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Log In Sign Up. Umar Riaz. Anyone who uses it as such does so at his own risk and peril. Street testing motorcycles can be dangerous. The author and publisher are not responsible for any damage caused by the use of any information contained in this book.

All rights reserved. No part to this book may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage and retrieval system, without permission in writing from the author.

However, this type of transaction takes place without the emotions and special relationship which have always bound me to motorcycles. I remember watching my neighbor get his Parilla ready. Dressed in black leather, he would slowly put his gloves on, push down on the pedal and finally drive off.

As the motorcycle disappeared into the distance I could hear the symphony created by its engine slowly fade away among the clouds: mine was true passion. It was the Sixties. There were the elegant and refined Mods with their shining scooters, and the Rockers, both feared and respected, with their motorcycles.

England was the homeland of motorcycles. When I got off the ship in Dover, I remember seeing a group of motorcycles next to some scooters. They were the wonderful English motorcycles of the Sixties and Seventies that left the sign of their passing with drops of motor oil on the road wherever they went.

I immediately knew that I was a motorcyclist. As soon as I got home, I managed to buy an old Guzzi Falcone I worked all winter, every evening, to perfectly restore it. My desire to hear the engine roar, to smell the air and to feel the wind blow across my cheeks drove me in my mission until one day in early spring everything was ready. My Falcone never betrayed me, it always gave me incomparable emotions. As I rode it, curve after curve, the engine pushed on almost as if it were a hammer strong enough to forge any type of steel with violent blows of metal on metal.

This book is the result of this past and present passion of mine for motorcycles. I have tried to offer a new approach to technical-scientific writing by combining the exact and often aseptic nature of scientific discourse with my passion for this perfect vehicle.

I realize that this is no small challenge, but it is this very passion, of a man who feels more at ease on a motorcycle than behind a desk, which has motivated my research in the field of motorcycles. Together with its thorough technical discussion, this book also takes into account the fascinating history of the motorcycle and motorcyclists. No business will ever be able to take away the adventuresome, and somewhat crazy, nature of the motorcycle.

Therefore, in this chapter, in addition to the kinematic study, some simple examples of the dynamic behavior of motorcycles are reported in order to show how kinematic peculiarities influence the directional stability and maneuverability of motorcycles.

Each revolute joint inhibits five degrees of freedom in the spatial mechanism, while each wheel- ground contact point leaves three degrees of freedom free. While he drives, the rider manages all three major movements, according to his personal style and skill: the resulting movement of the motorcycle and the corresponding trajectory e.

This generates one maneuver, among the thousands possible, which represents the personal style of the driver. These considerations have been formulated assuming that the tires move without slippage. However, in reality, the tire movement is not just a rolling process. The generation of longitudinal forces driving and braking forces and lateral forces requires some degree of slippage in both directions, longitudinally and laterally, depending on the road conditions.

These parameters are measured with the motorcycle in a vertical position and the steering angle of the handlebars set to zero. The wheelbase p is the distance between the contact points of the tires on the road. The trail a is the distance between the contact point of the front wheel and the intersection point of the steering head axis with the road measured in the ground plane.

Together these parameters are important in defining the maneuverability of the motorcycle as perceived by the rider. It is not practical, however, to examine the effects produced by only one geometric parameter, independently of the others, because of the strong interaction between them.

Here we will present some considerations regarding the way in which these parameters influence the kinematic and dynamic behavior of motorcycles. The value of the wheelbase varies according to the type of motorcycle. It ranges from mm in the case of small scooters to mm for light motorcycles cc displacement to mm for medium displacement motorcycles cc up to mm, and beyond, for touring motorcycles with greater displacement. In general, an increase in the wheelbase, assuming that the other parameters remain constant, leads to: an unfavorable increase in the flexional and torsional deformability of the frame.

The trail and caster angle are especially important inasmuch as they define the geometric characteristics of the steering head. The definition of the properties of maneuverability and directional stability of motorcycles depend on them, among others. From a structural point of view, a very small angle causes notable stress on the fork during braking. Since the front fork is rather deformable, both flexionally and torsionally, small values of the angle will lead to greater stress and therefore greater deformations, which can cause dangerous vibrations in the front assembly oscillation of the front assembly around the axis of the steering head, called wobble.

The value of the caster angle is closely related to the value of the trail. The value of the trail depends on the type of motorcycle and its wheelbase. It ranges from values of 75 to 90 mm in competition motorcycles to values of 90 to mm in touring and sport motorcycles, up to values of mm and beyond in purely touring motorcycles.

