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USAAMRDL-TR-77-45B

AERODYNAMIC DESIGN AND ANALYSIS OF PROPELLERS FORMINI-REMOTELY PILOTED AIR VEHICLESVolume II - Ducted Propellers

00) Henry V. Borst4:t4 Henry V. Borst & Associates203 W. Lancaster AvenueWayne, Penn 19087

Z May 1978Final Report for Period June 1976 - March 1978

I Approved for public release;

II Idistribution unlimited.Q.J

~ Prepared for t K'

i APPLIED TECHNOLOGY LABORATORYU. S. ARMY RESEARCH AND TECHNOLOGY LABORATORIES (AVRADCOM)Fort Eustis, Va. 23604

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APPLIED TECHNOLOGY LABORATORY POSITION STATEMENT

This report, Volume II of a two-volume report, presents the design andanalysis of two small-diameter ducted propellers for use on mini-remotelypiloted vehicles (mini-RPVs). These ducted propeller thrustors havebeen designed for use with two-cycle, 20-hp engines with 8000- and 5860-rpmoutput speeds. In addition, an open pusher propeller was optimized forthe lower speed engine. Detailed airfoil data were presented for eachblade design as an aid to blade fabrication.Mr. James Gomez of the Propulsion Technical Area, Technology ApplicationsDivision, served as Project Engineer for this effort.

DISCLAIMERSThe findings in this report are not to be construed as an official Department of the Army position unless sodesignated by other amthorized documents.When Government drawings, specifications, or other data are used for any purpose other than in connectionwith a definitely related Government procurement operation, the Unhried States Government thereby incurs noreiponsibility nor any obligation whalsoover; and the fact that the Government ma y have formulaled, furnished,or in any wa y supplied the said drawings, specifications, or other data is riot to bI regarded by implication orotherwise as in any manner licensing the holder or any other person or corporation, or conveying any rights orpermission, to manufacture, use, or sell any patented invention that may in any wa y be related thereto.Trade names cited in this report do not constitute an official endorsement or approval of the use of suchcommercial hardware or software.

DISPOSITION INSTRUCTIONSDestroy this report when no longer needed. Do not return It to the originator.

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UnclassifiedSECURITY CLASSIFICATION OF' THIS PAGE M-.. D.t. Entered)

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UnclaunsfiednE1@UITY LAIPIBCATION OP TOeMAGIRWhai, D ae ,ti20. ABSTRACT (continued)

Cand ducted propellers were designed based on a procedure that wasestablished for determining th e lowest power and rpm to meet theperformance requirements at an y operating condition. The geometriccharacteristics of the four propellers designed based bn this pro-cedure are presented so that the blades of theme propellers can befabricated.An analysis of the propellers showed that at the deuiqn launchcondition of the advanced RPV the ducted propellers have greatlyimproved performance compared to the opon propellers. Purther,the duoted propellers operate at reduced rotational speeds, whichare essential for a low noise signature.The performance of the four-bladed open propeller installed onthe low-speed engine is superior to that of the two-bladed openpropeller on the high speed engine when operating at the cruiseand dash conditions. At cruise condition the performance of the.

ducted propeller on the high-speed engine is equal to , or betterthan, any of the other configurations analysed. At the cruiseand dash conditions the performance of the ducted propeller on thelow-speed engine is below that of the other two open propellersand the duoted propeller that were analysed.

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TABLE OF CONTENTSPace

LIST OF ILLUSTRATIONS a . . . . . . . * 5LIST OF TABLES 7.... . m e. . 7INTRODUCTIONDESIGN OPERATING CONDITIONS . " " " " " 10

Advanced RPV Design Operating Conditions i0Engine Power Characteris--ics .. .** 10

METHODS OF ANALYSIS . . . " " " " " . " " 13Propellers . * .6*** .. . 13Ducted Propellers . 13Selection of Optimum Configuration . . 15Optimum Propellers and Ducted Fans . . . 16

PROPELLER SELECTION FOR RPV'S . . . . . . . . 17Optimum Propeller Design for 8000 RPM Engine . , 18Performance of 2B81-2.5 Propeller on the8000 RPM Engine . . 22Optimum Propeller Design for the 5860 RMEngine . 22Performance of 4B81-2.5 Propeller on the5860 RPM Engine . * . , 26

DUCTED PROPELLERS . , . . . . . . . 31Optimum Ducted Propeller Design for 8000 RPM

Engine *..*********** 31Duct Design . . . . . .33Ducted Propeller Design . . 39Performance of 5D130-1.75 Ducted Propeller ;n8000 RPM Engine . *,. . . . . 39Optimum Ducted Propeller Design for 5860 RPMEngine . . . . 43Duct Design , . . . . . 43Ducted Propeller Design . . 45Performance of 5D130-2 Ducted Propeller on the5860 RPM Engine a a a . a e . . . 45

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TABLE OF CONTENTS (continued)

PagePERFORMANCE RESULTS . . .... .. . . 52

Open Propel lers . . . ..... ... 52Ducted Propellers . . . . . . . . . . * 53CONCLUSIONS ......... .. *. 54RECOMMENDATIONS , , * 55LITERATURE CITED . g.. .... . . . 56APPENDIX A, FINALIZED BLADE GEOMETRY DETAILS . . . 57LIST OF SYMBOLS ,, ,,o , ,. , 74

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SLI_ OF ILLUSTRATIONSSFigure Page

1 Thrust Power Required vs Velocity for Advanced RPV 11. . ... i2 RPV Engine HP Available at Full ThrottleWith Alternator installed . . 0 . o . 123 Efficiency Required for the Launch and LandingConditions vs Propeller RPM - 8000 RPM Engine * 194 Efficiency Required for the Launch and LandingConditions vs Propeller RPM - 5860 RPM Engine 205 Efficiency Required and Available with Open

Propellers at the Launch Condition vsPropeller RPM - 8000 RPM Engine * * * * 216 Blade Design Characteristics - 2B81-2,5Propeller# 8000 RPM Engine . . 0. 237 Performance Efficiency Map - 2B81-2.5Propeller 0 * a , 0 0 0 0 a a 248 Efficiency Required and Available With OpenPropellers at the Launch Condition vsPropeller RPM - 5860 RPM Engine . . .. 279 Blade Design Characteristics - 4B81-2.5Propeller, 5860 RPM Engine .... 28

10 Performance Efficiency Map - 4B81-2.5Propeller 9. . *... . 2911 Efficiency Required and Available with DuctedPropellers at the Launch Condition vs PropellerRPM - 8000 RPM Engine . . 0 * . . . . 3212 Conceptual Design of a Ducted Propeller Installation* for Advanced RPV With 8000 RPM Engine . o * 3513 Duct Thrust Coefficient vs Rotor ThrustCoefficient . . 0. 0* . . * * 3814 Duct Velocity at Rotor Face vs Rotor ThrustCoefficient 0 a 0 . . . * a . 0 0 . 40

