The Problem of Noise Reduction with Reference ... - CAFE Foundation

INATIONALADVISORY COMMITTEE .FOR AERONAUTICSTECHNICALNOTENo ● 1145 —..-THE PROBLEM OF NOISE REDUCTION WITH●ỊREFERENCE TO LIGHT AIRPLANESBy Theodore Theodorsen and Arthur A. RegierLangley Memorial Aeronautical LaboratoryLangley Field, Virginia●\fJBF?AFw(Twd. -— rwJws#L&c~~ uWIMP ON,=3!!WashingtonAugust 1946—

NATIO?-AIJADVISORY COMMITTEE FOR AERONAUTICSTECHNICAL N3TE NO. 1145THE PROBLEM OF 1:01SE FEDUCTION J’~TT~REFERENCETO LIGET AIRPLANESBy Theodore T!heodorsen and Arthur A. Re@erSUMMMW —.Experiments by Demlng at the Langley MemorialAeronautical Laboratory confirm completely the formulaof Gutfn, which pertits the convenient C&lCUl&ti On Ofthe sound level of any airplane propeller at low forwardspeeds. A simplification of the Gutin formula has beenachieved by the use of a set of functions gi~ing thesound level in the direction of maximum intensity. Thesound level can be read from graphs of W functionsfor various numbers uf blades and tip speeds.Two numri cal examples and one experimental exmpleare included;’ also, a radical fan-type propeller istentatively treated.Results of this study show that propeller noisedominates engine exhaust noise even though the exhaust —noise has a relatively higlhintensity. ,.~tis_ conclti.edstherefore, that In order to reduce the outside soundlevel of an airplane materially, it will be necessaryto modify the propeller to operate at low til speed:and to have a large nmbe r of blades. The practical w-eof this conclusion is a matter of considerable technfcal ““complexity involving many compromises. An effectiveengine exhaust muffler will also be required. .-INTRODUCTION-.The problem of designing airplanes deals chieflywith cost, performance, stabiltty~ safety, ard similarfactors; however, questions have occasionally beenraised concerning the elimination of airplane noise.‘Thisproblem must be considered from the ‘standpoint of

oth the airplane passengers and the people living inthe -71cinity of airports. The airports located nearresidential sections are usually sw.alland can accolimnodateonly light airplanes. The present ?aper emphasizes tkestudy of noise from light airplanes.In 1936 a ‘paper by Gut5-nwas published (reference 1)which gives tke theoretical expression. for the soundemission of’an airolane propeller as a function OJ?speed,number of blades, thrust and torque, end linear dimensionsof the propeller. The formula is, strictly speaking~applicable only to the case of a stationary propeller; inother words, Gutin did not include the effect of theforward or flight speed. It can be shown, however, that’the formula is sufficiently accurate for low forwardspeeds to make it adequate for application to low-poweredairplanes. The theoretical results of Gutin were confirmedby extens!.ve measurements by Deming at theLangley Memorial Aeronautical Laboratory, part of whichhave been reported in reference 20The present paper appliss the Gutin formula toseveral cases of light airplanes~ The formula has beenrewritten in a form convenient for engineering use.The representative sound level 5s obtained by the useof a single graph.The human ear is sensitive to sound energiesrangi lrom about 10-16 watts per square centimeterto lo-Ywatts ner square centimeter, at which Iovelthe sound becomes painful to the listener. Since thepower ratio at the two llmi.ts corresponds to a milliontimes a million, aco~~tic~l workers have adopted alogarithmic scale as a maasure ~f soUnd energy. Theunit of one ‘*decibel”is equivalent to a power r“atioof 1.259, which is the antilogarithm of 0.1. The baselevel. adopted by the Acoustical Society of America.(reference 3) is 10-16 watts per square centimeter. Thesound intensity level hence is given by the formula.c,.-I = 10 loglo —-lo~~6decibels(1).—where P is Dower in watts per square centimeter.Conversely, the rate of energy per square centlm.eter isgiven as9L

