Yup, I agree - the idea that one force is diminished by the other is wrong. Although for now I do not have a slightest idea for that situation:
Imagine you have constant slip ratio giving you Fy force lateral, your slip ratio gives Fx1 longitunal, when combined - on the limit (the box shows maximum forces and ellipse as combined). What happens when you add slip ratio so your vector goes out of ellipse?
BTW: I have to excuse Mr. Pacejka I only used his tyre model not "magic formula". The example is with elliptic approach - as soon as I get "magic formula" don't worry, I'll post it
its not entirely wrong since there is a sort of maximum capacity of force generation in a tyre that you cant go above so your tyre model shoudl show some clipping plateau behaviour as you have on the top right of that graph http://www.lfsforum.net/attach ... d=103311&d=1270163064
the idea that both force somehow cancel each other out and add up to 0 is however nonsense
the crude and not quite correct (but it should give you reasonably correct tyre behaviour) method would be to take the direction you get from Fy and Fx2 as the direction of the combined force vector but reduce the length of it so it ends up on the ellipse
so the resulting force would be the red vector
But when you add slip you go over the top so the tire characteristics is completely different - it is not symmetrical.
And notice that when you are on longitunal peak you can add as much slip angle as you want - it doesnt change you F combined at all anywhere. This is a better case - as with max lateral force you can obtain overall bigger vector if longitidunal peak is much bigger. Although it is just the same contact patch.
At this point I think you've realized this is not right. One main giveaway that this relationship was wrong were the 0 force valleys strewn across the landscape.
Have you heard of "friction circle theory?" If not, try searching for it.
You've got it
Pacejka's magic model is indeed an empirical model, meaning it has no real physical basis. It's a mathematical fit. However, it turns out to be a very good one and is pretty easily adjustable in terms of getting the initial slope, peak height and location, and drop off after the peak how you want. This is probably why it's so popular. You could use your own equations here too if you wanted. All they're trying to do is fit measured tire data with some equation that will reproduce the data given slip ratio, slip angle, normal/vertical load, and whatever else is desired. All sorts of approaches have been tried successfully to do this and it's an area of constant research. Even artificial neural networks have been done for this. Can you imagine that? Artificial intelligence tire models? (Granted, for that to work, you need seriously large and complete tire data sets that you won't ever find).
So you have a class of tire models like Pacejka's (pronounced "Puh ZHay Ka" by engineers in case anyone's curious) that are strictly empirical curve fit models. The other main class are what people commonly call "physically based" models such as brush models, string models, FEM, and others, that try to calculate the forces directly from various stiffnesses and frictional properties in the tread, perhaps the carcass, and so on.
Exactly! And this is the precise thing that most hobby game developers (and even most of the pros until perhaps just a few years ago) completely miss, myself included from 2000 on for three or four years probably. Even with a book that showed this change staring me right in the face, I didn't connect the dots.
Let's break this stuff down a little more into specific areas:
1) First there is the friction circle/ellipse trimming, which Shotglass illustrated with the red vector. The idea is that even though you may be below the peaks of both lateral/longitudinal force curves independently, you take (making up numbers here) 5 degree slip angle which gives 1000 force, and 0.1 slip ratio which gives 800 force separately from each other. The resultant force becomes (1000*1000 + 800*800)^0.5 = 1280 (^0.5 means to the power of 0.5, or the square root).
If this force goes beyond the friction circle/ellipse, you scale it back so it lands on the circle/ellipse as Shotglass showed. This is the "trimming a friction square to a circle/ellipse" that Bob mentioned.
This works and you actually do get a reasonably decent car to drive, but it's very knife edge and you get the "all or nothing" type of handling that was common in past (and some current) sims. Where you can wind up with a car that's understeer and then suddenly transitions to snap oversteer with little or no warning. Still though, if you make a sim that works this way, you're bound to get a few fans that love it and think it's the most realistic thing ever developed because it's so damn hard to drive it at the limit Then you can sit back and chuckle at the flame wars about realism that come up in your forum.
