ARR No. 3E19 NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS WARTIME REPORT ORIGINALLY ISSUED May 19U3 a8 Advance Restricted Report 3E19 FOEMULAS FOR PROPELLERS UH YAW AND CHARTS OF .THE SIDE-FORCE DERIVATIVE By Herbert S. Rilmer Leaigley Memorial Aeronautical Laboratory Lengley Field, Va. WASHINGTON NACA WARTIME REPORTS are reprints of papers originally issued to provide rapid distribution of advance research results to am 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. L - 217 :^^ 9^r q 7r^b"S"7S HATIOIIAL ADVISORY COMMITTEE FOR AERONAUTICS ADVAITCE RESTRICTED REPORT FORMULAS FOR PROPELLERS lU YAW AlID CHARTS OF THE SIDE-FORCE DERIVATIVE By Her"bert S. Ri'tiner SUMMARY General formulas are given for propellers for the rate of change of side— force coefficient v;ith angle of yaw and for the rate of change of p it ching— aoinent coef- ficient with angle of yav;. Charts of the side— force de- rivative are given for tv?o propellers of different plan form. The chart? cover solidities of tv;o to six 'blades and sinful e and dual rotation. The blade angles range from 15° or 20° to 50°. The equations, and the charts computed from the equa- tions, are hased on an unpuhlished analysis, v;hich incor- porates factors not adequately covered in previously puh— lished v;ork and gives good agreement v/ith experiment over a v;ide range of operating conditions. A study of the equations indicates that they are consistent with the fol— levying physical interpretation: In developing side force, the Tpropeller acts like a fin of vfhich the area is the projected side area of the propeller, the effective aspect ratio is of the order of 8, and the effective dynamic pressure is roughly that at the propeller disk as augmented "by the inflow. The variation of the inflow velocity, for a fixed— pitch propeller, accounts for most of the varia- tion of side force with advance— di am et er ratio, The charts may he applied to obtain the rate of change of normal— force coefficient with angle of attack of the axis of rotation if proper account is taken of the upv/ash or downwash from the wing. IJTTRODUCTIOH There has "been a need in sta"bility analyses for a systematic series of charts for the estimation of the rate of chan^je of propsller side force ';ith an^le o^ ya.\i. Al— thori.^h the formula developed 'b^ Harris and Gl'-j-uert in references 1 and 3 and 'liscassed in reference 3, which expresses the side force in vav; in ternis of coefficients for the unyavied propeller, is fairly satisfactory, there has 1:00:1 no adea^uabe formula hased priia.arily on the geDactry of the propeller "blades. An unpublished anp.lysis has resulted in such a formula.. -he hasic assumjjt ions are sir.iilar to thof.e of tl: e --orter: theory for the unin— clined propeller when the Goldstein correction for finite nuraoer of ■bl-..des is onitted. Ccnparison v.'ith a nuraher of e;:per ir. snt £,1 resrlts has indicated that the a,c3ura.c" of "±10 percent ootainaolc hy the analytical nethod is of the order ohtrined oy the uncorrected -rorter-: theor;'' for the v.ninclined propeller.'" The fcrnula, developed in the analysis and given 'herein. ha3 been \iced to prep-'.re a series of charts giving the rate of change of side— force coefficient vrith angle of yavr as a function of the advance— diaaet er ratio V/nll; the "blade angle and soiiaity are parameters; the charts ■covc-r "both single imddual rots^tionv' !ihe cor.putat ions 'were riad'e fo?r tv/o representative propellers , the- Hamilton Standard" S155-6 and the ITAGA 10-3bc2-045". " Means are given for int "erp olat ing for other pr ojieller's .