Check out my attachment. I challenge you to find any condition plotted to the right of my red slip lines (high slip) where you get a value as low as 600 like you get in the back left area of your graphs. You can not possibly be really plotting the vector sum. Check your math.
I was referring only to the bottom graph of figure 6, sorry. The top graph indeed is largely complete sliding.
I'm not sure I understand your question. My earlier post for figure 7 (top diagram) shows clearly no valleys or bumps. I'm not going to repeat the exercise for the top graph of figure 6. What I'm trying to show you is that your graphs are not showing what you think they are showing.
But if you want numbers: here you go (this is also the saddle but bit different as I dont have previous one and had to figure out again). And I know what you are pointing out - this is because I used linear or exponential proportion instead of hyperbolic for changing of force curve along the opposite coordinate because I didnt bother for big values (more than 8-10%and 8-10 degrees) of SR and SA.
edit: F*ck it - comma. For me it was all scalable but I was changing Fx 10x too fast
Okay, your graph is actually sort of making sense. Basically here's the deal. The data you uses measures combined SR and SA up to some value. The corner of the graph represents unmeasured values of SR and SA that you are interpolating. You are "guesstimating" that more combined SR and SA = less force, when in reality as slip becomes really big in either direction your force reaches a steady magnitude point in the SVx, SVy direction.
So I just tried making my own formulas (not pacejka) and ran into a similar issue as you. (falling off at the corners) so I just added an effect where Fx,Fy are just the naive Fx,Fy you get from the friction circle at very high values of slip. You can see the "ugly" effect in the 3d chart, but the feel might actually not be soo bad. Check it out:
@Nikn: I think you should zoom it in to get the feel of one quater 'cos it is symmetrical
BTW: I perceived those graphs as geometrical and forgot about units. In fact it doesnt matter if I use %, degrees or rads but the numbers should be used in the proper places for chosen units if taken from other charts
OK, I scaled the units, scaled change of longitudinal force according to the Figure 6.
And comparing to simple scaling to Fxmax (so Fx*Fy doesnt go over Fxmax) it looks bit different still . If anybody wants I attach .xls also.
Yes easier to implement, but then most of time you are not satisfied. IMO models based on slip curves don't set the problem the right way.
IMO this is the correct way to set the problem:
We have a tyre on the road, we push on the axis following a given force vector. What is the vector of the reaction force?
As soon as we set the problem this way, we sart using formulas involving time.
Even the simplest formula using time (model tyre as a set of non linear springs and dampers matching the slip curves) will avoid many pitfalls you get with slip curves. Because for example with slip curves and a discrete time physics engine, it is very easy to get reaction force stronger than the pushing force, tyres sliding magically at very low speed...etc.
All these flaws are already contained in the very beginning, when you decide to start from slip curves.
For me slip curves are tyre benchmark results, a very good way to check afterwards if your model matches real tyre...but not a starting point to write a model. But maybe I am crazy
A very true statement.
Tyre slip curves always represent a specific case, and even complex empirical data is only valid for a limited range of parameters (there are MF-based models with 81 coefficients).
Unless you're looking for a quick substitute for a tyre model (so you can e.g. check the plausibility a suspension model) avoid using special-case empirical data to make assumptions for a generic-case model.
Pacejka suffers from the same thing though, the cornering and braking stiffnesses act like springs and the car will just oscillate between the two slopes while stationary, and never settle as there is no damping.
The relaxation length stuff goes even more horribly wrong at low speeds though, and instead of a vibration, you end up with your car sliding side to side with a magnitude of the relaxation length. I seem to remember having troubles getting the damping to work correctly, I'll have to have another play with it at some point, see if I can get that method to work.