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LIST OF ILLUSTRATIOMS (continued)Figure Page

15 Blade Design Characteristics - 5D130-1.75Ducted Propeller . . . . . . . . . . 4116 Performance Efficiency Map - 5D130-1.75

Ducted Propeller . . . . . . .. ... 4217 Efficiency Required and Available With DuctedPropeller at Launch Condition vs PropellerRPM - 8000 RPM Engine .. . . .0 0 . 4418 Conceptual Design of a Ducted PropellerInstallation for Advanced RPV With5860 RPM Engine . . . . ... . . 4719 Blade Design Characteristics 5D130-2Ducted Propeller . . . . . . . . . . . 4920 Performance Efficiency Map 5D130-2Ducted Propeller . . . . . ...... 50

A-i Developed Blade Planforms .... . . . . 59A-2 Illustrative Section . . . . . . .... 61

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LIST OF TABLESTable Pace

1 Calculated Performance - Direct-Drive Engine . 252 Calculated Performance - Geared Engine . . . 30

A-i Blade Section Ordinates - RPV 2B81-2.5 . . . 62A-2 Blade Section Ordinates - RPV 4B81-2.5 . . . 65'A-3 Blade Section Ordinates - RPV 5D130-I.75 . 68A-4 Blade Section Ordinates - RPV 5D130-2 . . . 70A-5 Blade Planform Data . . . . . .72A-6 Blade Planform Data . . . . . . 73

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INTRODUCTIONPropellers for mini-remotely piloted vehicles must be designedfo r peak performance at relatively low forward speeds whenoperating on engines that have a high output speed. The noiselevel produced by the propellers must be low to.avoid detectionof the aircraft during its operation. Low noise levels aregenerally achieved by reducing propeller tip speed and by in-creasing blade number. Such changes may not be possible andstill meet the thrust and efficiency requirements of the air-plane within the power rpm characteristics of the engine.This is especially true if fixed-blade-angle propellers aredesired to eliminate complexity.volume I documents the work that was done to develop the nec-essary methods of analysis so that the performance of mini-RPVpropellers could be predicted and optimum configurations couldbe developed. Because of the small size of propellers neededfo r these RPV applications, it was necessary to determine cor-rections to account fo r operation at low Reynolds numbers. Thecorrections needed were developed to modify the airfoil datanormally used fo r analyzing full-scale propellers for the ef-fects of Reynolds number, so that the performance of the smallpropellers could be calculated with good accuracy. Using thenewly developed method of analysis, optimum propellers weredesigned for the Aquila RPV and the advanced RPV, both usingdirect-drive engines. To obtain the required performance, itwas necessary to operate the propellers at relatively high ro-tational speeds with correspondingly high tip speeds. Further#the propellers were designed for peak cruise velocity at themaximum available cruise power. Although the performance ofthese propellers is good at all the design conditions, includ-ing the maximum endurance cruise condition, it would appeartlatthe rpm is high so that the noise level would be excessive.Based on the performance of a ducted propeller designed forsimilar operating conditions# suitable configurations weresized fo r the design conditions of the advanced RPV config-uration. The results of this analysis, given in Volume I,indicate that large improvements in performance can be obtainedwhen using properly designed ducted propellers. These ductedpropellers will have a lower rotor diameter than the open pro-peller configuration, with a corresponding reduction in tipspeed to about 30 to 35% that of the open propeller.An engine with the same power output, but with reduced rote-tional speed would also make possible reduced propeller tipspeeds and thus lower noise levels. To determine the possibleadvantages of the use of such engines with either open orducted propellers and also to investigate the effects of

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operating at lower cruise speed, a Phase II study was under-taken. In this study it was required to design optimum openand ducted propellers installed on advanced RPV's usingengines with a maximum propeller rpm of either 8000 or 5860,as installed on advanced RPV' . The propellers were to bedesigned for peak performance when operating at the 60-knotlaunch and landing conditions, and also have good performanceat the 75-knot maximum endurance-cruise speed.

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DESIGN OPERATING CONDITIONS

ADVANCED RPV DESIGN OPERATING CONDITIONSThe design operating conditions for the advanced RPV, equippedwith either the direct-drive engine or an engine using a gearratio of 0.7325, ares

Mode Condition Power Setting Cliah Rate True AirspeedLaunch 4000 ft/95F Maximum 610 fpm 60 ktRecovery 4000 ft/950 F Maximum 200 to 610 fpm 60 ktCruise 4000 ft/95 F 0 75 ktDash 4000 ft/95 F Maximum 0 100 kt(min)

The thrust horsepower required for the advanced RPV is givenin Figure 1 for the launch, cruise, and landing conditions.The increase in thrust horsepower noted for the landing condi-tion reflects the drag increase due to the deployment of thespoiler flaps.ENGINE POWER CHARACTERISTICSThe advanced RPV is equipped with either a 20-horsepower di-rect-drive engine or a 20-horsepower engine which has a gearratio of 0.7325. The maximum propeller rpm for each engine is8000 and 5860, respectively. The full power characteristicsfor both engines as a function of crankshaft speed are given inFigure 2. Each engine is equipped with an alternator, whichreduces the output power to the level shown in Figure 2.

10

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METHODS OF ANALYSISPROPELLERSThe methods used for aerodynamic design and analysis of propel-lers for mini-RPV's are described in Volume' I of this reportand in Reference 1. Strip methods are used to calculate th eperformance of any given propeller-design. These methods de-epnd on theory for finding te 7 induced losses, and two-dimensional airfoil data fo r finding, the progi-4lo,"es;Tese'methods and airfoil data have been used for many years to cal-culate performance of propellers operating at high Reynoldsnumbers. As described in Volume I, corrections to the profile Adrag losses were developed to account fo r the lower Reynoldsnumber operation encountered with mini-RPV propellers. Withthese corrections for Reynolds number, the basic strip analysismethod as programmed for high-opeed computers, B-87, is accu-rate within 1 3% , based on comparisons of test and calculatedpropeller perfo.mance as shown in Volume I.DUCTED PROPELLERSBecause of the interlction between the propeller and the duct,the methods used for designing and calculating the performanceof ducted propellers are much more involved than those foropen propellers. To use the strip analysis for calculatingperformance, it is also necessary to find the induced or three-dimensional losses developed on the rotor operating within th educt and then find the profile losses on each blade sectionbased on two-dimensional airfoil data.With an extension of the Theodorsen 2 theory of propellers,Wright 3 and Gray4 developed the necessary coefficients for1 Beret, H.V., et al, SUbMARYOF PROPELLER DESIGN PROCEDURES AND

DATA, Vols. I, IIand lII, USAAMRDL Technical Report 73-34AB,and C, H.V. Borst & Associates, Eustis Directorate, U.S. AruTAir Mobility Research & Development Laboratory, Fort Eustis,Virginia, Nov. 1973, AD 774831, 774836, and 776998.

