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ACE No. L429 NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS WARTIME REPORT ORIGINALLY ISSUED September 1944 as Advance ConfidentialdReport L4129 CHARTS FOER DEiRMIIN PROPELLER EFFICIENC By John L. Crigler and Herbert W. Talking Langley Memorial Aeronautical Laboratory Langley Field, Va. WASHINGTON NACA WARTIME REPORTS are reprints of papers originally issued to provide rapid distribution of advance research results to an authorized group requiring them for the war effort. They were pre viously held under a security status but are now unclassified. Some of these reports were not tech nically edited. All have been reproduced without change in order to expedite general distribution. SL 14 . DOCUMENTS DEPARTMENT L:::vi;;;i::.~ j : .;:;.i i: Digitized by the Internet Archive in 2011 with funding from University of Florida, George A. Smathers Libraries with support from LYRASIS and the Sloan Foundation http://www.archive.org/details/chartsfordetermi001ang 3 GA IqeT7: [ACA ACR I~o. L4I29 IIATIOIIAL ADVISORY COMf ITTE FOR AERCIJUTICS ADVAIICE C',:IIFIDEI:TIAL REPORT CI:ARTS FOR DETRFLTIIIIillG PROPELLER EFFICIE'CY E' John L. Crigc'lr andi Herbert V. Talking SUMiRY A short meth.ti:.' of esti:nating propeller efficiency for a given operating condition is described. The efficiency Is deterit.ined" fjr any Cesign cniditioi, by evaluating separately froi': charges the ind'.uced losses and the proflledra, losses. The estimated efficiency is compared with excerimental results for a wide ranje of operating conditionsa.nd found to ,be in agreement near neak efficiency. The present aniialyzi covers sinrltr:.tatin pro pellers of two, three four, six, and eight blade. and includes charts showing the rot.aziccnalenerWy' loss for the given operating cronditiorn in order to assist in esti mating the gain in efficiency for cli..airotating propel lers. The change in efficiency to be expected fro'.i] body interference is discussed. T'.vo ex2nmplee illustratln.o the use of the method are fiven in an appendix. I'T PRODUCT IC: In reference 1, aialytically determined propeller performance is compared with experimental results for propellers having four, sFx, and ei'ht blades of con ventional design. The calculated results .se in agreement with the experimental results over the com plete range of blade angle investigated (5h to 65' at 0.75 radius). The calculations were made by a strip theory analysis by which the thrust and torque contri butions for several elements alon.. the radius are graphically integrated for each operating condition. The time required to analyze a single operating condi tion by the striptheory method is negligible compared with the time required to obtain experimental data for the same condition. The time required to analyze the NACA ACR No. L4I29 complete range of operation is considerable, however, and a shorter method is desirable. A method of estimating. the propeller performance supported by the results of reference 1 is presented herein. By this method, a large reduction in the time and effort required for propeller analysis is effected as compared with the striptheory method. The results obtained are in agreement with those from experiment. The basic propeller parameters are interrelated in charts that aid in the selection of a propeller for a given design condition. The charts are useful in analyzing data for any propeller and aid in the deter mination of excessive losses. The induced power losses for a conventional round shank propeller are compared with the losses for the optimum load distribution. The induced losses are divided into axial and rotationalenergy losses so that the maximum gains possible by the use of dual rotating propellers instead of optiinum singlerotating propellers can be estimated. The effect of profile drag is treated separately. Because drag losses are evaluated secirately, increased losses due to compres sibility can be estimated directly when airfoil data at high Lirh numbers become available. Detailed applications of the method are illustrated by examples in the appendix. a axialvelocity interference factor a' rotationalvelocity interference factor B number of propeller blades b chord of