Propeller Characteristics and Slipstream Effects on a High Wing Monoplane from Wind Tunnel Tests Citation Russell, James Sargent and McCoy, Howard Monroe (1935) Propeller Characteristics and Slipstream Effects on a High Wing Monoplane from Wind Tunnel Tests. Master's thesis, California Institute of Technology. doi:10.7907/91VQ-DG62. https://resolver.caltech.edu/CaltechTHESIS:08182010-095214810 Abstract No abstract. Item Type: Thesis (Master's thesis) Subject Keywords: Aeronautical Engineering Degree Grantor: California Institute of Technology Division: Engineering and Applied Science Major Option: Aeronautics Thesis Availability: Public (worldwide access) Research Advisor(s): Unknown, Unknown Group: GALCIT Thesis Committee: Unknown, Unknown Defense Date: 1 January 1935 Record Number: CaltechTHESIS:08182010-095214810 Persistent URL: https://resolver.caltech.edu/CaltechTHESIS:08182010-095214810 DOI: 10.7907/91VQ-DG62 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 5996 Collection: CaltechTHESIS Deposited By: Benjamin Perez Deposited On: 18 Aug 2010 17:58 Last Modified: 03 Oct 2019 23:48 Thesis Files Preview PDF - Final Version See Usage Policy. 55MB Repository Staff Only: item control page

PROPILLS2 CHARACTZRISTICS AND SLIPSTR#AM EFFECTS ON A HIGH WING NOMOPLANE FROM YIND TUNNEL TESTS Thesis by J. S. Russell and H, M. MeCoy In partial fulfillment of the requirements for the Degree of Master of Science in Aeronautical Engineering NANAAY —, California Institute of Technology Pasadena, California 1935 (1) ~ = DMerannne PROP .LLER CHARACTESXHISTICS AND SLIPSTRiav! (FFSCTS ON A HIGH ‘WING MONOPLANS FROM WIND TUMNIL TisTs Standard references on airplane propeller cheracteristics are N,...C.#. Report #{ 350 (‘‘eick) and N.A.C.A, Report ; 481 (Hartman). With increased engine powers, modern types of cowling, increased nu.ber of blades, higher airplane speeds and greater engine-body diameters, there has been @ growing need for investigation to extend the range of these references, “hile full scale data are desirable it is difficult to obtain them because of the limited capacity in size and airspeed in existing wind tunnels, The research herein reported was undertaken in order to examine the practicability of making propeller tests on a scale model in the wind tunnel. The model was that of a representative high wing monoplane at one sixth scale, The :odel was complete except for landing gear and any protruding cockpit enclosures. The propeller diameter was 10/6 feet, the power was 432/36= 12 horse power, the rated maximum revolutions per minute were 12,000 so that the linear velocities of the blade elements were equal to those of a full scale vropeller with rated maximum velocity of 2,000 2, P. ii, Since the lengths of chord of blade were one sixth full scale the propeller was operating at a Reynold's Nuxber of one sixth the Reynold's Number of the full scale propeller, The blade form was exactly that of a Hamilton Standard 141-0 propeller to one sixth scale. The tests made fall into two classe 8, 1. Production of working charts to determine the propulsive efficiency of two and three bladed propellers at various blade angles, velocities and powers, 2, Investization of the effect of slipstream on the performance and static loneitudional stability of the airplane at various anclss of climb and slide, ie Description of Apparatus The principal advantages of a powered model test over a full scale flight test are ease of control and facility in measuring the forces and moments developed. In the wind tunnel, power output results are read on the external balance system as in a normal wind tunnel test, The G.A.L.C.I.T. six component system is shown in Figure 1. Here, air velocity, geometrical angle of attack, thrust, drag, lift and moments are measured, The measurement of power input is more complicated and is accomplished by means of a revolution counter and a torque meter, The revolution counting system, or timing circuit, shown in Fisure 3, consists of a pendulum actuated, multiple relay circuit which counts the motor revolutions over an accurate time interval of about ten seconds, The timing system was oalib- rated for each run against a crystal controlled ec:urate fifty cycle current, The location and functioning of the torque meter is shown diagrarmatically in Figure 2, The adjoining sketch shows the arrangement, used in the experiment, of an alternating current Yheatstone Bridge for indicating torque. The torque being developed by the propeller is opposed , Variable in equal amount by the resisting moment Fixe. 'sTt Fresistance Freststnce in twist developed by the torque bar. che angle of twist varies the position of the Golrenomefer > soft iron armature between the pole faces of coils (1) and (2), thus varying their Cor! impedance, The relative change in impedance Hox¥ Coil (2) , 50% (1) is indicated in balancing the 3ridze by 5 UPRLY means of the variable resistance, The reading of the variable resistance of the “heatstone Bridse, in ohms, is converted to torque, in kilogram-meters, by means of a calibration curve constructed for 3c run, This curve represents the mean of calibrations made before and afte: th run, The calibration is sade by keying a bar of fifty (3) GALCIT REPORT /48 PAGE BALANCE ROOM MANOMETER Ze P 4 a TO STATIC RINGS IN ENTRANCE AND WORKING SECTIONS oN we ye 2 este ey ca TO SELSYN GENERATOR © Mint igi SIX COMPONENT SETUP FOR TEN FOOT WIND TUNNEL TESTS AT GUGGENHEIM AERONAUTICS LABORATORY CALIFORNIA INSTITUTE OF TECHNOLOGY WG. WT 26 FIG. | SUE IN997 euh7ror weep MoyTsa meg LI We) go hu IVES PUPA. vod ATuo JOVO! «ee O07 SATUSUBT | equ, voydThs Buy aps qnogng odvRtTesny req anhzoy, H | Zu F1Be8g enhio0y PUOL] \ auysur- go \ euy” oh / Ud | LUPAROE ySNATyTT, \ Li t— ' <LZZ RANA ARRAN | oe ket oroze gray" SUT LPeg SOLO ZUOLT / \ “SSS — \ STTOD \ (vor, OING aly POr: ; / i] j it i] Spvey % I6qu 2 A9q rene 7 ( esmul \ Spe, *duy co (3T°OA CTT gor ' ; By re 10904 °u°H eT UB, SUPLOOY TOTTOCOTG *B]. .08 L SPeTE € 10g 2 FIG YR ReseT COUNTER | st , COUNTER 4 _2 TIMING CIRCUIT POWER MODEL ' i | i i ! ! | I 1 | | i ' | t { ! I | ' msi oaths act as acs; 5) Gane SeRETERjeSeTEsS aaNen Gr ma pool 1 STARTING 1 ! ! | | | | ! | CounTER CuT-ouT TEST Circuit RESET Contactor 6V-D.c. Fa Hi] Prope ~ KEY COUNTER ACCURATE 50 CYeclreE 109 Imputses/ / SEC GEARED 2/4 l FIGURE BF. Model Disassembled Front View Side View Torque Calibration MS \ Pe ts : Motor & Model Parts Three Quarter View Side View Instrument Table centimeters length to the stator and placing known weights in pans suspended from knife edges at each end, In this manner a known toraue is given in terms of resistance reading. Photographs, Figure 4., show views of the model, instrument table, parts and torque calibration arrangement. PART ONE PROPELLERS The first problem of the investigation was the determination of the charact- eristics of two and three bladed propellers, A plot of initial data obtained from two bladed provellers, when compared with the full scale data recorded by Weick in N.,A.C.A. Technical Report #350, indicated sufficient agreement between model and full scale characteristics to warrant complete tests. If air were an incompressible fluid, if a degree of turbulence existed in the wind tunnel which was exactly that of the air in which the full scale air- plane was to fly, if propellers were made of infinitely rigid material of absol- ‘utely smooth surface then we might expect to get results.from wind tunnel tests which were fairly representative of geometrically similar full scale propellers. Fairly ee there remains an element of uncertainty as to the effect of the presence of the wind tunnel walls on the flow through the propeller, . An enumeration of the factors wherein differences between model and full scale propeller characteristics might arise which we have considered are:- 1. Seale or Reynold's Number, roughness, buxbulence. 2, Blade deflection. 3. Tip losses = compressibility. 