Motorcycle lift is dangerous since it reduces the load on the wheels and, thus, tire adherence. This is especially true regarding the front tire since the center of pressure is generally in front of and above the center of gravity. Typical motorcycles generate positive upward lift force, however, in order to counteract this phenomenon and increase load on the wheels, it would be necessary affix some sort of wing at the front of the motorcycle as in the case of racing cars.
To lessen the undesired lift effects, modern fairings are designed to reduce lift to a minimum. The aerodynamic characteristics of motorcycles are given by the drag area CDA drag coefficient times the frontal area and by the lift area CLA lift coefficient times the frontal area. The value of the product CDA can vary from 0. The resistance to forward motion is influenced in different ways by the various motorcycle components.
For example, the following are the effects of some components on the product CDA: front fairings produce an improvement ranging from 0. Reference values may vary from 0. Small displacement Grand Prix class motorcycles cc reach values around 0. If the frontal area A and the product CDA values are known, the resistance coefficient CD, which is usually on the order of 0. The product of the lift coefficient times the frontal area of the section CLA ranges from 0.
The pitching moment caused by the aforementioned forces can be dangerous, since it leads to a decrease in the load on the front wheel and an increase in the rear one.
These variations can significantly modify the dynamic behavior of the motorcycle. In rectilinear motion, if there is no crosswind, the x-z plane of the motorcycle with rider is the plane of symmetry and the forward velocity of the motorcycle lies in that plane.
The lateral aerodynamic force and the rolling and yawing moments are zero. However, they are not zero if the rider moves from a symmetric position, if there is lateral wind, or if the sideslip angles of the tires are not zero. In particular, when the rider moves into the curve, displacing his or her body and knee towards the inside of the curve, an aerodynamic yawing moment is generated helping the motorcycle move into the curve.
During the curve if the rider stays in this leaned position the lateral aerodynamic force persists. Since the power dissipated by the aerodynamic forces depends on the cube of the velocity, a lot of power is needed to attain high velocities. Figure shows the variation of the drag force against velocity for various values of the drag area. The forces and aerodynamic moments can be measured in a wind tunnel by mounting the motorcycle on a force balance.
The wind tunnel tests make it possible to identify the presence of vortices, if any, and the current lines surrounding the motorcycle. Smoke is used to visualize the current lines, as can be seen in Fig. If no wind tunnel is available, the drag area CDA can be determined in the following ways. The motorcycle can be driven at its maximum velocity on a straight road recording the engine RPM revolutions per minute and the maximum velocity.
The power, corresponding to the number of revolutions measured, is determined by the dynamometer curve. The product of the drag coefficient times the frontal area is: without considering the rolling resistance.
There can be significant errors if the maximum velocity is not determined correctly or if the actual power of the motorcycle does not correspond to the dynamometer curve used for the calculation.. A second approach is as follows. The motorcycle can be driven on a flat road at a sustained velocity and then placed in neutral. What is the driving force and power necessary to sustain the velocity under the conditions given? Its position depends on the distribution and quantity of the masses of the individual components of the motorcycle engine, tank, battery, exhaust pipes, radiators, wheels, fork, frame, etc.
This is one reason racing motorcycles are more heavily loaded in front. In addition, the greater load in the front partially compensates for the aerodynamic effects that unload the front wheel; this fact becomes important at high velocities. It is important to keep in mind that it is preferable, as a question of safety, to have longitudinal slip of the rear wheel in an acceleration phase, rather than longitudinal slip of the front wheel in a braking phase.
In general, the position of the rider moves the overall center of gravity towards the rear Fig. Once the longitudinal position of the center of gravity has been found, its height can be determined by measuring the load on only one wheel, for example, the rear one with the front wheel raised by a known amount as in Fig.
The height of the center of gravity has a significant influence on the dynamic behavior of a motorcycle, especially in the acceleration and braking phases. A high center of gravity, during the acceleration phase, leads to a larger load transfer from the front to the rear wheel. The greater load on the rear wheel increases the driving force that can be applied on the ground, but the lesser load on the front wheel makes wheeling more probable.
In braking, a higher center of gravity causes a greater load on the front wheel and a resulting lower load on the rear. The greater load on the front wheel improves braking but it also makes the forward flip-over more likely, which occurs when the rear wheel is completely unloaded. It is clear that the choice of the height of the center of gravity and its longitudinal position is a compromise that must take into account the intended use and power of the motorcycle.
