Anyone who has ever played golf has been there. The end of the round is approaching. You’ve been hitting well all day, so why not put a little extra muscle into your last tee shot? Answer: adrenaline steers your ball right, slicing hard into the woods. Insert expletive and/or club scolding. After collecting yourself, you shove your driver back into the bag and set off down the fairway, hoping that you’re still in play. The good news is that you find your ball (or one of its cousins) sitting up on a patch of pine straw. The bad news is that your ball is surrounded by trees, save for a small opening perpendicular to the green, which lies over one hundred and fifty yards away.
Conventional wisdom says take the hit. Punch the ball sideways, give yourself an angle to the flag and salvage a par (or a bogey, possibly a double, let’s be honest, you’re still mad about your drive). It’s the sensible thing to do, because there’s no way you’re going to thread the branches with the right amount of spin and loft. That is, unless your name is Bubba Watson, and you find yourself at the biggest golf tournament in the world, in a sudden death playoff, while your opponent, an unflappable South African with an albatross on the day and a major title under his belt, stands two shots away from vanquishing your dreams.
What followed, deemed the shot of year by the PGA, will likely be replayed for the next decade. The footage shows a gangly figure sporting white duds and Jesus hair, flanked by a parted sea of patrons. Our hero consults his sidekick before selecting a club—52 degree wedge, a weapon as esoteric and unwieldy as a bola. He surveys the terrain, clears a couple of wayward leaves, sizes up the ball. Then, after a practice swing that in no way resembles his actual swing, Watson lets her rip. The gallery gasps. The ball does not shank. It does not ricochet off of low hanging boughs. It does not dribble into the rough or sail towards other hazards. It does not even find the pear-shaped sand-trap guarding the green. Instead, like a heat seeking missile, it plops down twenty feet from the pin and rolls even closer. As the crowd erupts, as the broadcasters gush, as Watson hustles up the hill to putt for the win, the question on everyone’s mind—amateurs and experts alike—is this: what just happened?
To put The Shot into context, I enlisted the help of Dr. Sean Bailey, a professor in the Mechanical Engineering Department at the University of Kentucky. He makes a living studying things like unsteady vortices, turbulence, and boundary layers. In his post-doctoral research at Princeton University, Bailey also explored the fluid dynamics of golf balls, using a high speed wind tunnel to characterize their aerodynamics. From this data, he wrote codes that could predict shot trajectories accounting for an impressive range of variables, everything from crosswinds to humidity. When I asked him if there was a code for The Shot, he suggested that we start simpler, by looking at the factors that influence distance, accuracy, and spin.
“With aerodynamics,” he explained, “we’re really concerned with how the forces are effecting the ball. And there are two forces that we’re dealing with here—lift and drag. Lift is related to spin, and the drag is related to how well the flow follows the ball.” Sounds simple enough, but before we continue, I should offer a disclaimer: unless you are a scientist, forget everything you know about physics, because it’s probably wrong.
According to Bailey, an understanding of drag begins with something called the no-slip condition (and no, this does not involve pine straw). “When you have fluid flowing over virtually any surface,” he said, “right at that surface, the fluid is traveling at the same speed as the surface.”
Consider a paper glider mid-flight. Where the wind contacts the wing, a thin band of air is swept along for the ride, almost like a film of glue. This region, discovered in 1904 by the German mathematician Ludwig Prandtl, is known to fluid dynamicists as the boundary layer, and it helps explain why a glider, or any projectile for that matter, decelerates. Just as an eddy slows a river’s current, the boundary layer has a viscous tugging effect. This friction—picture stationary air grabbing a stream of faster air and slowing it down—is then transmitted to the surface of the projectile, creating drag. Questions remain as to what exactly occurs at the molecular level, but the basic idea is that the boundary layer transfers momentum from the flow to the surface, from the air through which the projectile travels to the projectile itself.
Now is where it gets complicated.
These boundary layers generally fall into two categories: laminar and turbulent. For most streamlined bodies, the laminar is more desirable. “Think of airplanes as the classic example where you want to minimize your drag,” Bailey noted. “So [with] big long bodies, where there [are] not a lot of angular changes, nice flat smooth surfaces, usually, you want a laminar boundary layer, because the flow will create less friction.” When it comes to spheres, however, the opposite is true—a laminar boundary layer, brought on by smooth surfaces, can't follow the curvature. As a result, the boundary layer separates from the surface and actually pushes the flow further from the body, producing bigger wake and more drag. To minimize these effects, the experts turn to turbulence which, it turns out, is good for something other than nausea. “Because turbulence is good at mixing,” Bailey explained, “it can take the fluid moving past the ball and bring it closer to the surface… So for bluff bodies, the turbulent boundary layer is actually better at reducing drag.”
Put another way: turbulent boundary layers create tighter, more energized wake structures. This is why golf balls have dimples; small surface irregularities instigate turbulence, effectively optimizing the low pressure region trailing the ball. Dimples reduce drag. They add distance and improve stability, allowing for more dramatic flight patterns. In fact, there’s a whole science behind dimple size and distribution, both of which are heavily regulated by the United States Golf Association. Companies like Polara Golf equip indoor testing ranges with robotic golfers and high-speed camera systems, hoping to squeeze that extra yard out of new prototypes. So while the golf ball proves a fickle companion on the course, from an aerodynamics standpoint, it is a marvel of engineering, as Bailey put it, “a lovely example of success in controlling the flow…so if you look at different balls, you’ll see that the dimple patterns [vary], and it’s all just trying to fine-tune this process of drag reduction, and when you reduce drag, the ball is going to go farther.” But drag is only one factor in the complex equation of The Shot.