2 Theodorsen, T., THEORY OF PROPELLERS, McGraw Hill, 1948.3 Wright, T., EVALUATION OF THE DESIGN PARAMETERS FOR OPTIMUMHEAVILY LOADED DUCTED FANS, Journal of Aircraft, VoL 7 No. 6,Nov.-Dec. 1970.

Gray, 1..B., and Wright, T., A VOREX WAKE MODEL FOR OPTIMUMHEAVILY LOADED DUCTED FANS, Journal of Aircraft, Vol. 7 No. 2,Mar.-Apr. 1970.

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calculating the performance of optimum loaded ducted propellers.These coefficients were calculated for the ducted propelleroperating with the optimum load distribution in the same way aswas done for open propellers. This is the same as assuming therotor is operating with the trailing vortices forming a rigidwake. In compressors, this is the equivalent to the case of avortex-free flow, which also gives an optimum load distribu-..tion. The K(x) coefficients were calculated assuming the Kuttacondition holds at the duct exit. Also, when calculating K(x)using the theory, the duct was replaced by vortices along themean camber line in a manner such as to cancel all normalvelocity components developed by the propeller.When calculating the performance of the rotor operating in aduct, the K(x) coefficients developed by Gray and Wright 4 areused in the same manner as the K(x) goefficients of open pro-pellers as determined by Thecodctsen.A Thus, the induced anglechange fo r applying two-dimensional airfoil data and determin-"ing the induced efficiency of ducted propellers is calculatedin the same manner as fo r open propellers presented in Refer-ence 1, except the K(x) factors of References 3 and 4 are used.Before the above procedures can be used for calculating theforces and moments on the rotor operating in the duct, it isnecessary to find the velocity ahead of the rotor disk. Thisis the velocity induced by the duct when the rotor is develop-ing thrust., This velocity changes with both the free-streamvelocity and the disk loading. The duct-induced velocity iscalgulated based on the vortex theory developed by Kaskel, etal,# which accounts for duct shape and size, rotor thrust,blade number, advance ratio, and rotor location within the duct.The pressure distribution and the duct thrust can also be cal-culated using the procedures calculated by Kaskel, et al. 5Thus, for an assumed duct shape and size, the performance of aducted propeller is calculated as follows:1 Borst, et al.2 Theodorsen.3 Wright.4 Gray and Wright.5 Kaskel, A.L., Ordway, D.E., Hough# G.R., and Ritter, A.# ADETAILED NUMERICAL EVALUATION OF SHROUD PERFORM4ANCE FORFINITE-BLAMED DUCTED PROPELLERS, Them Advanced Research,

Division of Therm1, Ithaca# N.Y., TAR-TR 639, Dec. 1963.14

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1. Assume a rotor thrusty calculate the velocity inducedat the rotor face by the duct, using the method anddata of Reference 5.2. At an assumed blade angle, calculate the thrust andpower developed by the rotor using ducted propellervalues of K(x) for calculating .the induced angle ofattack and suitable two-dimensional airfoil data,3. Adjust blade angle to a value so thathe t itdeveloped by the rotor is equal to the assumed valuein Step 1.4. Knowing rotor thrust and the flight condition, calcu-late the duct thrust and skin friction drag.

T' 5. Calculate the efficiency from the equations(TD+TR+DSp)Vo

550 H,he = duct thrustTR = rotor thrustDSF= duct skin friction dragVo w free-stream velocityHP = installed horsepower.

SELECTION OF OPTIMUM CONFIWUMIWhen selecting the optimum propeller or ducted fan configura-tion for an airplane with several critical design flight con-ditions, it is necessary to establish the relative merits andrequirements of each condition. Further, it is necessary todetermine what types of performance compromises might be in-volved at secondary design conditions, if the propeller wereoptimized only fo r the primary design condition. This is doneby determining the optimum performance at each operating condi-tion for comparison with practical propellers that may be de-signed for peak performance at any other flight condition.

5 Kaskel, Ordway, Hough, and Ritter,S~15

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Ogtimum ProDelJers and Ducted FansThe optimum propeller and ducted fan are defined as configura-tions that operate with minimum induced- and profile-drag loss-es at any flight condition. The performance of the optimumpropeller is a function of the blade number and diameter, andincreases With both of these variables. When theprofile dragis zero# the efficiency of the optimum propeller is equal tothe ideal induced efficiency. This correspondo to the effici-ency of a propeller operating with an optimum load distribution.The profile drag losses of a propeller designed for a given con-dition are a minimum when the lift/drag ratio of the entirepropeller is in the range of 60. This corresponds to a drag/lift angle Y of approximately 10. By assuming that the opti-mum propeller is operating with an ideal induced load distri-bution and a drag/lift angle of 10, the performance can easilybe determined at ':any condition using th e 'hort method given inVolume I. Knowing the optimum performance, it is possible tofind the change or loss in performance of a practical propellerin relationship to the best that can be obtained. This isvery useful for finding the best compromise propeller designfor a number of flight conditions.The actual design of an optimum propeller of a given diameterand blade number operating at any condition of power, speed1rpm, and altitude requires finding the loading distributionfor a ccmbination of minimum profile and induced losses. Thisinvolves finding the blade solidity needed to operate at alift coefficient and the corresponding blade camber for peaklift/drag ratiol it also involves determining the best distri-bution of loading, considering the induced losses for peakefficiency. This procedure involves the use of the theory o2The Calculus of Variations and is detailed in Reference 1.

Borst, et al.

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PROPELLER SELECTION FOR RPV'STh e choice of the best propeller configuration for a remotelypiloted vehicle depends on the flight conditions and theirrelative importance. For the advanced RPV aircraft, the flightspeedsat the launch and landing conditions are equal and theperformance requirements are suchthat one propeller will havepeak performance for both conditions. The design cruise speed* specified is that for maximum endurance where the power isminimum, At this condition the speed is close to that of thelaunch and landing speed conditions. Since the thrust requiredf or cruise is lower than the launch thrust requiredthe optimumpropeller chosen would be smaller than the vptimum propeller* designed for launch and landing conditions. It is thereforeimportant that the propeller selected to give peak performanceat the launch and landing conditions be as small as possibleto obtain peak cruise performance. This means that the propel-ler designed for launch should develop only the minimum thrust* needed for this condition.The fourth operating condition to be considered is the dashcase. Here, the specified requirement is to provide sufficientthrust so the airplane can exceed a speed of 100 knots. Thisis a full power or a maximum rpm condition depending on the opeller used. At the dash condition# the efficiency becomes ofsecondary importance as long as the thrust available exceedsthat required to obtain a flight speed of 100 knots. In Vol-ume I it was shown that the optimum propeller designed for thedash condition is too small to meet the performance require-ments of the launch and landing conditions. Thusfor peak per-formance at dash, the propellers chosen for the launch andlanding conditions should also be the minimum site needed.The thrust required for the launch condition must be met toobtain the needed rate of climb. When this level of thrust isobtained at launch, sufficient propeller thrust is availableat the landing condition so the rate of climb is in the re-quired 200 to 610 fpm range, since propellers required foroptimum performance at the cruise and dash operating flight* conditions are smaller than those needed at the launch condi-tion and will not develop the required performance at thelaunch condition at the lowest possible rpm necessary for peak. performance and minimum :,oise, the launch condition has beenselected as the primary design condition. At this condition#optimum minimum-size propellers and ducted fans are chosen tomoet the aircraft performance requirements.For RPV s equipped with fixed-pitch propellers operating at acertain engine power setting# the best configuration can bedetermined directly by finding the efficiency required at th e

