June 4, 2013

# The abbreviated guide to bicycle dynamics

## What keeps you upright?

Reference the following for more details: Motorcycle Chassis Design: Reference pages 33-43 How and why: Motorcycle Design and Terminology: Chapter 3 Motorcycle Tuning: Chassis: Chapter 1 Bicycles & Tricycles: Chapter XVII

Fundamentally larger two wheeled vehicles (ie. motorcycles) stay upright due to the simple principles of gyroscopic effect. As they move faster, the wheels create greater and greater gyroscopic forces which in turn keeps the bike under the rider staying upright. This effect is determined by speed (velocity) and under the certain ‘velocity threshold’ (approx 4ft/second for the pointy heads out there), it  is diminished until it becomes more of a combination of rider balance, skill and bike setup (geometry, center of gravity etc. discussed below) that ultimately keeps the bike upright.

In the case of bicycles, the gyroscopic forces created by the wheels are not enough alone to keep the bike upright, as the mass of the rider + the frame etc. (not including the wheels) far outweigh the wheels themselves. So here’s the cool bit….

Once past the threshold and the wheels are creating a sufficient gyroscopic force (even though that force may not be enough to balance the bicycle), the bike and the rider are subjected to an effect called ‘gyroscipic precession’ which occurs when the wheels, read the gyroscopes, are affected by a tilting or turning force. Put in simplest terms, when in motion and vertical, tilting the axle to the left (like when you are banking into a turn) will cause the wheel to pull strongly to the left but if you apply a turning force from the left (like being shoved by an invisible hand… or steering through the bars), the wheel will bank to the right. Yup, at speed, steering to the left makes the bike pull to the right. But what keeps the bike upright when shunted to the left? While the gyroscopic progression tilts the bike to the right, it creates an arc (through the front wheel) both you and the bike will travel on. A centrifugal force (which is created by spinning a mass, you in this case, which creates a force that pushes the mass away from the center of the arc) is then created which wants to throw you to the left, thus the two forces balance one another out and upright you stay. This is called the ‘righting effect’. You can feel these forces by holding the front wheel of your bike by the axle and having a friend spin it away from you. By tilting and turning the wheel while its spinning you will feel the different forces that act upon it.

## Steering and not falling over:

So how do you get a bike to turn if we know that when we turn the bars to the left, the bike wants to pull to the right and ultimately want to stay upright?

A secondary factor comes to play, the centrifugal force of the wheels and the bike+rider. OK, so the gyroscopic progression created aids in keeping the bike upright. By turning the bars to the left, we cause the wheel to pull to the right (an effect called ‘counter steer’, which is used to initiate a turn), this we know. We also know that by initiating the turn to the right, the centrifugal forces want to throw both you and the bike to the left, so a balance is achieved and the bike ultimately wants to stay upright. To break this, we push harder to the left which causes you and the bike to tilt more to the right. As you do this, the centrifugal forces continue to create a force that pulls you left and a thing called gravity wants to pull to to the ground. What happens next is an equilibrium of lean, and around the corner you go… without falling over. At a certain point though, the ground forces on the tyre begin to pull the tyre to the right, which is felt as a pull to the right. If you go with it, the turn tightens, if you leave it, your arc stays the same and if you push against it, you start to straighten up. So to sum it up, past a certain speed, you initiate a turn by counter steering. Once into the turn and at a certain point, you can steer the bike normally, turning to the right tightens the turn to the right while turning to the left straightens you up.

## Trail

Have a look at your forks, you’ll notice two things.

The first is that the dropouts place the axle in front of the forks. The second is that the crown actually offsets the fork legs from the centerline of the headtube. All up, the forks are forward of the headtube by ‘x’ amount. This is to create ‘trail’.

Trail, in a nut shell, is the horizontal distance of the front axle from the angle of the headtube where it intersects the ground; and is the complete distance created by the combination of rake/head angle and wheel offset (distance of the axle from the fork leg). While a simple measurement, trail affects the straight line stability of the bike by creating an angle between the contact patch of the tyre and the direction of travel, a factor known as ‘slip angle’. Slip angle works like so: When turning to the left, a force is created through the contact patch of the tyre. This force occurs because the axle path lies behind the steering axis (the trail) thus it swings in an arc, creating a friction force against the direction of travel. As we know, for every action there is an equal and opposite reaction, thus a righting force is created on the wheel when the opposite force reacts on the turning wheel – remember our example about what keeps a wheel upright? In the most simplest terms (and believe us, we have boiled this right down!), the amount of trail determines the automatic righting effect of the front wheel when subjected to external forces such as bumps. If the trail is negative, meaning the contact patch is in front of the steering axis, a bump that causes the wheel to deflect to the right will make the bike turn sharply to the right as the righting effect is minimised; in other words the axle is being tilted rather than turned. This is all bad and will make the bike highly unstable in bumpy scenarios. In the case of positive trail, where the trail puts the contact patch behind the axis of steering, the righting effect is increased as the wheel is being turned through the axle rather than ’tilted’. As such the ‘self righting’ effect comes into play causing the wheel to want to remain upright when affected by our external bump force.

So, if a bike is to be stable when the going gets rough, or highly stable on flat trails, there needs to be enough trail that will provide an element of automatic self righting. Too much trail though will make the bike’s steering sluggish and slow in tight twisty stuff, but to little and it becomes twitchy, fast reacting in tight turns but requiring higher levels of input from the rider to stay upright. Ironically, with telescpoic forks, as they compress under braking the trail is automatically reduced and the bike becomes twitchy when you least want it to! But wait, there’s more…

After 20 odd years working in and around the cycling industry, for myself and others, I decided riding bikes was more fun than working with them. Over that time though, I wrote (and some wrote for me) a lot of stuff about bikes, on blogs and the like. Some was good, some, well... not so much. Rather than loose it all when I shut everything down once and for all, I have kept some of my favourite, and more popular pieces here for... prosperity?

I also am working on new pieces as well...

Gerard