VOL. 18, NO. 11 J . NOVEMBER 1981

History o f Ke y Technologies AIAA 81-0491R

Historical Development of Aircraft Flutter

I . E Garrick an d Wilmer H . Reed II I NASA Langley Research Center, Hampton, Va.

Introduction Work in flutter has been (and is being) pursued in many EROELASTICITY, and in particular flutter, has in- countries. As in nearly all fields, new ideas and developments A fluenced th e evolution o f aircraft since th e earliest days in flutter have occurred similarly and almost simultaneously of flight. This paper presents a glimpse of problems arising in in diverse places in the world, so that exact assignment of these areas an d ho w they were attacked b y aviation's pioneers priorities i s often i n doubt. Moreover, a definitive historical an d their successors u p t o about th e mid-1950s. Th e emphasis account would require several volumes; yet we hope to survey is on tracing some conceptual developments relating to the some o f th e main developments i n a proper historical light, understanding an d prevention o f flutter including some an d i n a wa y that th e lessons learned ma y b e currently useful. lessons learned along th e way. It is recognized that detailed documentation of flutter Because it must be light, an airplane necessarily deforms troubles has nearly always been hampered by proprietary appreciably under load. Such deformations change the conditions an d b y a reluctance o f manufacturers t o expose distribution o f th e aerodynamic load, which i n turn changes such problems. th e deformations; th e interacting feedback process ma y lead From our present perspective, flutter is included in the to flutter, a self-excited , often destructive, wherein broader term , the study of the static and energy is absorbed from the airstream. Flutter is a complex dynamic response o f a n elastic airplane. Since flutter involves phenomenon that must i n general b e completely eliminated b y the problems of interaction of and structural design o r prevented from occurring within th e flight envelope. deformation, including inertial effects, at subcritical as well The initiation of flutter depends directly on the stiffness, and a s t critical speeds, i t really involves al l aspects o f only indirectly o n th e strength o f a n airplane, analogous t o aeroelasticity. I n a broad sense, aeroelasticity i s a t work i n depending on the slope of the lift curve rather than on the natural phenomena such as in the motion of insects, fish, and maximum lift. This implies that the airplane must be treated birds (biofluid-dynamics). I n man's handiwork, aeroelastic no t a s rigid body bu t a s n elastic structure. Despite th e fact problems o f windmills were solved empirically four centuries that the subject is an old one, this requires for a modern ago in Holland with the moving of the front spars of the airplane a large effort in many areas, including ground blades from about th e midchord t o th e quarter-chord position testing, use of dynamically scaled wind-tunnel (see th e article b y Ja n Drees i n list o f Survey Papers). W e no w models, theoretical analysis, an d flight flutter testing. Th e recognize that some 19th century bridges were torsionally aim of this paper is to give a short history of aircraft flutter, weak an d collapsed from aeroelastic effects, a s di d th e with emphasis o n th e conceptual developments, from th e Tacoma Narrows Bridge i n spectacular fashion i n 1940. Other early days o f flight t o about th e mid-1950s. aeroelastic wind-structure interaction pervades civil

After a long career a s research scientist an d manager, I . E Garrick retired from NACA/NASA i n 1972. H e remains active a s Distinguished Research Associate o f Langley. H e i s th author o f numerous publications in areas of aerodynamics, aeroelasticity, and aeromechanics, has served on many advisory councils, an d ha s lectured extensively. Mr . Garrick served fo r a year a s th e second Hunsaker Professor o f Aeronautical a t MIT. Hi s 1976 AIAA vo n Karman Lecture dealt with th e topic: "Aeroelasticity—Frontiers an d Beyond." Among hi s awards ar e th NASA Exceptional Service Award, the Langley Scientific Achievement Award, and the AIAA Sylvanus A. Reed Award. He is a Fellow of the AIAA. Wilmer H . Reed II I from 1972 t o 1980 wa s Head o f th e Aeroelasticity Branch which operates th e Langley Dynamics Tunnel, a national facility dedicated exclusively t o research an d development i n th e field o f aeroelasticity. Notably, this facility i s used b y th e i n develop- ment of practically all its military aircraft, commercial transports, and launch vehicles. At present, Mr. Reed i s Chief Scientist, Loads an d Aeroe'.asticity Division, NASA Langley Research Center. H e joined NACA/NASA in 1948 and holds Bachelor and Master degrees in Aeronautical Engineering from Auburn University an d th e University o f Virginia. Hi s professional experience includes research i n aeroelasticity, wind loads o n structures, devices, an d wind tunnel testing techniques. H e received th e NASA Exceptional Service Medal in 1979, holds several U.S. Patents, is a member of Tau Beta Pi, and an Associate Fellow of the AIAA.

Presented as Paper 81-0491 at the AIAA/ASME/ASCE/AHS 22nd Structures, and Materials Conference, Atlanta, Ga., April 6-8, 1981; submitted April 14 , 1981; revision received July 8 , 1981. This paper i s declared a work o f th e U.S. Government an d therefore i s n the public domain. EDITOR'S NOTE: This manuscript wa s invited a s History o f Ke y Technologies paper a s part o f AIAA's 50th Anniversary celebration. I t i s no meant to be a comprehensive survey of the field. It represents solely the authors' own reconstruction of events at the time and is based upon their own experiences. 897 898 I. E. GARRICK AND W.H. REED III J. AIRCRAFT engineering. The elastic response of an airplane to rough air (gusts o r turbulence) i s a n important aeroelastic problem requiring separate study an d documentation. A s th e phenomena an d concepts have unfolded, aeroelasticity, and flutter in particular, have been the subjects of many survey papers throughout the years. These papers often furnish valuable assessments of the state-of-the-art, give interesting bits of the history, and also furnish numerous useful references. A s i t feasible t o refer t o only a small fraction o f these references individually, w e have included a list of such survey papers separate from quoted references. In particular, we may refer the reader to the outstanding survey papers o f A . R Collar, which emphasize th e British developments, th e most recent o f which, "The First Fifty Years o f Aeroelasticity," came t o ou r attention during th e writing o f this paper. I t wa s Collar's "Aeroelastic Triangle" (1947) that showed graphically that flutter embraced all aspects of aeroelasticity. Fig. 1 Langley's aerodrome, which plunged into th e Potomac River The Early Years, 1903-1919 in 1903. Th e Wright Brothers I n their historic flight, Orville an d Wilbur Wright made Brewer3 on the collapse of monoplane wings. Brewer notes in beneficial us e o f aeroelastic effects fo r roll control o f their his one-page article i n Flight Magazine that a rash o f biplane by the use of wing warping in place of . They monoplane wings with stays had had "accidents in which the also were aware o f th e adverse aeroelastic effect o f th e loss o f wings break downward" and he remarks that "the greater the thrust o f a propeller, du e t o twisting o f th e blades, b y their span th e more readily will th e wing tips b e twisted"; an d that experiments o n th e performance o f thin propellers having the movement of the center of pressure with speed could put it broad blades. They found that th e propeller ti p under high behind th e attachment point o f th e rear stay, resulting i n thrust loads twisted to partially unload itself. We quote from 1 sudden wing flip. The Papers of Wilbur and Orville Wright : Professor Collar (see Survey Papers, 1958, 1978) ha s stated Orville Wright, i n later life, explained th e that part of the speculation about Langley's airplane disaster nature and function of the "little jokers" to Fred is based on the circumstances that some years after Langley's C . Kelley, wh o states i n hi s book, Th e Wright death the original Langley machine was removed from the Brothers, "After th e Wrights ha d made th e Smithsonian National Museum, modified, an d flown suc- blades o f their propellers much wider an d thinner cessfully a t Hammondsport, N.Y. These modifications, than th e original ones, they discovered that th e which involved substantial changes i n th e wing structure an d performance o f th e propellers i n flight di d no t trussing, s o strengthened an d stiffened th e original structure agree closely with their calculations, as in the a s t o significantly reduce th e probability o f aeroelastic failure. earlier propellers. They could se e only on e reason This led in later years to a long controversy (see Brewer4 and for this, and that was that the propeller blades Pritchard5) about whether the original craft was capable of twisted from their normal shape under pressure manned flight, preceding the Wright brothers in this aspect. i n flight. T o find ou t quickly i f this wa s th e real Brewer showed from photographs taken during th e first reason, they fastened to each blade a small launching that th e wings were twisting excessively. Professor surface, like an elevator, out behind the blades, Collar summarized the speculations with the remark, "It set a t n angle t o balance th e pressures that were seems that but for aeroelasticity Langley might have displaced distorting the blades. They called the surfaces the Wright brothers from their place in history." After the 'little jokers.' When they found that the 'little Hammondsport trials, th e machine wa s reconstructed from jokers' cured the trouble, they dispensed with the remaining components to its original configuration and them an d began t o give th e blades a backward returned to the Smithsonian Institute in Washington. sweep which served the same purpose." Recently, the authors were given a unique opportunity to shed some ne w light o n th e role aeroelasticity ma y have played S . P Langley an d Hi s Aerodrome relative to the collapse of the Langley machine in 1903. At the On December 8, 1903, only nine days before the Wright invitation an d encouragement o f Mr . Melvin Zisfein, Deputy brothers' flight at Kitty Hawk, Professor Samuel P. Langley Director of the National Air and Space Museum and a former of the Smithsonian Institute failed, for the second time, in an prominent aeroelastician, th e authors made some relevant attempted launch o f hi s powered flying machine from th e measurements o n th e restored 1903 Langley machine, which Potomac River houseboat (Fig. 1). In both instances, had recently undergone refurbishment to its original con- Langley's tandem monoplane plunged into the Potomac as a dition by the museum's restoration facility in Suitland, Md. result o f structural failures encountered during th e catapulted By applying a vertical point load t o th e wing a t various launch. The failure of the first attempt has been attributed to chordwise locations th e so-called "elastic axis," defined b y the front-wing guy post being caught on the launch the property that a load applied a t th e elastic axis does no t mechanism and not releasing as planned. The cause of failure cause twist, wa s found t o li e along th e quarter-chord line.* in the second flight, which involved collapse of the rear wing With th e elastic axis location this fa r forward, i t appears an d tail, is less certain. unlikely that the wing failed as a result of static aeroelastic I t ha s been conjectured that aeroelasticity ma y have played divergence, a s ha d been suggested. Nevertheless, because th e a major role in the second failure. G.T.R. Hill2 suggested that highly cambered wing produces a downward twisting moment th e failure wa s th e result o f insufficient wing-tip stiffness resulting in wing torsional divergence, a nonoscillatory These tests were conducted b y Wilmer Reed III, Rodney Ricketts, aeroelastic instability that ma y b e regarded a s flutter a t zero and Robert Doggett of the Langley Research Center with the frequency. Hill's argument i s bolstered b y a qualitative, bu t assistance o f Dr . Harold Walco an d Joseph Fichera o f th e highly perceptive, discussion given i n 1913 b y Griffith Smithsonian. NOVEMBER 1981 HISTORICAL DEVELOPMENT O F AIRCRAFT FLUTTER 899 an d because o f th e overall lack o f structural rigidity, determine, without solving for roots, whether any instability, especially torsional rigidity o f th e wing an d fuselage, i t still oscillatory or divergent, existed. Bairstow and Fage had to remains highly probable that the collapse of the machine make reasonable estimates fo r th e quasistationary during launch can be attributed to aeroelastic effects, such as aerodynamic constants, but the investigation fully confirmed overload due to elastic deformations during launch in an Lanchester's conclusions, and set a pattern for the extensive untrimmed condition. British work that was to evolve a decade later. The success of the Wright biplane and the failure of the Langley monoplane ma y have influenced early aircraft German Fighters, Anthony Fokker—Torsional Divergence designers' preference towards biplanes. Undoubtedly, the On the German side in World War I, many fatal structural structural justification fo r th e biplane v s th e externally braced failures on two fighter designs were attributed to aeroelastic monoplane comes from the inherent wing stiffness readily static divergence problems. Th e German Albatros D-III, a achieved on biplanes by means of interplane struts and cross biplane patterned after th e French Nieuport 17, ha d a narrow bracing (Fig. 2) . single-spar lower wing connected by a V-strut to a large upper wing (see Fig. 5) . Because th e lower wing spar wa s positioned Lanchester an d Bairstow—The First Documented Flutter Study to o fa r af t an d th e V-strut contributed n o torsional stiffening The first major development in flutter was accomplished by to it, the wing tended to twist and wrench loose in high-speed the preeminent British engineer and scientist F. W. Lan- dives. German ace Manfred von Richthofen, "The Red chester6 during World War I in troubleshooting why the Baron," was among the lucky few who were able to land Handley Page 0/400 biplane bomber had experienced violent safely after dangerous cracks developed i n th e lower-wing antisymmetric of the fuselage and tail. The air- spar during combat. craft's right and left elevators were essentially independent, Near the end of the war, Fokker introduced the Fokker D- being connected to the stick flexibly by separate cable runs. VIII, a cantilever parasol monoplane which wa s rushed into Lanchester recognized, an d described i n a masterful text o f production because of its superior performance. Almost only three pages, tw o important concepts: 1 ) that th e immediately, however, serious problems were encountered, a s oscillations were not the result of induced by described b y Bisplinghoff, Ashley, an d Halfman (see Books) vibratory sources but were self-excited and 2) that increase of "The D-VIII was not in combat more than a few days before the torsional stiffness of the elevators by means of a carry- wing failures repeatedly occurred i n high-speed dives. Since through torque tube could eliminate th e problem. Another the best pilots and squadrons were receiving them first, it epidemic of tail flutter resulting in pilot fatalities was ex- appeared possible that th e flower o f th e German Ai r Corps perienced only a year later by the de Havilland DH-9 airplane. would be wiped out. After a period in which the Army Th e cure wa s identical t o that suggested b y Lanchester; th e engineers an d th e Fokker Company each tried t o place th e torsionally stiff connection between the elevators has responsibility o n th e other, th e Army conducted static remained ever since an important design feature (Fig. 3). strength tests on half a dozen wings and found them suf- In Lanchester's investigation of the Handley-Page airplane Leonard Bairstow provided analytical backup i n th e in - vestigation o f th e Handley-Page airplane. A resulting paper by Bairstow and Fage7 is probably the first theoretical flutter analysis. They investigated binary flutter consisting o f th e tw degrees of freedom: twisting of the fuselage body and motion of th e elevators about their hinges, a s described i n Fig. 4 . Th e dynamical were patterned after small disturbance methods of the analysis of stability of rigid-body SOLUTION: TORQUE-TUBE aircraft that were under study from 1903, an d summarized i n CONNECTED ELEVATORS the classic book o f G . H Bryan.8 Bairstow ha d written many papers o n stability using Bryan's methods. Aerodynamic coefficients fo r stability analysis have been termed derivatives since they ar e applied fo r small deviations from equilibrium flight paths. Th e aerodynamic derivatives o f Bairstow an d U Fage were constant coefficients multiplied b y a n exponential TORSIONALLY WEAK FUSELAGE time factor, an d referred t o a s quasistationary constants. Th e ^-FLEXIBLE CONTROL CABLES two equilibrium equations of motion were homogeneous, so Fig. 3 Lanchester's solution to tail-plane flutter (1916). that the determinant of their coefficients gave a quartic polynomial fo r determining th e roots (eigenvalues) an d free modes (eigenmodes). By examination of Routh's criteria,9 obtained from th e coefficients o f th e polynomial, on e could

