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RESEARCH MEMORANDUM

PRELIMINARY EXPERIMENTAL INVESTIGATION OF FLUTTER

C-iIAR-ACTERISTICS OF M AND-ti ~GS

By Robert W. Herr

Langley Aeronautical LaboratoryLangley Field, Va.

NAT ONA ADVISORY COMMITTEE

$/F R AERONAUTICS -----.iL WAS HiNGTON. August 8, 1951

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RESFARCH Memorandums

PRELIMINARY EXPERIMENTAL INVESTIGATION OF FLUTTER

CHARACTERISTICS OF M AND W WINGS

By Robert W. Herr

SUMMARY

Results of nine experimental flutter tests involving two flat-plate

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models and two rib and spar models of NACA 0012 airfoil section arepresented to give a comparison of the flutter characteristics of wingshaving M and W type plan forms. Within the range of structural andaerodynamic parameters encountered in these tests, the W plan form gavehigher flutter speeds than the M plan fomns.

A technique is also presented in an appendix whereby the naturalvibration mode shapes of the model wings were obtained photographically.These mode shapes, along with the other structural parameters included,would be useful in a theoretical flutter analysis of the M and W wingconfigurations.

INTRODUCTION

Some attention has been given recently to the possibility of the useof wings incorporating sweepback of the inboard panel and sweepforward ofthe outboard panels (W plan forms) or vice vehsa (M plan forms) for highspeed aircraft. It has been suggested that such configurations mightdisplay better stability and deflection characteristics than the swept-back wing without appreciable sacrifice of the low-drag qualities of thelatter. Some investigations along these lines have been made in refer-ences 1 and 2.

In order to obtain some idea as to the relative flutter character-istics of the M and W configurations, tests were made in the Langley&.>foot flutter tunnel of two sets of models having M andW plan forms.One series of tests was made with extremely simplified models consistingof flat plates of 0.128-inch aluminum alloy. Other tests were made withmodels of rib and spar construction built to NACA 0012 airfoil shape.The results of the flutter experiments are discussed and a technique is

NACA RM L51E312

described forshapes of the

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obtaining photographicallythe natural Qbration modemodel wings. -.

SYMEOLS

semichord of wing in stresm direction

natural vibration frequencies in the nth moae, cyclesper second

lCG polar mass Doment offor a strip in theslug-feet

inertia about section center of gravitystream direction of on=”foot width,

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1 length of semispan model measured normal to stream direction

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m mass of wing per foot of span measured nonqal to streamdirection, slugs per foot — .—

M Mach number at flutter

v airspeed at flutter, feet per second -

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ztipb2dx

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o :=mass ratio,%otal

density of testing medium, slugs per cubic foot

angular flutter frequency, radians per &econd

APPARATUS —

Wind tunnel.- The flutter tests were made In the Langley ~.’j-footflutter tunnel. This tunnel is of the closed throat single-returnt~ein which the pressure may be varied from approximately-0.5 inch ofmercury absolute to atmospheric pressure. ---. -.. .—

Mode18.- The four models employed in these tefitsjere 24-inch geml-span cantilevers with a taper ratio of approximately 0.5 and a full-span

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vaspect ratio of 2.66. The midchord line of the inboard half of theW wings was swept back at an angle of 45° and the outb~ard ha”lf“wassw;pt ‘T“- ‘-”-”

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NACA RM L51J131

forward at an angle of 45°. Sweep angles onin direction from those of the W wings.

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the M wings were opposite

The first model tested (model A) was cut from a 0.128-inch flatplate of 24ST aluminum alloy and was of the same plan form as the modelsketched in figure 1. This model was tested as both anM andW configu-ration by reversing its position in the test section. The subscripts mand w added to the model designation denote the position of the model inthe test section. The second model tested, designated Bs, was used asa reference model and was also a 0.128-inch flat plate of the same semi-spsn, taper ratio, and aspect ratio as model A but with the entire semi-span swept back at an angle of 45°. The section centers of gravity ofthe flat-plate models were, of course, at the midchord.

The third and fourth models were constructed to have more realisticstructural parameters than the stiplified models and incorporated NACA0012 airfoil sections in the stream direction. One model is of W planform and is designated ~; the other of M plan form is designated ~.The models were of single-spar construction with very closely spaced ribsand were covered with rubber (figs. 1 and 2). The small lead weightswhich are noticed in figure 2 were inserted between each rib to make thesection centers of gravity coincide. The section centers of gratity forboth models were at @ percent chord over the inboard half and at 45 per-cent chord over the outboard half.

