The Physics of Motorcycling

Since I wrote a post on the Physics of Driving (March 2014), it seems only logical and fair to write one on the physics of motorcycle riding. The physics is more complex and counter-intuitive, but it’s also more intriguing.

In both cases the driving force (excuse the pun) is gyroscopic dynamics, though, in the case of a motorcycle, it’s both more central and more controlling. I can still remember the first time I went round a decent corner (as opposed to a street intersection) on a motorcycle and felt the inherent weightlessness it generates. This is the appeal of riding a bike and what separates the experience viscerally from driving a car.

As I’ve already explained in my previous post on driving, it’s the muscle strain on our necks that tells us how hard we are cornering, whether we are in a car or on a bike, though the effect is reversed from one to the other. In the case of a car we lean our heads into the corner to balance the semi-circular canals in our ears, and our neck muscles subconsciously tell us what the lateral force is in a subjective sensory manner. In the case of a bike we lean our bodies and keep our heads upright - because we feel effectively weightless - but the strain on our neck muscles is exactly the same, even though it is reversed.

So that explains how it feels but it doesn’t explain how it all works. The physics is not easy to grasp, but the effect is relatively easy to explain, even if one doesn’t understand the dynamics behind it, so please persevere with me. There is a second law of angular momentum, which effectively says that if you apply a torque around an axis perpendicular to the rotating axis, you will get a rotation around the third axis, called precession. One usually draws diagrams at this stage to demonstrate this, but I can do better: I will give you an example that you may be able to perform at home.

A surveyor’s plumb bob works best to demonstrate this, but a bicycle wheel can work as well. Take a plumb bob with its string wrapped around it, hold it horizontally so the wound string is vertical, then let it go while holding the end of the string. As it falls the unwinding string makes the plumb bob spin about its horizontal axis, but when it gets to the end of the string, it doesn’t fall over.  It precesses, giving the impression of weightlessness. This YouTube video demonstrates what I’m talking about rather dramatically with a heavy flywheel, and its sequel demonstrates it even better, and explains the so-called weightless effect. And this video explains the physics concerning the 3 axes using an ordinary bicycle wheel on the end of a rope (which you may be able to do yourself) .

So what has all this physics got to do with riding a motorcycle? It’s what gets you around a corner – as simple as that – but the way it does it is completely counter-intuitive. To get the bike to lean over we apply a torque, via the handlebars, perpendicular to the rotational axis, only we apply it in the opposite direction to what we might think. Basically, if you push on the bar in the direction you want to turn, it will lean over in that direction. By ‘push’ I mean you push on the left bar to lean left and on the right bar to lean right. This is the counter-intuitive part, because we would think that if we pushed on the left bar the wheel would turn right. In fact, I’ve argued about this with people who ride motorbikes, but I know it’s true because, I not only understand the physics behind it, I put it into practice in over a decade of riding.

Now, when the bike leans over, it behaves exactly the same as the fly-wheel in the videos, and, under the force of gravity, the bike precesses around the corner, generating a feeling of weightlessness at the same time.

So that’s the core of the physics of riding a motorcycle but there’s more. In a car you can swerve and brake at the same time, as any advanced driving course will teach you. But on a bike you can do one or the other but not both. If you brake in a corner, the bike will ‘stand up’ and there is nothing you can do about it. This is different to simply closing the throttle, when the bike will tighten its line (turn tighter). Now, why this quirk of physics may seem catastrophic, it’s what allows you to brake in a corner at all. You see the bike will still follow the same curved trajectory while it’s slowing down, and it does it without any intervention from you except for the application of brakes.

The other laws of physics I explained in my last post, regarding the inverse law of speed versus rate-of-change of direction, and the braking distance following the speed squared law still apply. In other words, it takes twice as long to change direction at double the speed, and it takes 4 times the distance to brake at double the speed.