Loops and Turns

When we think of coasters we usually think about them converting potential energy into kinetic energy, but modern coasters do not move in simple straight lines. Turns and loops bring up new questions of physics because they alter the forward momemtum that results from dropping the coaster down the first hill.

The track exerts forces that directs the momemtum of the train though gravity would pull it down to the ground and inertia would keep it moving in a straight line. That force is then transfered to the coaster as it moves along that part of the track and to the passenger through the seat of the train. The calculated force exerted on the passenger is referred to as the "seat force."

Remembering Newton's law--an object in motion will continue in motion along a straight line, you realize that passengers going have momentum pushing them straight forward. On a level turn, passengers are moving forward as the train turns...and as a result, they move to the outer side of the car. The side of the car then exerts the force that takes them through the turn. Coaster designers realized that they could make a ride more comfortable (passengers not squishing each other) and safer by banking the curves. By banking the curve, most of the force that pushes the passengers through the curve comes from the seat rather than the side of the train. Comparison of Forces in Turns

On a looping coaster, the general rules of centripetal force are in operation because the train is making a turn at every point during the loop--- remember Newton's first law that an object in motion will stay in motion unless another unbalanced force acts on it. The force that makes the train turn through the loop is centripetal force. The formula for the amount of centripetal force needed to move an object in a circular route is:

mass x velocity squared divided by the radius of
the circle.

Passengers feel "G FORCES" as they change their direction on rollercoasters. When the amount of force exerted by the seat to keep you up equals the amount of gravitational force pulling you down, you experience "1G"--the normal gravitational pull. If it takes more than that amount, (typically because you are moving upward) you can experience greater G forces. If you are not being pushed by upward by the seat, (typically because you are moving downward) you can experience less than "1G." "Pulling negative g's" is what happens when you are launched on a parabolic trajectory as you go over a hill and the train begins its descent attached to the track. For a brief period, you are not sitting on the seat. Eventually, you are stopped from your parabolic course by the lap bar and are pulled along with train. (The death on Collosus was caused because the rider's lap bar didn't work and she continued the parabolic course and was thrown from the train.)

To complete a vertical loop, a train must enter the loop with sufficient kinetic energy to reach the top of the loop and still be moving. It then has converted kinetic energy into potential energy and starts down the other side of the loop, and accelerates out of the loop. When the train starts into the loop, the track supplies the force to make the train turn (the seat force). As the train comes down the hill to enter the loop, it's gravitational force and momentum are pushing it toward the ground while the seat force is pushing upward. How much seat force it takes to change the direction of the train is determined by the train's weight and speed (mass X velocity). The more seat force it takes to start the loop, the more "G FORCES" the passengers will feel.

As the train starts the loop, gravity and momentum are pulling the train out of the loop, so the structure of the track provides the "seat force" that moves the train through the loop--the centripetal force. On it's upward climb, the train reaches a point where gravity is no longer pulling it out of the loop and thereafter it is acting as part of the centripetal force pulling the train toward the center of the circle. It is from this point until the top of the loop that it is important that the train has enough momentum to counteract the forces pulling it toward the center of the loop. That is a unique aspect of centripetal force on a vertical axis--there must be enough outward momentum to counteract the increase in centripetal force that occurs in the upper portion of the loop.

Once the train reaches the top, potential energy is again converted to kinetic energy and the train accelerates as it travels down the other side of the loop.

Rarely are the loops found on rollercoasters circular. This is because a rollercoaster gets its energy from a single lift hill and thereafter relies on its successive conversions of potential energy to kinetic energy and back. Because there is no lift motor in the loop itself, the train must be entering the loop with sufficient energy to make it through.

Coaster designers use what is called a clothoid loop because the added upward distance on a circular loop would slow the train, requiring greater speeds at the start of the loop and subjecting passengers to greater "G's". Typically, a passenger would have to experience 6g's at the beginning of a circular loop if the train would have enough speed to make it to the top. Because we are only comfortable at something less than 4g's, designers developed the clothoid loop. The design has a large arc at the bottom and a tight arc at the top. The large arc at the bottom means that the amount of "seat force" needed at any single point to push the train upward is less than it would be in a tighter curve. The small arc at the top means that there is less time where both gravity and "seat force" are pushing the train toward the center of the circle which is the period in the loop where the train must have the most outward momentum.

Because the passenger is being pushed into his/her seat as they go through the loops, the brain is fooled by the inversion. It interprets the pressure in the seat as indication he/she is in an upright position. The visual image still gives the passenger the awareness of the loop without the fear of falling. In fact, because the you are being pushed into the seat, you could ride through the loops without the shoulder straps--the straps are added for psychological security.

Next time you are on a looping coaster, use the accelerometer to measure your "g's" at the bottom of the loop and again at the top. Are the laws of physics being obeyed?

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