AC5 No. LtegS NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS WAllTIMK REPORT ORIGINALLY ISSUED Fe'bruary 191^^ as Advance Confidential Eeport LltB28 COUSIEEJRATIONS OF WAEE-EXCITED VlBRATOBy STRESS IN A PUSHER PROPELLER By Blake W. Corson, Jr., and Mason F. Miller Langley Memorial Aeronautical Laboratory Langley Field, Va. NACA ^ 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. L - IU6 tJOCUMENTS DEPARTMEf Digitized by tine Internet Arcliive 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/considerationsofOOIang "7// XiT S"1 NATIONAL ADVISORY COTMITTEE FOR AERONAUTICS ADVANCE CONFIDENTIAL REPORT NO. L4B28 CONSIDERATIONS OF WAKE-EXCITED VIBRATORY STRESS IN A PUSHER PROPELLER By Blake W. Corson, Jr., and. Mason F. Miller SUmiARY An equation based on simple blade-element theory and the assumption of a fixed wake pattern is derived and fitted to available data to shov.; the first-order relation between the parameters of propeller operation and the in- tensity of the wake-excited periodic force acting on the blades of a pusher propeller. The derived equation in- dicates that the intensity of the wake-excited periodic force is directly proportional to air density, to airspeed, to rotational speed, and to propeller-disk area. The derived equation indicates that the effect of power coefficient upon the intensity of the wake-excited periodic force is sm.all . In normal operation the vibra- tory force decreases with increasing power coefficient. If a pusher propeller is used as a brake, increasing the power coefficient v/ill increase the vibratory force. For geometrically similar pusher propellers, a pro- peller of large diameter v/ill, in general, experience less wake-excited vibratory stress than a propeller of smaller diam.eter. Limited experimental data indicate that the wake- excited vibratory stress in a propeller increases with the drag of the body producing the wake. INTRODUCTION Vj'ith the increased consideration being given to the use of pusher propellers there has arisen a concern over the magnitude of the periodic stresses peculiar to this type of propeller. A pxisher propeller usually operates in the v/ake of some other part of the airplane, such as the v^ing, engine mount, or tail surface. As the COKPIDENTIAL NACA ACR No. L4328 propeller rotates, each blade passes alternately frorp. a region where the slipstreain axial velocity is practically the same as the velocity of the free air stream into the wake region, where the axial velocity may be considerably reduced. Vfnen a blade passes through the v.-ake, the blade sections experience an increase in angle of attack and a slight decrease in dynamic pressure; the aerody- namic load on the blade thus changes periodically. The type of motion with which the propeller will vibrate may depend upon several factors, two of v;hich are the number of blades and the location of the propeller relative to the v;ake , The response as measured by the stress pro- duced in a blade depends upon the deflection shape of the blade as well as upon the intensity of the exciting force. The vibratory stress' in a four-blade single-rotating propeller operating in the wake of a v/ing has been meas- ured in the LMAL 16-foot high-speed tunnel and the re- sults of the tests have been reported in reference 1. In that report no detailed study v/as made of the influence of the aerodynamic conditions of operation upon the pro- peller vibratory stress. The purpose of the present report is to derive a simple expression that will show the first-order effects of airspeed, rotational speed, propeller characteristics, propeller size, and wake size upon the periodic force which excites vibrations in a propeller operating in the wake of a wing. If an attempt is made to account for all obvious effects of the propeller and wake upon each other, the problem becomes involved if not ^onmanageable. In order to m.aintain simplicity of the final expression, it v/as necessary to make several assumptions, which will be discussed herein. ASSUMPTIONS The problem of estimating the variation of the periodic aerodynamic load on the blade of a propeller operating in a wake is limited here, first, to a parti- cular type of propeller installation and, second, to operating conditions for which the induced velocities are negligibly small. The installation being con- sidered is a pusher propeller located, behind a wing with the axis of rotation centered in the profile of the wake CONFIDENTIAL NACA ACR No. L4B28 CCNPTDENTIAL of the vlng. It is assvimecL that the propeller disk is large