Posted by: drracing | March 24, 2013

Audi R18 Modeling – part 2

Ok. So now we have more or less all the main dimensions of the car and some values for CG location and inertias.

Let´s try to go on with the analysis of the Audi R18 modeling process I used to build up the physics side of this car into rFactor. As I said in my last topic, next points will be aerodynamics, tires and engine but, before to go on, I want to have a further comment on the importance of the moments of inertia (above all the Izz) from a driving simulation model perspective.
Although, as I said, they are quite difficult number to calculate or measure, they can have a massive influence on how the car behave (maybe not too much on how fast they car is on a lap, I should verify this point with some tests sooner or later, but on how it reacts to inputs) and even more on how the driver feels the simulated car reactions (what “sim drivers” normally love to define as “feeling”). Actually, the latter is quite a difficult topic, that at higher levels include, I guess, also the effects of cueing strategies (like moving platforms, tricks to make the driver´s mind to believe he is really experiencing accelerations while most of the times he is doing that only for a few instants).
In a normal “home” simulation experience, the only “physical” links between the driver and the car are the steering wheel and the pedals and only the steering wheel is somehow transferring to the driver a feedback (“force feedback”) about the reactions of the car. Together with controls, drivers´ eyes play an important role to help him/her to understand how the car behaves in a certain situation: he/she looks to the screen and tries somehow to anticipate car reactions.
So basically, compared with a real driver, the “home sim driver” is completely missing a physical link with the car, if you exclude the “force feedback” features of current steering wheels, which need anyway to be set properly. This is why, in my experience, when you increase inertia (above all yaw moment of inertia) in a driving simulation car model, the driver tends to feel the car in a better way and to better understand what is going on (he would say “I have a better feeling”).
Moreover, I guess at an higher level this could have also a huge influence on how the driver is replicating his real way of driving into the simulator: if he feels the car is behaving more or less in a similar way to what he is used to expect from the real vehicle in a real track situation, than it will be easier for him to trust the behavior of the model, to treat the simulated car as he would treat the real counterpart and also to drive as he would drive in a real racetrack the real car (although he will always miss some of the physical links that he has with the car in real driving situation). This latest point could, in my opinion, have a huge influence on making the driving simulation useful also for setup investigations or, at least, to study setup changes impact on both driver´s impressions and final performance.
Now, again, this could show on one side how important MoIs are to the final result and for the goodness of the handling behavior of the model but also how difficult/arguable is the way to define them before to even run the car on the track.
My experience about this topic teached me that, compared to the number I was using before in other kind of simulations (see proper Multibody Simulations), here I am forced to use higher values for MoIs, so I also modified my tools to include this need. I don´t know if this depends only on wrong assumptions on my side (maybe my calculations are completely inaccurate or the assumptions I am making are simply wrong), on some kind of issues in the code (since I also hear something about that around the web) or on both things.
This should also show how beneficial could be to proper measure MoIs for this kind of simulation, both to have a clearer picture about them and also to be sure that the driver is really feeling a car behavior that somehow resembles how the real car is. Actually, all the discussion about MoI could probably be skipped if we were able to easily and quickly measure Moments of Inertias of the car we want to model. We could even discover that all our calculations are more or less wrong and that´s why we have to work so much on them: do we simply need different numbers?

Let´s start with Aerodynamics now. Another topic about which, of course, I didn´t have any official figure nor any measured data. But, again, web was my friend and Mulsannescorner in particular was an invaluable source about this topic. Moreover, I had the possibility to talk to some race engineers who have worked on these cars (although mainly on LMP2, but better than nothing) and kindly ask for some figures about the level of downforce/drag this kind of vehicles are running.
What came out very clearly is that, above all after the regulation changes that came into play in 2011 and which force an improvement (because of an engine power reduction), LMP cars became very efficient from an aerodynamic perspective. We are here talking about efficiency values that go over 4 also for “smaller LMP2 teams” cars (at least for closed cars) and sometimes even go around 5 for official LMP1 programs, if my sources are correct. I don´t know about you, but that is quite impressive to me!
Another point which seems to be pretty sure is that teams are more and more looking for a very much forward biased aero balance. This goes quite well with the very forward weight distribution that these cars should use (we are talking of something around 50% of the weight on the front axle, as I said in my last post, at least according to what I have found) and with the choice to have more or less equally sized tires front and rear. To fully use tires potential, it makes then sense to look for a downforce distribution more or less in the same range of the weight distribution or, in “high downforce” tracks (so in slower ones), even more front biased.

How much downforce are we talking about? And how much drag?

Web sources (again mainly Mulsannescorner, but the numbers I have found there were also confirmed by the race engineers I talked to) talks about something approximately equal to 0.875 for “Cd x A” (coefficient of drag multiplied by frontal area) and an aero efficiency, as I said, of around 5, leading to a “Cl x A” (coefficient of lift multiplied by frontal area, although here we mean downforce and not lift) more or less equal to 4.4. This numbers find a confirmation also in Mulsannescorner “Race Car Aerodynamics Data Base” where some info about an 2011 spec Dome LMP1 car in 2011 spec show a CdxA of around 4.5 but with a lower efficiency (around 4.1).

