A little before midnight on September 29, 1959, a Braniff Airways Lockheed Electra was cruising at 15,000 feet between Houston and Dallas. Some of the 26 passengers may have been reading, but most probably dozed, lulled by the throb of four big turboprops. Then came a different sound, a shaking that grew gradually until the interior of the cabin began to rattle and creak. Passengers sat up and looked around anxiously. The shaking lasted 30 seconds, becoming rapidly more violent and ending with the terrible shriek of tearing metal.

The Electra had lost its left wing. Parts of the airplane rained down over an area four miles long. Witnesses on the ground described a glow like a meteor--bright, then fainter, then bright again--a screaming sound like a jet engine, and a boom. They later identified a recording of a runaway propeller as most similar to the sustained sound they had heard.

Accident investigators focused their attention on the failed wing's outboard engine nacelle, because scratches and tears in the metal indicated that the propeller and gearbox, mounted several feet ahead of the engine and connected to it by a long power shaft, had swung as much as 35 degrees out of alignment. But the sequence of events was baffling. Lockheed's engineers had, of course, anticipated that a propeller could shed a blade, throwing the engine out of balance and causing a catastrophic failure. But they had designed the nacelle to break away from the airplane before it could overstress the wing. Yet even though the wing had separated from the fuselage and the propeller and its gearbox had separated from the engine, the nacelle had remained attached to the wing.

The first hypothesis was that the primary failure had been caused by a wing overload, and the powerplant damage had occurred during the subsequent disintegration of the airplane. But it was hard to believe that this was a case of simple overload due to turbulence or pilot action. Wing failures in airliners were extremely rare--only five had occurred in the previous 40 years--and if the Electra had a structural weakness it would have surely turned up in Lockheed's rigorous ground- and flight-test programs or in Eastern Airlines' thousands of hours of high-speed, low-level operations along the eastern seaboard. This looked more like the work of the mysterious and deadly demon called flutter. But no plausible flutter mechanism could be found to explain this accident.

Flutter has always been aviation's dirty little secret. Seldom reported and little understood, it occupies one of those dimly lit and unsafe places that decent people prefer not to visit. The idea that an airplane could shatter, disintegrate, for no reason other than its own motion through the air--better to let sleeping horrors lie. Compared with most other concepts in aeronautics, flutter is obscure and difficult to grasp, but there are examples of the phenomenon in everyday non-aeronautical life. An out-of-balance tire is one; it begins to vibrate at a certain speed as the car accelerates; at some higher speed the vibration subsides. What is happening is that when the tire's natural bounce frequency matches its rate of rotation, the wobble due to imbalance--which is always present--is amplified by the bouncing of the tire on the road. Another example is a child on a swing: the amplitude of the pendulum motion increases when the motions of the torso and legs are properly synchronized with it, but not otherwise.

We use different terms for different instances of the same underlying phenomenon. When we talk about riding a swing, we call it "pumping"; when it's a vibrating tire, we say "resonance" or "sympathetic vibration." When the subject is music, we speak of harmony or being in tune.

"Flutter" is the term used for synchronized vibration when it takes place in a flexible structure moving through a fluid medium--for instance, an airplane in flight. It occurs when two regular, rhythmic motions coincide in such a way that one feeds the other, drawing additional energy from the surrounding flow. In airplanes, there are countless combinations of vibrations that can join forces in this way.

Each component of the airplane has, like a guitar string, a natural or fundamental frequency, plus a whole family of harmonics--integral multiples of the fundamental frequency--of diminishing strength. A classic case of wing flutter might combine wing bending--a flapping motion of the entire wing--with either wing twisting (torsion) or the flapping of an aileron, which has the same lift-amplifying effect as twisting the wing does. But there are myriad other possibilities involving all sorts of combinations of bending, twisting, and flapping, each with its own fundamental and harmonic frequencies, in wings, tails, fuselages, control surfaces, and trim tabs. Out-of-balance tires seldom lead to structural failure of the car because automobile suspensions are vastly overbuilt for the loads they normally encounter. But airplanes, which must be kept as light as possible, are not superfluously stout. They are capable of failing with explosive suddenness when flutter sets in.