DETERMINATION OF MODEL PARAMETERS

Although the investigation described herein was of an experimentalnature, it was considered desirable to obtain some of the structuralparameters of the models so that a reader who wishes to make theoreticalflutter calculations for the models may do so. These parameters ’includethe vibration mode shapes, the spanwise variation of mass and mass momentof inertia, and the loci of flexural centers.

The unorthodox plan forms of’these models indicate that the calcu-lation of the natural vibration mode shapes would be difficult. The modeshapes were, therefore, obtained experimentally by exciting the wings attheir natural vibration frequencies and photographing the resulting ampli-tudes. (See appendix.)

Variations along the span (normal to stresm direction) of the massand the mass moment of inertia are plotted in figures 3 and 4.

The loci of flexural centers of the models (fig. 5) were determinedas follows. The wing was clsmped rigidly at the root and at a given span-wise station was loaded successively at various chordwise points lying in

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4 NACAm L51E31

the stream direction until the point was found where no twist in the “-4

stresm direction occurred at that station. This procedure was repeatedat several spanwise stations until enough points were obtained to permita smooth curve to be drawn.

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The natural vibration frequencies of the models were obtained withthe aid of a calibrated electronic oscillator driving a magnetic shakerwhich in turn excited the wings. The frequencies so obtained are asfollows:

Model f~ fz fs f~

A 8.0 18.9 49 ----Bs 2k.8 57.5% z 13.4 , :: 63.0

h 5.6 16.8 42 ----

TEST PROCEDURE

Since flutter is generally a destructiveto exercise great care during a flutter test.

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phenomenon It is necessaryThe tunnel speed was,

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therefore, i~creased slowly during the runs, the increases smounting to—..

smaller increments as the critical flutter speed was approached. At thecritical flutter speed, the necessery tunnel data were recorded and anoscillograph record of the model deflections were taken. The tunnelspeed was then immediately reduced h order to preserve the model.

In these tests} the tunnel was operated at pressu~es from 0.25 atrno6-—

phere to atmospheric pressure, and at Mach numbers up to 0.60. The

Reynolds numbers at flutter varied from 1.2 x 106 to 3,6 x 106.

A total of nine tests was made. These tests incltidedtwo for theflat-plate model A (one in the M position and one in the W position),one for the flat-plate swept wing model Bs,”and three each for the W andMplan forms ofNACA 0012 sedtion (w and k).

In order to ascertain whether the model had been damaged or weakenedby flutter, oscillograph records were taken before and after each run atzero airspeed with the model manually excited at its first and secondnatural frequencies. These frequencies did not change-a measurable amount .:throughout the series of tests. w“

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NACA RM L51E31 5

RESULTS AND DISCUSSION

Table I lists the expertiental flutter velocities, the corresponding

values of the mass ratio parameter o1 K, the flutter frequency u.),andthe associated values of Mach number and air density.

The critical flutter frequencies were obtained frcm oscillographrecords taken at flutter. A ssmple record taken at flutter (v = 427.6,table I) is shown as figure 6. This mode,l,I& fluttered to destructionduring this run before the tunnel speed could be reduced.

In figure 7 the flutter velocities are plotted against the mass

Uratio parsmeter 1 K. The significance of such a plot lies in the factthat a given model will usually flutter at a velocity which is essentially

proportional to ~1/K provided there is no change in flutter mode (refer.ence 3).

Inspection of figure 7 shows the single value of flutter speedobtained for the flat-plate model A in the W position to he approxi-mately 25 percent higher than for the same model in the M positionwhereas the flutter speed of the swept flat-plate reference model Bsfell between those obtained for the M andW configurations. The NACA0012 section W model ~ showed an even greater increase in flutterspeed over the corresponding M wing ~, the difference being about50 percent throughout-the range of mass ratio parameters investigated.

Caution shouldbe used in generalizing the results of this investi-gation as the flutter speed is dependent on the relationship of numerousstructural and aerodynamic parameters, a change in any of which mayalter the conclusions. For example,”aspect ratio may have an importantbearing on the relative flutter’and divergence speeds.

CONCLUDING REMARKS

Within the range of structural and aerodynamic parameters encoun-tered in these tests the W wing plan form gave higher values of flutterspeed than the M plan form.

