Posted by: drracing | June 16, 2017

Testing suspension geometry in the simulator

Hi everybody!

As anticipated in my last post, this article will be a review of one of the project I was involved with during the winter. As for one of my latest project of 2016, also this case study is actually relative to an investigation I supported using driving simulation as a development tool, in a way I had not thought possible a few years ago. Life is full of surprises.

After during the summer I had a chance to prove myself how, even using a cheap software, a proper vehicle model could be used effectively to gain some more insight about car setup and its intricacies (helping the team I was supporting to further improve a bit their performance), this time I was asked to try to evaluate different design solutions and quantify not only their performance but also driver’s perception / feedback to each of them.
The study was focused more specifically on investigating the effects on car handling and performance of different front suspension layouts, differing sometimes pretty much one to the other (in one or more areas), with the aim to evaluated what the driver would feel driving each of them, together with their impact on the car-driver system’s performance.
The guy who asked me to support this project was initially mainly looking to understand the impact on driver steering feedback coming from different designs / geometries, but soon the study also evolved into a chance to evaluate which influence each setup would have on overall performance and why, identifying, also through data analysis, in which areas there would be the biggest differences and the reasons behind each Delta.

The model we used was actually the reliable and good validated 2016 LMP2 one, driven in Silverstone.
We starting establishing a baseline (lap time / performance and behavior) using the original design, then moving onto testing new solutions.
The parameters we worked on at the beginning were mainly scrub radius, king pin angle and caster trail, but inevitably we soon moved on also acting on camber change, roll center position and migration and caster angle and finding out how also other parameters that we underestimated at the beginning actually play an important role, at least in terms of steering feedback.

Before I dive a bit more into the details of this project, let me spend two words about the assumptions used by rFactor in terms of suspension modeling and my view about the software’s limitation.
First of all, it is clear to me, as it is probably clear to all of view, that rFactor was not though as an engineering tool and there are some limitations that are difficult to completely overcome, if not acting on the code itself (which is out of my skills, intention and interest).
I would of course be very happy to have a chance to use more “engineering” oriented and flexible software for my projects, but the budget required to buy one of them would probably be absolutely out of reach even for many small companies.
The truth is, anyway, that it is amazing how much you can test and understand, in terms of vehicle dynamics and even in terms of setup / layout even using a cheap product like rFactor, despite all of its limitations. Of course, “conditio sine qua non” is always to know exactly your assumptions and to build a model as close as possible to the real car (or at least to the data we have about it).

As we had a chance to briefly mention in one of my previous posts, rFactor simulates suspension behavior in a very advanced way, since it practically define each suspension component as a rigid body (with or without mass properties) connected to the surrounding ones through mechanical constraints, like spherical joints, hinges, etc. This means, for example, that the wheel and the “spindle” (which actually identifies the complete Upright – Hub assembly in rFactor) have their own (definable) mass and inertial properties. The links are defined as rigid elements with no mass, practically locking the distance between two points depending on their length.
There are a number of things to take care of, when modeling a suspension, including like rFactor adjust camber, caster and toe. But if these parameters remained locked or the “errors” that the software does when changing one of them are compensated in a proper way, the suspension kinematics is simulated in a very similar way to what a normal multibody package would do.
A bit of attention must be paid for layouts using a pushrod / pullrod with a rocker to activate the damper/spring unit, since the Rocker assembly and its functionality cannot be reproduced. Of course, since we are dealing with an LMP car, this is exactly the situation we find ourselves in, as we are considering a double wishbone with pushrod actuated rockers for both front and rear axle.
From a wheel rate / motion ratio perspective, this “issue” can be easily overcome producing very accurate results, as we have seen already in the past, the point here simply being to directly work with the Wheel Rates, instead of the spring rates. To do this, I am using a trick, playing with the pushrod’s hardpoints (and, consequently, with its orientation), to obtain exactly the wheel rates and wheel rates change (with respect to wheel travel) I want, independently from the rest of the kinematics.
This means that the “virtual pushrod” will have another position and another 3D orientation compared to the real one, in order to obtain the same wheel rate and wheel rate change of the real car.

From a statics perspective and, more specifically, if we want to isolate and quantify the load acting in each linkage (this is particularly important for this study, since the steering feedback was one of the parameters we would like to better understand and since rFactor and the plugins I used produce the steering wheel feedback strictly basing on the force acting on the steering tie rods), this actually can bring a difference in the results because, depending on the position and orientation of each beam, the loads acting on each of them (for a defined loadcase at the contact patch) will change. In other words, although the suspension “as a system” would still behave the same (at least considering every suspension link and the upright-hub assembly as a rigid body, so ignoring every compliance), the internal reaction forces would change.
Anyway, the good news here is that, for the suspension geometry and layout we are using, even if the absolute value of the force acting on the steering rod that could be measured in the real car is different than the one produced with our “rfactor alternative-pushrod position”, its trend and gradients are very similar: in other words, the load acting on the steering rod is changing in a similar way in both cases, for a certain change of the Fy, Fx or Fz acting at the contact patch. All of this has been checked first using a simple excel sheet I built to calculate the reaction loads in each suspension members, depending on the loadcase at the contact patch and on the pickup points position; to be absolutely sure, a second check has been done using a Multibody software and in both cases the results have shown exactly the behavior I described above.
What is important for this study is actually the trend shown by the reaction forces in the steering tie rod, since the steering forces produced by the simulator’s steering system are proportional to the steering tie rod loads through a factor that is actually what we use to tune the intensity of the steering feedback itself.

Beside the driving simulation itself, I also used some CAD and some Multibody modeling for this project; on one side, I did this to evaluate each layout before to test it with the simulator but, most often, also to tune each geometry a bit and try to isolate and change only the parameters we wanted to evaluate at each step, keeping the others as constant as possible, with the aim to limit their influence on the results (in particular the steering torques, but not only).
Anyway, in certain cases this was not actually possible because of real world physical limitations (for example parts colliding to each other) and we had to accept that, with a certain setup, some parameters that we would not want to change would indeed change (see for example Ackermann effect). It was nonetheless interesting to see how a certain set of parameters would work, both in terms of performance and driver perception.

It is probably not a case that the best performing solution was also the one which was received more enthusiastically by the driver (although, in my experience, this is unfortunately not always the case).

The first test was done using the baseline configuration, namely the front suspension geometry originally built in the car. We run some sessions with this solution and established a reference lap (and the relative logged data) to be used later as a base to evaluate the following setups both subjectively and through data analysis.

The second test was performed using a revised front suspension geometry (we will call it Exp1), mainly deviating from the baseline in the upright area. In particular, caster angle was reduced by slightly more than one degree, although the caster trail was slightly increased. The King Pin Angle was also increased by about 2 degrees, producing a smaller scrub radius. This setup also had a slightly higher Ackermann effect (more dynamic toe out) and a slightly higher roll center.
The feeling was immediately very good. The car showed a bit more understeer, above all in mid-corner and, sometimes, even in corner exit. This helps in certain situations, see for example turn 3 (a 1st gear corner, where traction is very important), but seems to be a limit in others, see for example the last chicane, above all in the exit of the second (right) corner leading to the last right tender before the box straight.
Beside showing more mid corner understeer, this setup actually also produced a more reactive behavior in corner entry, above all in quick corners.
From a driver feedback perspective, it was interesting to notice how the changes we did made the car easier to drive, giving to the driver some more confidence and also the feeling that the relationship between steering angle and front cornering forces remains more or less linear for the complete range of used angles (while the baseline had a more unpredictable behavior, above all at very high steering angles, where the cornering force seemed to drop more abruptly and in a less predictable way when exceeding with the steering angle and the driver had a feeling of “loosing front grip”), although producing more understeer.

An interesting point was the increase of steering forces, perceived by the driver and confirmed by data analysis. This seems to go somehow against the expectations of some the changes we did (see for example a reduction of caster angle).
Anyway, two factors must be considered: on one side, the caster (or longitudinal) trail was slightly longer (granting a longer lever arm to Cornering forces in producing Self aligning torques); on the other side, we noticed how, one of the side effects of the geometry change we did was a slight reduction of the length of the Steering Arm (distance between the outer tie rod point and the steering axis), thus creating a bigger force in the steering tie rod for a certain torque to be reacted.

In terms of performances, this setup produced a 3-4 tenths improvement compared to the baseline.

Here below you can see the traces relative to three logged parameters: speed, steering angle and steering force. The tested geometry is shown in red (Exp1).

Exp1 - speed

Exp1 - steering

Exp1 - steer forces

The third test (referred here as Exp2) was performed using a geometry differing from the baseline much more aggressively. Caster has been increased by about 3.5 degrees, producing also a substantially bigger caster trail (about 30% bigger than the baseline one). King Pin angle and Scrub radius were very similar to the original configuration. The Ackermann effect (or percentage or dynamic toe) was slightly lower, as was the camber gain. Finally the static roll center position was also substantially lower.

