# Roller Coaster Project

## Contents

## Project Members

## Project Motivation

## Project Description

For our final project, we decided to design a basic loop roller coaster using SolidWorks. We first created a sketch of a basic clothiod loop, and used conservation of energy to determine what height we would need to start the rollercoaster at to ensure that the loop would cleared.

## Equipment

SolidWorks

## Timeline

11/17: We are going to sketch the roller coaster on paper and using the physics principle of conservation of energy, we will determine the various dimensions of the roller coaster

-height of the top of the roller coaster -distance between the top and the beginning of the loop -the height of the loop -the radius of the circles that create the clothoid loop

11/24: We are going to begin sketching on SolidWorks

12/1: Finish designing the roller coaster on SolidWorks

12/8: Animate the roller coaster and work out any kinks to ensure "safety" of the the ride

## Report

**Simple Concepts in the Engineering of a Roller Coaster**

The objective of this research paper is to explain some of the simple mechanics involved in roller coasters. The starting point of the paper will logically be how to start a massive object like a roller coaster. The many parts of the ride itself will be the next point to be examined. The paper will finish by explaining some of the simple ways to stop a roller coaster.

The most popular method of starting a roller coaster is the chain lift method. In this method long chains run up the hill underneath the track. The chain is attached to a gear, which is then able to crank the roller coaster up the hill. The coaster has hooks on it, which attach to the chain, and release the coaster at the peak of the hill.

The newer method of starting roller coasters is called catapult-launch lift system. The idea behind this type of system is that it is given enough kinetic energy at the beginning of the ride to make it up the initial hill. The different types of catapult-launch lifts are either electromagnetic coasters or a wheel system. The electromagnetic coaster has become the most popular of the new designs. It builds two magnetic fields by having one magnet on the coaster and one on the rail. The motor pulls the train along this path at a high velocity. This method has become the favorite type for many engineers because it creates high speeds, it is more precise, it is very durable, and it is easy to control. The wheel method consists of a row of wheels above and below the rail, which rotate and push the train forward.

For any roller coaster, acceleration is an important factor to consider. When a roller coaster experiences a change in its speed, it is said to be accelerating. To have maximum enjoyment for the rider, the roller coaster must have a large acceleration. Also, if we are constructing a roller coaster with loops, centripetal acceleration must be taken into account. The centripetal acceleration of the car is effected by its velocity and the radius of the curve. A smaller radius would result in a large centripetal acceleration and vice-versa. The centripetal acceleration is represented by the equation: Ac=(V^2)/r.

In addition, one must consider the centripetal force, which is linked to the centripetal acceleration, and is represented by the equation: Fc=mAc=m(V^2)/r. A larger radius will result in a smaller centripetal force and vice-versa. A large mass and acceleration will result in a large force. This is why it is practical to small loops if you are concerned only about the speed and the enjoyment factor.

A simple design that includes the factors of a “model” roller coaster. This design maximizes both safety and the enjoyment factors. Medium sized hills from about fifty to sixty meters tall, because if the hills are too tall, then the roller coaster would not have enough energy to overcome them, assuming that it starts from rest. It should have gentle slopes based on the principles of projectile motion. The loops in the coaster should be elliptical, i.e. clothoid. If circular loops were used, then the acceleration of the car would be changing and there is a loss of kinetic energy as this car is climbing up and around the circular loop. The car would also experience a “jerk” which would pose a safety concern for its riders. The design of a clothoid loop is not only more enjoyable for the riders, but it is also safer for them.

The last part of the roller coaster to examine is the braking system. In most roller coasters, the brakes are built into the track, not the roller coaster itself. The braking system consists of a series of clamps that are positioned at the end of the track. These clamps are operated by a hydraulic system that closes the clamps causing friction, which slows the roller coaster down to a stop. The overall speed of the roller coaster towards the end of the track will determine how far away from the end the clamps will have to be activated to start causing friction.