Year 12 Rooks Heath Physics students at Thorpe Park
You might think that physics is all about boring things like electricity but it is important for fun things like animations and thrill rides such as those at Thorpe Park. The students were lucky to spend the day experiencing the rides and took part in a science workshop which looked at the physics behind the rides.
Simply speaking, a roller coaster is a machine that uses gravity and inertia to send a train of cars along a winding track. This combination of gravity and inertia, along with G-forces and centripetal acceleration give the body certain sensations as the coaster moves up, down, and around the track.
The three main rides they looked at were Stealth, Swarm and Saw but they also looked at the other rides too.
Why is physics important at Thorpe Park?
You need physics for designing the rides, building the rides, safety and of course making the rides thrilling.
Five people are involved in the safety of each ride. Four are in the control room and the fifth is by the ride. The ride does not go ahead unless all are in agreement.
Computers are used for simulations. They are also used for sensing and control. The mass of the ride (including the passengers) has to be measured in order to make sure the ride has enough speed to get around the circuit. This isn’t done for every ride but enough times to keep a running average.
Motion in a circle
The mass is important for centripetal force. In simple terms, centripetal force is defined as a force which keeps a body moving with a uniform speed along a circular path and is directed along the radius towards the centre. The year 12 physicists learn that the magnitude of the centripetal force on an object of mass m (in this case the ride plus passengers) moving at tangential speed v along a path with radius of curvature r is:
Where is the centripetal acceleration. The direction of the force is toward the centre of the circle in which the object is moving, or the circle that best fits the local path of the object, if the path is not circular. The speed (v) in the formula is squared, so twice the speed needs four times the force. The inverse relationship with the radius of curvature shows that half the radial distance requires twice the force. This force is also sometimes written in terms of the angular velocity ω of the object about the centre of the circle:
Expressed using the period for one revolution of the circle, T, the equation becomes:
A body experiencing uniform circular motion requires a centripetal force, towards the axis as shown, to maintain its circular path. The picture above right is showing Pameer being turned in a circle by Jack who was presenting the course. The demonstration showed that the smaller the radius of the circular path the faster the object on that path moves.
Roller coasters today employ clothoid loops rather than the circular loops of earlier roller coasters. This is because circular loops require greater entry speeds to complete the loop. The greater entry speeds subject passengers to greater centripetal acceleration through the lower half of the loop, therefore greater G’s. If the radius is reduced at the top of the loop, the centripetal acceleration is increased sufficiently to keep the passengers and the train from slowing too much as they move through the loop. A large radius is kept through the bottom half of the loop, thereby reducing the centripetal acceleration and the G’s acting on the passengers.
The Colossus at Thorpe Park has many twists and turns forming a corkscrew path. Each clockwise turn is followed by an anti-clockwise turn to prevent the passengers getting dizzy and allow their heads to re-balance.
The above left g force graph has a green line showing positive g-forces (a positive g force makes a person feel that their weight is increasing). The blue line shows lateral g (twists etc.) and the red line is about safety. The safe level for the g force is 5g. Above this will cause the passengers to pass out. Therefore don’t get inside your washing machine.
The above graph shows the speed of the ride.
A rollback occurs on a launched roller coaster when the train is not launched fast enough to reach the top of the tower. It will roll backwards down the tower, and will be stopped by brakes on the launch track. Any roller coaster on which it is possible for a rollback to occur will have these brakes.
There are several factors that can cause a rollback:
Unusual wind gusts could slow the train down enough to cause it to roll back. Cold weather increases friction in the wheels.
A rollback will often occur during the first few test launches each day, as the launch motor has not been sufficiently warmed up by this point. Intentional rollbacks are sometimes conducted during testing.
Fewer passengers on the ride reduces the momentum (mass x velocity) and could cause a rollback.
While the general public may not realize that rollbacks usually are completely safe and that coasters are designed with them in mind, many coaster enthusiasts look forward to being in one. Being in a rollback essentially gives riders a ride and a half, as the train will be launched again after the rollback. In a video of a rollback on Stealth at Thorpe Park, the train is seen to reach slightly over halfway over the midpoint at the top. The train proceeded to roll back, due to an insufficiently powerful launch, combined with an uneven distribution of weight on the train in April 2006. Stealth also had a rollback in March 2008 due to strong winds.
The above picture shows the students inspecting a wheel from one of the rides that has partly melted due to a lot of roll back.
Roll back can also occur because the force used to start each ride is based on the average force from previous rides and this may not be enough for the current ride. One of the students asked why the maximum force isn’t used for every ride and the answer given was that would greatly increase wear and tear.
There are several methods involved in stopping the rides from travelling too fast. The twists in Stealth slow down the ride. The brakes are very important especially if rollback occurs. If the coaster is not launched fast enough to clear the top (which can happen for several reasons) it will roll backwards down the tower and along the launch track. For this reason, the launch track is fitted with retractable brakes that are retracted for the launch and extended at all other times. The main brake run uses the same type of brakes, which are fixed in place. A power cut is irrelevant as electromagnetic forces produce braking. A-level students learn that a conductor moving in a magnetic field can produce a force that opposes the motion creating it.
An accelerator coaster’s hydraulic launch is much smoother than other launch technologies such as linear motors. While a linear motor-launched train’s acceleration is greatest at the beginning of the launch and decreases throughout the launch, a hydraulic launch produces nearly constant acceleration throughout the launch.
