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Pacejka magic formula not alll that magical?
(122 posts, started )
Quote from loopingz :Hi magic, remember that raising Hz has limit because with higher Hz you multiply the computation (and model) errors. There is a limit where accurracy is coming down with the hertz growing. Anyway I don't know where is this limit, it is hard to calculate and to test but possible.

Not sure what you mean there, Loopingz.. Higher frequency sampling is a way to increase accuracy rather than decrease it. One of my earlier tire models for VRC was running at 30,000 Hz at one point. That was way overkill though but it did run ok in real time. The current VRC tire model runs at about 600Hz IIRC.
Quote from axus :Very impressive indeed. I presume its in that Virtual RC simulation? Any plans for putting it in anything else?

Yes, that's in Virtual RC Racing. One or another variation of that same approach has been there since probably 2001. I use the same basic model (but beefed up a bit for better camber and other effects) in my full sized car sim:

http://www.performancesimulations.com/files/ToddSim13a.wmv
http://www.performancesimulations.com/files/ToddSim10a.wmv
http://www.performancesimulations.com/files/ToddSim11a.wmv
http://www.performancesimulations.com/files/ToddSim7a.wmv <--Drag car. This was using a much simpler model.
#53 - axus
Quote from jtw62074 :Not sure what you mean there, Loopingz.. Higher frequency sampling is a way to increase accuracy rather than decrease it. One of my earlier tire models for VRC was running at 30,000 Hz at one point. That was way overkill though but it did run ok in real time. The current VRC tire model runs at about 600Hz IIRC.

I think he means that to run it OK In real time increasing the sampling rate would have to be followed by a decrease in tyre modelling "resolution". There would be an optimum point for tyre model resolution and sampling rate to have it run OK in real time.
#54 - axus
Do you also have some form of surface displacement map also? That you can vary using things like surface roughness and density of uneven parts (just making up my own terms here but what I mean is how many protrusions there are per area of road and how much they protrude)? I guess that to simulate tyre behaviour accurately, you'd need to consider the road also.

EDIT: I looked at the one video (crap internet in South Africa takes ages to download), very very impressive. There's something that just makes it look so real. I'm certainly looking forward to this, assuming it will be released for PC at some point. Count me on the customer list!
Quote from axus :Do you also have some form of surface displacement map also? That you can vary using things like surface roughness and density of uneven parts (just making up my own terms here but what I mean is how many protrusions there are per area of road and how much they protrude)? I guess that to simulate tyre behaviour accurately, you'd need to consider the road also.

Not yet, but I plan on it. Road surfaces and the resulting rubber friction can be modelled pretty accurately on small scales with self affline fractals, so you'd be able to change the texture of the road and it would effect the grip, temperature, and so on.
Quote from jtw62074 :There are quite a lot of papers out there. Dr. Pacejka released a book a couple of years back on some his his models (not just the Magic Model). The only person I talk to specifically about my own model with is Dr. Gregor Veble of Racing Legends though, sorry

Mate, i dont want to steal or borrow piece of your work mate Dont spoil me the pleasure to work the tink myself
I just wanted to know if there were papers about this , so i can have somewhere to start.

Thanks for your answer I going to check what Dr Pacejka released

Maybe first i should read "Motor Vehicle Dynamics" from Giencarlo Genta, from begining to end for once
#57 - axus
Quote from jtw62074 :Not yet, but I plan on it. Road surfaces and the resulting rubber friction can be modelled pretty accurately on small scales with self affline fractals, so you'd be able to change the texture of the road and it would effect the grip, temperature, and so on.