(’) &16p=lo..,,watts per square centimeterand, if I is considered as a mean value, tinetotalenergy radiated per cecond is.+16E=4TTT2X1O L) watts (2)where L is the distance from tke source..The sound inten~ity level MY also be ex?ressed interms of tke root -me~-square pressure of the sound byuse of the following rormula:92P- X 10-7 watts ~er squzre‘mcentimeterwhere the root-meane squaz’ep mssure p is in dynes per -square centimeter, the dansity p is in &rms ‘per “cubiccentimeter, and the velacity of sound c is in centirlettir”sper second. Tjmder standard oondi tion~ t% energy levelof 10-16 watts ger square centimeter corresponds to a ‘—pressure of 0.QO02 dyne per square centimeter. Thus thesound intensity level may be expressed as= 74 + 20 Ioglo p decibels (3) ..-. —A pressure of one d~e per square centime txjrc orresp endsto 74 decibels.—.-.The following table conveys a concept of the stepstn the s~~m.d scale by Introducing the effect of distancefrom a given source and by a ccnnpafison with commonlyrecognized sound levels:—3

NACA TN No. 1115tSOUND LEVELFROMSOURCE OF 4T7 WATTS AT VARIOUSDISTANCESANDCOMP&ISON‘WITH KNOWN NOISESAbsorp-t-ion,refraction,[~nd reflection are ne~lected]DistanceSound levelKilometers/ Miles1/’100~Feet32.81Decibels IReferencestandards100 Elevated trains1/10328.of80 Printing press I10.6213280.860 Conversation101006.21362.1340 Dwelling20 I.1000121.3oThresholdSOUND THEORYThe formula for the sound emission from an airplanepropeller is given in an important paper by Gutin,whichwas publlshed in the Physikalische Zeitschrift der Sow.jetunionin 1936 (reference 1), as follows:CQ-2 )( Jqn qn sin (3~) (4)(oRIn this formula the symbols have the following definitions:P root-mean-square sound pressure, dynes per’ squarecentimeter (bars)n number of bladesq harmonic of soundu speed of revolution, radians per second4.-...I■

NACA TN ~!O.1145cLTvelocity of sound, centimeters per seconddistance from propel led-, centimetersthrust, dynes—Qmoment,dyne-centimetersPRJqn(x)vsngle from propeller axis (zero in front)propeller radius (mean value ), centime t6rsBessel function of order qn and argument —.x = qn ~ sin ~velocity of element 01 propeller at 0.8 radius(mean value ), centimeters per secondFigure 1 shows a typical distribution of the pressurefor the lowest harmonic of the sound. Note that the peakpressure is near $ =L20°. .Experiments by Deming (reference2) show virtually ~erfect agreement, particularlywhen the proper reference conditions are used.?3yuse of the O.~ radius as the mean radius and bysubstitution ol?the thrust for the torque, the Gutinformula may be rewritten in the simpler form .—whereBqnP. Rtp=——2v5 L= qnJqn qn ~(Mt 1.7 ~ -h~t2(sin ~)Coa pT’P. = ~ (full value of radius used)‘rfRt)‘qn(5)—‘t‘tradius of propeller (full value)tip Mach number of blade (rotation only)5

NACA TN ijo.114.5M Mach number of advance or of flow velocity throughpropeller disk (vo/c )V.flow velocity through propeller diskThe conversion factor for p expressed tr.poundsper square foot and in dynes per square centimeter ist,1 pound per square foot =’b.78.8 dynes per squar~ centimeter(bars)The formula for p may th8rGf0U0 be writtenP =—.where P. is given in po-..mdsper square foot.,In regard to the quantity %n~ it may be notedthat the subscript qn and the argument qn ~ sin @are related, If fixed values of 1, 0.75, and 0.5 arechosen for v/c and fixed values of 900 and 1200 arechosen for the angle p, the entire quantitymay be plotted against the argument or t’requency qn.i)yusQ of the foregoing values, six curves aue obtained,each @.ven by a double index v/c and p, Whero v/cis tho mean Mach number of the blade and (3 is the anglemeasured from the direction of’advanco as zero, Thesix curves, each labeled accordingly, are shown i.nfigure 2, Since the maximum sound.pressure is obtainodat a value of ~ of approximately 12C?o, the curverelating to this angle generally gives sufficientinformation on the intensity, since the pattern on thewhole repeats itself around-theintensity at Oo and 1800 and inMCos p = 1,7 ~,Mt6origin with zerothe direction for which●✎✜.m