propeller blade element CD section drag coefficient (Do/qS) CL section lift coefficient (L/qS) Cp power coefficient (p/pn3D5) C CI7T ID T:T'PIAL C 017 IDEI'T IAL HACA ACE Io. L4I29 CQ torque coefficient (Q/pn2D5) CT thrust coefficient (T/pn2,:4) D propeller dia;meter Do drag of propeller blade element for infinite aspect ratio Ea axial energy per unit time in rli trearn Ep rotational energy per uni.t time in slipstream F Coldstein corrections factor for finite number of blades J advancedia'meter ratio (V/nD) L lift of blade section n propeller rotational speed, revolutions per second P input power to propeller Pc power diskloading coefficient (P/qSV) q torque of propeller q dynarric pressure of air scream. R tip radius r radius to any blade element S disk area of propeller T thrust of propeller uo axial velocity in plane of propeller (propeller removed) V axial velocity of propeller x radial location of blade element (r/R) dCQ/dJ element torque coefficient dQndx Cpn'D COIFIDEUTTIAL C 01 IF IDEI T IAL 4 CONFIDENTIAL EACA ACR No. L4I29 dCT/x element thrust coefficient ( nD4 a0 angle of attack of blade element for infinite aspect ratio Q propeller blade angle at 0.75 radius 7 propeller or element efficiency p mass density of air a propeller element solidity (3b/2ir) aCL propeller elencnt load coefficient anle of resultant velocity to plane of rotation ( a t Subscripts: 0.7R at 0.7 radius D due to drag i for zero drag FORMULAS The derivation of the formulas for element thrust and torque calculations is even in reference 2, from which the element thrust coefficient is S_ B2 b ( + 2 ( C cos CD sin (1) dx R sin2 and the element torque coefficient is S )2 + C( cos (2) _B J, b( (I1+a' (I + snacos (2) dx 16 R s i112 L CO I: DET AL YACA ACR No. L4I29 COI FIDENTIAL 5 The expression for the axialvelocity interference factor a is a OCL cot 1 + a 4F sin The values .of the correction factor F as used in the present report are given in figure 1. The values of F for two, three, and fourblade propeller. are taken from reference 3. Tihe val3.es of F for Six and eightblade propeller v.ere extrapolated from these data by the method developed in reference 3. For calcu lations sho.winng, the effect of drap on propeller performance, the follor'.ig formulas wJere obtained from equations (1) to (3) for CL = 0: dx CD 0 J Jv + (Cx) S D TT T (4) 4 sin () dCQ 2x3 1 = 'J + (x) O TZXO J = CD in (5) Equations (4) and (5) are derived for zero loading without inflow and consequently are not exact for a finite loading. The formulas show, however, that the error in estimating the loss due to drag is negligible for light loadings which occur near peak propeller efficiency. C OIF TDEIT IAL NACA ACR No. L4T29 i"e formulas for the rotationalenergy and axial energy losses from reference 4 are .0 E5 a_ T dx P CQ F_ dx C) Ea J P Cp 1a0 dCTr f a djx O dx JO (6) (7) dCQ 2 a = dx 2Jx3(1 + a)F dCmr/dx 1 + 1 + 4  \l TT7XJ2F These formulas fr::m reference 4 have been modified herein by inclusion of the correction factor F. Charts for Induced Losses The basic propeller performance charts are presented in fi..:re 2 for two, tbree, four, six, and eight blade propellers. T'..: cr.inates represent values of the efficiency for propellers operating without drag and the abscissas represent values of D. Against V ci these scales, curves of constant element load coefficient CC1WIDE;.TIAL where and COCI I DE",i'T IAL NACA ACR iro. L4I29 ("jOC R are crossed ty longdash lines of constant V/nD and shortdash lines of constant power coeffi cient CpI. The O.p,curves shlow the variation or (oCL).* with V/nD for constant Cpi and are included for convenience of computation for constantspeed pro pellers. The curves were attained from calculated *:,ptLilum torque and thrust distributions rrraEphically integrated from the tip of the blade to x = 0.2. Thee performance charts are the same as thpepropeller selection charts in reference 5 E.cert that the dra. losses are not included. In the present report, the value of the solidity at 0.7R, G0. R, is taken as a convnient r,measure of the propeller solidity. The value of (O' T is corre spondingly taken as a measure of the overvr absorbed. The activity factor has freqr. ntntl7: been taken a. an index of