enough to e:ctend beyond the v/ing v:ake into the undisturbed air strearn. The wing drag coefficient is assuned to be constant with airspeed; this assumption implies a fixed wake pattern with the result that at a given point in the wake the velocity defect will always be proportional to the airspeed, A diagrara showing a typical distribution of velocity in the v/ake of a wing is presented in figure 1. (See reference 2.) In order to estimate the first-order periodic change of the aerodynamic load on a propeller blade due to Intermittent change in axial velocity, simple blade- element theory (reference 3) is assumed to be adequate. The effect of the changes in axial velocity upon the blade-section drag characteristics is regarded as negli- gible. Blade-section lift, therefore, is the only force considered in the blade- element analysis. For all conditions under which the propeller blade sections exert lift, they maintain a consequent induced air flov'/ having both axial and rotational velocity com- ponents at the propeller. At speeds above the take-off and cllm-b range the induced axial velocity is very small in comparison with the forward speed. For a steady con- dition of norm.al operation the velocities induced at various stations along the propeller blade can be esti- mated by the procedure given in reference 4. This pro- cedure, however, cannot be applied at present because the propeller operates with unsteady lift. V»'hen the rotating propeller blade traverses the v/ake, the blade sections exert a greater lift^ v/hDch creates an increase in the induced velocity. The instantaneous change in lift exerted by the profieller blade sections during their passage through the wake is less than is to be expected from the corresponding change in angle of attack, because development of the circulation in unsteady lift lags behind the angle-of-attack change (reference 5) . A com- prehensive treatment of the problem would require such specific assumptions concerning the shape of the v/ake and the distribution and m.agnitude of the velocity induced at the propeller that a.ny solution obtained would be neither simple nor general. The straightforward approach per- mitted by the use of simple blade-elem.ent theory and the assumption of a fixed wake pattern justifies the conse- qu.ent slight loss of accuracy. COIIPIDENTI.^ 4 CONFID.Ei)TT-IAL ' NACA ACR No. L4B23 SYM30I..S V airspeed and slipstream axial velocity at pro- peller disk, feet per second or miles per hour (assumed identical in this analysis) Vpj resultant velocity of air relative to any blade element, feet per second n propeller rotational speed, revolutions per second D diameter of propeller, feet J advance ratio (v/nD) R propeller tip radius, feet r radius to any blade element, feet X fraction of tip radius (r/R) Td chord of any blade element, feet 9 blade angle of an^/ blade element measured from zero-lift direction, radians effective helix angle for any blade element, ,-1 V 2Trrn radians tan a angle of attack of any blade element, radians (Q - 0) a-^ angle of attack of wing L lift, pounds Lc ■ coefficient of differential lift Cl lift coefficient dL dx pn^D^ Cl mean lift coefficient, effective over entire blade th = ~=rr - 5.7 (approx.) CONFTDSNTIaL NACA ACR No, L4B80 CONFIDENTIAL T thrust (propeller-shaft tension), xjounds Q torque, f oot-poi.uids P power, foqt -pounds per second p density of air, slu.^s per cubic foot Cqn thrust coefficient (T/pn^D"'^) Cp power coefficient (P/pn'-'D^) T) propeller efficiency B number of blades of a sinp;le propeller C]_» Co, C3 constants Subscript: 0.7R ■ at 0.7R DERIVATION OF EQUATION FOR EXCITING FORCE For a propeller operating in the vi/ake of an airfoil at thrust-axis level a relation between vibratory ex- citing force and the paraneters of propeller operation can be derived by first expressing the force on a pro- peller blade elernont. The lift force on a propeller blade, element of differential radial length (fig. 2) is dL - ^pV^^bCL dr (l) If the coefficient of differential lift is defined as dL "" pn2D4 equation (1) can be put into the forra p , ^c = ~ D^^L s®^^ CONFIDENTIAL L, = -^^ (2) COI^I^'IDENTIAL NACA ACR No. L4B28 The change In coefficient of differential lift can.sed by a differential change in forv/ard velocity is dj^c ir^bx^ dV 4D ^sec2^ ^ + Cl^ sec2^) (3) The lift coefficient may he expressed as the product of the lift-curve slope and the difference betv/een blade' angle and helix angle; that is, Ct = ma 'L = mO - jZf) If the blade angle is assumed not to change with rapid changes in axial