# How the Laws of Physics Apply to the Design and Action of a Roller Coaster

## Introduction

This study aims at investigating how the laws of physics apply to the design and action of a roller coaster by first giving a concise definition of a roller coaster and the types before expounding on the parts of the coaster and track that employ these laws. It also explains further why some materials and designs are used, there advantages and disadvantages, and the exhaustive calculations are done giving birth to the safe, thrilling, and energy-efficient rides we have today. The goal of this study is to gain a deeper perspective on the functioning of coasters so as to suggest more efficient, comfortable models. A roller coaster is a perfect example of physics at work as each track and train is as a result of careful analysis, calculation, evaluation, and cross-examining.

### 1.1. What is a roller coaster?

A roller coaster is an elevated rail track with curves and drops on which a train rolls. It is mostly found in amusement parks where families and friends go to experience the adrenaline rush.

### 1.2. Types of roller coasters

Currently, there are mainly two types of roller coasters:

• Wooden roller coasters.
• Steel roller coasters.

## 2. Laws of physics in relation to their design

### 2.1. General overview

A clear knowledge on all the forces acting on the train would help determine the size, design, and a number of support beams to be used. (How Products are Made). This is done by the use of Newton’s third law of motion for every action force, there is an equal and opposite reaction as the weight of the track when on the support beam should be greater or equal to the reaction force exerted by the support beams.

### 2.2. Magnetism in the design

While talking about the laws of physics in roller coasters, you won’t fail to mention Faraday’s law of induction which states that in a closed coil circuit, a change in magnetic flux would cause e.m.f to be induced in the coil. This and Lorentz force-force particles experience in the circuit due to electromagnetic fields are applied in the Linear Synchronous Motor used to power the coasters at the start. When A.C.'s current is drawn to the motor, a rotating magnetic field is created. Current is induced in the ‘squirrel bar cage’ which finally leads to the rotor turning and generating e.m.f. This powers a motor that turns the winch, which pulls the cable attached to the catch-car found below the train causing the launching of the train at the start.

Lenz's law, which states that when e.m.f. is generated by a change in magnetic flux, the polarity of the induced e.m.f generates a current whose magnetic field is in a direction opposing the change producing it, comes to effect when stopping the coaster at the end of the track as discussed later.

## 3. Laws of physics in relation to their action.

### 3.1. The Start and first drop.

#### 3.1.1. Pascal’s Principle

When the ride starts, an electric winch may wind the train to the top of the first hill or a hydraulic system may catapult it. Through Pascal’s Principle-pressure in an enclosed fluid is transmitted equally in all directions provided that the fluid is incompressible- hydraulic fluid is pumped into the hydraulic accumulator and it is separated from nitrogen gas by a piston. Nitrogen gas is compressed by the piston hence increasing its pressure. At high pressure, the valve is forced open by the hydraulic fluid and it rushes out, powers a motor that pulls a cable in the winch catapulting the train.

Electromagnets may also be used where they are aligned at the sides of the track and train, through the law of magnetic attraction, the north pole on the train and south poles on the track would attract when A.C. current is drawn causing the train to move. The current would then be passed in loops so as to cause the train to move continuously and faster.

#### 3.1.2. Law of Conservation of energy

The law of conservation of energy explains that energy can neither be destroyed nor created, it can only be converted from one form to another. Therefore, at the peak of the hill, the maximum potential energy is converted to kinetic energy as the train moves down the hill due to free fall due to gravity. This is called ‘airtime’. The track channels the force of gravity controlling the way the train falls. The energy constantly changes from kinetic to potential as shown below in the next hills.

#### 3.1.3. Newton’s First law of motion

Newton’s first law of motion – An object remains stationary or in motion with the same speed and direction unless acted upon by another force, takes place here thus the train continues accelerating. During this period of free fall, the riders experience a feeling of weightlessness since the force of gravity acting on their bodies is less than 9.81N/kg. Inertia force tends to keep the riders at the crest of the hill, hence, riders momentarily slightly rise from their seats at this point. At the bottom of the first hill, the kinetic energy is maximum and the potential energy minimum. Riders experience forces greater than 9.81N/kg hence pushed to their seats.

### 3.2. The second drop or loops.

The coaster then rises up another hill obeying Newton’s first law of motion. The second hill is usually lower compared to the first since the train’s acceleration is lower due to friction and wind force opposing the motion. Riders here have a second ‘airtime’ experience. Some roller coasters may have a second hill while others have loops shaped like a tear-drop so as to lower the force the riders experience to safe levels.

#### 3.2.1. Newton’s third law of motion

For every action, there is an equal and opposite reaction. Therefore when the train enters the loop, there is a reaction force, that is, centripetal force. The clothoid loop (Spiral of Archimedes), is much safer and subjects the train and riders to less stress. A smaller radius at the top equals a higher centripetal force to keep the riders and the train in the loop at safer velocities (figure 6 shows the formulae that prove this). The increased radius at the bottom reduces the centripetal force acting on the riders to safer levels (below 5×9.81N/Kg).

#### 3.2.2. Banking of the track (Circular Motion)

The Formula Rossa in Abu Dhabi, U.A.E travels at a speed of 240km/h. These speeds would not allow it to negotiate corners easily as the lateral force acting on the train would cause it to derail. To fix this, the track is inclined inwards, hence, the weight acting on the riders would contribute to the centripetal force keeping them in the circle. The equation used to produce a perfectly banked curve is

tan⁡θ=v^2/rg

### 3.3. The final part of the ride

After all the twists, lifts, and turns; The ride finally has to come to an end. After completing all the hills and turns, automatic brakes are applied. Through Newton’s first law, the train comes to a stop. Lenz’s law is applied when metal fins on the train are passed through a magnetic field created by rows of permanent magnets. This induces an eddy current that opposes the change, hence, the train will slow down because the kinetic energy is converted to heat by the eddy current.

## 4. Conclusion

From wooden to steel to polyurethane load wheels, it’s safe to conclude that technology is constantly evolving for smoother rides. Lenz’s law, Newton’s laws of motion, Faraday’s law, and the law of attraction are well in use in roller coasters. With the understanding on roller coasters gained from these investigations, the use of electromagnets should be put into consideration instead of load wheels which wear after some time. The coasters would then float on the track eliminating friction. V.R (Virtual Reality) coasters are safer and still pack in the thrill needed.

01 August 2022

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