The Most Beautiful Roller Coaster: Boulder Dash

(Natalie wrote this paper when she was in 6th grade)

Gravitational forces, also known as g forces, are the effect gravity (the force that pushes matter down) has on you when you move against it.  Normally, you experience one g on earth.   To look at how g forces work, it is interesting to look at how roller coasters work.  To understand how they work, it is important to keep in mind the Laws of Motion that Issac Newton discovered.  He stated that Every object on earth persists in a state of rest or uniform motion unless it is compelled into motion by forces impressed on it.   He defined force as equal to the change in momentum per change in time, seen or experienced as motion.   He also said that for every action, or motion, there is an equal and opposite reaction.  (Issac Newton’s Laws of Motion)

For instance, imagine that you are on a roller coaster.  It is a quick one, and as it starts its assent up its first climb, you momentarily feel your stomach fly into your chest and your body being pushed down.  Speed is only one cause of this effect.  The others are increased g forces.  If you were in a slow roller coaster, your stomach would stay where it was and you wouldn’t feel yourself being pushed down as much, but only because with less speed, you experience less g’s.  This is why.

You are back in that fast roller coaster.  When the coaster lifts off the ground, you experience the build-up, or acceleration of the roller coaster reaching its maximum speed.  This is when you feel yourself being pushed down, in other words experiencing increased g forces.  You feel these because the coaster is fighting against gravity; gravity is pushing you down, but the roller coaster is pushing you insistently up.  Once the roller coaster reaches its maximum speed you would feel the normal amount of g’s you feel on Earth: one.

When the roller coaster slows down at the top of the climb, you will feel as if you are floating for a moment.  Here, you are experiencing decreased g forces and inertia, the effect of the amount of Kinetic Energy that you have stored inside unconsciously.  Kinetic Energy is a type of energy an object gains from its mass and movement.  You have been storing this Kinetic Energy from moving upward rapidly, and even after the coaster slows, you still have a bit of this energy, which gives the effect of floating, which is inertia and decreased g forces.

Say there are two other people in the roller coaster car with you.  One of them has a greater mass than you, and the other has a lesser mass than you.  The person with the greater mass will experience the floating sensation, or inertia, for slightly longer than you because they have stored more Kinetic Energy.  The person with a lesser mass will feel inertia for a shorter period of time because they have stored less Kinetic Energy.

In a slower roller coaster you wouldn’t feel this or the acceleration, because the maximum speed is slower, so the acceleration is not as fast, and there is not much Kinetic Energy for you to store.

There is actually a limit on the amount of g’s a human is able to experience, as they can be fatal.  The way to make sure that someone does not experience 3.5 (the limit) g’s is to make sure the acceleration of something is not too great.  For instance, astronauts experience multiple g’s when a rocket upward after takeoff, or when stunt pilots do special maneuvers.

All right, let’s get back to Earth and the roller coaster.  Surprisingly, g forces actually make for a more thrilling ride.  Mixed with drops and banks and loops they add to the rush of excitement one feels while riding a roller coaster.  Some coasters are more thrilling than others, though (thrilling doesn’t necessarily mean fun, it can mean absolutely horrifying).

I am going to describe the roller coaster that I found the most inspiring.  Boulder Dash, the first roller coaster to be built atop a mountain, has been ranked as one of the top ten wooden roller coasters in the yearly Golden Ticket awards since 2001, the year after it was built.  First, the coaster climbs up the side of the mountain, and then disappears into the trees for some of the 2 minute 30 second ride.  Much of the roller coaster is hidden from view by the forest through which one rides.  Boulder Dash takes its first drop of 115 feet in the forest.  The tallest part of the coaster is 50 feet and its length is 4,752 feet (almost a mile).

Using a math equation, you can actually figure out how much force a body feels if you know the number of g’s and the weight of the person.  If an one hundred pound astronaut experiences 3 g’s, she will weight 300 pounds.

Another key part of a roller coaster is centrifugal force.  Centrifugal force has much to do with Newton’s first law of motion, which states that, “Every object persists in its state of rest or uniform motion in a straight line unless it is compelled to change that state by forces impressed on it.”  This means that if you, for example, had a marble sitting still on the floor, it’s not going to move unless a force, like your hand or gravity, interferes with or moves it.  This law also states that if the marble is moved, it will move in a perfectly straight line unless something interferes with it.

So on a roller coaster with a bank, a turn, it is this centrifugal force that is at work, making the rollercoaster maintain its course as long as it is moving at the proper speed and its mass (weight) keeps it attached to the rails.  Speed and mass of the cars is as important as the design of the rollercoaster for both a fun ride and safety.

In A Mathematician’s Apology, G.H. Hardy wrote:  “The mathematician’s patterns, like the painter’s or the poet’s must be beautiful; the ideas, like the colors or the words must fit together in a harmonious way.  Beauty is the first test:  there is no permanent place in this world for ugly mathematics.

Larry Bill, Principal Engineer on Boulder Dash, is part of a wooden roller coaster design company called The Gravity Group.  When a roller coaster designer creates something like Boulder Dash, he or she has combined math and science and art.


Newton’s Laws of Motion,

The World Treasury of Physics, Astronomy and Mathematics, Edited by Timothy Ferris, Little Brown and Company, 1991.

The Universal Book of Mathematics:  From Abracadabra to Zeno’s Paradoxes by David Darling, 2004.  (about Larry Bill)

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