velocity. dY dV (4) By performing the operations of equation (2) and using equation (4) , there is obtained dL, dV 4D -m sec V g ^ C:,(2 sec2^ tan ^ f| (5) By figure 2, tan jS - V TTxnD from. vi7hlch sec dV TTxnD ¥ These relations when substituted in equation (5) yield dL, -|^ (2VCl - -^--D) dV 4rJ CONFIDENTIAL NACA ACR Mo. L4E28 CONFIDENTIAL V whj-ch, from equation (2), gives The integration of equation (6) gives the following relation between the change in lift on the entire pro- peller blade and the change in axial velocity: ,'..1.0 ^ \ Ct ^ d.x - mrrnD / x^ dxjdV (7 '-'0.2 " -0.2 / ^ Examination of equation (7) shows that, of the terms within brackets, the one containing Cj will, in general, be small in comparison v/ith the other. An explicit rela- tion between C^ ^.nd x does not exist, but equation (7) can be simplified with small loss of accuracy by using a mean value of lift coefficient TTj^ regarded as effec- tive and constant along the blade. In reference 6 Lock shows that the thrust coefficient of a propeller can be computed with fair accuracy from an elemental thrust coef- ficient, at X = 0.7, by using the integrating factor tt/4, a derivation based on the use of this factor is given in the appendix, which shows an approximate rela- tion between the effective lift coefficient and the pro- peller operating characteristics « Cl = Cl 0.7R Urn ''^K^)o.7R VJ"^ -^ ^-^^ :8) When a mean value of lift coefficient is used, two in- tegrals that dexoend only on the geometry of the propeller blade remain in equation (7). For a given blade design these integrals are constants and may be evaluated graphi- cally from the relations CONFIDENTIAL 8 CONFIDENTIAL <'^1.0 NACA ACR No. L4B28 Ci = '0.2 D (ix Cg = a.o '0.2 •=rx dx Vvhen the constants Ci and Cg ^nd the expression for mean lift coefficient (equation (8)) are substituted in equation (7), there results dL pnD 3 64 ^1 Cm J x - mrrCo dV ^^/0.7R \/j2 + 4.84 The assumption of a fixed v/aks pattern permits the concept that the veloclt"/ defect at a given point in the Vifake is always proportional to the airspeed; thus AV 'O V (9) This definition is used herein without regerd to the ratio of blade width to wake thickness. Further con- sideration of the effect of wake size upon the vibratory exciting force is given under ""'Discussion.'* By re- garding dL and dV as finite increments and using equation (9) , the Intensity of the propeller-blade vibra- tory exciting force is expressed as AL = C^£^ mirCp - - 64 o TT^E C- r^ V J 4.84 V (10) The substitution of an average lift coefficient (equation (8)) in equation (7) provides a r.eans of ex- pressing the steady operating condition of the propeller in terms of custom.ary param.eters. The effect of dis- tribution of lift increment along the blade upon the CONFIDENTIAL NACA ACR No. L4B28 COWIDENTIAL wake-excited propeller vibration depends upon the blade- deflection shape. For a given type of blade deflection the vibratory force should be governed by equation (10), DISCUSSION General.- The expression for the magnitude of the vibratory exciting force (equation (10)) shows the rela- tion between aerodynamic exciting force and dimensions. If the quantities in the brackets are disregarded, the force is proportional to air density p, to an area D , and to the square of velocity having the components rota- tional speed nD and airspeed V, Of the terms within the brackets, mTrC2 determines the greater part of the exciting force that is due to the Increased angle of at- tack of the blade sections within the wake. The term that Includes GijiJ represents the change in force due to the decreased dynam.ic pressure v>?lthin the v;ake (equation (5)). Actually the term involving CrpJ (equal to CpT]) is relatively small and minimizes the effect of mrrCg in the range of normal operation. Retention of the term CijiJ is desirable, hov/ever, be- cause, if the propeller is used as a brake, the thrust coefficient becomes negative and tbe effects of the quantities within the brackets are additive; the result is that, other conditions being equal, greater vibratory forces are experienced. Effect of wake siz e.