4, Yind tunnel wall interference. 5. Experimental error. Keeping these factors in mind let us consider the method of working up the data obtained, lift, drag, and pitching moments were measured in the standard way by direct measurement of the forces transmitted through the model rigging to the automatic balances. Torque developed in the propeller shaft was recorded by a remote reading dynamometer. The revolutions of the propeller were obtained . by direct count over a time interval. (5) The indicated dragwise force, in the case of power-on, is transmited into a combination of thrust and drag. It is apparent that the presence of the slip- stream over the model must eause some change in drag. This small change in drag is nicely disposed of by including it alsebraically in the effective thrust. If we take the difference between the drag reading power-on, FR, and the ordinary drag of the model with the propeller off, Do», there remains a force which we can call effective thrust,-i.e. the true thrust minus the increment in drag due to the propeller slipstream acting over the model. PoweR Out POWER /N Q Vv. — {p) —_ Oo———_> = J i = = 2nn T, x V is then the effective thrust horse power being developed by the propeller. Against this power output is the power input represented by the torque "0" , multiplied by the rotational velocity "2mm", Efficiency is the ratio of power out to power in-i.e. TeV ° 21mn.Q 7 It is convenient to put thrust, torque, and velocity into dimensionless co- efficients, Since the velocity in the wind tunnel is recorded in combination with air density as the dynamic pressure being develonved in the workins section, the Form T= T,pV°D* is suggested, which can be written T= To2aD*, Likewise for torque, °= Qe2qD° . Velocity must be considered in the advance ratio of the propeller, = v. The wind tunnel sensitive manometer records a by calibration against a pitot tube traverse of the working section of the tunnel, Velocity can be obtained from V=7/2q/p where 0, air density, is a function of temperatur: and humidity of the air stream, barometric pressure, and gravity at the wind tunnel, yom de gotten directly from T, and % ;_ (6) — z a= Tel ~ gD ¥ 7 — _ J where j= kK P 27nQ2¢D? 27 Q. nD zy ray, : 2 2 from C.=£~, = a = 2 2 ot gl iS Cp and Cy » which are sometimes convenient, are simply T, x and % yz Hartmen's coefficients Co, and CT come out simply es Le ang Te When the experiment was begun it was the opinion that some kind of pre- liminary fairing would be essential in order to get smooth final curves, Therefore Ty and % were plotted against J, and points taken at even increments of J to solve for V4 and Cs, While this method produced smooth curves a very small displacement of the fairing caused comparatively large variations in peak efficiencies (1 - 2%). This method was discarded in favor of making 4 com- plete calculation for every experimental point and plotting the point without preliminary fairins on the final eurve sheet. This direct plotting of unfaired results was followed in every case except that of the three low blade angles of the two bladed propeller where it was necessary, due to blade deflection and tip loss, to fair ? against J before the final plot. Having indicated the manner in which the propeller charts were made up let us return to a consideration of those factors which might affect extrapvolation to full scale. Reynold's Number: ‘The actual velocities of the blade elements were made equal to those of full scale by increasing the rotational velocity of the prop- eller six times (2,000 r.p.m. full scale vs, 12,000 r.p.m, model), Axial wind velocities of 200 m.p.h. and upwards are obtainable in the California Institute of Technology wind tunnel, hence the airspeed of full seale flight could be used. The irreparsble difference in Reynold's Number lay in the characterictic length, which of necessity remained at one sixth full scale. It should be noted that 1< the length of chord be used for the characteristic le gth, the Reynold's Number of even a full seale propeller element is small com sred to the Reynold's Number of 6 full scale airfoil section as used in s wing. Research in the (7) t } } } F t | + come o t | f : } | i { I it 4.0 >: ie ! : .. GAVE Pkt Sunn Popes e¥ on] bed bed O00 ETSY OH Ft Fa aa et ne MUBOREGES He oe ti: VO BEE eR Re ee AL fa eee ed a RR aE Me EET Pt Th a fF BENG! Wieum Gouyd Dusan Beeee Dee a i pe ) pcbd Eta Faery Pt 0b eee Save eae it MEAG Whe in abl bia Mia eit he : i | i | Fr es a Fug TCE EEEGUn UES J cua wean FAI LGHA he . oe Led i = LEE ee 3 PEK (ordre Citra ERWOHCURER SaEOUGHEAHR sued ceSas ERGO RTC EE RECS A Ey> {RCE EEuOs ESLER RAC OMIT PER TUERSaa ype ccaeeeocareteeeeoeeT §«=©=©— RRR UII ER PRUE Ce TAVERN ENENN HOGG Gal Sil DRM Moimiea hcae Cond PSS00 NESEMUCOMG Rogue tawge eaews bees EMwen Oma Papas) eae + fy eee oeees 1 Baa keznl ne t oad 3.3 7.2 3 SSS oe 29 7 3.0 28 74mg 18 47 Ws Le ; 4 ee Se ee | See a L. Frativ rs rent 4 i A. 1 } =a Koa | i | 4 at { i ei Ht pea ae tcl a +-4~ “Y z a by a i ERE wap f 1a 9 4 } i | soi J ie i { GH aE ET Pel att LQ... ASS ea ae i ANY Bayes ies FITTS ae Fi sae | } 1 wg - a fz tek 7 OB eZ Wibe ee fst Wr: 2 ye f + 2°fec.. of -eyn:. i's “Sumber on extre viation oF wor. t sl. SOs. foils has sown the: Reynol?'s ‘tum er has -onside-- . ffect. It is ite reascu: +, and just:fication can 2e found in toth theor and experiment, :0 suprose th: larzer effects obtain in the differences =° such smsii Reynold’s ‘tumbers +» those of our propellor slements where the chords are so much smaller than the chords of model and full seale wing sections, The tyve of flow ovar t:i5 blade mst be affected by the nature of the surface, Our model blades were burfei to a hich polish, kept clean and rebuffed 2t intervals during the experiment. Roughness apveared due to impinging dust in the air stream, but it was not e..cessive nor could it be considered imcompatible with full scale operating conditions, Turbulence conditions in the California Institute wind tunnel are comara- tively favorable, Blade Deflection: Linear deflection of the blade can be shown by the andlor’ to a cantilever beam with distributed loading to be one sixth the lincar deflection full scale,and angular deflections to be equal.(See Sketch), It must be remembered that forces are one thirty-sixth,and lengths one sixth, full scale. . Blade deflection is caused by the aero- dynamic moment on the blade element arising as 4% Z Y Y q si wh . 3 2 = Ber shown in the sketch. Neglect drag es being q : oe | —— a &é rey emall in comparisen with lift. Note that for 4 BE &Y normal airfoil sections the moment about the = K(L) 25% point is small and constant in the work- ing range. The crincipal force acting on the ww Yo blade element is then, lift, which is resolved -¢» 7, . pu MeL Lae | +) =1 into thrust and torque. This force is Seketiots, by the elastic strength of the blade corcentrae ted at tne elastie centrum. However tnese two principal forces are not eollinesr, but, on the contrary, lift ucts at the 25° point snd t-. \ elastic centrum ocqurs at about the 33° porst (8) There results a couple tending to raise the enterin: edee of the -ude, The strength of this couple varits approxi ately with the square ©* the sir velocity over the blade element and linearly with its effective angle of attack, Tip Loss:- Inext ricably bound up with blade iePivetion ix our experimental data is tip loss, Our tip speeds were those of full scale, 3oth British and Amer- ican experiments have shown, however, that at high tip speeds scale effect will be more strongly in evidenre than at lower speeds. The plot of points for 12°, 16°, and 20° blade angles, two bladed propeller, showed effects of tip speed and blade ‘deflection. A special study was made of these conditions for the 16° blade setting and is presented in Figures 6 & 7, The 16° blade setting was chosen because the greatest variations in power and tip speed were obtained