# Traction Circle vs Seperate Forces

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I am now wondering which of the methods is better for accurate tire friction simulation:

• Seperate equations for longitudal and lateral friction where I calculate slip, plug in function and get friction force
• Traction circle method(which I haven't yet examined deeply).

What are your thoughts and opinions on this topic?

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somebody just asked this recently.

static and dynamic coefficients of friction is the short answer.

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Option 1 will not work at low speed due to a singularity in the definition of slip. During simulation artificial divergence will be introduced. In the past this seems to have been dealt with via damping equations, or by using a fake model at low speeds. If using a fake model it would probably be smart to lerp the results of the fake model with the model using slip around the point where slip begins to diverge, in order to avoid simulation jumps when swapping code paths.

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I actually clamp it at low speeds. It seems to work fine for me.

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Option 1 will not work at low speed due to a singularity in the definition of slip. [...]

... or you may use a definition of slip that doesn't have such problem. There are several definitions of slip out there. Nothing forces you to use the one that most appears when searching on internet.

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Option 1 will not work at low speed due to a singularity in the definition of slip. [...]

... or you may use a definition of slip that doesn't have such problem. There are several definitions of slip out there. Nothing forces you to use the one that most appears when searching on internet.

Like Brian Beckman's vector definition? I'm a bit new to this topic so if you have links or names of references it would be greatly appreciated.

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Yes, Brian Beckman's vector definition is a perfect example. At the time I investigated this subject (several years ago) I had found some ppt describing different slip ratio definitions, but I'm unable to find it again.

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Does this work well?

slip_ratio = (w["angular velocity"] * w["radius"] - w["speed"].y) / abs(w["speed"].y) * 100
slip_angle = math.degrees(math.atan(-w["speed"].x / abs(w["local speed"].y + w["angular velocity"] * w["radius"])))


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Does this work well?

slip_ratio = (w["angular velocity"] * w["radius"] - w["speed"].y) / abs(w["speed"].y) * 100
slip_angle = math.degrees(math.atan(-w["speed"].x / abs(w["local speed"].y + w["angular velocity"] * w["radius"])))


Not when the vehicle is stopped. These formulas become indeterminate (zero divided by zero) when the vehicle speed approaches zero.

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I do a check. If the w["speed"].y != zero, than I do the equation. Elseway if w["angular velocity"] != 0 than I've got a constant '0' number which I use(e.g. 1000 slip ratio * sign(w['angular velocity'])). Elseway it's 0. Similar principle works in slip angle(where the max angle in divergent case is 0 at no sideways motion and 90 * sign(w["speed"].x) at some sideways motion.

However, can you suggest a better method?

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