Driver’s feedback was again very good, although the car behaved very differently than in the previous test. A strong reduction of the understeering tendency was evident from the very first corners, with the front axle now having substantially more grip, above in mid-corner but also in corner exit, with a reduction of the power understeering tendency that disturbed a bit in the last chicane in the previous test. Interestingly, even showing much more front grip, the car didn’t become instable or unpredictable, nor it showed any “dangerous” oversteering behavior.
In quick corners, the vehicle was now a bit less reactive than in the previous test, but still showed very good driveability.
Steering forces increased slightly, compared to the previous test and were thus sensibly higher than the baseline setup.

The lap times we obtained were anyway very similar to the previous test, with this latest outing producing an about 0.02 seconds quicker lap time.

In the following plots, this test’s results are shown in orange (Exp2).

 

Exp2 - speed

Exp2 - steering

Exp2 - steer forces

 

The direct comparison between this setup and the previous one (not shown in these pictures) show slightly higher steering forces in this latest case, although the steering arm being now bigger than both the baseline and the first test.
To finally quantify the influence of this latest parameter we later did a very quick test using a very similar geometry compared to the one tested here, but reducing the steering arm to a very similar value compared to the baseline (and trying to keep the other parameters the same). This further increased the steering forces, making them substantially higher than both baseline and first test and, more important being a direct comparison, much bigger than this test 2.

I will not bore you with a description of all the other tests we did (some of them were not as successful as the first two and the following one) and I will just jump to the one that produced the best performances and the best driver feeling, also to show how much of a difference it did in terms of lap times and how good this could be felt in the simulator.
This latest test was performed using a front suspension geometry now having about 0.8 degrees more caster than in the previous one (and so about 4.3 degrees more than the baseline), a slightly bigger caster trail than test 2 (but much bigger than the baseline) and a smaller scrub radius (compared to both baseline and test 2), because of a sensibly bigger king pin angle. Roll center, camber gain, Ackermann effect and steering arm’s length were all kept practically the same as the baseline.
One of the interesting features of this geometry was how the camber evolves with the steering angle, not only on the outside tire but also on the inside. A caster increase normally always produce an increase of camber delta as a function of steering angle, but here this phenomenon seems to be amplified and probably also the contribution of an “effective” camber change on the inside tire helped.

Dirver’s feedback was immediately enthusiastic, as also proved by the lap times, that dropped by about 3 tenths of a second compared to the previous two tests (so overall about 7 tenths compared to the baseline).
The driver felt now even less understeer and the front axle, which ensures a very high grip, without generating oversteer or instability in any corner. The general feeling was actually of more grip on both the front and rear axle, but with even less understeer than the previous test.
This less understeering tendency could be felt also in corner exit, but somehow that didn’t deteriorate traction. The car was much easier to drive and allowed to push more easily, communicating always a feeling of stability and predictability. As a result, it was possible to go easier on the throttle on some corners’ exit, like the last chicane.
This was also true for the steering feedback: steering forces were now higher than any of the previous tests and the “linear” feeling we described about the first test remained, with the driver reporting that, even with very high steering angles, the front axle always seemed to produce cornering forces in a gradual manner, without abruptly loosing grip or generating oversteer or instability.
Interestingly, the steering trace data seems not always to confirms this strong grip of the front axle, at least compared to the baseline logged data. But it is also true that it still shows a more homogeneous use of the steering wheel, probably confirming how this more linear tendency in the relationship between steered angle and front grip and allowing the driver to maneuver the car more aggressively.

All of this seems is shown in the following plots relative to this test’s logged data, depicted in pink (Exp4).

 

Exp3 - speed

Exp3 - steering

Exp3 - steer forces

 

Beside finding extremely interesting all the tests and their outcome, I was once again amazed to see how much we can learn using (properly and also knowing the limitations and the turnaround to be used to compensate for some simplifications) a simple and cheap tool like rFactor, even from an engineering perspective.
The goodness of the results of this study is of course strongly dependent on how good also the vehicle model was built, in particular for all what concerns the tire model. I am pretty sure my model adheres pretty good to the data I have, but of course any model is only a model. Real testing is and will always be the best way to validate and decide on certain design decisions, but it is amazing to experience how much we can do in terms of pre-evaluation even with such a cheap tool.

By the way, it was really good fun to go through all these designs and also have a chance to see how they perform, getting a “more real” feeling of how the car would handle and being able to do 1:1 tests, with all the advantages connected to the use of a simulation (see deletion of the effects of track conditions, temperatures, rubbering, traffic etc).

Hi everybody!

Again a long time since i last wrote something, but it has been a busy winter and hopefully I will soon have a chance to write more about my latest projects. Some of them have been really exciting, including simulation sessions aimed at a new car development (front suspension) in cooperation with a very experienced engineer/designer.

This post will still be about 2017 LMP2 cars though, since they finally got the track for an official test (the ELMS and WEC prologues) and we have some first results to compare to the ones I published here back in December and to some new ones i collected, this time with a real driver (with LMP2 experience) seating at the wheel in my simulator.

During the last months I further refined my 2017 LMP2 model, basing on new data I received and some setup improvements, coming mainly from testing. Car’s behavior has improved a bit, also because of some aerodynamics effects I was previously not considering and i now included in the simulation and that seem to influence these cars’ behavior more sensibly than other kind of race cars (mainly in terms of stability).
As a side result to these updates, lap times has dropped a bit compared to the ones i mentioned back in December.

But let’s come to the facts: the week before the ELMS prologue, Fabian Schiller (a young driver with LMP2/Gt3 experience, who won in the Asian Le Mans Series at his debut in the LMP2 class and claimed a second place in his first Blancpain GT3 in Misano) came to visit me and spent a couple of hours at the sim, completing a few sessions with the LMP2 vehicle model in Monza.
This has been very useful, not only for the feedback he could give about my simulator (hardware and settings) and about the vehicle model, basing on his experience with “old” generation LMP2 cars, but also to understand how quick a real driver could be with (what should be) a representative vehicle model of a 2017 LMP2.

The first things to say (and this is something very pleasant for me) is that he felt immediately comfortable with the hardware and with the model and was able to drive naturally and fast from the very beginning.
After some laps, that he used to find the best braking points and the best line for each corner, he immediately produced very good lap times (already during the first session he landed in the 1’37” region), feeling immediately “home” with the vehicle model and its behavior.

His feedback about the car and the simulator itself was also very good. To mention his words, he said that the steering feedback the model produces is probably the best he ever felt in a simulator and that the model behaves in a very natural and predictable way, making it somehow easier to extract performance for drivers with real track experience.

To confirm all of this, he just did 3-4 sessions for a total of about 40 laps, with just some time between each session to take a look to the data logging and try to understand where he could still improve. Nonetheless, he was able to be immediately pretty quick and to probably go very close to limit of the “model + driver” system.

His best lap time was about 1’36″5, with a theoretical best lap time about two tenths quicker. As already mentioned in my previous article, the top speed at the end of the main straight was close to 308 km/h.

This compares extremely well with the best laps produced during the ELMS and WEC prologue by LMP2 cars.
During the two days ELMS test, the best lap was a 1’36″4 with more drivers running best lap times below 1’37” (results here). WEC guys produces some slightly better performance, with two drivers able to go close to a 1’36″0 , but with more drivers producing lap times in the region of 1’36″5 (results here).
Also the top speeds seem to match pretty well.
Unfortunately, we don’t have many other data to compare to, but this seems to be already a pretty good feedback, also because i am sure i can rely blindly on the quality of the track model (which has been validated already with some real world data in the past).

An important note, the model we run used a Sprint body kit in a Low Downforce configuration (Aero Map) and this is exactly what the real cars have done in Monza too, as far as i know.

Here below the main telemetry plots (you can also find them in High Res in my Flickr account).

speed and throttleLat Long gSteering

Here also a short video showing one of the first sessions Fabian run in the simulator (please apology the absence of car sound and the back noise, but for the driver himself wearing headphones is always the best solution).

Thanks a lot to Fabian for his visit and his support for this study.

I am already excited to see what will happen next weekend in Silverstone, when both the first ELMS and WEC season race will take place.
According to my results, if the weather is good and the track is in good conditions, we should see best lap times below 1’46”, probably close to 1’45″0.
Let’s see what will happen!

Posted by: drracing | December 23, 2016

2017 LMP2 – what’s the story?

Hi everybody!
This is my last post this year and i will try to make good use also of my new Youtube channel (here) to further visually (and not only through data and words) expand about the topic i am going to deal with.

As many of you probably already know, 2017 will mark the start of a new era for the LMP2 class, with new rules coming, a new spec engine built by Gibson and only four FIA mandated chassis manufacturers allowed to sell cars worldwide (Oreca, Ligier, Dallara and Riley-Multimatic).
There have been long debates about the need for a change in a class that seemed to work pretty well, with full grids pretty much in every championship, very good car variety, quick drivers and exciting races.