with this setting and the recorded data could be compared with a lower setting, 12°, and a higher setting 20°, It is to be noticed that only these three lowest settings for the two bladed propeller gave such variations in experimental data as to require fairing independent from the final plot. the three bladed propeller, having one additional blade lending its quota of work to provide a given thrust, showed insufficient scatter of points even at the lowest blade setting to warrant preliminary fairing. Returning to Figures 6 & 7, it can be seen that under the hizher power load- ings the characteristic curves of the propeller move over in the direction to join the family of curves of the next hizher blade setting. If one scales off the shift of the curve T, vs J in Figure 6, against the main interval between curves, 4°, an indication is civen of the effective twist of the blade in terms of blade setting at the .75 radius. As the tip speed increases, however, the effect of increase of blade angle is gradually overcome by tip loss and the curve drons back again, to or beyond, the curve obtained from lower power loading, The question arises as to how the fairing of 9? vs J curves of Figure 7, shall be carried out under such circumstances in order to represent practically the efficiency of the propeller at the given blade angle, The method actually used was something of a commromise, 3elow the peak efficiency ( and the region (9) y oes Turust | Conrr ice vs. } “ADVANCE FaATIO™ . For VAR sacet lous) Wino Tum 2 SPEEDS t¥ TERNS * SHOWING FPR =. 4, THE VELOCITY or Pane { it t Meereroie pelker cd i ‘ ' ‘ } an se: C2 a em). - Z, a { } 1 ec ie rt 8 Wer da. a im} 4 oF SESE R BB ose 2 } OF SOUR = Ve/o ! & i | 4 ee | 4 1 | a | { i i | ; Sarre ae ae es ee ee ae ina Pee pee pays Pa lh peoeee ta | ' \ | : I H Peas Ca | i 7 ee Pr ts | | i Peeeepe ds tay bety \ .! cy) ee) oi ESOS EUR SANG ATES SR SAPD SEE ERIS EEBAET ' | i \ eae nes ! a foe ea Sf Tuas Te gee pore { 1 ’ ! i pe {4 } | ! 4 re 4 ‘ ' Lied alte | ie | Ea eae bead Cae pote eh 4 CE CAG SEIN ik Pees BS tae Heep, bol an Streit Pete rw | petthy frat ies ite ee tit SN RSH peed PAE be GA RS He > gle, [3 et a aS i i "Blade a rt ' r¢ pare 3 3 1 res § L ie tones Gann bee Sanne Enene Wien ooo auetens rent Glade. | def! @ ctign =O shihe ; Sogn We ag soft} aise Stet 4 Saar S. FIGURE Saws Swe SSaeH wee Wes t artctit ty erage Kaul Denes wat | Hea aoped SNES A EES — Tod wre — SO RICLE s ™ E l Les: 7. FIGCRE in which the vropeller would ordinerily be working) the envelope of the curves was trken, “eick has worked un a Very comprehensive and complete set of data on the correction of propulsive efficiency for tip speed. The envelope of eff- iciency curves is our best estimate of the efficiency of the proveller without tip loss. A point taken from the curve then in this region may be corrected for tip loss using ‘eick's full scale results in this connection. The region to the right of the peak and the peak itself present a greater problem, Reasonably the lower power loadings could be used and a correction app- lied for power ( that is- blade deflection due to power loading), but lower power means Lower forces actually measured and st small forces our experimental accuracy falls off. Hence the writers took arbitrarily a mean of the points at the peak efficiency and beyond as being the best representation of the actual characteristics of the propeller at the given blade setting. The final faired curve used in presenting the data is shown dotted in “igure 7. Wind Tunnel Yall Interference:- A glance at the sketch Ky, , , JLLLELLLLL LL LL will indicate that free air - 7. ce. V eee eee eee Vv, Vita) —» Vib) eee we we mm ow we ee ee ee conditions do not exist in the wind tunnel, but that is TITIITITT ONSTRAINT OF Watts KAISES constriction of the walls Verociry AT PROPELLER on the flow sive a somewhat higher effective velocity to the air in which the propeller is working when compared to that velocity were the propeller onerating in free air, Glauert (in R.& 1°. 1566) has develoved a fairly accurate Séporoximate formula for this increase in velocity. Glavert's formla has been used to compute a correction for wind tunnel wall interference applicable to our conditions. Tigure 8, shows this correction in terms of the thrust coefficient T 3; Figure 9. shows the range of T, used in the experiment. It is evident that this correction can be safely neslected as it is well within the experimental error. (10) aan Raee oe pase see jaaee wna Hat is qd vas a Be nae ROSE: HHH = Tritt Tt +t StH + +t t nt cas as a oa Ht tho t e+e HTT aa te ee ener» + +4 +} o re ae bt] 4 mm oe i; eases } gay ey ass is ion pesaaty sma anuee ine bade ; Baht i EEE aUSSS! sgubsedaes ners foun: Lopes essadaness totes tata, tsaet Bick + = t a eee as tH cr} . ‘ tts Hiatt sua sou hpnes {+ wey @ awe re t cea aaa te TY t sees He +f 7 7 ou as : 4 ib t ae ; HH EL peucg tee He gS cs becscseeuscuscatsoeaes Hate HH sitet ae tit is Hite ities tH Bin pS SeSGeSeSSganeees raga sie a t one ; a By egen enemas os jft au aeess | AES pers 4 4 Toy 1 Be iyh bse Ss pr ttt as f penises: eugssegsege seat +t sage ses +4 +. Tt seer ae st TRH HH saps geassseae H rH tH sit E sussu: t r hn tf CY r + tT if TT r ise: sad see vac edad bsuet taceacaena bessapeats es eaee ae bi E i. 4 Hit i | jasseahwan t t = rH aa Ty 4 panne 4 eet at Saneee soates “| + i tt + tr + aa ee bas ee pedesses tH H t s pea esaags samee en as HE t aa eer tL ROE H tt iit SSE B Bae? oH 1 tt a an ue om is Boas nase: t t He a + tH : eet pebates tf reps aGaihateadl Ee. +5 4 bs 4 4 ry gee rot eebreganen H Hite Rasedeecescuegeeccoscaanee Sasapes.: Sisee sesepcges: 4 : | / aape of oh ane ‘s Sere mh jana " tt an + = 7 aba rt Ht ins H HE besa eaestcsaed cessuces Hh, Hos o }.] ay sae ke eu pa wa we ry iH + + Ht aS tees ote 0 + a bert 7H yu bgesseeces f | mabe as nap Seen Rages f peens ioe seneg css! H+44 *y + etaracess 4 : Sa adeun : nae hagesegusa danced con: + tH + ; : td as ees i 4 Ht scat +! a d 4 e+e dedat aH am ba : aa tt 0 ane ow: r ne : ; th tity penes Betcncceus it £ ; bees Bas sGi2e5s sens! apoee es ony tert steeds packs sua Se quaus H : tt HH Eigedapeeapsgucssgsgeeedl as +H yeba ne S80 gece tees st srt eae Ss poses Pitt edt Fe FIGURE 8. Ehre iG tT ++ gpa pate 9ee Beers spose. Bene Beads! pangs ceaat n mab anan sas age meee sea tH am t +} peas Hn ag ge aes. + e mus rt ott aamedpaves ina Tit swes © passa bessssees==: RE Y. Figy Experimental irrors Cuantity , Rance of |.easurement Probable Error lift, drag O = 600 “e. -002 Torque, Q -.2 to + .7 Ke. M. 2005 Blade ansle 12° to 36° 0°21 Revolutions/sec, ,n 50 to 250 r.p.s. 0.2 r.p.s. Every effort was made to renresent accurately the actual quantities measured, Discussion of Proveller Data:- It must be noted that with the model's thrust line horizontal the propeller was acting in front of a wing at a Cy = 0.3, Assuming elliptical lift distribution , (with no distortion due to slipstream), and an upwash at the propeller ahead of the wing equal to .75 of the downwash at the wing, (the value of .75 was estimated from Glauert's * Aerofoil and Airscrew Theor," page 162), it can be seen that the vropeller was acting in an upwash of [e} . Ti x57.3 = 0°68 This corresponds to about a cruising attitude, level flight, for the normal airplane, It must be noted also that the full length blade was used whereas in practice the blade usually has some of the tip length removed, Figure 10, shows the principal characteristics of the blade used, Figures 11. & 12. are two and three blided propeller, basic working charts. It must be emphasized that in conputin= Cy for entering the three bladed propeller chart( Figure 12.) that full power should be used, Figures 13. - 18. present various comparisons of the data obtained, In order to ascertsin the appropriateness of applying the model data to full senle provellers a considerable amount of data on full scale proveller settings was obtained, The writers