the powerabsorbing qualities of a propeller. For the Hamilton Standard 31556 propeller reported in reference 6 (for which comparisons are made in the present paper), the activity factor is 9'.' (per blade) and o .R is C.034EB; that is, for propellers of this design, the activity factor is 2GnO This number is approxi mately the same for all conventional propellers. If the exact relationship is desired, however, the activity factor A.F. may be obtained from A" x= 1.0 1000,C0 0r0 I b z A.F. = 16 / DX ,x yO .2 Breakdown of Propeller Power Losses In the calculation of propeller efficiency, it has been customary to compute the thrust and torque at a given value of V/nD for a fixed bladeangle setting. The analytical determination of proreller performance may be considerably simplified in many cases, however, by evaluating the several sources of power loss rather than by attempting the direct computation of thrust and torque. In the present paper, the efficiency is COrF IDE7:TIAL CO17 IDEITTIAL NACA ACR No. L4I29 determined by deducting the sum of the power losses from unity. The total power losses are divided into induced losses and profiledrag losses; the induced losses are subdivided into axial and rotationalener;, losses for use in evaluating the efficiency of dualrotating pro pellers. The blade drag has no appreciable effect on the induced losses for normal propellers but must be considered in obtaining the total power losses. This method of analysis has the advantage that compressibility corrections can be included when the airfoil section characteristics at the operating I7ach number become known. ERctal'n Il .rn I1 Ir . The losses of efficiency due to rtI 't.i ial v 'L.,ci: are shcwn in figure 3 for three, four, six, and eightblade propellers. The rotationalenergy loss for a given operating condition (constant Pc and V/nD) is seen to increase as the number of blades decreases. This increase in power loss arises from the increase in the tip loss as the number of blades decreases. Calculations for a 1irc number of load distributions show that overloadi:6. the inner radii is of secondary significance at values of operatinrg V/nD < 2.5. As an illustrative case, the calculated rotational energy for the fourblade Hamilton Standard 31556 propeller of reference 6, which has round blade she'nk, is compared in figure 4 with that for a fourblade propeller computed from the charts of figure 3. The rotational energy for the Hamilton Standard 31556 propeller was com puted for several blade anres up to 655 at 0.75R and the value of V/nD for peak pro. eller efficiency. The values of Er/P for the optimum propeller were taken from figure 3(b) at the same values of V/nD and Pc as for the Hamilton Standard 31556 propeller. Figure 4 shows that no appreciable difference in rotational energy exists between the two load distributions at V/nD < 2.5 and that the losses differ by only 1.5 percent of the total power at V/nD = 4.5, which corresponds to a bladeangle setting of 650 at 0.75R. 'The rotational energy losses given in fli'u;e 3 are therefore close approximations to the expected losses for conventional roundshank propellers over the usual presentda! operating'rane. Similar results are found even when airfoil sections are used over the inner radio v':hern V/nD < 2.5. It cannot be e.phasi.ed too strongly, however, that if cuffs are used to cover the round C 3G TIDSETIAL CO;I 7IDEiT' IAL EACA ACR i!o. L4129 shanks, the loss may become serious at high values of V/nD unless. the cuffs are set at an angle .f attack between 0 and the opcirr.u:n to si''e low loading over these sections. This dependence of the rotational energy in the slipstream on the l ading c:ver the inner radii is apparent from equation (.6), which shows how the effect of overloadir. the inner radii increases in importance as the operating V/nD increases. Axialenergv loses. The axialenergy los. for any operating condition may be obtained from the rela tionship =1 7, p "~ p P P where the induced efficiency ri is obtained from figure 2 and Erp/F is obtained from figure 3. The axialenergy loss shows but little variation among propellers in presentday usage operating near peak efficiency. As an illustration, the axialenergy losses for a