CHARACTERISTIC EQUATION

AX4 +BX3 +CX2 +DX+E=0 ROUTH'S DISCRIMINANT

(BCD-AD2-B2E) >0 DAMPED OSCILLATIONS -0 FLUTTER ON SET < 0 UNDAMPED OSCILLATIONS Fig. 4 Tail-plane flutter analysis given b y Bairstow an d Fage i n 1916. Fig. 2 Biplanes have greater torsional rigidity than externally braced (The /terms ar e moments o f inertia, k terms ar e stiffnesses, an d L an d monoplanes. M terms ar e aerodynamic derivatives.) 900 I . E GARRICK AN D W.H. REED II I J. AIRCRAFT

Post World Wa r I t o About 1930 von Baumhauer an d Koning—Mass Balance Concept Shortly after World Wa r I a major systematic study o f flutter wa s undertaken i n th e Netherlands following severe flutter o f a va n Berkel W.B. monoplane, a long- distance reconnaissance seaplane. A n experimental an d theoretical investigation undertaken b y A . G vo n Baumhauer and C. Koning12 was published in 1923. They dealt mainly with th e binary flutter o f th e wing i n vertical bending com- bined with motion of the ailerons. The most significant result of their study was the recognition that mass balance of the aileron, or even partial mass balance, could eliminate the problem (Fig. 6). Thus the concept of decoupling of in- teracting modes t o prevent flutter wa s emphasized. A letter t o IFQKKER the authors from H . Bergh o f th e National Aerospace Fig. 5 Wing collapse o f World Wa r I German fighters caused b y Laboratory (NLR) o f th e Netherlands rightly observes that aeroelastic divergence. the 1923 investigation already contained features o f a modern flutter investigation: 1 ) analysis o f th e observed phenomenon, 2 ) derivation o f th e equations o f motion, 3) determination of mass and stiffness properties, 4) measurement o f aerodynamic derivatives, 5 ) stability calculations, 6 ) flutter measurements i n a wind tunnel, 7) comparison o f theoretical an d experimental flutter results, 8) the special flutter remedy, the mass balance concept, 9) verification by wind tunnel experiments and flight tests. However, a main shortcoming not improved for many years, was the use of the approximate and empirical quasistationary aerodynamic constants. On e ma y ad d that i n th e tradition o f this work th e small Netherlands research group has been productive in flutter research to the present Fig. 6 Mass-balance solution o f wing-aileron flutter o f vo n time. Baumhauer and Koning (1923). British Experience and Research, 1925-1929 A year later i n th e 1924-1925 yearbook o f th e British ficiently strong t o support th e required ultimate factor o f 6." Aeronautical Research Committee (ARC) Chairman R.T. The only difference between the prototype wing, which had Glazebrook wrote, "Of increasing importance is the problem shown no structural deficiencies, and the production wing was of flutter which has been discussed with representatives of a a strengthening of the rear spar of the production wing. This number o f firms; a preliminary theoretical attack ha s been strengthening had been ordered by the Army on the basis of made on the problem. It would appear that the subject may regulations developed for wire-braced wings, which called for need a 4arge amount of experimental inquiry before a com- proportional strength i n th e rear spar an d th e front spar. plete solution is obtained. Information on the rigidity of Ironically, although made stronger, th e production wing ha d wings is being collected by the Airworthiness Department of unknowingly been made prone t o aeroelastic divergence the Air Ministry, and a series of accidents associated with because of the shift of its elastic axis (Fig. 5). In Fokker's own flutter is being investigated by the Accidents Subcommittee." words10: "I discovered (during the strength tests) that with This farseeing statement i s o f interest fo r several reasons. increasing load the angle of incidence at the wing tips in- The technical word flutter is introduced here as though it were creased perceptibly. I did not remember having observed this a commonly used term. Yet it appears for the first time, and action in the case of the original wings, as first designed by may have become familiar within the confines of committee me. It suddenly dawned on me that this increasing angle of discussions. Th e committee subsequently assigned respon- incidence wa s th e cause o f th e wing collapse, a s logically th e sibility fo r flutter research, fo r both simple model an d full- load resulting from the air pressure in a steep dive would scale work, t o tw organizations, th e National Physical increase faster a t th e wing tips than i n th e middle, owing t o Laboratory (NPL) and the Royal Aeronautical Establishment the increased angle of incidence. It was the strengthening of (RAE). Shortly afterward it established a Flutter Sub- th e rear spar which ha d caused a n uneven deflection along th e committee. wing under load.... The resulting torsion caused the wing to One of the first publications13 of the ARC Accidents collapse under the strain of combat maneuvers." It is Subcommittee describes in 1925 five incidences of wing- noteworthy that, as mentioned earlier, the Wright brothers aileron flutter on two similar single seater biplane designs, the ha d observed th e related aeroelastic effect fo r thin-bladed Gloster Grebe and the Gloster Gamecock. Flutter of about 15 propellers. cycles/s is described as having the appearance of a "blurr" to We mention here that in 1926, H. Reissner, author of many the pilot and as a "hovering hawk" to a ground observer. The papers on aircraft structures, developed a detailed analysis of remedy chosen wa s t o move th e aileron interplane connecting wing torsional divergence,11 showing the importance of the strut close to the center of mass and to reduce the unbalanced relative locations of the aerodynamic center of pressure and area near the tip (Fig. 7). It is of special interest that the of the elastic axis. This axis has been called the axis of twist, Subcommittee stated that "similar flutter experiences have o r i n th e British literature, th e flexural axis. I t is , a s men- been reported both in Holland and in the U.S." tioned, defined by the property that a section loaded vertically After three years o f intensive work, mainly described i n at the flexural axis does not twist, or reciprocally, that a unpublished documents, a remarkably comprehensive moment applied about this axis does not cause bending. It is a monograph b y Frazer an d Duncan14 o f th e NP L wa s useful concept primarily for beam-like wings of moderate to published in 1929, often referred to by British workers as high aspect ratio. I n general, fo r more complex structures th e "The Flutter Bible." It made use of simplified wind tunnel use o f nodal lines o f vibration modes, o r influence coef- models t o identify an d study phenomena, gave well- ficients is more appropriate. considered cautiously detailed design recommendations,15 NOVEMBER 1981 HISTORICAL DEVELOPMENT O F AIRCRAFT FLUTTER 901

thin airfoils (Max Munk had published his thin airfoil theory some months earlier, while H. Glauert gave an alternative formulation a year later). Birnbaum was able to extend his approach to the harmonically oscillating airfoil in uniform motion.17 H e made us e o f th concept o f a n oscillating

