What if a roller coaster were launched?

A roller coaster usually starts at the top of a tall hill. It rolls down and gets faster.

What if the car got a big push at the start instead? Could a push help it go around a loop?

On a traditional roller coaster, a chain pulls the train up a tall first hill, and gravity does the rest. The height is stored energy that turns into speed on the way down.

But some coasters start with a launch: a fast push that sends the train racing off. In this lab, Olly's coaster has a small first hill, only 15 meters tall, and a loop with a 7-meter radius. Can a launch get it around the loop when the hill alone can't?

Ann-Marie Pendrill of the University of Gothenburg explains that on launched coasters the lift hill is replaced by a horizontal launch, which supplies the energy as kinetic energy; after that, the ride trades potential and kinetic energy just like a traditional coaster.

This lab uses a model with a 15 m start, a 7 m radius loop and a small amount of friction, and asks whether a 10 m/s launch at the top of the first drop is enough to carry the car through a loop the drop alone cannot.

The car starts still at the top of a small hill.

It rolls down and goes into the loop. But it isn't fast enough. It can't get over the top!

First, no launch. The car starts at rest, 15 meters up, and rolls down. At the bottom it is moving at about 60 kilometers per hour.

The top of the loop is 14 meters high, and the car needs at least 8.3 meters per second up there to stay on the track. But it has lost some energy to friction, and it only started 1 meter higher than the loop's top. It never gets over the top, and it rolls back.

From rest at 15 m with μ = 0.02, the car reaches about 60 km/h at the bottom. The 7 m loop's crest is at 14 m, and the critical speed there is √(g·r) = √(9.81 × 7) = 8.3 m/s.

Even without friction, energy conservation would give only √(2g × 1 m) ≈ 4.4 m/s at the crest, well short; with friction the car does not reach the crest at all. Starting from rest, the model needs a first drop of at least 21 m to complete this loop.

Now Olly gives the car a big push at the start. Zoom!

It rushes down the hill even faster. Around the loop it goes, just barely!

Now the car is launched, already moving at 10 meters per second (36 kilometers per hour) as it starts down the same 15-meter hill. At the bottom it reaches about 69 kilometers per hour.

At the top of the loop it is moving at 8.4 meters per second. It needs 8.3. It makes it, just barely! Try a launch of 9.5 meters per second and it falls short. The launch did the job of a taller hill: without a launch, the hill would need to be about 21 meters high.

With v₀ = 10 m/s, the car reaches about 69 km/h at the bottom and crosses the loop top at 8.4 m/s against 8.3 m/s needed: the track's push there is almost zero. At v₀ = 9.5 m/s it arrives at 7.9 m/s and fails.

The launch adds ½v₀² = 50 J per kilogram, the same as about 5.1 m of extra height (v₀² ÷ 2g). With friction, the model's no-launch equivalent is a 21 m start, because a taller drop also loses more energy along the way.

A tall hill gives a coaster energy. A fast push gives it energy too.

More energy at the start means more speed at the top of the loop.

A roller coaster's energy comes in two kinds. Height energy (potential energy) is stored when the car is high up. Movement energy (kinetic energy) is what it has when it moves. On the way down, height energy turns into movement energy, and on the way up, back again.

A lift hill gives the car height energy. A launch gives it movement energy straight away. Either way, what matters at the top of the loop is how much energy is left after friction. The launch adds enough to get over.

Energy per kilogram at the start is g·H + ½v₀², and friction removes some along the way. At the loop crest the car needs ½v² ≥ ½g·r, so g·H + ½v₀² − losses ≥ g·2r + ½g·r. A launch raises the left side without raising the track.

The model's limits: a point car on a 2D track, a circular loop, friction and drag lumped into one coefficient, and the launch shown as a starting speed rather than a real launch track with its own acceleration. Its 10 m/s maximum is far gentler than real launches.

Some real roller coasters start with a huge push. They go from standing still to very fast in just a few seconds!

Some use strong magnets. Some use a cable that pulls them.

Real launch coasters are much faster than our lab's gentle push. Physics World describes Stealth at Thorpe Park in England, which uses a hydraulic system to catapult riders from 0 to 128 kilometers per hour in less than two seconds. A winch pulls a 'catch car' along the track, which pulls the train and then lets it go.

Other rides use electromagnets on the train and the track to pull and push the train forward, reaching more than 95 kilometers per hour in a few seconds. Some newer coasters add more launches partway through the ride.

Pendrill notes that horizontal launches date back to the 1970s, when Revolution, a shuttle launch coaster, stored its energy in a flywheel. Linear induction and linear synchronous motors arrived in the 1990s, compressed-air and hydraulic launches in 2002, and a hydraulic launch carried Top Thrill Dragster at Cedar Point to an altitude record in 2003.

Physics World reports Stealth's hydraulic launch from 0 to 128 km/h in under two seconds, and electromagnetic launches reaching more than 95 km/h in a few seconds, sometimes repeated mid-ride.