Ok, in my last posts I talked a bit about the procedure I used to model a car I know very well in a driving/racing simulation environment (rFactor in this case, but without having nothing against rFactor, the choice was made only for convenience reasons, I am more interested to the modeling and simulation itself than to the brand). Actually, when you have a good amount of info about a car and you know it pretty well, the modeling process is anyway tricky but you always have a feeling (above all when testing on track or looking to the data you acquire with simulation data logging system) that tells you if something looks more or less correct or completely wrong. Above all if you have worked for some time on the real car, then the modeling process turns to be somehow like a validation of what you input into the simulator: you know quite well what kind of performances to expect, in every area (maximum speed, lateral accelerations, suspension movements, longitudinal accelerations and decelerations, etc.) and you immediately recognize if something is much outside of the correct window: it is just a question of a glance to see something that doesn´t belong to your picture.

But what when you decide to model a car you don´t know (more or less) anything about (at least at the beginning of your process)? The story, then, change completely. But it can anyway be very interesting and instructive.

First of all, without a good amount of hours spent informing yourself about all the possible aspects of your new toy and its performance, looking for and at all the possible data that you can put your hands on (sometimes even data coming from similar cars, not exactly the one you are studying, could be very useful; they have been for me), you have really no clue of where to start and where you want to go.

This was the case for me when I decided to start working on the Audi R18. As you may imagine, I have never worked on such a car (not only on this one in particular (it could be a dream for me!) but on LMP prototypes in general) so at the very beginning I really didn´t have any reference data.

Ok, somebody could say that, in general (so also for other kind of cars) looking to lap times and maximum speed you have already something to start from. It could be easier to proceed this way, if you could be sure that the tracks you have in your driving simulator are modeled perfectly and looks exaclty the same as the real ones (which could be become a quite good approximation when laser scanned track will be available, but it was not my case) but anyway I would never expect that laptimes could be the final answer to understand if a driving simulation is producing realistic results; first of all you potentially have infinite ways to get to the same lap time; then, as I already said, in my opinion a driver acting in a race simulator will never behave exactly the same way on a real car.

Anyway, no reason to think about it: I am pretty sure the tracks I have in my list are far far from being perfect.

So how to proceed?

In this particular case, I have been quite lucky, since I am not the only one to be fascinated by these cars and around the world there are hundreds of guys discussing, posting pictures and all kind of info about them in forums and groups everyday (see for example Mulsannescorner, probably the most informative and interesting group/website I have found till now about race cars). This information range from very detailed pictures showing nearly every area of the car to some numbers (from different sources, ranging from measured data to calculated values) about engine power, downforce, etc..

Moreover, Audi this year made a big present to all of us by putting online a lot of nice on board videos of their cars during WEC races and showing also a rudimentary kind of visual telemetry which was anyway giving us some numbers for lateral and longitudinal accelerations, speed and RPM. Ok, no qualifying laps (and no precise info about tyre wear level, fuel on board, track conditions, etc.), so no ideal laps to look at. Moreover, the sample rate of this telemetry seemed very low, so not much for example about decelerations g peaks, but still better than nothing.

Last but not least, I had the possibility to take a look to some tires data which were of course not referring to the tires used on these cars, but still from similar tires (although slightly smaller). Maybe not the last word about these tires grip (who knows, for example, about compounds? Not to say the eternal debate of how much lab testing produce more grip than what you can have on a real track), but at least a feeling about it and about important parameters like load sensitivity, camber sensitivity, slip curves, etc..

Another source which turned out to be quite useful to me was the blog run by a guy (Paul Bischof) who builds race cars scale models out of paper (yes paper!). And he does it in a very detailed way. You can find something about his work here.

Luckily enough, his last project is about and Audi R18 in 2011 spec (exactly the same car I want to model in rFactor) and he has really a lot of useful info about it!

We have spoken for a while about what he is doing and what I wanted to do and he gave some good hints and was so kind to show me tons of pictures. Passion can be a very powerful link sometimes!

