Will your Rollercoaster get Stuck at the Top of a Loop-the-Loop?

What if we told you that you didn’t need safety harnesses in loop-the-loop roller coasters? Of course, they are a useful precaution and make riders feel more secure while riding, but if the physics behind the ride adds up then you will stay in your seat (whether you are upside down or not)! 

One of us remembers when their family used to visit Canada’s Wonderland in Vaughan, Ontario every summer and they were absolutely terrified of any ride that went upside down like their coaster, “The Bat”. This death-defying ride starts off with a 121 ft lift, soaring at 75 km/hr into two loop-the-loops, then doing it all over again backwards on the track.

The fact of the matter is, roller coasters rely on many physics principles, all of which allow them to continue moving on the tracks and maintain speed while optimizing the riders’ experiences. Today we explore the fundamental concepts behind these rides and how they keep us safe such as inertia, energy transformations, and centripetal acceleration. 

Why Roller Coasters? Newton of Course!

Rollercoasters appeal to their riders because they provide a variety of sensations like acceleration, high speeds, weightlessness, sinking, and many more. Newton’s laws of motion indicate that an object in motion tends to remain in motion--as seen in roller coasters continuing along the track, exhibiting what we call inertia. 

Picture a car just as it begins moving after a red light, as your foot presses the gas pedal, the car starts moving faster and faster, with a positive acceleration. There are a few forces acting on you in this moment, the force due to gravity (pulling you towards the ground), the normal force (the seat pushing back onto you with equal strength as gravity), and the force due to your acceleration, pulling the car forwards (pushing you backwards into your seat). If these forces were to suddenly change, like when you press the brakes quickly, you may experience a “sinking” feeling in your stomach as a result of this. 

Energy: It’s Not What You Think!

You may think that rollercoasters use some sort of electricity to propel themselves on the tracks, which although is true for some, most of the movement is created by harnessing a different form of energy. Energy, in physics, refers to the capacity to do work. It can exist as potential, kinetic, thermal, rotational and more! 
Kinetic energy is the energy an object possesses due to its motion and mass. The more mass and velocity an object has, the more kinetic energy it possesses. Potential energy, on the other hand, depends on an object’s position rather than its motion. If an object is being held still above the ground, it has the potential to increase its speed if dropped, as gravity pulls the object towards the Earth. 

Let’s imagine a scenario where the object is dropped from five feet above the ground. As the object falls towards the ground, its potential energy decreases as it gains speed. This means the kinetic energy is increasing, as it is dependent on motion. This is an example of one of the most important laws in physics, called conservation of energy, which is commonly stated as, “energy cannot be created nor destroyed”. Although energy cannot be created or destroyed, energy can transform from one form to another, as in the example above where the ball’s potential energy is converted into kinetic energy. 

Centripetal Force as Our Seatbelts

Using this concept of the inertia of accelerating objects, we now need to understand the physics behind circular motion and how it helps us stay safe at the top of a loop-the-loop.
Imagine you are holding a bucket filled with water. If you were to swing this bucket around with your arm over your head, we would see that all the water stays in the bucket without spilling! This is caused by what we call the centripetal force that acts on the water due to the circular path it travels. Roller coasters like The Bat use this concept in their loop-the-loops directly, as riders would actually stay in their seats if the cart travelled at the right speed for the size of the loop!

Putting This All Together...

Now how is all of this going to keep us safe? Let’s apply the concepts we’ve discussed so far and look at the forces involved with each section of the loops and how exactly this all comes together in The Bat. 
As the cart approaches the first loop, it experiences a few key forces: a force due to gravity pulling the cart towards the ground, a normal force that the tracks exert back onto the cart that is equal in magnitude yet opposite in direction, and your inertial velocity is pulling you forwards (Figure 4 left).

Next, the cart continues moving up the side of the loop, as gravity pushes you into your seat and your inertial velocity (remember, the cart wants to keep moving because it is already moving) keeps pulling you along the track. 

Finally the cart reaches the top of the loop and the thrilling “weightlessness” feeling takes over your body as the centripetal acceleration and inertial velocity balance the forces pointing towards the center of the loop and towards the sky (Figure 4, right). Adding to this “weightless” sensation, the cart moves slower at the top due to a partial conversion of kinetic energy to potential energy.

The cart then descends the other side of the loop, where we feel the benefits of the “teardrop” shape (they aren’t actually perfectly circular!) called a clothoid loop, a spiral shape that has a constantly changing radius (larger at the bottom, smaller at the top). This shape keeps its riders safe from feeling the bodily effects of very high velocities and allows the most amount of time at the top of the loop for those thrill-seeking roller coaster lovers.

The Verdict

After researching all the safety behind loop-the-loops, we feel confident in saying that they have passed the physics test! These beauties lean into topics of inertia, conservation of energy, and centripetal acceleration--all while providing so many thrills to their riders! Next trip to Canada’s Wonderland, you can find us on The Bat!

Questions? Keep Reading

https://science.howstuffworks.com/engineering/structural/roller-coaster7.htm
https://www.physicsclassroom.com/class/circles/Lesson-2/Amusement-Park-Physics
https://www.canadaswonderland.com/rides-experiences/the-bat

Michaela Hishon and Joseph Owen, undergraduate students at the University of Guelph, produced this article in the context of the 3rd-year course IPS3000 on Science Communication in the Fall 2023 semester (course instructor: Alex Gezerlis, TA: Carley Miki).