While this is a good place to start (I'd recommend it for anybody wanting to take a stab at writing their own sim), it is actually quite far off from reality. There is another effect that is completely missed in this approach, which brings us to #2:
2) Imagine another situation where we have combined slip, meaning we have a non-zero slip angle and a non-zero slip ratio at the same time. We're turning and acceleration/braking simultaneously. But imagine that the combined force (force resultant) is small enough that we don't need to trim it to the circle/ellipse. We have something like 2 degree slip angle and 0.05 slip ratio. In point 1, above, we simply look up the force that we get from the "pure slip angle" formula and constants to get the lateral force. Then we look up the same thing on the other formula for longitudinal force. The problem is, neither of these forces are correct any longer!
If we are sitting at 2 degree slip angle and 0 slip ratio, we get the correct lateral force that the magic formula or whatever other empirical formula we use shows, which is only correct for the "pure slip" case, meaning either in pure slip angle or pure slip ratio, but not both in combination. But as we start changing slip ratio, that entire lateral force curve changes! Both curves change, actually. This is what most hobbyists (again, I was guilty of this too) completely miss. The combined slip stuff influences and completely changes both of the curves. In the early 2000's I know for a fact that a lot of the sims that were out on the market also had this very same problem because we were all discussing this subject quite a lot on usenet at the time. I can feel immediately when driving a sim if this is how the tire model works or not. Nowadays most developers seem to have got this worked out, but it was a big problem back then.
This is why if you're using Pacejka's MM or other empirical model, you really need to make sure that you have a version of it that includes the modifications to the curves that account for combined slip behavior. And here lies the fundamental problem that we sim developers run into with empirical models like Pacejka's MM: You have to tune these parameters to make the combined forces work right. If you are a chassis engineer at Ford or something and have tire data where they measured all these combined slip maps and so on, you can tune Pacejka's MM and other empirical models to work just fine and dandy because you've got the real test data to look at.
This is one reason why I abandoned empirical approaches and came up with something physically based. It's not that Pacejka's MM is "bad" at all. It's just that as a sim developer, I don't have a single complete set of data like this for any single tire. Can you imagine poor Scawen trying to tune by complete guesswork something like this for multitudes of different tires all tuned to the bazillions of cars available in LFS? Yikes....
Anyway, I'd still like to encourage you to play with Pacejka's MM more. You'll learn plenty just by continuing with the exercise
Edit: Oh, one more thing. To keep things simple for now I suggest just sticking with a friction circle and keeping the Fx and Fy peaks the same. Once you get your mind wrapped around that then you might try doing the ellipse approach as Tristan rightly stated is a more accurate method. However, the combined stuff in point 2 has a far larger impact on vehicle behavior. Massive. Huge.
I guess this is evolutionary approach for solving equations - in theory simple: you get a set (resource) of basic equations with parameters and with evolutionary method leave those giving closest result and by couple of generations get better and better approximation
I am from eastern Europe - although Pacejka is Dutch the name sounds like Czech
Does it require tons of sets data or just examples on several types? Because many surveys on many types of tyres are made as university science - therefore they are open and available.
And here very interesting paper on Dynamic Tire Friction Models f ... nd Lateral Vehicle Motion - with results from empirical surveys on hysteresis when changing both angle slip and ratio and with differences on steady and dynamic changes.
