How Roller Coasters Work

The ride that runs on physics

A roller coaster is one of the purest physics demonstrations ever built. After the first climb, there is no engine pushing the train along the track. Everything that happens — the speed, the loops, the rush of air — comes from a single store of energy and the laws of motion. Let's take the ride apart.

Climbing the first hill: storing energy

Watch the start of any big coaster and you will see a chain lift slowly hauling the train up the tallest hill. This is the only point where outside energy is added to the ride.

As the train rises, it gains gravitational potential energy — energy stored because of its height. The higher and heavier the train, the more it stores:

Gravitational PE = mass × gravitational field strength × height GPE = m g h

This is the fuel tank for the whole ride. Once the train tips over the crest, gravity takes over and no more energy is added.

The first drop: turning height into speed

As the train plunges down the first hill, that stored height energy is transferred into kinetic energy — the energy of movement:

Kinetic energy = ½ × mass × speed² KE = ½ m v²

The train trades altitude for speed. By the bottom of the drop, almost all the potential energy has become kinetic energy, and the train is moving at its fastest. This swap between GPE and KE, back and forth over every hill, is the core of the conservation of energy.

Worked example: how fast at the bottom?

Imagine a coaster dropping from a height of 45 m. Ignoring friction for a moment, how fast is it going at the bottom?

All the gravitational PE becomes KE, so:

m g h = ½ m v²

The mass cancels, leaving:

v² = 2 g h = 2 × 9.8 × 45 = 882 v = √882 ≈ 30 m/s (about 108 km/h)

That is why even a coaster with no motor can reach motorway speeds — it is simply falling, cleverly guided by the track. (The real speed is a little lower because of friction, which we will get to.)

Why every hill gets smaller

Look along the track and you will notice that each successive hill is lower than the one before. This is not just for thrills — it is forced by physics.

In a perfect, frictionless world the train could climb back to its exact starting height every time. But real tracks have friction between the wheels and rails, plus air resistance. Each of these transfers a little energy into heat and sound on every section, just as in energy efficiency and transfers. Because energy is never created, the train always has slightly less than before, so it can never quite return to the first hill's height. Designers therefore make each hill lower to guarantee the train always has enough speed to get over it.

Loops and g-forces

The most dramatic moments are the loops and tight curves. To travel in a curve, an object needs a force pulling it toward the centre of the circle — the same idea as in circular motion and orbits.

• At the bottom of a loop, the track must push up hard to curve your path upward. That large upward push presses you into your seat, and you feel heavier than normal — a high g-force.
• At the top of a loop, you are upside down but moving fast. Gravity and the track together provide just enough inward force to keep you on the rails, so you do not fall.
• Over a sharp crest, the seat pushes up on you much less than usual, so you feel light, even briefly floating against the harness.

A "g-force" of 3g means you feel three times your normal weight. Engineers carefully limit these forces so the ride is thrilling but safe for the human body.

Try it yourself! 🧪 (safe version)

Build a mini roller coaster on a tabletop with foam pipe insulation (cut lengthwise into a half-pipe) and a marble.

1. Tape one end high up — on a stack of books — and let the track curve down and along the table.
2. Roll a marble from the top and watch it speed up on the drop and slow on the climbs.
3. Try adding a second hill. Make it lower than the first and the marble sails over; make it taller than the first and the marble stops short and rolls back.

That failed climb is conservation of energy in action: friction has stolen just enough energy that the marble can never reach a height greater than where it started. Change the starting height and you change the marble's top speed — exactly the GPE-to-KE trade real coasters rely on. For the forces that get the train moving and stopping, revisit work done and kinetic energy.