Laws of Physics Involved in the Designing and Working of a Rollercoaster: Newton's Laws of Motion

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Introduction

Since its first opening in Paris on July 8, 1817, the rollercoaster remains to be the prime attraction of every modern theme park. The rollercoaster ride focuses on exposing the riders to a variety of magnitudes of forces, at different times, without compromising on the health and safety of the riders. To give maximum enjoyment whilst ensuring safety, manufacturers have to study and understand the different forces and conditions riders are exposed to while in the ride. This paper will focus on explaining the various laws of physics involved in the designing and working of a rollercoaster. I will divide a modern-day rollercoaster into 6 sections and discuss which law(s) is applied in each;

Lift hill
Descent
Loop-de-loop/ Clothoid loop
Progressive hills
Banking
Breaking

This then gives an idea of how the rollercoaster has utilized the various laws of physics and gives room to explore ways in which the rollercoaster can use the laws more efficiently to make the rides better.

Figure 1; a model rollercoaster

Before discussing the lift hill, which is the most common way of starting rollercoasters, new ideas have come up and have been implemented in tracks;

Catapult launch

A catapult launch involves use of a large weight being dropped from a certain height to give a resultant force to start the coaster. This applies Newton’s Third Law of Motion which states that for every action force, there is a reaction force that is equal in magnitude and opposite in direction. The coaster is connected to the weight and therefore, as the weight falls on one side, the rollercoaster starts accelerating on the other. (Coasterbot)

Linear Induction Motors (LIMs) and Linear Synchronous Motors (LSMs)

These methods utilize Lenz’s law that states the current induced in a circuit due to change or motion in a magnetic field is so directed as to oppose the change in flux and to exert a mechanical force opposing the motion.

LIMs utilize electric motors that create opposing magnetic fields to propel a conductive or magnetic plate connected to the train. LSMs utilize electric motors that turn on and off as plates containing alternating pole magnets are propelled through a track.

A space is left between 2 fins placed on the track to allow for a fin found on the train to pass through the middle. See figure 2.

Figure 2

The fin on the train opposes the charge on the magnets of the track and therefore, eddy currents are passed through magnets found on the side of the track. This then creates a magnetic field that makes the rollercoaster take off and commence its journey. (Eddy currents are the currents produced by the fin moving between the magnets).

Lift hill

Figure 3; a lift hill

A lift hill is the most common way of starting a rollercoaster ride. It is a transport device that is used to pull a train up a hill on the rollercoaster track. The hill has chain dogs, which act as anti-rollback mechanisms to prevent the trains from going backwards. See figure 4.

Figure 4; anti-rollback system

There are different methods of lifting a train through the first hill; electric, cable or tire. I’ll discuss the drive tire.

A drive tire/ kicker wheel/friction wheel is a motorized wheel that alters or sustains the speed of a train through friction between the surface of the wheel and the underside of the ride vehicle. When single, they are oriented vertically but when in pairs, they are oriented horizontally. (How stuff works)

Eventually, the train is lifted to a certain height to generate enough energy, in form of gravitational potential energy, to power the train throughout the track. This is essential because the train has no engine or powering mechanism. The potential energy (P.E) is a product of the mass of the train (m), the gravitational pull on the earth (g) and perpendicular distance from the ground (h), as in, P.E=mgh

Following the lift, regardless of how the lift is obtained, the train travels under its own momentum. This follows Newton’s first law of motion which states that an object will remain in its state of rest or uniform motion unless acted upon by an external force. This inertial force is what keeps the train going till the end of the track. It is also important to note that any hills after the lift hill are not as high. This is because energy is lost due to friction on the track, air resistance thermal energy and sound produced along the way. (Coasterpedia)

Figure 5 showing reduced hill size

Descent

The Law of conservation of energy states that energy can neither be created nor destroyed; but only converted into other forms. In this case, gravitational potential energy is gained and is at a maximum when at the top of the lift hill. A sharp descent follows and therefore, the potential energy is converted into kinetic energy. Kinetic energy is half the product of the total mass of the train and riders (m) and the square of the velocity (v) of the train (K.E=1/2mv2). Maximum kinetic energy is reached at the bottom of the hill.

