FOREWORD
Aren't those brightly coloured little screws on the top of the fork or on the rear shock absorber reservoir absolutely charming?? And what about the pre-loading adjustment nuts? So cool! Each of us at some point has given in to temptation and started turning those screws in or out to adjust our bikes to our own personal riding style. And what were the results? Most of the times, simply awful: if some improvement was obtained on slower roads, in fast corners it felt as if you w

ere dancing twist on you bike, or vice versa Š

To change individual adjustments in order to obtain the best general set-up, it is necessary to become familiar with the principles and laws on which suspension work is based.
Please refer to the Paddock Garage sections Suspension Setup and Chassis Setup for the actual setting procedure.

GENERAL SUSPENSION CONCEPTS
The task of a suspension is to mediate between the bumps in the road and the vehicle attitude, which must be kept constant as much as possible (in other words, to keep constant the wheel-base, offset on fork yokes and centre of gravity position values).

The motorcycle as a whole can be ideally divided into two main groups: "non-suspended masses" or "unsprung weight" (masses in "direct" contact with the ground, such as the wheels, discs and brake calipers) and "suspended masses" or "sprung weight". Suspensions work as the interface between these two groups.

A suspension contains a mechanism able to deform, which connects the wheel and chassis: the part of this mechanism which can be deformed is the shock absorber, whose task is to determine according to which elastic principle and how soon the initial position can be regained. The shock absorber has a "spring" element and a "damping" element. The distinction between these two functional parts is visible in the rear shock absorber, while the same parts are hidden inside the front shock absorber (generally, of the "telescopic fork" type).

The SPRING
Let's consider a system in which a mass is connected to a frame via a spring.

Mass + spring system free to move on the x-z plane.

Let's suppose that no friction exists between the m mass body and the support surface. Let¹s assume that the body is moved in such a way as to compress or extend the spring. The force necessary to do this is given by the following law:

where k is the spring rigidity constant and x is the measure of the displacement from the rest position. This law produces a linear trend as shown in the graph opposite.

Spring characteristic (elastic law)

By moving the mass to a position different from its state of balance, the spring will be loaded with Potential Energy. Potential Energy is expressed by the following equation:

If we leave this system free, it will not be balanced: therefore, it will tend to return to its initial position. During the system¹s return to its initial position, the Potential Energy will turn into Kinetic Energy, expressed by:

where v is the body velocity. Once the initial position has been regained, all the Potential Energy will have turned into Kinetic Energy, therefore, the system will still be not balanced. This is the reason why the spring, if it had been compressed, will begin to extend by losing Kinetic Energy and acquire Potential Energy again. Under ideal conditions, this process would continue indefinitely in accordance with the following law:

The resulting movement is plain harmonic motion, according to the following law:

where x0 is the oscillation amplitude (i.e. by how much the mass has been displaced initially from its state of balance) while w is the system own frequency. I would like to remind you that the system own frequency is linked with the spring elastic constant and mass according to this equation:

This motion trend in time is shown in the graph.

Plain harmonic motion

From these simple considerations, you can understand that a suspension with just a spring would make it impossible to ride a bike. However, another consideration ought to be made. Let¹s suppose to apply a force F to the system, repeated over time with a frequency W . This is expressed by the following law:

This situation is obtained when riding a bike on cobblestone streets or roads with bumps placed at the same distance one from the other

Amplified damped harmonic motion

When the frequency W coincides with the system's own frequency w , critical conditions are obtained; the result is an amplitude increase that tends to continue indefinitely, which inevitably leads to a system crisis and subsequent destruction.

Summing up: a mass connected with a spring which is not at rest will continue to move according to the laws of plain harmonic motion with no time limit, if left free to do so.

By applying a pulsating force to the mass-spring system, the risk is to obtain a considerable increase in the oscillation amplitude.

This problem can be solved by using a device that brings the system back to its initial position in the smallest possible number of oscillations. This device is the shock absorber, which works as an oscillation damper. Its operation principle will be analysed in detail in the next section.

The DAMPER
It is used to dissipate the energy transmitted from the road to the suspension spring. It prevents the elastic element oscillating indefinitely or resonating, which would eventually break it.

A system made up of a body with a mass m, a spring and a shock absorber can be sketched as follows:

System including a mass+spring+damper free to move on the x-z plane

The damping action of the shock absorber is proportional to the displacement speed of the body with a mass m according to this law:

R is the damping force, is the speed at which the body with a mass m moves and c is the damping constant. By introducing a damping element we will obtain a damped harmonic motion, in other words, an oscillating motion whose oscillating amplitude tends to decrease over time. A "c" value exists, called critical damping, which causes the system to come to a stop in one single oscillation, as shown in the following picture:

Damped harmonic motion under critical damping conditions This is the ideal condition, the goal that we should set ourselves when we design or modify the set-up of a motorcycle. Obviously, we have only considered extremely simplified cases and expressed general concepts in this paper: reality, as always, is much more complicated...

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