Possible bug in tyre model / parameters ?

[HornetMaX]

@Piboso: playing with the graphs of the tyre model (see this thread: http://forum.piboso.com/index.php?topic=1920.0) I've found something strange: the longitudinal force can become negative (for positive longitudinal slips) when the side slip is large enough (camber at 0).

According to the equations on page 582 of Pacejka's book (Tyre and Vehicle Dynamics, equations 11.E50 - 11.E57), the term G_xa should always be >0 (weighting function for the combined slip case).

Now with the values of the murasama rear quali tyre (also happens with others), it gets negative for large side slip angles.
As far as I can see, this happens because C_xa (= r_Cx1) is > 1 (1.2) and/or because B_xa is too big (due to r_Bx1 and r_Bx2).

I'm not excluding I've written something wrong in my code, but the relevant equations are a few and I really can't see anything wrong with them. One can actually pull the numbers and do the computation by hand to find that G_xa is < 0.

If I'm right, there's definitely something wrong with the parameters of the tyres, at least for large sideslip angles.

For example, consider the longitudinal force for long slip = 0.1, camber = 0 and side slip = 45 deg (but I start seeing negative forces from roughly 18deg of side slip).

MaX.

[PiBoSo]

Pacejka suggests, for large slip angles, to use tan(slip_angle).

[HornetMaX]

Pacejka suggests, for large slip angles, to use tan(slip_angle).

Yeah, that's what I do, but the G_xa value still gets negative.

Example, with murasama rear quali tyre, equations 11.E57 ... 11.E50:

k = 0.1 (long. slip)
a = 45deg (side slip)
astar = tan(a) = 1

S_Hxa = r_Hx1 =  0

C_xa = r_Cx1 = 1.2

B_xa = (r_Bx1 + r_Bx3 * pow(gstar,2)) * cos(atan(r_Bx2 * k)) = 8.48528  (r_Bx1 = 12, r_Bx2 = -10, r_Bx3 = 0)

as = a* + S_Hxa = 1

G_xa0 = cos(C_xa * atan(B_xa * S_Hxa)) = 1

G_xa = cos(C_xa * atan(B_xa * as)) / G_xa0 = -0.17252 / 1 = -0.17252

The problem goes (obviously) away if C_xa (i.e. r_Cx1) is 1 instead of 1.2.
If 1.2 has to stay, one has to make B_xa smaller (using r_Bx1 ?), in order to keep G_xa > 0 always.

MaX.

[doubledragoncc]

I have to say how impressive it is to see the amount of intellect that is on this forum with such people like yourself Max and naturally Piboso lol. If people only realized the amount of effort and hard work you guys put into making this sim what it is. It makes me feel quite dumb just building control systems when I see the amount of mathematics you need just for the tyres!!!

I hope more appreiciate all you do, thank you so much Max and Piboso, have to add all the others too, to be fair lol.]

I hope that when you are not so busy Max we get to meet and talk about all this.

DD

[HornetMaX]

I have to say how impressive it is to see the amount of intellect that is on this forum with such people like yourself Max and naturally Piboso lol. If people only realized the amount of effort and hard work you guys put into making this sim what it is. It makes me feel quite dumb just building control systems when I see the amount of mathematics you need just for the tyres!!!

I hope more appreiciate all you do, thank you so much Max and Piboso, have to add all the others too, to be fair lol.]

My contribution to the game is very marginal, I just like to (try to) understand. Piboso is DA men.

I hope that when you are not so busy Max we get to meet and talk about all this.

With pleasure. But after a year spent in Scotland, I'm not really planning to come back to the UK: your weather beats me

MaX.

[doubledragoncc]

It beats me to Max after 18 years in Florida, Australia, Singapore, Malaysia, Thailand, and anywhere HOT, being in UK sucks bad eggs lol. I am always up for traveling bro. 

I think you do a damn lot for us all here, Piboso may be THE MAN but he got good helpers, ya feel me bra lol

DD

[HornetMaX]

Bump

Pacejka suggests, for large slip angles, to use tan(slip_angle).

Yeah, that's what I do, but the G_xa value still gets negative.

Example, with murasama rear quali tyre, equations 11.E57 ... 11.E50:

k = 0.1 (long. slip)
a = 45deg (side slip)
astar = tan(a) = 1

S_Hxa = r_Hx1 =  0

C_xa = r_Cx1 = 1.2

B_xa = (r_Bx1 + r_Bx3 * pow(gstar,2)) * cos(atan(r_Bx2 * k)) = 8.48528  (r_Bx1 = 12, r_Bx2 = -10, r_Bx3 = 0)

as = a* + S_Hxa = 1

G_xa0 = cos(C_xa * atan(B_xa * S_Hxa)) = 1

G_xa = cos(C_xa * atan(B_xa * as)) / G_xa0 = -0.17252 / 1 = -0.17252

The problem goes (obviously) away if C_xa (i.e. r_Cx1) is 1 instead of 1.2.
If 1.2 has to stay, one has to make B_xa smaller (using r_Bx1 ?), in order to keep G_xa > 0 always.

MaX.

[Hawk]

Yes. I see now Max...... That issue with the large slip angles could, in the way I see it, cause some issues with the way the tyres perform while cornering at times(if I've understood this correctly?).
The maths on this are way beyond me. Lol. But it seems you may have pin-pointed an issue there? I guess we will only find out in the next beta release whether we notice a difference, that's if Piboso thinks you have a point with this.....


Very nice work indeed Max! 

Hawk.

[HornetMaX]

Pacejka suggests, for large slip angles, to use tan(slip_angle).

Yeah, that's what I do, but the G_xa value still gets negative.

Example, with murasama rear quali tyre, equations 11.E57 ... 11.E50:

k = 0.1 (long. slip)
a = 45deg (side slip)
astar = tan(a) = 1

S_Hxa = r_Hx1 =  0

C_xa = r_Cx1 = 1.2

B_xa = (r_Bx1 + r_Bx3 * pow(gstar,2)) * cos(atan(r_Bx2 * k)) = 8.48528  (r_Bx1 = 12, r_Bx2 = -10, r_Bx3 = 0)

as = a* + S_Hxa = 1

G_xa0 = cos(C_xa * atan(B_xa * S_Hxa)) = 1

G_xa = cos(C_xa * atan(B_xa * as)) / G_xa0 = -0.17252 / 1 = -0.17252

The problem goes (obviously) away if C_xa (i.e. r_Cx1) is 1 instead of 1.2.
If 1.2 has to stay, one has to make B_xa smaller (using r_Bx1 ?), in order to keep G_xa > 0 always.

MaX.

Bump ?

MaX.

[Vini]

https://www.youtube.com/v/IAISUDbjXj0

[Vini]

soooo, i have no idea about the actual physics but I know that physicists like to exchange sin and tan some time when they feel like it doesn't really make a difference, maybe it does here?

[HornetMaX]

soooo, i have no idea about the actual physics but I know that physicists like to exchange sin and tan some time when they feel like it doesn't really make a difference, maybe it does here?

Hmm, no

With beta8 some values changed a bit, but the problem is still there, as far as I can see.

[Vini]

ok.

short clarification would be great: may this be causing the front tyre slip angle issues or is this unrelated?

[HornetMaX]

ok.

short clarification would be great: may this be causing the front tyre slip angle issues or is this unrelated?

Hard to tell, at least for me. But keep in mind the problem has not been acknowledged by PiBoSo, so it may be just me doing something wrong.