PHY 241 Net Research Project for 3/1/99

Physics on a Rollercoaster

Perhaps the first rollercoaster riders appeared in the 13^th century when Russian thrill seekers rode down ice covered wooden slides. But it was the French in the 1700's that built the first "roller" coasters, those that rode on wheels. Although the popularity of rollercoasters has gone up and down during its long history, there is presently a large enough group of enthusiasts to maintain a thriving industry that pushes the technological limits of what the human body and mind can withstand.

We've already studied the basic physics of a rollercoaster. The cars are raised to some starting height by a lift. The cars themselves do not have engines. Once at the top, gravity is the only source of energy. This makes sense both economically and for safety. The cars should not require any additional energy if the engineers have done their job. The kinetic energy at the any point will be equal to the change in gravitational potential energy from the top, minus energy lost to friction and air resistance. While minimizing friction is an important consideration, the speed at any point is primarily determined by how far you have "fallen" from the initial height. If you want more speed, start off higher. How does over 225 feet sound? That's how far the Steel Phantom (shown to the right), located in Kennywood, Pennsylvania drops at one point. It reaches speeds of over 80 mph. Click on the picture if you would like see it in more detail. If the rollercoaster track were nothing more than a straight incline, the physics would be very simple. But a truly exciting ride involves more than just speed. It should have undulations, banked curves, and loops.

Even if you've never ridden a rollercoaster, you have still probably experienced the effects of an undulation in a coaster track. Whenever you pass over a rise in your car, you might feel "light". And when you travel through a dip, you might feel heavy. It's a simple matter of Newton's Second Law (F = ma). In both cases, you have centripetal acceleration toward the center of curvature of the path you are following. The net sum of the normal force from your car seat and your weight must cause this acceleration. Over a rise, the centripetal acceleration is downward and the force of the seat must be less than your weight. At the bottom of a dip, precisely the opposite is true.

The task of the rollercoaster engineer is to design the track shape to maximize these effects within safety limits. At the top of an undulation, the limit to the acceleration (without strapping customers into their seat) is what can be supplied by gravity . If you design the track such that gravity is the only force acting act the top, the rider is in freefall! Many rollercoasters do exactly that. And a few try to stretch out the effect using a parabolic shape rise, the path taken by an object in freefall. In the 1920's, the "Cannon Coaster" at Coney Island was based on this idea. However, it had a very interesting twist that unfortunately never quite worked out.

And then there's the loop. This is undoubtedly the greatest innovation for scaring the fungi out of riders. At the top of the loop, the riders are upside down. The speed must be equal to or greater than that required for gravity alone to provide the centripetal acceleration. Anything less and there will be the danger of the customers falling out of the car. This is precisely the problem we solved in class with the pendulum swinging about the peg such that tension remained in the string.

There is another consideration. If you have a big exciting loop, then there is a problem with a simple circular track. If the speed at the top is high enough to keep the cars on the track, then the speed at the bottom may be so great that the centripetal acceleration exceeds what can be tolerated by the riders. The problem was solved some years ago by two engineers when they designed the specially shaped clothoid loop.

And we haven't discussed the mechanical engineering that goes into designing cars that can withstand the stresses and strains of a rollercoaster ride. Check out Iain Hendry's page for a more detailed discussion of both the physics and mechanical engineering of coasters. If you've ridden a rollercoaster and can't wait to do it again, or the very idea of riding the Steel Phantom excites you, then you may be a coaster maniac. Check out the World of Coasters. It will connect you with other insane people.

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