Rollercoasters 1: Horizontal G-force, curves and banking

I’m a big fan of the game RollerCoaster Tycoon, so when I went to Thorpe Park recently and my friends were talking about writing stuff on the physics of them (yes, we’re geeks like that) I decided to give it a go! This will (hopefully) be a series of features on the different aspects of rollercoaster physics. I’m afraid it’ll involve some of my (bad) drawings, though!

There are two types of corner: a “flat” corner and a banked corner. Flat corners are used most in single-car coasters (often called wild mouse rollercoasters), such as Rattlesnake at Chessington World of Adventures.

Flat corner on a rollercoaster, with starlings

Flat corners are most often used at the top of rides, where the cars are moving slowly. Looks like these starlings find them a nice perch, too! Image: humbert15

But why use any other kind of corner? Let’s take a look at the forces acting on a rollercoaster car going round a flat corner:

A rollercoaster car travelling around a flat corner

When a rollercoaster car goes round a flat corner, all of the centripetal force is acting at right angles.

The force you feel when you’re going round a corner – the centripetal force – pulls you in towards the centre. You might feel like you’re being pushed to the outside of the corner, because it’s a matter of perspective: to you, you’re being pulled out, although the force has to be pulling in, otherwise you wouldn’t be going round the corner!

As you can see, the centripetal force is at right angles to the gravity/weight of you and the car, and you feel its full effect pulling you inwards. You also feel it when it stops and you’re on a straight bit of track again, which is why you get bumped and shoved around so much on a flat corner, and why they aren’t used all that often. Generally, they’re used when the car isn’t travelling too fast, and when the idea is to bump and shove the passengers around! Until I figured out that I needed to use banked corners, I got very high “intensity” ratings on the rollercoasters I built on RCT, as the horizontal “g-force”, the force that acts inwards, was massive!

The other type of corner – the one that’s used more often – is a banked corner, where the corner is tilted up so that the outside of the corner is higher than the inside.

Wooden rollercoaster with banked corners

This awesome-looking wooden rollercoaster has lots of banked corners. Image: mgrayflickr

But what’s the point of the tilt? Again, let’s take a look at one of my artistic diagrams:

A rollercoaster car going around a banked corner

A rollercoaster car going round a banked corner. The weight still acts down, but now the inwards force (F) is acting diagonally.

Well, you get the idea. Because the inwards force acts diagonally, it “spreads out” the force’s effect. With all forces, you can do something called “splitting into components”: showing how a diagonal force is acting both sideways and up/down.

A rollercoaster car on a banked corner (again)

The inwards force (F) can be split, to show how its acting both sideways and down.

And now you can see why banked corners are better: only some of the centripetal, or inwards, force is acting into the centre. The rest is acting down, along with the weight: so not only do you not really notice it as much, but it helps to keep you steady and in your seat!

Next time you’re at a theme park, have a look at the rollercoasters: see if you can spot the banked and flat corners! (Hey – you’ve gotta have something to do in the queue!)

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