Back on Audi R18, Mulsannescorner propose a calculation for Drag based on 2011 top speeds and on an estimated engine power of around 550 HP at the wheel. The calculation should be referred to the total drag of the car, so my understanding is that they include also rolling resistance and other mechanical losses like bearings friction, etc.. Now, the goodness of this assumption for CdxA depends, of course, on the goodness of the assumption done for the engine power. Anyway, this value is somehow confirmed by a picture you could find again in Mulsannescorner website and showing an incautious photo of an 2011 Audi R18 tested in a windtunnel with non-rolling ground and showing an CdxA equal to 0.8486. Not far from Mike assumption, above all if we think that a non-rolling ground wind tunnel will surely produce slightly wrong results (probably the mistake is bigger for downforce than for drag, but we should probably expect a small error also on drag side).

To complete this picture about drag, I did as well an easy calculation based on the engine torque and power assumption I used for my model. So, first it´s maybe worth to spend some words about these assumptions.
Looking to the On Board videos from Audi WEC Races that you can find on Youtube, it seems that Audi drivers in 2012 shifted gears up at about 4500 RPM. Since the drivers upshift at around 4500 RPM, I guess maximum power is somehow at a lower point. Actually this is somehow different than what you could see in other videos from 2011, that showed gear changes at around 5000 RPM. Anyway on the web I also found a very interesting paper about the development of AUDI Le Mans 12 cylinders diesel engine used on Audi R10. Of course, no exact power values were shown there, but still a very useful image with a nice “specific Power output” curve in it, where values were compared to an AUDI street engine. Two main information could be taken from this picture: in first place, power curve approximated shape and maximum power RPM (for that V12 engine), but also a rough relationship between the maximum power of the engine used on Audi R10 and an Audi Diesel road engine with similar features. Although looking to 2011 videos I would think that maximum power would be at about 4500 RPM, according to this paper it is closer to 4000.
This was actually a very good starting point to draw a base engine power curve: I started from an Audi recent series production engine maximum power (somehow linkable to the race engine, as shown in the paper mentioned above), increasing it by the amount shown in the paper and placing the peak at similar RPM value to what you could see in the picture from Audi. This actually reflects quite well what can be seen from the Audi´s 2012 on board videos but a bit less what is shown in 2011 ones. Anyway, for the time being, I decided to go the 2012 way, so I assumed maximum power was at 4000 rpm with rev limiter slightly above 4500. I will leave myself the possibility to adjust engine power output in future.
It was anyway nice to see that at least the maximum power value that comes out working on Audi´s paper info is very close to the one mentioned by Mulsannescorner.

So, with an engine power output in my hands, it was possible to estimate the top speed we could expect using the drag numbers we said before and somehow realistic gear ratios for a “Le Mans” like track . This simple calculation showed that we could expect a maximum speed in slight excess of what it was measured in Le Mans in 2011, so the combination engine power and drag seems to be more or less in the right window. Of course, this is not telling much about torque and so about how the car accelerates out of a corner (and it has a huge influence on lap times, of course), but it is more difficult to find something about that. A more accurate study about this point is currently ongoing with (funny) on track testing, although it is very difficult to proceed without real car data to compare to. That´s life!
As I side not, I am not including for now any real drivetrain efficiency, since we are anyway interested to the final power output at the rear wheels. What I am only using, according to the normal rF modeling way, is a fixed clutch connected torque loss between engine and gearbox (together with other friction losses on hubs bearings and with rolling resistance). So actually, I used a similar way to the one used by “Mulsannes Mike” of targeting for the total drag, taking into account also mechanical losses (what you could measure with a coast down test).
A quick and dirty in game straight line test showed that the assumptions were quite right (and that also the modeling numbers used were correct!), since the car in its lowest downforce configuration had a final top speed very close to the one you could see in Le Mans (without slipstreams) and very close to the one shown by Mulsannescorner.

In summary, on Drag side, it seemed that the model could work quite in a similar way to the real car.
How to check if also the downforce estimation was correct?