So, after a long period spent gathering as more info I could about this car, finally time to start modeling came.

The first point for me was to identify the main dimensions, like wheelbase, track widths, tire dimensions, etc. and less easy numbers like CG height, weight distribution, moments of inertia of the complete vehicle, etc..

Regarding basic dimensions, I could find nearly anything I needed looking to both Mulsannescorner and Paul material. Track width could be calculated out of the maximum allowed width for the whole car and tires/wheels dimensions, just maybe taking a small margin. Since the car is using more or less the same tire dimensions for front and rear axle (360/710 R18 Front and 370/710 R18 rear, while using, according to the info I found, slightly wider rims at the front: 14.75” wide rims at the front axle, 14.5” at the rear) I simplified my work assuming front and rear track width are the same. I am quite sure this is a simplification, since from the picture I have seen I have a feeling Audi’s guys could be using different ET for front and rear rims, but it is really difficult to get accurate pictures or any precise info about this point. So, for the time being, I think I can assume the front and rear track width to be the same without having a too big mistake. To sum up, the values I used are:

wheelbase = 2953 mm

Front Track Width = Rear Track Width =1610 mm

Car + driver weight (no fuel, but ready to race) = 970 kg

Ok these are very basic information. What about more “sensitive” numbers like CG position (both in x and z direction)? Here of course I have no accurate info, so time for assumptions. Based on the car dimensions and geometry, info about similar cars I have found and based on the amount of ballast this car is supposed to carry (in 2011 the car was said to have an 850 kg weight without ballast) and looking the values I have found for similar cars, I believe Audi R18 weight distribution is very close to 50% on the front axle. Could it even be the case they have more weight on the front than on the rear? Perhaps. But honestly I don’t know and I had no time to make simulations with a LMP-kind model to see how much more front weight could be beneficial or detrimental for performances. To be on the “safe side” I decided to use 49% leaving some 1-2% still open as a tuning parameter. How can I be sure this assumption is correct? Of course I can´t! But do I have other ways to find better info? No. So that´s ok!

What about CG height? Again, nobody outside of the team (and I would bet even not many of the engineers there) could know this value. Anyway, I again did an educated guess based on my experience: although, as I said, I never worked on similar cars, I am quite sure we can admit the CG of a LMP seats a bit higher than in a F1 car (these cars have, for example, a roof that pull some weight up). On the other hand, if you look to pictures of how some details are placed and designed, you can really see that Audi guys put quite some effort to keep CG as low as possible, as you could expect.

If some of you use to read Racecar Engineering, some months ago (September 2012 issue) you may have found an interesting article describing a device built by Cranfield University to measure cars moments of inertia and CG position which Force India F1 Team uses every year to measure their cars. In this article, Force India Vehicle Dynamics Head was interviewed and one of the things he said was that CG height of a current Formula 1 is somewhere between 200 and 250 mm higher than the reference plane. I can tell you, this is the range where I have always found the CG of the single seater cars I worked on to be in and where also other single seater car CG probably is, as you may discover reading some documents about the topic “measuring CG height” you could find on the web. This is of course telling me that, probably, best F1 cars could even have a lower CG, but as Force India guy said in during the interview, aerodynamics stuff like to be very high and it is somehow a compromise you need to accept to bring the CG a bit up in order to have more downforce. And you know what? Again simulation could became invaluable to tell you how far you can go on this way before to reach a point where you start to loose instead of improving. But this is another story.

So where is the Audi R18 CG? I honestly don´t know, but I think I am not “too wrong” if I assume it is at a distance from the reference plane similar to some common formula cars, which normally have a CG height in the higher part of the range mentioned by the Force India guy; and that´s where I put my model´s CG. Again, can I be sure it is correct? I don´t think so, but I don´t have better ways to gather more detailed or trustable info. So again, it´s necessarily ok!

