We can't all be racing drivers or astronauts. Not everyone can dive
to the bottom of the sea or climb up Mount Everest. But we can all go on
rollercoasters and see what it feels like to push ourselves
to the limit. You might think rollercoasters are all about testing
your body, but your mind's being worked out too: the mentalpsychology of fear makes the whole physical experience so much more exciting. Let's take a closer look at the science of extreme
Have you ever wondered why rollercoaster cars don't have engines? Vehicles don't always need that kind of power to make them go. But they do need
energy of some sort. Before a rollercoaster ride begins,
an electric winch winds the cars to the top of the first hill. That can take a while, because some rollercoasters start off around 100m (330ft) in the air!
The winch has to use energy to
pull the rollercoasters up the hill, but that energy doesn't simply
disappear. The rollercoaster cars store it just by being up in the
air—and the higher up they are, the more energy they store. They'll
use the same energy to race back down the hill when the ride begins.
Because they have the ability (or potential) to use in the future
energy that was stored in the past, we call the energy they're
storing potential energy.
Photo: What comes down must go up! The kinetic energy that makes a rollercoaster car move at speed comes from the potential energy the car gained when it was hauled to the top of the very first hill on the ride.
Photo of the Jet Star roller coaster, Seaside Heights, New Jersey by John Margolies, courtesy of
John Margolies Roadside America photograph archive (1972–2008), Library of Congress, Prints and Photographs Division.
Once everyone's onboard, the cars are released and start to roll
down. When they round the brow of the first hill, the force of gravity
makes them hurtle downwards, so they accelerate (pick up
more and more speed). As they accelerate, their potential energy
turns into kinetic energy (the energy things have because
they are moving). The further they go down the hill, the faster they
go, and the more of their original potential energy is converted
into kinetic energy.
At the start of the ride, the cars have a certain amount of
potential energy. They can never have any more energy than this, no matter how
long the ride lasts. Throughout the ride, they are constantly
swapping back and forth between potential and kinetic energy. Each
time they race up a hill, they gain more potential energy (by rising
higher in the air), but they compensate for it by losing some
kinetic energy too (by slowing down). That's why rollercoaster cars
always go slower in the higher bits of a ride and faster in the lower bits.
In theory, this process could go on forever and the ride would never
end. But in practice, some of the potential energy the cars started
off with is constantly being used up by friction, when the wheels
rub against the track. Air resistance takes away more of the energy
as well. Even the rattling noise the rollercoaster makes uses up
some of its energy. The cars lose more and more of their original
energy the longer the ride continues, and, since the cars have no
engines, there's no way of replacing it. That's why the loops on a
rollercoaster ride always get smaller and smaller. It's why
rollercoaster rides must always come to an end sooner or later. The
cars simply run out of energy.
Artwork: How energy and forces change during a rollercoaster ride. To learn more about centripetal
force—the force that makes things go around in a circle—please take a look at our article on
Why are rollercoasters so high?
To make a rollercoaster fast, you need to make it
high. An important law of physics called the law of conservation of energy tells us that the maximum kinetic energy the cars can have when they're going at their
fastest is no greater than the maximum potential energy they had when they first started off.
Two simple equations help us figure out just how fast the cars on a rollercoaster can go.
We can work out the potential energy for something that's up in the air using the equation:
m × g × h
where m is the mass of the object, g is the acceleration due to gravity, and h is its height.
We can work out the kinetic energy of something that's moving using another equation:
½ × m × v2
where m is its mass and v is its velocity (loosely, speed).
If we assume that the cars convert all their potential energy to kinetic,
the two equations must be equal, so we find that:
m × g × h = ½ × m × v2, or
v2 = 2 × g × h.
In another words, v is the square root of 2 × g × h. You can see from this that the mass of the rollercoaster doesn't affect its speed: all that matters is its height.
For a rollercoaster 100 m in the air, the top speed is the square root of 2000 or ~45 meters per second, which is 162 km/h or 100 mph. That might sound absurdly fast, but the world's fastest rides do, in fact, reach just these sorts of speeds.
Because the top speed varies with the square root of the height, it follows that if you double the height of a rollercoaster, you don't double the speed. If you want to double the speed of a 100-m high coaster, you would need to quadruple the height. Using our simple equation, you can see that a 400-m-high coaster might manage ~90 m/s, 320 km/h, or 200 mph.
What about brakes?
If rollercoaster cars still have energy to spare when they reach the end of the ride, they can be rapidly brought
to a halt with brakes. There isn't a driver onboard to apply ordinary hydraulic brakes, so
the brakes need to be completely automatic. On older rollercoasters, there's usually some kind of a friction brake on the track that stops the train as it tries to slide over it. Modern rollercoasters have different (and usually more reliable)
eddy-current brakes, which use magnets to generate a braking force as the train goes past.
