TWO AND THREE-BLADED PROPELLER DESIGNFOR THE REDUCTION OF RADIATED NOISE
Howard Patrick*, Ronald W. Finn* andChandra K. Stich*
Embry-Riddle Aeronautical UniversityDaytona Beach, FL 32114
Abstract
The purpose of this study was to design quiettwo and three bladed propellers for general aviationaircraft. A combination of design technique andanalytic predictions using the NASA Aircraft NoisePrediction Program-Propeller Analysis System(ANOPP-PAS) was used to achieve this goal. Thepropellers were designed for an engine of 200 hp and afree-stream of 160 kts. The rotational speed wasreduced from a typical 2700 rpm to 2400 rpm, in orderto prevent the formation of shocks at the tip. A straight76 in. diameter two-bladed propeller was designed as areference for both the 76 in. diameter two-bladed sweptconfigurations and the 64 in. diameter three- bladedpropellers. A 9.5 dB reduction in the far-field OASPLand a 8.0 dB reduction in the near-field OASPL wasachieved when comparing the reference propellerspinning at 2400 and 2700 rpm. Comparison on an A-weighted scale reveals that the slower spinningpropeller produces a 14.0 dBA reduction in near-fieldOASPL. Through blade design modifications, theswept two-bladed configuration produced an additionalreduction of 2.2 dBA in the far-field OASPL. Thethree-bladed designs resulted in further predicted noisereductions of 4.2 dBA in the near-field and 4.8 dBA inthe far- field. These designs resulted in no appreciablechange in aerodynamic performance and minimalweight penalties.
*Associate Professor, Aerospace Engineering Dept.,Senior Member, AIAA.
'Graduate Research Assistant, Aerospace EngineeringDept., Student Member, AIAA.
'Graduate Research Assistant, Aerospace EngineeringDept., Student Member, AIAA.
BackgroundThe problem of propeller generated noise has
long been recognized as a major annoyance topassengers and crew members in aircraft as well as topeople located on the ground - especially near airports.This environmental noise problem has been accentuatedwith the growth of engine power of aircraft and hasbecome a major problem for general aviation (GA)because of increased population densities and newstringent environmental noise regulations.
Current GA propellers are very noisy despite thefact that the technology exists to significantly reducepropeller noise through new designs and materials. Thetwo primary sources of propeller noise originate fromblade loading, i.e. from aerodynamic forces, and theactual blade thickness1. For conventional propellerconfigurations, blade loading and thickness noisesources contribute about equally to the far-fieldradiated noise, although the directivities of thesesources differ. The frequency spectrum characteristicsof propeller noise due to these two sources consists oftones at blade-passing frequency (BPF) and associatedharmonics consisting of multiples of BPF. Forexample, a three-bladed propeller rotating at 2,400rpmwould have a BPF of 120 Hz and harmonics at 240 Hz,360 Hz, etc.
Significant noise reductions can be achieved byslowing propeller rotational speeds. It has been wellestablished that subsonic propeller noise increases atapproximately the fifth power of tip speed whichindicates that by reducing the rotational speed andblade tip radius, significant noise reductions can beachieved while delivering the same power.1Unfortunately, when using the same blade geometry,the propeller aerodynamic performance will decreaseresulting in a weight penalty for equal performance.The key to efficient low weight propeller design is toincorporate new airfoil shapes and loadingdistributions.
934American Institute of Aeronautics and Astronautics
With the advent of modern materials technology,propellers can now be fabricated using relatively thinblades resulting in reduced thickness noise.2 Thesesame blades also incorporate in-plane blade sweep thatresults in noise reduction due to distributed load noisecancellation in the far-field.3 These propeller designtechniques were used in the design of the propfandeveloped during the 1980's for commercial aircraftapplications. This same technology can beincorporated into the design and fabrication of quietand efficient propellers without paying a significantweight penalty.
In summary, existing GA aircraft propeller noisecan be significantly lowered by reducing propellerrotational speed and propeller diameter whilemaintaining similar thrust characteristics. Thiscapability can be achieved by designing new multi-bladed propellers of smaller diameter while takingadvantage of new blade design. Since rotational speedchanges, different blade advance ratios would be usedto assure that the propellers are operating in an efficientregime.
Objective
The design effort was to demonstrate theapplicability of using the UNIX version of the NASAdeveloped Aircraft Noise Prediction Program (ANOPP)Propeller Analysis System (PAS) to design quiet GApropellers.
Propeller blade cross section shape constituted thefirst step in this investigation. Primary candidates werelaminar flow blade sections because of the addedbenefit of decreasing skin friction drag and, therefore,increasing propeller efficiency. The radial bladedistribution was to be designed for optimumaerodynamic performance and low noise characteristicswith minimal weight penalty.
The next step was to design a two-bladedreference propeller of the same diameter and rotationalspeed (typically 2,400 RPM) as a typical propeller butincorporate the new propeller blade design. This newpropeller design would then be analyzed using theANOPP-PAS program which predicts the aerodynamicperformance characteristics as well as the near and far-field radiated noise characteristics
A multi-bladed propeller was also to be designedwith a diameter one foot less than the referencepropeller. This propeller was to be designed with thesame, or very similar, aerodynamic performancecharacteristics as the reference propeller. The noise
characteristics between the two would be compared andthe weight penalty estimated in the same manner aspreviously described.
The results of this investigation were to yield anew quiet GA propeller design that would significantlyreduce the far-field radiated noise with minimalaerodynamic and weight penalties. Included will be thepredicted far-field frequency spectrum noise andaerodynamic characteristics as well as the weight
Reference Propeller Design
For a fixed pitch propeller there are threedesirable characteristics required in selecting a bladeshape. They are; large maximum sectional liftcoefficient (Clmax), good trailing edge stallcharacteristics and smooth pressure distribution. Thepropeller advance ratio J is given by the relation,
J = Vo/nD (1)where V0 is the free-stream speed, n is the propellerrotational speed in rev/sec and D is the propellerdiameter. At zero advance ratio, i.e. when V0 is zero,the propeller is in a highly stalled condition. Thisrequires that the airfoil shape have a large CLmax toachieve large thrust levels and significant C, at anglesof attack (a) larger than where Clmax occurs. Thesestall characteristics are indicative of trailing edge stall.The NACA 44XX series of airfoils exhibit thesedesirable characteristics as can be observed in viewingFigure 1 where experimentally obtained Q is plotted asa function of a for a NACA 4412 airfoil.4
«U«g.)