GLOSTER GAMECOCK vorticity distribution bound over the airfoil and free floating GLOSTER GREBE in the wake, the total circulation being zero by Kelvin's theorem o f conservation o f vorticity. B y expressing th e free vorticity i n terms o f th e bound vorticity, h e obtained a n in - tegral equation which yielded the pressure in terms of the known normal velocity a t th e airfoil surface. A series ex - ORIGINAL AILERON pansion fo r th e pressure wa s introduced i n terms o f a non- MODIFIED AILERON dimensional frequency, th e reduced frequency co (the frequency times th e chord divided b y th e velocity), each term of which automatically satisfied the Kutta condition by the vanishing of the loading at the trailing edge. The numerical Fig. 7 Wing-aileron flutter le d t o intensive investigations b y th e British at the RAE and NPL (1925-1929). values, however, did not converge well beyond about A second basic approach t o th e theoretical problem o f nonstationary flow supplementing the harmonic approach of an d indicated broad programs required fo r measurement o f Birnbaum, was given by H. Wagner in a doctoral thesis in aerodynamic derivatives. They introduced a n important 1925. 18 He studied the growth of vorticity in the wake and the concept of "semirigid" modes which greatly simplifies the growth of lift on an airfoil in two-dimensional flow following theoretical analysis by defining a dynamical degree-of- a sudden change o f angle o f attack, o r a sudden acquisition o f freedom as a motion in a given "shape of oscillation." In unit downwash. This type of response is now called indicial, effect this concept enables th e problem t o b e handled b y after a terminology used in electric circuit analysis for the ordinary differential equations rather than by much less response to a Heaviside unit step type of excitation. Wagner's tractable partial differential equations. Th e concept i s directly analysis made auxiliary use of the conformal mapping of the related t o ideas o f Rayleigh i n th e us o f assumed modes i n straight line into a circle, an d le t o a n integral equation treating ordinary vibration problems o f conservative systems, giving th e growth o f th e free vorticity i n th e wake, from th e where the cross-coupling coefficients are symmetrical. In solution of which the growth of lift followed. The integral flutter w e ar dealing with fa r more complicated systems equation satisfied th e property that th e Kutta trailing-edge (nonconservative, non-self-adjoint). It must be stated, condition should hold a t each instant o f time. Th e resulting however, that the aerodynamic basis of the work of Frazer function giving th e growth o f lift with distance traveled ha s an d Duncan wa s no t satisfactory, resting a s i t di d o n em - been designated as Wagner's function kl (s) . pirical aerodynamic constants which took n o account o f th e In 1929, H. Glauert,19 following Wagner's methods, interaction effect o f th e wake o f shed vortices. Duncan treated th e flat plate airfoil undergoing steady angular himself remarks in the AGARD Manual on Aeroelasticity (see oscillations. H e gave integral expressions fo r th e lift an d Survey Papers), "All the early purely theoretical work on moment that were evaluated numerically, an d were no t flutter wa s marred b y th e inadequacy o f th e representation o f subject to the convergence difficulties of Birnbaum. (Several the aerodynamic action." years later, J. M. Burgers20 showed that Glauert's integrals Along with the work of Frazer and Duncan, which had used could b e expressed b y Bessel functions.) Glauert also called flutter models to study trends and validate theory, a com- attention t o th e circumstance that th e damping moment i n panion publication b y Perring16 (1928) initiated th e us o f pitching could change sign an d that i t indicated a mild type o f scaled models t o determine th e critical flutter speeds o f a n single-degree-of-freedom flutter occurring a t very lo w airplane prototype. The configuration selected for the study frequencies and for far-forward positions of the axis of was the single seater biplane whose wing-aileron flutter en- rotation. Study o f ho w this type o f instability i s affected b y counters in flight had been well documented by the Accidents configuration and by Mach number was made many years Investigation Subcommittee. Scaling laws developed in un- later in several investigations. published documents b y McKinnon Wood an d b y Horace I n th e very same year, H.G. Kussner,21 published a basic Lamb (1927) required that for dynamic similarity between a paper o n flutter, utilizing improvements o n Birnbaum's model an d it s full-scale counterpart there must b e similarity i n method. H e improved th e numerical convergence t o values o f geometry, mass, and elastic distributions. Scaling parameters the reduced frequency co«1.0, and applied the results, with involving the effects of compressibility (Mach number), viscosity (Reynolds number), an d gravity (Froude number) were considered i n these studies t o b e unimportant an d were therefore ignored. A one-third scale semispan model having the same mass density but with stiffnesses reduced to one- ninth that o f full scale wa s tested i n th e RA E 7-ft wind tunnel. The flutter speeds and frequencies of the model correlated well with those observed o n th e full-scale machine. This study was one of the first to demonstrate the efficacy of the aeroelastically scaled wind-tunnel model as a means for predicting critical flutter speeds o f a full-scale prototype.

Unsteady Aerodynamics i n th e 1920s In 1918, Professor Prandtl in Gottingen assigned a thesis problem on airfoil theory to W. Ackerman, and later reassigned the unfinished work to W. Birnbaum when Ackerman was called into war service. Birnbaum published tw o important papers, th e first o f which gave i n 1923 th e classical vortex theory of the two-dimensional steady flow of Fig. 8 Some ai r racers plagued b y flutter (1922-1931). 902 I . E GARRICK AN D W.H. REED II I J. AIRCRAFT the use of beam theory, to many examples involving bending R-3, ha d t o b e hastily stiffened i n order t o resist this and torsion including aileron motion. Significantly, he also heretofore little known bu t highly dangerous phenomenon. investigated effects of hysteresis-type damping to represent Th e flutter cure included, among other things, covering th e material damping as affecting the flutter results. Kussner also wings back to the rear spar with stiff plywood veneer. Later, indicated ground vibration methods aimed a t checking th e other builders o f wooden cantilever monoplanes adopted structural basis o f th e flutter analysis, fo r either model o r full- veneer wing covering as a means of providing the torsional scale structure, in the laboratory. rigidity needed t o avoid flutter; this prompted Bill Stout, It seems appropriate to remark that in October 1980 both builder o f th e all-metal Ford Trimotor which wa s flutter-free Wagner and Kussner, each in his eightieth year, were honored t o quip,... flutter i s a "Veneer-eal disease." for their lifelong contributions to aeronautics by the awards During the 1924 Pulitzer Race in Dayton, Ohio, the Army of the prestigious Ring for the years 1980 and entry, a Curtis R-6 racer, developed sudden , then 1981. shed its wings in a steep dive at the very start of the race. During the period 1925-1929, several other prominent There is some uncertainty here whether the breakup was German workers used beam-rod concepts t o investigate caused by wing flutter or by failure of the laminated wooden flutter, utilizing, however, quasisteady aerodynamics which propeller. The following year, Great Britain's prized entry in neglected the trailing wake effects. Among these were H. the 1925 International Schneider Marine Trophy Race, a Blasius (1925), B. Hesselbach (1927), and, notably, H. Blenk Supermarine S- 4 Racing Monoplane, experienced wing flutter and F. Liebers (1927-1929). during a prerace trial flight an d crashed into th e Chesapeake Bay at Baltimore. The pilot, who just managed to survive, Some Early United States Work said th e wings "fluttered like a moth's wings." I t i s significant to note that the S-4 was an unbraced cantilever- One of the earliest investigations of flutter in the United wing design; after its crash the designer, R.J. Mitchell, who States (1927) wa s that o f th e horizontal tail oscillations, a t later designed the Spitfire, reverted to externally braced wings about 6 cycles/s, of the Navy MO-1 airplane. After for the Supermarine S-5, S-6, and S-6b, which went on to win eliminating the wake of the main wing as the cause of the 22 three Schneider trophies an d tw o World Speed Records during excitation, Zahm and Bear made an analysis for flutter that the 1927-1931 period. Later, in an attempt at breaking the followed closely th e methods used i n th e Netherlands an d world's landplane speed record i n 1931, a Ge e Be racer an d England. Th e problem wa s traced t o flutter involving th e its pilot were lost in what has been attributed by some to wing- differential deflections o f th e two-spar system which aileron flutter during th e high-speed diving start. produced a strong coupling between bending and torsion. Recommendations given for its avoidance included increased I n some incidents, where flutter wa s more forgiving, th e torsional stiffness an d forward shift o f th e center o f mass. pilot an d hi s plane would return "shaken" bu t unharmed. Other introductory articles on flutter published in the 1927- When given this second chance t o correct hi s design, th e 1928 period were b y J.S. Newell, b y J.E. Younger, an d b y builder would sometimes resort t o bold, i f no t imaginative 23 solutions. Leon Tolv^ describes on e such incident i n a C.F. Greene. 26 In 1927, some flutter work wa s started a t th e Massachusetts historical account of flight flutter testing : "In 1934, during Institute of Technology (MIT) by Manfred Rauscher in a the National Ai r Races, on e o f th racers kept encountering student thesis dealing with th e us o f models i n th e wind wing-tip flutter. Each time the wing span was reduced by tunnel. Other student thesis work on models was initiated by cutting off part of the wing tip until the flutter stopped. As a result, the wing area was finally reduced from its original G.W. Grady and F. MeVay. A published version by 2 2 Rauscher24 o f this work, i n German, described th e us o f value o f 7 8 ft down t o 4 2 ft , bu t th e pilot ended u p with a models to attempt to verify the then current work of Blenk flutter-free airplane!'' and Liebers, with the conclusion that the comparisons were unsatisfactory and much remained to be done. 1930 to World War II It is appropriate to mention that a dozen years earlier at British Studies MIT, J.C. Hunsaker an d E.B. Wilson ha d published some I n contrast t o it s foresight i n 1924-1925, th e predictions o f gust and stability studies in NACA Rept. No. 1, "Behavior of the British ARC in the 1929-1930 yearbook completely missed Airplanes in Gusts," showing by theory and experiment that the mark with it s statement, "The Committee considers that the response of an airplane to given gusts, an aeroelastic the main practical issues of the subject of wing flutter have problem, was sensitive to the stability limits of the airplane. now been put on a satisfactory basis and that, from a purely Later, at the outset of World War II, Rauscher led the MIT practical standpoint, there does not seem any need to pursue Aeroelastic and Structures Research Laboratory in a the theory further." In fact, the 1930s were a decade of program, wherein elaborate models aimed at dynamic considerable ferment and progress in aeroelasticity, especially similarity of typical military airplanes were constructed and in th e theory. Th e structurally stiff biplane ha d lost ground t o tested. This laboratory had associated with it prominent the monoplane with its superior performance; the fabric leaders like R.L. Bisplinghoff, H . Ashley, R.L. Halfman, R . covered wings of wood spar construction were being replaced Laidlaw, Rene Miller, Eric Reissner, E. Mollo-Christensen, by metal covered wings o f semimonocoque construction with and Marten Landahl, and it served as an engineering training metal spars an d internal stiffeners, an d o f monocoque source for many of the industry's aeroelasticians. A more construction wherein the skin covering provided a large part complete story of the laboratory and of the individuals in- of the stiffness. Moreover, speeds were approaching an volved i s given b y S . Ober.25 appreciable fraction of the speed of sound (see Hoff, Survey Papers, 1967). In 1932, a series of accidents with fatalities was encountered Air Racers Encounter Flutter by th e d Havilland Puss Moth airplane, a general purpose After World War I, highly competitive attempts to break single-engined monoplane, whose wings were braced by world speed records and to capture coveted air-race prizes folding V-struts. A 1936 comprehensive report o f th e AR C stimulated designers to push for ever higher speeds. A price Accidents Investigation Subcommittee27 summarized more paid for this otherwise healthy rivalry was a series of flutter than 50 separate detailed investigations. Of special interest encounters, usually catastrophic, which occurred during high- was the conclusion that not only wing flutter but also rudder speed runs. Shown i n Fig. 8 ar e some o f th e racers which ar e and elevator flutter may have been involved, that the V-struts known, o r believed t o have been, plagued b y flutter problems. were a factor in the wing flutter, and that the rudder flutter In the 1922 Pulitzer Trophy Races the wings of two cantilever seemed to require a starting impulse such as stormy or tur- monoplane entries, th e Loening P- 4 an d th e Verville Sperry bulent weather. NOVEMBER 1981 HISTORICAL DEVELOPMENT O F AIRCRAFT FLUTTER 903

