Twists, turns, thrills and spills: the physics of rollercoasters

It’s a hot summer day, and you’ve been queuing for the better part of two hours. The line inches along agonizingly slowly, and your anticipation ebbs and flows each time you creep ahead or hear the distant screams and whoops….

It’s a hot summer day, and you’ve been queuing for the better part of two hours. The line inches along agonizingly slowly, and your anticipation ebbs and flows each time you creep ahead or hear the distant screams and whoops. Finally, it’s your turn – you pick your seat, strap in, take a deep breath and prepare to scream your head off. The rollercoaster train cranks to the top of a steep hill, then drops down. A mere one to two minutes later it’s all over, and you wobble off the track as the next bunch of giddy thrill seekers clamber on.

Every day (pandemics allowing), people all over the world flock to amusement parks, with the main attraction usually being a rollercoaster ride. The thrill of rollercoasters lies mostly in the fact that they allow us to go at fast speeds, experiencing sudden, hair-raising changes in acceleration and direction – all while putting into action some of the most basic principles of Newtonian mechanics. Hill thrills Rollercoaster trains have no engine or no power source of their own. Instead, they rely on a supply of potential energy that is converted to kinetic energy. Traditionally, a rollercoaster relies on gravitational potential energy – the energy it possesses due to its height. It is pulled to the top of a big hill, the highest point of the ride, and released. The UK’s tallest rollercoaster, The Big One at Blackpool Pleasure Beach, starts with the train being cranked to the top of a massive 65 m hill. On rides like this, your anticipation builds with the clank-clank-clank of the chain, as it pulls you slowly up the hill. Gravity then takes over, pulling the cars down a 65° drop. As the train dives, the potential energy decreases and the kinetic energy increases as it accelerates to around 119 km/h (74 mph). Thrills and spills Reaching a height of 65 m, The Big One at Blackpool Pleasure Beach used to be the tallest and steepest rollercoaster in the world. It is still the tallest in the UK and one of the fastest, with a top speed of 119 km/h. (Courtesy: iStock/onfilm) Instead of a lift hill, many modern rollercoasters use a launch to give the train kinetic energy. Stealth, at Thorpe Park in Surrey, for example, uses a hydraulic system to catapult the train out of the station, propelling riders from 0 to 128 km/h (80 mph) in less than two seconds. This system uses a winch to rapidly pull a catch car along the track. The catch car “catches” the rollercoaster train, pulls it along and then releases it, flinging it down the track. Other rides use electromagnetic propulsion systems, where electromagnets on the train and the track pull, and then propel, the train forwards. Like the catapult systems, these can create incredible amounts of acceleration, moving the trains to speeds of more than 95 km/h (60 mph) in a few seconds. Although you don’t have the nervous wait as you are pulled up the hill, these launches still provide a sense of anticipation as you sit in the station. Energy conservation Rollercoasters constantly shift between tapping into potential and kinetic energy. The kinetic energy gained when the train travels down the first hill – or fires out of the launch – gets it up the next, smaller hill. As it travels up the hill, it loses kinetic energy and gains potential energy, and the cycle starts again. Many newer rollercoasters also include further launches, which are often electromagnetic, that provide the train with additional kinetic energy part way through the ride. Most people like to sit at the front or the back of the train, with many rides offering separate queues for these prime spots. In these positions riders feel a greater sense of weightlessness, explains Ann-Marie Pendrill, an expert in using rollercoasters in physics education at the University of Gothenburg and Lund University in Sweden. Pendrill adds that the middle of the train is where one experiences the highest G-forces, but not many people choose to sit there. “The force if you are sitting in the middle will really be more straight up to you, not sideways, not back to front. It will be more or less the way it should be theoretically.” A unit that might make purists wince, the G-force is the difference between the acceleration, a, that you experience as a rider and the acceleration due to gravity, g, (9.8 m/s2) divided by g and expressed per unit mass: (a–g)/g. This force comes into play thanks to the movement you undergo on the ride– you experience a “positive” G-force when the train is at the bottom of a hill, and a corresponding “negative” force when it crests the top of a hill. When your downward acceleration is close to g, you feel weightless. This is why you feel so much lighter as you accelerate down the hill. But as the rollercoaster train pulls out of the dive, your body wants to continue travelling in the same direction. The sudden change in direction as the track flattens is why you squash into the seat and abruptly feel heavier: the ride pushes up, while your body tries to carry on travelling downwards. You experience similar “lateral” G-forces on the corners, where your body tries to continue moving in the same direction, while the train turns. If the track isn’t banked, you slam into the side of the