- In crder to nake the present report complete in it- self and to raJ:e the chitrts j.;ore intelligible, forniula,s for the side— force and },it ching— nonent" der ivat iv'es are given at the ov.tset v.'ith an e:cplanatcrv text. x'he other propellur stal:^ility derivatives v/ith respect to ya'-.r are zor c . ?or the purpose of expediting the' purl icat ion of the charts J- the derivation of the forinv.las has "been ouitted froit: the present paper. There is included herein, hove-'-er, a graph that sho^-;s a cor.pari~on of the theoretical values with the experimental data of Lesley, '•/'orley, and Hoy ( refer once 4) . SYIOOLS i'he for-ivilas of the present report refer to, a system of- "body axes. Jov single— rotat ing propellers, the origin is at the intersection of the axis of rotation and the plane of rotation; for diia-l—r ot at ing propeller?., the origin is on the axis of rotation halfv;ay "between the planes of rotation of the front s.ncl rear propeller;?. The S aicis is coincident vrith the a"is of rotation and is directed forward; the Y a:cis is directed to the right; and. the 3 a::cis is directed dov;nv;ard. She synods are defined as follows: D R r S« X Xo B Id a 3o P CCffi propeller diaaeter tip radius radiv.s to any Made eleraent disk area (ttD""/4) fraction of t i^p radius ( r /3 ) nini:n,LLrn fraction of tip radiius at which shanlc "blade f-.cctions develOT) lift (taken as G.2) ratio of spinner ro.dius to tip rs.di^is niinber of "blades "bla-de section chord solidity at 0.75H 4B Z' Id 1 ~ V L'-'TT \ \ . \ I) y . 7 5 E "bD. ade angle to zero— lift chord "lolade a,nE_-le to reference chord, measured at 0,75H station, degress an^le oi yaw, raaians o.n.jle of attack of thrust a;cis, radians Y free— stream velocity q free— st roan dynamic pressure (l/2pV^) a inflow factor A f(a) Cr, arvial velocity at ijropeller disk [V( 1 + a)j ho-" I .. ^ . (1 + a) -H (1 + 2a)^ I (1— I act or I { J. + a; l L . 1 + (1 + Sa)"' -■ thrust coefi'iciont ( thrunt /pn^D ) iciont ( thrust /pT^D^- or Gt/'T^) r Z M cm'.^,. n, Icr, ka I. rotational speed, revolutions per second r,c".v a:i c o— d i s.n c t er rati "> ( " /iiI' ) effective heli:-: an/:::le ^tan ■'• L Va/'(2 ;Tnr — r^lipstr eam rotational velocitjOjT side force (lod^ a:'es) normal f or cc pitcliinr noment (nod?,'- caxes) side--force cerivative: rate of chan^^e of side— force coefficient v/ith angle of yaw [ ( 5 Y /c>i.';/qS ' ] p it ching— Element derivative: rate of change of t) it ching— rr. Oiiient coefficient v;ith angle of ya--r [(3ll/H')/qD3'] r,vera,";c sloiie of section lift curve per radian ( taken as 0.9 5 X 2-.') spinner factor f idewash fact or constant in the equa.ticn for hs s i d 0— ar e a i n d e :c defined "hj equation (2a) (zero for dual— r otat ing propellers ) Is integral defined oy equation (SId) Ig integral defined hy equation (2c) m defined Tdj eqxiation (Sa) Su'oc cr ipt s : 0.75?. measLired at the 0.75E station (x '.75) POHHULAS P.ate of Change of Side— Force Coefficient with Angle of Yaw for Dual— Hot at ing Propeller The nature of the fcr;nulf,s for the side— force de- rivatives nahes it simpler to present the formula for the dus.l— r ot at ing propeller first. For a dual— r ot at ing propeller, the side— force derivative is Cv i'^^ hiJM ^ - kgf( B.)al^ qS 1 + hacrl. (1) where the sipinner factor kg ~ 1.14 the s i d e w a 3 h factor k g^ ~ o . 