplitudes and phases of the harmonics of these loading components are presented in Figure 23 for the hydrodynamic loads and in Figure 24 for the total loads. Appendix B presents tabulated values of the data in Figures 20 through 24. The values for each loading component are presented as decimal fractions of the time-average value of the corresponding loading component at the self propulsion condition (Condition 1 in Table 3). These average values for both hydrodynamic loads and total loads are presented in Table 8. 38 Figure 25 presents the Taylor wake fraction based on thrust 1-w,, and ae the Taylor wake fraction based on torque rele as derived from the measured values of ie and M, and the open-water characteristics of the propeller H H (Figure 11). These data indicate that (1-w,,) varies by only approximately 3 percent during the simulated acceleration. The value of Cy varies by only 1 percent for simulated time t>40 seconds; however, the value of (1l-w,) varies substantially during the initial portion of the simulated Q acceleration (t<40 seconds). Figures 20 and 22 show that for all measured hydrodynamic and total loading components, except Fy which is small, the peak values, including H variation with blade angular position occurred at the self propulsion con- dition. That is, for the acceleration condition simulated (see Figure 7 and Table 3), the propeller is not exposed to higher peak loads than those to which it is exposed during full-power steady-ahead operation. In contrast to the peak loads, for most components the largest time- average loads per revolution occurred at the first experimental condition (V=2.65 knots, n=10.21 revolutions per second, J=0.64) during the simulated acceleration maneuver. The largest measured hydrodynamic force and moment components, F andM_, yield (F /E )=1.21 and (M /M = *y vy *y MAX “H,SP Yu,MAx YH,SP 1.29, whereas for total loading (F pe )=1.16 and (M / Mou) =) leepoulie SP YMax Sp The conditions (FL /F ) > (F /F +) and (M /M ys ele pisie H,MAX “H,SP age YH,MAX H,SP (M /M ) occur because the centrifugal and hydrodynamic components are Ymax sp additive for Fy and Mt (i.e., they have the same signs) and the hydro- dynamic loads increase with decreasing rotational speed n, whereas the centrifugal loads decrease with decreasing n. Higher time-average and peak loads than those shown in Figures 20 and 22 could, of course, be developed during acceleration maneuvers, depending on values of v, nh, and P. Figure 21 shows the variation in the radial center of longitudinal FOGCe is and radial center of tangential force, r . These results F iE Vy show that the time-average radial centers of these force components vary F 39 monotonically with advance coefficient over the range evaluated. As the advance coefficient based on thrust effective wake, Jp=Jy -wy) increases from 0.63 (at V=2.65 knots) to its design value of 1.14 (at V=6.52 knots), = decreases from 0.76R to 0.71R whereas i increases from 0.66R to mE Vy 0.74R. This variation in he is the reason that (@ /E y< oh H,MAX “H,SP OL /M ) as discussed in the preceeding paragraph. Yu,MAX H,SP For all loading components, the variation with blade angular posi- tion tended to be dominated by the first harmonic for all conditions throughout the simulated acceleration maneuver. For all conditions at which there was significant variation in loading with blade angular posi- tion, the maximum and minimum values for all components except ES and Mm occurred for the blade spindle axis near 9=135 or 315 degrees (blade tip near §=115 or 195 degrees). This suggests that the variation in loading with blade angular position is produced primarily by the circumferential variation of the tangential velocity in the propeller plane (see Figure 10). The angular variation of each loading component retained basically the same shape independent of speed and advance coefficient. There was a dramatic reduction in the circumferential variation of all measured loading components with decreasing speed V and decreasing rotational speed n. Previous data have shown that for a given propeller in a given flow field, the circumferential variation in the hydrodynamic loading varies approximately as the product of ship speed V and rotational speed n; see Wersidisma. = Figure 26 presents results in a form which allows evaluation of how closely the measured unsteady loading varies with nV. The ordinate is the first harmonic of the components of hydrodynamic blade loading except Fo ,» which is very small, and the abscissa is nV. H The data shown in Figure 26 indicate that the first harmonic of each of the presented hydrodynamic loading components is approximately proportion- al to nV. = isseeiidieme R., "Tendencies of Marine Propeller Shaft Excitation," International Shipbuilding Progress, Vol. 19, No. 218, pp 328-332 (Octo- ber 1972). 