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launch condition as a function of rpm and matching this per-formance with that obtained with the optimum propeller design.The required efficiency depends on the thrust horsepower re-quirements of the airplane and is a function of the aircraftdrag, rate of climb, and the engine power/rpm characteristicsof the specified throttle setting. it is apparent that th epropeller efficiency required will increase as the power avail-able decreases,For the launch and landing conditions when the engines areoperating at a maximum power setting, the efficiency require-ments as a function of rpm are given in Figures 3 and 4 forboth the direct-drive and geared engines. These efficiencyrequirements were calculated using the thrust horsepower char-acteristics of the airplane and the engine power output datagiven in Figures . and 2. The aircraft performance require-ments used are given on page 10.OPTIMUM PROPELLER DESIGN FOR 8000 RPM ENGINETo find the peak propeller performance and corresponding powerand rpm that will meet the efficiency requirements of the ad-vanced RPV equipped with the 8000 rpm direct propeller driveengine as given in Figure 3, the performance of a series ofoptimum propellers must be found. At the design launch condi-tion, the optimum efficiency of a series of optimum two-,three-, and four-bladed propellers was found fo r a range Ofdiameters up to the maximum allowed of 2.5 feet. The varia-tion of efficiency with propeller rpm of these optimum propel-le r configurations is shcwn, along with the efficiency re-quired, in Figure 5. The lowest rpm where the efficiency ofthe optimum propellers crosses the efficiency-required curveis the best operating condition for any propeller. At thiscondition, the noise level of the propellers would also be aminimum, as the noise produced is a direct function of the tipspeed and, therefore, rpm. Since the peak efficiency and min-imum noise level occur at the lowest possible rotational speoadthis criterion was used for selecting the best propeller.This, then, determines the optimum propeller diameter, bladenumber, operating rpm, and input power to meet the efficiencyrequired to obtain the specified aircraft performance. Forthe direct-drive engine, the optimum two-bladed, 2.5-foot-diameter propeller meets the efficiency required at the launchcondition when operating at a rpm of 5600 and with an effi-ciency of 73% (Figure 5) * f a four-bladed, 2.5-foot-diameterpropeller were used, the rpm would decrease to 5500 and theefficiency would increase to 75.5%. In determining whethera two- or a four-bladed propeller should be used, a detailedblade analysis is necessary to find the solidity for peak per-formance. If the loading is low, the solidity of the bladew

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fo r the four-bladed configuration might be too low, resultingin an impractical configuration.In the above analysis only the operating rpm and power areestablished for each optimum propeller of the given blade num-bar and diameters the details of the blade, including solidity,camber? section type, and blade angle distribution, are notknown. The design details of the blade required to achieve thestated performance were determined by the methods describedpreviously and given in Reference 1. For the 8000 rpm engine,the analysis showed that the 2.5-foot-diameter propeller withtwo 81.1 activity factor blades is th e optimum configuration.The blades with an activity factor of 81 are as small as arestructurally practical, so that the propellers using three orfour blades requiring activity factors below 50 were not con-sidered. Since the improvement of performance using fourblades is small, the loss in performance using the two-bladedconfiguration in minimal. The detailed characteristics of thepropeller with two 81 activity factor blades designated 2B81-25are given in Figure 6, Tables of the design data needed forfabrication of this blade are given in Appendix A. An effi-ciency map for determining the performance at any design condi-tion of the 2B81-2.5 propeller i& k given in Figure 7. This mapwas calculated using the methods and data described in Volume Iand includes all the necessary corrections for the low Reynoldsnumbers encountered.Performance of 2B81-2.5 Propeller on the 8000 RPM EngineThe performance of the 2B81-2.5 propeller operating at a fixedblade angle using the 8000 rpm engine is given in Table 1 forthe advanced RPV. The performance of the optimum propellersfo r each condition is also shown in the table fo r comparativepurposes. This propeller meets all the aircraft performancerequirements given on page 10. It operates at peak efficiencyat the design launch condition and has an efficiency of 80.0%at the cruise condition, which is within 3.1% of the peak ef-ficiency possible for an optimum propeller specifically de-signed fo r that condition. The performance of the propellerallows a dash speed of 123.5 knots. This is well above theminimum required.

IPTIMUM PROPELLER DESIGN FOR THE GEARED 5860 RPM ENGINEWith the geared 5860 rpm engine the operating propeller rpmneeded to meet the performance requirements of the advanced RPV1 Borst, et al.

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are lower than the 8000 rpm engine. This occurs as the maxi=omoutput power is the same for both engines when the rpm timesthe gear ratio of the direct-drive engine is equal to that ofthe geared engine. Thus, the required efficiency of the opti-mum propeller occurs at a rpm of 4150 fo r the four-bladed,2.5-foot-diameter configuration as compared with 5600 rpm forthe direct-drive engine. As shown in Figure 8, the optimumefficiency of this propeller is approximately the same as thatof the propeller used for the direct-drive engine. It wouldtherefore appear that the main advantage of using the geareddrive engine is the reduction of noise due to operation atreduced rpm.As shown in Figure 8, the required efficiency can be obtainedfor the launch condition using propellers with lowar diametersthan the maximum allowable. These propellers will operate atin-creased rotational speeds and lower values of efficiency thanthe larger diameter propellers. Since the tip speeds of bothconfigurations are approximately the same, there would be nonoise advantage with the lower diameter configuration,The details of the propeller for the geared engine needed tomeet the performance requirement at the launch condition werefound using the same optimum strip analysis procedure as wasused previously. The results of this analysis indicated thata 2.5-foot-diameter propeller with four 81 activity factorbladeshaving an integrated design CL of .465, would be re-quired. The detailed characteristics of the blade are givenin Figure 9. Tables of the blade section ordinates, from whichthe blade can be manufactured, are given in Appendix A. Theblade is considered to be used with a 7.5-inch-diameter spinneiwhich gives an inboard cutoff of r/R of .25. This propellerconfiguration is designated 4B81-2.5.Performance of 4Q81-2.5 Proveller on the 5860 RPM EncineA generalized efficiency map for the 4U31-2.5 propeller wascalculated using the B-87 propeller computer program correctedto include the effects of low Reynolds number, and is given inFigure 10. From this map the performance of the propelleroperating at the fixed-pitch blade angle needed for the launchcondition is given in Table 2. The performance of this propel-ler meets or exceeds the requirementri at all conditions.Also shown in Table 2 is the optimutm efficiency of propellersfor each design condition. Comparison of the optimum propellerin each case to the 4B81-2.5 shows that this configuration hasexcellent performance at all the flesign operating conditions.