4 the inflow factor a ~ the q— factor f(a) = =- (-v^ 1 + ST^/rr - l)/2 (1 + a)[(l + a) + (1 + 2a )^] 1 + (1 + 2a) ^ (la) the solidity at 0.7'oR a 4B / h^ OTT \ L y 0.7 bH 1 the side— area inde" I ]_ = 3/4 itio / ( "o/'bo .75 H ^ ^ ^^^ ^o '^"'^ "0 md I^, f(a), kg, and k^ are discussed in detail later. Side— area inde:: -i-~ ^J^c product ctI^^ is pro— portioncil to the area projected "by the "blades on a plane through the propeller a:^is. This area nay "be called the projected side area of the propeller. "he significant factor 1 3^ hcs Deen termed "the side— area index"; a is the solidity at the 0.75S station. In equation (l), !cg_crlj^ is alv/ays snail in comparison v;ith unity, v;ith the result that CY*\i; is appr oicinat ely proportional to crl^ and hence to the projected side area of the pro- peller. The factor l/(l + '^'-aP'^x) ^^^ay be regarded as a correction for aspect ratio. If graphical integration is inconvenient, the side- area inde:: I ]_ nay oe evaluated auite sir.ip)ly and v;ith sufficient accuracy "by Gauss' rule for appro::imate inte- gration (reference 5), v/hich ordinarily req^uires fewer ordinates than Sinpson's rule for the same accuracy. Dete.ilc are given in the appendix. 1h e q— 1 a ct or f ( a ) . — By the definition of a , the e-pr ession T( 1 + a) is the axial v/ind velocity at the propeller disk. Accordingly, (l + a)''q is the dynamic pressure at the propeller disk. Ihe value of f(a,)q is only slightly less tha:; (l + a)^q for moderate inflov/s. Ecuaticn (l) shoTS , t'lerefore, that the side force for a given angle of yaw is roughly proportional to the dynamic pressure at the prcpeixer disk as augmented hy the inflow. A chart of the va,riation of f ( a) v;ith Tq is given in f i gur el. ■j'p inner i act or If the r^ropeller is i^rovided \;ith a spinner in comhination vrith a 1 iquid— co oled na- celle, the cir cunf er ent ial component of the side v/ind due to yaw is consider ahl;- increased in the region of the "blade ch?,nk3 'This circumstance increases the side force "by a f actor kg v:hich is closely given ~Qir K 1 + ' -' - (r-E/x)'" ( 0/D0.75H )sin 3o ^''--^ / (V^o, (lb) 7 5^ pjsin 3q d: xirhere xg is the 1,5 ■ tio of the spinner radius to the tip rali-CLS and K is a ccnstant which is appr oxi'Uit ely 0,90 for a nacelle finep.e5s ratio of 6 and 1.00 for a fineness r?.tio of infinity. Por the spinners of present— day usa~;e, is o: le order of 1.14 ±0.04 A sir.ilar effect undouht edly occurs v:hen spinners are used v/ith air— cooled nacelles, "out the estimation of kg is aore difficult. It is recoanended that the factor 1.14 "be u s e d . S i d e \r a s h factor -. g^ , due to t-ie side\;a,sh of the slipstrean is accounted for Td7 the sidev.'ash fa-ctor l-g_ and "by the deviation of f(a) fror. the value (l + a)'". IHie accurate expression for .— The reduction of side force -^a IS + P,-}.)'"^ r.l ^ 2 ( o/h . 7 5?. ) s in p <^''-^"-/- A ( 1 + 2a)'" (Ic) J The effect is analO£;ous to the reduction of v/ing lift by dov/nwash. An average value of >o is 0.4. E e nu ire d a c cur p. cy , --S an d To the de£;ree in vrhich conparison with erristini^ experiments est ablislies the accuracy — ahout ilO j-ercent — of the side— force formulas, it is sufficiently acciirate to use the mean valn.e 0.4 for >"a and, for the usual sir^e spinner ( X3 = O.ln), 1,14 for kg. Phy study of of t: le 3 data for t i n r- ?3 "^^ pr et at i acts lilc ar e a of ar e a •pr of r 1 at a z in uth; sical interpre t a t i on equations (l) i d e— ar e a index I , an d £._£^ o]2 el ler in yav: . — A and ( 2 ) in 1 i gh t of the d i s cu s s ■ l- t i'x e Q — f a, c t r i ( a ) , v; J- "" representative proxjellers, sho--:s that the eq^u e consistent with the following physical inter- n: In develcpinf; side force in yav;, the prope a fin of v/hich the area is the projected sid the propeller. (The projected side area is th .iected ly the "blades on a plane through the ax ion. i''or t-;o or one "blade, this area varies v "but the text refers to the average value, v/hi ion ith Her e e is ith ch is given to a close approximation by one— half the nunber of olades tiass the area projected by a single blade on a plane containing the blade center line and the axis of rotation.) iThis equivalent fin ma;- v/ith small error be regarded as situated in the inflow at the propeller disk and subject to the ccr r osponding auf!;mented dynamic pres- sure, 'J:he variation of inflov? velocity therefore acccLints for Liort he variation of side force v;ith advance- d i px\ 1 er ratio, for a f i :•: ed— p i t cri propeller. is ■!' J. less VIZ The effective aspect ratio of the projected side area of the order of tv.-c— thirds the geometric aspect ratio rotiition. The effective aspect ratio is much- single than v.ith dual r otat ion ; the smaller as- pect ratio accounts for a reduction in the side force, v/hich for the nix— ulade Hamilton Standai'd propeller cl55— S varies from 4 perceiit at p = 55° to 24 percent at P = 15° A mean val"ae of the effective aspect ratio for sin.^le— ,and dual— rot at inf; propellers of present-day usage is 8. 3.a,t e of Chan£;e of Side— Force Coefficient vfith Angle of Yaw for S ingl e— H ot at in£; Propeller Por a c in^:l e— r 1 at in^: propeller, the side— force der ivat ive is Cyl ii SY/o'i> k„f(a)al, Ii/( ^1 - ^') + r_^ai. (3) The definitions of eouation (l) still apply and v.'h er e A = V .";;a alp + 2 a c-( 1 + al^ ) (2a) T„ = I ^0 1 / (b/bo.-7 5R -OS p^ xd: cos rT) COS A. x^dx (2b) (2c) 3, s the A i''a:nilv cf appr oxirr.at e curves of It are given in fig- ure 2 a^ functions of V/nD, ^^'ith the solidity a pararaetaro T'hc curves are applica"ble for "blacl settings at a given value of V / nD in the range in vrhich the Dlades are not stalled. The data of figure 2 were compiited for a definite "propeller, Hajnilton Sta.ndard 3155—6, cut Ji'.aj'' 'oe applied to any other propeller \;ith negligilils error in Cyi,. The variation of 3a/n v.'ith T„ is given 1 1 ,e:ur e c^ The terra A is positive over the operating range of the propeller in flight and is roughly one— tenth of Ij_o Comparison of eriLiation (s) for single rotation V'ith equa- tion (l) for dual ro-ation s'lo-'s tha.t the effect of posi- tive A is a reduction in Gvi — that is, a single— rotating propeller experiences less side force in than t!ie corresponding dual— r ot at ing propeller. 'a''.' '^'ns for l0V7 duct ion d i s k loa. du c e s th pone nt of y av.f. suit ant load ings pen s ate. its av er ag e is 15 p or c e nt . T he fact that the asyrnuetry red-action in side force in yaw reaches 24 1 ad e an gl e c. is explained oy ding, which for the single— r ot at ing propoll e pitching moment due to yaw, also induces f flovi- tending to reduce the effect of the Por dr.al— r ot at ing propellers, there is no asj-jviinotry o a cause the as yH:.ie tries of the di of the two sections arc so dis'oosed as to 2:1 e r c e nt h e r e— of er pro— a CO.::— angle r e— sk coa— Rate of Change of Pitching Homent v/ith Angle of Yo^v 3?or a du.al— r ot at ing propeller, the p it chin g— moment derivative is ai:pr or.ii/.at ely zero for the reason previously mentioned. ?or a s ingle— rotating propeller, this deriva- tive is given "by "h.