40 Figure 27 presents the variation of the time-average values per revolution and peak values of the various components of total blade loading for both quasi-steady simulated acceleration (V=n=P=0) and unsteady simulated acceleration (V>0, n=P=0). There was only a small variation in the measured loading components between the quasi-steady simulated acceleration and the unsteady simulated acceleration. For all components except M,» the largest variation between the results from the two types of simulation expressed as a decimal fraction of the corresponding time-average value at the self-propulsion point was 0.05 for the peak values and 0.02 for the time-average value per revolu- tion. The corresponding variations for M, were no greater than 0.06 for the peak values and 0.05 for the time-average value per revolution. The variation in the results between the two types of simulation appeared to be essentially random. This suggests that these deviations are some measure of the experimental accuracy and do not represent any systematic trends arising from the difference in V between the two types of simulation. Data for the quasi-steady simulation were recorded and averaged for a minimum of 200 propeller revolutions, whereas data presented for the unsteady runs represent an average of only five revolutions. Further, the steady experimental conditions which were set during the quasi-steady simulation allow the values of V and n to be controlled more precisely than during the unsteady runs; however, the average of the five values of V and n during the unsteady runs for which data are presented was general- ly within one percent of the target values. The results presented in this section for a simulated acceleration maneuver follow trends similar to those in Reference 2 for a simulated crash~forward maneuver on a model of the FF-1088. Both sets of data show the following: 1. The values of (1-w,) and (l-w.) do not vary substantially except Q during the initial stages of the acceleration or crash-forward maneuver. 2. The variation of all loading components with blade angular posi- tion was dominated by the first harmonic throughout the simulated maneuver. 41 3. The amplitude of the first harmonic of all loading components varied essentially as nV. 4. The acceleration of the hull did not have a significant effect on the loads; i.e., the loads for quasi-steady acceleration V=0 and un- steady acceleration v>0 were not significantly different. The ratics of either the peak or time-average loads during the accelera- tion (or crash-forward) maneuver to the time-average loads at the self- propulsion point do not agree closely for the results in the present report (DD-963 Class) and Reference 2 (FF-1088). This difference is to be expected since these ratios are very sensitive to the value of V, n, and P for the simulated maneuvers, which are quite different for these two cases. The largest moment component for both cases ae gives /M = 1.40 from the present report and 1.51 from Reference 2. The Ypeak Ygp results from the present report show M /M = 1.21 whereas the results y. My, a i MAx ‘sp from Reference 2 yield M /M SValsos Ymax Ysp CORRELATION WITH FULL-SCALE DATA AND THEORY For operation near the self-propulsion point (Condition 1 in Table 3), correlation was made between the model experimental loads obtained in the present investigation, bending moments deduced from strains measured on the corresponding full-scale propeller, and analytical calculations. These comparisons were made for My 3 and Moo 4 which were calculated from the three measured forces and three measured moments. As discussed in the section on experimental results, My .3 is defined as the bending Moment applied on the spindle axis about the axis intersecting the spindle axis at r=0.3R and parallel to the expanded pitch line at r=0.3R. The My 3 vector as defined by the conventional right-hand rule for a right- hand propeller (left-hand rule for a left-hand propeller) intersects the plane normal to the propeller axis at the angle 9 3 = tan "(Py 4/(0.3nD)) and is directed so that a positive M 3 puts the face (pressure side) of 0 the blade in tension. The component M is defined in a manner analogous 0.4 to My 3 except it, is referred to r=0.4R. 42 The full-scale data used for correlation are preliminary values of strains ¢« measured* at several chordwise stations at r=0.35R and r=0.45R on both sides of the blade on the DD-963 CP propeller. Both time-average strains per revolution and variation of strain with blade angular posi- tion were recorded during full-power stready-ahead operation. By inter- polation, values of radial strain at the spindle axis at r=0.4R were ob- tained. Assuming that the variation in radial strain is proportional to the variation in total (hydrodynamic, centrifugal, and gravitational) bending moment; i.e., that (e /[€ ) = /Mo 4)? these full- (M 10.4 ax r0.4 0. 4vrax scale data indicate that (M /M. ,) = 1.48. From the model data 0. 4uax 0.4 [Me -)— ll W43and) OM 0.4 say ( 0.3 M /M,. ,) = 1.56. A cursory evaluation 0. 3ax 0.4 of the variation of the full scale strain with blade angular position indi- cates that it follows trends similar to the bending moment determined from the model experiments. The correlation with full scale data presented here is preliminary; a more thorough correlation with the full scale data will be undertaken when analysis of the full scale data is complete. Theoretical calculations of hydrodynamic loads were made by using the method of Tsakonas et afi, 22 which is based on unsteady lifting- surface theory and the method of Mecarehy co a quasi-steady technique which utilizes the open-water characteristics of the propeller. Although the method of McCarthy is a simple quasi-steady technique, it was judged that this method should be suitable to the cases under consideration in this report because the dominant unsteady loading occurs at a low reduced frequency and the dominant first harmonic of the wake is in phase radially *The full-scale measurements were conducted by personnel in DTINSRDC Code 1962 under the direction of G.P. Antonides. The results presented here are preliminary, and thorough analysis of the data is continuing. The details of this full-scale trial will be reported in a future DINSRDC report. a ieaoncice S. et al, "Documentation of a Computer Program for the Pressure Distribution, Forces and Moments on Ship Propellers in Hull Wakes," (In Four Volumes), Stevens Institute of Technology, Davidson Laboratory Report SIT-DL-76-1863 (January 1976). Revised April 1977. 