Table 1 Some U.S. flutter experiences, 1932-1934 Airplane Type of flutter YC-14 (General Aviation)Transport Wing-ailerona C-26A (Douglas) Transport Wing-aileron XO-43 (Douglas) Observation Wing-aileron YO-27 (General Aviation) Observation Wing-ailerona (free play a factor) YO-27 (General Aviation) Observation Rudder-fuselagea (violent flutter) F-24 (Fairchild) Civil Wing-aileron F-24 (Fairchild) Civil Tail flutter YA-8 (Curtiss) Attack Rudder fina YB-9A (Boeing) Bomber Rudder-fuselage (limited amplitude flutter) XV-7 (Douglas) Bomber Elevator-fuselagea (elevator interconnect-stiffened) YO-40B (Curtiss) Observation Elevator-tabb

aSolution: mass balance. bSolution: increased tab frequency.

Duncan and Collar28 extended the theory of Glauert to Theodorsen's work has played a major role in the include wing translation an d rotation, and, like Glauert, they development o f American methods o f flutter analysis, i n th e obtained their results by numerical integration. Cox and relatively simple us e o f strip theory fo r wings o f moderately Pugsley29 and Duncan and MacMillan30 investigated the high aspect ratios, and in several other approximate newly discovered aeroelastic control-problem aileron procedures. I t must b e stated that although Theodorsen made "reversal" wherein, a s th e speed i s increased, th e deflection no direct use of the work of Wagner and Glauert and gave no of the ailerons produces wing twist opposing the ailerons, so references, his method of analysis is clearly related to their that th e rolling power o r effectiveness o f th e ailerons work. This circumstance may have left resentments, and may diminishes, may vanish, and then act in the opposite direc- have a bearing o n th e divergence o f U.S. an d British methods tion. Although i t s no a n instability problem pe r se , th e of flutter analysis. control problem ca n b e dangerous. Theodorsen and Garrick33 developed numerous ap- The British were not alone with flutter problems. During plications and trend studies of the simple exact theory yielding 1932-1934, there were many flutter cases in the U.S. Table 1 insights into the individual effects of the many parameters: lists some of these. The information was supplied to the center of mass, elastic axis, moments of inertia, mass ratio authors by Leon Tolve. (mass o f th e wing t o a surrounding cylinder o f air), aileron hinge location, bending/torsion frequency ratio, etc. I n particular, the material damping, represented by hysteresis Theodorsen: Two-Dimensional Flutter Theory damping (g), which i s obtained b y multiplying th e elastic In th e U.S., attacked th e flutter restoring force by the factor e/g«!+/#, was also varied. problem in 1934 and within a few months of intensive con- Experimental studies o n simple cantilever models o f high centration produced NACA Rept. No. 496,31 .which has aspect ratio confirmed the basic theory with good agreement. played a large role in establishing methods of flutter analysis Aileron flutter, which often can occur only over a limited i n American aircraft industry. (Garrick worked closely with speed range, wa s also confirmed. I t wa s shown that fo r a wing Theodorsen over the period 1930-1946, and has described of high aspect ratio the flutter mode could involve much Theodorsen's many contributions to flutter and other areas in second an d higher bending modes. Th e confirmation o f th e a separate article.32) Theodorsen gave a succinct theory of the Theodorsen theory by means of flutter speed measurements is two-dimensional oscillating flat plate undergoing translation, a n indirect process. A direct experimental confirmation o f th e torsion, an d aileron-type motions. H e separated th e non- oscillating lift o f a n airfoil i n pitching motion wa s made b y circulatory part of the velocity potential from the circulatory Silverstein an d Joyner.34 part associated with the effect of the wake. Again the trailing- It is appropriate to record that, starting about 1935, flutter edge flow condition sets a relation between the two parts, was a topic o f discussion appearing i n Japanese, Russian, whose solution leads to a combination of Bessel (or Hankel) French, and Italian papers, as indicated in the bibliography in functions designated C ( k ) . This function establishes the lags Ref. 35. Illustrating the classic pattern of the evolution of between the airfoil motions and the forces and moments that ideas when the time is ripe, Placido Cicala36 in Italy, arise, and has been denoted as Theodorsen's (circulation) following Birnbaum's method, obtained a n independent function C(k), where, analogous to the Strouhal number, A: is solution o f th e oscillating flat plate only months after a reduced frequency, ub/V (co i s th e angular frequency, b th e Theodorseri, while Kussner37 developed a solution in the half-chord, and V the airspeed). The quasistationary con- following year (1936) in a paper which also summarized the stants used i n earlier work thus become frequency dependent. state-of-the-art in the development of the theory. In his paper Because th e various phases an d lags ar e crucial i n determining Kussner gave the method for obtaining the gust function whether energy ca n b e extracted from th e airstream, that is , denoted by k2 (s), the growth of lift following entrance of the whether flutter ca n occur, Theodorsen's theory represented flat plate airfoil into a sharp-edged gust. A n error i n sign i n the simplest exact theory for the idealized flat plate airfoil, th e derivation wa s corrected b y vo n Karman an d Sears. and has served a major role in so-called "strip" theory wherein representative sections are employed in wing flutter Propulsion of Flapping Wings and Aerodynamic Energy analysis. It is a source of satisfaction to aeroelasticians that their Theodorsen's method of solution for the flutter stability field ha s contributed t o th e understanding o f th e age-old equation differs from that o f hi s predecessors, i n that h e problems of the flight of birds and locomotion of fish. The makes no use of Routh's discriminants; for, as he deals with first hint of this is in an application of Birnbaum's theory to sinusoidal aerodynamics, th e determinant whose vanishing th e calculation o f th e horizontal forces o n a flapping wing b y yields the eigenvalues is complex so that both its real and J . M Burgers,20 wh o developed th e theory o f th e propulsive imaginary parts must vanish simultaneously to determine a forces on a flat plate airfoil including the effect of the suction flutter condition. This leads t o several parametric ways o f force a t th e sharp leading edge, which, paradoxically, holds finding the flutter solutions. Both binary and ternary types of for the rounded edge. Similarly, Garrick treated the flapping flutter were studied. an d oscillating airfoil with aileron.38 During more recent 904 I . E GARRICK AN D W.H. REED II I J . AIRCRAFT years T.Y. Wu has developed at the California Institute of Aerodynamic Hysteresis Technology a more complete theory, while Lighthill ha s The theory of Wagner on the growth of circulation or lift brought in biological studies and introduced a new field following a change i n angle o f attack wa s well demonstrated termed "biofluid-dynamics." Th e flow o f blood i n elastic in a water tank b y P.B. Walker42 working with W.S. Farren. arteries i s another example o f this field, a s i th e Farren examined experimentally the increase in lift coefficient "hydroelasticity" of planing surfaces. The aerodynamic for a wing whose angle of incidence is changing rapidly, and energy required to maintain the motion of the oscillating wing showed that the lift coefficient could increase well beyond in the airstream has also been a useful concept in flutter maximum lift.43 This phenomenon leads t o complex analysis. Perhaps th e simplest physical picture o f th e nonlinear hysteresis effects for an oscillating airfoil, which mechanism o f flutter i s arrived a t through th e aerodynamic ar e functions o f th e Reynolds number (Fig. 10). Th e energy, as by Duncan's ''flutter engine" wherein one could phenomenon occurs in stall flutter of wings, propellers, and extract energy from the oscillating airfoil in the wind tunnel rotors, and in high angle of attack buffeting. by means o f a crank an d flywheel (see Survey Papers, Experimental work at low speeds on the effects of angle of Duncan, 1951 andNissim, 1971). attack o n aeroelastic phenomena wa s started i n 1936. Th e effect o f high angles o n th e flutter speed, a n inherently Oscillatory/Indicial Aerodynamics nonlinear problem, was begun by J. Studer44 under direction There ar e interesting an d important relationships between of Professor Ackeret. A similar study of lesser scope was oscillatory an d indicial aerodynamics, noted b y Garrick,39 undertaken by Rauscher45 about the same time at MIT. The that are analogous to those of electric circuit analysis between significant result wa s obtained that with increase i n angle o f th e frequency response function t o alternating current an d th e attack the coupled wing flutter speed dropped markedly in the Heaviside response to unit step excitation. These relations neighborhood o f th e stall, an d became essentially single- correspond i n th e simple flat plate cases t o Fourier integral o r degree-of-freedom torsional flutter, a less violent type. The Laplace transform relations between Wagner's function prevention of this phenomenon is currently important for all kl (s) and Theodorsen's function C(k). Similar relations can types of high lift devices, for rotor wings, and for turbo- be developed for more general configurations; they rest machinery; i t sometimes ma y confound th e buffeting picture essentially on the validity of the principle of superposition for for high angles of attack associated with wake excitation and linear processes. Such spectral techniques are useful in other vortex separation. areas involving transfer functions, fo r example, i n th e determination of the response to gusts and turbulence. Empirical Criteria I n addition t o th e correction o f th e Kussner gust function 40 In 1935, Kussner correlated many flutter incidents an d k2 (s ) mentioned above, vo n Karman an d Sears a t th e accidents, an d developed a n empirical formula based o n th e California Institute of Technology developed another in- reduced torsional frequency (ub/ V), a criterion which gave dependent treatment o f th e oscillating flat plate i n in - only a ball park estimate of the flutter speed for the then compressible flow. The transfer function of k2 ( s ) , given by a current types of aircraft. A similar statistical study had been combination of Bessel functions, has been designated Sears' made b y Roxbee Co x (1933), however, based o n wing tor- gust function an d i s made us e o f b y hi m i n several gust 41 sional stiffness instead o f frequency. I t i s interesting that these studies. These reciprocal relationships between the indicial two empirical formulas, on e based o n natural frequency an d lift functions o f Wagner an d Kussner an d th e counterpart the other o n stiffness, actually reflect th e separate paths along "frequency response" functions of Theodorsen and of Sears which flutter theory ha d evolved. Whereas th e German ap - ar e graphically illustrated i n Fig. 9 . A E Lombard, another proach, typified b y Kussner an d also b y Theodorsen, con- doctoral student o f vo n Karman, gave i n hi s thesis (1939) sidered th e flutter motion a s sinusoidal expressed i n terms o f many numerical applications and a summary of the literature. natural frequencies, the British approach proceeded along the The esoteric and abstract mathematical nature of flutter lines of Bryan's stability theory using Routh's discriminants analysis gave th e subject a n atmosphere o f mystery, magic, an d involved th e stiffness, inertia, an d damping coefficients and skepticism in the design office, and led von Karman to that appear i n th e equations o f motion. A s a consequence, remark (as quoted by W. Liepmann), "Some fear flutter British researchers i n th e early stages o f flutter development because they do not understand it, and some fear it because tended t o overlook an y direct connection between natural they do." Indeed some designers would no t become true vibration modes an d flutter. During this period, resonance believers until confronted by flutter occurring in their own testing in England was neglected in favor of stiffness designs. measurements which were considered t o b e more directly applicable to needs. By 1936, however, resonance testing in connection with flutter investigations o f aircraft an d wind tunnel models ha d become a s accepted i n England a s elsewhere.