Many can hit the ball as far as Watson did; few can do so with such deliberate spin and fewer still could get it in a single attempt. The hook—the inward-curving trajectory Watson produced—is usually an accident, caused by one or more of the following: closing your hands, swinging too fast, swinging outside-in, swinging across your body, standing too close, placing the ball forward in your stance, losing your grip, losing your temper. In all cases, the club face contacts the ball at a lateral angle, spinning it sideways. Usually, the goal is to avoid this kind of motion, but even the best golfers in the world occasionally find themselves in thorny situations, where a large obstacle, such as a tree or television tower, must be circumvented. Intentional or no, the hook is often couched in terms of swing mechanics, as was the case in the aftermath of Watson’s victory. But once the ball leaves the club, the real story is lift.
If you took physics in high school, you may recall that lift has something to do with Bernoulli’s principle1. “If you get faster fluid moving over one part of the surface than over the other,” Bailey explained, “you get a pressure difference, so when there’s a velocity difference, there’s a pressure difference, and this difference is what creates lift.” Again, airplanes prove instructive here. A profile of most wings reveals a rounded top, which separates the flow into two channels—faster on top, slower on bottom. The resulting pressure difference, following from Bernoulli, creates an upward force.
Of course, the golf ball does not have wings. Nor is it asymmetrical, meaning that its shape does not produce lift. Instead, this force is a function of speed and, more pertinent to our discussion, spin, which creates a Bend-it-like-Beckham swerve known as the Magnus Effect. “As soon as you spin the ball,” Bailey explained, “because of the no slip condition, the ball is dragging fluid with it. And as it translates through the flow, one part of the ball is moving in the same direction as the fluid, while the other part is moving in the opposite direction.” In other words, the no-slip air moving with the flow accelerates; the no-slip air moving against the flow decelerates. Ergo, pressure differential, ergo lift. So the faster you spin the ball, the bigger the pressure differential, the bigger the lift.
With the exception of the putter, golf clubs are lofted for distinct lift effects. The typical driver, meant to produce a lower, straighter shot, requires only 9 or 10 degrees of loft. A 9 iron, on the other hand, is angled at roughly 40 degrees. Hit an iron shot right and lift works to your advantage, pushing the ball skyward, adding the kind of curvature you see on protracer replays to otherwise parabolic arcs. Top the ball and lift sends your shot into a sharp diving motion. And if you cut the ball sideways, with extreme loft, depending on your speed and axis of rotation, well, you might just be able to pull off the kind of wraparound masterpiece Watson put on display last April.
Or not. Looking at Bailey’s calculations, one realizes just how much touch, not to mention torque, went into The Shot. Working backwards from the footage—along with other variables like ball mass, humidity, and barometric pressure—Bailey whipped up a “very very crude estimate” of the Shot, an analytic portrait if you will:
The figures here give us an impressionistic sense of what happens post-impact. The ball leaves at 176 F/S, which, studies show, translates to a swing speed of just under 100 M.P.H. For a wedge, this is almost 30% faster than the average amateur swing, and Watson makes it look easy. As for the spin rate, 6,000 RPM rivals the upper reaches of a Ford Mustang. Surprisingly, however, this is not an exceptional number for a gap wedge, unless you consider that the ball is spinning sideways. And then of course there is the vertical launch angle, less than a third of the loft built in to the club, a mere 15 degrees to avoid overhanging trees. In fact, the more you look at this model, the more questions it raises. What kind of ball was Watson using? Did the pine straw have any effect on the flight path? If RPM varies from wedge to wedge, as Trackman diagnostics have suggested, then how does the mass distribution of this particular wedge enhance or inhibit spin?
That Watson entertained none of these considerations is probably for the best. In interviews after the Masters, he attributes The Shot to a number of different factors: his focus, a fortunate lie, childhood advice, divine intervention. But the common denominator, as Watson explained to CNN’s Piers Morgan last April, is feel.
“I trust everything,” he said. “Every ounce of my body, I trust it all. I trust in my abilities, I trust I can do it.” For all of our statistics, for all that we can say beforehand about club head speed or loft or spin, in the moment, the important thing is what Watson’s body knows. Feel is physical memory, reinforced through repetition, through thousands upon thousands of rehearsals. Feel is why somebody who has never had a lesson in their life, and whose swing is idiosyncratic enough to defy imitation, can pull off such an unlikely shot. Though at times imperfect, feel allows us to guess and check, to draw from a vast repository of kinematic data and to make educated adjustments. Watson chose not to over think the situation. Instead, he went up there and swung as hard as he could, hoping that, by hook or by crook, possibility would trump probability. It was worth a shot.
1. For the record, Bernoulli did not pull his principle out of thin air. His work traces to Newton’s Second Law, from which a number of assumptions and simplifications were made. But if you’re looking for the father of turbulence, the rabbit-hole runs even deeper, all the way to Leonardo Da Vinci, whose 1517 illustration“Deluge” anticipates complex flow, framed as a series eddies. In the caption beneath the image, he writes of “immense rumbles made in the lowering air by the fury of winds mingled with rain,” language signaling great interest in the movement among and between fluids.