Pacejka magic formula not alll that magical?

[axus]

Hi,

Yes, its another mad physics discussion that I'm starting. The pacejka model for tyre behaviour consists of 4 curves -

Tyre Longitudinal Force : Slip Ratio
Tyre Lateral Force : Slip Angle
Aligning Moment : Slip Angle
Normalized Force : Slip Ratio

My source: http://www.racer.nl/reference/pacejka.htm
(Correct me if a part of the model is not described on that page)

I think something is missing here. Surely, the aligning moment is not a function of slip angle alone, but of slip ratio too? If you have a tyre with a high slip ratio, it is twisted a bit in the longitudinal direction. If you try to get it twisted in the lateral direction at the same time, surely you should be having greater resistance (aligning moment). This would be because the longitudinal slip is trying to "twist the tyre into a straight line". This could also explain why so many sims struggle with low speed tyre physics. At low speed, you have a greater longitudinal slip and when you try to turn at the same time it feels awkward... you slide too much, because your slip angle is much higher than what it feels like it should be (I'm just guessing here). Any ideas? Could we do an experiment in the garage/back yard to test this? I have some tyres on rims lying around in there but I don't know where to start... I don't think I'll get enough force in there to twist the tyre significantly and I don't think I'll actually be able to calculate/estimate aligning moment. Suggestions are welcome though. This should make for interesting discussion.

Disclaimer: I do not know how the LFS model works at the moment, and as such I cannot know that this is not already in there. I am also not sure if it is in other sims and I am not sure my claim is correct.

[operator0]

I'm really not sure how you could come up with a physical test of this. Someone with an advanced math background might be able to figure up a way to test it in a theoretical environment though.

In all honesty, race car physics is an ever evolving science. Tomorrow, someone will come up with a new tire deformation model and the day after that someone will come up with one to supersede that one.

[Woz]

Originally Posted by axus

Hi,

Yes, its another mad physics discussion that I'm starting. The pacejka model for tyre behaviour consists of 4 curves -

Tyre Longitudinal Force : Slip Ratio
Tyre Lateral Force : Slip Angle
Aligning Moment : Slip Angle
Normalized Force : Slip Ratio

My source: http://www.racer.nl/reference/pacejka.htm
(Correct me if a part of the model is not described on that page)

I think something is missing here. Surely, the aligning moment is not a function of slip angle alone, but of slip ratio too? If you have a tyre with a high slip ratio, it is twisted a bit in the longitudinal direction. If you try to get it twisted in the lateral direction at the same time, surely you should be having greater resistance (aligning moment). This would be because the longitudinal slip is trying to "twist the tyre into a straight line". This could also explain why so many sims struggle with low speed tyre physics. At low speed, you have a greater longitudinal slip and when you try to turn at the same time it feels awkward... you slide too much, because your slip angle is much higher than what it feels like it should be (I'm just guessing here). Any ideas? Could we do an experiment in the garage/back yard to test this? I have some tyres on rims lying around in there but I don't know where to start... I don't think I'll get enough force in there to twist the tyre significantly and I don't think I'll actually be able to calculate/estimate aligning moment. Suggestions are welcome though. This should make for interesting discussion.

Disclaimer: I do not know how the LFS model works at the moment, and as such I cannot know that this is not already in there. I am also not sure if it is in other sims and I am not sure my claim is correct.

The way racer and many other sims use pacejka is from pre-calculated curves and so the figures are good up to a point. If you want to see the full dynamic pacejka in operation try NetKar Pro.

[Tweaker]

Originally Posted by Woz

If you want to see the full dynamic pacejka in operation try NetKar Pro.

But even then, I don't think it is a full representation of the model... as there are quirks people have pointed out to be very wierd with NkPro's tire model. Maybe flaws in the game, or maybe flaws in the model, I don't know

I think just having a solid tire model isn't the answer to having the simulation feel real. There is a large variety of other factors that are required, some of which is some really advanced suspension modelling, chassis ridgitidy, differential modelling, weight, etc etc... It all plays a part in how well the tire model can be executed. Maybe NkPro has it quite correct, but I think some other parts are missing from the entire equation to make it work right.

[J.B.]

