The Single Helix Some toys are destined to be broken in the child's attempt to discover the source of their magic sway. No doubt many engineers have sprung from such troublesome children, surrounded by the empty wreckage and clinging dust of a trashed Etch-a-Sketch. This gives us proposition one: a good toy is one with high mortality rates. Furthermore, a plaything's power rises in proportion to the simplicity with which it suggests elementary social or physical phenomena. Social toys date since the first time a stick was raised in mock attack (war) and a doll with the vaguest of human outlines was cradled (love). But in a second, more Apollonian category are objects--are they toys?--intended basically for admiring. Here's a list of current contenders and their provenance: Suspended metal clacking balls--Newtonian mechanics; the lava lamp--heat transfer and cavitation with non-Newtonian, low-Reynolds-number fluid dynamics; and the Slinky--wave propagation, somersaults, and the mysterious, entrancing animation of nothing but a dinky piece of metal tape. One Slinky expert's epiphany reveals the toy's pull. In 1946 W.J. Cunningham was midway in his first year as a professor in Yale University's electrical engineering department when someone gave him a Magi-Koil. It was a helical steel spring with about 80 turns. The helix was a ribbon of thin, rectangular steel, and if left undisturbed each coil stacked almost entirely on the next. The diameter was about 2-1/2 inches and the whole thing about the size of the box a baseball comes in. Oscillated with two hands it looks like pouring water, as energy is resupplied as the captivated user pretends he is weighing fruit. Or, you put it on a top step, pull one end to the step below, and let it do the rest. According to the ads, it could "walk as though it were alive." Today it would be difficult to find a child who disputes that. The Magi-Koil was renamed the Slinky, a mechanical engineer made a mint on it, and today it's essentially unchanged. Prof. Cunningham still hasn't figured out how it works. Forty years ago Cunningham had printed a paper quantifying the actions of his intriguing new toy. Today he still teaches at Yale, and also is chairman of the board of editors of American Scientist magazine. Writing in the May-June 1987 issue of the magazine, he denigrates his earlier self-assurance, now that he is "less sure he really understands all that goes on." In an interview he elaborated on the problems. "The general idea is pretty obvious, but even with all the physical measurements I wanted I couldn't tell you the minimum height of step to kick it off on a walk down the stairs." It's tied up with the damping in the spring, which is hard to measure to begin with. "What's clear is the larger the damping in the spring, the larger the step height, and I can tell you how long it will take to go down the step. But working from first principles I have not been abe to set up a predictive mathematical model." Before looking at the analytical theory of Slinkyonics (as we'll see, there is no one scientific domain within which its actions can be described), we can get a sense of its odd-ball usefuleness. In Vietnam, American soldiers used it as antennae for radios; its jiggles have been been used to predict the onset of an earthquake; while being observed intently from Earth, Space Shuttle astronauts have used it to while away the orbiting hours and prove--in case you were worried--conservation laws. Who needs the $4 billion supercollider when you have the Slinky? One paper in the American Journal of Physics suggested that a moving Slinky, when hung in the air by thread at various points, models the types of waves in gas plasma. Cunningham recently received a physics paper on "dispersion waves," from a woman who attached one end to the side of a door, which acts as a soundboard. She stretched the thing out, and snapped the wire at the far end. Try this at home. The first sound that comes out, says Cunningham, is called a "whistler"--a high-frequency whoop-whoop, like a descending bird cry with a sharp ascent, or, to my ears, an eerily synthesizer sound-alike suitable for a Star Trek episode. A short time later, said Cunningham, warming to the imitation, comes a deep voiced phew-phew, a sharply descending cry from the bird's older brother. There is far too much ambient noise in my apartment for me to ever actually hear these frequencies. But the point is that the high frequencies travel along the spring faster than the low ones, each at a particular dispersion. Stepping out. The Slinky in its preeminent role, as sinuous stair descender, exhibits different characteristics, most prominently what is called an extensional disturbance wave. A spring is a medium with distributed mass and stiffness. In a spring with a linear medium, an impulse--disturbance--will travel at a speed of the square root of the ratio of stiffness to density. But is the Slinky doing its stuff linearly? Midway through its jaunt down the steps, the Slinky has two essentially straight axes connected by a wide-linked, U-shaped arch through which the metal snake seems to draw itself. The mid-air portion of the spring is stretched out, compared to the compact back foot (the empyting pile) on the upper stair unseating itself, and the collecting pile of turns on the lower stair. Despite the event's apparent nonlinearity, Cunningham considers it analyzable as a linear case of small deflections along the length of the helical wire itself. In his study, he considers an idealized Slinky resting horizontally on a frictionless tabletop. (Surely Plato himself must play in the frictionless land stocked with idealized toys.) Say the right side of the spring is jerked to the right. An extensional disturbance travels along the wire with a constant speed. Each turn moves briefly to the right with a certain "particle velocity." The last turn of the slinky finishes up at twice the speed of the first one. (We'll see why the speed doubles in a moment.) Let's move from the heady world of ideals to the hall staircase. The researcher, or child, has piled the Slinky on one step and obligingly placed the free end on the step below. Inertial and elastic effects cause a wave to travel through the arched coil upwards--although it looks like the spring is pouring downwards--and the last turn is lifted off the step with velocity twice that of its brothers resting on the step above. (It's hard to keep it visualized that the spring is a continuum through which the wave passes, even though the visible parts of the coils seem to be knocked against each other one by one.) If the force is high enough at the critical take-off instant, two events occur: the arch stays arched due to centrifugal