43 (see Figure 10 and Appendix A). These calculations were made for Condi- tion 1 in Table 3 using the wake measured in the plane of the propeller both with and without the downstream dynamometer boat in place (Figure 10 and Appendix A), and with the mean velocity through the propeller deter- mined from thrust identity used as the reference velocity. The use of the speed of advance based on thrust effective wake, V,=V(1-w,) as the reference speed in these calculations is consistent with the use of this velocity to correct the time-average loads for the effect of the dynamometer boat as discussed in the section on experimental results. Tsakonas et Bae recommend using the ship speed as the refer- ence velocity, which is equivalent to using (1-w,,)=1.05 however, this recommendation was not followed here because the flow does not pass through the propeller at the ship speed. To evaluate the sensitivity of the pro- 2 : 252) to the reference speed, calculations were cedure of Tsaknoas et al, performed for the first harmonic using the thrust effective wake (1-w,p) and the volume mean wake determined from the wake surveys (1-wy)) + These calculations showed the following: Wake without dynamometer boat M (using (1-w,,) = 1.02) OPS rene oie sal = 0.99 HO-3e (using (1-w,,,) = 1.06) O04 by *yo.3, Ou = -0.3 degrees Wake with dynamometer boat M (using (1-w,,) = 0.97) si ie = 1.02 HO. 34 (using (1-w,) = 0.93) SMOuse nT a *yo.3, uw? = 0.5 degrees Therefore, the calculated unsteady loads using the method of Tsakonas et 25,34 Allain are not sensitive to the reference speed over the range of con- cern in the present case. 44 22S calculations were conducted For the method of Tsakonas et al, for the first ten harmonics of the Tae The "normal'' components of wake harmonics, as required by this method, were defined as the wake harmonics normal to the chord line of the blade section at the local radius rather than normal to the advance angle at the local radius as recommended by oh) With the wake harmonics resolved normal to the blade Tsakonas et al. chord, this method apparently considers both the unsteady flow normal to the resultant inflow and an approximation to the unsteady flow parallel to the resultant inflow. The quasi-steady calculations are based on the circumferential vari- ation of the wakes measured at the 0.7 radial station. These calculations were made at 10-degree increments of blade angular position ®. It is assumed that the radial centers of the unsteady thrust and tangential force are at r/R=0.70 for all blade angular positions. Figure 28 presents values of HO. 3y and one with and without the downstream dynamometer boat, calculated with the methods of Tsakonas et aio and Me Carew, Based on these calculated results it appears that the dynamometer boat does not have a significant influence on the cir- cumferential variation of the blade loads. Figures 29 and 30 present the variation with blade angular position and the first ten harmonics of My 3 and My I from the model experiments 34 “4 and analytical calculations. All data are nondimensionalized on the same quantity, i.e., the time-average bending moment determined from the model experiments and corrected for the downstream body as discussed in the sec-— tion on experimental results. This comparison indicated that the experi- mental unsteady hydrodynamic bending moments were substantially higher than the calculated results. A typical comparison is as follows: *These calculations were made by using the computer program developed by the Davidson Laboratory including refinements made through April 1977. None of the refinements made since December 1975 influence the calculated unsteady loads presented in this report. Therefore, this calculation pro— cedure is the same as that used in Reference 2 for calculating the unsteady bending moments on the propeller on the FF-1088. Tsakonas, S. et al, "Correlation and Application of an Unsteady Flow Theory for Propeller Forces," Transactions of the Society of Naval Archi- tects and Marine Engineers, Vol. 75, pp 158-193 (1967). 45 Prediction Method M -M M —-M 0 34 MAX 0.3, 0.45 MAX 0 4 My 3 (experiment) My 4 (experiment) H H Model Experiment 0.36 0.36 Quasi-Steady Procedure26 0.25 0.24 Unsteady Pregecdeae = 0.20 0.19 For this typical comparison the experimental result is approximately 47 percent higher than the quasi-steady prediction and approximately 85 per- cent higher than the unsteady prediction. The circumferential variations in the model experimental results of other components of blade loading F_ , F_ ,M _,andM_ were larger than x y x ny; H H H H the values calculated by the two indicated procedures by approximately the same ratio as shown for My 3 and Mo 4 . These comparisons are not H H shown. Previous investigators have compared experimental unsteady forces and moments on a single blade of various propellers in inclined flow with forces and moments calculated by a quasi-steady