Originally Posted by axus

Hi,

Yes, its another mad physics discussion that I'm starting. The pacejka model for tyre behaviour consists of 4 curves -

Tyre Longitudinal Force : Slip Ratio
Tyre Lateral Force : Slip Angle
Aligning Moment : Slip Angle
Normalized Force : Slip Ratio

My source: http://www.racer.nl/reference/pacejka.htm
(Correct me if a part of the model is not described on that page)

I think something is missing here. Surely, the aligning moment is not a function of slip angle alone, but of slip ratio too? If you have a tyre with a high slip ratio, it is twisted a bit in the longitudinal direction. If you try to get it twisted in the lateral direction at the same time, surely you should be having greater resistance (aligning moment). This would be because the longitudinal slip is trying to "twist the tyre into a straight line". This could also explain why so many sims struggle with low speed tyre physics. At low speed, you have a greater longitudinal slip and when you try to turn at the same time it feels awkward... you slide too much, because your slip angle is much higher than what it feels like it should be (I'm just guessing here). Any ideas? Could we do an experiment in the garage/back yard to test this? I have some tyres on rims lying around in there but I don't know where to start... I don't think I'll get enough force in there to twist the tyre significantly and I don't think I'll actually be able to calculate/estimate aligning moment. Suggestions are welcome though. This should make for interesting discussion.

Disclaimer: I do not know how the LFS model works at the moment, and as such I cannot know that this is not already in there. I am also not sure if it is in other sims and I am not sure my claim is correct.

As far as I understand it the aligning torque is merely a force that you feel in the steering wheel, not something that has any effect on handling.

The other point you make about both tyre slip angle and tyre slip ratio having an effect on the resulting forces is certainly correct. This comes into play after the "Magic Formulas" have been used and is known as force combining.

EDIT: Re-reading your post, I realize you were talking solely about aligning torque, so my comment about force combining doesn't apply to your question. It makes sense that the aligning torque should be influenced by slip angle as well as slip ratio. But again, I don't think that this small FFB tweak will have any large effects on feel and handling.

[axus]

Originally Posted by J.B.

As far as I understand it the aligning torque is merely a force that you feel in the steering wheel, not something that has any effect on handling.

The other point you make about both tyre slip angle and tyre slip ratio having an effect on the resulting forces is certainly correct. This comes into play after the "Magic Formulas" have been used and is known as force combining.

EDIT: Re-reading your post, I realize you were talking solely about aligning torque, so my comment about force combining doesn't apply to your question. It makes sense that the aligning torque should be influenced by slip angle as well as slip ratio. But again, I don't think that this small FFB tweak will have any large effects on feel and handling.

Aligning torque is what straightens a tyre once it is twisted (slip angle) and it also resists the tyre from being twisted further. This affects grip loss and grip recovery.

[J.B.]

Originally Posted by axus

Aligning torque is what straightens a tyre once it is twisted (slip angle) and it also resists the tyre from being twisted further.

Yes.

Originally Posted by axus

This affects grip loss and grip recovery.

How do you come to this conclusion?

The grip force is calculated by combining the other two formulas. Aligning torque doesn't come into play.

[axus]

Originally Posted by J.B.

Yes.

How do you come to this conclusion?

The grip force is calculated by combining the other two formulas. Aligning torque doesn't come into play.

Because the change of slip angle is influenced by aligning torque... and slip angle is what determines the lateral force. Upto a point, the lateral tyre force grows with slip angle and then begins to drop. The quicker the tyre is straightened once you are past that point, the quicker grip recovery. The more difficult it is to twist a tyre (because of aligning torque's resistance), the slower grip loss occurs.

[J.B.]

Originally Posted by axus

Because the change of slip angle is influenced by aligning torque... and slip angle is what determines the lateral force. Upto a point, the lateral tyre force grows with slip angle and then begins to drop. The quicker the tyre is straightened once you are past that point, the quicker grip recovery. The more difficult it is to twist a tyre (because of aligning torque's resistance), the slower grip loss occurs.

You assume that the aligning torque is a major factor in determining the current slip angle. The problem with this assumption is that cars have steering wheels which drivers use to "overide" whatever it is that the aligning torque wants to do to the tyre. While a strong aligning torque will try to straighten out the wheels very quickly, it won't be able to do anything if the driver doesn't straighten out the steering.

[axus]

Originally Posted by J.B.

You assume that the aligning torque is a major factor in determining the current slip angle. The problem with this assumption is that cars have steering wheels which drivers use to "overide" whatever it is that the aligning torque wants to do to the tyre. While a strong aligning torque will try to straighten out the wheels very quickly, it won't be able to do anything if the driver doesn't straighten out the steering.

