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.