Figure 1. Sectional lift coefficient C, versus angle ofattack a for NACA 4412
935American Institute of Aeronautics and Astronautics
For example, at a J of zero and r/R of 0.5, the referenceblade has an a of 24.8°, review of Figure 1, reveals a Qof 1.25. This airfoil series also exhibits smoothpressure distributions at small a which results in asmooth distribution of radiated noise tones at blade-passing-frequency (BPF) and harmonics.5
Shown in Table 1 is the distribution of airfoilsections for the propeller as a function of radial positionr/R where r is the radial position measured from thecenter of rotation and R is the blade tip radius which istaken to be 38 inches. Thus, the reference propeller is atwo bladed propeller with a tip diameter of 76 inches.The other design criteria are a free-stream speed of160kts and a propeller rotational speed of 2,400 rpm,resulting in a design advance ratio J of 1.07. Alsoshown in this table are the blade chord c, blade angle Pand sectional lift coefficient Q as a function of r/R.Inspection of this table shows that the NACA 4406airfoil is used at the tip and the airfoil thicknessincreases as r/R decreases until the NACA 4418 airfoilis used at a r/R of 0.2. It is assumed that the spinnerradius will be located at r/R of 0.2. The blade tippossesses an elliptical shape starting at r/R of 0.8, i.e.the outer 7.6 in. of the blade tip. Shown in Figure 2 isthe blade angle distribution, i.e. P is plotted as afunction of r/R, for the reference propeller. Presentedin Figure 3 is a top view of the blade planform shape ofthe reference blade as well as a leading edge view.
330&
06r/R
Figure 2. Beta versus r/R for reference propeller
Leading Edge View
Blade6.5-44s
Table 1. Blade angles p, chord c, and sectionallift coefficient C, as a function of radial positionr/R at a design advance ratio of 1.07.
Because of interest in determining any weightpenalty associated with quiet GA aircraft propellers, thepropeller volume is determined for all propeller designsreported. This volume is based upon a right circularcylinder located from r/R of 0.2 to r/R of 0.1 which iswhere the 6 in. diameter, 3.25 in. thick hub starts. Thishub has a 2.25 in. diameter hole at the centerline and 6mounting holes of 0.5 in. diameter equally spaced on a4.5 in. bolt circle diameter. Based upon these criteria,the volume for the 2-bladed reference propeller is 296.2in3 which is equivalent to approximately 30 Ib for thepropeller fabricated from solid cast aluminum. Thisweight compares to 35 Ib for the solid cast aluminumSensenich propeller of 74 in. diameter used for thePiper Cherokee 165.
Shown in Figure 4 are the propeller aerodynamicperformance characteristics where the thrust coefficient
936American Institute of Aeronautics and Astronautics
CT, power coefficient CP) and efficiency t| are plottedas a function of advance ratio J. The CT, CP, and r\parameters are given by the following relationships.
CT = T/pn2D4
CP = P/pn3D5
r, = (CT/CP)J
(2)
(3)
(4)This design is based on a free-stream speed of 160 kts,blade tip diameter of 76 inches, and propeller rotationalspeed of 2,400 rpm, which results in a design advanceratio of 1.07. Inspection of this figure reveals that atthe design J of 1.07, CT is 0.0447, CP is 0.00542, and r)is 87.9%. These aerodynamic performance coefficients,at standard sea-level conditions, result in a thrust of259.6 Ib and power of 145.0 hp which gives a thrust topower ratio (T/P) of 1.79 Ib/hp. Because of the tablescalculated in the ANOPP-PAS programming format,aerodynamic performance parameters less than a J of0.55 are not accurate but at least give a general view ofperformance. Because of the airfoils used in thedesign, CT should not be less than 0.07 at zero advanceratio assuring good take-off performance. The predictedpower of 145.0 hp actually constitutes the requiredpower for level flight which is based on approximately70% of the assumed available power of about 200 hp.This excess power is required for climbing andmaneuvering.
0.4 <L5 <L« 0.7 <LAdvance Ratio - J
Figure 4. Aerodynamic performancecharacteristics for reference propeller.
In comparing the predicted reference propelleraerodynamic performance parameters with publishedpropeller data, it is readily clear that the design is veryadequate for GA aircraft.6'7% 8 This reference propellerwill function as well or better, than presentlymanufactured GA aircraft propellers.
Reference Propeller Radiated Noise CharacteristicsShown in Figure 5 is the far-field unweighted
over-all-sound-pressure-level (OASPL) in decibels,with respect to 20 jaPa, predicted at ground level withthe aircraft flying overhead in level flight at an altitudeof 1000 ft, for the reference propeller. This noiseprediction is with the microphone placed 1.2 metersabove the ground, at the origin of the refernce frame.The maximum predicted unweighted OASPL of 76.9dB shown in this curve is equivalent to an A-weightedlevel of 65.9 dBA.As expected, the maximum OASPLoccurs shortly after the aircraft has passed the nearestpoint of approach because of the directivitycharacteristics of the radiated noise of propellers. It iswell known that the maximum radiated propeller noiseoccurs slightly behind the propeller plane of rotation.9
Figure 5. Far-field radiated noise at 1000 ft.(OASPL vs. time) for reference propeller
Presented in Figure 6 is the predicted unweightednear-field OASPL plotted as a function of directivityangle. The directivity angle is measured from directlyin front of the propeller in a vertical plane, i.e. directlyahead is zero degrees, in the plane of propeller rotationis 90° and directly behind is 180° as shown in Figure 7.All near-field noise predictions reported in this paperare located in a vertical plane at a distance of 5R (fivepropeller tip radii) of the propeller center of rotation. Adistance of 5R is 15.8 ft which is equivalent to 1.13 of awave length at standard sea-level conditions and ablade-passage-frequency (BPF) of 80 Hz. Inspection ofthis curve indicates that the maximum near-fieldOASPL of 111.2 dB occurs at a directivity angle of105°. At this position, the maximum A-weightedOASPL is 96.4 dBA.
937American Institute of Aeronautics and Astronautics
Figure 6. Near-Field OASPL re: 20 uPa as afunction of directivity angle
180 dcg.
Figure 7. Sketch of directivity angle y.
Shown in Figure 8 is the near-field sound-pressure-level (SPL) plotted as a function of harmonicnumber for the same prediction as presented in Figure6, at a directivity angle of 105°. This figure constitutesthe frequency spectrum where the harmonic numberindicates the integer times BPF, e.g. a harmonicnumber of three constitutes the tone at three times BPFof 80 Hz or 240 Hz. Inspection of this curve revealsessentially a monotonic decrease in the magnitude ofthe tones with the maximum occurring at BPF which isindicative of a smooth blade pressure distribution.Presented in Table 2 are the contributions of thethickness noise and the loading noise, both of which arelisted as a function of harmonic number and tonalfrequency, for the same near-field case as presented inFigure 8. This table shows that the loading noisedominates thickness noise at BPF and 2BPF, areessentially equal at 3BPF and at tones of 4BPF andgreater, that thickness noise dominates. Thisinformation indicates that the unweighted OASPL isdominated by blade loading noise, but that the A-
10
weighted OASPL is dominated by thickness noise.This phenomenon occurs because the A-weightingfunction greatly attenuates the low frequency tones, e.g.at BPF the actual SPL is reduced by 22.5 dB. Thereason that the sum of the loading and thickness noiseare less than might be expected is because of the phasedifference between the two components.