^ hll/c'i' kgf(a)ia qDS' " 1 + k^^ad. (3) whore the -.oositive sign is to "be taken for a right— hand propeller and the negative sign, for a left— hand propeller. 10 The definitions prcviouslj- given arc applicable here and CTI3 + ?.J ~ in = —rrz -r— v- (3a) 3(1+ crl3 ) S IDIl-F OH CE CH AP. TS J'oi-Kulas (1) and (2) have been used to compute a serie.?. of charts of the side— force derivative ^Y'^^' - ~irf~ This derivative, otherwise interpretec tvfice the .area of an equivalent fin os ratio divided by the disk area. is approximately average aspect for e. solidi blade E am i 1 1 r ical the 0. h a s a and a d i s t r i a en rang f c r ~i o n 3 abou eon v; i ;l r oun tut i ch ar t t- the V p,r i a t i n of e anf:l3S and a'pplies .VCG e c f b 1 a d There is a series of s. One blade forir; is v;i th V to a definite charts for each of tvro a CO nv ent-ion al t yj) e , /nD tandard 5155—6, v«'ith a plan form almost synr.ct— t the maxiE-am chord, which is at appr ovir^at ely station. The other blade form, ITACA 1 0-3 063-0 45 , , alTiOst uuif orra chord out to the 0,75?. station ded tip section. The plan forms and pitch ons for tJie tv;o propellers are shown in figure 4-, Hami lton Sta. ndard p rop ell cr 315 5—6 , — The c h ar t s of fifi;o.res 5 to 9 appl-- to Hamilton Standard propeller 3155—6, Fig-aros 5, 6, 7, and 8 are for the two-, three—, four—, and t'. ix— blade s ingl e— r ot at ing propellers, respectively. Figure 9 in for a si:-:— blade dual— r ot at ing propeller. The solidity g varies from 0,061 for the t\/o— blade propeller to 0,1S2 for the si:-:— blade xr oueller s . A 1 i-'V.id— coded nacelle of fineness ratio 6 vras tS — suracd and the spinner diameter v;as taken as 0,164 times the propeller diameter in determining the spinner factor kg. The averat,'c value of kg, v/hich depends slightly on :ho blade- an^.le setting, is about 1.125. ' • i : •alue signifies that, en the average, 12. o percent has been added to the values v/hich v.'ould be obtained in the absence of a s-D inner . 11 -2 ixsod in tho computations were o^otaincd irom figures S4 and 35 of referonce S for tho 25° p.nd 45° "blade angles and '-'crc int erpolfit ed for the other I'ladc -.Ufvlcs v'ith the aid of lifure 15 of refer- ence ?. iiMi: prop elle r 10-5055-045,- The charts of figures 10 to 13 apply to I'lACA pr opell or 10-3062-045. Pigurcra 10, 11, r:xd 12 arc for the tv-o— , three—, and four— blade single— roto.tin-v; propellers, r e sr)C ct ively . Figure 13 is for a six— I'lade dual— r ot at i r.fr propeller. The solidity a varies fro.-u 0.0325 for the tv.ro-olade propeller to 0.2-17 for the six— clad e prop oiler. The sp inner- nac ell e proportions were taken the same as for Ilauilton Standard propeller 3155—6, and tho corre- sponding avcrn,^-^o valiie of the spinner factor hg is 1.15. The values of Tp used in the coniput at i ons vero ohtained from unpubl isli ed cxp er fe. ent al carves for the three- "blade s ingle— r ot at ing propeller. The cxirves vrere extrapolated for fcv/er "blcades o,nd for xore blades and for dual rotation with the aid of figures 24 and 26 of reference Go It is "Ijelieved that the errors in ^yi , introduced hy errors in tlic extrapolation are vfithin 2 or 5 Tjcrcent. C onipar is on viith ^'^v er imen t . — It gur c 14 p r e s en t s t h e variation of the side— force derivati%'e v/ith advance— diaraeter ratio for tl.ie two— "blade model propeller of refer- ence 4. Curver. computed from the fornulas of the present report are plotted '-ith the experimental val^ies. In t er p 1 at i c n f o :: 'c 1 ad e sh a]'' e 'in d s ol idity .