- In deriving equation (10) no effort was made to account for the effect of variation , of propeller location downstream from the trailing edge of the wing nor of the v/ake thickness. The assumption of a fixed wake pattern permitted the statement that the ratio of wake-velocity defect to airspeed is constant (equation (9)). It is known that the wake pattern (velocity profile) in a given wing wake changes with distance downstream from the v.ring (reference 2). Close behind the v/lng the v/ake is thin and tbe velocity defect Is Intense; farther downstream the vi^ake is thicker and the velocity defect is reduced. Both wake profiles represent the same momentum loss, and the velocity de- fect integrated across the wake is approxim.ately the same at all stations v/lthin a distance of several wing chords behind the winp;. As the downstream location of COin^IDENTIAL 10 C01-IFIDENTIA.L NACA ACR No. L4B28 the propeller is changed, the tiine required for a blade section to traverse the v/ake chanf':es In 'inverse propor- tion to the velocity defect and therefore Inversely as the excitlnr-f orce intensity, 'i'he vlhratory exciting iripulse, which is the product of force and tine, remains constant. Although vibratory stress in the v;ing struc- ture nay be considerably affected by dovnstream location of the propeller, it is probable that the vjaice-excited vibratory stress in the propeller is very little affected. No data are available that shovv directly the effect of wake size but the vibratory stress in the propeller blade shank neasured at constant alrspee'd, rotational speed, and power varied d.irectly with estinated wing drag WD th and without flap (reference 1) . These limited data, as well as dinensional analysis, indicate that the con- stant C3 and. therefore wakc-exoited vibratory stress in a pu.sher propeller are proportional to the profile drag of the v-ing producing the wake. Ef f ect of prop e ller dianeter .- In general, , pusher propellers of larre~ diarueter will experience less wake- excited vibrator;^' stress than propellers of smal.l di- ■ arneter. Consider the follovi'ing cases? Case 1. Two pusher-propeller installations of dif- ferent size but geometrically sirnilar v/ith respect to " propeller, wing, and v/ake dinenslons operate at the sane airspeed and ¥;ith the sane rotational tip speed. Equa- tion (10) indicates an exciting load proportional' to. D^, If a blade is regarded, as a beam, the unit bending load Increases directly with D and the bending rnonent at a given station therefore increases as D'^ , ^The section nodulus at any station also increases as D'-'. The wake- excited stress would therefore be the sane for both pro- pellers for a given mode of vibration if the two resonant conditions occurred at the same rotational tip speed. Because the propeller rotational speed is inversely pro- portional to D, as is also the static vibration fre- quency fo"r a given mode, the resonant condition for the two propellers v;ould occur at the same rotational tip speed if the vibratory frequency did not change with rotational speed. 7/hen the effect of centrifugal force on the resonant frequency of the blade ic considered (reference 7), it is seen that resonance will occur for the propeller of large diameter at a lov-er rotational tip speed than for the smaller propeller and therefore, b^T' equation (10), the vibratory stress will be less. CONFIDENTIAL NACA ACR No. L4B28 COI^IDENTIAL 11 Case 2. On a given airjjlane a change is nade from a pusher propeller of small diameter to a similar pro- peller of larger diameter. The rotational tip speed and airspeed are the same for both propellers . This case is identical with case 1 except that the ratio of wake area to slipstream cross-sectional area at the propeller disk is reduced. For this reason as well as for the reason given in case 1 the vibratory exciting force and consequently the stress v/ill be less for a pusher pro- peller of large diameter than for a small propeller. Compressibility eff ect.- The compressibility of air affects the propeller vibratory exciting force only to the extent that it affects the blade-section airfoil characteristics and the v;ing wake. The quantity m within the brackets of equation (10) increases with blade-section operating Mach number and produces a cor- responding increase in the thrust coefficient Ct. The net effect is an increase in exciting force due to com- pressibllitAr with an increase in either rotational tip speed or airspeed. This increase in exciting force is in addition to the direct effect of the rotational tip speed or airspeed indicated by equation (10). In general;, airp)lanes do not operate at such high airspeeds that wing drag (wake size) is m.uch affected hj compres- sibility; however in some cases propeller vibratory stress tude at a value of Mach number close to the critical value (0.5 to 0.6) for the wing. It would be possible in a shallow dive to exceed the critical Mach number and thereby to Increase the wing d.rag and in turn the pro- peller vibratory stress. Excitatio n f requency .