Newton’s law of gravitational pull also states that every particle attracts every other particle in the universe with a force which is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. The earth’s gravitational force induces an acceleration on the train and therefore, the train achieves maximum velocity at the bottom of the hill.

Figure 4 shows how high the track is in order to generate enough energy.

Figure 6 showing descent after a lift hill

Loop de loop

Figure 7 showing a clothoid loop

After achieving maximum velocity, the train may arrive at a loop. The train comes with a forward velocity and goes up the curve creating centripetal acceleration. This creates a force directed towards the center of the circular loop called centripetal force. Because of Newton’s third law of motion, which states that for every action, there is an equal and opposite reaction, centripetal force directed to the center (action) is balanced by a centrifugal force that is directed outwards (reaction). Inertia (Newton’s first law of motion) also comes into play (acting outward) and therefore the seat of the train creates an equal and opposite reaction force. One wouldn’t need a safety belt to keep them in their seat while traveling through a loop as inertia would be enough to keep them in their sit.

For the train to complete the circular loop, the centripetal acceleration (a) of the train must be greater than or equal to gravity (g) as in, a>g. To achieve this, the circular loop is made to have a smaller radius at the top and a wider radius at the bottom. This is referred to as a Clothoid loop.

Figure 8 showing different radii in the clothoid loop

With centripetal acceleration(a) being inversely proportional to the radius (r) of the loop (a ∝1/r) the train doesn’t have to achieve very high speeds to complete the loop. Furthermore, on the way down the loop, the wider radius at the bottom reduces the centripetal acceleration thus exposing the riders to less forces.

Figure 9 showing g-forces in a clothoid loop

Progressive Hills

Progressive hills

Newton’s second law of motion concludes that force equals the product of mass of the object by the acceleration of the same object(F=ma). In this case we’ll refer to the force as G-forces/ Gs.

Hills and valleys are a good way of imposing Gs to riders. Positive Gs are directed downwards while negative Gs are directed upwards. At the start of the hill, the G-forces are greater than 1 (G>1). This means the riders feel heavier than usual (2g/ 3g meaning twice/thrice their weight). At the top of the hill, inertia makes the body want to continue in a straight path upwards; the G forces are less than 1 (G

Banking

When rollercoaster train navigates a turn and is therefore accelerating round it, a lateral G force is created. Newton’s first law of motion states that an object will remain in its state of rest or uniform motion unless acted upon by an external force. This phenomenon is called inertia and, if strong enough, can cause serious injury to the riders as a result of being pushed to the side opposite to the direction of the turn. To reduce the effect of the lateral G force, manufacturers bank the turns so that the lateral Gs are converted to positive Gs or negative Gs. (Worldsciencefestival)

Banking of a rollercoaster

Breaking

To bring the train to a stop, magnets on the underside of the train induce eddy currents in the braking fins, thus giving a steady rise in the breaking force and converting all the kinetic energy, absorbed by the brakes, into thermal energy. Eventually the train comes to a complete stop, with initial speed notwithstanding. This is because the faster the train, the stronger the currents produced and hence the stronger the braking force applied. It’s important note that not all braking fins are activated immediately the train enters the braking zone. The fins are activated one by one as the train travels past the first fin. This prevents sudden braking of the train that would cause potential injury. (physics.gu.se)

Conclusion

Summary of energy changes on the track

We can conclude that mainly Newton’s laws of motion come into play in the design of a basic rollercoaster. Research continues to be done to make the ride better and better. It may be important to note that the human body is not able to feel velocity; only change in it (acceleration), and therefore, if the rollercoaster utilizes this fact, it is what may give it an edge over other rollercoasters.

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Laws of Physics Involved in the Designing and Working of a Rollercoaster: Newton’s Laws of Motion

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