## PAC2002 MF Doubt - Determining Tire Normal Load and Deflection

Hello, guys.

I've started developing a solver for Pacejka's 2002 MF, when I reached a point of doubt, where I didn't understand how to figure out the value of one variable, because it would apparently lead to a system of equations with more variables than equations. I'm referring in particular to equations (Fz = Cz*rho*labmda_Cz + Kz*rho' , this eq. isn't numbered) and (9) of this reference text: http://mech.unibg.it/~lorenzi/VD&S/M...ls_pac2002.pdf

Being more specific, I was organizing the equations in a .m file, when at that point I see that the method requires me to determine the normal load on the tires (Fz) as a function of the tire deflection rho, and the deflection rate rho'. I noticed that the reference text never defined mathematically the loaded radius (Rl) value, although it just mentioned it. I assume this value should be a dynamic one. But even if it was the tire's static deflection, due to the conrner's normal load, there is still the problem of defining rho and rho'. I had thought at the beginning that this could be solved through simulink, and using the corner's normal load to find both rho and rho' with an integrator block, and with their respective tire spring and damping coefficients (Fz = Cz*rho ; integral Fz dt = Kz*rho'). But then it comes this question: while I had this idea, of taking the dynamic model Fz signal, integrating it and sending both values to eq. (9), the equation of Fz described above is already the one which should provide the normal load signal as a function of rho signal in the first place. On that same page 8 of the reference file, the PAC2002 seems to create a loop of undefined equations, where I need to know rho and rho' in order to find Fz, but rho and rho' themselves are not well defined. The text never mentions rho', and just vaguely defines Rl (loaded radius), and so it isn't clear to me how am I supposed to find those values. I tried googling for more information on this, but I didn't find anything useful yet.

Could anyone help me solve this question? It would be much appreciated.