- In turning through one revo- lution; each blade of a pusher propeller operating in the wake of a v/ing located at thrust-axis level receives tv7o wake-excited impulses. Any mode of propeller vibra- tion having a resonant frequency of 2n m.ay be excited by the wake. Because the wake region through which the propeller operates may be quite sharply defined, the excitation \vill contain harmonics of the frequency 2n. The harmonic components, however, are of relatively small importance according to the tests of references 1 and 8, Although previous tests (reference 9) indicate that it is possible to produce a second mode of vibra- tion with aerodynamic excitation, the f ii^st modes of GOWIDSNTIAL 12 COFPIDENTIAL KAGA ACR No. L4B28 vibration occur most frequently with such excitation (references 1, 8, and 9); therefore prinary interest is in the vihrations that have a frequency of 2n. APPLICATION OF EXCITIIia-FORCE EQUATION TO MmSIJR© DATA Apparatus and methods .- During the tests reported In reference 1 the propeller operated behind a v/in£: mounted at thrust-axis level (fig. 2). The plane of the propeller disk Vi^as located about 23 percent of the v;ing chord behind the trailing edge, or approximately 2 blade chords (at the CVSR) behind the v;ing trailing edge. The wing was tapered and had NACA low-drag sec- tions. A sim.ulated full-span split flap v;as attached to the wing for some of the tests. The propeller was driven by a Pratt & Whitney R-2300 engine mounted in a nacelle and supported in the wind tunnel separately from the wing. The single-rotating propeller was a Hamilton Standard hydromatic of 12-foot diai;ietsr, which had four aluminujii-alloy blades of design 6467-12 used in a hub of design 24D50. The propeller rotated at nine -sixteenths ' of the engine speed. The experimental data consisted in oscillograph and wave-analyzer records of strain, which v/ere converted to stress; electrical strain gages were used for pickups. The stress deterninations are believed to be accurate to within ±5 percent. The m^ethod and accuracy of strain recordings are explained in more detail in reference 9. The strain-gage circuits were completed through a com- mutator in front of the propeller. Leads from the commutator were supported by a steel cable o/S inch in diameter stretched^, across the wind tunnel just behind the wing. The propeller operated in the combined wake of the wing and the cable. Tests and resM.l ts.- The propeller-blade vibratory stress was measured during tests in which the rotational speed was held constant at the resonant speed and in which engine torque, and therefore power coefficient, was held constant. Only the airspeed was varied during a run. Three runs v^ere made v?ith different constant values of power coefficient. An edgewise reactionless vibra- tion was encountered., v/hich produced maximum stresses near the blade shank. CONFIDENTIAL NACA ACR No. L4B28 CONFIDENTIAL 13 If damping is assumed to "be constant, the vibratory stress for a given propeller is proportional to the exciting force AL for any given resonant frequency. In a strict sense, the damping changes when AL changes j for example, a change in airspeed V would be accom- panied by changes in aerodynamic damping and mechanical hysteresis damping. In the application of equation (10) to the available test data, however, it is assumed that, within the accuracy of the equation and of the vibratory- stress measurements, the change In the damping is small. For constant damping, the propeller vibratory stress under the conditions of the tests should have Increased directly as the airspeed Increased. A slight effect of power coefficient might have been expected but, because CpT) Is practically constant in the operating range, this ef- fect would be very small. The results of the stress measurem^ents are given in table I and are shown graphi- cally in figure 4, in v/hlch vibratory stress at the pro- peller blade shank is plotted against airspeed. The ' straight-line variation of stress v/ith airspeed required by equation (10) has been fitted to the data from refer- ence 1 by the method of least squares, and the agreem.ent is reasonably good. There was no consistent variation of vibratory stress with power coefficient. A few additional measurements of propeller-blade vibratory stress were made after a simulated split flap was attached to the wing ahead of the propeller. The deflected flap caused such a great increase in the vibra- tory stress that, when the airspeed was increased above 150 m.iles per hour, the vibratory stress became dangerous. The stress Increase produced by the deflected flap is attributed sclely to the increase In vi/ing drag and not to the downv/ash associated with the change in vjing lift; this conclusion is based upon the test results of refer- ence 1, which shov/ that increasing the angle of attack of the wing from 0° to 3.9^ produced practically no increase of vibratory stress at a frequency of 2n. There are available only two sets of test data by v/hlch wake- excited vibratory stress may be correlated ?