LIFT LIFT

TIME FREQUENCY Fig. 9 Fourier transform relationships between oscillatory and indicial aerodynamics. (Modified Sears function i s referred t o leading ANGLE O F ATTACK, a edge rather than to midchord. See Giesing et al. Journal of Aircraft, Fig. 1 0 Nonlinear behavior an d hysteresis loop near stall fo r 1970.) oscillating airfoil. NOVEMBER 1981 HISTORICAL DEVELOPMENT OF AIRCRAFT FLUTTER 905

Flight Flutter Testing flutter, propeller whirl flutter involves th e gyroscopic I n 1935 i n Germany, vo n Schlippe became th e first t o precession of a flexibly mounted engine-propeller system. employ resonance testing techniques in flight.46 The purpose Because th e conditions necessary fo r such a n instability were of hi s research wa s t o lessen th e extraordinary risks involved never encountered in aircraft designs of that time, the in testing in flight for flutter safety. The usual procedure for problem wa s considered t o b e f academic interest only. flight checking a new or modified design had been simply to However, after remaining dormant for more than two dive th e airplane t o it s maximum velocity an d hope fo r th e decades, propeller whirl flutter wa s suddenly "rediscovered" best. In justifying his work, von Schlippe stated the problem as being the probable cause of the crashes of two Lockheed in much the same way we would describe it today: "Lately the Electra turboprop transports (see Survey Paper, Reed, 1967). problem of spontaneous oscillations has become particularly The instability was attributed to a severe reduction in nacelle acute as a result of the trends in modern airplane design. support stiffness du e t o some form o f damage i n th e engine Thinner profiles, divided tail units, greater number o f cu t mount structure. I n undamaged condition th e aircraft ha d a n away sections in the wings, as well as the generally great ample margin of safety from whirl flutter. The cure involved weight of the fast airplanes, are all factors which, with the among other things stiffening and redesigning the mount demands fo r greater speeds, reduce th e range between critical system t o make i t "fail-safe." Whirl flutter stability ha s also an d maximum velocity, an d through i t promote th e danger o f become a n important design consideration fo r prop-rotor oscillation." VSTOL aircraft. Th e basis o f th e vo n Schlippe method i s that a t th e critical flutter speed th e resonant amplitude response o f th e airplane Matrix Methods structure to forced oscillations would be infinitely large, One of the timely publications of the prewar period (1938) unless modified b y nonlinear effects, s o that a plot o f th e was a unique textbook by Frazer, Duncan, and Collar49 on resonant amplitude against airspeed would have a n asymptote matrices an d their applications, spiced with several flutter a t th e flutter speed (Fig. 11). Th e estimated position o f th e examples. By this time the simple binary and ternary cases asymptote, an d hence o f th e flutter speed, could then b e were needing expansion to include many additional structural deduced from observations o f th e forced amplitudes a t air- degrees o f freedom. I n 1941, S . J Loring50 gave a prize paper speeds below th e critical speed. However, from wind tunnel outlining a general approach to the flutter problem that made an d theoretical studies o f vo n Schlippe's method, Frazer an d convenient and systematic use of matrices. The expansion of 47 Jones cautioned that under certain conditions th e damping numerical effort soon t o become overwhelming b y earlier could drop very suddenly near th e flutter speed fo r very small methods required th e employment o f systematic procedures changes i n airspeed. Th e Germans successfully carried ou t afforded b y matrix methods, both i n structures an d i n systematic flight flutter tests using the technique on a series of aerodynamics. Matrix methods also fitted i n with th e parallel aircraft, until i n 1938 a Junkers JU90, equipped with a 400- growth in the use and capacity of computing machines that h p motor i n th e fuselage t o drive vibrators i n th e wings, was to evolve during the next decade. Figure 12 sketches a fluttered unexpectedly during th e flight tests an d crashed. matrix form of the flutter equations. Because o f th e hazards o f flight flutter testing, there wa s a strong reluctance b y aircraft manufacturers t o perform such tests. Nevertheless, i t wa s recognized b y some that i f t wa s Compressibility Effects dangerous t o conduct a flight flutter test, then i t would b e fa r About th e mid-1930s th e effects o f airplane speeds in - more dangerous to fly without it. By the late 1940s flight creasing to near sound speed were becoming important; that is, flight Mach numbers were such that local Mach numbers flutter testing began t o gain acceptance b y th e industry a s 51 result o f improvements i n testing techniques an d flight in - approached one. A significant paper b y Prandtl i n 1936 o n strumentation, along with a better theoretical understanding steady aerodynamics in a compressible medium set the stage of the flutter problem. Methods for flight flutter testing have for its rapid generalization to unsteady aerodynamics. evolved into very advanced procedures utilizing flight and Prandtl introduced th e useful concept o f th e acceleration ground based digital computers, real time test and analysis, potential, in contrast to the usual velocity potential. The an d a variety o f methods o f excitation, steady-state, transient, concept has been useful however mainly for the small- pulsed, an d random (see Survey Papers, NASA SP-385 an d disturbance linear-theory approach. In this case the ac- SP-415, 1975). celeration potential i s a special grouping o f velocity potential terms (d(j)/dt) 4- V(d/dx) representing the normal pressure. Propeller Whirl Flutter Since there is no pressure loading across the wake, this term vanishes there, and the wake boundary condition is ac- In 1938, in a study of vibration isolation of aircraft engines, cordingly simplified. Prandtl's theory holds well for both Taylor an d Browne48 examined th e possibility o f a ne w form of instability that later came t o b e known a s propeller whirl flutter. Unlike propeller-blade flutter, a cousin o f wing

v = o p[A(U ,V)])jqj=JFJ

RESPONSE MASS MATRIX STIFFNESS MATRIX AERODYNAMIC MATRIX Fig. 12 Matrix methods enable \(\\ MODAL COORDINATES (COLUMN MATRIX) systematic calculations of aeroelastic effects. AT FLUTTER F = 0 AND

