# Cornering Stiffness Prediction Based on Geometric Method
## 1 Introduction  
Cornering stiffness is a critical tire parameter, which has a significant impact on vehicle handling performance [1; 2; 3; 4]. It depends on many things, such as tire size, type, ply, tread design, etc. For a given tire, load and inflation pressure are the two primary entities that influence its cornering stiffness. There is also the camber angle, which has shown a noticeable effect [5; 6; 7].  
Cornering stiffness description with different camber angles has been realized in many tire models, among which Magic Formula (MF) put forward by [PERSON] is extensively used in vehicle simulation. Cornering stiffness in MF is expressed considering the influences of load and camber angle [8]. The influence of inflation pressure is also expressed [9]. As a semi-physical model, MF shows high precision in cornering stiffness expression, but a set of parameters are used. The determination of these parameters requires numerous test data: side slip test data under different loads and camber angles are needed. These tests can be done on an indoor tire test rig or outdoor tire test trailer [10; 11]. Paruchasing or hiring this kind of equipment is very expensive, which makes tire testing a costly task. Different combinations of slip angle, camber angle and load generate a huge workload and long working time. Furthermore, test results under complex input conditions may lead to tire wear, which can influence test accuracy.  
UniTire was put forward by [PERSON] in 1986, and is also a semi-physical model [12; 13]. It has been successfully applied to the expression of many tire mechanical characteristics. Cornering stiffness in UniTire is also expressed considering the influences of load and camber angle. In a recent work, inflation pressure and temperature influences were included [14; 15]. Similarly to MF, cornering stiffness parameterization of UniTire also needs side slip data under different loads and camber angles. Therefore, the same drawbacks exist as for MF.  
The finite element (FE) method has been applied to tire mechanical characteristics research along with the development of computer technique. Since the 1970s, researchers have used the FE model to analyze tire mechanical characteristics. [PERSON] worked in Yokohama to analyze strain energy density change on each part of the belt layer caused by the drum test rig radius [16]. [PERSON] studied the influence of tire belt structure parameterson the stress distribution [17]. After the 1990s, FE analysis software, such as ABAQUS and ANSYS, made tire FE analysis more popular. Tire steady-state and transient simulation, stress and strain distribution analysis can all be carried out through the FE model [18; 19; 20; 21]. The FE model can also express tire material and structural details, which means a vast amount of calculation. When simulating cornering stiffness for different camber angles, either a high performance computer or a long calculating time is needed. Furthermore, mesh elements may experience convergence problems in large deformation situations [22]. Thus, the load, slip angle and camber angle coupling are limited.  
In view of the aforesaid problems, it would be time- and resource-saving to remove the need for measurements at different camber angles. This paper proposes a method for obtaining cornering stiffness with varying camber angles based on nothing more than pure side slip characteristics and tire size information. We explore the idea of regarding camber as an equivalence of the load shift in the contact patch.