by L.Mitolo, S.Garbin, R.Berritta
Motorcycle Dynamics Research Group, University of Padua
and Jim Gianatsis, FastDates.com
Forword
The kinematics of a motorcycle is particularly important because of its effects on the vehicle's dynamic behaviour. Our Kinematic references here refer to a rigid motorcycle, i.e. without suspensions and with non-flexible tyres, fitted to solid wheels represented as circular-section toroidal solids. Suspension movement, chassis pitch and tire flex / distrotion adds a wide range of variables to our measurements which we really don't want to conside in the basic explaination given here. The geometrical quantities normally used to characterize a motorcycle's front wheel operation are:

• Trail
• Pitch
• Inclination angle of the steering head
  

These quantities are normally used to determine the vehicle's handling, or in other words, the vehicle's ability to follow the controls given by its rider as quickly and as accurately as possible.

This chapter will examine in detail trail, and its effect on the motorcycle's dynamic behaviour. Trail is a key parameter in determining a motorcycle's dynamic characteristics. It is a geometric parameter, defined as "the distance between the point where the front wheel touches the road and the intersection point between the steering axis and the road".

In the figure above, trail is indicated by the letter a.
Normal trail (an) is equally important: it is defined as the distance between the point where the tire touches the road and the vehicle's steering axis.
The connection between the two types of trail is given by the following relation:

Where E is the inclination angle of the steering head.

Trail is very important for vehicle stability, especially in the rectilinear motion. In order to see how trail affects the vehicle's stability, let's consider a motorcycle travelling on a straight road at a constant speed V. Let us suppose that, at a given time, some intervening disturbance (e.g. a gust of wind, bumps in the ground etc.) causes a slight rotation of the steering towards the left. The steering rotation applies a lateral friction force F to the contact point between the tyre and the road. The friction force is the result of the tire slippage shown in the figure:

The inclined wheel speed vector V consists of two components. One is parallel to the wheel plane and indicates its surface speed, equal to Wf Rf .
The other component, perpendicular to the former one, indicates the slippage speed which produces the force F. This force generates torque which tends to bring the steering back to its equilibrium: this straightening force is proportional to the normal trail value.

Low trail values produce low lateral resistance to movements; steering manoeuvres require less rider strength, but the steering does not feel stable and is sensitive to any bumps in the road. High trail values increase the vehicle stability on straights, but also negatively affect the motorcycle manoeuvrability and handling: more rider's strength is required in corners.

We cannot extensively deal with trail without mentioning pitch (p) and hence, rear trail (an). Pitch is defined as "the distance between the points where the tyres touch the road", while rear trail is "the distance between the point where the rear tyre touches the road and the steering axis".

The lateral forces generated by the friction between the tyre and the road produce moments around the steering axis proportional to the distances an and bn; these could be expressed as functions of pitch and trail:

[Rf and d (see figure 1) are the front tyre toroid radius, and the distance of the steering head from the fork axis
(offset), respectively.]

This consideration suggests that pitch and trail are closely linked and should therefore be taken into account together: it would not be correct to talk about the trail value if this is not referred to the motorcycle pitch value. To compare different models of motorcycle, reference should therefore be made to the ratio of normal front trail to normal rear trail Rn.

Racing motorcycles have Rn approximately equal to 6%, while sports motorcycles have ratios of 6-6.5%; touring motorcycles range between 6 and 8% while custom bikes' values are 7-8%. Clearly, custom bikes must be stable at low speed, given their special use. By contrast, sports and touring bikes need lower trail than pitch values, in order to handle well throughout their application range. Finally, racing bikes must sacrifice high-speed stability to handling. This is a smaller problem than it seems, in terms of safety, because racing bikes are normally used by accomplished riders only.

Trail is most easily adjusted by altering a motorcycle's steering head angle E. Sportbikes and Superbikes handle best when the sterring head angle is kept low, or "steep" as often refered, at an ideal 23.5 degrees from vertical. Sportbikes like the Ducati 748/916/998 Superbike models have an adjusatable steeringhead that sets to 23.5 degress in its steepest setting. This provides a very small Trail amount for quicker steering and less dramatic changes in wheelbase and pitch as the bike turns and the suspension moves thoughout it's range of operation, helping to keep the handling quick, yet stable.