are indebted to the various airplane manufacturing concerns for their kind and helpful cooveration in this study. Vv When worke’ up and plotted on the oro eller char .cteristic charts, the mF vs C, (11) points sroup surpris!: ly well alon t+ : a4 o best efticiency 18 iecernine by the -odel tests (cf, Sieures 132.14. » blade angles iiffer considerably from those of the model propeller but this miy be exvected from the differences in blade design and the amount of the tip of the blade renoved to meet desizn conditions, The flight test data (cf. Tables 1 - 3) are included in this -aper because they were carefully compiled and should furnish good design information. It should be noted that blade angles, f, are taken at the 42" station in many cases instead of at the .75 radius as was done in the model experiment. A study of the flight test data and comvarison with Figures 13 & 14 will show that many of the points are special cases. Examples are two pitch prop- ellers at low pitch, and the same at high pitch where the propeller blade angle has been given full throw against a stop. Figure 15 compares the G.A.L.C.1.T. two bladed propeller results with those obtained by the N.A.C.A,. The comparison is made with the data from Fuselage 76, (Figure 14), of N.A.C.A. Report # 350, which resembled our configuration better than any of the other configurations used by the N.A.C.A. in thet it had a completely cowled engine. Unfortunately the fuselage is rect- ancular in cross section and wing and tail surfaces are absent, The lower envelope of efficiency curves from the G.A.L.C.I.T. data can be attributed, in the writers' opinion,to the presence of the wins, to different shape and relative size of fuselage, and to scale effect, In Figure 16,(comparison of two and three bladed characteristics), it is interesting to note that diff- erences are not so great as has been generally assumed. Figure 17 shows that Yeick's recommended 70% power absorption by a three bladed proveller as against a two bladed propeller is a good average assumption, but that at higher advance ratios the three bladed is operating under improving conditions, Figure 18 commares G.A.L.C.I.T. and N.A.C.A. curves( fuselage 6 Fircure 14 Report /550) of Blade Angles vs Cg directly. (12 poke a tt wd $i nae: rss: ena gene t aeut bs a > + t Be t Te iiti TT + t on seas pegs sugne capes paces Es r ase tt Hh T. Tr sh eden: 1 T t iebataces bacess Le oe + “by Seung Gugpaseseoaeseasseps H Bepesnespogapes seaascagee Fre Btesee THT rH H maqusee me Se seuauscsunegaunn i Hohet HEH bp HES aE > ep aR sum i eI cr Ht eee T rae 5 HE rr tH ey oes : Ht ttt + re aes ee peeecaee’ bee suseeucensus seas tt suse fescgesss tH geaze tages: Ht Steeet a, Het se rr pect isageraen “4 GAG r HEH rt t Gacceesecsuncd cabeenmnnd + H . Bed aee ka ; Rav ewsee ss f spens Becen Puasa 4 ea seeseeesss ete yaesse #oeuscuau suatdavies tata teat st tt Ht eae seges esa HH ie batts HH eee pases 4 soetH + pee ete ses ae | 1 is e ene +f SESS SESESSESSE ER eee =: 1: < + eistresai tH + rr + i rf ' H 3 im I a rt papecs . t rr Bsibd (Saabeees =} 1 sank ‘nascaens + tt eeetatese eH LA + aa bei : is st . + eh pon nageen =] Hy cones SE gia yee tre 7 goers rH igacuneneahanes sat rt aa gng hy 6 t s iss +t $ a s + + + i us cadens 3 1s im Baw + fess +H banga seeds 4 i] +H Et 2 + pense z 4! fae + pity tH i Hitt is aes + es eat + + fog ay Ssase t + +t pees 3 7 it + tt t sper : be a toeaaee sn bdest rH a Peet + at -4 +- rr re an agateud spss + + Torte iecaal he i: rth ray + + a Haat Ht H H aabbsdnadees : EEE 70 FIGORE N yr \ 3e— | H ? | \ve" Poe 7 ae TL} rd / /, LN ! = aa z8 ww eset al } 7 a | ne a 16° } #4 ; acizoat 75 Radius} — J NN ae Z GZ Z Z _W “a3 Line of man 7 for Cs ‘COEFFICIENT FOF VARIOUS BLADE ANGLES Two BLaoro PRopELER CHARACTERISTICS | EFeicrency & ADVANCE Feario us. SPEEO ~PowsR FROM $ SCALE MooEL Tesrs FIGURE UW, Cau. InsT. TEet, 67 AS. Russert, USN MAY | 1935 ut AM Mscor AC USA ZO. ; | 25 3.0 i { 50 7 o N & S i ze bs ’ ? / \ yj & s / \ ‘ 95 Redis 40 \ t a i \a \E TL = / / \ ; ae — 4 ff =<] aa a ° y 4 : ee Z = ZZ) PG a8 Oi zZ0- y— t _—— Se | 16° a LL 00 ZA ae —_ ia EP er paz = 2) S 4+—] a ch i = | LB = Three BLADED PROPELLER: CHARACTERISTICS Za Line of max » for Cs EFFICIENCY & AOVANCE RaTtO VS SPEED- POWER | / | eer nicrenT FOR VARIOVS BLADE ANGLES | | From SCaL€ Mopea TESTS Cause! Isr. TECH, At JS. FPussece. USN May 1935 Lr HM. MSCoy AC USA 0 1.5 sy 4 2,0 25 3.0 | FIGURE /2. = 2.9 49 THiS is; H /8 : tet it aE " ac haar’ fH . . afk tort 5 att a re oH ri x “a i 8 vy ly mi ~ , & . 3 ~ s] ~ Se ” 2 /. 4/7 1.0 isiene a tH py oes euEne Sens Susie v1 5m s6 ae A e4V PE FIievRe. /F¥. Cs: - TABLE 1 Design Propeller Characteristics from Flisht Test Data ait, | BHP Prop. V No. IProp. | B at Pat | [ V Vor. seaples ft, | PCF | om MPH Blades) Dia. '0.75R 42" 8 | Prop. | it | — Douglas O=43A S.L.' 675 | 1750 190.8 13 /[9"lo0" 24%4° ' 1,67 | 976 " C~29 } ™ ! 575 | 2220 | 164.6 12 |9'oO" 16"/2 1,28 .631 " 0-381 ; ™ | 625 + 2000 | 153.8 (3 j;B8tg" , 18.6 1.32 | 773 " YO-31C | mm | 600 | 1750 195 3 9tlow | 24.2 . 1.95 ! .907 " Y1Cc-26A | *™ 350 | 20095 137.5 2 9" | 15.2 1.27 | .6421, " X0-35 fo. 600 , 1760 178.3 3 910": 23.2 . 1.60 ; .907 " XB-? } oo 600 | 2410 174.2 2 85": 19 1.32 | ,754 " o25¢ " 600 1756 161 ;:2 (lotor: 21.6 1.45 750 " BT-2B ” 450 | 2100 . 133.5 ,2 \9°3" 14.3 1.18 -605 " 0-32 of 450 , 1920 133 2 lot | 16.8 . 1,22 .610 « X0-34 ; * 600 ; 1703:, 156.5 :2- 10t9":- 22 =--' «1,42 .752 i 0-324 _ ® 410 _ 1935 129.8 2 -9*1o" 15.3 1,22 600 " 0-22 5000 450 { 8095 142.3 2 “lot”. 15.5 - 1.23 596 " 0-25 S.L.. 600 } 1750 . 156.6 2 .10'9 * 22 1.89 .730 " X0—14 ; oo" 236 | 2020 121.4 2 .8flo" 14,1 1,24 2599 " DClA(S.E.): 6500 700 : 1440 11l 3 1lt6", 2g; 1,00 .590 i DC-1 ; 6100. 710 | 1320 211.2 3 (11'6" 24 1.95 1,225 cane 4100 720 | 1300 202 3 1l' 25 1.95 1,245 " sta, 011 8500-700 «se alR SL gH ay 1.84 1,129 " fin, air; 8100) 710 1930 , 197.8 5 lato" 25 (2.85 1.258 ' i { I " Vente | 5000! 400 | 2090; 145.5 j2 (9 {as | .32 681 ‘ Dolph, \ } I t ' " ; 2800 750 ; 1340 163.5 3 /12'6"° 19% 1.55 .395 ” Sit. B25 1600 167.5 {3 {11°6": 23.8 1.46 802 Pan Am, ‘ j ‘ i { "Grace DC 6000 675)~=s—s«dgoS-s«sa3l cl*#i3 25 Lp i llg9 ' L952 nS " " 700 1327. 208 3° i 544 He 1,93 1,285 " | Sta. O41 DC 7000 522 | 1367 #116 Cl 3 11'6" 21 IP 1,14 649 no " " 650 1340 203 3 11°6" 30.5 HP 1.91 1.16 no cnt (Sei) 4100 894 1416 1l7 3 lt | 2s 1.08 661 " | Std.O11 DC 7000 851 1433 110 3 llte" 21 1.02 587 " + Am Airy DC " 680 1362 129 3 11te" 24,5 | 1.21 272 locicheed} 1001 lect 6500 373 2170 203 2 8tgn £2 1.79 99" " + 1910 lect. 5000 400 2200 203.7 2 9° ' 20 1.76 09253 " { 1010 Beet, 7100 370 2180 115¢Cl 2 9° 14 IF 1,00 519 . 215 .ltair 5000 550 2230 215 2 9! Z 1.79 94: a , S.l. 429 2000 183.5Cr*2 9! 22 1,38 8 | " 370. 527 2200. 12301 2 9° WO, 1c. ata? ‘ 1094 10C El, 6000 450s 2080 +s 208 2 of | 23 Sst 35° , L064 190-1, 6800 410 2100 . 120 Cl 2 9! "1W7ZI?P 1.98 55 n { 1sl2 loa ™ = =69800 300s 2020. lod cr 2 gt 22} ULF Oto " "1009 103" =~=«-12000 «282 ~=—s1850.—s «ase cr 2 9 25 Pauai { .0e2 primer | WB { 342, | a8 | 2000 a a reve | 25.7 | | ate f danas * ' @ 9400 § 810 | 2180 | 225 2ier i aie | 1.75. | @és: " QT=1 5100 735 lg20 ; 215 (3 v6" . 25 ! | i728 | L.08° >> RT =] 5200 738 1905 | 217 ' 3, 986" | 25 1.78 1. " RT=1 13000 = 426-—ssa1750_-: «183 / 3 96" 24,5 1.625 .970 " ~G 7800 428 2040 203 2 9? 23.0 1.77 ov74 j=G 7800 438 2060 | 204 29° 23.9 1.76 .968 " LaBel Ba les 650 |; 1915 | 300 2 ote") 2a. t 1.795 .96U ' A i'S.L. i 420 | zovo | 165 ' 2,9" | 19,5 | i 1,505 | 30" i 1D 8000 675 1950 221.5 3 196" 24,25 1.765 ' 1,053 . 1D 7000 671 . 1880 = 220 2° lot 25,25 1.785 1.030 ‘ 1D-5 4000 719 1930 . 215.5 . 2 9%20" 25,25 1.74 © 1.u00 " Ip.f 8500 714 1950 : 217.5 3 9g" 24 1.695 1.033 " 1D=2 | 7400 . 