To verify my assumptions, it was then necessary to also start building up at least a very basic tire model, in order to be able to make some very easy cornering simulations and see if the maximum lateral accelerations achievable at different speeds were more or less similar to the ones shown in Audi´s onboard videos.
For this first study, I started working on some tire data I had initially only picking up basic numbers for tire maximum coefficient of friction for different vertical loads, coming up to a first estimation for load sensitivity; the data I used were not of course not LMP1 tires data, but still they were referring to tires I would expect to have a similar behavior to the ones used by Audi (at least in a qualitative way, since they have more or less the same diameter and the same sidewall height, although LMP1 are wider).
Just one word about this way of proceeding. Of course the data I have used was taken from a Pacejka model, it is nearly impossible to grab some raw data from manufacturers, above all at high level in motorsports (and if, like me, you are doing a project just for your own fun). The data itself was then already the result of a fitting procedure and so it already contained in itself some kind of “error”. That was anyway the best source I had and I have seen that the “linear load sensitivity” approximation that Pacejka models use was anyway leading to a good correlation with the only information I had about overall car performance (the youtube videos I mentioned before).
For this first basic calculation, I assumed that the car was perfectly symmetrical, so 50% of the weight at the front axle, same track width for front and rear axle, 50% of Total Lateral Load Trasnfer Distribution at the front and 50% of downforce acting on the front axle. As you may see, this is not a too crude approximation, since the model I have built in rFactor has very similar features. Then, based on speed (known the speed, from the chosen ClxA, aerodynamic load can be derived), static weight distribution, CG height and an initial assumption for lateral acceleration, I could find the vertical load on each wheel. From there, with my simplified tire model, it was straightforward to identify the maximum Fy each tire could produce and compare it with the one necessary to give equilibrium at the given lateral acceleration. Iterating on lateral acceleration until it reaches a maximum and still equilibrium could be obtained, I have then derived the maximum lateral acceleration the car could perform at the given speed (and so with the given level of downforce). I did that at two speed levels, to check car performance at both low and high speeds and at different downforce levels and then I compared the results to the values shown in Audi´s videos. It was immediately clear the model was at least in the ball park with both tires and aerodynamics (or at least with the combination of the values I assumed for them!), although some tuning was still necessary (Ay was a bit too high both at high and low speed, with a bit more of this tendency at lower speeds). This point could potentially open a discussion also about how much lab testing is overestimating tires forces, since normally, at least in my experience, you always have to scale them in order to obtain realistic results. In my case, in particular, being the data not even from the same tires, I had also no info about the compounds in use. It is anyway quite normal to apply somehow  scale factor (lower than 1) to obtain reasonable tire performances in simulations.
After I have reached a result close to real performance (to do that, I assumed that downforce level was correct and I worked on tires until my results were close to “real” numbers: is this correct? Again, I don´t know, but I was in a position to trust more the downforce figures I have found than the tire data I had, because of the reasons explained above; since the data was coming anyway from narrower than the one used by LMP1 cars, it was anyway a bit surprising to see I had to reduce friction to reach target results.
In this first stage, camber effects have been ignored, as well as Self Aligning torque, so some more small tuning had to be done also after the model have run for the first time on (sim) track (also to double check camber effects on tire grip and Self Aligning effect on driver feeling and in transient situations). But it has been nice to see that the sim car performance was not too far from the one shown in Audi´s videos.

I don´t want to start another long topic about tires here, but actually camber and self aligning torque are quite difficult-to-model features in rFactor, since there is very little documentation-knowledge around about them and, somehow, the modeling way chosen by the developers use some even more crude approximation than what have been used for other tires features. Actually, rFactor depicts camber effect on Cornering Force as a multiplier that reaches its maximum value at a certain Camber angle (growing following a part of a sinusoidal curve) and then decreases in a linear manner (actually, according to my understanding, this multiplier value is changing also depending on slip angle and it has a smaller effect at peak Slip Angle than what it has at low SAs, but I could not find many info about this point around). Its effect on longitudinal forces is represented even in an easier way, since it simply acts as a grip multiplier that can be equal to values from 0 to 1, although I think it should be allowed to use also values bigger than 1 (this parameter actually defines how much grip decreases in longitudinal direction at an ideal camber angle of 90°: the rate of change is linear, so depending on this number, the slope of a straight curve is defined and it then tells us how much grip you will have at camber angles between 0 and 90°). Although this is probably not producing a dramatic inaccuracy in the data, it is not always easy to take out the numbers you need to insert in rFactor to properly model tire behavior. So, it is not only the inaccuracy of the model itself to make things a bit harder, but the way you have to gather the data you need to insert into the model itself. Moreover, in real tires (and in Pacejka models in y direction) camber effects depends both in absolute and relative magnitude on a lot of other parameters, like vertical load and I don´t think it is represented in anyway in rF (the multiplier should change is value also according to Load in z direction for example).
Another point is that, normally, when you are so lucky to gather some tire data as a Pacejka model (as I said, to gather raw data is normally nearly impossible in a normal “motorsport environment”), the most of the times they tell you only something about Cornering, but nothing about braking/accelerating tire behavior (longitudinal forces). Moreover, whenever you are even luckier to get some Pacejka coefficients also for longitudinal forces, than you anyway don´t know anything about how much grip decreases when increasing camber, because this is something that Pacejka models don´t depict.
So how to evaluate how much grip to assign to tires in longitudinal direction? And how to estimate how much this is changing with camber (rF assumes the same load sensitivity for both longitudinal and lateral friction coefficients, so your Fx load sensitivity is the same than the Fy one)?
This latest point can be a bigger limitation factor than what we could expect; according to my experience with Pacejka data packs, in facts, longitudinal forces and lateral forces show different sensitivity to vertical load. So we are force to “tweak” the initial coefficient of grip value so that at the “typical operating loads” we have the right coefficient of friction value (and this is somehow another approximation, since there is really nothing similar to a typical operating load, above all with aero race cars).
The truth is that, you can spend a lot of time doing preliminary assumptions to properly model tire behavior but then you will necessarily have to test them on several tracks to see if the results you have are realistic.
In my case, I have been lucky to have access at some stages of my carrier to some tire raw data and to be able to measure (more or less) how much longitudinal force decrease when camber is added and how longitudinal and lateral forces are “related”. Of course, this is not something that can be assumed to be the same for all tires and depends very much on tire construction, shape, dimensions, etc.. So, although to have access to these information is at least useful to have a feel about the numbers you could expect, it is not anyway granting you are modeling anything close to the reality of the tire you are working at right now! In this particular case, the absence of reference real telemetry data is hence playing an even bigger role, but at least we have the mentioned videos to get some directions. It´s not much (very often they are not accurate or the data flow sometimes stops), but it is still better than nothing.