fourblade propeller obtained from the charts of figures Z and 3 are comparei in figure 5 with the calculated values for the fourblade Hamilton Standard 51556 propeller operating at peak propeller efficiency and for the ideal propeller (actuator disk). The values of Pc at V/nD for peak efficiency for the Hamilton Standard 31556 propeller were taken fror. reference 6. The axialenergy losses for the optimum propeller load distribution and for the ideal propeller were determined at the sare values .f V/nD and Pc as for the Hamilton Standard 31556 propeller. The axial energy losses for the optirmumn distribution of loading (figs. 2 and 3) and for the loading obtained with the Hamilton Standard 31556 propeller are nearly equal and are about 1 percent higher than for the ideal propeller over the range investigated. A part of this increase in axialenergy loss is due to the finite number of blades and therefore bec.mes less as the number of blades increases. A small part of the difference occurs because the load distribution differs from that of an actuator disk. The axialenergy loss for optimum distri bution, obtained with the aid of figures 2 and 3, is therefore sufficiently accurate for application to conventional propellers. CONFIDENTIAL COITFIDE ITIAL NACA ACR o. L4I29 Bladedrag losses. The effect of blade drag on the characteristic .f li htly loaded propellers (near pa!: efficiency) can be estimated from equations (4) and (5). These equations were obtained by eliminating the axial inflow and putting CL = 0 in equations (1) and (2). The equations are not exact but, near peak efficiency for modern highspeed propellers, the omission of the inflow factor a causes a negligible change in the calculated propeller efficiency. Equations (4) and (5) show that, for a given radius and value of V/nD, the element thrust and tor'.ie coefficients dL to crag are directly proportional to the drag coefficient. The profiledrag coefficients for infinite aspect ratio for several sections along the Hamilton Standard 31556 blade are shown aint lift coefficient in figure 6. These data were taken frcm reference 7. The profiledrag coefficients cb1. with lift coefficient but, since the change is very small for a wide ranre of lift coefficient, average values were used in the calcu lations for operation near peak efficiency. The profile drag coefficient increases rapidl: near the stalling angle of the section and the average values are accord ingly not representative for such conditions. Figures 7 and 8 show the effect of drac on the thrust and torque coefficients, re:ectively, for several values of V/nD. The values of the section profiledrag coefficient shovn in figures 7 and 8 were used in the calculations for the Hamilton Standard 31556 propeller. Curves of the differentialthrust and differentialtorque corrections due to drag, for the drag coefficients shown, are plotted acir.st the racial location x,and the interated corrections are also included in figures 7 and S. "Thse integrated values apply for one blade and the correction is directly pro portional to the number of blades and to the blade chord. The element thrust coefficient and the element torque coefficient due to drag at a :iven value of V/nD are directly proportional to CD, and a change in CD at any radius is represented by a proportional change in the ordinate of the differentialthrust and differentIal torque curves. For this reason, the method of analysis is adaptable to any blade section for which the airfoil characteristics are available. The s''r:stion is also made that the loss in efficiency due to ir& at high speeds at which the blade section drag becomes large C Ci DDT :A'T CO! FIDEITIAL HACA ACR No. L4129 can h. predicted when the drag coefficient at hi.ph !'ach ni.u.:bers become available TL.e calcZ ilat ion :.w that the drag correction to the thrust is chiefly due to the high draz of the inner secti.,not (sef fiU. 7) and that a change in the dria com efficient of th. principal workinF part of the blade du.e to I. change in the lift coefficient near peak efficiency (see fig. 6) results in a negligible clhan.e in the correc tion to the thrust coefficient. The effect of dra, on the eff cicncr envelope and on the integrated powerc