Well, yes. If there are problems with grip recovery and grip loss (which are much abolished in the latest patch, but still not gone), and aligning torque affects that, then I will assume that something may be wrong with the aligning torque simulation. And considering the fact that nK-Pro just throws grip at the issue in its linear zone (one of three "zones" for the tyre behaviour) to give the cars a more bity feel I think there might be something that is not considered in the current tyre simulation in most racing simulations. Technically you should be able to represent tyre behaviour "in a perfect world" (the same road everywhere and tyres being all the same and so on) with one set of equations alone and not have to change those equations for different conditions. It may be an inherent fault in the model rather than an actual fault with the current values which is what I'm getting at with this whole discusison.

[colcob]

Yeah, aligning torque forces are really pretty small compared to the aligning forces caused by caster and inclination.
If you've still got an old version of LFS that lets you do it, set caster and inclination both to 0 and see how much force feedback you get. That would presumably represent the aligning torque in the LFS tyre model.

Its an interesting question, but I dont quite follow the logic of it having a big effect on handling behaviour.

[J.B.]

Well we can agree that there may well be some effects missing from in the Pacejka aligning torque formula. I don't think it is off by enough to make a big difference in terms of handling though. There are more important things missing in the "Magic Formulas" IMO.

About NKP's "three zones": If you look at the Fx and Fy graphs in your link, you can clearly see the three zones (especially in the Fx graph). First it rises linearly, then it falls off, then it stays constant. So Kunos was simply describing what Pacejka curves look like, not saying that he was switching between three different modes.

Originally Posted by axus

Technically you should be able to represent tyre behaviour "in a perfect world" (the same road everywhere and tyres being all the same and so on) with one set of equations alone and not have to change those equations for different conditions. It may be an inherent fault in the model rather than an actual fault with the current values which is what I'm getting at with this whole discusison.

You have to realize that the Magic Formulas don't really model anything physically. It's just a mathematical method to retrieve data measured on a tyre testing rig without having to use large look up tables. It's just data, not physics simulation. Most coefficients have no physical meaning. This is one way to create a simulation but there are others. Sadly we don't know a lot about how LFS simulates tyres but there is no reason to believe that LFS uses anything even remotely similar to this model.

So yes, I agree that there are faults in the Pacejka Magic Formula model but this is probably more relevant to rFactor, Racer and nKP than to LFS.

[axus]

Originally Posted by colcob

Yeah, aligning torque forces are really pretty small compared to the aligning forces caused by caster and inclination.
If you've still got an old version of LFS that lets you do it, set caster and inclination both to 0 and see how much force feedback you get. That would presumably represent the aligning torque in the LFS tyre model.

Its an interesting question, but I dont quite follow the logic of it having a big effect on handling behaviour.

I just went and did some of my own research on the matter with racer. There you can edit the car's aligning torque curve. The defaul value for the shape factor for the Lambo which comes with the sim is 2.2. I set it to 0.1 from the car.ini file, producing a curve like so the one in the first attached image. This caused quite a big change in FF as well as extreme difficulty in catching the car once in a slide. The car "wanted to slide". Then I tried 1.0 which felt simmilar but the effects were not as obvious. It was still waaay too difficult to catch the car (I simply couldn't do it at any significant speed). I then tried the opposite extreme with 3.0 which felt very different indeed. There was a lot of understeer and once you steer the car past a certain point the wheel would just fling itself in the direction in which you are turning (note the graph crossing the X-axis again in the last sceenshot). Also, the car would be too easy to correct upto a point, but once you pass that point it would be impossible to catch again (I suspect also caused by the curve crossing the X-axis again). Also note that these were changes of aligning torque of less than 30Nm for the most part... I don't know how much slip ratio would affect aligning torque but aligning torque seems to have quite a big effect on car handling (in racer that is). Certainly something worth looking into.

Regarding J.B's comment about this not being very relevant to LFS, I think that if something has potential effect on an area that seems faulty in LFS and we are not sure if it is simulated (I don't think it is), then it is certainly relevant.

EDIT: Oops - forgot to attach the pictures.

[KiDCoDEa]

Originally Posted by Woz

If you want to see the full dynamic pacejka in operation try NetKar Pro.

Like if u want to see the full dynamic Professional Online racing code try NetKar Pro...

[colcob]

Kid, you're obviously not capable of contributing in a productive way to an in-depth discussion about tyre physics, so why dont you just can it and go and troll elsewhere.

I dont think anyone in this thread is interested in petty inter-sim rivalry, we're just interested in tyre models. And NKPro uses the full pacejka calculated in realtime rather than from look-up tables, so is an interesting point of reference.

[J.B.]

