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A motorcycle that is traveling along a track can be considered like a rigid body subject to the action of the forces that the road exerts in the contact points of the tires.
These forces are governed by the control action of the rider: the thrust force through the throttle command, the braking forces through the brakes; the vertical forces that depend on the load distribution between the front and the rear tire and on the load transfer, the lateral forces that depend on the roll angle and on the side slip angles. The aerodynamic forces (i.e. drag and lift) are applied in the pressure center.
As a consequence the motorcycle dynamics depends mainly on the position of the center of mass.
Forward positions of the center of mass mean higher forces on the front wheel, backward positions of the center of mass mean higher forces on the rear tire, high position of centre of mass generates higher load transfer in acceleration and braking maneuvers, the contrary for a low position.
Figure 1 External forces acting on the vehicle considered as a rigid body (motorcycle: Victoria on Monza circuit).
Which is the optimal position of the center of gravity?
To answer this question we use the software exclusively developed by MDRG: XOptima.
XOptima allows to evaluate the lap time on a specific circuit, given the geometrical and physical characteristics of the motorcycle, the characteristics of the engine and the adherence condition of the track.
We briefly explain how XOptima works.
It is suppose to perform a certain maneuver, for example, the "S" curve of Figure 2. Depending on the riding strategy, the rider can use the steer, the brake and the throttle in several different ways.
Among all the possible combinations of inputs (steering, braking, throttle) only one allows to ride on the track as quick as possible exploiting the dynamic characteristics both of the motorcycle and of the engine, for the current tires adherence and track conditions.
The obtained maneuver is called "optimal maneuver," the motorcycle is ridden by an ideal rider that is able to fully exploit the potentialities of the motorcycle for the specific geometry and adherence conditions of the track.
In conclusion, the ideal rider is capable to be always in the limit riding conditions.
Figure 2 Different possible paths
One of the possible applications of XOptima is to perform an optimization based on the concept of maneuverability, i.e. the ability of a vehicle to complete a given maneuver as fast as possible without exceeding existing physical limitations, like tire adherence or road boundaries, but without considering the physical and mental pilot effort, that are concepts typical of handling. According to this, the choice of an ideal optimal rider is necessary.
Realistic or just virtual?
A comparison with experimental data is presented in order to appreciate how accurate could be this kind of simulations considering the same motorcycle in different road-tire interaction conditions (e.g. dry and wet paved track) and thus to validate the model included in this tool. In the current example the tests are performed on the international circuit of Valencia (Comunidad Valenciana) by a professional rider using a 125cc race motorcycle.
Fig.3 Simulation results compared with experimental data for a 125cc motorcycle on Valencia circuit.
From this comparison it turns out how the accordance between simulations results and experimental evidence data is quite good and how the ideal rider of the ?Optimal Maneuver Method? is capable of changing its riding style end the amount of thrust and braking forces as the conditions of the track change (e.g. adherence conditions of the road). Fig.4 Reports a comparison between braking forces on dry and wet track to underline the different riding strategies adopted in the two road conditions. Trajectories are optimized for the two cases and are slightly different.
Fig.4 Braking forces comparison on dry (red) and wet (blue) track.
Let's go back on the position of the center of gravity.
The centre of mass optimal position depends on the type of the track (fast or slow), on the conditions of adhesion (wet or dry), and on the engine power.
In order to perform an optimization of the position of the centre of mass of the vehicle, in both dry and wet conditions of the road, a parametric analysis has been carried out.
The height h and the lateral position b of the centre of mass have been changed. The resulting maps reporting lap times for the different configurations are presented in Fig.5.
The reference lap time is equal to 103.9 seconds in the dry track and equal to 122.2 seconds in the wet track. In both cases an improvement will be obtained raising the center of mass and moving it backward .
Fig.5 Influence of the height and longitudinal position of the centre of mass on minimum lap time in DRY and WET track. .
It seems all trivial, but it is not.
Move the center of gravity backward means decrease the front vertical load with the result that the rider might feel it too light and could not be able to ride at its own limit. Raising the center of gravity means increasing the load transfer, which could make the motorcycle more unstable during a strong braking.
Therefore it is necessary to reach a compromise between the displacements of the center of gravity and the sensitivity of the rider. The changes that allow the ideal rider (i.e. the virtual one), to reduce the lap time may be not perceived in the same way by the real rider.
The rider acts on the controls of the motorcycle according to the sensations that receives by the movement of the suspension during acceleration and braking, and also according to the skidding of the front and the rear tire.
These sensations depends also on bending and torsional compliances of the frame, of the swingarm and of the front fork.
But this is a different topic. What is the ideal dynamic behavior of the frame?