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6 NACA RM L51E31

Natural vibration mode shapes, obtained photographically, alonga

with other pertinent structural parameters have been included to aid ina theoretical flutter analysis of these wing configurations. x

Langley Aeronautical LaboratoryNational Advisory Committee

Langley Field, Va,for Aeronautics

APP~DIX

NACA RM L51E31 7

EXPERIMENTAL DETERMINATION OF NATURAL VIBRATION MODES

The natural vibration modes were obtained photographically with theaid of two electronic flash lamps having a flash duration of l/xOO second.The wing was excited at its natural vibration frequencies by a calibratedelectronic oscillator driving a magnetic shaker. The amplitude of theoscillations was increased until the wing tip contacted two pairs of veryflexible wires, thus completing electrical circuits and firing the flashlamps at the maximum positive and negative amplitudes of the vibrationcycle.

The camera was mounted approximately 1.2feet outboard and 2 feetabove the tip of the wing. The wing was painted black with very thinstripes of white running in the stresm direction every tenth of the semi-spsn to make possible the measurements of deflections.

Sample photographs taken by this method appear in figure 8. Thedeflection amplitudes measured from these photographs must be correctedfor perspective; thus the actual value of the deflection smplitude atstation n is given by the equation yn = Ynt(cn/cnf) where cn isthe actual chord of the model at station n, cn’ is the chord at sta-tion n as measured from the photograph, and yn’ is the smplitude atstation n as measured from the photograph.

Because of the large smount of structural coupling inherent in the Mand W plan forms, the modes shown in figures 9 to 21 were not plotted inthe conventional manner, but as three-dimensional views adapted to givethe relative deflection at any point on the wing. Since the torsionaldisplacements involved are small, the torsional component of the natural .vibration modes may be obtained from figures 9 to 21 by simply sub-tracting the leading-edge amplitude from the trailing-edge amplitude anddividing by the actual chord of the model; that is

a= ‘%E - ‘%Cn

Some idea of the accuracy of this photographic method is indicatedin figure 22, which shows the photographically obtained experimentalvibration modes as well as the theoretical vibration modes of a rectan-gular 8- by 50- by 0.25-inch flat aluminum-alloy plate mounted as a canti-lever. Changing the point of attachment of the exciter to the wing madeno measurable difference in the deflection curves.

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REFERENCES., w.

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1. Csmpbell, George S., and Morrison, William D., Jr.: A Small-ScaleInvestigation of “M” and “W” Wings at Transonic~Spe~@_s. NACA ~.. ,+

o IO!L50H25a, 1950.L.,*m... .

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2. Katz, ElliEI,Marley, Edward T., and Pepper, WillismIl~: FlightInvestigation at Mach Numbers from 0.8 to 1.4 to D&ermine the Zero- “-Lift Drag of Wings with “M” and “W” Plan Fomns. NA~A RM L50G31,1950.

3. Castile, George E., and Herr, Robert W.: Some Effects of Density andMach Number on the Flutter Speed of Two Uniform Wings. NACATN 1989, 1949.

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TABLE I

EXTERIMENIAL FLUTI!ERDATA

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Mach(ft~sec) nuniber,M (radi&/see)

390.133.2.2354.5376.0

46L 9669.8250.1299.5427.6

0.3522.2820.2990.3300

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62.862.864.162.257.2

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Figure 6.- Sample oscil.lographrecord. Model Dm at flutter.~

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Figure 7.- Variation of the flutter s eed v with the mass-ratio,’

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Figure 8.- Photograph of natural vibration modes. Model A.L-69~

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Figure 10.- Second ?.wtural vibration mode, model Cw.

fp = 13.4 cycles per Becond.

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Figure 12. - Fourth natural vibration nude, model Cw.

fk = 63 cycles per second.

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Figure lk. - Second natural vibration nmde, nmdel ~.

f2 = 16.8 cycles per second.

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f3 = 42 cyclee per second.

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Figure 17. - Second natural vibraticm tie, nmdel A.r2 = 18.9 cycles per second.

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Figure 18. - TMrd natural vibration made, model A.f3 = 49 cycles per second.

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Figure 19. - First natural vibration mode, nmdel Be.

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Figure 20. - Second natural vibration mode, model BE.

f2 = 24.8 cycleB per second.

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NACA FM L51E31 31

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Figure 22. - Comparison of theoretical and expertiental vibration modesof an 8- by 50- by 0.25-inch aluminum-alloy plate.

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NACA-1,.W@ey -8-S-51 -375