coefficielrt for o:oerration at peak efficiency, in LunIobstr'._.cted air flowv, i' hl'wrI in figure 9. The values of' rl an'.L the c rrs.p:ndlr o,. without dra vere ta.:en frJ' fi'ure C2 or f.'oirolad propellers at oCL). = 07.0'" Fr p t i d bution of loadinT alon the radius for tn' e ;ol of the fourlblaLe 1Hmilton S3tan ar. J.1.,5C r r_. l: i , tnis value of (C').,, corresponds to C: , .1. The solid lines ir. figure 9 ive tie ' :. .: e''iency and the correspondir. power coef icier': _ .int V/.D for ortimrTum Clistributicrn for a fourbisafe friction:less propeller at (o L) . = 0.07. The sh.rt'tash line show T] and Cp as modified by blade C.ra7 integrated from O.2CR to the tip. The curve for rj for blade drag integrated f rom 0.45R to the rip is .bh.:'n by the longdash line. The Cpcurve is inot shown for the latter case but falls between the other Cpcurves. The introdu.?ri on of tlade drag of :he magnitude s~own in figures 7 and 8 has little effect on the total p.:'r absorbed during .peration near pea; efficiency, regard less of V/nD; the effect of the drag. on the integrated thrust and hence on the efficiency, however, is i.r.:'rtant and increases rapidly with V/nD. For e:xa.ple, the loss in efficiency for the entire blade varies from 5.5 rer V V lent at  1.0 to 2,.C percent at = C.O. n the nD r" other hand, the loss in efficiency due to the drag of the principal v'orking sections that is, from 0.45R co the tip Is relatively unim:portant. The loss in effi ciency for this portion of the blade (see longdash line,, fig. 9) is thus seen to vary from 2.5 percent at V 't 1.0 to 4.0 Percent at 6.0 these losses nD "nD CO:NFIDEUTIAL CO F IDEIITIAL NACA ACR No. L4I29 represent the upper limits for increases in efficiency that may be achieved by reducing the profile drag for the working sections of the blade operating at CL = 0.51 with optimum load distribution. The thick inner sections of conventional roundshank propellers, which are used for structural reasons, are therefore the chief source of bladedrag loss, especially at high values of V/nD. This.loss in efficiency due to drag may be greatly reduced by covering the inner portion of the shank with a spinner and the outer portion with cuffs, if the cuff angle is properly set. It is emphasized that cuffs may result in a loss in efficiency instead of a gain unless set at the proper angle of attack. Overloading of the inner radii results in a large increase in the power in rotational energy for singlerotating propellers, and the bladedrag loss also becomes large for blade sections operating near the stall. The losses due to the thick irner sections are also reduced when the propeller is operating in front of a blunt body, such as an NACA cowling, because.of the low velocity over these sections. Calculations of thrust and torque coefficients have therefore been made at the same values of V/nD and for the same distribution of the element drag coefficients as in figures 7 and 8 but with the inner portion of the blade assumed to be operating in a region of lowvelocity air as in front of a conventional aircooled installation. Ths velocity distribution in the plane of the propeller, as used in these calculations, is given in figure 10, for which the data are taken from reference 4. The region of low velocity air depends on the ratio of the nacelle diameter to the propeller diameter, the conductance of the engine, and the distance of the propeller in front of the cowlirg. The ratio of the nacelle diameter to the propeller dia!.eter in the setup in reference 4 was 0.417. The effect of operation in front of an opennose cowling (velocity dis tribution of fig. 10) is shown in figures 11 and 12 for a fourblade propeller. Thrust and power coefficiernt due to the distribution of drag in figures 7 and 8 are shown for freestream operation by shortdash lines in figure 11; the longdash lines represent operation in front of the 1TACA cowling. The value of the power coefficient due to drag (ACp)D is seen to vary but little with V/nD whereas (ACT)D rises rapidly. COCF IDE TTIAL CONFIDENTIAL NACA ACR No. L4I29 Equations ( ) and (5) also show this effect. The effect on the efficiency of operating a propeller in the velocity distribution of figQure 10 is shown in