All-terrain motorcycles are characterized by rather high centers of gravity, while very powerful motorcycles typically have a lower center of gravity. The main effects of the location of the center of gravity may be summarized in the following diagram: Forward center of The motorcycle tends to over-steer in curves the rear wheel slips laterally gravity to a greater extent.
Rear center of The motorcycle tends to under-steer in curves the front wheel slips gravity laterally to a greater extent.
High center of The front wheel tends to lift in acceleration. The rear wheel may lift in gravity braking. Low center of The rear wheel tends to slip in acceleration. The front wheel tends to slip in gravity braking. The height of the center of gravity of the motorcycle alone has values varying from 0. A 77 kg rider mass has his own center of gravity at mm from the center of the rear wheel. How does the rider change the overall percentage weight distribution? The measurement of the moments of inertia is based on complex identification methodologies, which are outside the purpose of this book.
The most important moments of inertia are the roll, pitch and yaw moments of the main frame, the moment of inertia of the front frame with respect to the steering axis, the moments of the wheels and the inertia moment of the engine. In the following table, the values of the gyration radii of the motorcycle and rider, with respect to the center of gravity, are presented the moment of inertia is given by the product of the mass times the square of the radius of gyration.
The yaw moment of inertia influences the maneuverability of the motorcycle. In particular, high values of the yaw moment obtained, for example by heavy baggage placed on the luggage rack reduce handling.
The roll moment of inertia influences the speed of the motorcycle in roll motion. High values of the roll inertia, maintaining the same height of the center of gravity, slow down the roll motion in both entry and exit of a curve. Table The pressure center of the motorcycle in which the drag force is applied coincides with its center of gravity.
In addition to the drag force, the following forces act on a motorcycle: the weight mg that acts at its center of gravity; the driving force S, which the ground applies to the motorcycle at the contact point of the rear wheel; the vertical reaction forces Nf and Nr exchanged between the tires and the road plane.
The vertical forces exchanged between the tires and the road plane are therefore: dynamic load on the front wheel: dynamic load on the rear wheel: These reaction forces are composed of two elements. The first term static load on the wheel , depends on the distribution of the weight force. We will now focus on the second term. The loads on the wheels can be represented in non-dimensional form with respect to the weight: Normalized load on the front wheel: Normalized load on the rear wheel: where Sa indicates the ratio between the driving force S and the total weight mg non-dimensional driving force.
Figure illustrates the phenomenon of load transfer. The variations in the normalized loads are indicated as a function of the normalized driving force for two motorcycles with the following characteristics. The weight mg is equal to the sum of the static loads acting on the wheels and.
The driving force S and the force caused by the transfer of the load Ntr, turned upward because it has a positive sign, are applied at the rear wheel contact point. The direction of the resultant of these two forces is inclined with respect to the road by the angle: which is therefore called the load transfer angle. In order for a motorcycle to maintain equilibrium, this resultant force must be equal to and opposite in sign to the resultant of the drag force FD and the load transfer Ntr, which acts on the front wheel directed downward because it has negative sign.
The maximum hypothetical forward velocity of the motorcycle depends on the load transfer from the front to the rear wheel. When the front wheel is completely unloaded, and thus the whole load moves to the rear wheel, the limiting condition is reached when maximum velocity is attained.
The power on the rear wheel is kW. In conditions approaching the limit of wheeling phenomena, the front vertical load becomes zero. The sum of the load transfer generated by the drag force and the front component of the lift force are equal to the front static load.
If we consider that the center of pressure coincides with the center of gravity, the lift force is distributed equally between the two wheels in the motorcycle under consideration.
The power at the rear wheel, ignoring the rolling resistance force should be at least kW. At this velocity the front wheel is totally unloaded, so that it becomes impossible to control the motorcycle. The equation of equilibrium for a motorcycle in horizontal motion takes on certain characteristics according to whether the motorcycle is in an acceleration or braking phase. From the viewpoint of dynamics, the motion law of the equivalent mass is equal to that of a real motorcycle Fig.
Equating the kinetic energies, we have the following expression. The drive sprocket is keyed on the secondary shaft. What is the equivalent mass?
The equivalent mass obviously depends on the gear engaged. The transmission ratio of the gear shift varies from values equal to about 3 for the first gear the gearshift functions as a reduction gear , to values that can approach or be slightly lower than unity down to about 0. The maximum value of reduced inertia is reached when first gear is engaged. Figure shows the variation of the driving force on the wheel versus velocity, in the various gears, for a racing motorcycle. The driving force, though lower than the maximum available in that gear, is greater than the resistance force, so that the remaining driving force can be used to accelerate or go up a slope at the same velocity.