Now, what about inertias? Unfortunately I have never had the possibility to use something similar to the nice rig built by Cranfield University to measure moments of inertia. Their values are numbers that I strongly believe just a very few people know in each team or company and even less of them have ever measured. To measure CG height is somehow boring and asks for great attention to details, to be done properly, but can be done quite easily in nearly every workshop. To measure the car moments of inertia is much more complicated and ask for a purpose built rig, at least.

MOIs can be somehow estimated, basing on CAD assembly (I have honestly never done it and I believe this is probably not the most accurate way, although you don´t have a really huge assembly file where ALL the components are modeled into details (including engine, gearbox, dampers etc.) or of which at least you know very well masses geometry and still you would not properly see the effect of fuel, oil, water, etc.) or basing on some empirical mathematical models some people have developed during the years. This is probably even less accurate than using CAD, but again we don´t need to worry here, since of course we don´t have any CAD model of any of the car components!

My method consists in using some of these empirical formulas based on coefficients I estimate looking to car shape and masses location, weight distribution, etc.. These coefficients link together known parameters (like CG distance from front and rear axles, track width, wheelbase etc.) to come to a basic number for Izz (yaw moment of inertia) from which you can then calculate Iyy and Ixx. The link between the known parameters and Izz is basically what some authors call *Dynamic Index*. This is a number related to vehicles stability and is of course (when investigated) jealously kept by the manufacturers, since it is an important metric about car behavior in transients maneuvers. Actually, it is related to the position of the yaw center of rotation of the car referred to the wheelbase and to CG longitudinal position. When DI is greater than 1, it means the center of rotation is behind the rear axle and the car is very stable (somebody would say even too much, so that it becomes even slow) in transient maneuvers. If DI is smaller than 1 the CoR is between front and rear axle and the more it is close to 0, the more “reactive” the vehicle is, since the CoR will be closer and closer to the front axle. When DI is equal to 1, CoR is on the rear axle. Some cars, like old VW Beetles and Porsche had something like DI<0.5, which made them quite “tricky” to drive at the limit.

I read somewhere that many good drivers end up to like a DI of around 0.8, but I believe this is really arguably/subjective. I also read that many road cars have a DI of around 1.0 or even bigger, but I am not sure about that.

This way of proceeding based on empirical formulas/DI estimation is of course not new and I am pretty sure other people proceed in a similar way. For me, it was very useful to discuss about that with other “driving simulations” people, with much more experience than me in modeling techniques (in particular with Aristotelis Vasilakos, the guy responsible for Assetto Corsa physics) and to go through some parts of the very good book “Multibody Systems Approach to Vehicle Dynamics” (by authors Mike Blundell and Damian Harty) which deals in a very detailed and useful way some of the most important topics connected to vehicle dynamics multibody simulations and to some other vehicle dynamics universal topics (again, thanks Aris!).

Now the one million dollars question: what is the DI of an Audi R18? I have, of course, no idea! Anyway, I have an idea about other cars I had the luck to see some values about. So, based on my experience, I can again make some educated guesses and estimate a number. Is it correct? Probably not, but maybe it is close enough to the real number to accept it, together with all the other assumptions I had to do. Some of them, as I have just said, are also connected on how Iyy and Ixx are linked to Izz. Again, the “right” coefficient to be used is unknown to me, but we can make a guess based on the car shape, mass locations, etc. That´s at least what I did.

As you may see, this process is actually a big “guesstimation”. One wrong assumption will drive all the values to be wrong. And I am quite sure that my numbers are not correct, but I hope they are not too far away from the real ones. I have anybody no way to check them, so they are fine to me!

I would say that, from a pure mechanical perspective, moments of inertia are probably one of the most difficult numbers describing a car to find or to measure. Would be nice, maybe, to take some time to play around a bit with them to see how sensibly car behavior changes when they are bigger or smaller.

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

In the next part about this topic I will discuss parameters even more directly related to final performance (at least from a mechanical perspective) like downforce, tires and engine.

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