figure 12 and com pared with the efficiency computed for operation in free stream. The increase in propeller efficiency' resiulting from the presence of the cowling varies from 1.0 percent V V at = 1.0 to 9.0 percent at = .0. In the calcu nD nD lations for the curves shown in figure 12, the only variation considered is the draq of the blade shanks. The lowvelocity jjr causes an increase in lift over the outer sections of the shankl and, accordingly, an increase in the rotationalenergy loss, which may result in a somewhat smaller gain in propeller efficiency than indi cated by figure 12. Tn order to determine exactly the magnitude of the charge in propeller efficiency, element calculations for each velocity distribution are neces sary inasmuch as a change in velocity distribution pro duces an effective change in pitch distribution. CO1MPARISCOU WIT. EXP2:.Ii.TIEiT The experimental efficiency envelopes for four, six, and eightblade Hamilton Standard 31556 propellers are compared with the calculated results integrated to 0.20R in figure 13. The experimental result for the four and sixblade propellers were taken from refer ence 6 and the results for the eightblade propeller were taken from reference 8. The singlerotating propellers were made up of two hubs mounted in tandem. The spinner in the setup for all the ex 'erimrental data covered the inner 0.1E9R of the front unit of onehalf the blades and the inner 0.232R of the rear blades. The results are in agreement over the entire ranre investigated for each set of blades. The calculated efficiency is about 1 percent lower than the experi mental efficiency at low values of V/nD and is higher than the experimental efficiency at very high values of V/nD; the calculated curve crosses the experimental curve at V/nD r 3.5. Part of the discrepancy is due to the use of the short method. CONFIDENTIAL COLFIDDEITI .L NACA ACR No. L4I29 CONCLUS IO S A short method of estimating propeller efficiency for a given operating condition has been developed by a theoretical analysis. The efficiency is determined by evaluating separately the induced losses and the profiledrag losses. A comparison of the estimated efficiencies with experimental results indicated the following conclusions: 1. The performance for operation at values of the advancediameter ratio equal to or less than 2.5 may be accurately predicted. 2. The approximate performance of conventional roundshank propellers may be predicted to values of the advancediameter ratio much higher than 2.5. 3. The upper limit of possible performance for other types of propeller (airfoil sections over the inner radii or the use of cuffs over the round shanks) is shown for values of the advancediameter ratio up to 6.0. 4. The cause of excessive losses may be determined for any propeller design. 5. The maximum .;';in in efficiency to be realized with dualrotating propellers over optimum single rotating propellers is evaluated for a wide range of operating condition. Langley Memorial Aeronautical Laboratory National Advisory Committee for Aeronautics Langley Field, Va. C;r'FTIDEI;TT.AL CC lD 'i ITIAL HACA ACE Ho. L4I29 C CIFIDEFITIAL ' APPEUDIX A P F IT E I( APFLICATIOH OF T.E !'EiTHCL The problem of determining the propellcr efficiency for a given design condition by the methods of the present report iay be resolved into two parts: (1) determLinai.Tion of the induced pouer losses and (2) determination of the profiledragi loscFs. The induced power losses for a given design condition are available from figure 2 as 1 r,. The induced losses obtained from ft.zurn e 2 at V/rnD < 2. are very close aprroxi nations to rt.he obtained with conventional proc,: ie rs. This ranc of V/nD cover most current hiLgspeed designs. The bl1ade drag is hai?dled separately and can therefore be ued fr hiph I'..ach numbers and high drags if the correct airfoil section character istics are used for the corresponding 1.ich n.umbers. The profiledraq losses are obtained from figure 11, which shows the variation of the thrust and rower coefficients due to dra_ for the values of the element drag coefficients shown in figures 7 and S. These drag values are repre sentative for the Hamiltcn Stsndard 31556 propeller operating near peak efficiency. The