Newton's Football, page 2
And so it is with the football.
In the latter part of the nineteenth century, rugby—and in turn its cousin American football—diverged from soccer in an important way. It became less about kicking the ball and more about carrying it. And with that, the ball moved away from soccer’s trend toward roundness and symmetry in favor of a more elongated shape that honored the ball’s porcine roots. The prolate spheroid became even more prolate.
Why? First off, it was easier to carry. A prolate ball could be tucked into the crook of the arm, with a hand positioned over the nose of the ball. Try that with a basketball or a soccer ball and the difficulty of doing so immediately becomes apparent. In rugby, the ball more or less stopped evolving right there. This somewhat elongated ball could be cradled more easily, and even today, the rugby ball remains largely watermelon-shaped.
In football, the evolution continued. In the early part of the twentieth century, the forward pass was first legalized and gradually became integral to the game. (We’ll explore this trend in detail in the chapters to come.) In 1934, the circumference around the ball’s belly was reduced from 23 inches to 21 5/16 inches and the nose was made more pointed, all with the goal of making it easier to throw.
Wait. What exactly does “easier to throw” mean? For starters, it means being able to throw a ball a long way. The strongest modern quarterbacks can throw a ball 80 yards in the air. But it also means being able to throw the ball accurately; the difference between a touchdown catch and a drive-killing interception can be just a few inches. The modern football addresses both of these requirements, which are sometimes at odds.
Basically there are two forces that a quarterback must contend with as he throws the ball: gravity and air resistance. Here’s Newton’s First Law of Motion: An object at rest stays at rest, and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force. Which means that if a passer could throw a football in a vacuum with no gravity, it would simply continue moving in the direction that the quarterback threw it.
What’s an unbalanced force? A good example of a balanced force is a tug-of-war between two evenly matched teams. A lot of energy is being expended, but the rope isn’t moving. But when you throw a football in the real world, it’s all about unbalanced forces. The biggest unbalanced force is gravity, which pulls the ball toward the center of the earth—or, in more practical terms, the ground. If you were to graph the flight of a ball, it would describe a smooth parabola, and gravity is the reason. Gravity is a powerful force.
Air resistance? That’s a whole different story.
Air is all around us, so we tend to take it for granted, but air resistance is a powerful and largely underrated force. Perhaps the best example of this is the land speed record for a bicycle. Set by Dutch cyclist Fred Rompelberg in 1995, it’s a mind-boggling 167.01 mph. How on earth can a bicycle travel that fast? For his record attempt at the Bonneville Salt Flats in Utah, Rompelberg drafted close behind a streamlined car with a specially designed fairing that broke the wind for him. With wind drag eliminated, Rompelberg demonstrated that a human being can indeed pedal fast enough to keep up with a Ferrari in fifth gear. Such is the seldom-acknowledged power of air resistance.
A football also cheats the wind. The elongated shape reduces its frontal area—the surface area exposed in the direction of travel. The smaller the frontal area, the fewer air molecules the ball has to push out of the way as it moves forward, which means less drag. Compare a football with a round ball with the same mass and total surface area and you’ll find that the football has less frontal area than the round ball and thus can be thrown farther. Another way of understanding frontal area is by putting your hand out of the window of a moving car. If you face your palm forward, the wind pushes hard against your hand. But if you turn your hand 90 degrees, so that just the side of your hand faces forward, the frontal area is reduced and so is the wind resistance. You can almost feel your hand slicing through the air. This is why sharks and rockets and race cars all have pointy noses.
But if you’ve ever seen someone try to throw a football for the very first time, you know how hard it is for the ball to maintain this nose-first attitude. Unless, of course, the ball is rotating. When a football spins around its longitudinal axis, this gyroscopic effect stabilizes the ball in flight. This is the same effect that’s at work in the world of ballistics, where a bullet can spin as fast as 300,000 revolutions per minute. And it’s the opposite of a knuckle ball in baseball, where the ball is delivered with next to no spin. A properly thrown knuckle ball makes only a fraction of a rotation en route from the mound to the plate. That lack of rotation, when the knuckle ball is thrown at just the right velocity, renders the ball susceptible to random air currents, which in turn cause the ball to dart and dive so unpredictably that hitters can’t hit it and catchers can’t catch it. A football pass that behaves that way is just asking to be picked off.
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A spiral.
That’s the poetic moniker that football fans use for a perfectly thrown, rapidly rotating pass. For all its aesthetic beauty, the real payoff of a spiral is its remarkable accuracy. An ESPN Sport Science segment did a breakdown of the throwing motion of Drew Brees, the All-Pro Saints quarterback, using a ball rigged with sensors. Brees was aiming at an archery target set 20 yards away. His mechanics on the slow-motion replay were not only poetry in motion but also physics in action.
Brees picked up the ball not with one hand, but with two, with his left hand doing most of the work of holding the ball, while the right hand assumed a relaxed grip across the laces of the ball. Brees held the ball in his fingertips, not his palm, leaving a bit of daylight visible in the arch between his thumb and his index finger. Brees’s throwing motion began with his weight on his back foot, hips closed, shoulder cocked. As the ball was thrown, his muscles fired and momentum was transferred from the big muscles in his legs and hips, through the rotation of his trunk, into his shoulder, elbow, and wrist in a fluid sequence. It was almost like cracking a whip.