One of the most famous and spectacular cases of destructive flutter befell not an airplane but a bridge. When the Tacoma Narrows Bridge, then the third longest suspension bridge in the world, opened to traffic in the fall of 1940, it had already acquired the nickname Galloping Gertie because it heaved rhythmically and visibly when the wind blew. In fact, people repeatedly crossed the bridge just to enjoy its roller-coaster-like undulations, which were considered harmless. On November 7, only six weeks after the bridge opened, a steady 42-mph wind was blowing along Puget Sound. The slender span began its dance. Then a cable near mid-span snapped, creating an unbalanced condition. Soon the bridge was performing twisting, heaving, and swinging motions of an incredible magnitude. These continued for more than half an hour before the center span fell into the water--long enough for an amateur filmmaker to record for posterity the astonishing spectacle of the giant bridge writhing like a wounded snake as a terrified motorist abandoned his car and ran for his life.

Even today the exact mechanism of the flutter of the Tacoma Narrows Bridge is disputed. The fact that half a century of reflection and analysis has not settled the question gives some indication of the abstruse nature of flutter itself. The case of the Lockheed Electra might have remained similarly mysterious--the Civil Aeronautics Board, precursor of today's National Transportation Safety Board, was ready to throw in the towel and label the crash "unexplained"--had not a second accident, almost a carbon copy of the first, occurred. This time it was an Electra flying a Northwest Orient route from Chicago to Miami in March 1960 that broke up in flight over Indiana, killing 63. The flight was known to have been operating in an area of severe turbulence, and the failure might have been attributed to structural overload had the damage signatures around one engine nacelle--this time the right outboard engine rather than the left--and the distribution of parts in the debris field not been so similar to those in the previous accident.

General Motors' Allison Division, manufacturer of the Electra's engines, dismantled and minutely examined all eight engines from both aircraft. NASA weighed in with detailed analyses of flutter modes that might occur if various structural failures had gone undetected in a wing or nacelle. Every path came to a dead end. All analyses found that the structure incorporated large margins of safety. Flutter, the only possible explanation, seemed impossible.

Then Lockheed structural dynamicist J. Ford Johnston had the idea of investigating the hitherto neglected contribution that might be made by small yawing deflections of the propeller. As pilots of propeller aircraft know from experience, the center of thrust of a climbing airplane's propeller shifts to the side of the downgoing blade. This phenomenon, colloquially called P Factor, occurs mainly because a component of the airplane's forward velocity is added to the speed of a downgoing blade and subtracted from that of an upgoing one. A similar phenomenon, rotated 90 degrees, naturally occurs when the engine swings to one side. Shifting the center of thrust flexes the engine mount, creating a new shift in the center of thrust and a new direction of flexure. As a result, a propeller and nacelle can vibrate continuously in a circular motion called "whirl mode". Johnston suggested that whirl mode vibration might have initiated an unsuspected flutter mechanism.

As early as 1938, a study on powerplant vibrations had raised the possibility of propeller whirl inducing structural flutter. But the relative weights of engines and propellers, the stiffness of propeller shafts, and the engine power outputs that were typical in the late 1930s made it a practical impossibility. As Lockheed mathematician Robert Donham, who participated in the accident investigation, says today, "Probably nobody involved with the design of the Electra even knew the paper existed. Nobody thought about whirl-mode vibrations causing flutter."

Lockheed's flutter analysts reprogrammed their computer to include whirl mode, and the mechanism of the accidents began to emerge. By an unlucky coincidence, the whirl-mode frequency of the Electra's big four-blade propellers happened to match the flapping frequency of the wing. The propellers, like the child driving a swing higher by small movements of her body, had eventually caused the wing to flap so violently that in 30 seconds it broke at the root without the propeller whirl ever overloading the nacelle structures.

