Fairway Physics

By Jeffrey Kluger|Thursday, August 01, 1996
They talked about a lot of things when Edmund Muskie died earlier this year, but his hole in one was not among them.

It was late 1968 when Muskie got his ace, and at the time, the former governor, sitting senator, and future secretary of state was running for vice president. Late 1968, as any active politician appreciated, was not the best historical moment to be running for any office. The Southeast Asian military offensive was at its most offensive; American cities were experiencing unrest (a term the press considered more polite than on fire); and the Chicago convention had wound up looking like a Shriners convention. And yet one evening in the midst of this, Muskie scheduled a television appearance, and the first thing he was asked about was his hole in one.

Even as a political naïf, I remember being taken aback by this. Here we were, if not on the eve of the apocalypse, then certainly approaching the late brunch, and all the usually inquisitorial media wanted to discuss with the Democratic vice presidential candidate was his triumph on the links. Après le déluge, they seemed to be saying, golf!

And yet the remarkable thing was, no one--not the Democrats, not the Republicans, not Muskie himself--objected. The questioners in this interview wanted to ask about holes in one, the audience wanted to listen, and that appeared to be that. I began to suspect then that there was more to this golf thing than I knew.

I was right. In the United States alone an estimated 24 million people call themselves regular golfers. In 1994, the last year for which figures are available, this near nation-state spent more than $2 billion on golf clubs, $10 billion on greens fees and club memberships, and over $2 billion on miscellaneous merchandise. And hidden in this last figure is possibly the most remarkable statistic of all: in 1994, as in most years, the American golf industry manufactured and shipped around 850 million golf balls--about 3.2 for every man, woman, and child in the country.

Perhaps more than anything else, it is the ball that is the central totem of the game of golf. But it’s not just the people on the links who find the little pill an object of reverence; it’s the people in the labs as well. Packed inside a golf ball’s 2.4-cubic-inch interior and spread across its 8.86-square-inch face are more parts per million of science than in virtually any other piece of sports equipment ever invented. What a golf ball lacks in a football’s size, a baseball’s lore, and a bowling ball’s mass, it may make up in sheer scientific complexity.

To appreciate the contemporary golf ball, one might appreciate its historical roots--and they are roots that go deep. The first known appearance of a golflike game was roughly 2,000 years ago when the Romans invented a club-and-ball sport they called paganica. While the Romans, with their powerful military, were among the world leaders in the sophisticated field of club technology, ball manufacturing was a different matter, and the earliest known paganica balls were little more than stitched, feather- stuffed skins that later came to be known, appropriately enough, as featheries. Built of only the finest ancient materials, the average feather ball could last a sportsman a lifetime, provided he didn’t do anything stupid with it like hit it with a club. This tended to make it fall apart and required the ancient player to run all the way back to the ancient pro shop to buy another one.

Though the featherie had its shortcomings, the Romans--with such workaday concerns as sacking and pillaging to keep them busy--did not have time to invent an alternative. Not until the nineteenth century, when more- contemporary Italians dreamed up the gutta-percha, or guttie ball, did golf make its next strides forward. The guttie ball was a solid one-piece golf ball made of the dried gum of the Malaysian sapodilla tree. This was a perfectly fine material for a golf ball with the exception that when the temperature drops too low, sapodilla gum grows a bit brittle--a lesson the cold-weather golfer learned the hard way when he hit a shot on the tenth hole and found his guttie ball flying off in the direction of the eleventh, twelfth, and thirteenth. Happily for fellow duffers who were tired of coming home from a day on the links with more shrapnel wounds than muscle aches, the guttie ball was later replaced by balls made of natural rubber and, then, synthetic rubber, both of which led to the modern balls in use today. While all these balls differed dramatically in design, one thing they had in common was that at some point they felt the wrath of a club. That is the moment when the sport of golf started to turn into the science of golf.

The act of swinging a golf club and striking a ball seems like a graceful one, says Joseph Stiefel, physicist and golf ball designer with the Spalding Corporation in Springfield, Massachusetts, but at the level at which club head meets ball, it’s also a pretty complex and violent one.

To understand how complex and violent, Stiefel recommends starting off by imagining a perfect, platonic golf swing with a club speed of, say, 100 miles an hour. For most of us, this isn’t easy. I haven’t played golf often, but when I have, the only thing about my game that stood a chance of reaching 100 miles an hour was the perfect, platonic Pontiac in which I drove to the perfect, platonic country club, hoping all the while I wouldn’t meet a perfect, platonic policeman. For accomplished players, however, a 100-mile-an-hour swing is by no means uncommon; for the ball, that can make things by all means unpleasant.

