The Divinely Random Bounce of the Prolate Spheroid
DeSean Jackson panicked.
The Philadelphia Eagles Pro Bowl kick returner was standing at his own 35-yard line on a chilly December afternoon at newly opened MetLife Stadium in the New Jersey Meadowlands, but the last thing that he expected was the ball.
The plan was simple. New York Giants punter Matt Dodge was going to kick the ball away from Jackson and out of bounds. That might give the Eagles just enough time to throw a Hail Mary into the end zone, allowing the Giants a chance to regroup as this wild game, in which the Eagles had come back from a 24–3 deficit to tie the score at 31, went into overtime.
And then the prolate spheroid did its thing. A bad snap almost fluttered over Dodge’s head. Dodge reined the ball in, and his plan was to make contact with the ball just off center and send it toward the sideline, away from Jackson. But Dodge hit it on center, just an inch or two away from where he intended. So instead of lofting harmlessly out of bounds, the ball made a beeline for Jackson.
The Eagles ace return man couldn’t quite believe what he was seeing. He watched the ball drop, wobbling like a dying quail. The quivering punt was falling to earth just a little short of where Jackson expected it, and instead of taking a step to get under the ball the way his coaches taught him in Pop Warner football, Jackson reached out for it. Starting to run before he had full possession of the ball, DeSean Jackson watched the Wilson “Duke” slip right through the fingers of his dark green gloves.
That’s when he began to panic.
With good reason. A herd of Giants defenders were heading toward him at full speed. If the ball bounced forward, one of them would scoop it up, leaving nothing but daylight between the Giants’ defender and the Eagles’ end zone. If it bounded backward, same deal. But this time the ball fell to Jackson’s right. It rolled cleanly, almost gently, end over end the way a small child might, twice, three times, four.
It would probably take the faculty of MIT a full afternoon to parse all the options of where and how that ball might have traveled after it slipped through DeSean Jackson’s hands. Almost all of them would have been disastrous for the Eagles.
Instead, the ball rolled around tamely, settling only a yard or two away, where Jackson could pick it up. And thus began the return that came to be known as “The Miracle at the New Meadowlands.” Jackson stopped in his tracks, retreating a few steps as he picked up the ball. As he stutter-stepped and pivoted to get going in the right direction, the Giants were in disarray. One defender fell down. Another ran into his own teammate. Still another Giant launched at Jackson and hit another blue jersey.
Jackson looked up, and instead of blue, he saw green—lots of it. The wobbling ball led him right to a crease in the Giants coverage. Now aligned with his blockers, he used his 4.4 speed to motor through the gap and down the right sideline. For dramatic effect, Jackson ran parallel to the goal line before landing in the end zone for the first game-ending punt-return touchdown in NFL history. All because of a random bounce.
It starts with the ball.
Pick up an official NFL football, Wilson Model F1100. It’s called the Duke, named after the late New York Giants owner Wellington Mara, who was named after the Duke of Wellington. But forget about that, and forget, too, about Commissioner Roger Goodell’s autograph branded into the leather. Instead run your fingers across the pebbled cover. Look very closely, and you’ll find a few tiny Wilson logos that are just a bit bigger than the period at the end of this sentence. Explore the stitches that join the four elliptical panels and the bright white laces that play counterpoint to the ball’s otherwise sleek silhouette. Pull back for a moment and study its simple, streamlined shape. The ball is nothing if not purposeful. It all but invites you to wrap your hand around it.
But looks can be deceiving. That shape is anything but simple. A mathematician would explain that a football is a prolate spheroid. The circumference around its poles (a minimum of 28 inches) is longer than the circumference around its equator (at least 21 inches). The earth, by contrast, slightly flattened at its poles, is an oblate spheroid. Why is a football that shape? Ask Arnold the Pig.
Rewind to the mid-1850s. America sits on the brink of war, the game of football is in its infancy, and the very first footballs are made from inflated pig bladders. A pig’s bladder itself is relatively small and, after it’s removed from the pig, resembles an uninflated balloon. But it’s also remarkably flexible, and with proper conditioning, a pig’s bladder can stretch to many times its normal size when it’s blown up.
As an example of proto-recycling, turning a bladder into a ball is ingenious. But these early footballs were better as symbols than as actual balls. They’d leak or split, and sometimes to keep their shape they’d be stuffed with straw or some other random material. For this reason, these pig-sourced balls fell out of fashion quickly, replaced by balls stitched from leather and rubber—but not before lending a cowhide football its evocative, if incorrect, nickname: pigskin. And not before establishing the unusual shape that would come to define the game of football.
Let’s clarify what we mean by football. In the days of pig bladder balls, football was something of a pastiche, its rules and style of play very much in a state of flux. The game that would come to be known as “American” football shared common roots with both rugby and the game that Americans call soccer and the rest of the world calls football. We’ll discuss the nuances of the game’s evolution later, but for the moment, let’s focus on the changes in the ball itself. Because in sports, the ball is everything.
In the middle of the nineteenth century, both football and soccer were played with roundish balls that were somewhat irregular in shape because of their origins as, well, part of a pig. As the games diverged, so did the balls. Soccer became a game that centered around kicking. And given the difficulty of controlling the ball with one’s feet, one thing became clear: the rounder the ball, the better.
As soon as advances in materials made it practical, soccer moved toward a ball that was as round as possible. The panels became smoother and more uniform, and the seams joining the panels became less prominent. The round balls used in sports like baseball, tennis, and even basketball feature a slight but crucial asymmetry. The orientation of the cover on the round core is what gives Justin Verlander’s slider its break and why Kobe Bryant will align a basketball just so—fingers spread across the seams, index finger pointing at the valve—for a free-throw attempt. The cover of a soccer ball, on the other hand, is made up of twelve pentagons and twenty hexagons, the panels forming a figure called a truncated icosahedron, which mathematicians have studied since the days of Archimedes. Leonardo da Vinci simply called it “divine.” A soccer ball may not be as purely symmetrical as, say, a billiard ball, but it’s functionally symmetrical. Players don’t care much about exactly where they kick the ball. A modern soccer ball may even be getting too round. In pursuit of more perfect sphericity, the soccer balls used in the 2006 World Cup abandoned the traditional thirty-two-panel geometric design in favor of one based on fourteen curved panels. Those sleeker balls were a source of controversy, as the smooth profile allowed the ball to dart in unpredictable ways. Sometimes, geometry is destiny.
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 1996, 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.
Excerpted from Newton's Football by Allen St. John and Ainissa G. Ramirez, Ph.D.. Copyright © 2013 by Allen St. John. Excerpted by permission of Ballantine Books, a division of Random House LLC. All rights reserved. No part of this excerpt may be reproduced or reprinted without permission in writing from the publisher.