procedure similar to that described by MEGAE Uy Mae These, experimental loads were obtained by direct measurement of unsteady forces and moments on a single blade (References 2, 3, 17, 18, and 19) or were deduced from measured steady transverse forces and moments along axes fixed relative to the flow, i.e., not rotat— ing with the propeller (Reference 36). References 2, 3, 17, 18, 19, and 36 all show that for noncavitating conditions, the experimental unsteady blade loading was from 1.5 to 2.0 times as large as the values calculated by the quasi-steady method. This agrees with the results of the present investigation; see Figures 29 and 30. eo enrachen F., "The Study of Ships' Propellers in Oblique Flow," Defence Research Information Centre Translation No. 4306, Copyright Con- troller: Her Majesties Stationary Office, London, England, October 1975; English Translation of "Untersuchung von Schiffsschrauben in schrager Anstromung,"’ Schiffbauforschung, Vol. 3, No. 3/4, pp 97-102 (1964). 46 Preliminary results from blade loading oaecimenne " conducted in idealized flows indicate that: 1. The unsteady blade loads in either axial or tangential wakes are not influenced by the presence of a nearby boundary above the propeller. 2. In inclined flow without an upstream hull, the experimental un- steady loading near the design advance coefficient is nearly two times as 25,34 large as that calculated by the method of Tsakonas et al, and approxi- mately 80 percent larger than that calculated by the method of MeCaceny oo 3. In an axial wake with a dominant first harmonic of blade angular position which was generated by upstream wire grid screens with zero shaft angle, the unsteady loading near the design advance coefficient is within approximately 15 percent of the values calculated by the methods of 25,34 2 Tsakonas et al, and McCarthy. ° This is in agreement with previous correlations with the method of Tsakonas et al for unsteady shaft (bearing) forces and moments for operation in axial calass Le These results indicate that the large discrepancy between the experi- mental and calculated unsteady bending moments presented in the current report appear to be due to the inability of the present theories to properly account for all important characteristics of the flow field for operation in inclined flow. All available procedures, including the un- 2252) and the quasi-steady procedure of steady theory of Tsakonas et al vieGaawy implicitly assumed that the propeller slipstream follows the propeller axis rather than the direction of the effective velocity into the propeller which is at an angle to the propeller axis in inclined f.iow. It is speculated that this failure to consider the true direction of the slipstream is the major factor in the analytical underprediction of the *The results in Reference 12 were at substantially higher reduced fre- quency than the results in the present study; therefore, the quasi-steady procedure of McCarthy over-predicted the unsteady loads in Reference 12. Boswell, R.J. and S.D. Jessup, "Experimental Determination of Period- ic Propeller Blade Loads in a Towing Tank,'' Presented to the 18th American Towing Tank Conference, U.S. Naval Academy, Annapolis, Maryland (August LOTT) o 47 unsteady blade loads in inclined flow. Numerical computations to check this hypothesis are planned. SUMMARY AND CONCLUSIONS Experiments were described in which the mean and unsteady loads, including hydrodynamic, centrifugal, and gravitational loads, were mea- sured on a single blade of a model of a CP propeller on the DD-963 Class Destroyer. The experiments were conducted behind a model of the DD-963 hull under steady-ahead operation, hull pitching motions, and simulated acceleration maneuvers. The discussion of experimental techniques in- cludes a description of the dynamometer and data analysis system. The results are summarized as follows: 1. For all significant loading components, except for radial force, the loads are predominantly of hydrodynamic origin. 2. The circumferential variations of all measured components of hydrodynamic and total blade loading are primarily a first harmonic, with maximum and minimum values occurring near the blade angular position which is 25 degrees past the position at which a radial line from the propeller axis to the tip is horizontal. 3. For steady-ahead operation: a. The maximum values and peak-to-peak circumferential varia- tions for measured hydrodynamic forces and bending moments were up to approximately 1.43 and 0.91 of the time-average values, respectively. b. The maximum values and the peak-to-peak circumferential variations for measured total forces and bending moments were up to approximately 1.41 and 0.88 of the time-average values, respectively. c. The model results for circumferential variation of bending moments about the nose-tail lines of the 0.3 and 0.4 radii agreed fairly well with loads deduced from strain measurements on the full- scale propeller, but they were larger than theoretically calculated values. 