sNACATN NO. ll!#~8By conventio~ the root-mean-square pressure of1 dyne per square centimeter corresponds to a soundlevel of 74 decibels and the sound level at a“presmire Pin dynes per square centimeter is thenI =7~+201f3g.. P decibelsAu(3)In order to obtain the total pressure of s’everalharmonics,it is noted that khe energy is proportionalto pz. Since the cross products contribute nothing,the pz values of the several harmonics may simply beadded and the, square root extracted, The total effectivepressure is thusand the sound level isI = ’74 + 10 loglo y p2 . (7)Only the factor Bqn changes with the harmonic (seeformula (5)); therefore,I = 74 + 20 loglo 169.3p.. . ~.+ 19 lo1310~BqndqRt~Mtl.7&-(Cos p~t2)“,, -—,.(8.)Thisformula may be writtenRt .1 = 118.6 + 20 log — Mt 1.7 —M- Cos p10 Po ~Xtp( )T2+ 10 10glO~Bqn (9).- .—

NACA TN ~0’: 1245●where” PO, which is in pounds per square foot, is theonly dimensional term. Note that formula (9) is veryconvenient to use since the Bessel functions appear onlyin the last term in the form of the sum of the squares.The last term can be given directly for a given numberof blades as .afunctior~ of v/c and the angle ~ only.As mentioned, the peak pressure corresponds to a valueof 9 of about 120°. Because only this peak pressureis referred’ to in the present pa~er, 120° is the valueof @ used. This function has been” plotted for two-,four-, six-, and eight-blade propellers in figure 3, which—gives directly the quantity 10 loglo L‘ Bqn2.qBecause the Gutin formula was developed for an airplaneresting on the ground, strictly speaking it shouldnot be used for the flight or”even the take-off condition.Actually the error is very small so long as the forwardspeed is small com,paredwith the velocity of sound.,.EXAMPLES OY CALCULATIONS AND MEASWFAWNTSCalculations are made for the cruising condition ofa small airplane A having the following specifications:Airplane speed, ‘miles per hour . . . . . . . . . .Horsepower. . . . ., . . . . . . . . . . . . . .Propeller speed, @m, . . . . . . . . ... . . .Fropeller efficiency, percent . . . . . . . . . .Propeller diameter, feet . . . . . . . . . . .Number bf propeller blades : . , ~ . . .. , . . . .Propeller disk loading, Pos pounds persquare foot. . . . . . . . . . . . . . , . . .Airplane Mach numbar, MPropeller-tip b!ach number, “Ml: : : :: : : : ::●J2‘21OO80‘5.8296.6.0980-57The values of Poj M, and Mt were obtained as follows:PowerPo =Airplane velocity X Disk area=1:.6X 550 X ().875x88x Tf60 c X (5.83)2= 6.9 pounds .per square8foot,

..NACA TN No. 145Airolane velocitySpeed of sound_7%, ~ N1120 a“”_. ----0.098Propeller tip speed—— .-.— ~Speed Of’&OU2d2100 ~ 5.t33Tr. ...1120 x~. 57From formula (9), forha. 6tI0.0c)8+ 20 loglo 6.9 x 0.57 1.7 + 0.5i_ (0.57)2..—. —=115.6i-12 -Thevalueofthe next to last term in fOrmula (10)isIogloL = Rt)..-.—.and20 logloX22.01 = 40 (for L= 300 ft )———9