Effects of Tip Shape on Radiated NoiseCharacteristics
The elliptical tip shape used in the referencepropeller is based upon a study where the referencepropeller tip shape is varied and the radiated noisepredicted and the results compared. For the casesstudied, the nominal thrust is 260 Ib and the nominalpower is 145 hp, all within a couple of percent of eachother. For the elliptical tip, the ellipse is faired into theblade such that maximum thickness is located wherethe blade chord is 6.5 in. and 7.6 in. from the blade tip.The blade chord is zero at the tip for the elliptical tip. Ina similar manner, a parabolic tip is analyzed. The thirdcase is a circular tip where the radius is half the chordof 6.5 in. with the blade chord being zero at the tip.The fourth case is a square tip where the 6.5 in. bladechord remains the same all of the way to the blade tip.
Shown in Table 3 is the maximum unweightedand A-weighted OASPL for fly-by at 1000 ft in levelflight, i.e. far-field, and the near-field at 105° directivityangle, for the different blade tip shapes considered inthis investigation. This blade tip evaluation is with the2-bladed, 76 in. diameter propeller rotating at 2,400rpm in a free-stream flow field of 160 kts. Inspection ofthis table shows that the near-field unweighted OASPLfor all tip configurations are 111 dB with minorvariations, but for the A-weighted far-field OASPL, thesquare and circular tip are 97.5 dBA and the OASPLfor the parabolic and elliptical tips are respectively 1.5dBA and 0.7 dBA less.
Table 3. Unweighted and A-weighted OASPLfor maximum fly-by levels and near-field levelsat a directivity angle of 105°, for different bladetip shapes.
Max. OASPL
Near-Field, dB
Near-Field, dBA
Far-Field, dB
Far-Field, dBA
Square
1 1 1 . 1
97.5
84.5
72.3
Circular
1 1 1 . 1
97.5
84.5
73.9
Parabolic
110.6
96.0
83.5
69.9
Elliptical
110.9
96.8
84.0
73.5
Table 3 also shows that the unweighted far-fieldOASPL for the square and circular tips are 84.5 dB andthe OASPL for the parabolic and elliptical tips arerespectively 1.0 dB and 0.5 dB less. For the A-weighted far-field OASP, the circular tip is the noisiestat 73.9 dBA and the levels for the elliptical, square andparabolic tips are respectively 0.4 dBA, 1.6 dBA, and2.4 dBA less.
The difference between the unweighted and A-weighted OASPL is due to the differences in thicknessnoise and loading noise frequency distribution aspreviously discussed. In three of the four noisecatagories, the parabolic tip resulted in the lowest noiselevels and the elliptical tip resulted in the secondquietest configuration. Due to these noisecharacteristics, the final selection of the tip shape isnarrowed down to the parabolic and elliptical tipshapes. The parabolic blade is eliminated fromconsideration due to its transition characteristics i.e. theintersection of the parabolic tip distribution and theconstant blade chord results in a sharp corner on theblade. This corner will inherently cause problems inmanufacturing and creates problems due to stressconcentrations. In summary, the elliptical tip shape ischosen to be the best configuration based upon noiseand manufacturing considerations.
Aerodynamic Performance Characteristics of theReference Propeller Rotating at 2.700 rpm
When rotating the reference propeller at 2,700rpm, the propeller advance ratio decreases from 1.07 to0.95. Referring to Figure 4, the curves indicate that thenew advance ratio will result in aerodynamicperformance characteristics where CP is 0.075, CT is0.0679 and an efficiency of 87.0%. These quantities atstandard sea level conditions, result in a thrust of 394 Iband power of 200 hp, which gives a thrust to powerratio of 1.96 Ib/hp.
Noise Characteristics of the Reference PropellerRotating at 2.700 rpm
Rotating a 76 in. diameter propeller at 2,700 rpmwhile generating lift at the tip will always result inshock waves being formed which, of course, generatesa considerable amount of noise. The airfoils near thetip for the reference propeller are designed to have asectional lift coefficient of 0.40, as can be seen byreviewing Table 1, while rotating at 2,400 rpm. Atthese conditions, a study of the pressure distributionreveals that the peak flow velocity near the tip is 0.92Mand, therefore, no shock waves will form on the bladetip.
Shown in Figure 9 is the fly-by OASPL radiatednoise characteristics of the reference propeller rotatingat 2,400 rpm and 2,700 rpm. Inspection of these curvesindicate that at 2,700 rpm, the OASPL is higher than at2,400 rpm by approximately 6 dB during approach and9.5 dB greater at the peak level as well as during thedeparture. Actually, the noise is 3 dB to 10 dB greaterthan predicted because the ANOPP-PAS program
939American Institute of Aeronautics and Astronautics
predicts the noise associated with the shock waveinteraction with the blade but not the direct radiationfrom the shock nor the shock oscillation.5''°
Figure 9. Flyover OASPL far-field radiatednoise characteristics of reference propellerrotating at 2,400 rpm, and 2,700 rpm.
Presented in Figure 10 is the predicted frequencydistribution of the near-field SPL for the referencepropeller rotating at 2,400 rpm and 2,700 rpm, both at adirectivity angle of 105°. It is important to note thatBPF at 2,400 rpm is 80 Hz and at 2,700 rpm BPF is90Hz, hereafter referred to as BPF,0 and BPFhirespectively. Review of this figure reveals that at thefirst tone that BPFhi is approximately 8 dB greater thanBPF,0 and the decibel difference steadily increases tothe highest harmonic tone at 20BPFhi (1,600 Hz) whichis approximately 34 dB greater than 20BPFlo (1,800Hz). For the data shown in Figure 10, the unweightedOASPL is 111.2 dB at 2,400 rpm and is 9.6 dB greaterat 2,700 rpm, while the A-weighted OASPL is 96.4dBA at 2,400 rpm and is 14.0 dBA greater at 2,700rpm.
|R*I Blade. 2700 RPM|g«f Bl»d«, 2400 RPM
Frequency {harmonic number)
Figure 10. Frequency Distribution of Near-Field SPL of the Reference Propeller Rotating at2,400 rpm and 2,700 rpm, both at a DirectivityAngle of 105°.