  1. Hello, again. Hope you don’t mind a few comments.
    First off, fantastic exploration of your modding experiments and your opinions on simulations (February 2013 and March 2013).

    Regarding load sensitivities…rFactor does allow you to distinguish between longitudinal and lateral variation of the coefficient of friction with load. There are two variables, LoadSensLat and LoadSensLong, that can be used to do just that. Other sims, also based on ISIMotor2, deprecated these variables, forcing upon the modder a loadsens parameter to deal with.

    There are a few things to take into consideration.
    1- Grip estimation on the limit
    It seems some people believe physical models do not have problems with grip estimation in the non-linear region (over 5º SAs), and the problem is circumscribed to Pacejka-based models. I don’t think this is the truth at all – there are methods for circumventing the loss of grip due to low estimation. I believe ISI did that with their tire model, but another company using the same platform, called SIMBIN, did a great job at this with one of their racing games: Race07.

    2- Combined grip
    What I said above also applies to this.

    In order to take the best out of ISIMotor2 (whether in rFactor or Race07), we have to do as you are doing – use as much real life data as possible and, on the limit and in the absence of further data, make the proper assumptions (which, by themselves, should be already based on scientific and empiric data).

    Grip estimation on the limit and combined grip require both – real data and proper assumptions.

    It must be observed that lateral force falls somewhat gently even in the nonlinear region. The graphs I was given access to prove that.

    Moreover, as an example, for a 4000 N load, some racing tires can expect to develop a lateral force in excess of 6700 N. If we do a normalization, it is easy to see that the coefficient of grip of those tires can reach values above 1.6. Nothing amazing (a recent test by BMW on the M3 pointed to coeffs in excess of 1.8 and lateral/longitudinal forces in excess of 1.7g – and this in sustained/stable conditions, not actually peaks), but something often overlooked.

    Furthermore, it is vital to get right the load sensitivity curve profile. The curve must allow for lateral and longitudinal forces following values similar (in proportion) to that above. Easy to see that a car, with its mass, weight distribution and negative lift, hits certain figures of g which are spot on if we dare to force this profile.

    So, how do we do just that in rF or Race07?

    Firstly, the slip curve (which influences the grip factor) must be as steady as possible. Something like reaching 1.0 at 1.6º SA and going down slowly and reaching 0.88 to 0.96 at SAs between 85 and 90º.

    Secondly, we don’t need ridiculously high lat/long coeffs (2.2 or 2.1 as some mods use) – we can look at figures already exposed here and there which point to slick tires used by GT cars with an average coeff around 1.6 to 1.8.

    Thirdly, use the proper loadsens curve profile. The initial parameter should not be too aggressive, the multiplier should be low enough (0.20 to 0.27) and the third parameter ought to be below 30 000N.

    Add to that a high speedeffects_param1 and you’re basically set to have a car that definitely has its limits but feels mostly on rails just below the limit (as GT drivers have described to me).

    When you do that, you effectively decouple tires from downforce. Tires are tires and the same tire in different cars works somewhat differently due to many factors – so, there is no need to design tires on a car by car basis. Different cars, however, have different inertias (even with the same mass) and obviously different suspensions; downforce levels for each, even regulated by stringent rules, also differ. So, when tires are effectively modelled, we are then “free” to apply known figures for downforce.

    Sorry for the long-winded post, hope this helps or is interesting enough for you.

  2. Hi Miguel,

    welcome back! as in the past, your comments are always interesting, so i don´t bother at all for you to leave your thoughts and i would be happy if you will go on doing it!

    First of all, reading your comment i recognized i wrote something wrong about load sensitivity in lateral and longitudinal direction. Actually, i am using both the parameters you mentioned (LoadSensLat and LoadSensLong), but my post was written quite some time later than when i did the tires modeling work in rfactor! My Fault!

    Anyway, as i wrote, it is normally quite hard to find something useful about longitudinal forces (it is normally hard to find something useful about tires in general, since companies are not happy to share and their measurements are anyway performed in lab conditions and this makes then anyway necessary to rework the data you receive to adapt them to the real track conditions).
    Moreover, when you get pacejka coefficients, they normally still miss a lot of info, above all about camber effects. Not to talk about temperature effects, but that´s a separate world! So, to summarize, it is normally a bit easier to get info about load sensitivity for lateral forces than for longitudinal ones.
    My experience (based on raw data) tells me that they are not the same at all, but when you have no info, i still think the only reasonable way to proceed is to use the same values for lateral and longitudinal load sensitivity. What do you think about this point?