If we consider the same set velocity with higher ratios, we see that there is less driving force available for accelerating. As the velocity gradually increases, the passage to the higher ratio makes a lower quota available. Maximum velocity is obviously reached when the resistant force is the same as the driving force in the highest gear.
The comparison between the driving force curves and the resistance curve can also be made in terms of power. A diagram of useful power to the wheel can be obtained for each ratio by multiplying each curve by its corresponding forward velocity. In this case as well, the intersection point of the resistance power curve with the useful power curve, in the highest gear, determines the maximum velocity that can be reached. This is an ideal case in which the efficiencies are independent of the velocities, represented in Figure by a horizontal line.
Maximum motorcycle acceleration can be determined by integrating the following differential equation: where Pmax indicates the maximum power of the engine. By carrying out the numerical integration of the preceding differential equation, we can calculate the maximum acceleration the motorcycle is capable of reaching. Example 7 Consider a motorcycle with the following characteristics. Let use examine how changing the mass affects the velocity and acceleration. The curve of the velocity versus time, obtained by carrying out a numerical integration of the differential equation of motion, is given in Fig.
In reality the accelerations the gradient of the curve are actually lower because of the time intervals needed to change gears, during which the useful driving force is zero. Maximum acceleration is reached when the resistance force FD is zero, i. As the velocity increases, the acceleration under limiting friction conditions diminishes. This happens because part of the driving force is equated to the resistance force and therefore cannot be used to accelerate.
As the forward velocity gradually increases, the acceleration at which the wheeling phenomenon begins, decreases. This is the case since the motion of wheeling is also favored by the drag force FD, the value of which increases with velocity. Example 8 Consider a motorcycle with the following properties. The maximum acceleration of the motorcycle, at the rear wheel friction limit, is represented in the graph in Fig. As the velocity increases, the maximum acceleration decreases, since part of the driving force is equated to the resistance force and cannot be used to accelerate.
The horizontal line representing wheeling-limited acceleration is explained by the fact that acceleration does not depend on the driving force coefficient. These considerations suggest that it is appropriate to limit the maximum torque the engine can deliver, if the intention is to avoid motorcycle wheeling and rear wheel slippage. In the case under consideration, the acceleration as shown in Fig. In fact, many motorcycle riders tend to forget the rear brake, which in certain circumstances provides a useful contribution.
Its correct use is important both in braking when entering a curve and in braking during rectilinear motion when an unforeseen obstacle appears in front of the motorcycle especially when road adherence is precarious. Rol e of the re ar brake i n s udde n s tops During curve entry the use of the rear brake can be quite useful.
Expert riders use the rear brake not only to decelerate the motorcycle but also to control the yaw motion. Rear braking in entering the curve increases the sideslip angle and therefore the yaw motion of the motorcycle.
In sudden deceleration a dangerous condition could arise especially when the load on the rear wheel diminishes toward zero due to load transfer. If the motorcycle is not in perfectly straight running the force of the front brake and the inertial force of deceleration generate a moment that tends to cause the motorcycle to yaw. This is illustrated in Fig. As shown in the in Fig. On the contrary, the presence of a rear braking force generates a torque which tends to align and stabilize the vehicle as can be seen intuitively in Fig.
These simple considerations suggest that proper utilization of front and the rear brakes has a positive effect on vehicle stability.
Load trans fe r duri ng braki ng In order to evaluate the role of the rear brake during a braking event at the limit of slippage, we need to bring up some points regarding the forces acting on a motorcycle. During deceleration, the load on the front wheel increases, while that on the rear wheel decreases and thus there is a load transfer from the rear to the front wheel. If we consider a motorcycle in a braking phase Fig. To prevent a tire from slipping during braking, the value of the braking force applied to it must not exceed the product of the dynamic load acting on that tire times the local braking traction coefficient.
This latter product represents the maximum braking force applicable to the tire, that is, the braking force at the limit of slippage. Both the loads on the wheels and the braking force have been reduced to non-dimensional status with respect to the weight. We can note from the graph that the dynamic loads on the wheels are approximately equal to 0. In conclusion, the following general principles can be stated. The optimal distribution of the braking force varies according to the braking traction coefficient.