Anyway, the change is a fact now, so the only thing we can do in this early development stage is try to understand how exactly these new LMP2 machineries will perform.
Technical rules have changed in many aspects: first of all, 2017 cars are some 100 mm narrower than the previous generation ones (from 2000 mm overall width to 1900 mm), following the direction taken already since some years by LMP1; they also use a spec engine (provided by Gibson, as we mentioned already) producing more than 600 hp; they are also aerodynamically different: beside being narrower, they have also a wider rear wing and they are slightly longer than 2016 ones. Finally, because of a late addition of an air conditioning system, they have a slightly higher weight, moving from 900 kg to 930 kg.

All of these changes will surely lead to different performance compared to previous generation cars and there are already both speculations (sometimes pretty solidly-based ones, actually, mainly figures coming from the manufacturers themselves) and first test results suggesting that lap times will probably drop by about 3-4 seconds on a sprint track, assuming same track conditions and even more in Le Mans.

On my side, the excitement of seeing new cars hitting the track was made even higher by being these cars LMP2. Having worked previously on LMP2 vehicle models, I could not help myself but try to gather as many data I could and to build a 2017 LMP2 vehicle model, to see how it performs and behave on track and to get myself a feeling of the performance these cars will achieve this year.
I was lucky enough to be able to collect a pretty big amount of very detailed information about 2017 LMP2s, more or less in every area (engine, aero, suspensions), with the only exception being the gearbox and the tires; the gearbox itself will be this year a sensible area, with only three sets of gear ratios allowed for each chassis (including Le Mans, that will most probably use one of them just for itself), practically meaning only two set for the complete ELMS and WEC calendar; not too bad for this article purpose though, cause I think using the tire model I developed during 2016 could still be a good starting point with some minor changes and I can work out pretty easily some sets of gear ratios, to fit the engine curve and the speeds achievable based on the available data and the track the cars will run.

Analyzing the data I got was already pretty revealing, since this has highlighted immediately some first important points.
The engine has, as we said, about 100 hp more than a 2016 one, with its torque and power curve looking significantly different than, say, an “old” Nissan. The power band has moved sensibly upward, with less torque available at lower RPMs and gearshifts happening at higher revs than before.
The cars are now narrower and that normally doesn’t help handling, reducing a bit the cornering capabilities.
All the manufacturers also went to a slightly longer wheelbase, with values now above 3m, because of a more severe application of a rule about the chassis region immediately behind the driver seat.
On the aerodynamic side, the data I got shows important differences compared to what I have seen till now. Let’s start saying the information I got could well refer to a “x” development stage that is probably not the latest one and are not coming from a 1:1 wind tunnel; according to my experience and to what some engineers with much more experience than me say, this is surely driving some “errors”, although it is difficult to evaluate exactly how big the delta could be. Moreover, some later development and track testing could bring to different numbers in terms of aeromap.
Still, analyzing the available information about 2017 cars performance during testing and the results of my simulations, these data seem to be pretty realistic.
The most significant difference compared to what I have seen previously is a significant step in efficiency, with the new car producing similar level of downforce compared to the ones I worked on before but a lower drag.
For now, I only focused on the “Sprint” package, ignoring what could come out for Le Mans.

The result is what I think being a pretty realistic representation of what 2017 LMP2 cars (or at least one of them) will finally look like in terms of performance and handling.
Basing on this assumption I performed some simulation sessions on several tracks to analyze how quick the new cars will/could be.
Since I didn’t have a driver available to help me, I drove the model myself and that sure left some margin on the final performance that this car (or vehicle model) could achieve. I am pretty sure a good driver could well be up to a second quicker than me, if not more, even in a simulator. Still, comparing the 2017 spec performance to 2016 ones (with both cars driven by who writes) can give a very good indication of what to expect next year.
Beside this, we are going to take a look to the logged data, trying to evaluate how the main metrics look like.

Before to dive into the data analysis, here is the link to a video I recently did with the vehicle model we are dealing with. It shows some laps in Silverstone. Hope you like it! Again, it is me driving, so don’t expect too much!

The very first test I have done was in Monza, since this was one of the first tracks where new LMP2 cars tested, with some lap times that leaked through the press.
In particular, according to the info I found, these new cars have run in Monza with lap times around 1:36 minutes (Ligier, in particular, who drove in Monza back in October, I think). Interestingly, I was able to drive the model with a best lap time of about 1.37.
First thing to keep in mind here is that I suspect my vehicle model (and hence the data on which it is based) is on the low side of both Downforce and Drag, probably fitting a track like Monza pretty well, since here the straight line speed is crucial in obtaining competitive performances.
Unfortunately, I don’t have any 2016 LMP2 data to compare with on this track, but it could still be interesting to take a look to the logged to have a feeling about 2017 cars performance (please note all the following pictures/plot can also be found in High-Res in my Flickr channel).

 

monza-speed

 

First thing catching the attention here is, of course, the top speed the car achieves, which is about 308 km/h. Keeping in mind this is achieved with a Sprint Aerodynamic setup, it is interesting to think that this top speed is already higher of what most teams could reach in Le Mans last year (at least without any slipstream), with a dedicated low drag configuration.
This is sure the result of the much higher power the engine can produce but, partially, also of the particular low drag that the model has.

For reference, here below the plots of some other important metrics: lateral acceleration, longitudinal acceleration and RPM.

 

monza-lat-g

 

monza-long-g

 

monza-rpm

Monza doesn’t have super quick corners, but still the car is able to reach lateral acceleration marks in the region of 2.4 – 2.5 g in some occasions (see, for example, the two Lesmo corners and the Parabolica).
Not too much to say about the longitudinal acceleration, with very similar values to the ones we saw analyzing LMP1-L cars (the difference being driven mainly by the higher weight of 2017 LMP2 compared to 2016 LMP1-L, about 80 kg).
The RPM plot helps to see how the new engine will most probably be used, with higher power band of previous Nissan motors.

The test has gone forward in Silverstone, using a slightly higher Drag/Downforce configuration and shorter gear ratios, to better fit the English track, requiring probably the highest possible setup on the downforce side.
My best lap time was a 1.46.5, which is, as I said already, surely not even close to the best lap time we could expect next year, if track conditions will be good, but is already comparable to what the LMP1-L cars did in 2016 during the race (Qualifyingtook place in wet conditions).
More interesting, this lap time is some 3-3.2 seconds quicker than what I was able to do with the 2016 LMP2 model I worked on this year (about 0.54 sec/km); it is useful to keep in mind that this vehicle had anyway a higher downforce/drag compared to the 2017 one I am testing, so probably a more suitable setup for this particular track.
The gap between 2016 and 2017 lap times seems to match quite well to what media sources communicated, following indications coming from the manufactures. Also, this is very close to the gap that a lap time simulation would produce for the changes in weight, downforce/drag and engine power (compared to 2016) we are dealing with.

Let’s take a look to the data plots for Silverstone too.

 

silv-speed

 

First thing we can see is that, with this vehicle model and the setup I used for Silverstone, the car can achieve a top speed of about 287 – 288 km/h at the end of the Hangar Straight.
Silverstone is also an interesting track because drivers have to face the challenge posed by several pretty quick corners. The first one is Abbey, where a minimum speed of about 235 km/h was registered (with the corner being driven in 5th gear), while at Copse we can see a minimum speed of about 219-220 km/h (again 5th gear).
This translates to sustained lateral acceleration marks of about 2.7 g for both Abbey and Copse, but with peaks close to 3 g.

 

silv-lat-g

 

Car’s cornering potential (or how many g the car can pull in a certain corner) is driven by some main factors: downforce, tires grip, weight and track width, to name some. We are assuming, in the absence of better data, the same tires as in 2016. Anyway, downforce (which is lower than the 2016 LMP2 I worked on), weight, and track width all plays again achieving better performance.

Again no big surprises looking at the longitudinal acceleration trace, showing similar maximum values compared to Monza.

 

silv-long-g

 

The RPM trace shows instead the shorter gear ratios I used in Silverstone, to better suite a slower track where a slightly higher downforce/drag setup was also used.

 

silv-rpm

 

First gear is used only once, at the Loop. The engine works below 5000 RPM only once, at the left corner after Vale (before Club corner), where second gear is used.
This shows anyway how the power band is mainly located on the higher side, also compared to previous generation Nissan engines, which confirms some of the feedback given by some drivers during development which suggested that new cars, even if having so much power, should be relatively easy to drive also for gentlemen drivers.
The latest track where I tested the model on was Spa, to have again a reference against previous simulations I did with a 2016 LMP2.
The final lap time (again, with me driving, so most probably not the best lap time achievable with this particular vehicle model) was a 2.03.6. Again, more important is the gap between this lap time and the best lap time I could achieve with a 2016 LMP2 vehicle model; the difference between the two is close to 3.8 seconds, again about 0.54 sec/km; as I already told about Silverstone, I would expect the best real lap times to be lower than this, above all if the track will be in good conditions.
In any case, the gap between 2016 and 2017 LMP2 performance seems to match well with the media communicated 3-4 seconds difference between the two.

Let´s take a look to the simulation results. First to come is speed plot.