This comparison clearly shows that shock waveformation creates considerably more noise at the higherharmonics than at the lower ones and has a greateraffect on the A-weighted level than for the unweightedcase. In other words, the effect of shock waveformation will result in a greater increase in the A-weighted level than in the unweighted level.
This comparison clearly shows that large diameterpropellers should be designed in such a manner thatshock waves are not formed at the tip. A 76 in.diameter propeller should not be operated at rotationalspeeds greater than approximately 2,400 rpm. Clearlythe reference propeller is designed to meet this lownoise criteria by avoiding tip shock waves duringaircraft operations.
Effects of Inplane Sweep
It has been well established that swept propellerblades can reduce propeller noise using both inplaneand out-of-plane sweep."' l2 The basic concept is thatthe noise source is distributed over the propeller bladesource13'' and that there can be noise cancellation at apoint away from the propeller because of acousticpressure wave cancellation. ' ' The scimitar shapedblades used on the ultra-high bypass prop-fan aredesigned based upon this concept using both inplaneand out-of-plane sweep.
The investigation being reported considersonly inplane sweep because of the difficulty ofmanufacturing propeller blades with out-of-planesweep. Three basic sweep configurations areconsidered all of which use the reference propeller, i.e.the 2-bladed configuration previously discussed.Sweep is incorporated into the reference propellerdesign by creating an ellipse and then forcing theleading edge of the reference propeller to follow onequarter of its elliptical arc. The trailing edge was thendefined from the new leading edge with equivalentchords from the reference propeller. This methodtransforms the elliptical tip shape such that the leadingedge is drastically elongated and the trailing edge isslightly elongated and straightened. The degree ofchange due to sweep of the reference blade is thendependent on the chosen sweeping ellipse and thelocation of where it was incorporated into the design.The first configuration is based upon the sweep startingat the 0.2 r/R position sweeping aft and is called fullsweep, with the designation IPSE following by anumber designating the amount of sweep displacementat the tip in inches, e.g. IPSE-3 means 3 inches of tipsweep. The IPSE configurations are evaluated with
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3in., 6.5 in. and 13 in. of tip sweep. The second basicconfiguration consists of the aft sweep starting at 0.5r/R position and designated as HIPSE with a tip sweepof 6.5 in. only. The third configuration consists of aftsweep starting at the 0.75r/R position which isdesignated as QIPS with tip sweep of 6.5 in. and 9.75inches. Shown in Figure 11 is the twisted planformview for all of the configurations discussed, labeledwith the appropriate configuration designation. Thereare many other swept configurations that could beevaluated including forward sweep near the hub and aftsweep near the tip.6
HIPSE 6.5
QIPS 65
QIPS 9.75
Figure 11. Planform View of all Swept BladeConfigurations Evaluated.
-15 -10
Figure 12. Far-field OASPL at 1000 ft for Hipse6.5 and reference propeller configurations.
Shown in Table 4 is the maximum far-field andnear-field OASPL for all configurations including thereference case. The maximum peak far-field OASPL ispredicted during fly-by at a 1000 ft altitude and thenear-field OASPL is at a 105° directivity angle.Inspection of this Table reveals that sweep does reduceboth the far-field and near-field unweighted and A-weighted OASPL. The HIPSE-6.5 and QIPS-9.75swept configurations exhibit the lowest noise levelsrelative to the reference propeller. For example relativeto the reference propeller, the HIPSE-6.5 in the far-field is 0.6 dB and 2.2 dBA quieter, and in the near-field is 0.5 dB and 1.4 dBA quieter.
The far-field fly-by OASPL as well as the near-field OASPL and SPL frequency spectrum noise levelsare evaluated for all swept configurations and the thrustand power at cruise conditions are all within 2% of thereference propeller. Shown in Figure 12 is theunweighted far-field OASPL at fly-by during levelflight at 1000 ft altitude for the HIPSE-6.5configuration as well as the reference propeller.Comparing the two OASPL curves in this presentationreveals that the swept blade is 1.0 dB quieter than theunswept case during approach and at the peak levels,while during departure very little difference is seen inthe OASPL.
Table 4. Maximum OASPL, Near and Far-Field,for all Blade Configurations.
F«r OASPL(dB)
Fur OASPL(dBA)
Nor OASP(dB)
Nr. OASPL(dBA)
Ref.Prop.76.9
65.9
111.2
96.4
IPSE3
76.6
65.5
111.0
96.0
IPSE 6.3
76.3
65.2
110.9
95.6
IPSE 13
76.0
65.0
111.0
95.4
QIPS6.576.0
64.6
110.7
95.0
QIPS9.7575.5
64.0
110.4
94.3
HIPSE6.576.3
63.7
110.7
95.0
For the cases considered it appears the greater thesweep the lower the noise. Based upon thesepredictions, the HIPSE-6.5 configuration isrecommended because it exhibits superior noisereduction characteristics than the reference case, i.e.that it is significantly quieter in the far- and near-fieldsespecially in the A-weighted case. The half-swept with6.5 in. of tip sweep (HIPSE-6.5) configuration is alsoeasier to manufacture than the full-swept (IPSE) andquarter-swept (QIPS) configurations.
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Two-Bladed NLF PropellersDesign Using Natural-Laminar-Flow (NLF) Airfoils
Airfoil skin friction at high Reynolds numbers hasbeen significantly reduced by the successful design ofairfoil shapes that exhibit large regions of laminarboundary layer flow on both the upper and lowersurfaces.17' '* It was decided to design propellers usingthese NLF airfoils in the hope that there would be anincrease in propeller efficiency because of the reductionof airfoil parasite drag. It was also of interest todetermine if NLF propellers would exhibit lower noisecharacteristics than propellers using more conventionalNACA airfoil sections.
Jeffrey Viken of Innovative AerodynamicTechnologies (IAT), an NLF design specialist, anddesigner of the NASA NLF(1)-0414F airfoil, designeda set of NLF airfoils for propellers based upon the samesize and with the same performance characteristics aswas used to design the reference propeller. Based uponthe sectional lift coefficient and Reynolds numberdistribution required as a function of blade radialposition, Mr. Viken designed the NLF airfoils aslabeled in Table 5 as a function of radial position r/Rfor the 2-bladed NLF propeller. Inspection of this tableindicates a twist angle ((3) and sectional lift coefficient(Q) distributions very similar to that used for thereference propeller.