FLUTTER DETERMINANT I S

-u2B + E + pA = 0

Fig. 1 vo n Schlippe's flight flutter test technique. 906 I . E GARRICK AN D W.H. REED II I J. AIRCRAFT small disturbance subsonic (M<1) an d supersonic (M>1) Th e equation relates th e unknown load distribution L over th e speeds, however, th e linear theory i s no t valid fo r th e tran- lifting surface and the known velocity normal to the surface, sonic and hypersonic speed ranges. the downwash w by means of a quantity AT, known as There followed shortly afterward two short outstanding Kussner's kernel function, which represents th e normal contributions b y Camille Possio i n Italy. I n 1938,52 h e applied downwash induced at any point by a unit point load. The the acceleration potential t o th e two-dimensional non- function K depends on the retarded solution of the acoustic stationary problem and arrived at an integral equation wave equation an d holds fo r th e subsonic range. I t wa s left b y (Possio's equation), the solution of which gives the loading Kussner i n th e form o f a highly singular integral whose over a flat plate airfoil in the airstream for a known motion of solution could be found in special cases. For example, in two the plate, i.e., for a given downwash. Possio indicated a dimensions it reduced to the kernel of Possio's equation. It procedure for its numerical solution, although several others was no t until 1954 that a general explicit expression fo r K wa s later contributed more convenient methods. Possio also gave developed a t th e NACA Langley Aeronautical Laboratory b y an outline of the parallel problem for a supersonic main- C. E. Watkins, H. L. Runyan, and D. S. Wollston60 which stream.53 Possio's brief brilliant career ended with hi s death opened the way to fuller development of appropriate methods during th e wa r years. of solution o f th e integral equation, a s th e primary basis an d focus for numerical methods for the aerodynamics needed in Finite Span Considerations flutter analysis. In th e case o f steady flow about finite wings, Prandtl's I t i s pertinent t o remark that numerical lifting surface integral equation for determining the induced drag and the methods utilizing the velocity potential are also in contention; spanload distribution played a well-known an d important for incompressible steady flow, discrete numerical methods were initiated by V. M. Falkner61 and were extended to role. It was natural to try to generalize this approach for 62 unsteady flows while keeping the two-dimensional exact oscillating flows b y W . P Jones. Very recent work o f theory a s limit fo r th e infinite aspect-ratio wing. This Morino (see Survey Paper, 1974) hinges o n such methods, resulted in what had been referred to as lifting-line and which can go beyond the linear approximation. multiple lifting-line methods fo r oscillating wings o f finite span. The first of these methods was developed by Cicala54 World Wa r I t o th e Mid-1950s (1937). Other related work of interest was given by W. P. During World Wa r II , rapid changes took place i n airplane Jones55 (1940), Kussner56 (1943), and Reissner57 (1944). development. Th e trend toward higher speeds an d toward all- These methods played an important interim role until metal aircraft persisted. Fighter aircraft and long-range computational methods applicable to true lifting surface bombers of diverse configurations, of low and high aspect methods evolved some years later. R . T Jones58 contributed ratios, carried external armament, tip tanks, and other ap- t o this area from th e viewpoint o f th e indicial aerodynamics. pendages. A tip-tank flutter problem, fo r example, occurred He gave an approximation for the Wagner function in a form o n th e P-80 airplane. Flutter problems occurred i n th e field useful in applications with transfer functions: due to appendages or battle damage which could cause loss of balance weights o r reduced stiffness. b s b s k](s)=l-a1e i -a2e 2 ... The V,g Flutter Diagram and gave similar developments for finite elliptic wings of various aspect ratios. As an aid to flutter analysis and practice, Smilg and Wasserman63 i n a 1942 document gave comprehensive tables General Lifting Surface Theory of unsteady aerodynamic coefficients based o n th e theory o f Theodorsen, an d supplemented b y tables o n control-surface Th e basis fo r a general lifting surface theory fo r finite 59 aerodynamic balance from Kussner and Schwarz (1940). wings was given by Kussner in a classic paper published These tables, together with th e suggested computational during the war, issuing from his newly formed Institute for procedures, served as the handbook for flutter analysis in the Nonstationary Phenomena i n Gottingen. (The unique issue o f United States for a number of years. the journal in which this paper appeared was devoted to Their flutter computation procedures adapted th e struc- nonstationary aerodynamics, an d included other papers o f tural damping concept involving th e parameter g t o give a lasting interest.) Kussner made direct us e o f Prandtl's ac - useful wa y o f graphically exhibiting a flutter solution b y celeration potential an d o f th e effect o f a uniform moving means o f th e V, g flutter diagram. I n this commonly used doublet t o obtain a n integral equation o f th e form procedure, with abscissa the speed V, and ordinate the damping factor g, the flutter solution is conveniently represented b y th e crossing o f th e g = Q axis b y a particular frequency branch (Fig. 13). I n this sketch mode 2 shows a flutter crossing, while mode 3 indicates a low damping sen- sitivity. Each point i n this representation i s a harmonic flutter solution with a n artificial damping g, namely, that required t o MODE 2 sustain harmonic motion. Th e appropriate flutter solution i s that which corresponds t o th e actual damping i n th e structure, often taken as g = 0. The actual damping in each mode can be DAMPING modeled and included by means of separate g's. REQUIRED, 9 Unsteady Aerodynamic Measurements an d Aeroelastic Models While significant strides had been made in the advancement of aeroelastic analysis, researchers and designers continued to MODE 3 place heavy reliance o n obtaining complementary ex - perimental data. Aeroelastic model tests i n wind tunnels, supported b y mathematical analysis, gave designers that much MODE 1 needed feeling of confidence that neither theory nor ex- periment alone could provide. These wind-tunnel in - VELOCITY, V vestigations ranged from measurements o f th e oscillating Fig. 1 3 Flutter solution b y th e V, g method. airloads to flutter-proof tests using complete aeroelastic NOVEMBER 1981 HISTORICAL DEVELOPMENT OF AIRCRAFT FLUTTER 907 models of prototype aircraft. In addition to providing tests probably represent the first flutter-model experiments in designers with solutions that might not be obtainable by which simulation o f free flight wa s attempted (see Survey theory i n a reasonable length o f time, such experiments also Paper, Biot, 1945). are extremely useful tools for evaluating and guiding the The popularity of replica-type plastic flutter model con- development of theory. struction eventually waned because o f limitations i n I n a survey o f oscillating aerodynamic derivative manufacturing tolerances, changes in material properties with measurements during the years 1940-1956, Hall64 cites 53 temperature and humidity, and high cost of fabrication. The published studies, conducted mainly b y British an d U.S. replica model concept was replaced by a much simpler model- investigators. This survey revealed that much of the work design approach wherein only those modes o f vibration ex - during the war years was done by the British, however, at low pected to be significant from the standpoint of flutter were subsonic speeds; after the war, in the U.S., the main emphasis represented by the model. With this approach, beam-like was o n obtaining results fo r th e transonic an d supersonic wings could b e simulated b y a single metal spar having th e speed ranges. proper stiffness distribution to which were attached Since th e earliest attempts i n th e twenties a t measuring ai r aerodynamic contours in the form of light balsa wood pods. loads on oscillating surfaces it was realized that the Th e correct mass an d moment o f inertia a t each spanwise development of reliable testing techniques was important and station could b e matched b y means o f weights installed i n th e difficult t o achieve. Early methods fo r measuring amplitude pods. Model studies of this kind, as shown in Fig. 14 for the an d phase o f th e pitching moment o f a n oscillating airfoil B-47, were instrumental in guiding the flutter design of the B- relative t o it s motion were often laborious an d inaccurate, 52 an d th e je t transports that evolved from it . involving th e reading o f photographic records o f vibration For research purposes models can be far less complex than time histories contaminated b y extraneous noise an d th e elaborate development-type models described. Indeed, th e vibration. An ingenious yet simple electrical measurement simplest model that enables study o f th e particular technique, which overcame these difficulties, was developed phenomenon of interest is usually the best model. A com- by Bratt, Wight, and Tilley.65 Known as the "wattmeter" pilation of experimental flutter research in the U.S. using harmonic analyzer, the technique made it feasible to greatly simplified wing an d wing-aileron flutter models, covering th e expand th e scope, an d improve th e accuracy o f oscillatory postwar period through 1953, is documented by Cunningham aerodynamic derivative measurements. an d Brown.68 Other examples o f th e role o f wind-tunnel The wattmeter analyzer in combination with the Kennedy- models in aeroelastic research prior to the mid-fifties are Pancu vector method o f vibration measurement an d given b y Templeton69 fo r low-speed models, b y Targoff an d analysis66 played a n important role i n other areas o f dynamic White70 for transonic models, and by McCarty and Half- testing, such a s ground an d flight resonance testing o f air- man71 fo r supersonic models. craft; it may be regarded as a forerunner of present-day A special 4-ft wind tunnel designed exclusively for flutter vibration analyzer instruments. research a t high subsonic Mach numbers (u p t o about 0.8) The usefulness of wind-tunnel flutter-model tests to became operational a t th e Langley laboratory i n 1946. A validate theory, study flutter trends, and determine margins novel feature o f this tunnel wa s i n th e test medium, which of safety fo r full-scale prototypes ha d already been well could be either air or freon gas and which could be varied over established fo r low-speed aircraft o f th e early thirties. A a ratio of 30 to 1 in density. The freon test medium is par- decade later, with flight speeds approaching that o f sound, ticularly desirable fo r scaled flutter-model testing a t subsonic an d aircraft o f all-metal construction, ne w requirements arose and transonic Mach numbers because of its higher density by for th e design an d fabrication o f aeroelastically scaled flutter a factor o f 4 , an d lower speed o f sound b y about one-half, models. During th e wa r years a popular method o f con- compared with that of air. This tunnel, later modified by structing low-speed flutter models fo r us e i n th proof testing means of a slotted throat to give transonic capability, became of prototype designs utilized a readily workable plastic, a precursor fo r th e Langley Transonic Dynamics Tunnel, poly vinyl-chloride. This material, having a density and elastic which today is the key facility in the United States dedicated modulus much less than that of the full-scale aluminum to experimental investigations in the field of aeroelasticity. aircraft structure, permitted th e internal a s well a s th e ex - ternal construction o f th e model t o b e geometrically similar t o Transonic Flutter Problems that o f th e prototype structure; that is , i t made replica-type With the advent of flight at transonic speeds brought about construction feasible. Experiences with such models are 67 mainly by the jet engine, came a host of new and challenging described by Wasserman and Mykytow (see Survey Papers, aeroelastic problems, many of which remain to this day, as Williams, 1951). W e ma y note that a s early a s 1938 a !4-scale the transonic speed range is nearly always the most critical one complete replica wing model of the PBM-1 seaplane was from the standpoint of flutter. One such problem to capture tested in the NACA Propeller Research Tunnel. Investigators the attention of aeroelasticians was a violent form of aileron were Felix Nagel, William Bergen, Rene H. Miller, and Edwin oscillations encountered in 1944 by NACA pilots during high- P . Hartman. Th e tests i n this instance disclosed a wing divergence speed very near to the wing flutter speed. A flutter model o f this kind, tested about 1942, wa s o f a n un - conventional fighter design, the Vultee XP-54. With a pusher propeller on the aft fuselage and twin booms extending aft from the wing to support the horizontal and vertical tails (Fig. 14), it was expected that this configuration might have some unusual flutter problems. Elevator flutter was, i n fact, detected during wind-tunnel tests an d th e problem corrected in time t o eliminate it s occurrence o n th e airplane. I n Ger- many, a complete aeroelastically scaled replica-type plastic model of the Junkers JU-288 was tested in 1944. The model, with a wing span of more than 7 m, was flexibly suspended by wires i n th e wind tunnel t o enable simulation o f rigid-body free flight modes. Results from these tests were employed to guide selection of such design variables as the stiffness and mass balance o f control surfaces, empennage connection stiffness, and also engine mounting stiffness (Fig. 14). These Fig. 1 4 Flutter models o f prototype aircraft i n wind tunnels. 908 I . E GARRICK AN D W.H. REED II I J. AIRCRAFT speed flight tests o f th e ne w P-80 airplane. This phenomenon, of radar and telemetry at hand the Langley Laboratory, in called "aileron buzz," was identified as a single-degree-of- 1946, began experimental flutter studies in the transonic range freedom type o f flutter caused b y th e coupling o f aileron by means of models dropped from high flying aircraft and by rotation an d ehordwise motion o f shock waves o n th e wing. ground-launched rocket-propelled models (see Survey Papers, As first described qualitatively by Erickson and Stephen- Shortal, 1978). In another method, the wing-flow technique, son,72 i t s attributed t o th e aerodynamic la g effects over th e th e model wa s placed o n th e upper surface o f a n airplane wing control surface associated with th e shock location an d it s in a region of nearly uniform transonic flow. Also, rocket movement as affected by speed and angle of attack (see also sleds capable o f accelerating t o transonic speeds were used i n Smilg73). Th e phenomenon ma y also involve periodically flutter investigations both for models and full-scale com- separated an d reattached flow behind th e shock. First at - ponents. tempts at eliminating the problem were along lines known By th e early fifties transonic wind tunnels ha d become a from past experience t o b e effective fo r other forms o f aileron reality, because o f development a t Langley o f vented test- flutter, fo r example, b y th e us o f control-surface mass section walls fo r which much credit i s du e John Stack. Flutter balance. Wind-tunnel tests in the Ames 16-ft tunnel showed experiments at transonic Mach numbers could now be per- that mass balance, even large amounts of overbalance, had formed i n wind tunnels, an d with much greater efficiency an d virtually no effect on the severity of the oscillations. Even- less cost than b y th e methods mentioned. A t Langley th e 4-ft tually, after extensive flight and wind-tunnel investigations Freon Tunnel was converted to a 2-ft continuous flow (as there were no suitable transonic theories), practical means transonic tunnel and used in flutter research. Also, a 26-in. of dealing with the problem evolved. The solutions included transonic blowdown tunnel became operational and, because increased control stiffness, dampers, and profile shape of its versatility and economy, was particularly useful in changes. aircraft development work employing small wing and tail A n empirical criterion fo r the avoidance o f transonic flutter models. control-surface flutter was given by Arthur A. Regier (Survey Systematic flutter tests at supersonic speeds were begun by Paper, A CARD Manual, Vol. V ) in the simple form Regier about 1950 with the use of a small blowdown tunnel. (C00C0/20) >0.2 to 0.3, where co^ is the control-surface To avoid the initial shock characteristics of such tunnels, he frequency, c^ th e control-surface chord, an d a th e sound developed a technique fo r injecting th e model after th e initial speed. A similar criterion of Regier for avoidance of propeller shock ha d passed, an d uniform flow wa s established. Later a stall flutter wa s (coac/2a) >0.4, where o?a i s th e blade tor- similar technique, involving initial restraints, wa s used i n th e sional frequency and c the chord. 9- b y 6-ft (M=3) Thermal Structures Tunnel which wa s used Following concepts first given i n 1945 b y R.T. Jones (and for many flutter tests. These included actual components o f for supersonic flow, earlier by A. Busemann), sweep as a the X-15, a n airplane which flew above M=7 an d reached design feature t o allow efficient penetration o f transonic 300,000-ft altitude. During development i t ha d several panel speeds wa s introduced. Th e Boeing B-47 bomber made us e o f flutter problems. sweep and aeroelastic tailoring to produce a highly efficient design for the time. The placement of the nacelles on the Flutter at Supersonic Speeds wings wa s dictated b y conditions fo r avoidance o f flutter, a s Flutter a t supersonic speeds began t o b e studied more well as for reduced wing-root bending moments. Since the seriously as speeds in dives could readily become supersonic. wings were highly flexible (there was a demonstrated 30-ft Supersonic speed i n level flight wa s achieved i n 1947 b y difference in tip deflection for maximum up and down loads), Charles Yeager in the X-l research airplane. Analytical flutter careful design was needed to obtain the proper jig shape to studies were undertaken a fe w years earlier b y Collar an d b y achieve the desired flight characteristics. Because sweep was Temple and Jahn74 in England, by von Borbely75 in Ger- t o become almost universally used, th e effects o f sweep o n many, an d b y Garrick an d Rubinow76 i n th e U.S., expanding flutter opened a new dimension and became an important o n Possio's work. I t i s o f interest that th e potential fo r consideration from both structural an d aerodynamic points o f supersonic speeds is composed equally of both the retarded view. and advanced potential forms as noted by Kussner (see Survey Th e need fo r thin wings fo r high-speed aircraft com- Papers, 1950) and by Garrick (see Survey Papers, Princeton pounded th e difficulties i n meeting stiffness requirements t o University Press, 1957). Although, in general, because of the avoid transonic flutter; moreover, the nonlinear flow theory rearward shift of the aerodynamic center, classical coupled was lacking, an d transonic wind tunnels di d no t ye exist. I t flutter seemed less likely to occur, because of the changes in became imperative therefore to develop alternative suitable altitudes o f flight an d i n configurations, especially sweep, experimental means for investigating flutter in this critical flutter could not be ruled out. Moreover, the nonlinear effects speed range. Four methods fo r meeting these needs b y means of thickness are more pronounced at supersonic than at of aeroelastic models evolved (Fig. 15). Tw o f th e methods subsonic speeds, a s indicated b y th e simple piston theory made us e o f free flying models. With wartime developments approach of M. J. Lighthill77 wherein the pressure and local velocity become point functions of each other. The single- degree-of-freedom negative damping i n a pitching motion uncovered b y Glauert i n 1929 fo r certain cases i n two- dimensional flow persists into the subsonic and lower supersonic ranges. Fortunately, it is alleviated by damping an d b y span effects. A new type of flutter, panel flutter, could occur involving the skin covering wherein standing or traveling ripples in the skin persisted, which could often lead t o a n abrupt fatigue failure. Panels are natural structural elements of both aircraft and spacecraft so that avoidance of panel flutter is important. Panel flutter depends on many parameters, including the Mach number and the boundary layer, but especially on any compressive or thermal effects that tend to create local buckles i n th e skin. Wernher vo n Braun informed on e o f th authors that more than 7 0 failures o f th e V- 2 rocket occurred ROCKET SLED — WING-FLOW METHOD during th e wa r i n period when i t underwent development Fig. 1 5 Early transonic flutter experimental methods. an d test. Many o f these failures were found t o b e caused b y NOVEMBER 1981 HISTORICAL DEVELOPMENT OF AIRCRAFT FLUTTER 909