    About your second point, related to grip estimation at the limit, i totally agree with you. I normally use curves which are slowly decreasing after peak and still having quite a high grip at very high slip angles. This is not what some documents and some books (even good ones) shows, but this is what i have seen with some raw data sometimes and also what it seems to produce a more realistic behavior. There are two things we should always keep in mind, in my opinion: the first one, is that we are always talking about models: real life is anyway different and no tire will follow any curve, doesn´t matter how good you draw it! Secondly, when discussing what is happening at slip angles higher than 20 degrees, it is even not realistic to talk about slip angle anymore: the tire is probably then behaving much more like something scrubbing on the ground than something still sliding on it: the difference between the heading direction of the tire and the middle plane of the wheel is simply to high to apply this way of modeling anymore.

    I have never looked to Race 07. What did they do exactly?

    Regarding your points about the tires grip coefficient and load sensitivity curve, i think i did not totally understand what you meant.

    What i normally do is very much based on the data i have.
    So, for example, i normally don´t use the speed effect, simply because it is something i cannot model relying on the data i have: normally tire suppliers doesn´t show much about how the grip falls off at certain speed, although it is documented in some books that it is happening. For me, it is simply i don´t know how it happens, so i don´t recreate anything similar in the simulation.

    Anyway, some tire engineers told me it is normally a second order effect.

    Also, about the high lat/long coefficients, I think it is again up to the data you have (and that maybe you have already reworked to get reasonable performances). The values you use at 0 N vertical load, as the ones you input in rF, don´t make much sense by themselves, you must at least consider also the load sensitivity you are putting in.
    Since Pacejka depicts load sensitivity in a linear manner, you are probably anyway making a mistake here (my experience again with some raw data i have seen tells me that often tire coefficient of grip doesn´t evolve in a linear manner against vertical load), but what i normally do it try to follow as much as i can the line i can get out of Pacejka, because very often this is the only source i have.

    This sometimes lead to high initial coefficients, but normally it happens when tires have a very high load sensitivity.
    At the end what you are trying to achieve is a model that produce the right forces at a certain vertical load. If you know how big both Forces and vertical loads are, playing with your coefficients you should be able to reach your target, right?

    What i have seen is that often many mods use pretty low load sensitivities. Probably then they correct this with the speed effect, which is normally used in these mods.
    I honestly don´t feel very comfortable to work this way, also because i think you are then loosing some effects at low loads. But maybe there is something i am ignoring…

  3. Thank you for your words, Andrea.

    >>”it is normally a bit easier to get info about load sensitivity for lateral forces than for longitudinal ones. My experience (based on raw data) tells me that they are not the same at all, but when you have no info, i still think the only reasonable way to proceed is to use the same values for lateral and longitudinal load sensitivity. What do you think about this point?”

    I agree it is easier to find data for lateral forces or even combined forces than for pure longitudinal forces. Some of the projects I worked on in the past allowed me some access to raw data or text-based telemetry data, from which we could derive graphs and tendencies. [Which is a good thing; the bad thing is that all the data and associated derivations are proprietary and I, the developer/consultant, cannot retain one bit of proprietary information…Hence why, knowing exactly what to expect, I search around the web for data that I can get my hands on and is of a similar nature (validity) to that of proprietary data.]

    Two observations I made from several samples:
    – for the same tire, the coefficient of friction from a load of 0N to approx. 1500N is slightly higher for longitudinal forces than for lateral forces. This “slightly higher” is around 1.5%.

    This is somewhat odd, considering it is the same tire we’re measuring and therefore the same contact patch. But obviously, the contact patch distorts differently when being pulled sideways (pure cornering), when being pulled sideways and longitudinally (combined forces) or when being pulled longitudinally (pure braking, pure acceleration).

    Obviously, transfer load sensitivity is different between lateral forces and longitudinal forces (or even combined). Furthermore, the load transfer front to back/back to front is quite different from the transfer load in sideways transfers. Maybe this also accounts for the differences. What puzzles me is why, for the same tire, the friction coeff at zero load is slightly higher for longitudinal situations than for lateral ones.

    – Also, load sensitivity, according to those samples, which are corroborated by reports I read, is slightly lower for longitudinal forces than for lateral forces – the difference, in this case, is even lower than 1% (example: at 2000N vertical load, the coeff is around 1.15; the same coeff at 4000N vertical load is around 1.08; compare this with the lateral coeff of friction at 1.15 at a vertical load of 2000N, and 1.075 for a load of 4000N).

    Now, the results from these samples may not apply to all tires, or even to most racing tires, but they show at least a tendency for some tires.