Table 5. Blade angles, chord and lift coefficientas a function of radial position for 2-bladed NLFpropeller.
a t/c of 12.75% at a r/R of 0.5 and 0.6, the jv-prop.70with a t/c of 10.5% from a r/t of 0.7 to 0.8, the jv-prop.85 with a t/c of 8.25% at r/R of 0.85 and 0.9, andthe jv-prop.95 with a t/c of 6.75% at r/R equal to andgreater than 0.95. To gain insight into the unique shapeof the NLF airfoil shapes, the NACA 44XX series andthe jv-prop series are presented side by side in Figure13 at various radial positions. For example, theNACA-4406 airfoil is plotted next to the jv-prop.95airfoil both of which are used near the blade tip at aradial position of 0.95 r/R, noting that the NACA airfoilis used on the reference propeller.
Investigation of Table 5 reveals that the jv-prop.20 airfoil with a maximum thickness of 18%, isused at a r/R of 0.1 and 0.2, the jv-prop.40 with a t/c of15% is used at a r/R of 0.3 and 0.4, the jv-prop.55 with
Figure 13. Comparison between NACA 44 and NLFseries airfoils.
Aerodynamic Performance of 2-Bladed PropellerUsing NLF Airfoils
Shown in Figure 14 is the propeller aerodynamicperformance characteristics for the straight 2-bladedpropeller with the NLF airfoils, where the thrustcoefficient CT, power coefficient CP, and efficiency \\are plotted as a function of advance ratio J. Thispropeller essentially exhibits almost identicalaerodynamic performance characteristics as thereference propeller. Both propellers are 76 in. diameterrotating at 2,400 rpm at a cruise speed of 160 kts,resulting in a cruise advance ratio J of 1.07. Inspectionof Figure 14 reveals a thrust coefficient CT of 0.0447,power coefficient CP of 0.0537, and efficiency of88.7%. At standard sea-level conditions and level flightof 160 kts, these coefficients result in a thrust of 143.6hp and 259.4 Ib compared to 145.0 hp, and 259.6 Ib atan efficiency of 87.9%. for the reference propeller.This comparison shows that the straight 2-bladedreference propeller exhibits approximately the samethrust and power as the NLF propeller but is
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approximately 1% more efficient. The implication isthat using the low drag NLF airfoil sections in thedesign of a propeller increases the efficiency of thepropeller by approximately 1% while generating nearlyidentical aerodynamic performance characteristics.
Shown in Figure 15 is the far-field unweightedOASPL levels for both the straight 2-bladed NLF andreference propellers for fly-by at an altitude of 1000 ftand a speed of 160 kts in steady level flight. Bothpropellers are rotating at 2,400 rpm. In comparing thetwo curves in this figure it is clear that the OASPL arenearly identical near and at the peak levels, but that theNLF propeller is slightly quieter during approach thanthe reference propeller and slightly noisier during thedeparture. At least for the unweighted case, there areno significant differences in the far-field OASPLbetween the NLF and reference propellers.
r
«* 60
rv Ref Prop, 2400 rpm]LNLFBWi I
Figure 15. Fly-by unweighted OASPL far-fieldradiated noise characteristics of straight 2-bladedNLF propeller and ref. propeller at 2,400 RPM.
Presented in Figure 16 is the frequency spectrumof the near-field unweighted SPL for both the 2-bladedNLF propeller and reference propeller rotating at 2,400rpm and directivity angle of 105°. Comparison of thebar charts in this figure indicates that at BPF, i.e.harmonic number of one, that the SPL for both are thesame but that as the harmonic number increases, theSPL for the NLF propeller progressively gets largerthan the reference propeller as the harmonic numberincreases. In fact, at harmonic number of 20, i.e.20BPF, the SPL of the NLF propeller is approximately7 dB greater than for the reference propeller. As statedearlier, the thickness noise dominates the loading noiseat the higher harmonics and comparing Table 1 withTable 4, shows that the thickness distribution as afunction of radial position is different between theNACA 44 series and jv-prop (NLF) airfoil sections.Review of Figure 13, where sketches of both theNACA 44 series and the jv-prop airfoils are shown atvarious radial positions, there are significant volumedifferences between the two airfoil series. Because ofthese geometrical differences, it is not surprising thatthe thickness noise is significantly different and is thereason why the SPL at the higher harmonics is greaterin the NLF propeller than the reference propeller.
Figure 16. Frequency Distribution of Near-Field Unweighted SPL for the NLF Propellerand the Reference Propeller rotating at 2,400RPM and at Directivity Angle of 105°.
Because of the importance of the A-weightednoise levels, Table 6 is presented to show theunweighted and A-weighted OASPL for maximum fly-by levels and near-field levels at a directivity angle of105°, for the straight 2-bladed NLF propeller and thereference propeller as well as as the HIPSE-6.5 andswept NLF propellers. Both the HIPSE-6.5 and theswept NLF propellers have the same sweep, that is 6.5in. of aft sweep starting at the 0.5 r/R radial position.
943American Institute of Aeronautics and Astronautics
Table 6. Unweighted and A-weighted OASPLfor maximum fly-by levels and near-field levelsat a directivity angle of 105°, for straight andswept 2-bIaded NLF propeller and referencepropeller.
the two and three-biaded reference propellers are thediameter and the blade angle distribution. The airfoilsections and sectional lift coefficients for the three-bladed propeller are shown in Table 7 which are thesame as the two-bladed propeller.
Table 7. Blade angles,as a function of radialreference propeller.
chord and lift coefficientposition for the 3-Bladed
All four of these 2-bladed configurations exhibitaerodynamic performance characteristics within 2% ofeach other. Inspection of this table indicates that theunweighted far-field OASPL of the reference propelleris 76.9 dB and the unswept NLF propeller is 0.2 dBnoisier while the HIPSE-6.5 and swept NLF propellersare respectively 1.0 dB and 0.6 dB quieter. The far-field A-weighted OASPL of the reference propeller is65.9 dBA and the unswept NLF propeller is 0.2 dBAnoisier while the HIPSE-6.5 and swept NLF propellersare respectively 1.3 dBA and 2.2 dBA quieter, i.e. bothswept configurations are significantly quieter thaneither swept configuration when comparing the A-weighted levels. The near-field differences are not assignificant when the swept NLF propeller generates thesame A-weighted levels as the reference propeller andthe HIPSE-6.5 is 1.5 dBA quieter. This comparisonindicates that both the HIPSE-6.5 and swept NLFpropellers are generally quieter and that the A-weightedlevels are significantly quieter, than the referencepropeller.
3-Bladed PropellersTip speed is a significant factor in propeller noise.
