Abstract
Road cars are characterized by having an open differential and no significant aerodynamic downforces. These two aspects allow for some substantial simplifications of the vehicle model. With the additional assumption of equal gear ratio of the steering system for both front wheels, it is possible to formulate the single track model. Quite contrary to common belief, it is shown that the axle characteristics can take into account many vehicle features, like toe-in/toe-out, roll steering, camber angles and camber angle variations. The steady-state analysis is carried out first using the classical handling diagram. Then, the new global approach based on handling maps on achievable regions is introduced and discussed in detail. This new approach shows the overall vehicle behavior at a glance. Stability and control derivatives are introduced to study the vehicle transient behavior. Moreover, the relationship between data collected in steady-state tests and the vehicle transient behavior are thoroughly analyzed in a systematic framework. To prove the effectiveness of these results, a number of apparently different vehicles with exactly the same handling are generated.
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- 1.
Some sports cars and all race cars have a limited-slip differential. Several race cars also have wings that provide fairly high aerodynamic downforces at high speed. The handling of these vehicles is somehow more involved than that of ordinary road cars and will be addressed in Chap. 7.
- 2.
The left and right wheels of the same axle are normally equipped with the same kind of brake. Therefore, the braking torque is pretty much the same under ordinary operating conditions, and, again, (6.2) holds true. However, there are important exceptions. The left and right braking forces can be different if: (a) the grip is different and at least one wheel is locked; (b) the friction coefficients inside the two brakes is different (for instance, because of different temperatures, which is often the case in racing cars); (c) some electronic stability system, like ESP or ABS, has been activated.
- 3.
We call no-roll center what is commonly called roll center.
- 4.
In this model the roll inertial effects are totally disregarded.
- 5.
For instance, vehicles equipped with a locked differential and/or with relevant aerodynamic downforces always need (at least) two parameters.
- 6.
A vehicle model with compliant steering system is developed in Sect. 6.16.
- 7.
This step would not be possible with \(F_{y_i}\) as in (6.30).
- 8.
All the effects of the lateral acceleration \(\tilde{a}_y=u r = u^2\rho \) on Y and N are already included in the axle characteristics .
- 9.
We remark that this is no longer true in vehicles with limited-slip differential and/or aerodynamic vertical loads.
- 10.
- 11.
To keep, for the moment, the analysis as simple as possible, we also assume that \(\hat{Y}_1(x) = \hat{Y}_2(kx)\), with \(k>0\).
- 12.
- 13.
Tests with constant steer angle are the most general: they can be performed on any kind of vehicle.
- 14.
Actually, the real critical speed can be lower than the value predicted by (6.174), as shown in [7, pp. 216–219]. Basically, (6.174) may not predict the right value because in real vehicles we control the longitudinal force, not directly the forward speed. Therefore, a real vehicle is a system with three state variables, not just two. This additional degree of freedom does affect the critical speed, unless the vehicle is going straight.
- 15.
Here \(\alpha \), \(\beta \) and \(\gamma \) are just constants. They have no connection with slip and camber angles.
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Guiggiani, M. (2018). Handling of Road Cars. In: The Science of Vehicle Dynamics. Springer, Cham. https://doi.org/10.1007/978-3-319-73220-6_6
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DOI: https://doi.org/10.1007/978-3-319-73220-6_6
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