This term gives the distance effect. From figure 3 thevalue of the last term is 10 loglo ‘qn2 = -16 forv&a two-blade propeller at - = o.oll~~e The appropriateMach number is obtained bycusing the 0.8 radius as areference -. station and disregarding the forward speed.Thus, : = o.8~ = 0.455,.The sound inteniity due to the propeller can”nowbe obtained sirmly by adding the four terms on the righthand side of equation (10). J.nthe order given, therirst of these terms is a constant, the second is due tothe disk loading and. Mach number of the al.i’qlaneandthe propeller, the third takss into account the distancefrom the propeller, and the fourth is a function obtainedfrom f’lgure3 for various values of v/c and variousnumbers of blades. In the foregoing example, tbrefore,the sound intensity at a distance cf 1 radius from the .propeller isI =118.6+12-0-16 = 114..6“ daclbelsAt a distance of 300 feet the sound intensity ofpropeller isthe samei—- .—.I = 118.6 + 12 -Lo - 16 = 74..6 decibels‘I%epropeller sound intensities have also been calculatedfor a somewhat larger airplane, which will becalld airplane B, having the following specifications:Airplane speed, miles per hour . . . . . . . . . . 165HorseDower. . , . . . . . . . . . . . . . . . . . Ij3Propeller speed~ rpm . . . . . . . . . . . . . . . ~~r)()Propeller dianeter, feet . . , . i . , . . . . . . 5.5‘Ihedetailed calculations for airplane B are omitted.For comparison. the calculated ~roneller soundintensities ;or aifilsnes A and 1 at’a distance of 3 feetand 300 feet, respectively, are ~ .ven asAirplaneABI at3f~t114.6127I at~OC) feet(db)k*7i7.,..10❑■

NACA TN No. 1145The sound energy radiated frcm the airplane propellermay be obtained by use of formula (2). Forsimplicity, the intensities in all directions are assumedto be constant and equal to the intensity obtained atP = 1200, ti therefore the total energy radiatedthrough the surface of a sphere of 300-foot radius isFor the propeller of airplane A the energy radZated isconsequently=2 wattsand for airplane B ,the energy isStrictly speaking, these figures are too high, since themaximrm intensity at 120° was inserted in the formulasinstead of the mean intensity. On the other”hand, thereflection from We ground generally oaused a doubling ofthe sound intensities, particularly in the horizontalplane. The figures given are therefore reasonablyrepresentative for the sound energy,*Measurements were made on a certain small airplane,which will bs called airplam c, having the followingspecifications:,11

NACA TN ~0, 1145Airplane speed.,tiles per hour . . . . . . . . . . ‘-oHorsepower . . . . . . . . . . . . . . . . . . . . 1Propeller speOd, r,pm . . . . . . . . . . . . . . . 215;Propeller diameter,” feet . . . . . . . . . . . . . 6Number cf propeller blades . . , . ● . . * . . . . 2.xNoise intensities were measured in the oabi.n of thisairplane with a c omnercial portable meter; the absolutereadin(;s are therefore not too accurate. The measurementswere made to give an idea of’the noise level fordif fal’e~tflight cotiitt ons ati.are in t?air agreementv j.t~ ~Elculat~ OKIS made for airplane A, whi ch this airplaneresembles> The data obtained ~or airplane C are as follows:tIIAir;?lane~ou.ndintensityJ?rGpe-Ller(db) speed lsp9ed(mph) (rpm)—.I90 tO 929410698 to 10193 to 958.4925040608565I10CY31500230023ao2150 ,,300TaxiingMagnetoTake-offClimbCm-dsingRemarkscheckNorma 1 glideLard ing approacẖ ---Finallv. a radical modification of air~lane A is.‘plane D, !s supposed.-to efiploy a fan-type propellersThe val~e of the propeller adva,n~eratio Ls i.n_creased~omI?,51Jfor atrplane A to 1.62 for airplane D by reducing thetfp speed of””the propeller in tlm ratio of 3 to 1.efght”ublade fan-t,yp’~. propeller ts chosen for airplane Dto reduce the nols6 level, Tn order to keep the induced1.0ss0s of the propeller at a corlstant value, it isnecessary to increase the disk area fn the ratio of themass coefficients (reference ~.), The mass coef#’icientfor airplane A at cruising speed Is 0! 68. For theprojected eight-blade propeller the mass coefficientis 0.4.0.The disk area must be thus increased in theratio of O,68/0.4.8 or l.hl and the propeller diameter12v .