48 4. For simulated hull pitching (maximum pitch angle of 1.85 degrees): a. The maximum values of measured total forces and bending moments increased over the corresponding values without hull pitch by 5 percent for quasi-steady simulation and by 23 percent for un- steady simulation with model pitching frequency equal to 0.8 hertz (full scale equivalent frequency is 0.16 hertz). b. The peak-to-peak circumferential variation of the measured total forces and bending moments increased over the corresponding values without hull pitch by approximately 5 percent for quasi- steady simulation and by approximately 50 percent for unsteady simulation with model pitching frequency equal to 0.8 hertz. MThere- fore, any quasi-steady simulation of ship motions is completely in- adequate for estimating the effect of ship motions on unsteady pro- peller blade loading. 5. For the simulated acceleration maneuver: a. The dominant first harmonic of the measured hydrodynamic forces and bending moments varied in a nearly linear manner with the product of ship speed and propeller rotational speed. b. The acceleration of the hull did not have a significant ef- fect on the measured loads. Therefore, propeller blade loading during an acceleration maneuver can be adequately estimated by quasi-steady experiments. c. The maximum time-average values of measured forces and bend- ing moments per revolution were in the range of 1.21 to 1.29 of the time-average values during full-power steady-ahead operation for hydrodynamic loads, and in the range 1.16 to 1.21 of the time-average values during full-power steady-ahead operation for total loads. d. The simulated acceleration condition did not expose the pro- peller to higher peak loads than those to which it is exposed during full power steady-ahead operation. However, these loads are very sensitive to the maneuver simulated and substantially higher peak loads could be developed during other acceleration maneuvers. 49 e. Except for the initial portion of the simulated accelera- tion maneuver, the Taylor wake fractions were within three percent of their values at the self propulsion point. All of the results presented here on a model of the DD-963 Class Destroyer follow close to previously reported results of similar experi- ments on a model of the FF-1088. ACKNOWLEDGEMENTS The authors are indebted to many members of the staff of the David W. Taylor Naval Ship Research and Development Center. Special apprecia- tion is extended to Mr. George Gilbert for the design modifications of the experimental apparatus, to Mr. Michael Jeffers for development of the on- line data analysis system, to Mr. John Gordon for development of electro- nic and mechanical systems for the experiment, and to Mr. Jack Diskin for assistance in data analysis and analytical calculations. 50 APPENDIX A DETAILS OF WAKES* Tables 9 and 10 present the velocity component ratios and the harmonic content of the wakes in the plane of the propeller, both with and without the downstream dynamometer boat. The data at even radial sta- tions were obtained by interpolation and extrapolation of the measured data as described in-Reference 38. *Al11 data presented in Appendix A were obtained from wake surveys con- ducted by R.F. Roddy, DINSRDC Code 1524. Further details of these wake surveys will be presented in a future DINSRDC report. 2S oiyeae H.M., "Analysis of Wake Survey of Ship Models - Computer Program AML Problem No. 840-219F,"' David Taylor Model Basin Report 1804, March 1964. 51 bi ky i by i APPENDIX B DETAILED EXPERIMENTAL RESULTS Table 11 presents detailed experimental results, including variation with blade angular position and harmonic analyses, for steady-ahead opera- tion at V=6.52 knots, n=14.08 rev/sec. The data in Table 11 are tabulated values of the data presented in Figures 12, 13, 14, 16, 17, and 18. Tables 12 to 15 present detailed experimental results including variation with blade angular position and harmonic analyses, for the quasi- steady acceleration conditions. 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N : Wis = (Wal) » (Ven sin (n Oy + (dye)n) § wiTHOUT DYNAMOMETER BOAT (A WITH DYNAMOMETER BOAT Ff r/R = 0.80 re 10b (Continued) 68 (VA a/V (Oyen Figure 10 (Continued) MB without DYNAMOMETER BOAT Z WITH DYNAMOMETER BOAT r/R = 0.80 — N * Vp = (Vp) + D> (pln sin (1m Oy, + (yr )n) n=1 A G, (Z vA "Ma D z 2 3 4 5 6 7 8 HARMONIC NUMBER, n HB witHoUT DYNAMOMETER BOAT [A WITH DYNAMOMETER BOAT r/R = 0.80 Figure 10b (Continued) 69 PROPELLERS 4660 AND 4661 3.0 TO 12.0 FPS 13.0 RPS 5 NOVEMBER 1974 @® LEFT HAND TEST Vp: Q 2 < < - < 2 oc oO S © © vt a. O x a PROP 4661 (°4) AON31IDNI433 GNV (O0L) LN3I9I43309 JNOYOL 1 as IN31ID1443509 LSNYHL ADVANCE COEFFICIENT J Figure 11 - Open-—Water Characteristics of DTNSRDC Model Propellers 4660 and 4661 70 Figure 12 - Influence of Extraneous Signals on Measured Loads V= 6.52 KNOTS n = 14.08 REV/SEC 4 MEASURED VALUE —— CONSTRUCTED FROM HARMONICS, n= 1 TO 10 0 45 90 135 180 225 270 315 360 POSITION ANGLE, 0 (DEGREES) Figure 12a - i 71 Figure 12 (Continued) 6.52 KNOTS 14.08 REV/SEC 0 45 90 135 180 225 270 315 360 POSITION ANGLE @ (DEGREES) Figure 12b - a 72 Figure 12 (Continued) 1.20 V= 6.52 KNOTS n = 14.08 REV/SEC 1.15 1.05 1.00 0.95 0.90 4 MEASURED VALUE — CONSTRUCTED FROM HARMONICS, n= 1 TO 10 0.85 0.80 0 45 90 135 180 225 270 315 POSITION ANGLE 6 (DEGREES) Figure 12c - EY 73} Figure 12 (Continued) V= 6.52 KNOTS n = 14.08 REV/SEC & MEASURED VALUE — CONSTRUCTED FROM HARMONICS, n= 1 TO 10 M,/| My, | 0 45 90 135 180 225 270 POSITION ANGLE @ (DEGREES) Figure 12d - M x 74 Figure 12 (Continued) 1.08 6.52 KNOTS 14.08 REV/SEC 1.06 1.04 1.02 1.00 0.98 0.96 4 MEASURED VALUE —— CONSTRUCTED FROM HARMONICS, n= 1 TO 10 0.94 0.92 0 45 90 135 180 225 270 315 360 POSITION ANGLE @ (DEGREES) Figure 12e - F. 75 Figure 12 (Continued) V= 6.52 KNOTS n = 14.08 REV/SEC 4 