But the magic was still in the hand. As Brees’s arm came forward, his wrist snapped. Using the laces for leverage, he put a clockwise spin on the ball. Like Michelangelo’s Creation of Adam, Brees’s index finger was extended heavenward, and it was the last thing that touched the ball. After the ball was gone, his thumb was pointing down, evidence that he had supinated his wrist properly—in other words, rotated it counterclockwise—and his throwing hand arrived safely in the vicinity of his left hip.
Of course, Brees can replicate this smooth and easy motion all day long. Without a defensive end threatening to flatten him, his delivery is so accurate it’s almost boring. The instrumented football revealed that Brees throws the ball at a consistent 52 mph, with a 6-degree launch angle and nearly 600 rpm of all-important spin.
Armchair quarterbacks wax poetic about the importance of a “tight spiral,” one where the rotation is perfectly smooth without a hint of wobble. But in this video, the super-slow-motion footage reveals that all of Brees’s passes have a bit of built-in wobble. When photographed by an ultra-high-speed camera, the nose of Brees’s ball actually travels in a tight circle around the ball’s horizontal axis, tracing three slight wobbles for every five revolutions. This slight but clearly visible deviation—only a couple of degrees off center—certainly didn’t affect Brees’s accuracy. From 20 yards out, he was able to hit the 4.8-inch bull’s-eye with perfect precision: ten times in ten tries.
If the game’s best passer can’t throw a perfectly tight spiral, can anyone?
That’s what we asked William Rae. The SUNY Buffalo professor is the world’s foremost authority on the flight of the football. He’s also the contrarian who debunks the Myth of the Tight Spiral. Watching his own slow-motion footage and studying data from his own instrumented ball, Rae discovered that the flight of the football is more complex than it seems. And that a wobble-free spiral is essentially impossible.
Rae began his research by confirming that a football thrown with little or no spin will do a belly flop once some air gets under the nose. “How do you convince this thing that it ought to continue pointing into the wind?” Rae asks. “The answer is spin.”
Or as a physicist calls it, gyroscopic torque. Gyroscopic torque keeps the ball stable in flight, just the way the gyroscopic force of a bicycle wheel keeps your mountain bike upright when you’re out for a ride. It also does something more subtle. If you spin a toy gyroscope and lay it on its side and let gravity drop the nose, the gyroscopic torque will move the gyroscope at a right angle, gently resisting the force of gravity.
With a football in full flight, this interaction sets in motion a complex dance between the forces of gravity pulling the ball down and the gyroscopic torque resisting that pull. As the ball spins, there’s a cycle of deflection—first slightly to the right, then down a bit, then to the left, then up, and then to the right again. The result is that the spin axis traces out a cone-shaped path called a precession. Which is to say, a spiral with the slightest bit of wobble. Just the way Brees throws it.
Even the gyroscopic torque of a ball spinning sixty times a second isn’t strong enough to stabilize the ball indefinitely, Rae explains. If you were to throw a football off the rim of the Grand Canyon, eventually—after ten seconds or so—the cone would get bigger, the wobble more profound, and eventually the ball would start tumbling. In an actual game, that’s a moot point because even the longest pass has a hang time of only four seconds, which isn’t enough time for the flight of the spiral to collapse completely.
Believe it or not, the inherent asymmetry of the ball has little or nothing to do with this wobble. “The laces have almost no effect,” says Rae. He explains that if you were to construct a totally lace-less ball and hand it to a skilled quarterback, and then compare that pass to a throw from the same quarterback gripping a conventional ball on the non-lace side, you’d find no difference between the two passes.
In crunching the numbers determining the trajectory of a thrown football, Rae found something else he couldn’t quite account for. A ball thrown by a right-handed passer tends to veer to the right—and by a surprisingly large amount. This deflection can be as much as a yard or two on a 20-yard pass. It took Rae a fair amount of experimentation to realize that this drift wasn’t just a glitch in his equations but an actual characteristic of a flying football. But since (a) there are few longitudinal lines on the football field and (b) you rarely see an overhead camera angle of a quarterback passing, almost no one ever notices it.
One who did notice was legendary Green Bay Packers quarterback Bart Starr. A Packers fan who read one of Rae’s papers directed the professor to a page in Starr’s biography, in which the Hall of Famer explains that his passes naturally trail to the right and that he has to compensate for it.
Shortly after, Rae heard an interview with San Francisco 49ers wide receiver Jerry Rice, just after the right-handed quarterback Joe Montana had been replaced by the left-handed Steve Young. The announcer asked Rice about the differences between the two quarterbacks, and the wide receiver explained that he did detect a difference between their passes but that he couldn’t quite put his finger on it.
“It’s the gyroscopic torque,” the professor could be heard shouting at his television.‡
The members of Team Madden at EA Sports have a chip on their shoulders. In the gaming world, action-oriented games like Halo and Call of Duty get respect from players and programmers alike. But the guys responsible for the bestselling sports franchise in the video game world are quick to explain that their work is underrated.