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DUCTED PROPELLERSThe existing RPV's incorporate shrouds to protect the propellerfrom damage and operating personnel from injury. The shroudsused are not effective'for improving the rotor performance, asthe tip clearance is large relative to the rotor diameter.Thus, the duct cannot control the tip losses by counteractingthe radial flow velocity as in the case of a properly designedducted propeller. In Volume I it was shown that with properlydesigned ducted propellers, important improvements in perform-ance could be achieved compared with the open propeller. Fur-ther, it was shown that the performance increase would be ob-tained with rotors of lower diameter operating at reduced tipspeeds. Because of the projected increase of performanceshown, ducted propellers were designed fo r optimum performanceon the advanced RPV's using both the direct-drive 8000 rpm andthe geared 5860 rpm engines.To determine the size requirements of the ducted propeller, ananalysis was conducted in a manner similar to that performedfor the open propellers. This is feasible# as variation ofthe efficiency required with rpm depends only on the enginecharacteristics and airplane requirements, and does not dependon the type of propeller or fan used. The efficiency neededto meet the performance requirements of the airplane fo r thelaunch condition is then compared to that produced with ductedpropellers of various sizes. The efficiency of the various-size ducted fan configurations was determined from the charac-teristics of a known ducted propeller designed fo r operating inthe same speed range as the RPV's. It was necessary to use theperformance characteristics of an existing fan configurationfor estimating the required fan size, as single-point methodssuch as those used for open propellers have not been developedas yet. Such methods would be useful for this purpose.OTkM DU oPROPELLER DESIGN FOR 8000 RPM ENGINEBased on a five-bladed ducted propeller operating in a ductwith a length to diameter ratio of 0.75, the efficiency at thelaunch condition was estimated for a series of diameters at arange of rotational speeds. Rotor diameters from 1.5 to 2.5feet were considered. The results of these calculations areshown in Figure 11 in comparison with the efficiency requiredat the launch condition. The performance of rotors from 1.5to 2.0 feet diameter will meet that required,'with the 1.75-foot-diameter configuration having the best efficiency at thelowest rotational speed. This rotor diameter was thereforeselected for further analysis and optimization.

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Duct DesiqnAS the duct and rotor interact, the design of each componentdepends on the other. The fl.ow velocity at the rotor face isinfluenced by the shape of the duct and the thrust produced bythe rotor. Since the design details and performance of therotor are influenced by the upstream velocity, it is necessaryto establish the duct configuration prior to designing the

* rotor blades.The duct design parameters to be considered for a given rotordiameter are the duct lbongth-to-diameter ratio, the airfoilcross section, the location of the rotor disk within the duct,and the angle of attack of the duct section with respect tothe duct centerline. In choosing the above parameters for agiven ducted propeller design, the main considerations are theavoidance of separation at the inlet and exit and controllingthe flow in the propeller plane so that radial flow losses,such as those encountered with open propellers, are eliminate6or reduced to a minimum.The propeller or rotor of a pusher installation operates down-stream of the enginey as a result, part of the rotor will beoperating in the wake produced by the engine. This wake in-fluences both the aerodynamic performance and the structuralcharacteristics of the blades. Two opposing cylinders extendinto the stream ahead of the rotor and thus will influence theflow into the rotor. To reduce the effect of the cylinder wakewhich can have a high velocity decrement, it appears pos,.ubleto duct the airflow through the rotor hub in a manner illus-trated in Figure 12. The exhaust flow can be mixed witI, theflow over the cylinders required for cooling and also passedthrough the rotor hub. The spokes of the rotor hub vuay bevanes or blades to force the flow through the spinnej., andthus provide positive cooling airflow.To provide minimum interference, the rotor hub has a conicalshape to increase the axial distance between the struts andtherotor blades. This gives an axial distance to the propeller ofapproximately two stator chord lengths. This in the minimumdistance for the rotor to be spaced from the stator vanes tominimize interference and noise. As a result of the above con-siderations, the engine/propeller was positioned in the ductwith a length-to-diameter ratio of 75 at the mid-duct locatimas shown in Figure 12. The mid-duct location of the rotor alsomakes it possible to control the expansion of the flow prior tothe exit of the duct. This is done by limiting the includedangle of the duct to 70, To maintain low skin friction drag,the duct length was kept relatively low at a length-to-diameterratio of .75 where the diameter is the diameter of the rotor.

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Calculations of the performance of several duct shapes indicatedthat ducts with a low thickness ratio will have small values ofnose ratios, which can lead to separation at relatively lowangles of attack. Further, ducts with low nose radii do notproduce the thrust necessary for the development of the optimumratio needed for peak performance, For these reasons, a 15%section using the ordinates of the NACA 23015 airfoil was cho-sen fo r the duct cross section. This duct section is orientedso that the normal upper surface is he inner surface of theduct. The above conclusions on the effect of leading-edgeradius, duct length-to-diameter ratio, and propeller location* are confirmed by the experimental data given in Reference 6.Using the methods of Reference 5, the performance characteris-tics of the duct were calculated for a range of operating con-ditions that are encountered on the advanced RPV's. It wasfound that the thrust produced by the duct in only a functionof the thrust loading of the rotor and is independent of therotor rotational speed. The variation of duct thrust withrotor thrust is expressed in coefficient form, Cr and C,where C'T = TR/qA = rotor thrust coefficient

Ct = TD/qh = duct thrust coefficientTR = rotor thrustTD = duct thrustq = free-stream dynamic pressure 0PV2A = disk area rD 2R/4

The variation of the duct thrust coefficient with rotor thrustcoefficient is given in Figure 12 fo r the duct configurationgiven in Figure 11.The velocity induced by the duct and the propeller is dependenton the rotor thrust coefficient C . This velocity is a func-tion of the radial station and in expressed as the ratio of VDto Vo. It is calculated (knowing the duct geometry) using themethod and data given in Reference 5.