When a moving seven-ounce club head collides with a stationary 1.62-ounce ball, the first thing that happens is that the ball is temporarily flattened, losing about a third of its usual diameter. The club head, for its part, responds to the impact by sacrificing not size but speed, going from 100 miles per hour to just 81. Since energy can be neither created nor destroyed but only altered (and then only within 30 days of purchase), the 19 miles per hour the golf club seems to lose isn’t lost at all but merely transferred to the compressed ball in the form of elastic energy. With the help of this kinetic infusion, the so-far passive golf ball suddenly becomes active.

A ball will remain compressed for only so long before it springs back into shape, Stiefel says. When it does, it pushes backward on the club head. This tiny push is enough to slow the golf club down further--to about 70 miles per hour--at the same time that it speeds the ball up, causing it to fly away from the club at about 135 miles per hour.

To be sure, not all golf balls will display such pop. Just how well any given ball jumps off the club depends on what’s known as its coefficient of restitution. The coefficient of restitution, for all its multisyllabic heft, is nothing more than a term scientists use to talk about bounciness. Why they don’t just say bounciness is unclear, but from a community of people who say high viscosity when they mean gooey, high adhesion when they mean sticky, and dissertation pending when they mean My dog ate my homework, some obfuscation is inevitable. Nonetheless, the coefficient of restitution is a deceptively simple idea.

When a ball is dropped from a given height, says Michael Sullivan, Spalding’s senior director of research, the material it’s made of will largely determine how high it bounces, and that height will be the measure of its coefficient of restitution. A rubber ball dropped from 100 inches may, for example, bounce back up to 60, which would give it a rough coefficient of restitution of .600. A billiard ball may bounce only 10 inches, for a rough coefficient of .100. A piece of clay, which would hit the floor and simply stay there, scores a perfect zero on the coefficient- of-restitution scale. (To calculate a true coefficient of restitution, Stiefel explains, these rough figures must be square-rooted or cube-rooted or root-root-rooted or something, but for anyone not planning on going into the golf ball manufacturing field this afternoon, rough numbers are probably okay.)

As soon as scientists devised the coefficient-of-restitution test, they realized that golf balls had been flunking. The featherie and the guttie ball had low to modest coefficients of restitution. When rubber balls were introduced in the twentieth century, the rough number climbed above .600--better, but still a little leaden for many golfers’ tastes. It was only in the 1970s that golf balls achieved true state-of-the-art spring, thanks to a substance known as polybutadiene.

Essentially a petroleum-based polymer, polybutadiene had been little more than a chemical curiosity until the late 1960s, when the überball known as the Superball hit the toy market. Resembling a squash ball, the Superball was advertised as the ultimate rubber ball, and its bounce lived up to its billing, achieving a coefficient of restitution reaching the middle 800s. Not surprisingly, parents of that era were reluctant to buy children so high-octane a toy, and with good reason. Fully 30 years after the introduction of the product, suburban communities across the country still conduct occasional drills, as Superballs bounced in mid- 1968 suddenly reappear menacingly over the horizon. Even the name of the company that manufactured the Superball--Wham-O--vaguely suggested mayhem, though other names reportedly under consideration (including Oops, Smash, and I Hope You Had Coverage for That) would almost certainly have been worse.

Predictably, a ball that could be bounced in Central Park and wind up in Fenway Park soon caught the eye of the golf industry. At Spalding, a chemist named Bob Molitor began toying with polybutadiene and immediately discovered that while a ball made of the polymer was more than strong enough to be bounced, it was a little too soft to withstand the punishment it would take when hit by a club-wielding golfer. To toughen the stuff enough to make it fit for the links, Molitor decided to fortify it with an unlikely material: zinc. Just what would make even the most optimistic industrial chemist conclude that the performance of any piece of sporting equipment could be improved by an element drawn from the ductile metals section of the periodic table is unclear (Holy cow, Nolan Ryan really put some zinc on that pitch!), but Molitor was evidently onto something.

Polybutadiene, like all polymers, explains Sullivan, is made of molecules arranged in long strands. What Molitor envisioned doing was mixing zinc salt with polybutadiene and allowing it to attach to bonding sites along the strands. This would cause the molecules to become cross- linked--they would essentially attach to one another in a ladderlike configuration--which would help strengthen the material.

To Molitor’s delight, that’s exactly what happened, leading to a new form of fortified polybutadiene that could survive even the hardest blow from the fastest club. When all the ciphering for the true coefficient of restitution had been done, the new golf ball bounced back with a kangaroo-style .890. Before long, Spalding had converted most of its golf balls to polybutadiene, and soon the rest of the industry followed suit, formally consigning the ordinary rubber ball to the same sporting goods dustbin in which the guttie ball and featherie had long resided.