 

spa-speed

 

Again, first thing catching attention is the overall top speed of about 304-305 km/h, at the end of the Kemmel straight. Even more suggesting, though, is a minimum speed in excess of 270 km/h inside Eau Rouge, with the car literally flying through this iconic corner.
Very interesting is also the minimum speed at Pouhon, another very quick and grip limited corner, very interesting to evaluate the cornering potential of the car in a high speed condition.
The data shows here a minimum speed of about 206 km/h and a maximum lateral acceleration of about 2.7 gs, as shown by the following plot.
spa-lat-g

 

The same plot shows a maximum lateral acceleration in excess of 3 g at Blanchimont, although at such a high speed we are not really in a grip limited condition.

Again no big surprises in the longitudinal acceleration plot, with peaks always in the same region of what seen in the other two circuits and highest values achieved at the bus stop braking, where some bumps on the tarmac contributes to create higher peaks in the reading.

 

spa-long-g

 

Finally, we can take a look to the RPM trace, where we can see how the car (here using the same gear ratios as in Monza) doesn’t reach the 8500 mark at the end of the kemmel straight in sixth gear and operates significantly below 5000 rpm only once, at the bus stop, where first gear is engaged.

 

spa-rpm

 

It would now be interesting to let a quick driver to test this vehicle model to fully explore the performance potential of these cars, at least taking for granted that all my assumptions are correct.

Anyone interested?

It would be cool to work on this model and on such an analysis with a real LMP2 driver.

This article, together with the video I linked above (car driven in Silverstone), should anyway give a feeling of the level of performance to expect in 2017 in the LMP2 class.
The cars will be, as we could already expect, much quicker than the old spec ones and, probably close to or quicker than 2016 LMP1-L in many occasions. It will be interesting to see how far the performance will be pushed, also considering that many teams seem to be able to include very fast professional drivers in their lineups.

Our findings seem to generally confirms what communicated to media by the manufacturers, expecting a gap between 3 and 4 seconds between 2016 and 2017 lap times, but can show more in detail how and where these gap can be built and can give a more detailed idea about 2017 LMP2 performance.

Here again a link to Silverstone’s video.

It will definitely be a very exciting season.

Posted by: drracing | November 10, 2016

My new Youtube Channel

Hi everybody,

for the first time ever (i guess), i am posting twice in less than a month!

But this one will be really short.

First of all, i can finally hold in my hand the latest issue of 24 Hour Race Technology, featuring again an article i wrote, this time about the performance gap between LMP1 privateers and hybrids. The work behind the article has been done using driving simulation to investigate where the LMP1-L cars performance should be and why it is not there.

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The second important announcement is that i finally opened a Youtube channel , where you can see some of my vehicle models in action, with me or some better driver driving them around some of the tracks i use for my studies/projects.

The first video shows me driving in Imola the latest LMP2 vehicle model i worked on.
I know i am not the best driver, so be gentle if you want to leave a comment!

I will try to post more videos soon and always keep the channel up to date with the latest projects. It will also be showing something of a list of the vehicles i worked on on the simulation side and, basically, my available portfolio.
It gives also a chance to take a look to my home simulation setup.

I am currently working on something very very interesting and i hope i can share soon something about it here and in Youtube. It is a very new car…

In the mean time, i hope you enjoy it! Here is the link!

It is always the same story: I always promise myself I will post more often here but the time is always playing against me!

Again a long time since my last post, so I thought I could maybe write some updates about my latest projects and some of the things I have done during the last months.

First of all, I am extremely glad to say that, as it happened in 2015, an article I wrote will be published in the “24H Race Technology” magazine this year too. As for my latest post here, it will cover some performance studies I did with the simulator about LMP1-L cars. I hope many of you will have a chance to read it without getting too bored!

Beside this, I was pretty busy lately, both on fun (technical) and private side. I moved into a new apartment, this meaning that for a certain time I could not really access my pc freely and all the simulation work had to stop. Anyway, the new apartment offers me a new room for my simulation hardware, this meaning I could even post some videos sometime in the future because I know have some space for some interesting upgrades and I should be able to have something to show on video without having to shame myself!
Luckily, before I moved, I had some time to both perform the simulations required for the above mentioned article and to support an LMP2 team I came into contact during the season.

The latter has really been a very interesting task, first of all because these cars are really amazing pieces of engineering and show some incredible performance, but also because a new project always means coming into contact with new data, acquiring new knowledge, experience and new perspectives even when looking to known problems.
What made this project even more interesting though is that, for the first time, I was involved in a study only and exclusively focused on setup optimization.
As you may know, I worked already on other LMP2 cars during the last two years, but the whole work was always focused on creating something mainly aimed to driver training. This doesn’t mean that the previous projects had no interest from an engineering perspective or that the modeling had been approached differently, since the goal is always creating a model that performs as close as possible to the real vehicle.
This basically means following some basic, important steps:

  1. analyzing the available car data
  2. creating a vehicle model that matches these data as good as possible
  3. validating the model against track logged data to be sure there are no unexpected differences
  4. using the model for training (or other) purposes

This is exactly the same thing I did this time too. What was substantially different was mainly how the fourth point of the above list was tackled, since the final goal was to help the team to improve their setup and, finally, their lap times.

Before we go on describing shortly how the project has been run and the results we obtained, I would like to focus the attention on what I consider an extremely interesting point.
As you may know, the software I currently use for this kind of projects is rFactor, since I think that its physics is still among the best available on the market in this price range.
Since some time, looking to the matching between simulation results and logged data I achieved, I started thinking that actually, up to a certain point, it must be possible to use a “simple” software like rFactor (which actually is not that simple) to perform more “engineering related” simulations, more or less what an engineer could need to improve, at least directionally, its car’s setup.
Of course, as we said thousands times, such a software have some limitations, mainly connected to rFactor being still a cheap product, which must have a much lower complexity than professional programs like the ones used by OEMs or big teams (which also require a completely different computing power); this very expensive tools surely offer much more flexibility also in terms of igniting subsystem models built up in external environment.
As I briefly mentioned in some previous articles, there are some areas where the user must be careful in order to get accurate results (see, for example, setting suspension geometry and angles, like camber and caster, or the way some strongly non-linear devices like the bump stops are modeled).
Some of these limitations can be overcome, knowing how the software works and how certain things are calculated. Paying attention to some aspects, it is possible to achieve extremely low errors, both when comparing vehicle data during the modeling phase (like tire forces and stiffness, aeromaps, suspension kinematics, etc) and when checking simulation results against real logged data.

Having the chance to use a commercial software like rFactor to perform engineering work opens to a different approach when using “home” driving simulation.
Of course, there is still a point in running multimillion simulators with extremely complex (and heavy) software and models and I am in no way saying that all of this can be simply exchanged for a much easier tool. On the other hand, it is now clear to me that, even for people/teams not able to access the expensive and complex tools that big teams have, there is still room to run productive simulator sessions with the aim to also better understand how the car works and where it can be improved.
In general there are still some phenomenon which are extremely complex if not impossible to simulate properly, mainly because there are no real data about them (see for example how much tire behavior change for a certain temperature variation, or how much aerodynamic properties change with roll angle) and conditions which are nearly impossible to replicate (we discussed already, for example, how much track conditions could change during a weekend, depending on different factors; different cars running on the track during the same day could even change the ideal driving line from one day to another). Experience surely help to replicate all these aspects in a realistic way, but perfection, of course, doesn’t exist and there is always a point behind the team being ready to do more or less everything to have more track time.
A simulator will always be a simulator, not the real thing. But being able to understand and to investigate how certain things work and (maybe more important) why something happens can be a really exciting and useful experience, at any level.

Something that further confirmed that driving simulation (even in our “simple form”) can still be an extremely useful tool even from an engineering perspective has come to me last May, in Spa, during the WEC race weekend, where I had the chance to speak to the drivers of Strakka (LMP2 team running a Gibson car in WEC this year). Strakka runs a professional simulator and they are also using rFactor (as far as I know). The simulator is mainly used by the team for his own programs (they have also cars running in the Formula Renault 2000 and in the Formula Renault 3.5 V8 series), but is also hired to private customers from time to time.
Strakka drivers confirmed to me that they not only use the simulator to evaluate setup solutions before a race weekend or a test, but also rerun the solutions they found on the track at the simulator after event, to double check them and further confirm that they went in the right direction (the simulator offers a “disturbance free” environment for testing). Moreover, a certain setup setting can thus be evaluated more in details, also looking to the effects they have on parameters that would be hard to measure and trace at the racetrack. Again, it could be an invaluable help to understand not only what happens but also why.

Of course, in order to use the simulator for setup investigations, it is even more important to have an accurate and reliable model that produces realistic results. This point cannot be stressed enough. Accurate data are key for whatever simulation, doesn’t matter if it is run on a driving simulator or with other tools.
The good thing is that building up a vehicle model and running simulation can sometimes also be a way to better understand your car and your data, even when they are affected by any sort of flaw. Sometimes, comparing simulation results with real data is the best way to identify measurements inaccuracies, or the areas where the model or the available car data could be wrong.