Kaskel, Ordway, Hough, and Ritter.Black, D.M., Wainauski, Harry S., and Rohrbach, C., SHROUDEDPROPELLERS - A COMPREHENSIVE PERFORMANCE STUDY, AIAA Paper68-994, Oct. 1968.

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Thus, VD/Vo = duct velocity ratiowhere VD = velocity in the duct

Vo = free-stream velocity.The duct velocity ratio " is given as a function of the thrustcoefficient C'T and x as shown in rigure 14. In the range ofoperation of the advanced RPV's, A is independent of the rota-tional speed.Ducted Propeller DesionThe analysis of the efficiency requirements at the launch con-dition using the direct-drive 8000 rpm engine showed that aducted propeller with a rotor diameter of 1.75 feet, operatingat 5650 rpm, was the best configuration. At this condition,the details of the rotor were determined to give the optimumperformance. The criterion used to establish the optimum bladeconfiguration is basically the same as that used for optimumpropeller designs. This blade loading condition corresponds tothe vortex-free condition used in the design of compressors,which is the same as the rigid wake case used in propeller de-sign, Based on this design criterion, a rotor with optimunblades was established, This rotor, operating in the duct givenin Figure 12, has five 130 activity factor blades with an inte-grated design CL of 0.6. The characteristics of the blade aregiven in Figure 15 , with the detailed section ordinates fromwhich the blade can be fabricated given in Appendix A.PERFORMANCE OF 5D130-1.75 DUCTED PROPELIER ON 8000 RPM ENGINEAn efficiency map for the optimum ducted propeller describedabove and designated 5D130-1.75 was developed fo r the expectedoperating range and is given in Figure 16. The thrust deter-mined from the efficiency given includes the thrust producedby both the rotor and the duct, The duct thrust includes thedrag loss due to skin friction, which was calculated using thedata given by Hoerner. 7 Due to the location of the engine withrespect to the duct and propeller, intarference losses can beexpected. These were estimated to be 1.5%of the calculatedefficiency. It was assumed that a tip clearance of 0.1 inchwould be maintained. Based on the test data given Sn Reference7, the loss in performance was taken as 2.5% over the entireranga *7 Hoerner, S.F., FLUID-DYNAMIC DRAG, publishedbythm authoi:,

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For the design operating conditions of th e advanced RPV's, theperformance of the 5D130-1,75 ducted fan was calculated and isgiven in Table 1. At all the flight conditions fo r the ad-vanced RPV, the efficiency of the ducted fan is excellent andexceeds requirements. The hioi" values of efficiency are main-tained over a wide range of power with the ducted propellerconfiguration.OPTIMUM DUCTED PROPELLER DESIGN FOR 5860 RPM ENGINEThe efficiency of a series of ducted propellers having a length-to-diameter ratio of 0.75 and installed on the 5860 rpm engineis shown in Figure 17. This efficiency, as a function of rpm,is compared with the effipiency required to obtain the thrustneeded at the launch condition. Based on the criterion of.operating at minimum tip speed, the ducted fan with 2-foot-diameter rotors appears to be optimum. This configuration,operating at 4000 rpm and full power, meets the efficiencyneeded at full power for obtaining the required rate of climbof 610 fpm at 60 knots. At this condition, the rotor tip speedis only 41 9 fps, which should result in low noise output.puct DesianThe duct selected for the ducted fan used with the 5860 rpmengine has a length-to-diameter ratio of 0.75 and a cross sec-tion corresponding to a NACA 23015 airfoil section. This air-foil section was chosen as it has an essentially flat lowersurface, which becomes the outer portion of the duct, and alarge leading-edge radius, which tends to eliminate separationproblems at the duct entrance. The airfoil is mounted in theduct with an expansion angle of 70 to provide a configurationwith a high duct efficiency. The duct shape chosen is th esame as that used with the 8000 rpm engine.The cylinders on the 5860 rpm engine are large relative to thepropeller, so that the wake produced will have a significanteffect on performance. As the propeller operates aft of th eengine, the blades go in and out of the wake produced by thecylinders with a corresponding periodic change of load. Thisis similar to a pusher propeller operating aft of a wing, andcan lead to high alternating blade loads with correspondinghigh vibratory stresses. To minimize this effect, the loca-tion of the engine and fan relative to the duct has been ar-ranged to reduce the wake size and the velocity relative tothe cylinders. This was done by locating the cylinders Justin front of the duct where the velocity is lower than that atthe propeller face and using splitter plates aft of the cylin-ders. The splitter plates tend to reduce drag and so reduce

43

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the width and velocity decrement in the wake. The splitterplates are also used to support the outer portion of the duct.The general arrangement of the engine, duct, and rotor isgiven in Figure 18.The arrangement oa the duct, engine and propeller shown in Fig-ure 18 resultsin a relativly large distance between the frontsupports of the duct and the duct trailing edge. To reduce themovement of the duct relative to the propeller so that minimumtip clearance can be maintained, the rear spinner is fixed sothat it does not rotate. Six vanes, attached to the Spinner,stabilize the duct. At the end of the fixad inner surface isa rotating shaft that can be used to start the engine.Since the duct shape and length-to-diameter ratio of the ductedfans designed for both engines are the same, the thrust andvelocity characteristics given in Figures 13 and 14 will apply,to both designs.Ducted Progeller DeuianThe propeller for the low rpm ducted fan was designed in thesame manner as the one for the 8000 rpm engine. Based onoperation at a minimum rpm of 4000 for the launch condition,the rotor using five 130 activity factor blades was optimizedto find the best distributions of design CL and blade angle.This resulted in a blade with an integrated design C of 0.7.This blade, installed in a five-blade hub operating in theabove duct design given in Figure 18# is designated the 5D130-2ducted propeller , The detailed blade characteristics aregiven in Figure 19. The section data needed for the blade fab-rication is given in Appendix A.PERFORMANCEI OF 5D130-2 DUCTED PROPELLER ON THE 5860 RPM ENGINEA generalized performance efficiency map was developed for the5D130-2 ducted propeller configuration and is given in Figure

* I20. The efficiency shown includes the thrust of the propellerand duct as determined from Figure 20 . The duct thrust in-cludes a correction for skin friction based on the operatingReynolds number as determined from Hcerner. 7 It is assumedthat the tip clearance between the blade and the duct is 0.1inch. This results In an efficiency loss of 2.5% based on thedata given by Black. An additional efficiency of 2.5% was6 Black, Wainauski, and Rohrbach.7 Hoernor.

