The Hammer

For every airplane, there’s a region of the flight envelope into which it dare not fly.

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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.