I think there's a confusion here. That method is the Brian Beckman's proposal for combining longitudinal and lateral slip, but it's not related to solving the numeric instabilities or the singularities of the slip calculation. In fact, "logitudinal_slip" and "lateral_slip" above are still slip ratio and slip angle respectively.

Yeah, and since the rho term can't be negative then there cannot be an oscillation of signs about zero, correct?

Correct about the sign, but that won't remove the numeric instabilities. Those happen at the two previous calculations (s and a) when the velocity approaches zero. At that time, rho would be heavily oscillating among very small and very large values, and it would end as NaN when the velocity is exactly zero.

Earlier you said Beckman's vector formulation is a perfect example, well combining long/lat slip ratios *is* forming a vector equation. Or am I missing something still?

I specified Beckman's vector definition of slip. I didn't said anything about the other formulations presented in his book.

[attachment=31893:2016-05-16_114631.png]

His combination method is mostly fine (I use my own refined version though). But the main issues come from the slip calculations. These expose the issues mentioned above at low speeds and are not applicable (undefined, NaN) when the vehicle is stopped.

Here I explain further what I think about slip ratio and slip angle:

http://www.edy.es/dev/2011/12/facts-and-myths-on-the-pacejka-curves/

This doesn't have any sense. There's no such thermo-dynamics equation.

The Pacejka method is a curve-fitting method, where the coefficients are chosen so the resulting curve matches the experimental results. In that chapter Beckman proposes a Pacejka-like curve that requires three parameters only, and compares the results with the full Pacejka 11-parameters curve. The proposed curve doesn't have any physical meaning by itself.

Why isn't it sensical? Take the 3-coefficient equation, match the curve to your Pacejka curve, and you've got a good approximation that doesn't involve trig functions. That makes sense to me. Note: if you watch his video he does call it a thermo-dynamics equation. Or am I yet again missing something?

I hadn't seen that video. Very interesting! The thermodynamic part sounded odd to me. I understand that it's an equation that produces a curve similar to pacejka, but there's not a thermodynamic relationship with the tire physics.

OK! I think that I am gone try the relaxation length method. I could set it up right now if I knew a generic function f(x) that returns ~63% at x = 1, ~86% at x = 2, ~95% at x = 3 etc. Maybe somebody knows such a formula?

http://se.mathworks.com/help/physmod/sdl/ref/tiremagicformula.html

I found the low-speed version pointed here to work well for my needs:)

http://www.control.lth.se/documents/2003/gaf+03.pdf

Hm... If I read this and understand it, I think that it would result in pretty good tire model. What do you think?

http://code.eng.buffalo.edu/dat/sites/tire/tire.html - I found this resource and it seems to be the most promising one so far. It seems to be kind of accurate and stable and at the same time I can understand it very well. I should, however, test it in game.

http://code.eng.buffalo.edu/dat/sites/tire/tire.html - I found this resource and it seems to be the most promising one so far. It seems to be kind of accurate and stable and at the same time I can understand it very well. I should, however, test it in game.

Great, did it work for you? I already found this tire model somewhere else, but that one didn't give any of the magic tire constants. Without those it was just a pile of useless math :)

I'm curious about its combined slip behavior.

This paper also forgets to mention about the Ygamma at camber calculations :)

I'll check when I have some time.

http://code.eng.buffalo.edu/dat/sites/tire/tire.html - I found this resource and it seems to be the most promising one so far. It seems to be kind of accurate and stable and at the same time I can understand it very well. I should, however, test it in game.

Great, did it work for you? I already found this tire model somewhere else, but that one didn't give any of the magic tire constants. Without those it was just a pile of useless math :)

I'm curious about its combined slip behavior.

This paper also forgets to mention about the Ygamma at camber calculations :)

I'll check when I have some time.

Hi! I actually forgot about checking this. I was making a coloumb friction based multi-sampled spring/damper system softbody tire model(using generic equations, but the concept and system is fully developed by myself). I will try this method later. However, in case of success, I will have a more physics-based approximated softbody tire for real-time applciation:)

Hi! I actually forgot about checking this. I was making a coloumb friction based multi-sampled spring/damper system softbody tire model(using generic equations, but the concept and system is fully developed by myself). I will try this method later. However, in case of success, I will have a more physics-based approximated softbody tire for real-time applciation:)

So, I did, and my results are not realistic at all.

The Fx looks ok, but the Fy is totally off, I tried to figure out, and double-checked the formulas, but can't see anything.

with these inputs, only slip angle:

Fz = 2500

s = 0

alpha = 10degrees (in radian)

camber = 0 (gamma maybe)

The magic parameters are taken from the 3rd column (P185/70R13)

Fy is ~69.9