Energy is what makes a rollercoaster ride last, but forces are what
makes it so thrilling. You can't see the forces pushing and pulling your body as
you race round the track. But it's forces that knock you backwards.
It's forces that make you feel as light as air one minute and as
heavy as a rock the next. It's also forces that keep you safely in
your seat when you're suddenly spinning upside down.
Wherever you are in the ride, lots of different forces are always
acting on your body. The biggest force you feel is your weight—and the
weight of the cars and the other people on the ride. All that weight doesn't
simply pull you straight down. It pulls you forward when you race
down a hill and backward when you climb. There are other forces at
work too. Air resistance pushes against your face and limbs. There's
also a frictional force between the cars and the track. And because
you push down on the seat with your body, it pushes back up on you.
All these forces acting on you are never quite in
balance—that's why you zoom down the track, why the car rattles, and why you shake
about so much.
Photo: You have to wear a safety harness to keep you in your seat when you're flung about and loop the loop. But that's all part of the fun.
According to Isaac Newton's third law of motion, when you press against the seat restraints,
they press back on your body. All those forces pushing you one way and the other only add to the enjoyment!
Photo by Matt D. Schwartz courtesy of US Air Force and
From moment to moment, the forces you feel are never the same—and
that's why the ride is so unpredictable and exciting. When you do a
loop-the-loop, the direction you're moving in is always shifting.
That means the forces you feel are also changing from one second to
the next. Coming into the loop, you barely feel any force at all. As
you start to climb, you feel an enormous force dragging you backward.
The force gets stronger and stronger. At the top of the loop, you
feel like you're going to fall out of your seat. Then the force
gradually gets weaker again as you come back round to the straight.
How big are the forces on a rollercoaster?
We measure forces by comparing them to the force of gravity, or g. You're currently feeling a
force of about 1g, sitting in a chair. A force twice as big as the
force of gravity is 2g, four times as big is 4g, and so on. The
biggest force you're likely to feel on a typical rollercoaster is no more
than about 2–3.5g, though some rides claim to achieve as much as 5–6g.
By comparison, a jet fighter pilot feels a force of
about 9g—and the record g force
endured by a human in an experimental test
(Colonel John P. Stapp) is 46.2g! But the exact amount of force you feel varies according to
where you are on the ride and how steep the track is at that
point. The biggest force comes when you're just starting to move down
a hill. The force is lowest in the dips between the hills. (Your
speed is in exactly the opposite pattern: it's lowest when you've
just gone over a hill and highest in the dips between the hills.)
Chart: Rollercoasters produce significant g-forces (red), but well within the limits of what humans can safely withstand.
The forces you feel also depend on whereabouts in the train of cars
you're sitting. If there are lots of cars and the train is quite long,
different cars can be at different
points on the ride. The front cars may be racing down a hill while
the back cars are still climbing up behind them. All the cars are
coupled together, so the front cars pull the back ones along at the
same speed. But the forces on people sitting in different cars can be
quite different. When the front car goes over a hill, it's barely
even moving. Sometimes it goes so slowly you wonder if it'll even get
to the top. Then, as it starts racing down the hill, it pulls the
other cars along behind it. When the back car starts climbing a few
seconds later, it's whipped over the top really quickly—and you
almost fly out of your seat. As the back car races over the hill, you
feel weightless for a second or two. That's why, for sheer
exhilaration, the back car is often the best one to sit in. If you
like a good view, though, sit at the front!
Rollercoasters past and present
If rollercoasters remind you of sledges, that's not surprising. The
first rollercoasters were built during winter in Russia in the 14th
and 15th centuries. They were huge blocks of ice with holes carved
out of them, lined with fur and straw to make seats. The blocks slid
along a wooden framework sprayed with water to make it really icy
Today's rollercoasters are mostly made from metal, with enough steel girders in a typical rollercoaster to make around 1000–2000 cars.
All that metal makes an incredibly sturdy structure: the cars can go faster and
have tighter curves and higher loops and still travel in perfect
safety. The cars are made from steel as well as the track and, unlike
their icy Russian predecessors, they're more like trains than
sledges. They have two sets of wheels that run both above and below
the tracks (that's how they stay on the rails when they're going
Some very modern rollercoaster rides are still built
out of wood and, though you might think that's not so safe, it's a
perfectly designed part of the fun: the idea is that the tracks
rattle, shake, and groan to make you feel more afraid!
Anywhere else, all those screams and yells might give cause for concern. But in an amusement park, it's what we expect. A rollercoaster that didn't make you scream wouldn't be worth the ride. You'd feel short-changed; you might even demand your money back! But the perfect rollercoaster has to fool our minds into thinking they're in imminent danger while keeping our bodies safe at all times. When accidents happen on rollercoaster rides, people are understandably upset and concerned. Amusement rides are places where families go to enjoy themselves, not to meet real-life horror and disaster.