Microscopic examination of fractures in the wreckage of the two airplanes revealed engine mount damage that had preceded the inflight breakups. The cause of the earlier damage was uncertain--in one case a hard landing was suspected--but Lockheed redesigned the engine mounts and no Electra ever suffered from whirl-mode flutter again. Flutter is all about stiffness, not strength; even the strongest structure may fail if it flutters. In general, structures that are light and stiff vibrate more rapidly; they are said to have higher natural frequencies. Structures more massive or less stiff have lower frequencies. The usual treatment for a flutter problem is to raise the natural frequency of one structure by stiffening it, but sometimes the opposite approach is used: lowering a frequency by the careful placement of damping weights. The essential thing is to eliminate coincident frequencies in structures that can feed energy to one another. A wing that is very stiff in bending should be made "softer" in torsion, and vice versa.

Flutter specialists speak a language incomprehensible to ordinary engineers. For a long time, the designers of aircraft structures confined their attention to static loadings and ignored dynamic loading. The late Raymond Bisplinghoff, a specialist in aeroelasticity whose career included top-level roles at the Massachusetts Institute of Technology and NASA, recalled his time at Wright Field's Aircraft Laboratory during World War II in Hugh Flomenhoft's book The Revolution in Structural Dynamics: "The design-desk officers would frequently fly into a rage when told by an apple-cheeked youngster that weight or speed restrictions had to be added to their airplane to prevent aeroelastic problems. I was thrown out of their offices on an almost daily basis and frequently told "that flutter was a figment of my imagination."

At the time, the tools available for the mathematical analysis of flutter were primitive, though, as has often been the case in the history of aviation, theoretical understanding was far ahead of practical application. Problems that today take barely a split-second's attention from a desktop computer then required weeks of manual computation on battalions of mechanical calculators--what physicist Richard Feynman termed the "many females" approach to mathematics. Alternatively, analog computers, in which physical objects were simulated by electrical circuits with similar resonant characteristics, were programmed with data collected by shaking airplanes with variable-speed electric motors swinging unbalanced weights. Bisplinghoff recalled pressing his head against the underside of vibrating wings to locate their "nodes," the points that remained still while the wing vibrated.

Another approach to flutter analysis is testing scale models in a wind tunnel. This is tricky, requiring duplication in the proper scale of not only the geometry of the airplane but the mass and elastic characteristics as well. Since small structures naturally tend to have higher resonant frequencies than large ones, wind tunnel models for flutter studies were originally built with wooden spars and rubber skins to lower their natural frequencies. Today, glass-fiber laminates are used because their flexural behavior can be tailored by changing the fibers' orientation.

The world's premier flutter-testing facility is the 16- by 16-foot Transonic Dynamics Tunnel at NASA's Langley Research Center in Virginia, which provides its clients with empirical data that they use to fine-tune their computer models. It also provides occasional moments of excitement when a model actually flutters. Sometimes, says TDT research engineer Don Keller, this happens only once per model, because afterwards, "you are sweeping it up into a bag." Because the tunnel can operate at up to Mach 1.2, it allows engineers to explore the critical speed range, around the speed of sound, where the unpredictable behavior of shock waves creates a "transonic bucket" in which flutter is much more likely to occur. Even with the tunnel and extremely sophisticated software, however, some flutter modes are elusive: "You can't predict them," Keller quips, "until they happen."

In the absence of detailed computer analysis or costly ground vibration testing, airplanes can be tested for flutter resistance in an ad hoc way. The late John Thorp, whose design career spanned the glory days from 1930 to 1960, called this "tickling the dragon's tail." Beginning at a low speed where the airplane was known to be flutter-free, the test pilot would accelerate by a mile or two per hour, then deliver a sharp slap or "pulse" to the control stick or the rudder pedal. He would pay careful attention to the immediate aftermath of the disturbance. Did the stick or pedal immediately return to center, and the airplane appear unperturbed? This was a "dead beat" response; it indicated that no tendency to flutter was present at that speed. The pilot would then increase speed by a small amount and repeat the test.

