Why Doesn't a bike fall over whilst turning?

POSTED 21.12.16

EASL are experts in all things structural integrity. Be it a finite element analysis of an individual component, or the operating capacity of a large scale structure, we pride ourselves on producing a high quality, clear expert service.

With our team of highly specialised engineers and scientists, we love figuring out and discovering how things work and so as part of a series of blogs we’ve taken to task some everyday engineering queries you might have wondered about but never known the answers to.

The first of these is just like riding a bike, because that’s what it is! Whilst it may be one of the first skills many of us learn, often whilst learning the how, we forget the why. Whether it’s a country ride or a MotoGP final, we take to task the factors at play when tackling tight turns on two inline wheels with an engineer’s eye.

As single track vehicles, bicycles and motorcycles lack lateral stability. This lack of lateral stability presents a problem whilst cornering. If you were to stay vertical and try to corner, the bike would topple over, taking the rider with it, as many of us learnt through our first attempts with the stabilisers.

To counteract this, we learn to lean a bike into the corner. If the bike were stationary and leaning, a bike would fall. So, whilst we figure out that leaning whilst moving is important, why does the bike not fall over whilst leaning and moving?

There is a complicated way to consider at this problem that takes into account steer angle, caster angle, wheelbase and more and drifts into the stability of a bike. This focuses on the more generalised and simplified answer that looks at the problem in an inertial reference frame.

But first, let’s look at the bike sitting vertically and turning. In this situation you have four forces acting on the bike:

• Gravitational force
• Reaction force
• Frictional force
• Negative centripetal force.

The gravitational force acts downwards through the centre of mass, the reaction force acts upwards through the tyres contact patch, the frictional force acts laterally through the tyres contact patch (the frictional force that is created by the tyres), and the negative centripetal force acts laterally through the centre of mass.

So the areas of the force at play are:

• Gravitational – Centre of Mass
• Reaction – Contact Patch
• Frictional – Contact Patch
• Negative Centripetal – Centre of Mass

The direction of the negative centripetal force and frictional force can change depending on the direction of the turn, however, despite all of the forces balancing each other, the moments acting on the bike do not. With a bike, the point of lateral rotation is the contact patch of the tyre.

Since the gravitational force, frictional force, and reaction force are acting through the contact patch the moments are zero. However, the negative centripetal force is creating a moment about the contact patch. This moment results in the bike moving in the direction of the moment.

This is to put it simply, when it is upright and turning it will fall to the floor, as the forces pulling laterally are producing a moment that nothing is counteracting.

Next, let’s look at when the bike is leaning. There are still the same four forces, all acting in the same way as above. However, now the centre of mass is not vertical with the contact patch. Instead, it is displaced into the turn.

Now, there is a moment created by the gravitational force as well as the moment created by the negative centripetal force. These two moments are acting in opposite directions, therefore cancelling each other out and keeping the bike in equilibrium.

With this in mind, we can see that the quicker a bike is going, the larger the forces will be acting on the bike, and so the greater the lean would need to be. With this in mind, it’s clear to see how a MotoGP rider will need to lean much more than the daily cyclist commuter, unless they are in a significant hurry!

Have you got any engineering questions you’ve always wondered about the answer to? Let us know on twitter @easlstress and be sure to keep an eye for our next quick question blog!