One way to reduce tip speed, is to reduce propellerdiameter while maintaing the same rotational speed.To achieve the same performance with a smallerdiameter, it is necessary to increase the number ofblades. The reference 3-bladed propeller has adiameter of 64 in., or one foot less than the reference 2-bladed propeller. The reference 3-bladed design issimilar to that of the 2-bladed design in that the chord isconstant from the spanwise position of r/R = 0.2 to 0.8,at which point the shape becomes elliptical. The chordlength from 0.2 to 0.8 is 7.5 inches. The design criteriaare the same as that for the two-bladed propeller, i.e.free-stream speed of 160 kts and a propeller rotationalspeed of 2400 rpm. The primary differences between
Based upon the same hub size and shape as thetwo-bladed propeller, the volume of the 3-bladedstraight NACA propeller is 439.8 in3, which isequivalent to approximately 44.0 Ib for the propellerfabricated from solid cast aluminum. This weight isapproximately 14.0 Ib greater than the 2-bladedreference propeller. A weight increase is expected,even though the diameter is one foot less, due to theaddition of a third blade, and the increase in averagechord length. The 3-bladed propeller weight can befurther reduced by increasing the blade angle whiledecreasing the chord. This design change can result inreduced take-off performance, i.e. low advance ratios,because of increased blade stall angles.
Aerodynamic Performance of 3-Bladed PropellerUsing NACA Airfoils
Shown in Figure 17 are the propeller aerodynamiccharacteristics, CT, CP and r\ as a function of advanceratio J, for the 3-bladed straight propeller. The designadvance ratio for the 3-bladed configuration, operatingat 2400 rpm, free-stream speed of 160 kts and blade tipdiameter of 64 inches, is 1.27. The figure reveals thatat the design advance ratio, CT is 0.0899, CP is 0.1330,and r) is 85.6%. These aerodynamic performancecoefficients at standard sea-level conditions result in athrust of 262.4 Ib and power of 150.6 hp, which gives athrust to power ratio (T/P) of 1.74 Ib/hp. It is important
944American Institute of Aeronautics and Astronautics
to note, that while these values for thrust and powercoefficient seem very high compared to the valuesobtained for the 2-bladed propeller, the relationshipsgiven earlier in Equations 2 and 3, are a function ofdiameter to the fourth and fifth powers respectively.Thus, the decreased blade diameter results in the thrustand power presented above. The thrust for the 3-bladedstraight propeller is approximately 1% greater than thatproduced by the 2-bladed reference propeller.However, the required power is 3.8% higher than thatrequired for the 2-bladed configuration, and this higherpower requirement is reflected in the efficiency, whichis 2.3 % lower.
It 0.1 (12 »J (1.4 «_S (1.6 11.7 (Wt ti-9 1 1.1 1.2 U 1.4 1J
Advance Ratio - J
Figure 17. Aerodynamic performancecharacteristics for straight 3-bladed referencepropeller with NACA 44!! airfoils.
Noise Characteristics of 3-Bladed NACA Propeller
Shown in Figure 18 is the far-field unweightedOASPL in decibels, for both the 2-bladed referencepropeller and the straight 3-bladed propeller, predictedat ground level for fly-by at an altitude of 1000 ft and aspeed of 160 kts in steady level flight. The maximumpredicted unweighted OASPL of 74.0 dB is equivalentto an A-weighted level of 59.7 dBA. Inspection ofthese curves reveals that the OASPL is 2.9 dB lower atthe peak level than the 2-bladed reference propeller.During approach the levels range from 15.3 to 2.6 dBlower, and up to 14.0 dB lower during departure. Themaximum OASPL occurs shortly after the aircraft haspassed its nearest point of approach, this is consistentwith the characteristics of radiated propeller noise.9
Figure 18. Fly-by unweighted OASPL far-fieldradiated noise characteristics of straight 3-bladedpropeller and 2-bladed reference propeller at 2400RPM.
Figure 19 shows the frequency spectrum of thenear-field unweighted SPL for both the 2-bladedreference propeller and the straight 3-bladed propellerrotating at 2,400 rpm and a directivity angle of 105°.Comparing the two bar graphs shows that at BPF, theSPL of the 3-bladed propeller is 2.6 dB lower than thereference propeller. At harmonics of 12 and greater,the predicted SPL is lower than the threshold ofhearing, therefore Figure 19 only shows up to the 11 thharmonic.
1004
JJ60ffi
Frequency (harmonic number)
Figure 19. Frequency distribution of near-fieldunweighted SPL for the straight 2 and 3 bladedrefernce propellers.
The data in Table 8 shows that for the 3-bladedpropeller, loading noise dominates at BPF only, and atall harmonics of BPF, thickness noise dominates.Further inspection reveals that as harmonic numberincreases, the difference between the 2 and 3-bladed
945American Institute of Aeronautics and Astronautics
propeller becomes more drastic, for example at the 4thharmonic, the difference is 18.6 dB. From the 12thharmonic upward, the SPL for the 3-bladed propellerbecomes negative. This comparison indicates that atharmonics greater than the 12th, the sound pressurelevel is lower than that of the reference sound pressurelevel of 2 x 10~5 Pa which constitutes the threshold ofhearing for humans.
Table 8. Near-field thickness and loading noisecomponents as a function of harmonic number atdirectivity angle of 105° for 3-bladed referencepropeller.
The 3-bladed swept NLF propeller is based on thesame design criteria as the straight 3-bladed propeller.The sectional lift coefficients, and airfoil distributionare the same as defined for the 2-bladed NLF propellerand are shown in Table 9. The blade angle distributionfor the 3-bladed propeller is different than that for the2-bladed propeller.
Based upon the same hub size and shape as thereference propeller, the volume of the 3-bladed sweptNLF propeller is 425.5 in3, which is equivalent toapproximately 42.6 Ib for solid cast aluminumfabrication. This is approximately 1.4 Ib less than the3 bladed unswept propeller, but 13 Ib more than the 2-bladed reference propeller as shown in Table 10 wherethe volume and weight estimations for all of the variousblade configurations are presented. The 2-bladedpropellers all have essentially the same weight, with theonly variations being the two NLF configurations. TheNLF 2-bladed propellers are approximately 0.6 Iblighter than the blades using the NACA airfoils.Presented in Figure 20 is a top view of the bladeplanform shape for the 3-bladed swept NLF propeller.