The project I was involved with has actually started with a study mainly related to tire data analysis, to try to understand why what was working pretty well in 2015, was not doing the same in 2016.
Analyzing purely the tire data (so ignoring a lot of other issues also connected to tires, see for example their thermal behavior and assuming the tire data were telling the truth!), was immediately evident how much different they were behaving compared to 2015 and the balance upset they could produce on the car. Even only looking to the vertical stiffness, it was already possible to identify some of the required setup changes needed to try to compensate for the different characteristics and come dynamically to similar ride heights.
We already pointed out in other articles how important ride heights are for LMP cars and how the ride heights sensitivity is for overall downforce and balance. So it is immediately evident how important even a basic chance, like the tire vertical stiffness, can be on cars final performance.

Anyway, a deeper look to the Pacejka coefficients set and to the relative plots was enlightening to understand where and how car’s balance and behavior could have changed and which performance differences to expect.
Above all at the front, 2016 tires were producing completely different friction levels and trends compared to the 2015 ones.
The team I worked with was somehow hit by these changes and wanted to confirm what they saw on the track through data analysis with some simulation.

As described in the list above, the first step has been going through all the available data and creating a vehicle model as accurate as possible. Of course, the validation phase has also played a central role about this, above all to be sure about how much exactly the tire forces needed to be scaled down to obtain realistic performance. Luckily enough, previous experiences came to help and the results were very close to the real car already at the first attempt, as confirmed comparing real and simulated data (here in Imola).

lmp2-imola

The light blue trace refers to the real car, while the orange one is the simulated one. Not too much effort was spent to fix the small difference in top speed (probably a small flaw on drag data, to go back to what we discussed above and an example of a situation where, simulating, you could spot an error on the provided car information compared to the real car logged data), since this particular issue was not going to influence how useful this study could be. Anyway, I still think that this graph confirms once more how close you can get in terms of vehicle performance to the real thing using rFactor and a good vehicle model.

Once the validation phase was over and matching between real and virtual vehicle was acceptable, I started working on the setup. The approach agreed with the team was for me to know nearly nothing about how they were setting the car, not to be influenced in anyway on the direction to be taken.
Basing also on my previous experience, I set up the car at first “on paper” (or, better said, in excel!), using some reference metrics like the roll gradient, Lateral Load Transfer Distribution, dynamic ride heights, corner and axle natural frequencies and targeting from the beginning values that, based on previous experience and on the analysis of the available data, I would expect to work.
For some “non-linear influenced” parameters, like ride heights, I did some checks calculating the load I would expect during certain maneuvers, evaluating the dynamic ride heights basing on these loads and using a certain setting for each subsystem (in this case, for example, springs, bump stops, static ride heights, etc). This allowed to also have a basic settings for parameters like the bump stops and their free gaps.

Once the car finally hit the track (or, better, the vehicle model was driven on the virtual track) the work I did was pretty much similar to the one of a “normal” race engineer, basically running sessions, evaluating logged data and driver feedback, trying to understand which areas could be improved or, simply, which differences there were between a session and another and, based on the conclusions I came to, finding and testing new solutions. And then repeat again and again, till the time I had at my disposal was over!
The interesting thing about doing something similar with a simulator is that you have perfectly repeatable conditions (track conditions, track temperatures, tires wear, engine power, atmospheric conditions, etc), so you can potentially really isolate the effect of each change on the car-driver package performance. Another important point is, of course, that, if time allows, you can test a lot of solutions and do as many back-to-back tests as you want, without having to pay anything or without having to explain to your boss about why you are testing the same thing again!
Since a driver is a human being (even professional ones) back to back tests can sometimes be a good idea to isolate driver’s effect on final performance and understand if a certain setup modification has really produced an improvement and why. It is also good to remember that race cars (and an LMP2 car in particular) are complex systems, where each parameter could potentially influence also many others. This means, it could well happen that a certain change produces a different consequence when married with a certain base setup than what it would do starting from another basic setup. Another good reason to do back-to-back tests is thus to really understand if a certain final solution, where we came after many small changes is really our optimum or not.
And now, we could start a philosophical discussion to decide if an optimum really exists, but I will avoid it.

The simulation work has focused on nearly every area of the setup, excluding the aerodynamics hardware settings (like wing angle, for example) which was basically taken as an input. The reason behind this is that the team already had a chance to perform its own evaluation and simulation (mainly lap time simulations) to define the best aero solution for the track they would be going to race in.
Effectively, saying I didn’t work on the aerodynamics at all would anyway not be true, since some mechanical settings have an influence on other parameters which directly define how much downforce and drag and which balance you have (see ride heights, for example).
Areas where we particularly focused were vertical stiffness (both in terms of corner springs and third elements, with particular focus also on the bump stop), dynamic ride heights, roll stiffness and total lateral load transfer distribution and differential settings.
There have been initially an “adaptation time” for the driver to find the most effective way of driving the car on the chosen track. As every driver probably knows, “practice makes perfect”, thus meaning that actually, nearly every driver would probably continuously improve him/herself for the whole time he/she goes on driving on the same track with the same car, but normally this happens at the beginning at a substantially higher rate than after some track time, thus allowing us to assume that after a certain practice time (its length depends strongly on driver’s skills and experience), if we log an improvement on the lap times following a setup change, that should be really a result of the car-driver package achieving a better performance and not only of the driver improving his technique.

As a side note about this point, it is worth to say that, sometimes, a setup making theoretically the overall car performance envelope bigger (see, producing better laptimes in a lap time simulation) could even not be the one achieving the best performance with the driver in the loop. This happens more often with non-professional drivers than with professional ones, but could also be the case with very expert ones. These situations are exactly the ones that make having access to driving simulation (even if in a “simplified” form, as in our case) even more useful.

I will not go through every setup change we tested, since it would take too much time and too much space. But I would like to focus on some specific corners and just one setup modification, to show the effects of a certain change on car behavior, driving style and overall performance.

I will try to keep it simple and just analyze the effect of a change on the rear roll stiffness, with a difference between the two cases of 17% of the rear antiroll bar stiffness contribution (this meaning that, in our second case, the rear antiroll bar has 1.17 times the stiffness it has in case 1). This is just a very simple case which doesn’t actually show the full potential I have seen and, more important, the parameters influencing the final performance the most, but I think it is still useful to identify if and how to obtain some setup related results (even at our “easy” level) and which intricacies could come from such a simple setup change in a complex car like an LMP2.
The final lap time gap between the two setups was around 2 tenths (the stiffer being the quicker); nonetheless, as we are going to see, some corners show very different performance and some handling surprises.

The first track section on which we will focus is a slow corner, driven in second gear, which is located at the end of a straight where the car travels downhill. In this turn, the car normally exhibits understeer, above all in corner entry.
The advantage of the stiffer rear antiroll bar here is immediately clear looking at the speed trace.

corner-3-speed

In the above picture and in the following ones, the red trace refers always to the softer rear antiroll bar setup, while the blue one always to the stiffer one.
As we may immediately see, the advantages brought by the stiffer setups are here evident: the driver is able to hit the brakes a tiny bit later, let the car turn in more easily, thus having a higher minimum corner speed and still being able to go on the throttle a bit easier.
The steering trace confirms that the car has better balance, with less understeer in corner entry and at the apex. Namely, the steering angle is smaller, still being the cornering speed higher, as we saw.

corner-3-steering

Looking at the corner exit, we can also notice a very small steering correction, underlining how the car tends to now have even some on-power oversteer in corner exit. In this particular event, hitting a curb in corner exit was also destabilizing the rear end of the vehicle a bit.
Also the throttle trace, here below, seems to confirm what we saw. The driver get away from the throttle a bit later coming to the braking zone and goes again on the throttle a tiny bit before, with only a small hesitation at the same instant when the steering correction takes place.

corner-3-throttle

On a more technical side, it is interesting to take a look at how the front and rear roll (here calculated as a difference in mm between left and rear wheel travel) changed because of our setup modification.
Looking at the Front Roll trace, we see a small difference, practically only driven by the overall roll stiffness being changed because of the different rear antiroll bar setting.

corner-3-roll-front

At the rear the difference is more evident:

corner-3-roll-rear

Regarding the roll angle, it is worth to mention that the simulations don’t consider any chassis flexibility and all the components are simulated as ideally stiff.