703 1950 § 219 2 ior 24,25 1.70 £983 " 2D 8000 689 1960 223 2 910" 25,75 1.745 1,020 _% 1D-3 3200 633 , 2040 , 201 2 96" 22 - 1,62 913 — | * Cl = Climb, IP = low pitch, HP = High pitch, Cr = Cruising. } a oes Sain Saas 4 = 1S. ras FIGURE she HH peaal i tr yea ees ifn iowa ‘s rit sth paeas aay TH i Sanus pase +H ae Seees base Ht aete eaues Sage Spent + Gre Bu sees rEss Sastes B: res ae + t as pace seags eres Tt + +o rt enees iit 3 falee cocethar pus cai th onee Pitted 43+ Tae Et etus seeee Beane Ey + HE: Birth TT = jnaae Qoeerure s: Bes tty ot Irth pees wueEs abe Ty + 445 Het tort} gees HH | seeut 3 Ht +t ttt aual te use Weuascoer pHisredl HHS eawe pees tt tT 4 ggeusgeengsa: LF Y Z 5 ne Pig FIG i? i pa aa H ry dares sapes serge cussdcceal sesascs = arte Ht Sot x, suas oo RE /6 rtt sam gees -- t ps ane oe + ro got eH t pee apa bei ubes on ann in ase + ut ttt sags esses pases +t peace pues ween 31 Bai {Re BS Be Sagas peea: FigevRE (7. a, {fH FL > pert thd +r j= Oye testes fs ienen bas is oe ie 4 f 4 zt PART [WO Airplane charscteristics Power-On Power introduces another dimension into wind tunnel calculations in that it is necessary to specify under what power condition the model is acting. However, of the infinite amounts of power invut which might be investigated for every attitude of the airplane, only certain ranges are of oractical importance. In order to obtain an estimate of the rance of vxowers which it was felt desirable to investigate, a typical conventional airplane corresponding to the model was cmsidered, The uvper limit on power was taken as that corresponding to the maximm power available for such a plane as a function of its velocity at sea-level, The lower limit was taken as that corresponding to the power required for level flight at sea-level as a function of velocity, In order that the results might be applicable to other normal planes with somewhat different characteristics, the ranze of vowers in- vesti cated was considerably extended beyond these two limits, It - should be explicitly pointed out that the characteristics assumed for the full size airolane are used only to determine the limits of power investigated and do not enter into the deternination of the- effects of power. In order to oresent the stability and pitching moment results, it was also necessary to assume 4 center of gravity location relative to the mean Adieaeniilite chord, This was chosen from the full scsle characteristics of the typical conventional airplane mentioned above, (15) The typical airphane was taken as the Lockheed Vega since its geomtrical form, wing section, etc. correspond fairly closely to those of the model. The following full scale data were asgumed: Weight, ¥ = 5000 lbs.; center of gravity at 36% of the mean aerodynamic chord and four inches above the thrust line, and maximum brake horsepower 550, From model tests were taken: Equivalent parasite area, ps 6.44 rt.” Airplane efficiency factar, e: .89 Maximm propulsive efficiency, 7 max: 825 Blade angle at .75 radius, B: 30.3° Revolutions per minute at maximum power, N: 1350 These data in combination with the physical dimensions of the model to full scale gave, in Oswald's notation: (see NACA Report 7408) 1g = 5.23, lp = 777, le = ll, f\ = 8.5. A table of thrust horsepower required against velocity was then made up using sinking speed de to parasite loading Wgp and sinkin= speed due to effective span loading Wag 8% various velocities. Thrust horsepower available at velocity was determined approximately by Ry = = ; -Ry and B to get Cs; -Cs,7, to get Thra- The standard thrust horsepower available end thrust horse- power avainst VY curves were transmuted to a form suitable for wind tunnel work, The ordinate, power, via B, VY, and Cg, became J; and the abscissa V via ly and Cy, became Gy. (Qy = wind tunnel angle of (14) attack). The conventional thrust horsepower avail: "le and required curves are shorn in figure 19, These two curves converted to a form suitable for wind tunnel work are represented in figure 20, The appropriate wind tunnel "q" was determined by examining data of T,. against J from previous wind tunnel runs, A vertical traverse was made across the power curves using "n" as the controlled variable, as indicated in figure 20, For example, at a wind tunnel angle of attack of +2° a wind tunnel velocity corresponding to q x = 10 grems per square centimeter, was used, and the revolutions per second of the model propeller were varied in seven equal incremats from 69 to 112 r.p.s. It is evident then that all power conditions, from that somewhat under the power required for level flight, to that corresponding to somewhat more than maximum power output, were covered. This was the laboratory procedure for the power-on condition, The effects of power on lift, drag, and pitching moment were desired, in order to furnish information on free flight performance stability, and control characteristics of high wing monoplanes, Effect of Power on Lift, Drag, and Performance In order to give a satisfactory discussion of this subject, it is necessary to analyze the problem somewhat more closely than is customary. ith this in view, let us consider an airplane in (15) feaass Euas sases tone Le +ttH it Ht i? FIGURE ae ee rine PU San Ba a ee Pe”; A eS + DRE i tbistih dace siiele eee wpe foure pe — aati =o heehee de ae coe 1 9 H we: L£ a ie) St i s to Y 942 Lat - as Log BRE / OF he | | { t ae : a 2 ——— ss i i [ pert | Ge) ! ‘ ! ” wit Pia cs ‘ SS Soe —— | i SS eee : ( ONT wan bt azinp — ear rraat DFA ORAS B-I7F : 4 H { aT AE | i FievR&:.4 0 climbing (or glidim-) unaceelerated fliz-*. “he forces ac tine in the direction of the flight path may be srlit up irto = thrust, a drar, and a gravity force as shown in the accompanyin: diarren, ~, Horizonta/ where T = component of thrust in the direction of the flight path, D = drag, @ = angele of climb, Y = weight, VY = velocity alons the flight path. The equilibrium condition is 1) D+ Wsine = T The precise definition of D and T has not yet been given. However, before discussing this question, let us first transform 1) to a more familiar and convenient form, s‘ultiplyine by VY, expressing T in terms of brake horsepower P, and a proreller efficiency 7's (16) and introducing the drag coefficient, Cp, we obtain: 2) Cpla,J) qSv + Wsind.V = P 7"(a55) where the variables upon which Cp and "" may depend have been ex= plicitly indicated, It will be noted that equation 2) is just the usual performance equation. We have just stated that the precise significance of D and T in 1) had not yet been given, This means that in 2), Cp and ” have not yet been exactly defined. Actually we may de- fine either one in a rather arbitrary fashion, the other is then determined by bin fact that the forces mst be in equilibrium, i.e. equation 2) must be satisfied. It has been customary in the past to define Cy(a, J) by equating it to Cp,( a) which is the drag coefficient of the air- plane without propeller, Then in order that 2) may be satisfied, the propeller efficiency 7*(a, J) should be replaced by a propulsive efficiency 7 (a53) determined from wind tunnel tests on an airplane or model with propeller running, and for all pertinent values of J and a, 2) would then take the form 3) Cp,(@) qaS-V + WsinO-V s P7 (a5) Practically all propulsive efficiency investigations in the past have been restricted to the case of zero inclination of the thrust axis, so that the dependence of ij on J is well known, while its dependence on @ has been very little discussed. It was one of the essential aims of the present series of tests to furnish data on, (17) this variation of propulsive efficiency with thrust axis inclination, The data so obtained could be presented in the form of a series of normal propulsive efficiency charts each corresponding to a definite value of @ or thrust axis inclination. However, the complications introduced into normal performance calculations, through the neces= sity of using such a family of propulsive efficiency charts, would be so overwhelming that it is very doubtful whether the data would be of ay practical service. An entirely different method of pre- senting the