    So, with that in mind, it is legitimate to consider that either (a) load sensitivities are similar or the same between lateral forces and longitudinal forces or (b) load sensitivities differ slightly (by around 1.0 to 1.5%), with the Load sensitivity for lateral grip being slightly higher (i.e., the coeff of lateral grip will vary faster with increasing loads). Again, my emphasis is that this effect is very small, with single digit percent diffs (actually, below 2%).

    I see ISI and some modders also design this behaviour into their tires, with differences being slight in the loadsens_param1, and slightly higher in loadsens_param2.

    >>”There are two things we should always keep in mind, in my opinion: the first one, is that we are always talking about models: real life is anyway different and no tire will follow any curve, doesn´t matter how good you draw it! Secondly, when discussing what is happening at slip angles higher than 20 degrees, it is even not realistic to talk about slip angle anymore: the tire is probably then behaving much more like something scrubbing on the ground than something still sliding on it: the difference between the heading direction of the tire and the middle plane of the wheel is simply to high to apply this way of modeling anymore.”

    I agree (though I don’t understand “scrubbing on the ground than something sliding on it”).

    I have seen two tires, of the same brand and series, fabricated under the same process, having the same dimensions, mass and materials, behave somewhat differently than predicted – even behaving differently between them. Obviously, the differences, in such cases, are not significant, but they do exist; and differences grow when on the limit (past 30º SA, or past a certain temperature threshold, or a certain pressure threshold, or even a certain degradation level).

    Even with the most powerful supercomputers, I doubt that we could model a tire and have predictive features with a high degree of accuracy. There are too many things at work, things we cannot control (mechanical adhesion: the surface of a track varies during a race, varies during the day, varies from day to day, with more rubber, more dirt, higher or lower temperatures;effects at the molecular level from bonding of different materials, from temperature/pressure/mechanical forces; effects resulting from mechanical forces between rubber and rim).

    But the models we have at our disposal can help a lot in providing accurate (enough) behaviour or (some) predictive features.

    Some people, though, are putting too much emphasis and faith on physical modelling as a way to predict behaviour on the limit (very high slip angles, high temperature/pressure/forces/degradation). I do not. To model a tire physically one needs to build a digital tire with as many elements as the real one (and we know each series can be radically different, even within the same brand), with the same structure (exactly the same structure) and understand how the many parts interact with one another and derive all of it in a equation or a series of equations.

    If the digital tire is exactly replicating the real one, if the physics/math is spot on, then we can have a tire behaving almost exactly like the real tire and then there should be no need for tables or behaviour curves.

    Problem is, no one thus far has achieved that with a single tire, let alone for any tire.

    So, in my humble opinion, the best way to capture tire behaviour is by experimenting with the tire across a wide range of situations (0 to 80º SA; high temperatures, low temperatures, very low pressure and very high pressures; from no degradation to a tire which is on the brink of exploding; from very light loads to almost impossible loads (per tire, something in the range 0N to 50 000N)).

    We can then derive the physical and mathematical relations (whether a pure MF approach with all the parameters known and a few more, or a SWIFT-MF approach, as the Delft University proposed a handful of years ago with their new iteration of the industry standard model) and model behaviour according to tables or curves which capture a very wide range of situations.

    >>”I have never looked to Race 07. What did they do exactly?”

    Well, though I never had access to the source code, we were told by the developer that the tire model suffered important changes – namely in the estimation of grip and combined forces, making tires more stable than originally.

    I can attest to that. I designed a new physics model (actually, a new physics calibration model) for the exact same car, with the exact same figures for everything and tried it on GTR2, rFactor and Race07. [All these sims use ISIMotor2 – GTR2 an older release, rFactor a release as recent as 2007, and Race07 with a reworked version as recent as late 2007. ]

    Results were interesting:
    – GTR2, the car is quite stable but still evidencing some troubles upon brake application and steering. On the limit, spins occur less frequently than with default GTR2 cars, the car is driftable.

    – rFactor, the car is very stable, more than in GTR2, but still evidencing the same problem (very easy lock-ups and steering very difficult under medium to heavy braking). On the limit, the car is driftable, normal spins are controllable and happen when they should happen.

    – Race07: the car is very stable. On the limit, the car is driftable, normal spins are controllable and happen when they should happen. Steering and heavy braking (one major complaint pilots have about “racing simulation games”) is fully possible, the transition between combined forces to pure forces is a bit smoother than that in rFactor.

    Recently, I got the same “feeling” and telemetry data from Racer (by Cruden, the makers of the Hexatec professional simulators for high end teams) when that sim uses a new “friction circle method” in use by their main simulator. Very realistic.

    However, truth be told, the physics calibration model has to be very precise.

    >>”Regarding your points about the tires grip coefficient and load sensitivity curve, i think i did not totally understand what you meant.

    What i normally do is very much based on the data i have.
    So, for example, i normally don´t use the speed effect, simply because it is something i cannot model relying on the data i have: normally tire suppliers doesn´t show much about how the grip falls off at certain speed, although it is documented in some books that it is happening. For me, it is simply i don´t know how it happens, so i don´t recreate anything similar in the simulation.”

    Yes, and you’re right, speedeffects should be used with some care. Reason why I set speedeffects_param1 at a very high number: between 1400 and 2000. This will make sure it will stay a second order effect.