— "he computations show that, within the usual range, "blade tvirist has a relatively s'nn.11 effect on Cvi..,. The three in-portant - w par-'mc t cr 3 are solidity, "olade angle at 0.753., and plan form, for a given Y/nD. The charts for .a given ;plan form may be interpolated line,arly from the charted values for varia- tions of solidity cr and olade angle P, "he det era inat i on of Cy',i, for plan forms "betv;ecn those of hamiiton Standard prorjeller 3155—6 and FACA propeller 10—3062—045 would be expected to require a doLible interpolation, one for solidity, because the two IP. propellers aro not chsxted at the same solidities, and a second cue for plan form. A simpler proccdv.rc rGGults fro;.: tliG f ollO'-.'in>r considerations: Poi- a given solidity, it is found that the plan fora of ■^he ITACA propeller 10—3063-045 yields aeout 13 percent ffi-jro si.lc force than does the plan foru of th 3 Hamilton Standard propeller ?155— 6 at the same V/r.D. The factor 1,13 holds v/iTihin 2 or 3 percent near the line of zero thrust although the error increases to ahout 6 percent at lov/ T/n3 and hi^h thrust. "o this accuracy the side- force coefficient for a propeller of a given plan forn azid solidity a - 0-091, for ci-ample, could ha estii'iatGd from the a ~ 0.091 chart of Hamilton Sta.ndard propeller 3155— G hy co.v.pc-r in.'?; the f:iven plan form '-/ith the plan forms of Eainilton Standard 3155— G and iJAOA 10— oCo2— 045 propellers in figiirc 4 and increasing the ordina,te3 from the cha.rt h;' the apipropriate fraction of 13 percent. In making the plan- f orm compar i s on , most ght should he f?;iven the root sec- tions of the "olado. If the solidity a does not corre- spond to that cf one of the cha,rts, tv;o charts of different ■e saiwe propeller aay he interpolated linearly. solidity for the u o o 1 c I : s for propellers i n p i t ch , - cnar ts v;ith pit ch 3 uus t rate of ch an ge thrus t axi s, if flov: at th e prop t aken into a ccou v/ing, Dy m ul tipl ituted for ya,;: can oe uced to ohtain the f ncrinal force vith angle of .■'ttack of the influence of the wing on the angle of oiler is included. 'The upv;ash can oe Lt, the 'ororseller in front of the ying the value of Cyt,,, — now interpreted / ls — / ocr,rp hy 1 plus the rate of change with an glo of a J. J. ,1/ U ack PC Her hy th v; i th e fa c 1 r s hou 1 of att aclc of th e hy the M i n g. of the angle of upvash indiiced at the pro- ng. If the propeller is "celiind the v;ing, d he 1 minus the rate of change with angle angle of downwash induced at the -nro-Doller COUCIUDIFG- HSIIASKS 3nuo,tions for propellers in yav; and charts o: side— force derivative have oeen given herein for single— and dual— r otat ing propellers in terms of a side— area index and a d7,-n..c -ijI-t-— f ori?. variable. 15 HSITEHEIICIS I i-'-i 1, Harrin, 3., fe , : Forcon on a Fx-opcllor L j o to Sido— 3l:.p. R. :j I:. 2io. 427, 3ritiF:h A.C.A,, 1918. 2. G-lauort , H . : The StaDilit;^ D sr ivr t i-rcjs of an lirscrcv H,. & M. I'd. 642, British A.C.A. , 1919. 3, G-cctt, Kn.rry J., r-nd Prss, H. H.: Iffect of Propollor Operation on the Pitchinc MoniantG of 3 in.f^l e— Sngino Honoplanos. IT AC A A.G.2., May 194].. 