results, based on a rather different point of view with respect to the performance equation has been suggested by Dr. Clerk B, Millikan, and gives the data in such a form that the designer can use them in performance estimation without any essential modi- fication to the normal calculation procedure, In introducing this new method we return to equation 2) and replace 7'( 25) by a propulsive efficiency Zot ) which is determined from measurements at zero inclination of the thrust axis, i.e. 7° is just the propulsive efficiency which is customarily given in the standard propeller charts, Then in order that 2) may be satisfied, we must replace Cp by an effective drag coefficient, CDp, so that the performance equation now takes the form: 4) Cp, (2,5) qSs-V + Wsin@-V = P 73) . (Note that at zero inclination of the thrust axis, equations 3) and 4) are identical, i.e. 7 - Zo and CD, = Cy). With this equation, performame is calculated in exactly the normal manner, using the standard propulsive efficiency charts, the only (18) modification being that Cp, is used instead of Cp. We shall re- turn later to the discussion of how this modification is accom- plished and shall see that no considerable additional labor is required, We must first, however, investigate the manner in which Cp, may be determined from our wind tunnel tests, In the accompanying diagram, the forces in the direction of the relative wind which act on the model mounted in the wind tunnel are indicated. Ris the resultant force exerted by the mode] LLLLILILILISIIL LIZ LI LIISA LLL LT on the drag rigging, taken as positive in ——> «C__», 19 oO ~~ the direction of the drag force, Hence the external WITITTTTIVITVITITTATIT IT 77777, =‘*oree which the drag rigging exerts on the mode] is R, take@m as positive in the direction of the thrust. The diagram, which has been drawn with all forces positive, is exactly analogous to the previous free-flight diagram except that the wind-tunnel diagram corresponds to a case in which T < D, i.e. to an airplane in gliding rather than climbing flight. The condition that the forces be in equilibrium leads to the equation D = T+R, or mltiplying by V_ and defining the drag coefficient and pro- pulsive efficiency exactly as in 4): 5) Cp.(a,J)}qSV-RV = P 7 of J) Comparing with 4), we see that the wind tunnel and free-flight equations are identical if 6) R = -W sin @ (19) This means thet the resultant force exerted by the drae balance on the mojel plays exactly the same role in the wind tunnel as does~ the camponent of the gravity force alon; the flight path in un- accelerated free flicsht. If we deter.ine values of CD, in the wind tunnel for a series of values of R, the former are identical with the values of Cp, in free flight for the corresponding values of W sin @, It appears now that we mst determine Cp, as a function of three independent parameters a, J, and R, However, it is easy to see that only two are independent. Dividing 5) by q S V and intro- ducing the coefficient of resultamt force Cr = R/qs we obtain P%” Cp.(a,J) = Cp + —W& De(%J) R asv But, at a given a, Cp is a fumtion only of J, i.e. J = J(a,Cp). Hence, introducing torque and revolutions per second, Cy.(a,C = C,+27™Q 0 Delp) = Cp +22 F 70 It is convenient to replace the variable a by the lift coefficient Cy since the latter is the essential parameter in the free flight case, If we define the lift as the resultant aerodynamic force perpendicular to V (including any contribution fram inclined thrust) then the wind tunnel measurements zive @ = a(Cz), (cf. Fig. 22). Hence we obtain the final equation for the determination of CDe? 272 old) Dia,-q 8 J 7) Cog(Cr, CR) = CR (20) + Cr, Cp, 2, q, and J are measured in the wind tunnel, Dia. and S are known, and Told) is obtained from propulsive efficiency charts corresponding to zero thrust inclination, It now only remains to express CR in terms of a paraneter having a significance in free flicht. If we follow the definition given above and take L as the resultant aerodynamic force perpendicular to the relative wind (flight path) then we see from the first dia- gram of this section that for unaccelerated, rectilinear flicht L = Wocos 6, Combining with 6) ra) Eos or finally s Hence our wind tunnel observations finally cive The complete results may then be expressed in the form of a family of polars of CD, vs. Cr, each polar corresponding to a constant angle of climb (or glide) 6. These polars will have somewhat the character ‘of those in the accompanying sxetch, possessing a common intersection at the Cy corresponding to zero thrust axis inclination, which will normally be near the high speed attitude of the airplane, (21) Ye return finally to the question of how such data can most easily be used in performance analyses, fol- lowing Oswald we may define the airplane Tarust ax along Fight Poth ra efficiency factor e by the equation P 2 CL + C e- Ff AR Dp (AR = aspect ratio = oF /5 and Cp, = parasite drag coefficient) where e is ee, so as to determine as nearly a constant value of CDp as is possible over the flying range, Now since all of the polars will normally intersect close to the axis, Cr =0, CD, will be practically the same for all, and the effect of variations in ® can be taken into account by varying e mly, | This means that we may present all of the wind tunnel data pertinent to normal performance calculations by giving 11) e = e(@). Performance calculations may then be carried out in the conventional manner except that for any particular ansle of climb the appropriate value of e, and hence of span loadings, mst be taken, Before proceeding to a discussion of the experimental results in the light of the above considerations, it micht be vointed out that the ansle of climb as introduced above appears to be the most satis- factory dimensionless parameter which can be found for describing the eandition of power output under which an airrlene is operating. Not only the performance characteristics of this section, but also the (22) stability and control regilts of the next are »oresented in terns of tnis convenient paraneter 6, The experimental lift and drag results are civen in vies. 21 and 22, "ig. 21 shows that the addition of nower has made very little chance in the conventional polar curve at low lift coefficient. There is, as we misht expect, an extension to hizher lift coefficients due to (1) liftwise force cenerated by the propeller when inclined to the free air stream velocity, and (2) the effect of the increase in velocity of the air stream over the center of the wins in delaying the break down of flow, (This may be considered as due to the scouring action of the accelerated flow on regions of incipient break down of flow as in the interference drag region at the intersection of wing and fuselage). In Fig. 21, power conditions other than that for level flight are omitted for clarity, They coincide, practically iden- tically with the level flight curve given, up to the point where the power-on polar departs from the power-off (no propeller) polar. Beyond this point increasing deficiencies in power corresponding to increasingly steeper gliding paths, cause the power-on polar to ap- proach the pover-off polar more and more closely. Fiz. 22 shows the effect of power on the lift against ancle of attack curve, The velocity curve for the equilibrium condition of flizht is superimposed and it is interestins to note that the velocity at stalling, and also for landing at a siven attitude, is reduced by about 4 miles per hour in the power-on condition, The practical results of this portion of the investigation are, then, that for high (23) (IID SIMO | DY | NO: \MIMOy ‘| pretie pases ens ts + ve eagess 2 See as fas tT saad Freupe kf yan atabetd gies nants 88 oot a! 1 MO = MRM Qe BLO. pas ‘— — me ob ALIDOTIA — wv oo/ ot “t- zal! - +1 ° y ~ + j Bess as O9/ og! | -— Hot Ore Fraver i | | | oped cones Beene Seeen Bones ar }: ! ! 