The seat-of-the-pants approach to flutter testing is possible for the same reason that an automobile tire that vibrates most severely at 60 mph starts shaking at 55 and stops at 65 or 70. The tendency to flutter does not usually rise instantly to a maximum when one parameter or another--say, airplane speed--reaches a critical value. It normally ramps up gradually enough for speed increments of one or two mph to give the pilot warning of impending trouble. The pilot relies on the feel of the stick to warn him of diminished damping. The dead beat response softens; the stick wobbles once or twice before returning to center. Sometimes a control surface actually flutters with a low intensity, so the structure flexes but does not fail and the pilot, by slowing the airplane down, can arrest the flutter.

Still, "usually" and "normally" must be added. On occasion, catastrophic flutter occurs at a speed only very slightly above a speed that was considered "safe," and sometimes even below it. Today, except in the lowest-budget flight test programs, sensitive electronic motion sensors and strain gauges measure and record vibrations that are triggered by a mechanical shaker rather than from the pilot's hand or foot. The slightest decrease in damping is instantly detected. Nevertheless, testing for flight flutter is no test pilot's favorite activity.

Until after World War II, structures were built as lightly as possible, and balanced and stiffened later as needed. Flutter problems were mainly attacked with empirical methods, often crude and sometimes quite drastic. Before the National Air Races in 1934, Steve Wittman's midget racer Chief Oshkosh repeatedly encountered severe but non-destructive flutter of a wingtip. It happens that short beams, like short piano strings or organ pipes, have higher natural frequencies than long ones. Therefore, after each test flight on which flutter was encountered, Wittman chopped a few more inches off the wing. Eventually the span was reduced to 16 feet, and the wing area from a minimal 78 square feet to a microscopic 42. The airplane landed awfully fast, but at least its wing was free of flutter.

William R. Laidlaw, former chief of the Structural Dynamics Section at North American Aviation, describes in The Revolution in Structural Dynamics a similar approach to controlling stabilizer flutter in the 1950s. During a test flight, an FJ-4 Fury, a carrier-based derivative of the F-86 Sabre Jet, lost more than half of both horizontal stabilizers to a flutter incident (the pilot managed to land safely). Engineers mounted a Fury tail assembly on a rocket sled at the Navy's test facility at China Lake, California, and the flutter was duplicated. North American engineers considered various modifications to solve the problem, but finally settled on the crudest one: They sawed 12 inches off each end of the tail. A few months later, however, an FJ-4 shed its tail during a pullout from a high-speed dive, killing the pilot. The experts went back to work. They then discovered that putting a heavy load on the tail reduced its flutter margins. Another amputation, this time of a mere six inches, solved the problem for good.

Today, the practice of carrying armaments and auxiliary fuel on external pylons, and the vast variety of possible combinations of external loads, make flutter analysis of modern fighters especially difficult. On the other hand, composite structures using carefully controlled arrangements of graphite and other exotic fibers are much stiffer than aluminum or steel, and can even be made to deform under load in such a way as to reduce aerodynamic loads and therefore the chance of flutter.

Increasingly, new fighter and transport designs rely on electronics for stability and control, and in some cases for flutter prevention as well. The F-16, for example, is prone to a non-destructive wing flutter when carrying certain combinations of external loads. The wings flap out of phase--the left wing goes down while the right one goes up--imparting a rocking motion to the fuselage. Rather than modify the wing, researchers at the U.S. Air Force flight testing facility at Edwards Air Force Base in California programmed the fighter's electronic flight control system to sense the flutter and use the ailerons to oppose the wing's flexing. The fix, which will be incorporated in a flight control software upgrade scheduled for 2002, is indicative of what electronic flight controls can do. But they are not a panacea for flutter; the number of control surfaces available on an airplane's wings and tail falls far short of the number of possible flutter modes they can exhibit.

Discernible in the future are "smart" materials that expand or contract slightly in response to electrical signals. "They're like muscles," says Tom Noll, head of the aeroelasticity branch at NASA's Langley center. "They're normally in a neutral state, but they can be 'flexed' when extra stiffness or resistance to deformation is needed." Another possible weapon against flutter comes from the new field of MEMS--micro electro-mechanical systems. Thin surface overlays could raise thousands of tiny spoilers on an electrical command, disrupting airflow and preventing the aerodynamic augmentation that is fundamental to flutter.