Table 2 Flutter incidences fo r U.S. military aircraft, 1947-1956 BARE WING Type of flutter No.

Tabs 11 FORE Control surfaces 26 Wings 7 Tails 7 Other 3 Total 54 AFT

0.8 V

Acknowledgments Th e authors ar e indebted t o many individuals fo r their helpful assistance i n th e preparation o f this paper. I n par- ticular, they wish to thank Sue K. Seward of the Langley Technical Library fo r he untiring efforts t o retrieve long- forgotten documents; Laurence K. Loftin Jr. and Martin Copp for providing some photographs and little-known interesting facts about some early airplanes; Professor H . Bergh fo r comments o n pioneering work i n th e Netherlands; Professor Robert L. Half man for supplying historical material on MIT's early role in aeroelasticity; Leon Tolve for sending data from his files on flutter experienced by some Fig. 17 Some technology areas supported by the Langley Transonic U.S. airplanes of 1930 vintage; and Melvin Zisfein of the Dynamics Tunnel. Smithsonian National Air and Space Museum for helping make available th e restored 1903 Langley Aerodrome fo r detailed examination. 2) b e capable o f operating over a wide density range i n order t o simulate various altitude conditions, because flutter References characteristics often change with altitude; 3) use Freon gas as 1 th e test medium which, based o n previous experience, enables McFarland, M.W., ed., The Papers of Wilbur and Orville Wright, the use of heavier, less expensive models, permits higher McGraw-Hill, New York, 1953, p. 510 (Kelly, F. C., The Wright Brothers, Ballantine Books, Inc., Ne w York, 1956, p . 80.) Reynolds numbers, and requires less tunnel power; and 4) be 2 Hill, G. T. R., "Advances in Aircraft Structural Design," Anglo- capable o f operating a t Mach numbers u p t o 1.2. American Aeronautical Conference, Th e Royal Aeronautical Society, This proposal was implemented, starting in 1955, by Brighton, Sept. 1951. converting the Langley 19-ft Pressure Tunnel to a 16-ft (4.87- 3 Brewer, G., "The Collapse o f Monoplane Wings," Flight, Vol. 5 , m) transonic tunnel with Freon-12 a s test medium. Jan. 1913, p. 33. Designated the Transonic Dynamics Tunnel (TDT), the 4Brewer, G., "The Langley Machine and the Hammondsport facility became operational i n 1960 an d ha s since been used Trials," The Aeronautical}ournal, Vol. 25, Dec. 1921, pp. 620-664. almost exclusively t o support research an d development 5Pritchard, J.L., "The Wright Brothers and the Royal testing i n th e field o f aeroelasticity. Figure 17 depicts th e TD T Aeronautical Society," Journal of the Royal Aeronautical Society, an d some o f th e important programs i t supports. Fo r Dec. 1953, pp. 742-818. Manchester, F.W., "Torsional Vibrations o f th e Tail o f a n example, the facility is used to verify, by means of dynamic Aeroplane," R&M 276, Part 1, 1916. models, th e flutter safety an d aeroelastic characteristics o f 7Bairstow, L. and Page, A., "Oscillations of the Tail Plane and most U.S. high-speed military aircraft and commercial Body of an Aeroplane," R&M 276, Part 2, 1916. transport designs; t o explore flutter trends an d aeroelastic 8Bryan, G.H., Stability in Aviation, MacMillan, London, 1911. characteristics of new configurations; for active control of 9Routh, E.J., Treatise on Rigid Dynamics, MacMillan, New York, 1905. aeroelastic response o f airplanes an d rotorcraft; fo r ground 10 wind loads, flutter an d buffet testing o f space launch vehicles; Fokker, A.H.G., The Flying Dutchman, Henry Holt, New York, 1931. an d fo r unsteady aerodynamic load measurements o n H oscillating wings and control surfaces. Some wind- Reissner, H., "Neurere Probleme aus der Flugzeugstatik" (New 81 Static Structural Problems o f Wings), Zeitschrift fuer Flugtechnik tunnel/flight correlations presented b y Reed indicate that undMotorluftschiffahrt, Vol. 17 , April 1926, pp . 137-146. predictions from aeroelastic models in the TDT were, in 12von Baumhauer, A.G. and Koning, C., "On the Stability of general, substantiated in flight. Oscillations o f a n Airplane Wing," International Ai r Congress, London, 1923; also, "Onstabiele trillingen van een draagvlak-klap- Systeem," Rapport A 4 8 Ryks-Studiedienst Voor d e Luchvaart, Amsterdam, 1923; also, NACA T M 223, 1923. Concluding Remarks 13 Accidents Investigation Subcommittee, "Accidents t o Aeroplanes Involving Flutter o f th e Wings," R& M 1041, 1925. Although w e have concentrated o n th e contributions o f 14Frazer, R.A. an d Duncan, W.J., "The Flutter o f Aeroplane individuals, many organizations have contributed to the Wings," R& M 1155, 1929. growth of knowledge in the areas of aeroelasticity and flutter. 15 Recommendations extracted from the monograph (Ref. 14) were Among these are the RAE and NPL organizations in England, published a s R& M 1177, 1928. NLR i n th e Netherlands, ONERA i n France, an d DFVLR i n 16Perring, W.G.A., "Wing Flutter Experiments Upon a Model of a Single Seater Biplane," R&M 1197, 1928. Germany. In the United States there has been the U.S. Air 17 Force Flight Dynamics Laboratory, th e Navy Bureau o f Birnbaum, W. , "Das Ebene Problem de s Schlagenden Flugels" Aeronautics, the NACA and its Subcommittee on Vibration (The Plane Problem of the Oscillating Wing), ZAMM, Vol. 4, 1924, pp. 277-292; also, NACATM 1364, 1954. an d Flutter, th e Aerospace Flutter an d Dynamics Council 18 Wagner, H., "Dynamische Auftrieb von Tragflugeln" (Dynamic composed o f industry specialists, th e MI T Aeroelastic Lift o f Wings), ZAMM, Vol. 5 , 1925, pp . 17-35. Laboratory, and the Cornell Aeronautical Laboratory. 19Glauert, H., "The Force an d Moment o n a Oscillating Special mention should be made of the NATO-AGARD Aerofoil," R&M 1242, 1929. organization, which has sponsored the six-volume AGARD Burgers, J.M., Aerodynamic Theory, Vol. II , edited b y W.F. Durand, Julius Springer, Berlin, 1934, pp. 380-410 (reprinted, 1943). Manual on Aeroelasticity, and many specialist symposia 21 publications. Kussner, H.G., "Schwingungen von Flugzeugflugeln" (Flutter of Aircraft Wings), Luftfahrtforschung, Vol. 4 , June 1929, pp . 41-62. We leave the subject approaching its maturity in the mid- 22 1950s. I n closing, ma y w e state that w e ar aware o f th e many Zahm, A.F. and Bear, R.M., "A Study of Wing Flutter," NACA Rept. 285, 1926. shortcomings o f this brief historical account. Th e Survey 23Greene, C.F., "An Introduction to the Problem of Wing Flut- Papers should help furnish interested readers with other vistas ter," Transactions of the American Society of Mechanical Engineers, of aeroelasticity and flutter and will supply the numerous AER-50-10, Vol. 49-50, Part I, 1927-28. individual references that could not be included. We may fully 24Rauscher, M., "Uber die Schwingungen freitragen der Flugel expect that, in time, the historical task will be done to the (On the Flutter of a Wing), Luftfahrtforschung, Vol. 4, July 1929, depth an d breadth this intriguing subject merits. pp. 94-106. NOVEMBER 1981 HISTORICAL DEVELOPMENT O F AIRCRAFT FLUTTER 911