7 | LY, AO): FIAIOD | Lesh eb Tce re dea bile! a Blades Sool real a Ma ead ARE AA Seeded I x2 wing monoplanes similar to that investicated, power-on increases Cr quite noticeably, while e, power-on, may be taken as identical with e, vower-off, for performance calculations. Effect of Power on Pitching Moment, Static longitudinal Stability, and Zlevator “ffectiveness Pitching moment coefficients about the assumed c.2. position were determined in the usual manner from the observed pitching moment about the axis of rotation of the model, the lift force, and the resultant drag force R, Fig. 23 shows the effect of power on the pitching manent vs. lift curve. The definite destabilizing effect is apparent, In the case of the wing and image allen, as well as that of the complete model, the slope of the moment curve has been siven a vositive increment by the addition of power, The effect of varying degrees of power is shown in the curve for the complete model, <- contours are drawn in for tan @ = 2,05, +4.10, etc., in equal incre- ments, It appears desirable to extend the study to the case of the idling propeller where the power is negative, i.e. a brakinz power, which would involve developing a negative torque equal to the friction torque of the idling engine (itself a rather variable quantity). Developing and recording a negative torque was quite feasible with our apparatus but involved operating delays which would have drawn out further an already extended investigation. Fig. 24 shows the effect of power on the effectiveness of the elevator. It is seen that the effectiveness of this control at all "up" engles, and at the larger "down" ansles, is enhanced by the (24) 1A Cie, TM pat tee ee WITH Oe 7 TAL + as eg peaee au 23 FIGURE _ ELEVATOR EFFECTIVENESS, POWER ON & OWE! ~~ YURE presence of the slipstream, In woke of propeller: — tf g OY Ax, hence AL, AE V my {ij aa AV, U sh hence AL, : SS The addition of the operatins propeller to an airplane in flight introduces forces and maments as shown in the sketch, The normal force, "F", is caused by the anzle of pitch. It exists whenever the propeller is deliverine (or absorbinz) torque and when the thrust axiS and the velocity vector of air throuzh the vroveller are not coincident, It has been evaluated in various British "Reports and Memoranda", and the evaluations have been clearly summarized by Dr, C. 3. Millikan whose summary is appended to this report. "F" is a relatively small force but in this tyne of airplane acts at a relatively large distance from the center of rravity, hence may exert considerable moment in pitch. Thrust, T, is a large force but acts st 2a small distance from the center of gravity. The aerodynamic moment of the propeller, Mp, is small and transfers directly to the center of gravity. Ye have an accelerated flow over the center section of the wine and a change in the effective angle of attack, Hence the lift distribution and the downwash must change. When this accelerated and redirected flow arrives at the tail surfaces a change in lift of the tail results. Upon this lift at the tail we depend, in normal desicm, for proper longitudinal (25) stability. Nothing thus far has been said of the rotating character of the flow behind the propeller. Unfortunately difficulties in technique and lack of time prevented an investigation in this direction, An effort was made to unearth some satisfactory method of predicting the slipstream effect on longitudinal static stability. The technical staff of the Curtiss Company some years ago combined contemporary theory and some empirical propeller formulae, in order to express the change in angle of attack at the tail surface for various power conditions. nowine the change in effec- tive angle of attack at the tail and the increase in velocity due to slipstream, the chanze in lift on the horizontal surface can be estimated and hence the chanze in pitching moment. (See Curtiss Revort #2721 "Slipstream Effect on Wings and Tailplane", ‘m. 4, Miller). _In applying this method, some assumption as to the portion of the horizontal tail surfaces effectively within the slipstream should certainly be incorporated, Ustimated chanzes in moment by this method when applied to the model tests of this report showed a rather generous margin of conservatism, A second method suggests itself. A tail effectiveness analysis such as that given by Dr. C,. 8. Millikan in his course in Aerodynamics of the Airplane, can be used with an arbitrary cor- rection to the tail efficiency factar, VAD to allow for slipstream, The arbitrary correction can be found by reference to standard tests, (26) vower-on, in the wind tunnel for the t:~e of plane under desicn, This appears 4a very avoroximate method of correctins for slipstream effect, but it can be used to sive the desimer st least some idea of the truth, The method of tail moment estimation may be summarized as follows: Consider the difference of m-le of attack for zero lift of tail and wing. Aq = 4 between Cy = 0 for wing ~~ Wing alone and Cy = 0 for tail alone, Se ~ Hevigental Tail Y ~ ~— Surlace SS —‘“‘a‘“R—— SN Aes ee _ = w at ¥ ~ ~h Oy =O + Oy = 0, Oy = ty = Og Sly é = = downwash at tail due to tail. t tw, ARt € = downwash at tail due to wing CL « “Gree downwash et wing due to wing Now the effective angle of attack of the tail is ites seometrical anzle of attack from zero lift minus dovmwash due to its own finite AR and minus dovnwash die to the winz operating ahead of it. This last we assume in nractice to de twice the dowmrash of the wine at the wing, Defininse 290 8s the slopes of the lift curve for infi-ite AR, which may be co lered aa a universs] conetent “or all normal sirfoils, (27) Then CL, = 89 x effective mele of attack of the tail = A(a, - & = Ee) wa, (a fq = fy - € = Gg) by the underlined assumption above, Cy CLy Assuming elliptic Clg * 80% ~ So ~*o Win, ~ *e@ litt distribution y AR for wing and tail surface Q Cte * Fay Oly * OL - ACL - Mota Go 1 2 ees Cle me TAR Cr - "9 ad : 1+_30_ l + MAR AR, Now the pitching moment of the complete airplane is made up of that of tail and of another term primarily that of wing and fuselage but including all other factors. Me=eMp+M = Me- i, 2 where £ = tail length 2 Cy = Cyr + Cy where Oy, = “t --4 £% or, Ve - a t+ s Using Cr. above 2 le ao ’ 5 vt s a b= &o “a 1+——— Li But write rc ’ and Tt will account for effective velocity at the tail, and other errors sich as that of the assumption of wing downwash at the tail. (28) It will be noted that the term containing dg in the expression derived above for pitching mament due to tail is con- - trolled by the pilot with a stabilizer or trimming tab adjustment, but that the mltiplicative factors, —the tail volume coefficient, ix » and,within narrowelimits, tail efficiency, %t» — are controlled by the designer, Differentiating the tail moment expression with respect to Cr we get: . ao ee - 714 1 - WAR acy +S % ug. ais AR, 7 4 can then be determined by graphical solution on Cyr VS. Cy curves for any operating range desired, This can be done for the ordinary wind tunnel model without tropeller and then an appropriate correction applied for power-on for the type of plane and position of tail. The correction can be estimated by reference to power-on tests of models of similar type. In our experiment the slopes of the tail moment curves against Cy for various conditions were determined graphically, and the tail efficiencies computed, For our model ai e i a 228 x 60,2 [1 ~- °°°/7 5.97 ee icy = 7 (t 87.8 x 293 “+226 (4 5.5/__ re lr 4.07 “80g or te = (29) rom) —— is a Ar Z7GUeres Condition ~ “atz uc’ A+ Power-on, Cy renge for normal flight 244 916 -,046 Power-off, " " ai - ™ .256 .962 Power-on, entire range of C;, mean value, 2252 872 -.026 Power-off, " * " «a * a -249 898 4 ‘Hence if Y%_ were determined from an ordinary wind tunnel model of the airplane type used in this experiment, it should be re- duced 0,04 in order to approximate power-on effectiveness, A comparison of the