Thinking deeper into it... I presume that when a [front] tyre bounces on the ground in real life, during understeer, it is caused by the road surface being uneven. The force acting on a [small] piece of road [ie. the actual texture of the road surface which you were saying you would represent using fractals] like that Force->/Road will surely cause some vertical force on the tyre, causing it to lift a bit. Can your engine run at a high enough tyre resolution to be able to simulate something like that accurately?
I'm not really sure what you mean there. Are you talking about bumps? In reality, even on a very smooth surface at a constant slip angle (there is no such thing as understeer to a single tire, there is only slip angle/slip ratio) the lateral/longitudinal forces are rather noisy indeed. The graphs you see with the nice, smooth line are averaged values, not the pure data. You don't lose anything by using that though as if the force jumps from one time step to the next like this: 100, 110, 100, 110,100, 110, you'll get the same results as if you were using 105 all along, so I wouldn't get too hung up on the high frequency/resolution stuff.
#59 - axus
Quote from jtw62074 :I'm not really sure what you mean there. Are you talking about bumps? In reality, even on a very smooth surface at a constant slip angle (there is no such thing as understeer to a single tire, there is only slip angle/slip ratio) the lateral/longitudinal forces are rather noisy indeed. The graphs you see with the nice, smooth line are averaged values, not the pure data. You don't lose anything by using that though as if the force jumps from one time step to the next like this: 100, 110, 100, 110,100, 110, you'll get the same results as if you were using 105 all along, so I wouldn't get too hung up on the high frequency/resolution stuff.

Um... true.
Note to self: Think before you post... and word your sentences carefuly.

What I'm talking about is vertical forces caused by small unevenness of the road surface - road texture. You were talking about using fractals to represent the road surface accurately. What I'm talking about is if you look at each of those tiny little bumps and imagine the small bits of tyre pushing against them. This would cause a vertical force, making the tyre bounce at high slip - as seen with the front tyres in understeer. I guess this could quite easily be mapped by two curves - one for vertical force against lateral slip and one for vertical force against longitudinal slip (combined by Pythagoras' Theorem I guess).

EDIT: Changed the first post a bit to make more sense.
Quote from axus :Um... true.
Note to self: Think before you post... and word your sentences carefuly.

What I'm talking about is vertical forces caused by small unevenness of the road surface - road texture. You were talking about using fractals to represent the road surface accurately. What I'm talking about is if you look at each of those tiny little bumps and imagine the small bits of tyre pushing against them. This would cause a vertical force, making the tyre bounce at high slip - as seen with the front tyres in understeer. I guess this could quite easily be mapped by two curves - one for vertical force against lateral slip and one for vertical force against longitudinal slip (combined by Pythagoras' Theorem I guess).

EDIT: Changed the first post a bit to make more sense.

The little grains and roughness in the road don't cause the tire to bounce, do they? I haven't seen it happen and wouldn't expect them too. They're downright tiny. All you're really getting there are localized high and low pressure areas at the road/tire interface and hysteric effects from the vibration in the rubber as it moves across the pattern. The surface roughness/pattern influence the real area of contact too, which is an important part of the picture.

As for the mapping of the two curves, I'm having a tough time visualizing what exactly that would accomplish.
#61 - axus
Quote from jtw62074 :The little grains and roughness in the road don't cause the tire to bounce, do they? I haven't seen it happen and wouldn't expect them too. They're downright tiny. All you're really getting there are localized high and low pressure areas at the road/tire interface and hysteric effects from the vibration in the rubber as it moves across the pattern. The surface roughness/pattern influence the real area of contact too, which is an important part of the picture.

As for the mapping of the two curves, I'm having a tough time visualizing what exactly that would accomplish.

Hmmm. I never actually knew what causes those bounces of the tyres. I really wasn't sure how significant the effect I was talking about is. I couldn't come up with any other explaination for the bouncing though. As for the two curves, its just a vertical force exerted by the tyre (hmmm, come to think of it, as much as... 30N at most with extreme slip, if even?) due to high slip and the effects of road graining. I suppose some investigation and testing would be appropriate. I doubt I can get a tyre to slip enough to measure this with my bare hands though.
Quote from axus :Hmmm. I never actually knew what causes those bounces of the tyres. I really wasn't sure how significant the effect I was talking about is. I couldn't come up with any other explaination for the bouncing though. As for the two curves, its just a vertical force exerted by the tyre (hmmm, come to think of it, as much as... 30N at most with extreme slip, if even?) due to high slip and the effects of road graining. I suppose some investigation and testing would be appropriate. I doubt I can get a tyre to slip enough to measure this with my bare hands though.