Of course I read only Conclusions (and chapter DYNAMIC RESPONSE OF THE MODEL )
of course it doesnt change the combined force becasue thats the whole idea of the friction circle
the tyre has some of maximum force generation capability and if youd try to exceed the physics work out in a way that limits the combined force to that maximum of what the tyre can generate
Do you mean that longitudinal force is somewhat "chosen" and it consummes all the friction and when you turn wheel nothing happens - no lateral force is generated because it was taken by the longitudinal (component of, in fact, one force applied to the contact patch)?
are you sure you understand the term combined force correctly? of course you will generate a lateral force but the combined force ie the (vectorial) sum of both wont add up beyond the friction ellipse (or whatever probably not quite so idealised shape it actually is)
the point is what you expect to see when you plot the (absolute) combined force under combined slip conditions is a zero at the origin then some kind of rise up to a more or less circular peak and a more or less flat plateau at around peak height anwhere beyond that
you certainly dont expect to see any zeros in there anywhere else but at the origin
Could be www.xmotorracing.com a useful tool here? One can see there in real time the use of these models and functions. It's pretty nice from that point of view. On the other hand it's away from LFS (or iRacing) in terms of handling and feel.
I have another issue, a more philosphical one: isn't it possible that even if you manage to nail the model that best replicates the empirical data, the actual feel during the play is not good? Is it necessary that the best feel of the game overlaps with the best fitted tyre physics model?
I was referring to artificial neural networks. Those are a big set of equations, but the idea is it would learn the existing data set for a single tire rather than groups of many types in order to reproduce it. In the end it's just a neural network. A black box. You don't know how or why the tire works the way that it does, but as long as it reproduces a set of overly complicated test data accurately, you don't care. This is something chassis engineers would be more interested in than tire engineers though, of course.
You can, however, use evolutionary algorithms to come up with constants for other models like Pacejka too though. In fact this is quite commonly done especially with versions of Pacejka MM that have a huge number of parameters to solve for. There was a program called TireGene years back that used genetic algorithms to solve for them given a set of tire data. This is getting a bit off the original point though.
Each neural network setup would be a solution for a single tire. It needs a big set of complete tire data (very expensive to obtain) in order to work. Hence you won't see it in video games any time soon.
Yes, these are the types of papers you should be looking at
Adding to what Shotglass said about resultant force: AndRand, perhaps you are referring to the magnitude of the force not changing? This is true enough given the context of the discussion, but I think where there might be some confusion between you and Shotglass is that I think he's referring to how Fx and Fy change as a result of trimming to the circle. When tire modelling the magnitude of the force is important of course, but the direction of that force is even more important. I think that's what Shotglass is probably getting at.
Just gave that sim you linked to a shot. Think I'll pass on this one, but I can see it being interesting to people that want to watch all the variables changing in real time and play with the physics through a friendly interface.
wouldnt you only need a relatively straight forward set of 4d data to reproduce a tyre in all its behvioural characteristics?
doesnt sound too complicated to me... maybe 5d if you add aligning torque too
you could probably also represent the pure fx fy data as a 4d matrix with the actual data represented as the difference force vector in both magitude and angle from the force vector youd get through simple force combining and traction circle trimming
while not a particularly practical way of using the data it might produce some rather revealing plots
Or friction ellipse theory? How close are these theories to reality?
Rather than consider friction as being limited to some total maximum magnitude of force from the sum of force vectors, its' seems reasonable to assume that due to tire construction, contact patch dynamics, ... that the maximum force possible will vary depending on ratio between lateral and longitudinal forces. Speed seems like it could be a factor because of the amount of centripetal force exerted by the plies in the tires at speed. My guess it that like everything else in the real world, tire phyiscs modeling will end up complicated, requiring the equivalent of the Navier Stokes methods used to deal with aerodynamics.
This isn't something I follow much myself, so perhaps there are papers or articles that address these issues, and I'm just not aware of them.
Are you sure you understand the components in tyre characteristics? Both Fx and Fy that are used here were measured with other component equal to zero. You try to derive a combined force using non-combined characteristic.
Yes, I agree it isnt simple diminishing one force by another. Thing is more complex, but first I tried to figure out what is wrong with elliptic approach. Yes, the plateu flattens. But it is certainly not happening at the level of Fx max as it is with elliptical approach. I just found that paper on Dynamic Response yesterday and I am to figure out an equation for Pacejka model that will generate Fx in function of Slip Angle according to those diagrams attached (and Fy with slip ratio correspondingly).