Originally Posted by axus

I just went and did some of my own research on the matter with racer. There you can edit the car's aligning torque curve. The defaul value for the shape factor for the Lambo which comes with the sim is 2.2. I set it to 0.1 from the car.ini file, producing a curve like so the one in the first attached image. This caused quite a big change in FF as well as extreme difficulty in catching the car once in a slide. The car "wanted to slide". Then I tried 1.0 which felt simmilar but the effects were not as obvious. It was still waaay too difficult to catch the car (I simply couldn't do it at any significant speed). I then tried the opposite extreme with 3.0 which felt very different indeed. There was a lot of understeer and once you steer the car past a certain point the wheel would just fling itself in the direction in which you are turning (note the graph crossing the X-axis again in the last sceenshot). Also, the car would be too easy to correct upto a point, but once you pass that point it would be impossible to catch again (I suspect also caused by the curve crossing the X-axis again). Also note that these were changes of aligning torque of less than 30Nm for the most part... I don't know how much slip ratio would affect aligning torque but aligning torque seems to have quite a big effect on car handling (in racer that is). Certainly something worth looking into.

Regarding J.B's comment about this not being very relevant to LFS, I think that if something has potential effect on an area that seems faulty in LFS and we are not sure if it is simulated (I don't think it is), then it is certainly relevant.

EDIT: Oops - forgot to attach the pictures.

Interesting. Did you try disabling FFB completely to see if you can still feel differences in handling?

[axus]

I'm a bit busy atm but I'm gonna be testing more with racer later (before Kid complains - I don't think racer's physics are more realistisc than LFS, but what is in there should affect things correcly and is adjustable. I don't think my first set of curves are exactly comparable. Is there any form of telemetry logging for racer?

EDIT: Thanks for the FF idea, J.B - I will look at that also.

[Frankmd]

I'm not so much into tyre stuff, but maybe you can find some more information about Pacejka and a simulation that is derived from it here : http://www.delft-tyre.com/Home.htm

Edit: here is another document that explains tyre modeling in relation to Pacejka http://repository.tudelft.nl/file/107014/088296

[axus]

Here's another curve. I managed to just get a "general decrease" of aligning torque. This lead to the twitchiness and difficult grip recovery I was expecting (as well as a decrease in feedback)... so I think that just about proves my theory about the aligning torque having an effect on this. Now to prove that slip ratio affects it... I will be speaking to my physics teacher tomorrow to see what we can come up with.

[Ball Bearing Turbo]

Excellent thread!

[Levi1]

I guess longitudinal slip does indeed change the aligning moment.
If the longitudinal force rises with longitudinal slip (up to a certain point) the contact patch moves. (For example, if you're braking, the contact patch moves backwards relative to the wheel.)
If you're then turning, the point where the lateral force is acting on the tire (contact patch) is more to the back of the tire, thus you have a bigger aligning moment.

This is how I understand it works, I may be completely wrong.

[KiDCoDEa]

Originally Posted by colcob

Kid, you're obviously not capable of contributing in a productive way to an in-depth discussion about tyre physics, so why dont you just can it and go and troll elsewhere.

I dont think anyone in this thread is interested in petty inter-sim rivalry, we're just interested in tyre models. And NKPro uses the full pacejka calculated in realtime rather than from look-up tables, so is an interesting point of reference.

take a hike dude.
as if u know what i know or not about tyre models. as if u have a clue of what i test or not. see my name in gtp and lfs testing? chill please.
You seem to enjoy the magneto-rail technology invented by fisherprice in the late 70s and how its built in nk, so be it. praise it at will.
just dont tell other ppl to shut it, invoking dillemas u clearly have, disguised under some fascizoid moralistic attitude.
it wasnt me that brought nkp to the discussion. in fact i thought the discussion was around dat theme.
and if u believe everything kunos writes, then how do u explain the nkp fiasco and the history of lies he has behind him (and no i dont mean the un-met schedules).
let ppl express their opinions freely and please dont talk for everyone else on matters that are clearly subjective to each own.
have a nice day, bully.

ps: discussing tyre model of nk, is like discussing if blue is the new yellow while there's a nuclear war going on.
nk doesnt even need tyres. u can drive cars without tyres. on air. or even flip it over and drive upsidedown. yeah its a "bug", dat was supposed to be cleaned and done 3 years ago. he even mocked ppl who reported it, saying the "no brainer" was squashed. Oh the delight. Funny its still here, just like the rest of the game. funny indeed. we do have fun with it. and we dont even need to play it. thanks nk.

