What if a roller coaster had greater friction?

A roller coaster climbs up a tall hill. Then whoosh! Down it goes, fast!

Rubbing slows things down. What if the coaster's wheels rubbed much more?

On many roller coasters, a chain pulls the cars to the top of the first hill, and then lets go. From there, the cars coast through the rest of the ride with no more help, which is where the name comes from.

All the way around, friction is slowly taking energy away. In this lab, our coaster drops from 40 meters, races around a loop and climbs a 25-meter hill. What happens if the friction is four times bigger?

Once released at the top of the first drop, a coaster is a closed energy budget: gravitational potential energy and kinetic energy trade back and forth, while friction and air drag remove energy as heat. Every later hill and loop must fit inside what is left.

This lab lumps rolling friction and drag into one coefficient μ (the friction force is μ times the normal force) and raises it from 0.02 to 0.08. Where along the track does the energy budget run out?

Our coaster has smooth wheels. Down the hill it goes, faster and faster!

It zooms around the loop and over the next hill. Then the brakes stop it. What a ride!

With smooth wheels, the coaster reaches about 98 kilometers per hour at the bottom of the first drop. At the top of the loop it is still doing about 17 meters per second, comfortably more than the roughly 10 meters per second it needs there.

It also clears the 25-meter hill, and the brakes stop it at the end. Along the way, friction has quietly turned about 30 percent of its energy into heat.

With μ = 0.02, the model gives 97.7 km/h at the bottom of the drop and 16.8 m/s at the loop top, where contact needs v² ≥ g·r, at least 9.9 m/s for r = 10 m. The car clears the 25 m hill and reaches the brakes having lost 29.9% of its starting energy.

With no friction at all, the bottom speed would be 100.9 km/h and the loop-top speed 19.8 m/s, so even this small friction has a visible effect.

Now Olly makes the wheels rub much more. The coaster still zooms down, but not as fast.

It goes around the loop very slowly. Then it can't get up the next hill. It rolls back!

Choose the sticky wheels: four times the friction. The first drop is still exciting, about 88 kilometers per hour at the bottom. But the friction keeps taking energy away all through the ride.

At the top of the loop the car is down to about 7.5 meters per second, too slow for the track to keep pushing on it. In the model, extra wheels hold it on the track; most real coasters have wheels on both sides of the track for safety. Then it climbs only partway up the second hill and rolls back. In fact, the ride already fails at less than twice the normal friction.

At μ = 0.08 the bottom speed falls to 88.3 km/h and the loop-top speed to 7.5 m/s, so v² < g·r: the normal force at the top would be negative (−0.42 g), meaning the car would leave the rail without the up-stop wheels the model assumes. It then stalls on the 25 m hill, having lost 68.2% of its energy, and rolls back.

The threshold is low: μ = 0.03 still clears the hill, but μ = 0.035 does not. At μ = 0.07 the loop-top speed is already 9.4 m/s, just under the 9.9 m/s needed.

The coaster gets all its energy from the first big hill.

Rubbing turns some of that energy into heat. More rubbing uses the energy up faster, so there isn't enough left for the end.

At the top of the first hill, the coaster has stored energy because it is high up. As it drops, that turns into the energy of movement, and on each climb it turns back into height. Friction from the wheels rubbing on the track and from the air turns some of it into heat instead, and it never comes back.

More friction means more energy lost on every meter of track, so less is left for the loop and the last hill. Our model is simple: it lumps wheel and air friction into one number and uses a perfectly round loop.

Energy per unit mass obeys ½v² + g·h + losses = constant, with the losses growing as μ × |N| × distance, where N/m = v²κ + g·cos θ. Curves raise N, so the loop and dips cost extra energy; higher μ multiplies every loss.

Model limits: one μ lumps rolling friction and air drag, though drag really grows with speed squared; the car is a point; the loop is a circle, which gives higher g-forces than real teardrop or clothoid loops; there is no train length, track flex or wind. The rollback assumes wheels under the rail keep the car on the track.

On a real roller coaster, the first hill is the tallest.

That is because rubbing starts slowing the coaster right away. Builders try hard to keep the rubbing small.

Engineers at Duke University explain that the first hill of a roller coaster is always the highest point, because friction and air start taking energy as soon as the cars drop. Friction comes from the wheels rubbing on the track and from air rubbing against the cars, and it turns the ride's useful energy into heat.

That's why a coaster can't climb back to its starting height unless it has a second chain lift. Keeping friction small is one of the biggest challenges for coaster engineers. For safety, most coasters also have wheels on both sides of the track.

A TeachEngineering lesson from Duke University's Pratt School of Engineering notes that the first hill is always the highest because friction and drag immediately begin removing energy; friction from wheels on track and from air converts gravitational potential and kinetic energy into heat; cars cannot regain their initial height without a second chain lift; minimizing friction is one of the biggest challenges for coaster engineers; and most coasters have wheels on both sides of the track for safety.

OpenStax describes friction as a nonconservative force: the work it does converts mechanical energy into thermal energy, so the total mechanical energy falls. The model's rollback is the result of exactly that bookkeeping.