The Calculus Diaries - Jennifer Ouellette [42]
The riders can spin their teacups as fast as they want by turning the metal wheel at the center of the cup, applying a torque to increase the teacup’s angular momentum, and hence the rate of spin. As Sean and I strain mightily to spin our teacup as fast as possible, I notice something intriguing. Every now and then we achieve an especially sharp, fast rotation, whereas at other points, no matter how hard we pull that metal wheel, we can’t achieve much rotation at all. Sean explains that this is because of dueling vectors. Sometimes the vectors work against each other, pulling in different directions and canceling each other out, to varying degrees. At other times in the rotation, they add together, all pulling in the same direction, so we spin that much faster.
Space Mountain—Tomorrowland’s main attraction—provides us with the quintessential example of a calculus problem involving vectors. When Walt Disney first designed Tomorrow-land, he noted that it would be out of date almost immediately. By twenty-first-century standards, the “future” it envisions is downright quaint, harking back to a more innocent era. Tomorrowland didn’t even have a roller coaster until Space Mountain opened in May 1977, after the original ride proved so popular at Disney World. Disney didn’t live to see it completed. Space Mountain took two years to build and cost upwards of $20 million, and the park set an attendance record the first weekend the ride opened. Six of the original seven Project Mercury astronauts were on hand for its inauguration.27
In the 1968 film 2001: A Space Odyssey, astronaut Dave Bowman (played by Keir Dullea) walks down a long white circular tunnel to the space ship that will carry him on his mysterious mission into deep space. It’s difficult not to recall Kubrick’s masterpiece while waiting in the long line for Space Mountain. The ride’s interior is eerily similar in design. We follow winding metal ramps down into the bowels of the coaster, encountering the occasional video screen showing famous astronauts talking about their missions. Finally, we reach the front of the line and take a seat inside our little rocket-shaped car.
We rise to the top of first one, then another lift hill, winding through a passage that features glowing red bars that seem to be rotating. At the top of the third and final lift hill, our rocket pauses briefly as we gaze out into the vast darkness of “space”—there appear to be thousands of stars and galaxies, when in fact it is simply a clever effect achieved with mirror balls scattered throughout the ride’s interior. A voice announces, “You are go for launch,” and pure gravity takes over as our rocket begins its rapid descent, accelerating through the remainder of the track. The sensation is enhanced by gusts of wind from strategically placed air vents as we careen and lurch through the darkness. When it is time for our “reentry,” we decelerate and return to the docking station.
For all its futuristic trappings, Space Mountain is a classic roller coaster, from a physics standpoint.28 Roller coasters operate on inertia, gravity, and acceleration—and the greatest of these is gravity. Our rocket builds up a large reservoir of potential energy while being towed up those three initial lift hills. The higher we rise, the greater the distance gravity must pull it back down, and the greater the resulting speeds. As our rocket starts down the first hill, all that accumulated potential energy is converted into kinetic energy and our car speeds up, building up enough kinetic energy by the time it reaches the bottom to overcome