The rear brake is of little use on optimal roads and with high grip tires high coefficient of friction , but becomes indispensable on slippery surfaces reduced coefficient of friction. This limiting condition represents the forward flip over of the motorcycle when the dynamic load on the rear wheel goes to zero.
The equation of equilibrium of the moments with respect to the center of gravity provides the expression for the braking force at the point of turn over: A low value of this limit braking force indicates an increased propensity for a forward flip over. It can therefore be concluded that forward fall is favored when a motorcycle is light and when it has a high and forward position of the center of gravity.
It is important to note that the deceleration at the flip over limit depends only on the position of the center of gravity, and not on the weight of a motorcycle. It is easy to verify that the maximum deceleration is equal to gravity. If the velocity is also taken into account, deceleration increases as the velocity increases due to the effect of the aerodynamic resistance force. Obviously it is very difficult, if not impossible, to brake at the flip over limit with a zero load on the rear wheel.
In this condition nearing the limit, the best riders are able to attain decelerations equal to 1. The distribution curves for braking and deceleration are shown in Fig. This behavior is understandable since, as has already been explained, during braking there is a load transfer from the rear to the front wheel. The solid lines represent the distribution of braking between the front and rear wheels. The figures show the utility of using the rear brake, especially when the braking traction coefficient is low.
Its usefulness diminishes until it becomes almost negligible in the presence of very high braking traction coefficients. In this case, the curve 1. Suppose we wanted to brake the motorcycle with a deceleration equal to 0. The possible combinations of use of the front and rear brakes that could provide the desired deceleration are infinite.
For example, braking only with the front brake, the deceleration of 0. Figure shows that by using the same braking coefficient for the two tires, we obtain the maximum possible deceleration. For example, if the braking force coefficient is equal to 0. The maximum use of the two tires is attained with this distribution. The figure further shows that using only the front brake gives a deceleration that is lower at 0.
If the road is more slippery and the braking traction coefficient of both the wheels is 0. This example shows that optimal braking requires a different distribution of braking between the two wheels when varying the desired deceleration. This means that the devices for automatic distribution of braking that are present on some motorcycles, should adapt the distribution to the conditions of the road.
Furthermore, it is worth pointing out that in the example considered it is not a good idea to use a rear braking force greater than the front one. The optimal line of braking is always tangent at the origin to the braking distribution line having the same distribution between the static loads on the two wheels. To maintain equilibrium the rider applies a torque to the handlebars that can be zero, positive, in the same direction of the handlebar rotation, or negative, i.
We introduce the following simplifying hypotheses: the motorcycle runs along a turn of constant radius at constant velocity steady state conditions ; the gyroscopic effect is negligible.
In conditions of equilibrium the resultant of the centrifugal force and the weight force passes through the line joining the contact points of the tires on the road plane.
This line lies in the motorcycle plane if the wheels have zero thickness and the steering angle is very small. In reality, if a non-zero steering angle is assigned, the front contact point is displaced laterally with respect to the x-axis of the rear frame and the line joining the contact points of the tires is not contained in the plane of the rear frame.
Therefore, the use of wide tires forces the rider to use greater roll angles with respect to the angle necessary with a motorcycle equipped with tires that have smaller cross sections. Furthermore, with equal cross sections of the tires, to describe the same turn with the same forward velocity, a motorcycle with a low center of gravity needs to be tilted more than a motorcycle with a higher center of gravity. By leaning with respect to the vehicle, the rider changes the position of the his center of gravity with respect to the motorcycle.
Figure illustrates the possible situations. If the rider remains immobile with respect to the chassis Fig. If the rider leans towards the exterior of the turn Fig. As a result, he needs to incline the motorcycle further so that the tires, being more inclined than necessary, operate under less favorable conditions.
Certainly this rider is not an expert. If the rider leans his torso towards the interior of the turn and at the same time rotates his leg so as to nearly touch the ground with his knee, he manages to reduce the roll angle of the motorcycle plane Fig.
When racing, the riders move their entire bodies to the interior of the turn, both to reduce the roll angle of the motorcycle and to better control the vehicle on the turn. The displacement of the body towards the interior and in particular, the rotation of the leg cause an aerodynamic yawing moment that facilitates entering and rounding the turn.
In the front wheel there is longitudinal slippage in the braking phase, while under steady state conditions the slippage is negligible because it is only due to rolling resistance.