MEASURED VALUE — CONSTRUCTED FROM HARMONICS, n= 1 TO 10 45 90 135 180 225 270 315 POSITION ANGLE 6 (DEGREES) Figure 12f - M, 76 (F,)/F Figure 13 - Experimental Data Showing Extraneous Higher Harmonics 0.07 HARMONICS USED HARMONICS NOT USED ) IN ANALYSIS IN ANALYSIS | 0.06 i | F,(0) =>) (Fx), 608 (nd - (oF),) | n=1 0.05 0.04 0.03 0.02 0.01 il i Big | 0 \ : Nos — — — WN | S HARMONIC NUMBER n Figure 13a - F x NN HARMONICS USED HARMONICS NOT USED IN ANALYSIS IN ANALYSIS mM, (0) 2S) (My), 605 (0 - (my)) n=1 (my), /My IH HI r Desi 1D 6 7 8 9 aa ais sas lists: 2 GABE HARMONIC NUMBER n Figure 13b - He Figure 13 (Continued) HARMONICS USED HARMONICS NOT USED IN ANALYSIS IN ANALYSIS Fy (9) > (Fy), cos (no : (Sey)q) HARMONIC NUMBER n Figure 13c - Be Figure 13 (Continued) 0.0 HARMONICS USED HARMONICS NOT USED IN ANALYSIS IN ANALYSIS 0.07 a N M,.(@) => (My), cos (no - (6mix)q) 0.06 | n=1 (M,,)_ /M ° ° BSS i ig If i i Lg iT if | Whee. aN\NnnwnnNs _aall ll 23 4A Geel 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 HARMONIC NUMBER n Figure 13d - M, 80 HARMONICS USED HARMONICS NOT USED IN ANALYSIS NALY IN ANALYSIS | F,(0) aS (F,),, cos (no - (F2),) n=1 mm th | Wiebe AnAV AAA On HARMONIC NUMBER n ure 13e - F Zz V= 6.52 KNOTS n = 14.08 REV/SEC SX IS VA pt tS SEE aS Bes wa Z ~ cia | a dee a 0 45 90 135 180 225 270 315 POSITION ANGLE 6 (DEGREES) Figure 14 - Variation of Experimental Hydrodynamic Loads with Angular Position for Steady—Ahead Operation 83 Zw o ! wo |] vt \ SO Se oases bia! 1S} oO ue} vd i) (=) Ss =| n (oe) iss} = i= re V= 6.52 KNOTS n = 14.08 REV/SEC POSITION ANGLE @ (DEGREES) Figure 16 - Variation of Experimental Total Loads with Angular Position for Steady—Ahead Operation 85 Figure 17 - Harmonic Content of Experimental Hydrodynamic Loads for Steady—-Ahead Operation V= 6.52 KNOTS n = 14.08 REV/SEC Ti Ti Tl BS x NX AEBOS N = N 1 2 3 4 5 6 7 8 9 10 HARMONICS NUMBER n Figure 17a -— Amplitudes 86 (PF xy) (omy) (Oryy) (OMixy) (Or2y) (Sniz4)) Figure 17 (Continued) | it | | : | et | I | ; | NXHABOB ae = BaF x \| V= 6.52 KNOTS n = 14.08 REV/SEC 4 5 6 7 HARMONICS NUMBER n Figure 17b — Phases (RQ Eso (id) lithe, (Rp lee (M,),/Mi, (10 F,), /F,, (M,). /M, Figure 18 - Harmonic Content of Experimental Total Loads for Steady—Ahead Operation V= 6.52 KNOTS n = 14.08 REV/SEC n27 <3, N NWNABOB 7s x = N HARMONICS NUMBER n Figure 18a — Amplitudes 88 (Ex) ,° (omy), (Fy). (Omx) 9° (SF 2) (oyz),, V= 6.52 KNOTS n = 14.08 REV/SEC 7 HARMONICS NUMBER n Figure 18b -— Phases (saayDaq) “°n- 4 (dN NY3LS) <—_}+—» (NMOG NUY31LS) cL x J -— 6T e1n3Ty (SGNO93S) 1T3GOW NO AWIL GALVINWIS LL OL 60 80 £0 90 G0 v0 £0 c0 eTsuy yoItd TINH YITM BUTpeOT speT_ TeIO] Jo squsuodwoD Jo uoTIeTAeA — ST DANSTY ih) *4/*4 (mn 90 (saauD3a) “a - (dN NY3LS) —+—e (NMOG NY31S) cL a O'L k W - 96T 24n3Ty (SGNO93S) 140OW NO AWIL GALVINWIS 60 80 £0 9°0 G0 v0 £0 (penutzuo0g) 6T ean8Ty c0 LO t) “w/“w (Mn 91 (SaayD3aq) “°n- f (dN NY3LS) <—_{—-» (NMOG NHALS) A I —- 0671 eArn3ty (SGNO94S) 1SGOW NO AWIL GALVINWIS cL LL OL 60 80 £0 9°0 S'0 v0 £0 c0 LO 0 80 a) *4/"4 (mn (panutquop) 6T eansTq oz (saauDaq) “A - f (dN NY3LS) <-—}—® (NMOG Nu3 11S) cl LL OL x W- P6l ean3ty (SGNO93S) 130GOW NO JWiL GALVINWIS 60 80 £0 90 G0 v0 £0 (penutquoDj) 61 ean3tgq c0 LO h) “W/W (oe 93 (SaayDaq) “hn - (NMOG N¥31S) (dN NY3ILS) cl OL Zz W - 861 eansty (SGNO93S) 13GOW NO 3WIL GALVINNIS 80 9°0 v0 (penutquoD) 6T 2an3T¥q c0 94 (saaHD3q) “A - ft (dN NH3LS) {+ (NMOG NULLS) cl OL eo - 361 ean3Ty (SQNO93S) 130OW NO AWIL GALVINWIS 80 90 v0 (penutjuo9) 6T ean3sTy 20 ih) © Oye Ow (CoG 95 Figure 20 - Variation of Experimental Hydrodynamic Loads with Angular Position for Quasi-Steady Acceleration Vv .65 KNOTS n .21 REV/SEC 3.55 KNOTS 10.96 REV/SEC V= 5.36 KNOTS n = 12.70 REV/SEC ae V= 6.26 KNOTS n = 13.78 REV/SEC Fry Pay, SP V= 6.52 KNOTS n = 14.08 REV/SEC 0 45 90 135 180 225 270 315 360 POSITION ANGLE @ (DEGREES) Figure 20a - F 96 Figure 20 (Continued) V= 2.65 KNOTS n = 10.21 REV/SEC ia V= 3.55 KNOTS n = 10.96 REV/SEC 5.36 KNOTS 12.70 REV/SEC V= 6.26 KNOTS n = 13.78 REV/SEC : 6.52 KNOTS 14.08 REV/SEC 0 45 90 135 180 225 270 315 360 POSITION ANGLE 6 (DEGREES) Figure 20b - M YH 97 Fyu/Fyu sp Figure 20 (Continued) V= 2.65 KNOTS n = 10.21 REV/SEC - V= 5.36 KNOTS n = 12.70 REV/SEC V= 6.26 KNOTS n = 13.78 REV/SEC SLi ees V= 6.52 KNOTS n = 14.08 REV/SEC 0 45 90 135 180 225 270 315 360 POSITION ANGLE 6 (DEGREES) Figure 20c - F Ty 98 Figure 20 (Continued) 2.65 KNOTS 10.21 REV/SEC V= 3.55 KNOTS n = 10.96 oy, V= 5.36 KNOTS n = 12.70 REV/SEC V= 6.26 KNOTS n- = 13.78 REV/SEC V= 6.52 KNOTS n = 14.08 REV/SEC 45 90 135 180 225 270 315 POSITION ANGLE @ (DEGREES) Figure 20d - M 99 360 Fay/! Fy sp! Figure 20 (Continued) V= 5.36 KNOTS n = 12.70 REV/SEC V= 2.65 KNOTS n = 10.21 REV/SEC V= 3.55 KNOTS n = 10.96 REV/SEC V= 6.26 KNOTS n = 13.78 REV/SEC V= 6.52 KNOTS n = 14.08 REV/SEC 135 180 225 POSITION ANGLE @ (DEGREES) Figure 20e - F oH 100 Figure 20 (Continued) 2.65 KNOTS 10.21 REV/SEC = V= 3.55 KNOTS n = 10.96 REV/SEC V= 6.26 KNOTS n = 13.78 REV/SEC 0 45 90 135 180 225 270 315 360 POSITION ANGLE @ (DEGREES) Figure 20f - M 74 101 Mo.34/Mo.34 sp 45 Figure 20 (Continued) V= 2.65 KNOTS n = 10.21 REV/SEC V= 3.55 KNOTS n = 10.96 REV/SEC = 6.26 KNOTS = 13.78 ——s 6.52 KNOTS 4.08 REV/SEC 225 270 315 360 90 135 180 POSITION ANGLE 6 (DEGREES) Figure 20g - nos, 102 Figure 20 (Continued) 2.65 KNOTS 0.21 REV/SEC 5.36 KN OTS eee REV/SEC V= n=1 6.26 KNOTS 3.78 REV/SEC V= 6.52 KNOTS n = 14.08 REV/SEC 45 90 135 