[Frankmd]

Could a mod please remove those off topic posts. Finally we got a bit of a good discussion going on and now this. Just stay out please, for once.

[al heeley]

[Shotglass]

Originally Posted by Tweaker

But even then, I don't think it is a full representation of the model... as there are quirks people have pointed out to be very wierd with NkPro's tire model. Maybe flaws in the game, or maybe flaws in the model, I don't know .

from what ive hear pacejka becomes vastly incorrect at slipangles above ~20° which would possibly explain the weird behaviour nkp shows when sliding and the way too light wheel in understeer situations

btw doesnt the alinging moment also influence the way the contact patch deforms ?

[Woz]

Originally Posted by KiDCoDEa

Like if u want to see the full dynamic Professional Online racing code try NetKar Pro...

Originally Posted by KiDCoDEa

take a hike dude.
as if u know what i know or not about tyre models. as if u have a clue of what i test or not. see my name in gtp and lfs testing? chill please.
You seem to enjoy the magneto-rail technology invented by fisherprice in the late 70s and how its built in nk, so be it. praise it at will.
just dont tell other ppl to shut it, invoking dillemas u clearly have, disguised under some fascizoid moralistic attitude.
it wasnt me that brought nkp to the discussion. in fact i thought the discussion was around dat theme.
and if u believe everything kunos writes, then how do u explain the nkp fiasco and the history of lies he has behind him (and no i dont mean the un-met schedules).
let ppl express their opinions freely and please dont talk for everyone else on matters that are clearly subjective to each own.
have a nice day, bully.

ps: discussing tyre model of nk, is like discussing if blue is the new yellow while there's a nuclear war going on.
nk doesnt even need tyres. u can drive cars without tyres. on air. or even flip it over and drive upsidedown. yeah its a "bug", dat was supposed to be cleaned and done 3 years ago. he even mocked ppl who reported it, saying the "no brainer" was squashed. Oh the delight. Funny its still here, just like the rest of the game. funny indeed. we do have fun with it. and we dont even need to play it. thanks nk.

I think you need to step away from the PC and clam down or back out of this thread.

If you re-read my post you will see there is no mention about NKP online code. This is due to the fact this thread is about tires, tire models and pacejka. I simply pointed out that Racer and other sims use a static pre-calculated version of pacejka while NKP uses the full dynamic version of the model. This was an answer to the person that started the tread as was to let him see that there are different ways to implement pacejka.

What would be really good is if you could let me know how you managed to get from my post, which you quoted, to your response also re-quoted below.

Originally Posted by Woz

The way racer and many other sims use pacejka is from pre-calculated curves and so the figures are good up to a point. If you want to see the full dynamic pacejka in operation try NetKar Pro.

Originally Posted by KiDCoDEa

Like if u want to see the full dynamic Professional Online racing code try NetKar Pro...

I have tried to be as nice as possible in my response and not attack you personally by please do not try to hijack this thread with another LFS vs NKP, LFS vs rF or LFS vs ??. There are many "My X is bigger than your X" threads here and on RSC for you to fight in, this is not the thread for that and please do not try to make it so.

[tr1ax]

Don't feed the trolls, just ignore KiDCoDEa he will get bored eventually.

[Ball Bearing Turbo]

Meh, he's just passionate. Nothing wrong with that

[axus]

Originally Posted by Shotglass

btw doesnt the alinging moment also influence the way the contact patch deforms ?

I should expect so... I'm thinking maybe ithe alingning moment didn't really influence the handling of that car in racer, its just the general feel of racer (and most other sims out there) with all the oversteer and lack of control... Does anyone know how the slip angle is calculated in a simulation? Is aligning moment part of that equation? I have two equations (front and rear) which look a bit dodgy and lacking certain parameters...

Calculating the slip angle of a front tyre
   
SlipAngle_f = ArcTan([v_lat + v_angular * {[Distance from the wheel to the CoG on the Y axis]}]/v_long) - ([Steer including toe and ackerman]) * sgn(v_long)

(sgn(x) = 1 for x > 0, sgn(x) = 0 for x = 0 and sgn(x) = -1 for x < 0)
  

Calculating the slip angle of a rear tyre
   
SlipAngle_r = ArcTan([v_lat + v_angular * {[Distance from the wheel to the CoG on the Y axis]}]/v_long)

[jtw62074]

Slip angle is just the angle between the direction the tire is pointing versus travelling. I.e., you can project the tire side vector (the axis the tire spins around) onto the ground, then do a dot product with that and the velocity vector of the center of the tire to get slip angle. Aligning torque doesn't "cause" slip angle at all, rather it's the other way around. Slip angle is just the angle.