4, Lesley, B. F., Worley, Goorge F., and I'.oy , Stanloyt Air Propjll3T-s in law. 3ev. Fo. 5? 7, ITACA, IS 37. 5, Mtink, Ke.x II,: Fundaiuent al s of Fl-aid Dynair^icc for Aircraft Fesi:5ners, "he Sonald Press Co., 1S39, -n "O 6 . E V. n c 1: G 1 , J .■^ c; k Jho Effect of Fitch on For. arc of FivG Solidities. i"ACA A.H.F., June 1942. 7, Ficrrriann, David, and Hfirh;an, Edwin P.; Tests of Two Full— Scale Propellers v/ith F^ifforcnt Pitch Distri— 'butions, at Blade Aiz.<^les, up to 60°, P.gt). STo. 653, NACA, 13 o9. ITAGA li.-s. 1,2 ?.0 / ! / ' "\" r ' ! " ■H h-- r !— i I j i 1.0 1.4 1.8 ?.0 Figure 1.- VaricJotion of .|-factor f(a) with T:^. 1^ = Cq]/ (v/nD)^. Figure ?.- "'ariation of I3 with v/nD and solidity. Appr-ixinate ciirves for blade -ani'le settings at v;hich ths blades KA?A I .8 i.O 1.2 1.4 l.S 1.3 ?.0 Figure 3.- 'variation of Pa/rr with T^ • T,. = C'l/ i'j/nD)^ . 1.2 r T" L I ! I ! i I HACA propeller 10-3052-0-±5>'^i i I , I 1 1 w 1 1 — __j£;r_. — L in ■ , o Hpmilton Stauiard proTDeller 31b:3-r pip .b II I ^ ,^_Wbo.75R --^- i--h- ■f ..-._4- V--V- V" i I — ITACA propeller 10-3002-045, 3 =- ■13.2'^ at O.VdH ' U ! I '/ I P/D,, 1' i.^-. I i I I _HairJ.lt oxi_' btaridard _pr^3peller__31ot)-G, 3 - 2D°^at 0.7oH -j" ' I I I ! _'. J L .1 .3 X - v/r T .7' 3.0 2.0 p/d 1.0 .y 1.0 Figiare 4.- Plan forins and pitcli iibtri-^-'j.tions of IJAQA iO-SO^c-04o anl Harr.iiton Standard 31^5-6 propellers. I HACA .40 ,3? ?i^S. 5,'^ .S4! .08t— 1 1 ., 1 1 i 1 i ! 1 ■ 1 1 i ^A .~r] 1 1 1 i i 1 1 1 I i 1 j 1 O'r ,^ U_j__ ^ tt,' •-' 1 — , Soo' 1 \ ^ M-J .(- >l \ -'\- -" •iO'^ -430 - -►■■■■ ; 1 i ^ ■• " T 35- 1 1 1 ~^.. ■}.'.".] : "xno, 1 s ^'-^~f~i: Sc^i 1 1 .-;— - .. \ I in t=~ 8 ^ io' at J. V;; I ^- ! ! i 5 OT Z -• ! ru I 1 St ■ i ; 1 1 1 1.? 1.^ ?.0 ?.4 ?.b 3,? 7/nD 4.0 Fiirure o.- Slie-force ieriv'ttive for sinsle-roto tins Fairiilton Stsr.iard prooeller 315o-" with spinner. Two blaies, S, 0.0--1. .08 OL B ^ lo'-' at O.VoR j-ine of zero tnrust "T" ..._L.. J L . O 1.? 1.6 ?.0 P.i ?. ■VnD 3.? 3.6 4.0 Jie^are 6.- Sile-force derivative for i?in^le-rotatine Hamilton Standard propeller 3165-6 witn soinner. Three l^lades, cr, 0.0^1. 1 . £ 1 . S v/nD ?.« 3.2 o.'^ 4.0 Fisrare V._ Siie-force ierivative for sini?le-rntatinj?' Hamiltori Staniari prapeller Slob-o with spinner. Fo-ur blades, o', 0.1?1. 4.0 ?i£nire 8.- Siie-force Ierivative for single-rotating Hamilton Staniari propeller 31o5-'^ witn spinner. Six blaies, a', O.is?. ui:-A. . B 3.? 3.-^ 4.0 i'i^^ire b.- Siie-force ierivgti"''e for iu'^.l-r■Jt^ti1?■ Familton St-niari propeller "^loj-P --vitli Kpinner. 3i" lr;lai.es, o'. 'i.lPP. v/aD ■) . j-force dorivativo for sin^lo-rotating flACA propeller 10-3052-0-i5 T/ith spinner. Four blades, o", 0.165. 'ifir.s. 13,14 .8 1.2 V r/nD 2.4 ?.8 3.2 3.6 4.0 Fit]xirt=! 13.- :jiie-force derivativa for di;al-i-otating ilAOA prone] lur 10-3032-045 with spinner. Six Dlaies, a, 0.247. I .1': OY I .12 .OS .04 "T" — T" I -I |_Sat0.7oR iSxperimental Calc-alated -J ^ _ (i;-:) •■■■0..= L\ I 24. o D 23." V ^ - -r J ,u--i I l._ L rfmtmm^^^^ -^,-r^r.^ --.L- 1-- i-^Llni 4 — ^- of zero thrust .8 1.0 1.2 1.4 1.6 ■J = '^/nD 1.8 Fi^re 14.- Comparison of calc^alatcd and oxperincntal side-force derivatives for tv/o-tlade raoiel propeller. Curves ar£! tenninatad, uxcopt for p = 16. G°, rt point '.vharo oV/ious stalling of "blades occi-'.rs. Ei^rp^riincntal data from rererence 4. UNIVERSITY OF FLORIDA 3 1262 08106 520 2 UNIVEBSnV OF FLORIDA SSra 33611-7011 US.