car (or another passenger). If the track is banked, the force acting against you from the seat is along the same axis, which helps to smooth out the ride. My stomach is in my mouth Pendrill has taken her smartphone on rollercoasters all over Scandinavia, to collect data using an accelerometer (figure 1). Her favourite rollercoaster, the Helix at Liseberg in Gothenburg, Sweden, begins differently to many others. It starts at a high point and just rolls out. Riders reach the station at the top of the hill via an escalator or stairs. Pendrill’s accelerometer measurements show that at the bottom of Helix’s first drop, the force exerted on the riders is 3.5g, known colloquially as 3.5G. This is similar to that experienced at the bottom of the first drop on The Big One. What are referred to as negative G-forces on a rollercoaster are, in reality, often less than 1G, rather than actually negative, which means that you experience a feeling of nearly being lifted out of your seat. This is referred to as “airtime”, when riders experience moments of weightlessness, as the train travels over a peak at speed. “I like the airtime hills where you kind of float,” says Pendrill. “I really like the equivalence principle – the equivalence between gravitational and inertial mass – so that you float, you are weightless as you are in freefall over the hill. You can have that for a reasonable amount of time, if the hills are well built.” On Helix’s two airtime hills you experience around 0G and –1G, according to Pendrill’s measurements. She explains that these features rely on projectile motion, much like a zero-G flight. As in the valleys and corners, Newton’s first law of motion comes into play: an object in motion tends to stay in motion, so your body wants to carry on travelling in the same direction. As the train drops away when it goes over the hill, your body tries to carry on moving upward and forwards, leaving you with a feeling of weightlessness. Your internal organs also try and follow the same path, which is why it can feel like they are floating inside your body, and your stomach is in your mouth. These airtime hills are where you will experience the lowest G-force if you are sitting in the front or the back of the train. “Think about a train going over the hill,” Pendrill says. “As it comes up it will slow down until the middle, and then it will speed up again. So both the front and the back of the train move faster over the hill, which means that you lift more.” What goes up Rides at Liseberg in Sweden include the Helix (green) and the Valkyria (yellow). (Courtesy: Liseberg) Rollercoasters are designed so that you are constantly experiencing changes in forces. On the Helix ride in Sweden, a launch halfway round the ride fires the train up a steep hill into an inverted top hat. Pendrill’s data show that after this launch, riders experience around 4G as they fly up the hill, before it drops to around 0G as they travel upside down through the top hat; then rapidly increases to more than 4G as the train flies into the valley at the bottom. Coming out of the valley the train shoots over an airtime hill, with riders experiencing –1G, before diving into another valley where the force hits 4G again. This all happens in about 15 seconds. Heightened senses It is these rapid changes that make rollercoasters so exciting, explains Brendan Walker, a researcher at Middlesex University London and rollercoaster consultant, who describes himself as a thrill engineer. “If you look at people’s physiological response when they are on a rollercoaster, the arousal aspect of emotions is very much tied, almost inextricably tied, to changes in G-force,” Walker explains. “So we’ve got the jounce and the jerk, which are the differentials of acceleration – velocity, acceleration, jerk, jounce – every one of those has an impact on our levels of arousal, as they change.” Indeed, when you ride, you experience a heightened state of stimulation, as your heart is pumping fast and your blood pressure increases. What happens next depends on the ride. Do the changes in force feel nice? Are there exciting or dramatic visuals? Can you see other people watching in awe, or terror, as you fly past? “All those other elements that are more aligned with the arts, theatre, dance, body movement; that is where the pleasure comes in,” Walker says. “If you manage to get that as you are delivering the hard levels of arousal through the physics, then you’ve got a thrilling moment on a ride.” Round and round The Kumba at Busch Gardens in Tampa, Florida, had the world’s tallest vertical loop when it opened in 1993. It features seven inversions across a three-minute ride. (CC BY 2.0 Jeremy Thompson) Pendrill adds that rides need to strike a balance between changes in force that are a bit more violent, and ones that creates a sense of excitement. “You want things to change, but not too rapidly or too smoothly,” she says. Frank Farley, a psychologist and expert in risk-taking and thrill-seeking at Temple University in Philadelphia, US, believes that most people go on rollercoasters for the simple thrill of it. “The excitement, a feeling of riskiness, the escape from the humdrum of everyday life, the contrast with everyday life, the challenge as to how you will handle it.” Walker agrees. “People I’ve interviewed without fail say that it is the moment they feel truly alive when they are thrilled, yet we are starved of that in a safety-conscious western world, so people gravitate