Let’s now take a look at what happens in two left, mid speed corners, one following another and with cornering speeds in the 140-170 km/h range.
In this case, the softer roll antiroll bar (red trace) seems to work better, with the driver carrying more speed inside both of the two corners.

corner-45-speed

The difference seems to be even more accentuated in the second turn, where the driver even brakes a bit later and with less energy, carrying more speed during the complete corner duration.
In the first one, which is the slower one between the two, we see the stiffer rear setting producing an effect somehow similar to what shown in the previous example in corner entry, with the driver being able to brake later; but here it happens at the cost of a lower apex speed.
In the second corner, as we mentioned, the driver seems to simply have more confidence (as per his subjective feedback) and/or grip with the lower roll stiffness setup, being able to brake later, decelerate less and carry more speed.
In general, the lower rear roll stiffness solution seems to work much better in these two corners, improving significantly driver’s confidence and overall performance.
The steering trace, anyway, reserves some surprises: we would expect the driver using a lower steering angle with the stiffer antiroll bar, confirming a less understeering tendency. But actually the steering angle doesn’t differ too much in its magnitude between the two cases, with actually the softer bar setup showing a slightly lower steering angle in both corners.
corner-45-steering
This seems to show a car with a less pronounced understeer in these two corners when using the lower rear antiroll bar stiffness setup. How is it possible?
This is confirmed by the following picture too, showing a channel I always use as a kind of “understeer-oversteer index” and which compares the actual steering angle to the ideal one, normalizing the difference between the two on lateral acceleration. When this channel is positive, we have “understeer” (or, anyway, a steering angle bigger than the ideal one).

corner-45-undover

All what we see here seems to go against what we would theoretically expect, when reducing the rear axle roll stiffness (namely, more understeer because of a more front biased Lateral Load Transfer Distribution).
The reason for this is probably to search in the higher speed that the driver carries into the corner with the softer rear antiroll bar, as a consequence of “trusting” the car more: this means, among other things, more downforce (ignoring how much downforce changes with ride heights, more speed means normally more downforce, as aero loads depend on the square of speed) and, because of different dynamic ride heights, a slightly different Aero balance (downforce distribution between front and rear axle), as shown in the following picture (where we show the front downforce distribution as a ratio between front vertical loads and overall vertical loads: higher values mean an higher portion of downforce acting on the front axle). Please focus your attention on the areas highlighted by the green circles, since these are the points corresponding, more or less, to the two corners apexes.

corner-45-aero-balance

Beside this, the driver is also driving slightly differently, as we may see not only looking to the braking points and to the steering trace, but also to the instant cornering radius of the path he is traveling on:

corner-45-radius

Above all in the first corner, it is evident how the cornering radius reduces quicker and a bit before with the lower rear antiroll bar stiffness setup. This means the driver closes the line, pointing the car to the apex, a bit before, than with the stiffer solution. As a consequence, he tends to release the car a bit before, leaving it sliding toward the outside of the corner.
As a sanity check, the two pictures below depict the front and rear roll respectively, calculated, as already explained, as the difference between left and right wheel travel.

corner-45-roll-front

corner-45-roll-rear

As we already saw analyzing the previous corner, both plots show an higher roll angle in the “lower stiffness” case, as we would expect, with the difference between the two cases being bigger at the rear, where we actually decrease the antiroll bar stiffness.

What all of this show is that, while in the first corner the stiffer bar seems to work better and the car has less understeer, as we would think, in these two particular corners more factors are contributing together leading to exactly the opposite reaction than what we would expect on paper, when setting a softer/stiffer rear antiroll bar, at least from a handling perspective. Not only the vehicle is quicker with a setup that produces overall slower lap times, but we actually identify a handling reaction which seems to go against basic vehicle dynamics theory.
As you may have seen, also the driver is playing a key role here in defining how the car reacts and this is something that a session in a simulator can show at best, while such a thing would be difficult to predict or simulate with a different kind of software. How the car behaves and performs on track is always influenced by how the driver can manage certain handling features and how he reacts to them (we have seen in this case how our driver was most probably using slightly different lines with the two setups).
At this stage, as we said, we are also not really simulating complex phenomenon like aerodynamics roll sensitivity, just to say one. Still, even such a simple setup change has shown a reaction that we would “normally” not expect.
Still, there is an objective change in how the car handles depending directly on vehicle dynamics and aerodynamics reasons, which not only is somehow counterintuitive basing on a simple reasoning focused on lateral load transfer distribution, but also can only really be identified in a simulation environment where also the driver is playing a role.

The conclusion is that, even with a cheap software, we could still extract a lot of useful indications about car setup and we can work also on technical aspects, not only on driver training.
For the record, the setup we came to using the simulation was extremely close to the one the team finally used on track, even after the “day specific” tuning.
As I said probably more than a thousand times, it is absolutely key to have an accurate, reliable and well validated vehicle model, to be sure to be capturing as much as possible what the car really does on track. For a study involving setup investigations, this is even more important than when working on driver training “only”.

What I find amazing after conducting this study is that it proved (to me in the first place) that, at least up to a certain point, a cheap simulation software like rFactor can even be used for pretty useful setup investigations, leading to results which are both close to the real world and helpful for the preparation/development work. Of course, track time is always the best a driver and an engineer could wish, but when this is not possible and/or when certain phenomenon needs to be analyzed in more “controlled condition”, the simulation can be a real deal. In general, it always helps to understand not only what happens but, even more important, why.

I am now even more convinced than before that a similar tool could be of real benefit for every team, not only for driver training but also from an engineering perspective.

Posted by: drracing | April 12, 2016

Perrinn MyP1, LMP1-L and driving simulation

Hi everybody!

This post will be about a project i actually worked on last year, but never found the time to write about. And, finally, will be again a bit about something technical.
This will be a long (but hopefully not too boring) entry, so take some time, some drinks and seat comfortably!

As I already wrote in some of my previous posts, some time ago I decided to create a vehicle model of the Perrinn MyP1, the open source project created by Nicolas Perrin with the intention to share with the community much of what is connected to the design of an LMP1 car; Perrin’s dream was to find the funding to finally build the car and bring it to Le Mans, using a new and exciting approach where a whole community could potentially be involved. Unfortunately, this dream didn’t come true yet and, most probably, will sadly never do: the project is now already two years old and, beside the funding collected through the chance given to people to subscribe to it and to access all the data available, I am not aware of any big backers who materialized till now.

This is for sure sad, but takes nothing out from the goodness of the initiative from Mr. Perrin which, if nothing else, gave to many curious and passionate people a chance to access some very professional material, that would normally be kept and guarded very secretly.
This includes a lot of detailed CAD 3D models, aero data (coming from CFD simulations), suspensions data, something about the tires (although this was probably the least useful provided data) and still much more. Basically, what is still missing is only what should be provided by external supplier and cannot be shared for legal reasons; this unfortunately includes the engine, which is a pretty sensitive element to define any car performances.

The whole project has been developed planning to build a car to compete against the big manufacturers (Toyota, Audi and Porsche) thus the original idea was to include also a Hybrid system, targeting the 8MJ class.
Anyway, my idea have been from the very beginning to use it as a base to evaluate how quick an “non hybrid” LMP1 (like the privateers are, see Rebellion and ByKolles) could be: Perrin data and general design would serve as a realistic foundation for a LMP1-like design, about which would otherwise be impossible to find any detailed information.

Assuming that Perrin did a job at least as good as Oreca did for Rebellion and Adess engineering did for Kolles, my assumption is that MyP1 “platform” can be used to understand, at least on paper (or maybe we should say in a simulation) how quick such a car (LMP1-non hybrid) could approximately be.
As I will show later on, I reworked a bit some of the settings provided by Perrin with the goal to optimize vehicle’s performance/driveability, when something was looking not perfect to me (of course not “cheating”, like artificially increasing aerodynamics efficiency, but only working on setup parameters, like springs, antiroll bars, gear ratios, ride heights, etc) and I tried to approximate the best I could all the missing data: as I said, the complete powertrain system is a very important example (not only the engine was not shown in CAD, discussed or described, but also important parameters like gear ratios or differential setup were not available at the time I built my vehicle model).
The model and the final results are anyway probably still not really on the edge, in terms of performance, but could still form a good base to get a feeling about how such a car behaves.

But let’s start from the very beginning. How the car designed by Perrin looks like and which parameters are available about it?

As I initially said, a pretty big amount of CAD data has been shared with the “users”, including the complete bodywork, suspensions, cockpit items, wings and diffusers.
As soon as it has been presented, a couple of years ago, it was immediately noticeable how the design took a “different path” (compared to the other manufacturers) in some areas, like the engine cover and the front aero package: the first is very much “Bubbly”, with a shape that doesn’t resemble any of the Manufacturers design and looks, for somebody not too much into aero design like me, a bit strange and apparently too big; Perrin ensures anyway that this has no real bad effect in terms of performance.
The later shows a high nose, with a clean front wing design and with the nose itself being smaller than the one of other cars using a similar front end concept, see Audi and Porsche.
Interesting is also the position of the two air intakes immediately beside the nose, but a bit more rearward; it is a solution partially similar to the one proposed also by the unraced HPD LMP2 car at the beginning of 2015, although in that case the intakes were at the very front of the car, just beside the nose itself.