Aerodynamic Performance of 3-Bladed PropellerUsing NLF Airfoils
Shown in Figure 21 is the aerodynamicperformance characteristics for the swept 3-bladedpropeller using NLF airfoils, where the thrustcoefficient CT, power coefficient CP, and efficiency r|are plotted as a function of advance ratio J. A cruiseadvance ratio of 1.27 results in a thrust coefficient CTof 0.0896, a power coefficient CP of 0.1302, and anefficiency of 87.1%. At standard sea-level conditions,these coefficients result in 261.5 Ib of thrust and apower of 147.4 hp compared to 262.4 Ib and 150.6 hpat an efficiency of 85.6% for the straight 3-bladedpropeller. This propeller exhibits very similaraerodynamic performance characteristics, with nearlyidentical thrust and approximately a 2% decrease inrequired power which translates into a 1.5% increase inpropeller efficiency.
NLF 3-bladed propeller is approximately 1.0 dB noisierthan the 3-bladed reference propeller.
ai 02 cu lu of <i6 0.7 im a9 i 1.1 u u 1.4 is uAdvance Ratio-J
Figure 22 shows the far-field unweighted OASPLlevels for the 3-bladed straight and the 3-bladed sweptNLF propellers for fly-by at an altitude of 1000 ft and aspeed of 160 kts. Both propellers are rotating at 2,400rpm. Similar to the 2-bladed design, these curves showthat the OASPL are nearly identical near and at themaximum level, but that the NLF propeller is slightlyquieter during approach and slightly noisier duringdeparture. There are no significant differences in thefar-field OASPL between the NLF and reference 3-bladed propellers, for the unweighted case. Duringapproach, the unweighted OASPL is approximately 1.9dB lower for the swept NLF propeller, but at the peak,the difference is only 0.5 dB. During the departure, the
I
OA
SP
L
/
I*1"" 30.
10
f# 3 Blade Ref Prep ' i
fc**^ m NLF swept 3Wadei !
V-15 -10 -5 0 5 10 15
Tin. (<)
Figure 22. Fly-by unweighted OASPL far-fieldradiated noise characteristics of straight 3-bladedNLF propeller and reference 3-bladed propeller.
Shown in Figure 23 is the frequency spectrum ofthe near-field unweighted SPL for both the 3-bladedNLF and 3-bladed reference propellers rotating at 2,400rpm and a directivity angle of 105°. This figureindicates that at BPF and its harmonics, that the SPL isessentially the same for both configurations up until9BPF. At 11BPF, the SPL of the NLF propeller isapproximately 6.5 dB greater. Similar to the 2-bladedpropeller, thickness noise dominates the loading noiseat all harmonics except at BPF, and at 2BPF the levelsare essentially the same.
field levels at a directivity angle of 105°, for the 2-bladed reference propeller and the 3-bladed referencepropeller, as well as the swept 3-bladed NLF propeller.The aerodynamic performance characteristics of all 3propellers is within 4% of each other, with the 3-bladed swept propeller having almost identicalefficiency to the 2-bIaded reference propeller. Thetable indicates that the unweighted far-field OASPL ofthe 2-bladed reference propeller is 76.9 dB. The 3-bladed straight propeller is 2.9 dB quieter than the 2-bladed reference propeller, while the swept 3-bladedNLF propeller is an additional 0.5 dB quieter than theunswept 3-bladed case. The far-field A-weightedOASPL of the 2-bladed reference propeller is 65.9 dBAand the unswept 3-bladed propeller is 6.2 dBA quieter,while the swept NLF 3-bladed propeller is 0.8 dBAquieter than the straight 3-bladed propeller. Comparingthe unweighted OASPL for the near-field, the 3-bladedpropeller is 3.9 dB quieter then the 2-bladed propeller.However, comparing the two 3-bladed configurations,the swept NLF 3-bladed propeller is slightly noisier(0.2 dB) then the unswept blade. More significantly, incomparing the A-weighted levels, there is a 4.2 dBAreduction from the 2-bladed reference propeller to the3-bladed reference propeller, we see that the sweptNLF 3-bladed configuration is 0.1 dBA noisier than theunswept 3-bladed propeller.
This comparison shows that the 3-bladedconfiguration is certainly quieter than the 2-bladedconfiguration, however, the swept NLF 3-bladedpropeller is much noisier than the straight 3-bladedpropeller, in terms of A-weighted near-field OASPL.
Table 11. Unweighted and A-weighted OASPLfor maximum fly-by levels and near-field levelsat a directivity angle of 105°, for the 2-bladedreference propeller and both the straight andswept NLF 3-bladed propeller.
Far OASPL (dB)Far OASPL (dBA)Near OASPL (dB)Nr. OASPL (dBA)
Reference2-bladedPropeller
76.965.91 1 1 . 296.4
3-Bladed
Ref. Prop74.059.7107.392.2
Swept NLF3-bladed
prop73.558.9107.592.3
In summary, the 3-bladed 64 in. diameterpropeller results in a far-field OASPL noise reductionof approximately 4.0 dB and 6.0 dBA and near-fieldOASPL of 4.0 dB and 9.0 dBA. This significant noisereduction is achieved with essentially no degradation inpropeller aerodynamic performance characteristics but
there is an estimated 14 Ib (49%) increase in propellerweight.
CONCLUSIONS
The NASA Aircraft Noise PredictionProgram-Propeller Analysis System (ANOPP-PAS)was used to design quiet two-bladed and three-bladedgeneral aviation (GA) propellers. This theoreticalinvestigation resulted in the following conclusions:1. Based upon noise and manufacturing
considerations, the elliptical blade tip shape wasdeemed best when compared with square,parabolic and circular tips.
2. Using propeller rotational speeds of 2,700 rpm fora 76 in. diameter 2-bladed propeller will alwaysresult in extremely high radiated noise levelsbecause of shock wave formation at the blade tipand that this excessive noise problem does notoccur at 2,400 rpm.
3. Using inplane sweep with a 76 in. Diameter and 2-bladed propeller, resulted in a predicted far-fieldOASPL reduction of 0.6 dB and 2.2 dBA, andnear-field OASPL reduction of 0.5 dB and 1.4dBA when compared to the straight 2-bladed caseof the same diameter. Both propellers wererotating at 2,400 rpm and were designed usingNACA 44XX series of airfoils.
4. Using natural-laminar-flow (NLF) airfoil shapesfor a 76 in. Diameter and straight 2-bladedpropeller, resulted in a one percent increase inpropeller efficiency and slight increases in thenear- and far-field OASPL when compared to thestraight 2-bladed propeller using NACA 44XXseries of airfoils. Both propellers were of the samediameter and rotating at 2,400 rpm.
5. A 2-bladed propeller with inplane sweep and witha blade geometry based upon NLF airfoil shapes,resulted in approximately the same near- and far-field noise levels as for the straight 2-bladedpropeller with NLF airfoil shapes. Both of thesepropellers were of the same diameter and rotatingat 2,400 rpm.