Flutter analysis is often called a black science. Even though flutter is today well understood and largely preventable, it is still as formidable a foe as ever, and its malevolent unpredictability remains. "Some fear flutter because they do not understand it," said the famous aerodynamicist Theodore von Karman. "And some fear it," he added, "because they do."

Tuning Up for Disaster

When a musician wants to ensure that his instrument is playing at the proper pitch, he compares a note to that of a vibrating tuning fork.  The tuning fork is a reliable standard because it always vibrates at exactly the same frequency and therefore hums at only one pitch, regardless of how you hold it or how hard you strike it.

When, hundreds of years ago, clockmakers needed a reliable way to measure small units of time, they turned to the pendulum.  As Galileo had discovered in 1582, and as a child on a swing may notice, a pendulum of a given length always oscillates with the same frequency, regardless of the arc through which it swings.

The utility of tuning forks and pendulums as standards is due to a common physical phenomenon.  A great many objects and structures have what is called a natural frequency of vibration.  The natural frequency depends on the mass of the moving object and the stiffness of the "spring" that makes it oscillate.  In the case of the pendulum or the swing, the spring in gravity, and in the case of the tuning fork, the elasticity of the steel.  All elastic systems have this property, including the structures of airplanes.  If you timed the up-and-down motions of an airliner's wingtip as it flies through rough air, you would find that its frequency is constant, regardless of the strength of the turbulence, because and airplane's wing is like a huge, very-low-frequency tuning fork.

An object is said to "resonate" when it begins to vibrate in tune with some other vibrating object.  A sufficiently loud sound at 440 cycles per second, for instance, will set a tuning fork in the key of A to humming.  Resonance occurs because it is easy to make things vibrate at their natural frequency, but difficult to make them vibrate at any other frequency.

Resonance is at the root of the phenomenon of flutter in aircraft.  Just as a crystal goblet, set to vibrating by just the right "forcing frequency," may shatter, a structure on an airplane, set in motion by another structure whose natural frequency is very nearly the same, may vibrate so violently that it breaks.

Rocket Science

The Saturn V rocket experienced a novel and unexpected kind of structural resonance.  The five first-stage engines were ignited at 0.3-second intervals, the center engine first, followed by the others in symmetrical pairs.  Each ignition sent a jolt through the rocket and built up tension in its hold-down mechanism.

On launch the hold-downs flipped back to release the rocket--and the 360-foot-tall, six-million pound monster might have crumbled on its pad if aeroelasticity analysts at Boeing had not discovered in advance that the rocket resonated in tune with the rhythmically timed additions of thrust.  The "twang" of the sudden release would then make the fuel and oxidant, which accounted for 90 percent of the Saturn's total weight, settle downward in the gigantic tanks, stretching their thin aluminum skins.  The tanks would recoil like rubber bands, pumping the liquids back upward.  The rhythmic bouncing of the entire fluid mass, which engineers nicknamed "Ka-Doing-a-Doing-a-Doing mode," resembled the motion of a shaken water balloon.  It produced structural loads well beyond the rocket's flimsy safety margins.

Various solutions to the problem were investigated, including baffles in the tanks--discarded as too heavy--and releasing the hold-downs before full thrust had been attained--too dangerous for the human occupants, in case the engines failed to attain full thrust.  The eventual solution included altering the ignition timing and adding what came to be nicknamed the shoe-in-the-mud: a simple mechanical damper that slowed the rocket's initial acceleration after release, just as deep mud slows the extraction of a foot.

Early Saturn flight tests revealed that the bouncing liquids in the tanks was also excited by the random vibrations of the engines.  It launched a vicious cycle: pressures in fuel and oxidant lines began to fluctuate, throttling the engines up and down in time with the bouncing liquids.  This "pogo effect" was cured by placing accumulators in the fuel and oxidant lines to damp out the pressure fluctuations.

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