Hysteresis on dynamic changes is, I fear, beyond my capabilities
well no of course its not quite correct but as todd and i said it is a crude and quite reasonable first step that will result in something that drives more or less like a car up to and beyond the limit
Yup, when trimming the circle, or ellipse, combined force is constant. But, when combined force exceeds the ellipse, it is not "trimmed" on the level of non-combined force. It is trimmed on new characteristics.
btw. about availability of sets of data - the paper I found is a scientific paper. It means it is open for verification, so when someone is interested authors are obliged to share with raw data.
As W126 pointed out, you'd need data at lot of different loads for the network to learn how to predict forces at non-tested loads. I doubt 2 loads would be nearly enough, and you'd need full Fx/Fy testing. Multiple loads at lots of slip angles and slip ratios, then multiply that again by the number of camber tests, then again by the number of different air pressures, etc.. I'm just guessing here, but supposing if Pacejka or another model couldn't be made to fit a big set of data like this, the network might be able to learn the patterns that are too complex for humans to tune. I've never seen a set of data for a single tire that's this comprehensive. Even combined data is fairly rare and I don't recall seeing any for multiple loads on a single tire, let alone all the other stuff. It's probably been done, but with such an expensive test it's unlikely to be posted for the public in a paper somewhere. (If anyone finds some, please point me to it.)
I haven't read any papers on neural net tire models. It was just a thought that occurred to me some years ago and then eventually I ran across a paper or two mentioning their use. So your point could very well be right, but I'd suspect you'd need huge, expensive data sets.
The equations you'd use for an ellipse would be different of course, but it's the same concept. I couldn't tell you how close they are to reality since I don't use these concepts in my own modelling and so haven't gone looking for an answer to this one.
The lateral/longitudinal force dependence approach used depends on how it's modelled of course, as would a split in peak lat/long force (ellipse effect at limit). At one extreme with FEM tire modelling as is done at tire manufacturers, I doubt there is any of this done directly at all. The forces come directly from the stresses at each node which should produce all this without needing to try to account for it with separate equations. In the context of other models I'll leave that to others to find, but a similar thing happens. That's getting a little too close to discussing how my stuff handles things and I don't want to post that stuff publically.
This is exactly what I meant by the combined force screwing up the curves. You can't just say "slip ratio is 0.05 and slip angle is 3" and then find the forces by looking them up on their respective pure slip graphs (this is a friction square approach with the friction circle limiting added on top of it as a separate step). The curves change dramatically when you have both slip ratio and slip angle occuring at the same time even when you're well under the peaks.
Many sim developers historically haven't bothered to emulate this. It has a profound effect on the controllability of the car. A sim with this done well is also a lot more fun and realistic to drive This is an area where when done well, "easier = more realistic" rather than the other way around.
yeah my mind had a bit of a boo boo there and i completely forgot about load sensitivity and all that other nonsense that these annoying black round thingies do
ok, so I messed around a bit with Pacejka model to see where to insert some simple proportional/exponential formulas, made two separate diagrams for Fx and Fy and combined them (I wasn't sure though, because the diagrams from "Dynamic Tire Friction..." have one axis titled as vector Fx*Fy but they are plotted separate :shrug.
And there is one thing I wouldn't expect - when you are on peak force non-combined (especially with Fx) and add slip angle the combined force diminish... but there is strange hill like island and even very rough steeps of both Fy and Fx have not much impact on it
I only used his tyre model not "magic formula". The example is with elliptic approach - as soon as I get "magic formula" 
don't worry, I'll post it
(Granted, for that to work, you need seriously large and complete tire data sets that you won't ever find).
Then you can sit back and chuckle at the flame wars about realism that come up in your forum.
and even very rough steeps of both Fy and Fx have not much impact on it