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applied to account for the interference of the engine cylin-ders on the flow. Thus, the efficiency determined from theefficiency map (Figure 20) includes all the losses for skinfriction and interference.The performance of the 5D130-2 ducted propeller operating onthe advanced RPV, using the 5860 rpm engine, was determinedusing the efficiency map (Figure 20) and is given in Table 2.Where the efficiency of the propeller intersects that requiredat the launch condition (Figure 17), the blade setting angleand rotational are established for the ducted propeller. For* the 5D130-2 ducted propeller this occurs at an efficiency of*', 84% and 3750 rpm at the 60-knot launch condition. This higherperformance compared to the original estimate is a result ofthe blade optimization, which made possible decreasing rpm andincreasing efficiency.With the propeller operating at a fixed blade angle, the per.-formance of the 5D130-2 configuration was found at the designcruise and dash conditions using the efficiency map given in 4!Figure 20. The performance is given in Table 2. Excellent"performance, exceeding requirements, is obtained at all th eoperating copditions.

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OPEN PROPELLERSThe performance of optimum open propellers is accurately deter-mined using the single-point method given in Volume I andassuming a drag/lift angle of 100,. This is illustrated inFigure5 by comparing the performance calculated at the launchcondiion.,,using the single-point method, with that foundforan actual 2B81-2*5 optimum propeller. At the design-rpm ofthe c.Limum propeller the efficiency determined by the twomethods is nearly identical, Thus, the performance calculatedby the single-point method at any rpm, assuming a drag/liftangle of 1.00, is truly representative of wihat would'be deter-minid and expected fo r the optimum propeller. It should benoted that the actual blade configuration o) tChe optimum pro-peller would bo'3 different for each rotational s.p6ed seMeted.As shown in Table 1, he performtnce of the 219,8.-2.5 propelleris excellent at all the design tlight conditiono of the ad.,.vanced RPV. At the launch and lanaing conditions thb p'rform-ance is within 0.5% of the ideal configuration, whi16 thecruise condition the performanct of the selectad propeller iswithin 4% of the ideal. This performenue Is doinsidered to beexcellent fo r a fixed pitch propeller. The 2B81-2.5,propellerdevelops sufficient thrust so a dash speed of 123.5 knobts sobtained, which is well above the minimrum required of 100 knots.Even at this condition the efficiency is within 10%.of the op-timum for the engine operating at maximum power. Thus, itwould appear that the fixed-pitch two-bladed propeller is thepractical optimum configuration for +,e high rpm engine. Fur-ther, except for the possibility of reducing rpm at cruise todecrease the noise level, a variable blade angle propeller isnot required for this installation.As shown in Table 2, he performance of the 4B81-2.5 four-bladed open propeller, designed for peak efficiency mt tbelaunch condition, exceeds that of the propeller with theassumed drag/lift angle of 10. This shows that the blade isoperating with minimum profile losses at this condition. Theefficiency of the four-bladed propeller exceeds that of thetwo-bladed configuration due to the better lift/drag ratiosand higher induced efficiency. If higher rates of climb arerequired at: the launch conditions, it would thus appear thatthe four-bladed configuration installed on the low rpm enginewould provide the greater growth potential.At the 75-knot cruise condition the performance of the four-bladed propeller on the low-speed engine is superior to thatof the two-bladed configuration operating on the high-speed

52- - - - , - .. -

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engine. The four-bladed propeller also operates at an effi-ciency very close to the optimim. At the dash condition, goodperfonrance is obtained and the required dash speed of 100knots is exceeded, With the lower operating rpm of the four-bladed propeller operating on the lower speed engine and itskhigh performnnce, this configuration appears to be superior tothe two-bladad propeller installel on the high-speed enginefrom both a noise and performance considerdtion.DUJCTED PRI'VELLERSThe performance of the 5D130-1.75 ducted propeller operatingon the 8000 rpm engine is significantly better at the launchcondition than the two-blacked open propeller. An increase inefficiency of almost 10% is obtained with a reduction of tipspeed of over 35%. At the cruise condition the performanceis better than the open propeller, and a similar reduct'ion oftip speed is obtained which ahould be important in reducing+,he noise level of. he configuration. At the dash flight con-dition the performance of the open propeller is slightly betterthan that of the ducted propeller, but the difference is insig-nificant as the dash speed difference is only one-half a knot.The performance of the ducted propeller designed for the 5860rpm engine is approximately 8% better than that of the openpropeller at the launch condition. At the cruise and dash con-ditions, however, the open propeller has better efficiencythan the ducted configuration. At these conditions there isa reduction of 28% in the tip speed ofUthe ducted propellercompared to the open propeller, which may be important fr*omno1 se conaiderations.Although improved performance is obtained at the launc-h condi-t on with the ducted propeller as compared with the four-bladedopen propeller, the overall advantages do not appear to be asgreat as in the case of the installation with the 8000 rpm4engine.

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CONCLUSIONS

Based on the design and analysis of open and ducted propellersoperating on advanced RPV's using engines With different out-put rotational speeds, it is concluded that,,1. At all the flight conditions analyzed the perfor~ance ofthe best open propeller ,for the high-speed engine will

th e low-speed engine.2. Ducted propellers pan be designed with ,sgnificanr rim-provements in perforianoe at the launon conditon ('andclimb condition).3. The ducted propeller ,-operating on.the high-speed enginehas higher efficiency than either Qf the open propellersat thelaunch and cruis'e condition., with nearly the

same performance at the dash condition.4. The duct.ed propeller on the low-speed engine has thebest performance'at' th launch condition.5. 1p'.r either engine the dU.,ted propellers operate at alower tip speed than the open propellers, Which should'resalt in a corresponding noise reduction.6. The tip speed of either the open or ducted propeller is

less for the low-speed enginu at corresponding condi-tions, which should result in a noise reduction.

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REC9WEkMLTZONSBecause the ducted propeller appears to have the greatest po-tential for peak performance and low noise, the following arereooomended,

a1.bricate and test in a wind tunnel thetwo'ductedpropoller configurattons designed for this program.%'hbox tests should be run with the actual engines todupl'icate the range of operating conditions to develop, e eficnecy map. and cover the ,design operating con--ditions of the advanced RPV.' :Pressure distributionmdasurements on the duct should be made* .2. Cond uct rade-off studies to-determine, he effect ofchanges in the pertormance at ,.he laUnch and, cruiseconditions and tIeir relative advantages. "3. Develop short methods for the design and analysis ofducted propellers, such asthose given inVolume I for"open propellers.