6. A straight-bladed, 64 in. diameter 3-bladedpropeller designed using NACA 44XX series ofairfoils and rotating at 2,400 rpm, resulted inappreciable noise reductions when compared withthe straight-bladed, 76 in. diameter propeller usingthe same airfoil shapes and rotational speed. Thepredicted far-field OASPL noise reductions were2.1 dB and 6.2 dBA, and the predicted near-fieldOASPL noise reductions were 3.9 dB and 4.2 dBA.The propeller aerodynamic performance
948American Institute of Aeronautics and Astronautics
characteristics for the 2-bladed and 3-bladedpropellers were essentially the same but there wasan estimated 49% increase in propeller weight forthe 3-bladed propeller when based upon solidaluminum construction.
7. A swept-bladed, 64 in. diameter 3-bladed propellerdesigned using NLF series of airfoils whencompared with the straight 3-bladed propeller ofidentical propeller diameter and both rotating at2,400 rpm, resulted in a decrease in the far-fieldOASPL of 0.5 dB and 0.8 dBA. The swept-bladedpropeller near-field OASPL was 0.2 dB and 0.1dBA noisier than the straight-bladed propeller.
RECOMMENDATIONSAnechoic wind tunnel tests should be
performed to validate the design and radiated noiseprediction capability of the NASA Aircraft NoisePrediction Program-Propeller Analysis System(ANOPP-PAS). The propeller designs used in thisinvestigation should be used in performing anechoicwind tunnel tests to verify the predicted propelleraerodynamic performance and radiated noisecharacteristics. These model tests would also be usedto develop and verify the radiated noise scaling laws foruse in full scale evaluations. Propeller aerodynamicscaling laws are reasonably well understood but this isnot the case for radiated noise characteristics.Anechoic wind tunnel tests in conjunction with thetheoretical prediction capabilities of the ANOPP-PAScomputer code will allow the development of accuratepropeller radiated noise scaling laws. Thisrecommended validation will result in the ability ofGeneral Aviation (GA) aircraft and propellermanufacturers to use the ANOPP-PAS computer codeto design quiet and efficient propellers with areasonable degree of accuracy and confidence.
These anechoic wind tunnel tests should alsoinvestigate propeller installation effects. The ANOPP-PAS computer code does not have the capability ofpredicting installation effects, therefore, a simplifiednacelle installation algorithm should be developed andincorporated into the code. Incorporating thiscapability will greatly strengthen the ANOPP-PAScomputer code capabilities.
The ANOPP-PAS computer code should alsobe used to design 4-bladed and possibly 5-bladedpropellers, to investigate the practicality of usingsmaller diameter propellers to further reduce radiatednoise characteristics. Needless to say, there will be alimit in reducing propeller radiated noise characteristicsby using smaller diameter multi-bladed propellersbecause of the aerodynamic interaction effects betweenthe propeller and engine nacelle. The present
investigation showed a significant weight penalty using3-bladed instead of 2-bladed propellers, and it is to beexpected that 4-bladed and 5-bladed propellers wouldresult in very large weight increases even though theaerodynamic performance penalties might be minimal.
Further inplane and out-of-plane sweepdesigns should also be studied to determine the fullcapability of using sweep to reduce radiated noisecharacteristics for GA aircraft propellers. These futurestudies must look carefully at the practicality ofmanufacturing highly swept-propeller blades as well asthe strength characteristics. It is easy to envision a casewhere a highly swept propeller was designed that wasefficient and quiet but would experience blade failurebecause of inadequate strength capabilities.
ACKNOWLEDGMENTS
The authors wish to acknowledge the fundingsupport that made this study possible. Funding wasthrough the NASA Lewis Research Center via a STTRPhase 1 contract (NAS3-27768) with AeronauticalTesting Services. Without the NASA LangleyResearch Center supplying the ANOPP-PAS computercode, this study would not have occurred.
REFERENCES
'Hubbard, H. H., "Aeroacoustics of Flight Vehicles:Theory & Practice," NASA RP-1258, 1991.2Rathgelber, R. K., and Sipes, D. E., "The Influence ofDesign Parameters on Light Propeller Aircraft Noise,"SAE-770444, 1977.3Nystrom, P. A., and Farassat, F., "A NumericalTechnique for Calculation of the Noise of High SpeedPropellers with Advanced Geometry," NASA TP 1662,1980.
"Jacobs and Pinkerton, "Tests of NACA Airfoils in theVariable Density Wind Tunnel", Series 44 and 64"NACATN-401, 19313Farassat, F., "The Unified Acoustic and AerodynamicPrediction Theory of Advanced Propellers in the TimeDomain," AIAA J., Vol.24,1986, pp. 578-584.6Borst, Henry V., Volume 1, "AerodynamicPerformance and Installation", USAAMRDL TR-73-34A, 19737Dwinnell, J. D., "Principles of Aerodynamics,"McGraw-Hill, 19498Mises, Richard Von, "Theory of Flight," New York:Dover Publications, 1959
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9Goldstein, M.E., "Aeroacoustics", NASA SP-346,1974.
'"Richards, E. J., and Mead, D. J., "Noise and AcousticFatigue in Aeronautics," Wiley, 1968.
"Metzger, F. B., "A Review of Propeller NoisePrediction Methodology 1919-1994," NASA CR198156, June 1995.
'2Metzger, F. B., "An Assessment of Propeller AircraftNoise Reduction Technology," NASA CR 198237,August 1995.
'3LighthilI, M. J., "On Sound GeneratedAerodynamically: I. General Theory," Proc. R. Soc.London, Ser. A, Vol. 211, 1952, pp. 564-587.
'4Fowcs Williams, J. E. and Hawkings, D. L., "SoundGeneration of Turbulence and Surfaces in ArbitraryMotion," Philos. Trans. R. Soc. London, Ser. A., Vol.264, 1969.15Hanson, D. B., "Compressible Helicoidal SurfaceTheory for Propeller Aerodynamics and Noise," AIAAJ. Vol. 18, pp. 1213-1220.16Succi, G. P., "Design of Quiet Efficient Propellers,"SAE Tech. Paper 790584, 1979.i7Mcghee, R.J., Viken, J.K., Pfenninger, W., Beasley,W.D. and Harvey, W.D.: "Experimental Results for aFlapped Natural Laminar Flow airfoil with HighLift/Drag Ratios," NASA TM-85788, 1984.l8Sewall, W.G., McGhee, R.J., Viken, J.K., Waggoner,E.G., Walker, B.S. and Millard, B.F.: "Wind TunnelResults for a High-Speed, Natural Laminar FlowAirfoil Designed for General Aviation Aircraft," NASATM-87602, 1985.
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