The coaster’s power source is several hydraulic pumps, each capable of producing 500 horsepower (370 kW). These pumps push hydraulic fluid into several accumulators. These accumulators are divided into two compartments by a movable piston, one side filled with hydraulic fluid and the other with nitrogen gas. The nitrogen is held in large tanks directly beneath the actual accumulator.
As the hydraulic fluid fills the accumulators (energy storing devices), it pushes on the pistons, compressing the nitrogen. It takes approximately 45 seconds to pressurize the accumulators with all pumps operating. All of this pressure is released during each launch, which typically lasts between 2 and 4 seconds.
The heart of the launch system is a large winch, around which the launch cables are wound. This winch is driven by hydraulic turbines. The two launch cables are attached to the winch on its ends, and run through two grooves on top of the launch track. The cables are attached to the sides of the catch-car, which runs in a trough between the grooves. A third, single retractor cable is attached to the rear of the catch-car, it runs around a pulley wheel at the rear end of the launch track and returns to the hydraulic building along the bottom of the launch track, where it is wound in the opposing direction on the winch’s drum. The aim is to produce enough force to get round the track.
One of the students asked if the ride had ever been stuck at the top of a loop. The answer was there is a 1 in 10 million chance of this happening because the ride is designed to roll back if there isn’t enough force to get over the top.
The catch-car connects to the train to launch it with a solid piece of metal known as a “launch dog” that drops down from the centre car. The launch dog is normally retracted and is held in place by a small magnet, but the launch area has electrical contacts that demagnetize the magnet and cause the launch dog to drop down. The launch dog drops down at an angle, similar to the chain dog that a lifted coaster uses to connect to the lift chain.
The picture above right shows the arrangement of the train and the track.
During the workshop the students re-visited some of the physics they had learnt in school and did some calculations based on the Thorpe Park rides.
Newton’s first law says that an object will remain at rest or move at a constant velocity if no external force acts on it.
Newton’s second law says that the force applied to an object is proportional to the acceleration providing the mass of the object is constant. Or the force applied to an object is proportional to the mass of the object providing it is moving at a constant acceleration.
Newton’s third law says that if an object exerts a force on another object then that other object exerts the same force back on the object. These forces must be the same type and size but act in opposite directions and on different objects.
The above picture is an illustration of Newton’s third law in which two skaters push against each other. The first skater on the left exerts a normal force on the second skater directed towards the right, and the second skater exerts a normal force on the first skater directed towards the left. The magnitude of both forces is equal, but they have opposite directions, as dictated by Newton’s third law.
Electromagnetic brakes (also called electro-mechanical brakes or EM brakes) slow or stop motion using electromagnetic force to apply mechanical resistance (friction). The original name was “electro-mechanical brakes” but over the years the name changed to “electromagnetic brakes”, referring to their actuation method. Since becoming popular in the mid-20th century especially in trains and trolleys, the variety of applications and brake designs has increased dramatically, but the basic operation remains the same. Both electromagnetic brakes and eddy current brakes use electromagnetic force but electromagnetic brakes ultimately depend on friction and eddy current brakes use magnetic force directly.
Eddy currents are electric currents induced within conductors by a changing magnetic field in the conductor. These circulating eddy currents induce magnetic fields and these fields can cause repulsive, attractive, propulsion, drag and heating effects. The stronger the applied magnetic field, or the greater the electrical conductivity of the conductor, or the faster the field changes, then the greater the currents that are developed and the greater the fields produced. Eddy currents act as a brake because they produce magnetic fields that oppose the force causing the original motion.
Faraday was one of the first people to come up with the idea that a changing magnetic field can induce a current in a conductor inside that magnetic field.
Faraday’s law of induction is a basic law of electromagnetism predicting how a magnetic field will interact with an electric circuit to produce an electromotive force (EMF). It is the fundamental operating principle of transformers, inductors, and many types of electrical motors, generators and solenoids.
Lenz’s law is a common way of understanding how electromagnetic circuits obey Newton’s third law and the conservation of energy. Lenz’s law is named after Heinrich Lenz, and it says:
An induced electromotive force (emf) always gives rise to a current whose magnetic field opposes the original change in magnetic flux.
Energy transformations on a roller coaster
Roller coasters have no engines. Instead, the car is pulled to the top of the first hill and released, at which point it rolls freely along the track without any external mechanical assistance for the remainder of the ride. The law of conservation of energy states that energy can neither be created nor destroyed, thus, the purpose of the ascent of the first hill is to build up potential energy that will then be converted to kinetic energy as the ride progresses. The initial hill, or the lift hill, is the tallest in the entire ride. As the train is pulled to the top, it gains potential energy, as explained by the equation for potential energy
Where m is the mass, g is acceleration due to gravity and h is the height which the object is raised.
As the roller coaster train begins its descent from the lift hill, the stored potential energy converts to kinetic energy, or energy of motion. The faster the train moves, the more kinetic energy the train gains, as shown by the equation for kinetic energy:
where K is kinetic energy, m is mass, and v is velocity. Because the mass of a roller coaster car remains constant, if the speed is increased, the kinetic energy must also increase. This means that the kinetic energy for the roller coaster system is greatest at the bottom of the largest downhill slope on the track, typically at the bottom of the lift hill. When the train begins to climb the next hill on the track, the train’s kinetic energy is converted back into potential energy, decreasing the train’s velocity. This process of converting kinetic energy to potential energy and back to kinetic energy continues with each hill. The energy is never destroyed, but is lost to friction between the car and track. Brakes bring the ride to a complete stop.
The pictures from top left are Swarm, Saw, Stealth and Colossus.