The vertical force at the tire is for the most part going to equal whatever the load is on it. I.e., whatever portion of the car's weight it's supporting.

I'm not sure what this bouncing you're referring to is though. Keep in mind the entire tire is a flexible, springy type of thing, so maybe that is causing whatever you're picturing to some extent?
#63 - axus
Quote from jtw62074 :The vertical force at the tire is for the most part going to equal whatever the load is on it. I.e., whatever portion of the car's weight it's supporting.

I'm not sure what this bouncing you're referring to is though. Keep in mind the entire tire is a flexible, springy type of thing, so maybe that is causing whatever you're picturing to some extent?

Go on an autocross or skidpan and swing the car into understeer. You feel heavy vibrations through the wheel and you can hear knocking sounds (not the most pleasant sound you'll hear your car make). If you look at the tyre it is bouncing (or maybe loosing grip and regaining it within instants, but I can't explain that one with anything apart from it bouncing). Considering this is a flat surface, I'm struggling to explain this bounce otherwise... although come to think of it, perhaps the limitations of having an anti-roll bar and hence not entirely independent suspension :doh:.
#64 - J.B.
Quote from axus :Go on an autocross or skidpan and swing the car into understeer. You feel heavy vibrations through the wheel and you can hear knocking sounds (not the most pleasant sound you'll hear your car make). If you look at the tyre it is bouncing (or maybe loosing grip and regaining it within instants, but I can't explain that one with anything apart from it bouncing). Considering this is a flat surface, I'm struggling to explain this bounce otherwise... although come to think of it, perhaps the limitations of having an anti-roll bar and hence not entirely independent suspension :doh:.

I always assumed that this had to do with the fact that road tyres are treaded. Perhaps the tread pattern gives the bits in between room to stretch and vibrate. I've no idea what sliding slicks feel like though so it might be BS.
#65 - axus
Quote from J.B. :I always assumed that this had to do with the fact that road tyres are treaded. Perhaps the tread pattern gives the bits in between room to stretch and vibrate. I've no idea what sliding slicks feel like though so it might be BS.

Good point also. Todd, about your model, does it use a tyre displacement map or something of the sort to grooved tyres correctly?
Quote from jtw62074 :The little grains and roughness in the road don't cause the tire to bounce, do they? I haven't seen it happen and wouldn't expect them too. They're downright tiny. All you're really getting there are localized high and low pressure areas at the road/tire interface and hysteric effects from the vibration in the rubber as it moves across the pattern. The surface roughness/pattern influence the real area of contact too, which is an important part of the picture.

wouldnt the rubber also bend around the fractal pattern creating spots of upwards forces where the rubber sliding across the fractal deforms when it slides towards a peak ?
#67 - axus
Quote from Shotglass :wouldnt the rubber also bend around the fractal pattern creating spots of upwards forces where the rubber sliding across the fractal deforms when it slides towards a peak ?

That's just about what I've been trying to say, but better worded in your case.
Quote from axus :Go on an autocross or skidpan and swing the car into understeer. You feel heavy vibrations through the wheel and you can hear knocking sounds (not the most pleasant sound you'll hear your car make). If you look at the tyre it is bouncing (or maybe loosing grip and regaining it within instants, but I can't explain that one with anything apart from it bouncing). Considering this is a flat surface, I'm struggling to explain this bounce otherwise... although come to think of it, perhaps the limitations of having an anti-roll bar and hence not entirely independent suspension :doh:.

