The Calculus Diaries - Jennifer Ouellette [90]
It is easier to maintain that critical balance on a shorter board; the tradeoff is that it’s harder to catch the initial waves. So for a beginner, like me, a longboard is best, and that is what I am using. Garces assures me the board will “catch anything” (or it would, with a better surfer wielding it); but it means it gets a bit trickier when I try to stand up once I’ve caught a wave. Like Twain a century before me, I wipe out on a regular basis and never quite get into a full stand; the best I can manage is a low crouch.
Hawaiian legend tells of Mamala the Surf-Rider, an Oahu chieftess who skillfully rode the biggest and roughest of waves, far from shore. I am no Mamala. Still, twice I manage to maintain my balance sufficiently to ride a baby wave all the way to the shore, with no fancy turns, but no spills, either. I’m relying on hydrodynamic forces to work their magic as water moves up the front of a wave, collides with my surfboard, and is deflected around it. If I were moving faster, there would have been a telltale spray in my wake. A good surfer—defined as “not me”—is skilled enough to keep just ahead of the break, turning up and down the face of the wave all the way into shore.
Ultimately, surfers are dancing with the waves, exploiting the same basic principles as roller coasters. They gain kinetic energy by dropping down the face of the wave and exploiting gravity, although they trade off potential energy as they lose altitude. But then they use that accumulated kinetic energy to ride back up the face of the wave to the crest, and the whole process begins all over again. Ideally, at the end of the ride, a good surfer will shift his or her weight to the back of the board, causing it to drop and the nose to rise, effectively applying “brakes.” The wave rolls past, and the surfer is ready to drop back down onto the board and paddle out to catch another wave. Alternatively, you can try my cunning strategy of wiping out before I reach the shore.
That is the basic physics of surfing; where is the calculus? One simple example can be found in the knotty problem of catching that initial wave: so simple in concept, so tricky to execute. Recall that I need to reach a specific velocity—the same velocity as the traveling wave—at a specific time and place: the point at which the incoming wave reaches me bobbing in the water on my borrowed surfboard. A baseball outfielder merely has to be in the right place (position) at the right time; a surfer must match velocity as well. From a calculus standpoint, it’s a matter of integrating acceleration over time in order to hit the matching velocity at precisely the moment the wave reaches me. Technically, we have to take two separate integrals—one to determine velocity by integrating over acceleration, and another to determine position by integrating over velocity—to ensure I catch that incoming wave.
“Really, it’s amazing that anyone can possibly surf at all,” Sean observes as he ponders the mathematical realities of the sport. And yet excellent surfers abound, every last one of them a master at making that intricate calculation within seconds, many without consciously realizing they are doing so. The human brain is capable of performing amazing feats of calculation, although this is as much a learned as an innate ability. When it comes to sports and motor skills—and calculus, for that matter—practice makes perfect.
WHAT’S YOUR SINE?
Surfing entered the international mainstream in 1959 when the film Gidget hit the silver screen, coining the term “the Big Kahuna” to describe the best surfer on the beach. Traditionally, a kahuna was a local priest or magician who would intone special chants to christen new surfboards and bring promising surf conditions. In reality, the size and shape of ocean waves depends not on mystic chants, but on three variables: wind speed, the “fetch” (the distance of open water the wind has been blowing over to form the waves), and how long the wind has been blowing