ordinates of the curves in figures 7 and 5 are directly proportional to the drag coefficients at each radius so that, if other drag values are used, new curves .:ivinr the thrust and power coefficients due to drag may be easily plotted. Since the total power losses are divided into induced power losses and profiledrag losses, the method aids in determining excessive losses for any design condition. Excessive losses may be due to the fact that the propeller is either too heavily loaded or too lightly loaded, to a poor load distribution along the blade, or to high blade drag due to compressibility. The use of the performance charts determines the lift coefficient at a representative station and thus the loading. Two examples are given to illustrate the use of the charts in the determination of the propeller efficiency for a given design condition. Examle 1 In example 1, the propeller selected operates on a liquidcooled installation in the tractor position and all the sections are assumed to operate at freestream velocity. Ho compressibility corrections are applied. CCITFIDEIiTIAL NACA ACR No. L4129 The following design conditions are assumed: Power, hp .. .. . Altitude, ft . Velocity, miph . Rotational speed, rps . Propeller diameter, ft Number of blades . S Bb 0.7R 21r . Activity factor .. .. V/nD . . SP pn3D5 are . . 2000 S. . 25,000 S . 425 S . 23 . .. . 12 . Four . .. .. 0.1380 . . 90 . . 2.26 S. . ... 0.342 The calculated values for operation in free air (ACp)D (fig. 11) . Cpi = p (ACp)D . C iO.7R (flg. 2(c)) CLO.7R . Tli (fig. 2(c)) . Er/P (fig. 3(b)) , S= iCpi CT = ......nD (ACT)D (fig. 11) . CT = CTi + (CT)D CT V 1' p= T D . . .. 0.006 . . 0.336 ..... .. ... .. 3. 7 * .. . 0.07 . . 0.51 . . 0.931 . . 0.039 S. .. 0.1385 . . '..01 3 . 0.1.232 0. 843 In order to determine whether the propeller selected is loaded properly, the value of CLO.7R is first deter mined in the selection chart in figure 2. Since the design conditions are given and l/Tci and V/nD have been predetermined, the value of (CL)O.7R is read directly from the chart. The value of CLO.7R required COMF' I DE7 TIAL CC IFIDE TRIAL . 4 NACA ACR No. L4!29 is found to be 0.51 and indicates a satisfactory design condition. This lift coefficient has been found to be that absorbed near peal: propeller efficiency for the Hamilton Standard 31556 propeller for operation at the given V/nD. The power loss due to rotational velocity Er/P, which is equal to 0.079, is the maximum increase in efficiency to be expected from the use of dual rotating propellers of the sar..e cdiareter and solidity. The induced efficiency is 0.C3 but the introduction of drag of the rragnitude of tIh.t sho.'n in figures 7 and S reduces the overall propeller efficiency to 0.848. The use of 1/\/F with drag included, instead of 1//Pc, results in negligible chsnces in r.i and (CL)TC . Example 2 The only difference between example 2 and example 1 is that the propeller in example 2 is mounted in front of an opennose cowling (aircooled installation) with the inner sections of the propeller in retarded air flow. The design conditions, example 1, are which are the same as in Power, hp . .... .. 2000 Altitude, ft . . 25,000 Velocity, mph . . 425 Rotational speed, rps . 25 Propeller diameter, ft . 12 Number of blades . .. Pour ctvity factor. ................. 1390 Activity factor . . 90 V/nD . . 2.26 P Cp =  .. . 0.342 nI D" The calculated values for operate NACA cowling are (ACp)D (fig. 11) . . Cp = Cp (AC )D . . 1/ P4 T . ..... . ion in front of . 0.006 S. .336 3.67 CO 0NFIDENTIAL CO1FIDEITTIAL CCIFIDLEITIAL CLO. R .... OT) (fig. 2(c)) ... C3 O/ . . Er/P (fig. 3(b)) . . 'iiCpi CTi V/nD . . (ACT) (fig. 11) . . CT = CT (ACT)D ...... NACA ACR No. L4!29 S 0.07 S. 0.51 . 0.931 . 0.039 S. 0.1385 S. 0.0065 CT V p D . Cp nD . 0.872 CO :IDET TRIAL IIACk ACR INo. L4I'12 _FEFEfEI'ZC E3 1. Cr'i eler, J:hn L.: T Ccmpari Os.i o f Calculated and :perimental Propeller1 Characte ri t ic f:,r Four, Six. End Z1ghtB3.lade Sinr:leRotat ing, Pro eller.. li:.CA .A.CR lio. 4304, 1 ' 4. 2. Gla".rt, H.: Airplane P opeleers. V1o. IV of Aero d;.rnarrlc T!iher; ,iiv. L., '. F'. Durand, ed., JulFius prinrer ( erlic) I0?, pp. 189.3.0. 