According to this point of view , the steering system could hypothetically be made up of two little rockets placed perpendicular to the front wheel which, when appropriately activated, could, although not without significant if not insurmountable difficulties for the rider, generate lateral thrusts, that is, perform the same function as the steering system.

To develop this concept, let us consider a motorcycle driving straight ahead, at constant velocity V, and let us suppose that an external disturbance for example, an irregularity in the road surface or a lateral gust of wind causes a slight rotation of the front wheel to the left.

For the time being, let us ignore the fact that the motorcycle starts to turn to the left and that because of centrifugal forces, begins at the same time to lean to the right, concentrating our attention instead on the lateral friction force F generated by the contact of the tire with the ground.

In other words, let us suppose that the motorcycle is driving at constant velocity V and that the front wheel contact point also has velocity V in the same direction. A frictional force, F, therefore acts on the front tire. F is parallel to the velocity of slippage but has the opposite sense, as illustrated in Fig. Since the trail is positive, friction force F generates a moment that tends to align the front wheel.

The straightening moment is proportional to the value of the normal trail. If the value of the trail were negative the contact point in front of the intersection point of the steering head axis with the road plane and considering that friction force F is always in the opposite direction of the velocity of slippage, a moment around the steering head axis that would tend to increase the rotation to the left would be generated.

In Fig. Figure 1- 5 demonstrates that the road profile can make the trail negative, for example, when the wheel goes over a step or bump. Small trail values generate small aligning moments of the lateral friction force. Even if the rider has the impression that the steering movement is easy, the steering mechanism is very sensitive to irregularities in the road.

Higher values of the trail obtained with high values of the caster angle as shown in Fig. Fig Summary of the effect of trail during forward movement. During curvilinear motion, road gripping is assured by the lateral frictional forces, which are perpendicular to the line of intersection of the wheel plane with the road.

This simple consideration shows how the wheelbase and the trail are intimately connected to each other and should therefore be considered together. Since the load on the front wheels is high due to the weight of the motorcycle, the choice of a small trail lowers the value of the torque that the rider must apply to the handlebars to execute a given maneuver.

In addition, it is worth pointing out that these motorcycles are normally used at rather low velocities, and they do not therefore need long trails, which, as previously noted, assures a high directional stability at high velocities.

This ratio is also low for scooters since they are used or should be used at low velocities and therefore maneuverability has a higher priority than directional stability. Strictly speaking, the ratio should take into account the distribution of the load on the wheels. A motorcycle that has a heavy load on the front wheel needs a shorter trail.

In fact, heavier loads on the front wheel generate greater lateral frictional forces in proportion to the lateral motion of the wheel. Therefore, for the same aligning torque acting around the axis of the steering head a smaller trail is sufficient. Let us add the following assumptions: the roll angle of the motorcycle is zero; the wheels have zero thickness. As shown in Fig. The distance OD of the wheel center from the road plane is greater than the radius of the wheel OP.

Actually, the wheel is not raised from the ground but rather lowered. Supposing that we keep the axis of the steering head immobile, the center of the wheel moves along the steering head axis to the point O1. Consequently, the contact point P1 moves forward, as shown in Fig. In the final position the distance OP is obviously equal to the radius of the wheel OP. When the steering angle is zero Fig. This value must be subtracted from the lowering of the front axle, calculated without the offset.

In conclusion, with offset, there is less lowering of the front wheel center than with zero offset. The example shows that ignoring the offset causes a significant error in calculating the lowering of the front wheel center. Lower caster angles reduce the lowering of the front wheel center. The value of the trail slightly depends on the steering angle. In the following section, a more complicated kinematic model is used taking into account both the roll angle and the radius of the front tire cross section.

For example, let us consider a motorcycle in rectilinear motion at velocity V, which at a certain point enters into a curve. We have seen that the rotation of the steering, considering zero wheel thickness, generates a small lowering of the steering head, which causes a small forward rotation of the rear frame around the axis of the rear wheel pitch rotation. We will now see how, in reality, following the roll motion, the contact point of the rear wheel with the road plane is displaced.

The origin is established at the contact point Pr of the rear wheel with the road plane. The axis x is horizontal and parallel to the rear wheel plane. The z axis is vertical and directed downward while the y axis lies on the road plane. Consequently the triad fixed to the rear axle Ar, Xr, Yr, Zr rotates at the same angle around the x-axis.


Motorcycle Dynamics

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