    What I meant is this: when you plot Tire Load versus lateral accelerations (g), you have a certain curve profile depending on the values used for 5 different factors:
    1- car mass
    2- initial friction coeff
    3- loadsens_param1
    4- loadsens_param2
    5- loadsens_param3

    For the same factors (2, 3, 4, 5), the heavier car will be unable to reach the same values of lateral g for the same downforce. A lighter car will develop higher lateral accelerations.

    So, some modders mistakenly design tires with quite different loadsens params depending on the mass of the car. As if that is not enough, they also tweak negative lift so that all cars have basically similar performances. Wrong and wrong again.

    What I advise is:
    – target a curve profile which enables a car to reach a (per design, but also reflecting real life telemetry for different classes) peak lateral and longitudinal acceleration typical for that class.

    -GT cars can corner, sustained, at 1.7 to 1.9 g (obviously, this is not cornering as in skid pads, but rather cornering around long corners such as (IIRC) T2, T3 and T5 of Road America), and have peaks around 2.8g (obviously, peaks lasting a tenth of a second or slightly longer).

    -DTM cars can peak at 3 to 3.5g. SuperGT cars can peak at 3 to 3.5g as well (this by pilots and a couple of engineers from the japanese series).

    -GT4 cars will peak well under 2g (negative lift is not particularly relevant; mechanical grip is, though).

    -Prototypes can peak between 3.5 and 4g.

    -Formula cars (in particular F1 and Indy/Champ cars) can corner (sustained) around 3.5g to 4g and peak above 5g.

    So, these are my targets, cars that can reach certain levels of performance (in the form of longitudinal and lateral accelerations). I design tires to reach these levels of performance, which means they have specific curve profiles for SA vs load plots and lateral/longitudinal accelerations vs load plots.

    Then, the appropriately realistic levels of negative lift are designed into wings (splitter and rear wings), diffuser and body elements. So, it is perfectly acceptable to have a MP4-12C reach 352 kgf of negative lift at 200 kph (McLaren people say that it can be higher), or a Maserati MC12 reach slightly above 400 kgf of downforce at 200 kph.

    If we then compare the behaviour of a GT1 or GT3 car with that of a supercar like a Koenigsegg CCX (with a small rear wing), it is easy to understand, even using the same slick tires, why Marc Basseng said the CCX is very hard to drive on the limit (on the Nordschleiffe).

    It all makes sense if we design tires around performance levels and the mass of the car – for any car of the same class. We can then adapt downforce levels pretty much as racing teams do within regulation constraints.

  4. Miguel,

    sorry for the very very late reply, but it has been a busy period!

    Anyway some of the things that kept me busy were related to sim or real racecars, so i cannot complain after all!

    Regarding tires friction coefficients and load sensitivites, i can tell you all the data i have seen till now were somehow showing higher forces in longitudinal direction than in lateral (so, to speak in rF terms, in longitudinal direction i have always seen a higher initial friction coefficient). The same way, sometimes i have also seen a lower load sensitivity in longitudinal direction compared to the one in lateral (so this confirms what you have found as well and that, in general, also at higher loads longitudinal forces should still be bigger than lateral ones).
    I don´t know if this can be somehow generalized. It probably depends on a bunch of factors (tire geometry, construction, pressure, wear, etc).

    This is something somehow reflected also by cars logged data (real cars data logging files), although there are some considerations to be done (normally, for example, when drivers start braking, they are at high/top speed and so the car experiences “high” downforce, anyway often higher than what you have at corner speed).
    I would not include load transfer in this equation, since when you talk about grip coefficient, you normally refer to a specific load (so it is somehow as if you keep it constant and you take pictures of tire behavior at different loads).

    Regarding tire behavior at high slip angles, what i meant is that, when the slip angle grow over a certain limit, the angle between the wheel middle plane and the tire heading direction is so big that it is unrealistic to believe it could be due only to tire contact patch distortion. I imagine this phenomenon more as the tire sliding on the road, instead of slipping. Something like when you use and eraser to delete a pencil sign.
    In this condition you probably experience a combination of more effects and this is probably why it is not ideal to use tire curves (Force vs Slip angle) where force reduces too much at high slip angles and why i prefer to have a curve that goes down smoother after the peak.

    I am not an expert about physical modeling, but i still think a pure mathematical (empirical, if you want) model is the most efficient way to simulate tires in a simulator. As you said, two tires that should be identical will never be identical, in real world applications. You will always see a difference. This happens with tires as it happens with a lot of other things (see engines, for example). What we are doing in our magical simulated world is to somehow represent a trend. Or at least, that is how is see the thing.
    When working on track, you experience far too many times how a set of tires could give you better performance than another one, still being the “same tires”. The same it´s true for an engine. Let´s say a manufacturer (in a spec series, if you want, where all the cars should be the same, except for the setup; or at least where all the teams should have access to the same material quality) has a tolerance of 1-2% on their component performance. Try to calculate how this can affect lap times!