MyP1 Iso view

MyP1 Front viewMyP1 side aero

MyP1 side view

 

Perrin’s creature features a 2950 mm long wheelbase, with front and rear track widths being very similar to each other and in the region of 1545 mm (the four tires have the same dimensions, although the rims are different front to rear, as also seen in other LMP1 cars; the main difference is normally a different wheel offset).
According to the info provided by Perrin himself, in a non-hybrid configuration the car should be able to stick to the allowed minimum weight of 850 kg, of which about 48% should act on the front axle statically (also with the driver on board).
According to the designer, the CG height should be around 280 mm higher than the reference plane, which is not the lowest point of the car, as we will see shortly analyzing the front and rear suspensions.
Below the floor find in fact place a wood plank, as mandated by the rules; in its thickest point, it is 25 mm thick. This means that the CG should be more or less 305 mm higher than the lower point of the car body, assuming an idealized surface running through the two thickest points of the plank, one at the front and one at the rear.
MyP1 Iso low view

MyP1 Front aero

 

A very important point regarding dimensions and inertial properties is also linked to the moments of inertia of the complete vehicle that, as i mentioned in some older entries, play a very important role in defining how the care behaves dynamically. Since these data are normally not available, I use a simplified approach to estimate them, which consists in dividing the car in several blocks with simple shapes, calculate each block moments of inertia (basing on the mass assigned to it, which is calculated to finally achieve the “desired” static weight distribution, also basing on each block position) and then in “moving” each block’s effect to the CG using parallel axel theorem, to finally have the Moments of Inertia of the complete vehicle referred to the car’s CG (as required by rFactor).
Going “under the skin”, it is evident how the design was driven by the aerodynamics, including all what concerns the front suspension. Here, another important element is surely the maximum lateral width allowed by the rules, which forces to use relatively shorts control arms, making it harder to really optimize the geometry.
The front suspension employs a typical double wishbone scheme, with unequal length arms, pushrods and torsion bars. The antiroll bar is connected to the rocker through (more or less) vertical rods and it seats on the lower portion of the chassis, attaching to the front bulkhead. Although not shown, two linear dampers are meant to be used (this is one of the contents belonging to suppliers and that cannot be shown in CAD).

I analyzed it using a very well known Multibody software, focusing only on the pure control arms/Steering geometry (not on the motion ratios, for example, since the wheel rate contribution of each corner spring and of the antiroll bar was provided “separately” by Perrin’s data).
The results show a very high kinematic roll center (much higher than the rear), a pretty sensible track width variation with respect to heave motions, a relatively big scrub radius and a pretty small caster angle.
Also, bump steer is not really optimal, although not being out of sight. This underlines once again some of the compromises accepted in the design phase for the front axle for the sake of a higher overall benefit, probably.
Camber gain is also not too high, but this is not necessarily bad: for sure, together with the low caster angle, it doesn’t help to have an “optimal” tire vertical inclination for the outside tire in cornering situations, but it is also probably not a performance killer.

To be honest, if I had to wish something for “my ideal front suspension”, it would definitely not look like this. But this is only my opinion and I am sure there were reasons to justify the decisions taken, including (as we already mentioned) maybe freeing some space on air’s way through the front aerodynamics devices and to the sidepods. And anyway, this is only my personal opinion, which comes from a very different experience than the one of Mr. Perrin and surely not at such a high level.
In any case, some of the compromises connected to front suspension geometry are strictly linked to the short control arms in use, which are a direct consequence of the rules in place (maximum track width, chassis width in the driver’s leg zone) and also of the intention to design the front end leaving the chance to package a front electric engine to power the front wheels (not shown in the pictures).

MyP1 Front susp - Front w chassis

MyP1 Front susp - Front

MyP1 Front susp - Iso

 

MyP1 Front susp - Top
Beside the aero and package driven compromises we mentioned, it is easy to recognize a certain “F1 style” on the complete front suspension concept, see for example a very high attachment of the lower wishbone to the upright (relatively close to wheel center), to free air’s way in the region where it exits the front wing/diffuser (but surely not helping overall stiffness in cornering situations) and, also, the upward oriented front wishbones.

 

MyP1 Front susp - Front Upright - ISO

 

 

 

Here below a summary of front suspension’s most important features. Please note that the front ride height (plank) is referred to the lowest point of the car, namely the lowest point of the wood plank sitting below the floor and mandated by the rules (please see notes above about this part). It actually doesn’t extend up to the front axle, but, being its front edge pretty close to it, this approximation should not drive a big error.

 

Front Susp summary
I didn’t perform any calculation about the anti-effects, but it looks like there is something going on in this regard. A picture tells more than a thousand words!

 

MyP1 Front corner side view - Anti

 

Looking at the rear end of the car, Perrin provides the CAD models of the complete suspension (again with the exception of dampers and springs, probably third parties properties), the bell housing, the rear end of the gearbox and a solid block working as a placeholder of the main portion of the gearbox itself.
As for the front, the car employs a double wishbone scheme with pushrods, rockers and a general layout that could potentially allow both torsion bars acting directly on the rocker or coil springs mounted coaxially to the damper (I suspect the latter being actually the planned solution). The system allows the use of a third spring-damper unit, seating between the two rockers (not shown in the pictures) and activated by a traditional T antiroll bar, connected to the third element on the middle of the upper arm.

Again, it is evident how much of an influence the aerodynamics had on the general layout: this becomes clear, for example, looking at how low the rear top wishbone is attached to the upright, with its outer attachment z coordinate seating extremely close to the wheel center. This choice, which surely has a strong impact on suspension overall camber stiffness, had most probably a very beneficial effect in allowing the rear engine cover to be as low as possible. As far as I have seen, something very similar should also be used by the “big guys”, Porsche, Audi and Toyota.
Another interesting point is also the pushrod attachment to the upright being very low, probably (but surely not only) also to have a better kinematic alignment with the rocker plane.

 

MyP1 Rear corner side view - Anti

 

MyP1 Rear corner iso view - upright

Talking about suspension, also the rear one seem to be partially compromised for the sake of a bigger overall benefit, although the longer control arms undoubtedly helps to improve the situation.
I analyzed it again using the same Multibody software I used for the front one, again focusing on the pure control arms driven effects, since the wheel rates were anyway provided separately.
The results show a better bump steer, compared to the front axle, a much lower rear roll center (and also more in the region where I am used to see it, from my previous experience), a higher camber gain (which is, in my view, beneficial at the rear) and still a pretty high track width change, although not as high as on the front axle.

A summary of what I found is shown here below:

Rear Susp summary

 

For the ride height, what I said about the front is of course still valid also at the rear, with the plank value referring to the lowest point of the car, below the plank thickest area.

 

MyP1 Rear Iso view

 

MyP1 Rear Iso view 2

 

MyP1 Rear top view

 

In general, the design looks very neat, although any particularly new solutions have been deployed, compared to the standards visible of F1 cars or other LMP1 vehicles.
It is interesting to notice how all the rods (pushrods or tie rods) that need to have an adjustable length use a spacer system with plates in between, which is (or at least was) a standard in Formula 1. I am not totally sure of what the other LMP1 manufactures do, about this particular feature. For sure this is not a standard in LMP2.
It is also interesting to notice how the front upright is mounted to the upper control arms where the “clevis” on the arm side, while for all the other connections between control arms and upright (front and rear), the opposite solution is in place (clevis on the upright/chassis side).
Staying on the suspensions side, the vertical stiffness (wheel rates, spring contributions) suggested by Perrin in the provided datasheets was pretty high, with a stiffer setting at the front than at the rear (270 N/mm at the front, 230 at the rear).
According to the unsprung mass provided by Nicolas, this lead to a pretty high suspension natural frequency, both at the front and at the rear (in the region of 6Hz at the front, 5.4 at the rear).
As we will see later on, I had to work on the setup a bit, because the car was really hard to drive. More on this later, but I also tried to reduce the corners spring stiffness using third springs, with positive results.
A role about this issue was surely played by the tire model, which was basically carried over from my LMP2 project, but using four rear tires, since in LMP1 all the tires seem to be the of the same size (31/71-R18). For intellectual honesty, I have to say that, according to the information I have, LMP2 tires are vertically stiffer than many Michelin tires with the same dimensions (Michelin is used by all LMP1 work teams) and this could play a role, increasing the overall wheel rate; but, since in 2016 all the non-hybrid LMP1 teams should switch to the brand now producing LMP2 tires, this approach was (accidentally) useful to have a better picture of how the car should behave or could be set. Of course, we cannot know if the new LMP1 tires will be the same (or have similar features) as the LMP2 ones, but this was the only trustable data I had, so I had to stick to it.

Regarding the Antiroll bars stiffness, the material provided was pretty unclear, showing actually a negative stiffness for the rear, probably because of calculations done to achieve a certain roll gradient.
The reference value for front antiroll bar stiffness at ground (so its wheel rate contribution) was 380 N/mm. Even with no real antiroll bar, this would produce already a pretty high roll gradient, mainly because of the high roll axis and the relatively low CG. Anyway, rear roll stiffness was an important study parameter in my simulations, more on this later.