Aligning torque is caused by slip angle, essentially. In that Pacejka paper earlier in the thread there are some diagrams that show what's happening in the contact patch in the case of pure slip (where slip angle exists, but there's no slip ratio). Rubber enters the contact patch a little bit pulled to the side of the wheel center plane, then is progressively pulled further and further to the side as it travels toward the rear. At some point it then slips back toward the center.

What happens is that the "force centroid," or the effective center of that force, is not in the center of the tire in most cases. The force centroid is like a center of gravity really. All the little forces throughout the contact patch, when added up, are the same as some bigger force acting at one specific spot in the patch. You can see more distortion in the rear of the tire than the front in most cases, so it should be fairly intuitive that the force centroid is usually toward the rear of the tire.

This distance from the center of the tire to the force centroid is called the "pneumatic trail," and since that force is acting behind the center of the tire it tries to twist the tire. Generally it tries to straighten it up, but actually at really large slip angles it can reverse itself (i.e., it makes a torque). The aligning torque is simply this pneumatic trail times the lateral force.

Caster angle then adds an additional distance to that pneumatic trail. I.e., a line through the steering axis intersects the ground at a point. The lateral force acts behind that, so you get an additional torque. The distance from that point to the center of the tire is called the "mechanical trail." So aligning torque becomes (mechanical trail + pneumatic trail) * lateral force.

The aligning torque really doesn't do much to the handling. All it really indicates is that the force centroid is moving a little bit forward/rearward as a function of slip angle. This primarily is just a steering force feedback thing happening.

What about slip ratio and aligning torque?

The simpler answer is that slip ratio produces a forward force in the tire plane. If that force acts in the center of the contact patch along the width of the tire (even if it's toward the rear or front of center), then there would not be any aligning torque contribution due to slip ratio. The force goes straight forward in the tire plane so there's no torque generated.

In reality the situation is not quite so perfect. The force centroid could very well be slightly to the left/right of center (especially with camber) which indeed would give you a little different aligning torque once you change the slip ratio via throttle/brakes. The effect is generally not very big though, and again, for the most part all this is doing is changing the feedback through the steering wheel. Moving the center of force at the tire around in the contact patch a couple of inches isn't going to make a noticable difference in the handling. Although the feel through the steering wheel would be different, and some people appear to judge the handling by the force feedback more than they do the actual balance/understeer/oversteer characteristics of the car.

A little on Pacejka: First, Dr. Pacejka has written a TON of tire models, not just the well known Magic Formula used in Racer and several other sims. I've got a book here published in 1971 that has several other tire models written by Dr. Pacejka, and they're quite advanced. He's been doing tire models for at least 35 years then in that case. There's a reason his Magic Tire model is used in real vehicle dynamics research. It's possible to reproduce real tire test data very accurately with it.

The snag that sim developers run into when trying to implement specifically his Magic Formula is in combining lateral/longitudinal forces. I.e., if you use that formula with say 4 degrees slip angle and no slip ratio, and the constants are chosen correctly to match up with a real tire, the force and aligning moment you get out of the model matches the real tire exactly. If you ran 0 slip angle and 0.05 slip ratio in the same equation with the proper constants for longitudinal slip, again, you'll get the right force.

However, once you start putting in slip angle and slip ratio at the same time, the forces all change. I.e., 4 degrees slip angle with 0 slip ratio produces a different lateral force than 4 deg and 0.05 slip ratio does. If that's not done correctly it impacts the handling in a major way. I think LFS had this problem all along until the latest update, where this now works much better. The result is a car that's easier to drive for sure, which is realistic. Don't let yourselves be fooled into hard=realistic. It just isn't the case at all...

If you get a chance to play the old arcade game Hard Drivin' or Race Drivin', give it a go. That's a vehicle model created by Doug Milliken and associates of a Corvette that uses a tire model with real tire data. I.e., that's a professional engineering model you're driving there that's dead accurate. Is it hard to drive? Not at all compared to a lot of sims, but it sure was harder to drive than Pole Position or any of the arcade games that were out at the time it was released.

You could also try Silicon Motor Speedway, the Nascar simulation. This was done by Doug Milliken too (in fact, they have a Milliken Raceway in his honor that the employees run on occassion). That again uses real tire data and is the same model they use for real research and engineering on real cars.

So if you guys are looking for a benchmark for simulation reality, try those titles and then judge all these other sims based on those.