individual contributions of the wing and fuselage as a unit, and of the tail, to the destabilized condition, power-on, is of interest. td Cr = Cige + Cate aC AC Ch acy acy, acy Power-on -.059 = .185 — ,244 Power-off -.086 = .170 = .256 Change 2027 =» .015 + .012 which indicates that the wince and fuselage, and the tail, have shared almost equally in reducing the longitudinal static stability. The writers feel that in this reaearch problem of power effects on a high wine monoplane, the field of power-on investigation has been barely touched. The model used can be readily converted to low wine, moe there is, in process of manufacture, 4 tail on which the horizontal surface can be displaced vertically as well as having (30) adjustable stabilizer incidence, elevator an-le, and tab anzle, It is hoped that the next class of graduate students in aeronautics at the California Institute of Technology will be able to extend the glimpse we have had of power effects on the airplane, Grateful acknowledgment is mde to the staff of assistants in the wind tunnel, to Dr, 4. L. Klein for his able desicn of our apoaratus, to Dr. C. B. Millikan for his direction of our research schedule and valuable assistance with many ‘motty vroblems, and to the head of the Department of Aeronautics, Dr, Theodor von Karman, for his inspiring interest and clarifying suggestions, (31) TABLE OF NOTATIONS meets LS ee aspect retio of wing aspect ratio of toil surfaces éraz coefficient = 1 qo drag coefficient, pover-on, defined as in text lift coefficient = ey qo pitching moment coefficient e ats coefficient of resultant force dragwise, porer-on = + q torque speed coefficient thrust coefficient = EN fe) n“p* tornne coefficient = _ 2 rf) n”p? 1/5 Vv speed vnower coefficient = 375 r 5 n velocity of sound propeller diameter drar, force in direction of air velocity parasite drar drar, force nower-off and a = 0 drar, force vower-on, defined as in text airmlane efficiency factor* equivalent parasite aree* force developed by a propeller normal to its axis of rotation altitude shove sea-level propeller advance ratio = —~ n a constant lift, force normal to air velocity teil leneth, e.c. to elevetor hinge parasite loading verformance maraneter = = * evan loadin: -erformeance pirameter =_* * ; ,2 e\K D7 * wejor’t + 2 c% nowep nerram: ters * Shy, 7a 32 4 < @ ZJI~wVs Mmm dp wes 4 W wing loading =; BS) pitching moment of model about c.r. pitching moment of propeller about intersection of its axis of rotation and plane of the blades revolutions per minute revolutions per second power (normally brake horsepower) torgue developed in propeller shaft Qo . 9 0 v2p5 agp torque coefficient = ratio J to design J ratio N to design naxinum N ratio V to design mximim V dynamic pressure = £v resultant dragwise force, power-on wing area chord length thrust © effective thrust thrust horsepower available thrust horsepower required air velocity air velocity in slipstream weight of airplane doenwash velocity ancle of attack (measured from thrust axis in this experiment) dvlade angle of propeller indicates "increment in" total linear deflection dommwash ansle 7.7 propulsive efficiency = — at ae=0 propulsive efficiency at “:'s other than 73ro 33 Do 3 xe) n Us +4 ~aeee = tail efficiency = ancle of climb (negative values indicate slide) = airplane verformnce parameter* =z air density = air density relative to standard density at sea-level = total engular deflection = "corresponds to" = “implies and is implied by” = "“anelet eee eee www 34 = P/ 0 SIDE FORCE ON A YAWED PROPELLER*™ Aopendix by C. 3. Millitan Let a thrust loading per unit lensth of span alone a blade b = torque force loadin~ per unit lensth of span alonz a blade adr = thrust on a blade element dr rodr = torque on a dlade element dr X,Y,2 = forces on propeller X = thrust, Y = side force The relative wind striins the propeller has components U, v; In general v < V, i.e. we consider small an-les of vaw. “cf. R, G. Harris "Forces on a Propeller Due to Sideslip", R @M Wo. 427; and H, Glauert "The Stability Derivatives of an Airscrew", R &¥K No. 642. At a fsiven instant let 8 “@efine the vosition of a propeller blade. = inticates summation over all (8) vropeller bdlades. Rr wR ra fear : y= Zf sin.8@ dr 8 ps B oO 1) Xx Consider the propeller acting in a mrely axial velocity U and at a siven J = - Then the equilibrium conditions are: U.., nD Y Yo = O, andX¥ = XY We asit for the chanzed X,Y que to a side wind v. If v is small, we assume R= X+2hv = x+y Y= Yy+@hv = vy Now a and > are »roportional to the local u@ (u = circumferential velocity) and to a function of the local J = J', i.e. a,b #9 u2r(JZ) where J's U - ru enr u Write a = ku*?f(J"'), Let & corressond to an increment at a given blade element due to a chanze in conditions at the element. Sa = im2.c(s') . 2a 4 ite af SF u aa! f = ou Qa = ae2-—= 2a ' ss + apt Od “au 262 ad! put gts SE Sse el mV Su sz _yr Su a uou u 2 8 S Su a-2'22 a= 25R (a-3 ag) So = 28u(p-J' Bb) u 2 OJ! andu=2Tnr, Su =-v sin @ . Su v_sin 9 u 2mnr a Sa = _ v.sin 9 An nr 3) So = -MsSin® ay nr J = U oR A()=a-$3)() nen Here we have replaced the local J§ =-—U by J= U (or 2.5. ewnr 2 tenR nD This is justified by the following argument: J 2 f(r) = U af ad nk sity = U of og! nr g WU nr Now consider a siven blade element, i.e. r = const. ‘Then we fet the variation in f by varying 0 keeping r constant n e se J Or rh VY » u Cy U 2a n9 sIc But our partial derivative in M means just this, i.e. we consider the variation in force on a -iven blade element as the aerodynamic con- ditions chance. « «ae 2. = i 2. .°. Mis indenendent of r. Now R R $X = vX, = 52 J aar = 2 {Soar fo] ° B o R SY = Z [Sbsine ar CG ° Here the intecration and variation are interchan-enble since the ex- »ressions are linear in a and db. ron be} R . SX 5 -xsme faa 6 tn a R r= 2 -zsmte [ara CG n , = Nov since 4 is independent of r we may interchanre its nosition with that of the intesral sisn. We are interested only in the averege force which means we mst intezrate over 6 fron 0 —»> 27 and divide by 27 , This will sive the averare force ner blade. ‘For the whole propeller we mst mltivly ty the number of blades 3B, This scives §X = 0 Sy = ~3X% yn ya ern A r Hence the thrust due to side-slip is zero for small side-slips. In discussing the integral in }) it is convenient to define a dimensionless torque loadins factor eC H = 3 BB .. Bb =g2 @ = 3% e 2, R K - * = B ) brar = rdr = 92 = a -_ 5) 6-3 bse se ate R Now, in the R& M's (loc. cit), it is assumed thet ! 6) fs k ind 8 7 = = universal co:stent independent of J, °o i.e. all torque sradins carves for all provellers are similar and have a shape independent of J. . 8 Y = vk4Qq = ~2kJ (Q - J ag : 2 7) A AQe k = 3.6 aJ g2 +4 @ Qc from 2. & Me G42 Qe = torque coefficient Determination of k In R. &@M. 427 it is assumed: ofS £5 A G-o ; § sual g = Ro toe « feras-1 AED ar nae IN a N AV) Dy i] — 5 is taken as 0.175 .°. TF = 2.06 .°.k = 2.06 los, 5.72 = 3.6 Q.E.D. Hence the side force F on a vropeller inclined at angle 9 to the airflow T D 8) Ag = LJ MM 2 a F is in the sane @irection as tho side vector ve In R. &M. G2, it is assumed that % = Apa - Ar?) Bf T= Ap(1 - A?) =~-J/.. - ‘ ‘ where A= tsi Jog > T, = 0, i.e. J for zero thrust A Ao (-3 A?) x3 mR 2 Aga - A3) 2 a- Q3 3 Tv Faria i ° = B t = TU a « = TT, ~ 7 2% ng ‘ ¢ eray . _ ake 2-a+3A? - ha Az 3g, 2 21.6325, K= 3.6 The mimerical values for a and K are those riven in the R. & M.'s. We have already discussed the mmerical value of AK. Consider a tao ai J 9) Ey J i) s a Hence ea = 1.325 corresponds to the assurmtion J(Qs0) 5. i 20) (1.325) 1.10 In Fig. 26 are vlotted quadratic and cubic ap- proximations to Cp and Cg. It is seen that these’ approxi- mations ma; be determined so as to fit the experimental points very well indeed. However, we have here J(9 2 0 Tipe cy = 1.oh0 i.e. a = 1.12 From GALCIT measurements 3 bladed »~roneller; 6 = 30.3°. eee ESS TT RE FEICIENTS , us ey i i Z usr FIGURE ZG