/lth the drag of the body producing the wake. These- data taken from reference 1 are presented in figure 5, which shows vibra- tory stress of frequency 2n mieasured at the blade shank. The drag coefficient based on v/ing area was com- puted from the combined estimated drag of the wing and electrical-lead support cable. CONFIDENTIAL 14 COtlPIDSNTIAL IIACA ACR No. L4B2S C0NCLU3I0WS The derived, equation that shows the first-order relation between the intensity of the wake-excited peri- odic force acting on a propeller blade and the parameters .of propeller operation and limited experimental data in- dicate the follov;ing conclusions: 1. The intensity of the wake-excited periodic force acting on the blade of a propeller operating in the wake of a wing varies directly with air density, airspeed, rotational speed, and propeller-disk area. 2. The magnitude of the power coefficient has a very small effect upon the magnitude of the wake-excited periodic- force that causes -ibration in a pusher pro- peller. In normal operation, lnn;.--easlng the power coef- ficient decreases the vibratory force. '/Then the pro- peller is used as a brake, increasing the povi^er coeffi- cient intensifies the periodic force, 3. For geom.etrically similar propellers, a pusher propeller of large diameter v/111, in general, experience less v/ake-exclted vibratory stress than one of smaller diameter. 4. The wake-excited vibratory stress in a propeller Increases with the drag of the body producing the vmke . CONFIDENTIAL NACA ACR No. L4B28 COTJFTDSNTIAL If APPEITDIX DERIVATION OB^ EXPRESSION FOR EPPECTIVS LIFT COEPFICiniT Refer to figure 2, dT = 3 dX cos (^ dl r ..2 = 7^-p[_V + (2TTrn) _GLb dr CO s d = 2iTrn \/v2 + (£TTrn)2 iTT \/j^ + (r rx dT = p TTx h/^ + ( 2 Tr?-n ) ^J BG -j^b 2 V -J'^ + (ttx)^ dr dT pn^D^ [ J^ + (ttx)2]gl I^BTTx D 4 \/j2 + (rr:::)' C1.X dC T Spn^D^x dx .(x2) ^\/j2 + (rrx: B^G] By re;':arding the operation of propeller sections at X = 0.7 as representative of average operation of sec- tions at all radii, Lock in reference 6 nakes the ap- proxl-^xation CONFIDENTIAL 16 COIvTIDENTIAL NACA ACR llo . L4B28 Ct dCr d(x-) 0.7R which is also made here for convenience < 't - 5i \/ j' ^ 4.84 e(|) + 4.84 E(^ Cy ^/C.VR ^0.7R ^L - Clo.vr Oc ^T VD/C.7R Vj"^ + 4.84 (8) OONProENTIAL NACA ACR No. L4B28 GOKFIDEIvTIAL 1'7 REFERENCES 1. Miller, Mason P.i ?«lnd.-Tunnel Vibration Tests of a Four-Blade Single-Rotating Pusher Propeller. ARR No. 3F24, NACA, June 1943. 2. Goettj Earry J.: Experimental Investigation of the Momentum Method for Determining Profile Drag. Rep. No. 660, NACA, 1939, 3. Weick, Fred E.: Aircraft Propeller Design. Me&raw-- Hill Book Co., Inc., 1930, 4. Lock, C. N. H., and Yeatman, D. : Tables for Use in an Improved Method of Airscrew Strip Theory Calcu- lation. R. & M. No. 1674, British A.R.C., 1935. 5. Silverstein, Abe, and Jo;^rjier, Upshur T.: Experi- mental Verification of the Theory of Oscillating Airfoils. Rep. No. 673, NACA, 1939. 6. Lock, C. N, H.: A Graphical Method of Calculating the Performance of an Airscrew. R. & M. No. 1849, British A.R.C., 1938. 7. Den Hartcg, J. P.: Mechanical Vibrations, McGrav;- Hill Book Co., Inc., 2d ed., 1940. 8. Forshaw, J. R., Squire, H. B., and Bigg, F. J.: Vibration of Propellers t)ue to Non-Uniform Inflov;. Rep. No. S.3938, RoA.E,, April 1942. 9. Miller, reason F.: V'/ind-Tunnel Vibration Tests of Dual-Rotating Propellers. ARR No. 3111, NACA, Sept. 1943. CONFIDENTIAL 18 COl-^IDENTIAL KACA ACR No. L4B28 TABLE I VIBRATORY STRESS AT SHAIJK FOR FIRST MODE OF EDGEl'/ISE VIBRATION [_Blade design, Hamilton Standard 6487-12; aluminuin- alloy _, blades; no simulated split flap attached to wing; a^^^, 0^ Airspeed (mph) Vibratory stress j (Ib/sq in.) Pov.er roefPicient, 0.048 106 185 280 ±2800 ±5650 ±7050 Pover coefficient, 0,072 142 185 280 1 ±5400 ±5500 ±6800 1 Povv'er coefficient, 0.096 157 185 280 ±4100 ±5500 ±6700 CONFIDENTIAL NACA ACR No. L4B28 CONFIDENTIAL Figs. 1,2 (0 r o qi ■n ^. ^ <* U) +- ■t~ c u Qi u ? E -5! Cf-