..NACA TN NO. 11459,68far airplane D becomes 5.83 — = 6.95 feet. Thev- 0.48disk loading p. for airplane D is 69x~=&9powds.0:-68per square foot, and the tip Mach number Mt -‘is-1~x 0.57 =0.19.3The propeller sound pressure for the case of airplaneD is calculated to be abbut 25 decibels at 1 radiusand about -13 decibels at 300 feet. The value of-13 decibels means that the sou@ from the fan-type propellerwould be below the threshold of human hearingssince the threshold under ideal conditions is by definitionat O deoibel. The sound of the pro~eller for qirplaneD would’be inaudible at about 50 feet. Such a_propelle& would,be vefg heavy~ would have to be ,geared~and, since it operates at a high advance ratio~ wouldrequire a v-ariable-pitch mechanism, Whether such changescan be incorporated will be left uzlanswered, as theproblem involves ‘several fields of engineering otherthan that of sound and must be arrived at by extensivecompromises or regulations imposed by law.Recently a series of tests has been made on two-,four-, and seven-blade propellers driven by an electricmotor. The results of these te~ts show good agreement. with the Gl~tin formula, particularly at tip Wach numbersḟr.orl0.5’to 0.9.. The agreement between theory andexperiment is good over a sound energy range of as muchas 10,000 to 1. For conventional propellers, therefore,the Gutin .ftitimula gives the sound output correctly. Fora fan-type, propeller as suggested for_airplane D, thepossibility exists, however, that the sound as.calcul.atedby the Guti”n formula at a sufficiently low level ma~become masked by vortex noises..~he foregoing fo~ulas give physjcal noise levelsas measurredby, instruments. The s’ensittvityof~ the humanear is dependent on the frequency, particularly at low _.noise lev”els. A correction factor must therefore-b?a~plied in order to obtain the audibility of a particlfiarsound. Thus , an indicated physical reduction is notnecessarily accompanied by a correspo~ing reduction inaudibility. It should be rew.embered that the greatestsensitivity of the ear is in the range-of approximately1000 to”.4C100cycle’sper second. The fundamental..f the : ~propeller noise is therefore rarely audibla. . .ljj.-

NACA TN NO. 1145The effect of exhaust noise was studied in connectionwith the light airplanes A and B. It is contendedthat an index of the relative importance of the exhaustnoise may be obtained by the use of the ‘tmaskingtfeffectof the propeller noise. By masking is meant the properti .of a certain loud noise to render the ear unable toperoeive a simultaneous weake’r noise, If the averageobserver is uncertain as to whether ho can hear theweaker noise, this noise is said to be masked by thelouder one, which in the present ease is the propellernoise. In such a ease the elimination of the weakernoise is technically without merit.BY means of aural listening tests it was determinedthat the e~aust noise on airpl;ne A was drowned out bythe propeller at a speed of about 2100 rpm. Since ,thisspeed is about the cruising speed, the effect of anexhaust muffler might just be discernible but theexhaust muffler would not reduoe the sound outputappreciably exoept when the atrj?lanewas idling on theground, On a larger airplanes elrplane B for ~xample,the exhaust noise was masked at about 1500 rpm. Thisspeed is very far from the cruising speed of’the airplane$which is at about 2900 rpu. Airplane B wouldtherefore definitely not gain from an improvement in ‘“the muffler,In order to check these conclusions further, exhaustnoisemeasurements were made at a distance of 3 feet froman unmuffled gasoline engine having about the ssme exhaustfrequency and power as a light-airplarm engine. Themeasured values were 82 decibels for idling and 92 decibelsfor full power. Since the airplane engines usually haveshorter efiau6t stacks than the engine tested, it maybe assumed that the exhaust noise of a light-airplaneengine is 95 to 100 decibels at a distance ,of3 feetfrom the exhaust opening. By useof these values forthe efiaust intensity, the combined exhaust and provellernoise is computed by means of formulas (3)ind (7). Thus, the-following table is obtained:#I I AssumedL-Lirplaneexhaust noiseat 3 ft(db)calculatedpropeller noiseElt~ ft.(db)—.11406 ‘14127.0...1(db).114.68227.m --lCombined propellerandexhaust noiseELt3 ft,,.