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LITERATURE CITED

1. Borst, H.V., et al, SUMMARY OF PROPELLER DESIGN PROCEDURESAND DATA, Vols. I, Il, and III, USAAMRDL Technical Report73-34AP B, and C, HoV. Borst & Associates, Eustis Director-ate, U.S. Army Air Mobility Research and Development Labor-atory, Fort Eustis, Virginia, Nov. 1973, AD 774831# 774836,and 776998.2. Theodorsein, T., THEORY OF PROPELLERS, McGraw Hill, 1948.3. Wright, T., EVALUATION OF THE DESIGN PARAMETERS FOR OPTIMJUHEAVILY LOADED DUCTED PANS, aournal of Aircraft, Vol. 7No. 6, Nov.-Dec. 1970.4. Gray, R.B., and Wright, T., A VORTEX WAKE MODEL FOR OPTIMUMHEAVILY LOADED DUCTED FANS, Journal of Aircraft, Vol. 7No. 2, Mar.-Apr. 1970.5. Kaskel, A.L., Ordway, D.E., Hough, G.R., and Ritter, A.,A DETAILED NUMERICAL EVALUATION OF SHROUD PERFORMANCE FORFINITE-BLADED DUCTED PROPELLERS, Therm Advanced Research,Division of Therm, Ithaca# N.Y., TAR-TR 639, Dec. 1963.6. Black, D.M0, Wainauski, Harry S., and Rohrbach, C.,SHROUDED PROPELLERS - A CCKPREHENSIVE PERFORMANCE STUDY,AIAA Paper 68-994, Oct. 1968.7. Hoerner, S.F., FLUID-DYNAMIC DRAG, Published by th e author,1965.

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APPEMDIX AFINALIZED BLADE GEMETRY DETAZLS

The necessary data for, the fabrication of the blades for thetwo open propellers and two ducted propellers are given inthis appendix. These data correspond to the blade designcharacteristic data given for the open propellers in Figures6 and 9. The corresponding data for the blades of the ductedpropellers are given in Figures 12 and 15. The developedplanform for each of the blades in given in Figure A-i.Both engines considered run clockwise when viewed from theanti-propeller endy thus, when used with pusher propellers,the blades are left-handed or rotate in the counterclockwisedirection when viewed from the downstream or wake end.To fabricate a blade, the detailed section ordinates are neetdat a series radial station. Also needed is information on thestacking of these blade sections on the blade centerline andthe section setting angle, defined an the blade angle. Thedetailed nomenclature used is shown in Figure A-2. The de-tails of the blade shank will depend on the blade materialand on the blade retention system used. The blade shank char-acteristics given in Figure A-I are based on the preliminaryretention designs given in Figures 12 and 18 and must be struc-turally analyzed prior to the blade fabrication. The outboarddetails of the blade are based on aerodynamic considerationsas discussed in the body of this report. Small changes in thethickness ratio could be made without affecting the perform-ance, if required for structural reasons.The design characteristics necessary for fabrication of thefour blades shown in Figure A-i are given in the followingtables and figures.

Blade Blade Section Blade Plan-,lad Charagoeriotics Ordinates DataFigures: Tables: Tabless2B81-2o5 6 A-I A-54B81-2.5 9 A-2 A-55D130-1.75 12 A-3 A-65D130-2 15 A-4 A-6

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Table A-5.BA PLANTOR DATA

Blade B 8 1.-2 5

STA b TAn) LIR YTER YTi. in, n in. i2.in in. in. *p.i4.5 2.7 1.038 .249 .057 .014 .o2 .005 42.36.0 2.48 1.o9 .223 .047 .010 .004 33.37.5 2,49 1.107 s182038 .008 .004 27.69.0 2.36 1.056 .153 .028 .006 .004 23.9

10.5 2.1 .. 958 .117 .2 ,004 .004 21.012. 1.79 .808 .088 .02 000o004 18.213o.5 1,34 .606 .060 .02 .002, .004 15.91405 1.10 .49a .o47 .02 Ao01 .Q04 15.01462.5 .9A,'435 6040 02 o0 4003 14.2

4.5 2.37 1.038 .249 .057 0 .02 0 30.26.0 2.48 1.095 .223 .047 .012 .005 26.47.b 2,49 1.107 .182 .038 .011 .006 22.89.0 2.36 1.056 .153 .028 .008 .006 19.4

10.5 2,13 .958 .117 .02 .005 .005 18.112. 1.79 .808 .088 .02 .003 .005 16.213.5 1.24 .606 .060 .02 .002 .004 14.514.25 1.10 .498 .047 .02 .001 .004 13.814.625 .96 .435 .040 .02 .001 .003 13.4

72

Table

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A-69PV 6D139-1.75 Sadec

TA b L I,in.. in in. ins in. in. .. g

3 1.75 .762 . .201, .048 .010 .02 .004 .5 a a4,5 1.75 .775 .149 .031 .008 .005 35.76.0 1.75 .782 .118 .022 .007 .005 28.775 1.75 .7187 .096 .O .006 .005 24 ..005 20T.79.0 1.75 .791 .081 .o2,, . .006 .00510.5 1.75 .792 .074 .020 .006 .005 16.4

Data for'3,5 2 .873 .22 .050 .013 .02 .005'" 49.6 FairingOnly5.0 2 .865 .172 .031 .009 .006 40.26.5 2 .892 .14 .022 a007 33.8a 2 .898 .117 ,02 .006 29.59.5 2 .902 .10 1 26*11* 2 .905 .0oe 2.5M12 2 .906 .084 * 22.0

- I- -----------.-----. 73

LIST OF SYMBOLS

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A disk area -sq ftAP blade activi~ty factorB blade numberb blade chord - ftCD drag coefficientCL lift coefficientCLi section design lift coefficientCp power coefficientCC torque coefficientCT thrust Coefficient = T/Pn 2 D4C'T propeller thrust coefficient = T/qACt duct thrust coefficientCG center of gravityD propeller diameter - ftDR rotor diameter - ftDS duct skin friction drag - lbFA face alignmenth maximum blade thickness - fthL vertical ordinate from chord line, lowerbu vertical ordinate from chord line, upperhp horsepowerJ advance ratio = V/nDK(x) circulation function - single rotation propellersL lift -lb

74

LIST OF' sUMOLS (continued)

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LEA lead.edge alignm6ntLER lead-edg. rtosdi. .mph miles per hour

N propeller rotatibo~l speed - r'n propeller rotational speed - rpuP power i ft-lb/sec,"Q. torque - ft-lbq dynamic pressure - psfIt, propeller radius, - ft

I~iR.N. Reynolds number,"r propeller radius at any station - ftrpm revolutions per minuteT thrust - lbTD duct thrust - lbTR rotor thrust - lbTS propeller shaft thrustTER trail-edge radiusTbp thrust horsepower'IVD velocity in duct - ft/secVo free-stream velocity - ft/secx fractional radius at any station r/Rx horimontal location of ordinatesxoq horizontal location of center of gravityYU.; vertical locatiun of center of gravity

75, i__________ -

iI

LIST OF Smk4DOLS (continued)

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YL vertical center of lead-edge radiusSYTertical center of trail-edge radius

a angle of attack - dog"inducedangle of attack - degblade angle - dog .

v drag/lift angle .= tan"1 CD/tLpropeller efficiencyduct velocity ratio = VD/Vomass density of air - slugs/ou ftpropeller solidity

ref reference.75 conditions at x = .75i induced

76