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For my racing game I am using a simplified Pacejka Magical Formula:

$\mu_{lateral} = \mu_{0} * \mu_{1} * D * \sin(C * \arctan(B * x - E * (B * x - \arctan(B * x))))$

Where:

  • $\mu_{lateral}$ is sideways coefficient of friction
  • $\mu_{0}$ is wheel friction coefficient
  • $\mu_{1}$ is surface coefficient friction
  • $B$ is wheel lateral stiffness
  • $C$ is wheel lateral peak factor
  • $D$ is wheel lateral shape factor
  • $E$ is wheel lateral curvature

However, I don't know what are realistic values for $B, C, D, E$. I know well the first ones and I also assume that $C$ may be around 1.1. However, what's realistic stiffness, shape factor and curvature in sideways directions for different types of real-life tires?

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The actual parameters for real tyres tend to be heavily protected intellectual property, you won't find those anywhere. However, have a look at these various pages, they give indicative values of the various parameters:

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  • $\begingroup$ OK! Thanks! I already checked first 2 links. The thing is that it requires some values that I don't have access to: camber(I haven't implemented it), Fz(I don't know what is it, if it is magnitude of normalforce, than I have it). Also, this seems to be a non-game-friendly math. Can B, C, D and E be all constants? $\endgroup$ – Adrians Netlis Mar 11 '16 at 18:55
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    $\begingroup$ Fz is the downward force on the wheel. To be accurate, this should vary from wheel to wheel during cornering, braking and acceleration due to weight transfer. Unless you're going to resolve the suspension kinematics, just assume that camber is 0. Also, this formula was developed for practical engineering purposes (vehicle design and tuning). However, it's probably the best way to get realistic grip behavior into your game engine. $\endgroup$ – Dan Mar 12 '16 at 1:14
  • $\begingroup$ Thanks for information. So $F_{z}$ is the load on wheel, right? Than I have it, with all the suspension stuff etc. That's great:) So I must try plugging up all the things. However, I'll still need to find out theese values for several tire types. $\endgroup$ – Adrians Netlis Mar 13 '16 at 21:59

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