180 225 270 POSITION ANGLE 6 (DEGREES) Figure 20h 103 = M 0.4, 3.55 KNOTS 10.96 REV/SEC 315 360 ese OSS arc 0 i] 2 << Figure 21 (Continued) POSITION ANGLE 6 7a oe Eig AN | (HES BE < aa 9 10 (SEx),, Figure 24 (Continued) ——————— ———— ol : Bi I i 1 I ‘(| 45 | Hall 1 Hh Wo A Ladd dl f \K il al i Ni | | Hl Ni i NM | we | | ih i Ni oe Li | i| i | il V (KNOTS) n (REV/SEC) | ny | -90 ae | | ain | l i 135 10.21 M | -180 1 2 3 4 5 6 7 8 9 10 HARMONIC NUMBER n Figure 24a (Continued) (My),/My op 0.40 Figure 24 (Continued) V (KNOTS) n (REV/SEC) 6.52 14.08 6.26 13.78 5.36 12.70 3.55 10.96 2.65 10.21 5 6 BE) Wie. OU er eee el _| 7 8 9 HARMONIC NUMBER n Figure 24b - HL 135 10 Figure 24 (Continue A steal -45 V (KNOTS) n ieee -90 S§ 6.52 14.0 6.26 nae is : 12.70 - 135 @ 3.55 10.96 Z. i 10.21 -180 1 2 3 10 ontinue (GNP icy: 0.14 Figure 24 (Continued) V (KNOTS) n (REV/SEC) S 6.52 14.08 6.26 13.78 O 5.36 12.70 @ 3.55 10.96 2.65 10.21 HARMONIC NUMBER n Figure 24c - ay, 137 Figure 24 (Continued) Ti bit | V (KNOTS) n (REV/SEC) 6.52 14.08 & 6.26 13.78 CG 5.36 12.70 @ 3.55 10.96 2.65 10.21 2 3 4 5 6 7 8 9 10 HARMONIC NUMBER n Figure 24c (Continued) 138 0.24 0.20 | 0.08 | | 0.04 Figure 24 (Continued) 6.26 5.36 3.55 2.65 HARMONIC NUMBER n Figure 24d - M x 139 i | l ! i AA | Ni i Pr ry k (| } i { i 1 | | ! 4 | \ ; eM” Jina Woes Dien santay’ neh sae oy MAT sate PMN Amana es SmI PN TS J.” 9400) HARMONIC NUMBER n (F,),/Foce Figure 24 (Continued) ban ) Hy tH (it tI} 1 NBUSBGA 4 5 6 V (KNOTS) n (REV/SEC) 14.08 13.78 12.70 10.96 10.21 6.52 6.26 5.36 3.55 2.65 7 HARMONIC NUMBER n Figure 24e - F, 141 ae SS —————— = es 2.6 : 80 1 Be De gh eh AG TG Ae 2 MB sok OSE O. HARMONIC NUMBER n Figure 24e (Continue (M,), (Mize Figure 24 (Continued) V (KNOTS) n (REV/SEC) S 6.52 14.08 & 6.26 13.78 Oo 865.36 12.70 Es 3.55 10.96 2.65 10.21 1" VAN I Mt HARMONIC NUMBER n Figure 24f - M, 143 Figure 24 (Continued) V (KNOTS) n (REV/SEC) S 6.52 4.08 SB 6.26 13.78 OH 865.36 12.70 & 3.55 10.96 ZA 2.65 10.21 P ey 1 ! (omz), | Ail i h | H/ il (Mo,3),,/Mo.3 0.45 0.40 Figure 24 (Continued) 4 5 Figure 24g - M 145 6 0.3 NBO V (KNOTS) n (REV/SEC) 6.52 6.26 5.36 3.55 2.65 7 HARMONIC NUMBER n 14.08 13.78 12.70 10.96 10.21 (0.3), Figure 24 (Continued) | il i ) , iI He Aa if Al I; fi S ———— ————S— el SS SSS _| ll Vl] ! ih | te al ia ——S——S]> V (KNOTS) n (REV/SEC) 6.52 14.08 i & 6.26 13.78 | i a Bee 12.70 i | 3.55 10.96 2.65 10.21 1 2 3 4 5 6 7 HARMONIC NUMBER n Figure 24g (Continued) (Mo.4),,/Mo.4 Figure 24 (Continued) 0.40 | il 0.30 0.20 | | 0.10 V (KNOTS) n (REV/SEC) 6.52 14.08 6.26 13.78 5:36 12.70 & 3.55 10.96 ZA 2.65 10.21 HARMONIC NUMBER n Fi - igure 24h M4 147 : bee | } Fe ail 1 3 { Lil ill ili iit | : | : LT i) || ——=— = ™ i SSE 5 (ee ae” ee ee an YN a May me A a IRS AY» (0) (1 -wr), (1 - Wq) 1.15 1.05 1.00 0.95 (P/D)97 = 1.54 10 20 30 40 50 60 70 80 SIMULATED TIME (SECONDS) Figure 25 - Taylor Wake Fractions during Simulated Acceleration Maneuvers 149 Figure 26 - Variation of First Harmonic of Experimental Hydrodynamic Loads with nV for Quasi-Steady Acceleration 0 20 40 60 80 100 120 140 160 nV (R-FT/S2) Figure 26a - F 0 20 40 60 80 100 120 140 160 nV (R-FT/S2) Figure 26b - M YH 150 Figure 26 (Continued) (Eye) eye. o- 20 40 60 80 100 120 140 160 nV (R-FT/S2) Figure 26c - F YH (Mg) Macy, SP On 20 40 60 80 100 120 740 160 nV (R-FT/S2) Figure 26d - M 151 (Moy) Mou sp (Mo.344),/Mo.3u sp Figure 26 (Continued) 60 80 100 120 ~ 140 160 20 40 nV (R-FT/S2) Figure 26e - M 74 80 100 120 140 160 nV (R-FT/S2) 20 40 60 Figure 26f - OKO, 152 x A - ®/7% 9an3Tq SLONY ZG9=A SLONY9Z9=A SLONN9EG=A SLON)IGSE=A SLONAGIC=A A A A cL L= ff vol=f o8'O= fF cl N N NETEIT| NETET | N N N NENT] NETL | ON N N NEES] NETBST | NET ie N N NEE | NETBHTT NET v0 \ N Niel] NUTT] NEE N N NET NEVE} NUTEVE] Jo \ \ NEN | NUE] NET] oe" N N NET] NET | NETE | \ \ NOT NET T NETE N N NUTT | NEST] NETE N N NEES] NETRST) NETR 1 \ N NEIPU Nie | NERY \ \ Ni NOUEU NIE N N N x N N Od \N N NE N N N N VL UOTILABTOIOV pewepTNutTs Apeeqsup pue Apeeis-tsend 103 B3urpeoyT epetg TeIO]L [Te ,ueUtrAedxy Jo sjueuodwoD snoTie, JO SonTeA yeeg pue UoTANToOASY Jed senTe, o8er0Ay-oWT], Jo uostzedwog - /7 9an3Ty CoP 153 & W - 4Zz eansTty SLON) 2G9= A SLONI929=A SLOND9ESG=A piL="r ZuL="P vol =" NER NIE IS NET RST] NET] NEGRIL | NETBS NV Ed BS NE LBS NV Fd BS N ETRY N 2 Boss Ni TES NE TBS NERS NE TES NE TET | NETH | NETR N ree N ed BOY N BS Ni ved | NETH] NEE N ie \ Ba BS N 1&3 NTE | NUTB N BS Ni ES N EBS NET NESE] NETBSTT NET \ NI \ N NE N ‘ie N NS 0 Slb6° £0 £eo°t "e0°T HeO°T Se0°t S80°T HSO°F eeo°t Te0°t e20°T S20°T c20°F SAO AE 220° 920°T T20°R 890°T 90°F T20°R F220 °F 8H O°T GcO°T 6Tto°t S66° ude {Sy 886° 9°0 GOT °E L050 Sie ZOT°T ZOt°r Q90T°T 90T°T 30T°T HOT eT cOt°t e60°t 950 °T BOC °T cOTt*t 2460°T 660 °T 260°T QO °F HAO eal T20°R 60 °T cect 606 ° Gala Siew ALS) G0 x A/ A dO SUNTVA GHLVIOdYAINI - 46 AIAVL St tT BOEY ootet 60°F 680°T 690°T feuct 7 ONT Zeo°t g60°T AT 7 nica 6TE*t SHOT 2otct ZG 4 L0°T 596° 2t6° ogee AXE 908° agR° gece 26e° €'0 = y/4 IN CO NoMWomomMmonw WN om D WMW-o = 176 eSo0°T TSsG°t os0°T 60°F 646 °F 6n6°T 6nb°t 0S0°t 050° eS6°t "S0°T 9S0°T 6S50°T T3b°T £90°F S90°T 990°T 290°T 290° 230° 290°T 990°T sg0°t “90°T £90°T OL 206° EtO°t STO °t £to°t STO°t BtO°T 120 °T ne0°t Be0°t O£0°t Teo °t ef0°t cf£0°t cf£0°t Feo °t FEO °F reo°t cfb°r ceo°t H2O0°r Se£0°t S9fte°t 9f0°T 220° 220 °t 60 cto°t S00 °T 200°F 6c0*tT ebo°t ST0°T Oc0°t "e0°t eca°t o£0°T Beo°t Of0°Tt 620° eco°t 920° S20° "c0°R "20°F Sc0°Tt 2c0°t ec0°t 6ca°t Of£o°t B20 °t c£0°R 80 2£0°t S£0°t EO °T 90° eco°t en0°Tt ShOct 840 °T 250 °t £S0°F £50 °T £50 °T tS0°T 640 °F 840 °T 940 °T “H0°T Hh °T S40 °T S40 °T 940 °T 9n0°T 270 °F 290 °T 240 °F £0 760 °T £60°T £60°T 760°C S60°T 960°T 260° B60°T 6690°T 660°F 660°T 860°F 8O0°T 260° S60°T 60°F £o0°t c60°T 060°T 6eo°t ee0°T 2e0°t 990°T seo°t £e0°t 9°0 (penufquog) 6 aa Soa § Zet°t Och eT ect°t 6et°t bct°t 9ct°t 3¢ct°T 5ct°t nett ral a § Get °t ScT°t Het°t ect°t cett Oet °T otto ITT°t HTT TT °t ett tr TTT °F OTT °t SOT°T S'0 aTave 2cb°t Bet eT Oftet ckT et a ee SST et OFt °t 921 °T adr oF ect ct Sct et Set°t IA) Se § GSel°t Het °t cet °t 6TT°T 2Tt°t HTT °T Tt ct HTT eT OTT °T 8ST ct 6TT°T OTT °T v0 Q0T*T 60T°T DEE OTT °t ETT 1 eae GTE*t 90T°T Z20T°T Z20T°T GOT°T 60T°T STT*t TIT 60T°T GOT °T ZOT*T 660° 260°T 360°T TOT°T gOTet GTT°t QTT°t GUO £0 = 4/4 O°UctT G*2Tt C°SttT Garcavar Hott GP gZws 0°SOT S°20T C°ROT GS°26 0°S6 Gr ale o°%6 5°28 0°S? 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Tsakonas, S. et al, "Documentation of a Computer: Program for the Pressure Distribution, Forces and Moments on Ship Propellers in Hull Wakes," (In Four Volumes), Stevens Institute of Technology, Davidson Laboratory Report SIT-DL-76-1863 (January 1976) Revised April 1977. 35. Tsakonas, S. et al, "Correlation and Application of an Unsteady Flow Theory for Propeller Forces," Transactions of the Society of Naval Architects and Marine Engineers, Vol. 75, pp 158-193 (1967). 288 36. Gutsche, F., "The Study of Ships' Propellers in Oblique Flow," Defence Research Information Centre Translation No. 4306, Copyright Con- troller: Her Majesties Stationary Office, London, England, October UWS’ English Translation of "Untersuchung von Schiffsschrauben in schrager Anstromung,"' Schiffbauforschung, Vol. 3, No. 3/4, pp 97-102 (1964). 37. Boswell, R.J. and S.D. Jessup, "Experimental Determination of Periodic Propeller Blade Loads in a Towing Tank," Presented to the 18th American Towing Tank Conference, U.S. Naval Academy, Annapolis, Maryland (August 1977). 38. Cheng, H.M., "Analysis of Wake Survey of Ship Models -— Computer Program AML Problem No. 840-219F," David Taylor Model Basin Report 1804 (March 1964). 289 Ca at vans MENS ah aN Copies 23 INITIAL DISTRIBUTION Copies ARMY CHIEF OF RES & DEV ARMY ENGR R&D LAB CHONR 1 Code 438 1 LIB NRL ONR BOSTON ONR CHICAGO 1 ONR LONDON, ENGLAND 1 ONR PASADENA USNA 1 1 LIB 1 JOHNSON 1 NAVPGSCOL LIB 1 NROTC & NAVADMINU, MIT 1 NADC 1 NOSC 1 1 1311 LIB 1 6005/FABULA 1 1 13111 LIB 1 2501/HOYT 1 1 NELSON 19 NWC NAVSEA 1 NAVSEA 0311G 5 NAVSEA 033 1 NAVSEA 034 1 NAVSEA 03412 1 NAVSEA 037 1 NAVSEA 037Z 291 NAVSEA 08 NAVSEA 09G32 PMS-378 PMS-380 PMS-381 PMS-383 PMS-389 PMS-391 PMS-392 PMS-393 PMS-397 PMS-399 PREP HE EPP EPP PDE FAC 032C MILITARY SEALIFT COMMAND (M-4EX) NAVSHIPYD/PTSMH NAVSHIPYD/PHILA NAVSHIPYD/NORVA NAVSHIPYD/CHASN NAVSHIPYD/LBEACH NAVSHIPYD/MARE NAVSHIPYD/PUGET NAVSHIPD/ PEARL NAVSEC 1 SEC 6100 SEC 6101A SEC 6101D SEC 6110 SEC 6114H SEC 6120 SEC 6136 SEC 6140 SEC 6140B SEC 6144 NEP RPP PRP RPE Copies Copies 1 SEC 6144G 4 CIT 1 SEC 6145B 1 AERO LIB 2 SEC 6148 1 ACOSTA 1 SEC 6152 1 PLESSET 2 SEC 6334B 1 Wu 1 SEC 6600 NORVA 1 CATHOLIC U i DDC 1 COLORADO STATE U/ALBERTSON i BUSTAND/KLEBANOFF 1 U CONNECTICUT/SCOTTRON 2 HQS COGARD 1 CORNELL U/SEARS 1 US COAST GUARD (G-ENE-4A) 1 FLORIDA ATLANTIC U OE LIB 1 LC/SCL & TECH DIV 3 HARVARD U 9 MARAD 1 MCKAY LIB 1 DIV SHIP DES 1 BIRKHOFF 1 COORD RES 1 CARRIER 1 NACHTSHEIM 1 SCHUBERT 2 U HAWAII/BRETSCHNELIDER 1 FALLS 1 DASHNAW i U ILLINOIS/ROBERTSON 1 HAMMER 1 LASKY 3 U LOWA 1 SIEBOLD 1 ROUSE 1 IHR/KENNEDY 2 MMA 1 IHR/LANDWEBER 1 LIB 1 MARITIME RES CEN 2 JOHNS HOPKINS U 1 PHILLIPS 2 NASA STIF 1 INST COOP RES 1 DIR RES 1 U KANSAS CIV ENGR LIB 1 NSF ENGR DIV LIB 1 KANSAS ST U ENGR EXP/ il DOT LIB NESMITH il U BRIDGEPORT/URAM 1 LEHIGH U FRITZ ENGR LAB LIB 1 U CAL BERKELEY/DEPT NAME il LONG ISLAND U 1 U CAL NAME/WEHAUSEN 1 U CAL SAN DIEGO/ELLIS 2 UC SCRIPPS 1 POLLACK 1 SILVERMAN 292 Copies iL d Copies U MARYLAND/GLEN MARTIN INST 1 MIT 1 1 OCEAN ENGR/LIB 1 OCEAN ENGR/KERWIN 4 1 OCEAN ENGR/LEEHEY 1 OCEAN ENGR/LYON 1 OCEAN ENGR/MANDEL 1 OCEAN ENGR/NEWMAN 1 PARSONS LAB/IPPEN i U MICHIGAN 1 NAME LIB 1 1 NAME/COUCH 1 DEPT/HAMMITT i 1 NAME/OGILVIE 1 WILLOW RUN LABS 2 1 NAME/VORUS U MINNESOTA SAFHL 1 KILLEN il 1 SONG 1 WETZEL 1 STATE U MARITIME COLL 1 1 ENGR DEPT 1 INST MATH SCI 1 NOTRE DAME ENGR LIB 1 PENN STATE U ARL 1 1 LIB 1 HENDERSON 1 1 TSUCHIMA 1 PARKIN 5 1 THOMPSON 1 PRINCETON U/MELLOR all RENSSELAER/DEPT MATH 2 ST JOHNS U SWRI 1 APPLIED MECH REVIEW 1 1 ABRAMSON 1 BURNSIDE 1 2 293 STANFORD U/ASHLEY STANFORD RES INST LIB SIT DAVIDSON LAB 1 LIB 1 BRESLIN 1 TSAKONAS 1 VALENTINE TEXAS U ARL LIB UTAH STATE U/JEPPSON U WASHINGTON APL LIB WEBB INST 1 LEWIS 1 WARD WHOI OCEAN ENGR DEPT WPI ALDEN HYDR LAB LIB ASME/RES COMM INFO ASNE SNAME AERO JET-GENERAL/ BECKWITH ALLIS CHALMERS, YORK, PA ARCTEC, INC/NELKA AVCO LYCOMING BAKER MANUFACTURING BATH IRON WORKS CORP 1 HANSEN 1 FFG PROJECT OFFICE BETHLEHEM STEEL NY/DE.LUCE BETHLEHEM STEEL SPARROWS BIRD-JOHNSON CO 1 CASE 1 RIDLEY Copies BOEING ADV MAR SYS DIV BOLT BERANEK AND NEWMAN 1 BROWN 1 JACKSON BREWER ENGR LAB CAMBRIDGE ACOUS/JUNGER CALSPAN, INC/RITTER EASTERN RES GROUP EXXON DES DIV FRIEDE & GOLDMAN/MICHEL GEN DYN CONVAIR 1 ASW-MARINE SCIENCES GEN DYN ELEC BOAT/ BOATWRIGHT GIBBS & COX 1 TECH LIB 1 OLSON 1 CAPT. 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