3. Loc:, C. I:. H., a&.i Yefat.a r,, D.: Tatle f .r Usl in n Im proved .'et.hd o Airs .rew Str'ip Theory Calculation. 3. t .' c. 17'74, r .itih A.:?.C., 4. Stic:le, e r1e V.., and Criltr, JotLn L.: Pr:.pller Anialy "l from L.:xperiertaenl Dta. .AC. ep. ,IT. r, : !r. 1l2, 1941. e. Crilr.. T J:hn L., ard TallJ:in, l r .* .: Frrecll r l.: i : tior f r..rr: Aer od;rnr: ic Con ratio c.n C [kR, Julr: 10iE. 6. Bier.iiRann, D .avi", c .i H.rtmf.n, EL .i,' P. YI:.: .':J nrnel Te t ?, F ';. I !, lT :"do E in ,ae and C u l tetin;. Tractrc r Pro.peL rT' .. ac.T Fc 2I' , i9 2. 7. Pincerton, F,.o h rt :., and 0 r : t'b r Ii. r : .ai 'i'y n .'C:1 Ch acn : i oi: f a T".r i. .. o : rf ?iio Tctl in t 'X.*:.*i..leL. n.. i c. ind ui.inn I. ..ACA f. I G6 , 8. Biier.arn.n D"'ii, d Grey, i. : ; 'iniT'.unr : Tests oaf ''.. t it. .in ,c rn.. D..a.1 R: t ' rPrje liD ers in t. e Tract.: r Z.osit ron I aCt. AR, ,i0 1941. r"017!IDETIAL COI)n rFTLETTI AL NACA ACR No. L4I29 CONFIDENTIAL (a) For rwob/ade prope//ers. (Dt~a Orom reference J.) Fiyure 1. Curves od Fayama/nt . Fig. la i. 4 NACA ACR rio. L412'J CO I TEE IR A uTO  I I V7wsre / am \ \ _\ __ _,_  \ ', \ \ r \ \ \ __ ^__ ___ ^a __  \ s^_"'; z rz= CONFIDENTIAL Fig. Ib NACA ACR No. L4I29 1 3 .S/ I f __ I I i I F/re / Cont d. 2,/ .3 \1 J9 70 90 Fly&n[re roo nn jKaunc i''',' ~~ ~ Fo orie prp /er:,. rv fo rfeeni.  \iur ..oniuid Fig. lc CONFIDENTIAL NACA ACR No. L4I29 /0 w j0 o4 4,,a'eqg S 60 1d) r r' 61g' /;rirpe'/erJ. (rbtraoc. biea froTr reference 3.) 'Ure /. C':t.,nued. CONFIDENTIAL Fig, Id NACA ACR No. L4I29 III COM ITIEE CONFIDENTIAL o I_ I I I I __ 0 /0 w 30 40 0,deg 0 60 (e) For eyhlblode propelelrs. (EXT/rpolt/ed from reference J.) ,gure / Coaluded. CONFIDENTIAL Fig. le NACA ACR No. L4129 Ch 8 k. I di1 ^ tq^ 34 PI Fig. 2a NACA ACR No. L4I29 Fig. 2b NO "a ft. r, IIJ C j 'I' NACA ACR No. L4I29 Fig. 2c (yL  o I0IV ____ __ _I _ C '\ 1 I   1 \'. ', vW\\F^^ r __ \ ^\ \ .\ \ \ \ ^\ __ __ _ 1  \ T \ \^ v  _____o I ^ S. ^. ^. NACA ACR No. L4I29 r l I  LV ^ ^   \o E tB\I. \ f :N A 0 S __ __ __ % i~ .^. s Fig. 2d z.1 o 0 NACA ACR No. L4I29 '.4 r. Oj E) 0 I) SSa I'v M0 Fig. 2e NACA ACR No. L4129 Fig.  ' V Ir"' k CC , 45_  0 \  o a t e ^"'^. \r " L\ "\> \ \\\ o uz +0 / I c1  cg _ . S ^ " 3a NAC ACR No. L412') '4J Fig. 3b 0 SLU : U= K Qj IJ 3 IU S NACA ACR No. L4I29 Fig. 3c K  o \ / \ ' .0 C P= N N \ c S^< ^\< \^^)(At ^ x ^^ T~n0 >^ ^ V ^ \ \\ V :l< __^^__ ZI\ \E^ ^^s^t1c "SOSM  ^v W^ * NACA ACR do. L4I29 Ez (9 \c ^ \J ^SS o IZ Lu~ Fig. 3d NACA ACR No. L4I29 F/G6nE 4. 0fokim'/o/ernery s or P correspoax/ 0o pe*o ed/f/vey a; /urtede Ham/itoan S5rendard 3J/56 prope//er 1,6     OPtium "/stribi /on, = 4  Prope//er 3/556, 8=4 Idea / prope//er I /6 ~e Axio/ energy /oss at R corresponding to peao efficiency of ourblade Hami/ton 5tanda ~ r 3/556 prope//er CONFIDENTIAL z z I z CONFIDENTIAL Figs. 4,5. NACA ACR No. L4129 as 'no SLJ io g OL.J 0 s 0r I( I o I I 1 I I 1% U, qj J Nr . P'I I~ Fig. 6 NACA ACR No. L4I29 Zl II III b' C(LI L Ii iT K ,t3 NZ I* s K Fig. 7a I  \ \ N N. M $ I ! I I I ' I I I  B O NACA ACR No. L4129 Fig. 7b We i I" I '  ,I I I II 0 N o oN ,. ..., O I IZI I0  ~ ~~ % I*\ I NACA ACR No. L4I29 10 o 0 0 0 Fig. 8a 0 cc U E" 2= N 11 1^ I NACA ACR No. L4I29 Fig. 8b Ss/ / o a S5 O _I / I1 F  ,, I I II 0 0 ^ S 5$ NACA ACR No. L4129 Cp /2  CONFIDENT AL /c/6U/UE 9. EFFECT OF Dx46 ON EFF/C/ENCy RA/O oOWE COEFFfC/EN'T R"F PEAK EFFICIENCy FOR rOU/RBLADE I MILToN S STANDARD 3/1.56 PeOPEL ee. Fig. 9 NACA ACR No. L4I29 d/L a'773 dOfc!d 0 ,. u, uj .r.' "Oo t " ___ __ __ __ __ __ ___ __ __ __ o j __ __ 5 1 rd^ r ^ "r"         ^ \ g    _ A__ ___ __ \ naHjfyw ?vry ^ \ Fig. 10 4' k i ft 8 S '% 1 G` ^. NACA ACR No. L4I29 707 .6OS :O V/no 'S6au /A VyA/ar/W o T10eWsT dAoPowvE co F C/Ars oW 7 DWnS w/r# Y1W 9oeR CNwsrW9N7 r V Ysr*/PJr4O. 0= CONFIDENTIAL CONFIDENTIAL Fig. 11 NIACA ACP No. L4129 K; I I r  N o I Fig. 12 NACA ACR Ho. L4I29C   Ca/calated   xperimenta l(erferences 6andi CONFIDENTIAL 0 / Z 4 S 6 V/770 F/iure /3 CnomparisoV of ca/culated acnd ejperimenta/ prope//er efficiency enve/opes. CONFIDENTIAL Fig. 13 r UNIVERSITY OF FLORIDA 3 1262 08104 984 2 UNIVERSITY OF FLORIDA DOCUMENTS DEPARTMENT 120 MARSTON SCIENCE UBRARY P.O. BOX 117011 _'"AJNESVILLE, FL 326117011 USA 
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