25Ober, S. , "The Story o f Aeronautics a t MIT, 1895 t o 1960"; 54Cicala, P. , "Nonstationary Motion o f a Wing o f Finite Span," also, "Development o f Aeronautical Engineering a t MIT: Depart- Rendiconti Accademia Nazionale Lincei, Rome, Vol. 25, Ser. 6a, mental Laboratories 1933-1960," M.I.T., Cambridge, Mass., 1965. 1937, pp . 97-102. 26Tolve, L., "History o f Flight Flutter Testing," Proceedings o f 55 Jones, W.P. and Skan, S.W., "Calculation of Derivatives for the 1958 Flight Flutter Testing Symposium, NASA SP-385 (new Rectangular Wings o f Finite Span b y Cicala's Method," R& M 1920, printing, 1975). 1940. 56 27 Accidents Investigation Subcommittee, "Report on Puss Moth Dingel, M. and Kussner, H.G., Contributions to Nonstationary Accidents," R&M 1699, 1936. Theory o f Wings, Part VIII, "The Oscillating Wing o f Large Span," 28Duncan, W.J. an d Collar, A.R., "Calculation o f th e Resistance ZWB,FB, 1774, 1943. Air Materiel Command, USAF Transl. F-TS- 935-RE, 1947. Derivatives of Flutter Theory," R&M 1500, 1932. 57 29Cox, H.R. and Pugsley, A.G., "Theory of Loss of Lateral Reissner, E., "On the General Theory of Thin Airfoils for Non- uniform Motion," NACATN-946, 1944; also, TN-1194, 1947. Control Due to Wing Twisting, "R&M 1506, 1932. 58 30Duncan, W.J. an d McMillan, G.A., "Reversal o f Aileron Jones, R.T., "The Unsteady Lift o f a Wing o f Finite Aspect Ratio," NACA Rept. 681, 1940. Control Due to Wing Twist," R&M 1499, 1932. 59 31Theodorsen, T. , "General Theory o f Aerodynamic Instability Kussner, H.G., "General Airfoil Theory," Luftfahrtforschung, Vol. 17, 1940, pp. 470-478; also, NACATM-979, Dec. 1941. and the Mechanism of Flutter," NACA Rept. 496, 1935. 60 32Garrick, I.E., "An Appreciation of the Contributions of Watkins, C.E., Runyan, H.L., an d Woolston, D.S., "O n th e Theodore Theodorsen," Proceedings o f th e Theodorsen Colloquium, Kernel Function of the Integral Equation Relating the Lift and Det Kongelige Norske Videnskabers Selskab, , , Downwash Distributions of Oscillating Finite Wings in Subsonic Flow,"NACATN-3131, 1954; also, NACA TR 1234, 1955. 1976. 61 33Theodorsen, T. and Garrick, I.E., "Mechanism of Flutter—A Falkner, V.M., "The Calculation o f Aerodynamic Loading o n Surfaces o f An y Shape," R& M 1910, 1943. Theoretical an d Experimental Investigation o f th e Flutter Problem," 62 NACA TR-685, 1940 (issued in 1938 as a memorandum report). Jones, W.P., "Aerodynamic Forces o n Wings i n Non-uniform 34 Motion," R&M 2117, 1945. Silverstein, A . an d Joyner, U.T., "Experimental Verification o f 63 the Theory of Oscillating Airfoils," NACA Rept. 673, 1939. Smilg, B. and Wasserman, L.S., "Application of Three- 35Klemin, A., "Bibliography of Vibration and Flutter of Aircraft Dimensional Flutter Theory to Aircraft Structures," Air Corps Technical Rept. 4798, 1942. Wings an d Control Surfaces," prepared a t Ne w York University fo r 64 th e U.S. Works Progress Administration, 1937. Hall, H. , " A Record o f Information o n Oscillatory Aerodynamic 36 Derivative Measurements," R& M 3232, 1962. Cicala, P. , "Aerodynamic Forces o n a Oscillating Profile i n a 65 Uniform Stream," Memorie della Reale Accademia delle Scienze, II - Bratt, J.B., Wight, K.C., and Tilly, V.J., "The Application of 68, 1935, pp . 73-98. the 'Wattmeter' Harmonic Analyser to the Measurement of 37 Aerodynamic Damping for Pitching Oscillations," R&M 2063, 1942. Kussner, H.G., "Zusammenfassenden Bericht Uber de n in - 66 stationaren Auftrieb vo n Flugeln" (Comprehensive Report o n th e Kennedy, C.C. and Pancu, C.D.P., "Use o f Vectors in Vibration Nonstationary Lift of Wings), Luftfahrtforschung, Vol. 13, Dec. Measurement and Analysis," Journal of the Aeronautical Sciences, Vol. 14 , Nov. 1947, pp . 603-625. 1936, pp. 410-424. 67 38Garrick, I.E., "Propulsion of a Flapping and Oscillating Air- Wasserman, L.S. an d Mykytow, W.S., "Model Construction," AGARD Manual o n Aeroelasticity, Vol. 4 , Chap. 7 , 1961. foil," NACA Rept. 567, 1936. 68 39Garrick, I.E., "O n Some Fourier Transforms i n th e Theory o f Cunningham, H.J. and Brown, H. H., "A Compilation of Experimental Flutter Information," NACA RM L53KO2a, 1954. Nonstationary Flows," Proceedings o f th e Fifth International 69 Congress o n Applied Mechanics, Cambridge, Mass., Sept. 1938, pp . Templeton, H., "Models for Aeroelastic Investigations," ARC 590-593. Tech. Rept. C.P. 255, 1956. 40von Karman, Th. and Sears, W.R., "Airfoil Theory for Non- 70Targoff, W.P. an d White, R.P. Jr., "Flutter Model Testing a t Uniform Motion," Journal o f th e Aeronautical Sciences, Vol. 5 , Transonic Speeds," Cornell Aeronautical Laboratory, I.A.S. 1938. Preprint No. 706; also, Aeronautical Engineering Review, Vol. 16, 41 Sears, W.R., "Operational Methods on the Theory of Airfoils in June 1957. Nonuniform Motion," Journal of the Franklin Institute, Vol. 230, 71McCarty, J.F. Jr. and Halfman, R.L., "The Design and Testing July 1940, p. 95 . of Supersonic Flutter Models," Journal o f th e Aeronautical Sciences, 42 Walker, P.B., "Growth o f Circulation about a Wing an d a n Vol.23, June 1956, p . 530. Apparatus fo r Measuring Fluid Motion," R& M 1402, 1931. 72 43 Erickson, A.L. an d Stephenson, J.D., "Transonic Flutter o f Farren, W.S., "The Reaction on a Wing Whose Angle of Attack Control Surfaces," NACA RM No. AT F30, 1947. is Changing Rapidly," R& M 1648, 1935. 73 ^Studer, J. , "Experimental Investigation o f Wing Flutter" (i n Smilg, B., "The Prevention o f Aileron Oscillations a t Transonic German), Mitteilungen au s de m Institut fu r Aerodynamik, ETH, No . Airspeeds," Paper presented at the International Congress of Applied 4 , Zurich, 1936. Mechanics, Paris, 1946; also, Army Ai r Force Technical Report 5530, 45Rauscher, M. , "Model Experiments o n Flutter a t MIT," Journal Dec. 1946. of th e Aeronautical Sciences, Vol. 5 , March 1936, pp . 171-172. 74 46 Temple, G . an d Jahn, H.A., "Flutter a t Supersonic Speeds," von Schlippe, B., "Zur Frage der selbsterregten Flugelsch- R&M 2140, 1945. wingungen," Luftfahrtforschung, Vol. 13, Feb. 1936; also, NACA 75 TM-806, 1936. von Borbely, S., "Aerodynamic Forces o n a Harmonically 47Frazer, R.A. an d Jones, W.P., "Forced Oscillations o f Oscillating Wing a t Supersonic Speed," (Two Dimensional Case), Aeroplanes, with Special Reference to von Schlippe's Method of Zeitschrift fur Angewandte Mathematik und Mechanik, Vol. 22, Aug. Predicting Critical Speeds for Flutter," R&M 1795, 1937. 1942, pp. 190-205. 48Taylor, E.S. and Browne, K.A., "Vibration Isolation of Aircraft 76Garrick, I.E. an d Rubinow, S.I., "Flutter an d Oscillating Ai r Power Plants," Journal o f th e Aeronautical Sciences, Vol. 6 , Dec. Force Calculations fo r a n Airfoil i n a Two-Dimensional Supersonic 1938, pp . 43-49. Flow," NACA Rept. 846, 1946. 49 Frazer, R.A., Duncan, W.J. and Collar, A.R., Elementary 77 Matrices, Cambridge University Press, Cambridge, England, 1938. Lighthill, M.J., "Oscillating Airfoils at High Mach Number," Journal o f th e Aeronautical Sciences, Vol. 20 , June 1953, pp . 402- 50Loring, S.J., "Outline of General Approach to the Flutter Problem," Society o f Automotive Engineering Journal, Aug. 1941, 406. 78 pp.345-356. 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