Oh, ok, I understand. I don't usually use FFB except for the spring centering effect so never noticed it. Indeed, the tire is essentially a spring, so if you're getting some bouncing that's probably why. Wouldn't really be because of surface roughness so much I think.
Quote from axus :Good point also. Todd, about your model, does it use a tyre displacement map or something of the sort to grooved tyres correctly?

Nope.
#70 - axus
Quote from jtw62074 :Nope.

Any plans to model this?
Quote from Shotglass :wouldnt the rubber also bend around the fractal pattern creating spots of upwards forces where the rubber sliding across the fractal deforms when it slides towards a peak ?

Yes. The hysteretic friction component is primarily this that's occurring. If you slide rubber across a rough surface (imagine just one protrusion), on one side of the protusion you have higher side pressure than on the other because the rubber acts a bit like a damper (since it's viscoelastic) and doesn't immediately "snap back" into position and apply full pressure on the back side of the protrusion. It's a bit like a car moving through air or a boat through water where the pressure is greater at the front than the rear and causes an opposing force. In that analogy the air is the rubber and the car is a surface protrusion.

That's only the hysteretic (damping loss) part of the friction though, which is relatively minor compared to the adhesive, "true surface area" part of it. Something like 5-15% depending on the rubber compound.

But yes, you'd have vertical pressure variations on a microscopic level throughout the whole nominal contact area.
Quote from axus :Any plans to model this?

Not at the moment. If you're going that detailed you might as well be using FEM. That's not quite possible yet though. Just saw one online that takes two hours to run a single second's worth of simulation for one tire on a 3.4Ghz workstation, so that sort of thing is a ways off yet. You could probably do some cheaper workaround that sort of emulates the behavior though, I suppose, but for the most part I think with tread you're mainly reducing contact area. If you want to model all the tread blocks squirming around and so on accurately you'd need FEM. And with the unknowns in that you might not be any more accurate than if you skipped it entirely and just tweaked the cornering stiffnesses and so on to match up with the basic tire type you're doing anyway. I.e., the exact rubber properties and so on aren't going to be known anyway. Garbage in, garbage out.
#73 - axus
Well... that's the type of simulation I was thinking of using interpolated lookup tables for rather. I'm no fan of the ones available at the moment but I think that as long as your data is accurate and consistent (which seems to be most of them's problem - the lateral behaviour doesn't match the longitudinal behaviour, or it feels like that anyway... you can almost tell the engine is canned if you know what to look for) it might work. Get sim racers to use their spare CPU cycles to create the lookup table and send it back via the internet a la SETI@home and voila! You get a few percent closer to modelling tyre physics.
Quote from jtw62074 :the rubber acts a bit like a damper

btw concerning this ... is there any reserch on the frequency response of a tyre to find the minimum frequency for a tyre model to be correct ?
Quote from axus :Well... that's the type of simulation I was thinking of using interpolated lookup tables for rather. I'm no fan of the ones available at the moment but I think that as long as your data is accurate and consistent (which seems to be most of them's problem - the lateral behaviour doesn't match the longitudinal behaviour, or it feels like that anyway... you can almost tell the engine is canned if you know what to look for) it might work. Get sim racers to use their spare CPU cycles to create the lookup table and send it back via the internet a la SETI@home and voila! You get a few percent closer to modelling tyre physics.

Oh, sure, that's always a possibility. I've always thought it would be cool to run an FEM model, then just use Pacejka's Magic Formula to match it up as though it was a real tire test. Then you could essentially run the steady state FEM model in real time in the sense you're outputting the same forces the FEM model produced in the first place.

One of the tire models I wrote a few years back modelled each contact patch with about 50 2-D springs, so it was a sort of super-simple wannabe FEM model, I suppose (and didn't run particularily fast either). That worked pretty well actually, but with the calculations I was doing it dawned on me that the whole thing could be done with a little calculus much faster and you'd effectively have an infinite number of springs.

Pacejka magic formula not alll that magical?
(122 posts, started )
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