But just because the interior of the golf ball had been reinvented did not mean all was well with the exterior--particularly with that most identifiable feature of the exterior: the dimple. While the presence of the golf ball dimple has always been something of a given in the sporting goods world, the purpose of it hasn’t. In a recent, utterly unscientific survey I conducted of a sample group known as Drivers of New York City Cabs I’ve Been in Recently, the three most common answers to the question What is the purpose of a golf ball’s dimples? were:

1) Uh, something to do with grip?

2) Uh, something to do with appearance?

3) Tnj d Vfy[fnfy?

Not surprisingly, number three is the closest to being correct. When a golf ball in flight plows through the atmosphere, it leaves a sort of semi-airless trench behind it. Since nature abhors even partial vacuums, it immediately tries to fill them, and in the case of the golf ball, that means that air and suspended particles in the vicinity are going to be drawn toward the low-pressure wake. One other--less expected--thing affected by the partial vacuum is the golf ball itself, which is pulled subtly backward by the trail it’s created. Over the course of the ball’s flight, this insistent tug acts like a brake, dragging the ball down to Earth sooner than it would otherwise have fallen. In the early part of the twentieth century, when golf balls were still smooth, designers discovered that the balls that suffered least from this phenomenon appeared to be the oldest ones, those with the most pits and gouges in their surface. Somehow the exterior flaws seemed to be able to snag and hold the air as the ball passed through it, keeping it swaddled in atmosphere throughout its flight.

A ball that travels through the atmosphere wrapped in a corona of air leaves not a vacuum trail in its wake but simply a stream of more air, Stiefel says, and this can help keep it aloft. When designers realized this, the idea of putting flaws in the ball on purpose--dimples, in other words--was born.

As a general rule, the more dimples a ball has the better it flies, provided those dimples are about .15 inch in diameter, the average size shown to favor flight-worthiness. Sprinkling the dimples evenly over the face of the golf ball gives a total dimple population of about 336. For decades the 336-dimple ball held sway, but in recent years manufacturers have discovered that the size of an effective dimple can vary by one- hundredth or two-hundredths of an inch, meaning that the number of dimples can vary, too, by 50 to 100 per ball.

In recent years, says Sullivan, more and more golf balls with 400 and even 500 dimples have appeared on the market, with new ones being tested all the time.

Some of the most dramatic test-ing is taking place not at Sullivan’s and Stiefel’s own Spalding, but across the state in Fairhaven, where the competing Acushnet company manufactures the popular Titleist ball. Standing in a wing of the Acushnet factory is the industry’s--and, indeed, the world’s--only wind tunnel designed exclusively for golf balls. While wind tunnels have always been helpful in designing such things as passenger jets and missiles, their record with consumer products is a little spottier. It was the aerodynamic ideal established by wind tunnels, after all, that was at least partly responsible for the finned family cars of the 1960s, a time when the average automobile had all the sleekness of the average shopping mall. Despite this history, the Acushnet wind tunnel seems just the thing if you’re trying to build the perfect golf ball.

The tunnel we use to study our balls is far smaller than ordinary wind tunnels--about 40 feet long with a 75-horsepower fan, says Steve Aoyama, Acushnet’s product research manager. At one end is the fan, at the other is an opening from which the fan draws in air, and in the center is a 36-inch-by-18-inch test chamber along with an observation room for engineers. In order to test our products, we suspend a prototype ball over the test chamber, get the fan going, drop the ball in, and see what happens.

On the surface, this sounds pretty scientific, but unless I’m missing a Newtonian step here, what should happen is that the ball will--as physicists like to say--fall down. And indeed that is what happens, but in the instant it is falling, a lot of other things are going on, too.

Before the ball is dropped, Aoyama says, we set it spinning with the same rpms it would achieve when hit by a golf club. As it’s falling, a battery of high-speed cameras take its picture. To the untrained eye, the path the ball takes to the floor does not look like much, but the trajectory can actually tell you a lot about the ball’s lift and drag properties. When the pictures are digitized and entered into a computer, the computer analysis helps us change the ball’s dimple pattern to improve those properties accordingly.

How much the golf ball’s dimple pattern--or its polymer core or its coefficient of restitution--will continue to change is uncertain, but what is certain is that they will change. Even after two millennia, it is this mutability that probably most distinguishes the golf ball from practically every other ball used in every other sport. Unless tennis tournaments are suddenly sponsored by depilatory makers, tennis balls are unlikely to get any less fuzzy. Unless bowling leagues suddenly become popular in the squid community, bowling balls are unlikely to develop many more holes. Unless Olympic coaches begin serving frosty mugs of androgens during qualifying trials, shot puts are unlikely to get any heavier. The golf ball, however, and thus the game of golf in general, are works in progress. Now if only they could do something about the checkered pants.
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