.,NACA Tl!?No. 12.45The foregoing table shows that “the combined engineand exhaust noise is absolutely indistinguishable fromthe propeller noise alone even when the relatively highsound intensity level of 95 to 100 decibels is used forthe exhaust noise. Conversely, it is to be noted thatif or when the propeller is silenced a ‘tperfect~[mufflerwill be required on the exhaust$ since the exhaust noisemust be brought down to approximately the same level..CONCLUSIONS..10 EXtOnSiVO measurements on many propellers atthe Langley Memorial Aeronautical Laboratory show thatthe Gutin formula gives the sound level for propellersat low forward speeds with adequate aoouracy; thereforethe neoesstty for measurements of the propeller noise nolonger exists.2. A type ‘ofmeasurement of the relative level ofthe exhaust noise is indicated. A masking of the.exhaustncise by the propeller noise at a certain low speed andfractional power is a condition necessary to insureadequate muffling. The exhaust noise should not beaudible through the propeller noise at some given lowpropeller speed. The sound is dominated by the propellerto such an extent that excessive muffling is useless inthe average case.3* A general large reduction in the sound levelof an airplane can be achieved only by extensive andradical changes in the design of the propeller. Thenoise from a fan-type propeller is shown to bepractically inaudible. In such a case perfect mufflingis necessary and permissible. The imaginary airplaneconsidered, with a low-tip-speed fan-tyoe propeller andpresumably a perfect muffler, tg virtually inaudible atless than 30Clfeet (except for possible vortex noises)~~. It is evident from the theoretical formulaspresented that the main and essential factor in propellernoise reduction is the propeller tip speed and the secondfactor is the number of propeller blades. Whether anypractical application can be made by incorporatingfeatures of the fan-type propeller will depend on

—NACA’ TN NO. 1145●conditions beyond the scope IJfthis paper. No othersolution is available for a propeller-driven airplane.●Langley Memorial Aeronautical Laboratory “National Advisor,y Committee for AeronauticsLangley Field, Vs.”, June 3, 1$46—REFERENCES1. Gutin, L: @er .da,sSch.allfeld einer rotierendenLufts.chraube. Phys. ,Zei.tscly?* der Sowjetunion,B. 9, Heft 1, 1936, PP. 57-7L2. Deming, Arthur F.: Propeller Rotation Nois’e Due toTorque qnd,Thrust. NACA TN No. ,747, 194003. Anon.: American Tentative Standard AcousticalTerminology. ASA Z Z4Wl, Americsn Standards,. .,Assoc., 1936..~. Theod.orsen, Theodore: The Theory of Propellers.I - Determlnatiqn of the Circulation Function andthe Mass Coefficient for Dual-Rotating Propellers.NACA ACR No. L4m3, ~944.I

1NACA TN No. 1145 Fig. 1,●#.,—— .-. Figure1.-Ex~erimentalsoundmeasurementsof firstharmofic~romtwo-bladepropellgrcomparedwithG~tingsformula.~FIs.l(a),reference2.) l–

Fig. 2 ‘ NACA TN NO. - 1145r. .,,, ..-. .-.-—YTICS“o 10 20 30 40 50,~tgure2.- ~unct.lon ‘;~qn~qn~ ‘in P)for variousvalues of V/c and P.’

NACA TN Noo 1145 Fig. 3?:.[,.@od.o .2 .4 .6 .8 1.0V/c of effective propellerradius2Figure 3.- Function 10 loglo { ‘qn forvarious numbers of propeller blades.