force, and the last rung vaults over to the next lower step. The arch inverts, and by the time the last rung lands, a few adjacent turns are thrown in contact. The turns pour onto the once high flying turn, now the bottom of the pile. A new disturbance has begun in the opposite direction. It may seem that having the free end of the coil moving at twice the speed of the initial coil, while receiving no additional energy, violates conservation laws. But the explanation is related to the theory of transmission lines. As the pulse comes down the line, the quantity of material that is moving becomes smaller. With a decrease in mass, the velocity has to increase to conserve the energy. It's similar to when you snap a towel--considering here the snap made in mid-air, not on someone's wet skin--or, even better, to popping a whip. Massive energy is needed to whip the massive stock of a bullwhip. A uniform amount of energy travels down the steeply tapered whip. The crack of the whip is the shockwave when the featherweight flick-end breaks the speed of sound. A physical case closer to that of the Slinky--propagation made visible by discrete points along the line, and uniform material dimensions--is apparent in curtains made of hanging beads. (A locale of an exotic boudouir comes to mind.) Large bead curtains also have a nicer planar aspect and lovely billowing effects, a phenomenom I once noticed as I stood from the second-floor balcony of Avery Fischer concert hall in New York, trying to flick, in exhilarating slow motion, strands of the enormous bead rope against the ankle of a dowager in the lobby. But a Slinky in action is different than the flick of a beadstring. The Slinky's two ends are constantly changing their relative situation: one end initiates the pulse, and one end awaits it, and then back again. Energy is certainly lost inside the spring itself, although with steel it's probably fairly small; energy is also lost when the free end makes an inelastic impact with the step. The takeoff speed and the material design of the Slinky are critical. The speed must be high enough to propel it down and over two steps, but the entire rippling effect must be slow enough to be visible. To slow it down, you need relatively more mass per unit length. How do you keep down stiffness per length (not the lateral stiffness)? Edge-wind it: flatten the wire (give it rectangular cross-section) which simply reduces the ratio of stiffness to mass. The edge-winding of the Slinky reduces the axial length for a fixed mumber of turns, helps the windings stack, and gives a larger lateral stiffness to resist shearing forces--which keeps the slinky from slip-sliding around as it pours into its invisible glass. The scaling factors for the Slinky are linear, for those of you familiar with the Slinky Jr., a half-size, half speed offspring. The plastic, brightly-colored Slinky now in the stores moves twice as slowly as the steel one, and is better for engineering demonstrations (and children who gnaw on everything) but is a loser as a toy compared to Old Reliable. Cunningham's first Slinky is still the only one in his eyes. Today's brass model, for example, doesn't work nearly as well as the steel, he claims. The brass doesn't have the the right relationship between Young's modulus and the density--it's not stiff enough against lateral deflection. Perhaps we need something like the original-instrument movement among the music buffs; otherwise we will never know the true stuff of the device. Birth and transfiguration. In November 1945, Gimbel's (remember Gimbel's?) sold out 400 of the brand-new items in 90 minutes. Two years later a patent for the Slinky was given to Richard James, a Penn-State mechanical engineering graduate working for Newport News Shipbuilding. The original design was first licensed out to one Leroy Shane, who marketed the Magi-Koil. (As we will see, there are some grey areas in the genesis story of the Slinky.) Eventually, the enterprising engineer founded James Industries Inc., Holidaysburg, Pa., now run by James's widow Betty. The company's flagship model is made of "cold-rolled spring steel," as divulged by a tight-lipped Mrs. James, fabricated from round wire rolled out at zero tension, flattened, and twisted into the helix. The company turns out 6000 Slinkys a day. What engendered the idea for the Slinky? At one time voice coils in loudspeakers were made edge-wound, like a Slinky, in order that as much metal as possible could be within the magnetic field. So goes one theory for the initial design concept, its adaptor to toydom unknown. But according to Mrs. James, Richard James got the idea when he dropped a "torsion spring." The quotes you see around the words are because I could not discover exactly what this object is, and Mrs. James could not, or would not qualify her information any further. Interestingly, Prof. Cunningham received a letter containing a third story, one with darker overtones, but plausible nonetheless. According to this Deep-throat-delivered story, someone ran a machine shop in Philadelphia making helical piston rings for small gas engines. (Within each engine cylinder, placed over the piston, are two or three springy helical coils of tape that bear against the cylinder wall. Their expansion keeps the cylinder gas-tight, and the flat coil keeps lubricating oil away from the burning fuel.) The story goes that, after slicing off the tops of the steel helixes to make the rings, whoever ran the machine shop noticed the properties that now we all know. The identity of this "whoever" remains shrouded. Some time later Richard James got wind of the doctored piston rings, and marketed the concept. The relationship of humanity and staircase was irrevocably altered. Copyright 1989 Copyleft 1989 Robert Braham Scitech Publishing Services 1315 Third Ave. New York, NY 10021 Voice: 212-879-1026 E-mail: CIME-ISE (Computers in Mechanical Engineering, Information and Software Exchange BBS (pronounced "Siamese") 608-233-3378 (Madison, Wisconsin) (An abbreviated, edited, and unsigned version of this text, Slinky.txt, appeared in 1988 in Mechanical Engineering magazine.) X-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-X Another file downloaded from: NIRVANAnet(tm) & the Temple of the Screaming Electron Jeff Hunter 510-935-5845 Rat Head Ratsnatcher 510-524-3649 Burn This Flag Zardoz 408-363-9766 realitycheck Poindexter Fortran 415-567-7043 Lies Unlimited Mick Freen 415-583-4102 Specializing in conversations, obscure information, high explosives, arcane knowledge, political extremism, diversive sexuality, insane speculation, and wild rumours. ALL-TEXT BBS SYSTEMS. Full access for first-time callers. 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