    Regarding your performance targets, i worked in a similar way, as i have mentioned. But you should be careful with the numbers…which speed are you referring at? Probably here we should talk about g-g-v diagrams (v = car speed), thus to take actual downforce into the equation. Moreover, as you said, the same car in different configurations could set completely different targets.
    But i understand what you mean and i agree. We have somehow to start from somewhere, right?

    Anyway, again, thanks for your contribution. It is always very appreciated!

  5. Very interesting read! Just wanted to point out one thing which you may have realized by now, but anyway – there are separate parameters for lateral and longitudinal load sensitivity in the TBC file. Simply replace the combined LoadSens parameter with 2 other – LoadSensLat and LoadSensLong. Personally I’m developing a modern F1 mod for 2 leagues, but it’s really difficult to find actual data or anything close to modern data, so it takes a lot of blind guessing and experimenting to get things right. At least I now have some ideas about what kind of setups they use in reality so it will be helpful to set setup parameters close to the real ones and go from there.

    • Hi,

      thanks for your comment.

      Regarding the lateral and longitudinal load sensitivity, you are actually right. It was more a “Blog” mistake than anything else: i didn´t have any real data regarding longitudinal force for the tyre i have used as a base for Audi R18 physics. So, at the end, i have used the same load sensitivity for both longitudinal and lateral forces.

      I am aware this is somehow wrong, since, as it has been discussed here before, normally longitudinal and lateral load sensitivity are not the same. But since i had no data about that, i chose to stay on the same value as the lateral one, although the initial grip coefficient i have used is different.

      Your project sounds also very exciting!

      I am not a big big fun of formula 1 cars, but still they are very interesting.

      I guess you have one more issue this year to simulate: tyre wear!

      Anyway if you need any help (and i am able to give any contribution) i would be happy to discuss.

      • Yeah, I’ve tried to simulate the tires in a way that if you push them too much they overheat and wear quickly, but in reality the Pirelli’s main issue is thermal degradation, not wear. I’ve read somewhere that they can actually last a very long distance without wearing down to a puncture, but the layers of the tire simply degrade and fall apart if you drive them on the limit. Something which can’t be simulated in rFactor 1, unfortunately.

  6. Actually, no – we can simulate several curves for wear/grip, and we can use latpeak/longpeak, heatbasepeak, rollingresistance, wearRate to properly simulate the consequences of heat and driving style on the tire. Obviously, you have to know what exactly you are doing, otherwise emulating RL will be not be achieved.

    Same thing (as you said/implied about wear) was said about drifting/grip and peakslip and slipcurves but experience and the use of proper data proved otherwise. On top of that, at least 2 other developers (not counting SIMBIN) confirmed the versatility of ISIMotor2 in regards to grip/slip/wear, even comparing to physical models or semi-empiric with a physical basis (such as that used by NetKar Pro).

    After studying all the models being used, the conclusion for many of us seems quite simple if not obvious: MF based models are as good as or even better than physical models (which depend on a number of assumptions made by people who have little knowledge about the physics and chemistry of the materials involved and their thermodynamic properties). On top of that, the ease of use by modders far surpasses what is now becoming apparent with physical models (such as the SM from C.A.R.S., rF2’s TM or iRacing’s NNNTM).

    Finally a word of caution for anyone who likes racing simulations: flat spots, graphical damage on the tire, non-linear heat models – all this is very interesting and jaw-dropping, but how close to RL is it? What are the scientific basis for these eye-candy stuff being put on tires (with the exception of Stefano’s work and quite probably Gjon’s)?

    Anyway, Drracing, interesting posts from you.

    • Well, could you please explain how you simulate multiple curves for wear/grip for a single tire? As far as I can see there is just a single parameter about that. Likewise for the other parameters, per tire.

      • Before misunderstanding what I posted about, allow me to “just” point out a few “things which you may have realized by now”:
        – WearRate – a constant you apply for wear
        – WearGrip1 and WearGrip2 – allows the dynamicist/modder detail the connection between grip and wear from 0% wear to 100% wear. One might argue the internals can treat this linearly or nonlinearly (T-bone explained this once, and it’s clearly non-linear), but it is effective in providing an approximation to RL wear curves.
        – many parameters influence tire performance and wear, and they are all interconnected. The relationship is not a simple one and tries to incorporate some of the effects TNO incorporated into MF&SWIFT in the last 8 or 9 years.
        – you can generate several curves (slip curves, loadsens curves, wear & grip curves) and decide what is the best fit for the data you available to you. That is what I have been doing for years (since v1.150, a little over 6 years ago), certainly what many others did too (Bristow, Kalma, Niels, Chris). The effects (heat, wear, slip, sensitivities) are actually dynamic even if the model itself is not fully dynamic (NetKar Pro itself became dynamic in the last version or so).

        You do have to explore many different avenues and come to a model that makes this all work. But it is doable, even if it is not perfect.

  7. Andrea, just a quick note: the above comment of mine was directed at the post by mr. Itchov – I meant to put this as a reply, but my fault, I did not. If you can do some editing and correct this, would you delete this note?

    Take care.

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