“People think that first-person shooter [FPS] games are sexy,” says Tim Cowan, EA’s group technical director. “But when you look at a lot of other video games, our physics is a lot more complicated.”
While dispatching a virtual terrorist with a rocket-powered grenade or blasting a zombie with a 12-gauge shotgun may seem like a taller order than simulating a play in a football game, Cowan and friends will tell you it’s not. One of the reasons is that most gamers don’t have much firsthand experience with the kinds of weapons brandished in FPS games, so the designers can get away with creating an experience that’s entertaining without worrying about whether it conforms to reality. Not so with football. “Every American kid understands what it’s supposed to look like when a football bounces,” says Cowan. “And when it doesn’t look like that, it’s very, very obvious.”
So you can’t blame the Madden programmers for getting a little obsessed with the bounce of the football. They spend hours in offices and hallways and even on the lawns outside dropping, bouncing, and rolling footballs and then poring over the results. They have 10 million lines of code at their disposal, but capturing a football in a way that looks good to the casual observer continues to be a daunting task.
“It’s just hard to understand what ‘good’ looks like,” says software engineer Ryan Morse. “If I throw a spherical ball in the air, I know exactly where it’s going. If I throw a football in the air and it lands, it can go thirty different ways.”
“It’s more like thirty thousand. Or thirty billion,” adds physicist Toan Pham, the group’s technical director.
To see for yourself, pick up a soccer ball, raise it to waist height, and drop it. No surprises there. Drop the ball straight down, and it will bounce straight up toward you. Its bounce is so predictable that after a while you can close your eyes and still catch the ball as it bounces right back into your hands.
Try doing the same thing with a football and watch what happens. The first time, the ball might careen to the right. The second? It wobbles straight ahead. On the third try the ball might squirt to the right again. The fourth, it might veer to the left. Or not. On the fifth, it might bounce backward and hit you in the shin. And those are just broad descriptions. Sometimes the ball bounces up, and other times it wants to squib along the ground. It can come to rest two feet away from where it was first dropped—as it did on Jackson’s fumble—or keep rolling until it’s ten feet away. Even a few degrees of tilt in one direction or another can send the ball rocketing off in an unexpected way. And a ball that seems to be rolling in a predictable fashion can suddenly change direction on the third or fourth bounce.
“When you roll a football on the ground, it does a lot of unique things,” Morse explains. “Sometimes it does exactly the opposite of what you’d expect. You might think it would come to a nice rest and spin about its long axis. But its impetus shifts to the end and it starts to wobble. It always starts to turn. It’s a function of its shape.”
Play Madden NFL 13 for a while, and it’s clear that all of the team’s effort paid off.
Sit back and watch as a virtual Tony Romo is sacked by a digital Justin Tuck, and look closely as the Dallas quarterback fumbles the ball. The virtual “Duke” is impressively detailed—you can not only see Roger Goodell’s signature, you can also zoom in on the virtual valve stem—but more important, it behaves in a believable way. The ball wobbles as it first hits the ground, and then it squibs away end over end, skidding on the turf, before it spins and finally bounces up so that Romo’s teammate Doug Free can recover it.
If you want to quibble, the Madden ball seems to take fewer quirky bounces than a real one, but on balance, the movement of the ball is even more impressively realistic than the action of the players.
What is it that this oddly shaped ball lends to the game of football, both the Madden version you’ll find on your Xbox and the one played in stadiums on Sundays? In a word, randomness.
In the real world, randomness is a force that’s both ubiquitous and sneakily powerful. Random movements of molecules are at the center of all kinds of chemical change. Random mutations of genes are the driving force behind evolution. Randomness is the engine behind the cryptography that keeps terrorists from sabotaging nuclear power plants and allows you to use your credit card to buy Springsteen tickets online.
In football, the randomness of a bouncing ball adds an element of uncertainty that coaches and players try mightily to minimize. Indeed, the unpredictable bounce of the prolate is powerful enough to determine which teams will be vying for a trip to the Super Bowl and which ones will be watching the playoffs from the comfort of their couches.
Consider the fumble. Forcing a fumble is a skill that can be practiced and learned. And so is covering the ball. But once the ball hits the ground, all bets are off. It will elude the grasp of a future Hall of Famer and leap into the arms of a sub from the taxi squad. The subsequent change of possession—or lack thereof—from a fumble can result in a swing of 14 points or more. In a league where the average margin of victory is 12 points, it’s no exaggeration to suggest that one random bounce can determine the outcome of a game or even a season.
In the 2012 regular season, the San Francisco 49ers recovered 23 of 37 fumbles, for a 62 percent success rate. The Detroit Lions recovered only 9 of 24, or 37 percent. Their success at collecting bouncing footballs is one of the reasons why San Francisco went 11–4–1 and made it all the way to the Super Bowl. As for the Lions, they ended up a disappointing 4–12.
In large part because of a certain quirk of a pig’s anatomy. And the random bounce of the prolate spheroid.
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* Three chemists won the Nobel Prize when they discovered this shape in a carbon molecule dubbed buckminsterfullerene for its resemblance to Buckminster Fuller’s geodesic dome.
