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The Calculus Diaries - Jennifer Ouellette [89]

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hostage for the return of the boat—a common leveraging practice in negotiations by British mariners—but were rebuffed. Tensions mounted, the British opened fire, and a chief named Kalimu was killed. The enraged Hawaiians attacked in revenge, and when the British stopped firing to reload their muskets, they were driven to the water’s edge at Kealakekua Bay. Cook was stabbed repeatedly with an iron dagger his crew had traded to the natives, and his body was dragged off and disemboweled, the flesh stripped from the bones. As barbaric as it sounds, it was meant as a great honor. Such were the funerary rites for the remains of a deceased high priest.

Despite the hostilities, when Lieutenant James King finally recorded the details of that ill-fated voyage in the late Captain Cook’s journals, he included not just an account of the fighting, but also of the more joyous aspects of Hawaiian culture—notably surfing, “a diversion that is common upon the water, where there is a very great sea, and surf breaking on the shore. . . . They seem to feel a great pleasure in the motion which this exercise gives.”

There is very little record of how surfing came to the Hawaiian islands, but by the time of Cook’s visit, surfing was deeply embedded into the culture, with myths and legends about surfing heroes (and heroines) and an annual celebration called Makahiki in which surfing played a central role in honoring Lono. There were even separate reefs and beaches for royalty and commoners, a stratification that still exists in some form today: There are surf sites that cater to tourists and more-hidden local spots favored by residents.

King couldn’t help admiring the skill of those eighteenth-century Hawaiians as they rode the waves, and for good reason. La famille Garces makes it look easy, but surfing is one of those activities that is quite straightforward in concept yet difficult to master—as Twain found out over a century ago. Following Garces’ instructions, paddle a decent way out from shore, turn the board around, and wait for a promising wave. At this point, the primary physical mechanisms at work are gravity and buoyancy. (Think Archimedes and his eureka moment.) There is no acceleration and thus no net force. There is just me, on my surfboard, bobbing gently in the ocean, waiting for the perfect wave.

Whenever he spots a promising wave, Garces calls out and urges me to paddle furiously toward the shore. The trick is to accelerate to match the speed of an incoming wave just as it arrives at my position in order to “catch” it; otherwise it just shoots right past, leaving me bobbing forlornly behind on my surfboard, watching everyone else have all the fun. This happens far more often than I care to admit, due in part to my lack of upper body strength. But every now and then, I succeed and feel that telltale tug as the wave pulls me with it. At least that’s what it feels like; from a physics standpoint, the moving wave pushes my surfboard forward, accelerating me to match its speed. At that point, I must paddle with wild abandon to ensure I end up “riding” the wave.

The first time this happens, I am so exhilarated that I throw myself off balance and promptly take a nosedive into the salty surf—a common occurrence for first-time surfers. A moving wave is literally a slippery slope, with constantly shifting forces acting on the surfboard—not just gravity and buoyancy at this point, but also hydrodynamic forces (the force exerted by a moving fluid) that push the board forward, along with a certain amount of friction or drag along the bottom of the board. You’ve got to keep shifting your weight back and forth to stay near the board’s center of mass as you ride the wave to keep the proper balance of forces: between the downward force of gravity and the upward buoyant force. When these forces are out of balance, the board torques, or twists. If the nose is too low, you pitch forward; if you shift too far back and the nose is too high, you lose your momentum, the board stops, and you pitch into the water. In this case, the nose dipped too low,

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