Photo: Rollercoasters make our brains feel terrified while keeping our bodies safe.
Photo of Ferrari World in Dubai by Ian Kinkead courtesy of US Navy and
Psychology: enemy or friend?
Rollercoasters are cleverly designed to maximize fear; they're as much about human psychology as the physics of energy conversion. But psychology can and does play tricks. We love rollercoasters because they feel more dangerous than they actually are. But when an accident happens at an amusement park, the newspaper and TV coverage persuades us that rides like this really are dangerous. The psychology that attracts us to rollercoasters works in reverse—and makes us stay at home!
So how safe are rollercoasters, really? It's no more sensible to answer that than to answer "How safe is crossing the street?" It depends on the street, how you cross it, and when you do so. Researching this topic, I found an online news item suggesting that the risk of having an accident on a rollercoaster is greater than that of being attacked by a shark. Most people, living and working in cities, are at zero risk of being attacked by sharks, so what does that comparison tell us? Not very much. Instead of helping us figure out whether the risk is one we feel comfortable taking, it plays another sly trick with psychology: it compares one thing (instinctively perceived to be dangerous by most people—sharks) with another (about which we instinctively have no reliable information—rollercoasters).
What do the numbers tell us?
It's easy to list all the accidents and fatalities that have ever happened at amusement parks and conclude that rollercoasters are "dangerous." But how dangerous are they compared to everyday risks that we happily endure? The news report comparing rollercoasters to sharks went on to say "The number of rollercoaster deaths are also relatively high." But relative to what? Relative to reading a book or relative to parachute jumping?
Chart: Almost half of those killed on rollercoaster rides (blue) had a medical condition that might have killed them anyway. About a quarter (yellow) were ride operators. Only about a quarter (red) died through the kind of ride accident that makes sensational media coverage. Drawn using data from Pelletier and Gilchrist, 2005. (Figures are rounded in the original study, which is why they don't add up to 100 percent.)
According to a 10-year scientific study of rollercoaster accidents (Roller coaster related fatalities, United States, 1994–2004 by A.R. Pelletier and J. Gilchrist, published 2005), "approximately four deaths annually are associated with roller coasters." Compare that with the number of deaths annually from all forms of accidental injury (130,557), falls (30,208), motor vehicle accidents (33,804), and accidental poisoning (38,851) [Source: Accidents or Unintentional Injuries, Center for Disease Control and Prevention, 2013.] It's not an exact comparison (far more people routinely use cars than ride rollercoasters, so we'd expect the number of deaths to be greater), but at least it's a meaningful comparison: we
all have a pretty good idea how safe cars are, for most people, most of the time.
Perhaps even more telling than this, only about a quarter (28 percent) of the people who died on rollercoasters (listed in that study) were killed by traumatic injuries from the rides themselves.
The study found that "approximately half of deaths associated with rollercoasters occur from medical conditions in people without external signs of injury." In other words, they're people who have suffered things like brain hemorrhages or had heart attacks that might well have killed them in other circumstances (about a third of those people were already aware of their own medical conditions). The remainder were ride workers killed by safety failures. There are millions more people riding rollercoasters than operating them, but the relative number of deaths is 2:1. Logically, then, you should be more concerned about the safety of rollercoasters if you work with them every day than if you simply ride them from time to time, but even here the absolute risk is fairly small: rollercoaster operators are not dying in their hundreds and thousands.
The lesson here is a scientific one. When people ask "Is something safe?", think hard about what that really means. What do we mean by safe? Safe for whom? How does the meaningfully measured risk compare with comparable, everyday risks? What does the evidence tell us when we look more closely? Don't take sensational media reports at face value: think about the science, crank the numbers, and see for yourself.
How to understand risk in 13 clicks by Michael Blastland, BBC News, March 11, 2009. This simple article explains how sensational media coverage can exaggerate real, everyday risks.
The World's Wildest Roller Coasters by Michael Burgan. Capstone Press, 2001. How do roller coasters actually work? This 48-page book briefly covers the science as well as the history of wooden and metal coasters.
All About Physics by Richard Hammond. Dorling Kindersley, 2015. A fun look at physics for young readers previously published under the title Can You Feel the Force. (If you're interested, I was one of the consultants and contributors to this book.)
Energy by Chris Woodford. Dorling Kindersley, 2007. Another one of my books. This one explores exactly what "energy" means. Where does it come from and how does it power everything in our world?
Force and Motion by Peter Lafferty. Dorling Kindersley, 2000. One of the superb DK Eyewitness books, with science, technology, and history explored side by side.
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