towards thrill rides.” He adds that it is no surprise to him that theme parks first started to appear in places like Coney Island, New York, and the peripheries of other cities like London as the world became more industrialized and more urban. Upside down, you’re turning me Of course, the biggest thrill on a rollercoaster is going upside down, on the loops. As you travel through a loop, inertia – the tendency of an object to resist change in its state of motion – pushes you outwards and keeps you in your seat. Gravity tries to pull you down, but the stronger acceleration force counters this, pushing you first sideways and then upwards. Thrill ride The Great American Scream Machine (1989–2010) at Six Flags in the US included a teardrop-shaped loop. (CC BY 2.0 Jeremy Thompson) Rollercoaster loops are most often not perfect circles – instead, they are teardrop-like in shape. This is because it takes a greater amount of acceleration to get the train around a perfectly circular loop. Pendrill says that for such a loop, the acceleration would change rapidly between about 6g and 1g as you travelled around the loop. It is this change, rather than the high G-force itself, that is dangerous: the jerk is not good for your body. “They built them like that in the early 20th century and people had whiplash,” Pendrill says. With teardrop-shaped loops, the radius of curvature changes as you move through the loop. It is larger at the bottom and sides of the loop and smaller at the top. This reduces the acceleration required at the sides. Pendrill says that forces are typically around 4G as you enter and exit such loops. There are now a huge number of different “inverting elements” or styles of loops that modern-day rollercoasters employ, with a confusing array of names, such as sea serpents, a bent Cuban eight, pretzel loops and knots, batwings and even the terrifying-sounding “demonic knot”. One popular inversion that is the final feature on many modern rollercoasters is the “heartline roll”. In this, the train performs a 360° roll, but it rotates around your centre of gravity, or your heartline. “Since it is constant velocity, the force acting on you is compensating gravity and is pointing up, but if your head is down it feels different from when your head is up,” explains Pendrill. Walker adds that such rolls “create a very different sensation” and have a very different effect on the blood in your body, as compared to other aspects of the ride when your blood is usually rushing to your feet. Virtual reality From a physics point-of-view there is a lot more we could do on rides, Walker says, but the human body is a limiting factor. One way some people are looking to push rollercoasters to the limit is with virtual reality (VR), where riders wear headsets and travel through a virtual world during the ride, adding extra levels of visual simulation and illusion. According to Malcolm Burt, an expert in disruptive media, thrill rides and VR at Central Queensland University in Australia, VR has a number of advantages when it comes to amusement park rides. It can revitalize old rollercoasters, and it is easier and cheaper to update than a physical ride. This means you can change it quite quickly, offering different, perhaps even seasonal or topical, experiences. Indeed, it is possible to create unique sensations by combining the G-forces of a rollercoaster with a virtual world. The human body isn’t particularly adept at sensing direction and speed, just that there have been changes. This means it is quite easy to trick people into thinking that a ride is much more aggressive than it actually is. You can make slopes appear much steeper or higher than they are in reality, for example. “Little movements can have big impacts on your brain when you have the right visual stimuli,” Burt says. Virtual thrills Theme parks are starting to incorporate virtual reality into some rollercoaster rides to enhance the experience, including Valkyria at Liseberg in Sweden. (Courtesy: Stefan Karlberg/Liseberg) It is important, however, to make sure that people are not receiving information that is contradictory to what is going on in the physical world, adds Walker. Burt agrees, stating that most VR rides give you clues as to what is coming so you can be ready, to prevent discomfort. For example, if there is a blast-off in the virtual world, it might coincide with a launch mechanism on the rollercoaster. Burt recalls once having a “horrible experience” on a VR rollercoaster that was still in development, before the headset was working properly. “It was terrifying,” he says. “There was no sensory feedback whatsoever, it was literally like having a blindfold on, on this very aggressive rollercoaster. I was thinking, ‘just breathe, just breathe, you’ll be fine, you’ll be fine’.” When Walker works on VR rides, the software he uses contains an advanced physics simulator. “We have methods to simulate the physical forces in real time and then build our virtual world around that,” he explains. “Our virtual representation of a fantasy world has a very close correlation to the physics of the real world.” So the next time you’re queueing up at the amusement park – be it to ride the longest, tallest, scariest rollercoaster you can find, or even one that is in space, thanks to your VR headset – don’t forget to think about all the physics in action that you’re about to experience. Chances are, it will all go straight out of your head the minute the ride begins.