It is important to note that, with the same forward velocity, the angular velocity of the wheels increases during turning with respect to the angular velocity of the wheels in straight running, because contact does not occur on the largest circumference of the wheels. When sideslip angles approach zero, steering is called kinematic steering. The lateral reaction forces depend on the sideslip angles of the tires, roll angle and vertical loads.
The larger the sideslip and camber stiffnesses are, the smaller the sideslip angle necessary to generate the lateral force on the tire is. The turning radius of the trajectory described by the rear wheel is also a function of the sideslip angles and of the kinematic steering angle: If the sideslip angles and the kinematic steering angle are small, the radius can be calculated with the following approximate formula: where p indicates the motorcycle wheelbase Fig. Tire properties, in particular, are very important because the effective steering angle depends on the difference between the side slip angles.
Otherwise, the effective steering angle is smaller or larger than what is expected by the rider and the vehicle has under or over-steering behavior. If the sideslip angles were zero, the turn center point Co would be determined by the intersection of the lines perpendicular to the planes of the wheels and passing through the contact points.
The radius of curvature remains approximately constant and equal to that relating to kinematic steering. This behavior is defined as neutral, since the curvature radius depends only on the steering angle selected by the rider and not on the value of the sideslip angles. Here the radius of curvature is greater than the ideal one associated with the kinematic steering. The vehicle in this case has an over- steering behavior. Now consider a motorcycle that is under-steering while it is rounding a turn.
Since the vehicle tends to expand the turn, in order to correct the trajectory the rider is obliged to increase the steering angle so that the lateral reaction force of the front wheel will be increased. When the rotation of the handlebars becomes considerable, the force needed for equilibrium can overcome the maximum friction force between the front tire and the road plane, with the result that the wheel slips and the rider falls.
On the other hand, with an over-steering motorcycle, if the force needed for equilibrium overcomes the maximum friction force between the tire and the road plane, the rear wheel slips, but the expert rider, with a counter steering maneuver, has a better chance of controlling the vehicle equilibrium and avoiding a fall.
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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. Xi Motorcycte Dynamics 8. Therefore, in this chapter, in addi- tion to the Kinematic study, some simple examples of the dynamic behavior of motoreyeles are reported in order to show how kinematic peculiarities influence the directional stability and maneuverability of motoreyeles 1.
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. It is a definitive book on how to survive the early stages of the motorcycling experience. It provides insights that will be valuable throughout your riding career. It covers virtually every aspect of your early riding career from your days as a wannabe through being a newbie at the sport, with lessons on the specific skills required to be a truly competent rider and explains why.
Jim and Cash have distilled the results of over a half million miles of combined experience plus Jim's detailed analysis of the physics of motorcycling. You'll ride smarter after reading and studying this. Paperback, black-and-white, pages. Enhanced e-book includes videos Many books have been written on modelling, simulation and control of four-wheeled vehicles cars, in particular. However, due to the very specific and different dynamics of two-wheeled vehicles, it is very difficult to reuse previous knowledge gained on cars for two-wheeled vehicles.
Modelling, Simulation and Control of Two-Wheeled Vehicles presents all of the unique features of two-wheeled vehicles, comprehensively covering the main methods, tools and approaches to address the modelling, simulation and control design issues. With contributions from leading researchers, this book also offers a perspective on the future trends in the field, outlining the challenges and the industrial and academic development scenarios.
Extensive reference to real-world problems and experimental tests is also included throughout. Key features: The first book to cover all aspects of two-wheeled vehicle dynamics and control Collates cutting-edge research from leading international researchers in the field Covers motorcycle control — a subject gaining more and more attention both from an academic and an industrial viewpoint Covers modelling, simulation and control, areas that are integrated in two-wheeled vehicles, and therefore must be considered together in order to gain an insight into this very specific field of research Presents analysis of experimental data and reports on the results obtained on instrumented vehicles.
Modelling, Simulation and Control of Two-Wheeled Vehicles is a comprehensive reference for those in academia who are interested in the state of the art of two-wheeled vehicles, and is also a useful source of information for industrial practitioners. Covering the latest developments to Pacejka's own industry-leading model as well as the widely-used models of other pioneers in the field, the book combines theory, guidance, discussion and insight in one comprehensive reference. While the details of individual tire models are available in technical papers published by SAE, FISITA and other automotive organizations, Tire and Vehicle Dynamics remains the only reliable collection of information on the topic and the standard go-to resource for any engineer or researcher working in the area.
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