Moving away from the suspensions, a very important area, where no data was provided, as I said, is the powertrain.
I tried my best to replicate a Turbo engine with more or less the same features of the AER used by both Rebellion and byKolles, the two teams currently competing in LMP1-non hybrid class. Probably it is more correct to say that I tried to replicate the known features of this engine, since I found few or no data about it.
As far as I know, it should rev pretty low, with a shifting point around 7000 rpms, but I could not find any useful data about the overall power. I tried to enquire Mr. Perrin himself about a realistic power figure for an LMP1 engine and it came out he also had no trustable info to provide. I also had no direct contact to people working on the AER engines and all the people I could talk to were not really able to help or could only provide figures flying everywhere between 500 and 900 hp.
Sticking to the fuel flows (updated in September 2015) allowed by the FIA (106.5 kg/h, for the LMP1 non-hybrid class) and to what I think (hope) could be a realistic BSFC figure (219.5 g/kWh), at least for the peak power, I derived something in the region of 485 kW (640-650 horsepower, depending on the definition of hp/ps you want to use).
To draw a realistic power curve, I based on an engine produced by a tuner with more or less the same features (6 cylinders, low revs, high torque and about the same power) and came to something like this:

 

Engine

 

The gear ratios were not provided and I tried to build up something realistic, basing on engine power, drag and rolling resistance. For this first study, I only considered the sprint aerodynamic configuration, assuming a fixed rear wing angle and, thus, just one possible aero setup; it made it easy to define a single set of gear ratios that would more or less fit every track (not optimal, I know, and probably not completely realistic, but still enough to get a directional performance estimation, in my opinion).
The gear ratios I used at the beginning are listed here below and are based on the input from Nicolas, stating that the plan is to go with a 7 gears solution:

 

1st: 14/34
2nd: 16/31
3rd: 19/31
4th: 21/29
5th: 21/26
6th: 20/23
7th: 23/25

Bevel: 22/21
Crown and Pinion: 15/43

 

As we will better see later on, I had to work a bit on the ratios to allow a better use of engine power even at the exit of low speed corners, using lower gears, without relying too strongly on traction control.
As you have seen, the engine is pretty strong in terms of torque.

We will cover the setup work more in details a bit later, not only regarding the gear ratios.
Before we move to the next topic, though, I think we need to spend a couple of words about a pretty important missing input, which is again a part of the powertrain system: the differential. It has a very sensible influence on how the car handle and it is normally a tuning parameter whose effect than can be felt very clearly by experienced drivers.
Unfortunately, there were no info about it in MyP1 server, as the gearbox itself was not yet really defined in details.
To be honest, I don’t even know exactly what kind of differential setup do the other LMP1 cars use, being them hybrid or non-hybrid.
For my simulations, I have assumed a Salisbury Type limited slip differential, with ramps and clutches to set the desired locking effect and with a tunable internal preload.
Without going into details about how such a differential works (this could require an article in itself and is anyway very well explained in many other articles on the web), it can suffice to say that its tuning was initially based on the experience I had with other LMP cars and was finally brought to slightly different settings, with a pretty high locking percentage in braking (around 80%), an average one on power side (about 30%) and some 100 Nm of preload. All of this has made the car pretty stable, maybe even increasing a bit too much the understeering tendency on corner entry and “helping” in showing some other small issues, mainly connected to the front suspension. On the other hand, I guess no endurance drivers would probably love an understeering car.

Another very important performance area is, of course, aerodynamics.
All the available Perrinn MyP1 data was derived, as far as I know, performing CFD simulations, since no real car or wind tunnel model has been built so far.
According to the shared information, Perrin and his team worked mainly on the low drag configuration, meant for Le Mans, including testing the virtual model at different ride heights, to have at least a feeling about ride height sensitivity.
Regarding the Sprint configuration, only minor data was provided, giving baseline figures of drag and downforce/balance. The data sheet provided also included the effects of increasing or decreasing both front and rear wing inclination in terms of drag, downforce and balance shift.
To derive a complete aeromap (downforce, drag and balance depending on front and rear ride height), I used a combination of the data provided about the low drag setup (scaled up) and my previous experience with similar cars.
The reason behind this decision, instead of simply relying on Perrin data (appropriately scaled to match with the downforce and drag levels provided for the sprint configuration), is that, as far I could see for other projects, the low and high downforce setup of an LMP car behaves completely differently not only in terms of absolute drag and downforce, but also from a ride height sensitivity perspective. The reason behind this is that, if the rules allow it, the team will try to also optimize diffusers shapes; they are the parts creating probably the strongest ride height dependence.
One thing to keep in mind is that, anyway, we cannot say anything about the accuracy of the data provided, also considering the complete design was developed aerodynamically using “only” CFD simulations.
I personally have no direct experience in this field and I cannot say much about the accuracy that can be achieved and I heard very different opinions about it. What is for sure is that, if big LMP1 and F1 teams invest so heavily in wind tunnel testing, there must be a reason.
Data accuracy is anyway an extremely sensitive topic, for anybody doing simulations, no matter in which field. Every measurement is subject to an error and race cars are no exception: my experience taught me also how much of an influence the “human factor” could have, for example calibrating a sensor poorly or simply ignoring other issues in the measurement chain.
Beside this, every data derived through lab measurements, see for example a wind tunnel test, is something that refers to more or less ideal conditions, which are practically impossible to replicate on track.
With this, I don´t want to say that measurements are always wrong and that we should not rely on the data provided. I personally strongly believe that data are the key element distinguishing engineers by other professionals and, as long as I have access to reliable sources, I heavily rely on them for my models.
Simply, I know that sometimes it is not easy at all to identify and quantify error sources. That’s the reason why, for this study, which aimed mainly to produce directional results about Perrin’s car performance and behavior and, maybe, more in general, about an LMP1-L like vehicle, I felt I could took the freedom to “shape” the input data a bit, basing on my previous experience, more than simply relying on what was provided.
After this (probably boring) excursus about data in general, you can find here below the aeromap that could be derived from Perrin’s data for the Low Drag configuration:

Aeromap Low Drag

 

As we have seen talking about the suspensions, the ride heights refers to the wood plank below the car, so they are trying to represent the lowest point of car’s body.
As you may see, the efficiency is mainly between 4 and 4.5, showing the highest values when the downforce is higher, mainly because drag seems to be less sensitive than downforce to ride heights.
One very interesting point is the general effect of pitch/ride heights on Downforce and balance shift. We can get a better feeling about it looking to the only situation where we have two different rear ride heights value (25 mm and 31 mm) for the same front one (15 mm). Although 6 mm could seem a very small delta for the rear ride height, it is interesting to observe how downforce balance (portion acting on the front wheels) moves from 43.4% to 44.9%: a shift of 1.5% is in general something producing effects relatively big effects, easily detectable by an engineer when looking to telemetry data and normally clearly felt by the driver.
If you think that this shift was produce by “only” 6 mm difference in rear ride height (or pitch, in this case), you can immediately get a feeling of how important ride height (and pitch) control could be for such a car. This phenomenon goes hand in hand with an increase in overall downforce (CzA moves from 3.36 to 3.43, more than 2% difference).
The aerodynamic efficiency is, in general, pretty high, to underline once again, if needed, how effective could an LMP prototype be from this point of view. Anyway, keep in mind that, as far as I know, the efficiency obtained with Perrin’s design is not even close to what the “big guys” achieve with their cars.
Regarding the Sprint configuration, I took into account only a single point of the map, using it to determine a sort of scale factor, as I explained already.
In particular, for the base Sprint Setup, the data provides the following values:

 

aeromap sprint

 

As we may see, some interesting things are happening here: beside the expected increase in downforce and drag, we have a slight increase of the aerodynamic efficiency and very pronounced shift in terms of front downforce distribution, which saw a relative increase of more than 4%.

Before to dive into the simulations results, I think it could be worth to spend some words about the initial setup proposed by Perrin and the modifications I did in order to achieve a somewhat satisfying handling. We will mainly focus here on the mechanical settings, as we have seen how the aero was basically fixed. Please keep in mind, I will always refer to wheel rates from now on, when talking about stiffness.

According to the suspension setup proposed by the designer, the car should have a corner wheel rate of 270 N/mm at the front and 230 N/mm at the rear. The antiroll bar rate shown was of 380 N/mm at the front, with a negative value provided for the rear. Assuming, as a starting point, a contribution of 150 N/mm of the rear antiroll bar and bringing the front one to 400, we get a Total Lateral Load Transfer Distribution of about 60.8% on the front axle and an overall roll gradient (including tires) of about 0.22 deg/g, at the ride heights considered (15 mm front, 25 mm rear).
The TLLTD is, even with this base setup, pretty aggressively moved toward the front; if we consider that Perrin note seemed to suggest (see the strange negative roll stiffness contribution of the rear antiroll bar) the need to have an even bigger portion of the overall weight transfer acting at the front axle (with this being also partially driven by the suspension geometry features we saw at the beginning), you can already foresee some of the handling features of this car and some of the problems it may have or the designer was trying to anticipate.
After some testing, I came to a setup solution where some of the vertical stiffness was removed from the corners and partially transferred to the third elements, both at the front and at the rear. For this first evaluation stage, I didn’t use any bump stop, although it would probably make very much sense for a car like this, with pretty high downforce and high ride height sensitivity. It is something that could probably be further and investigated in a second step.
The final corner wheel rate I have used is of about 190 N/mm at the front and 160 N/mm at the rear, with both front and rear third elements using a 50 N/mm spring. Roll stiffness has been further decreased at the rear, coming to 100 N/mm and slightly increased at the front (420 N/mm) thus coming to a final Total Lateral Load Transfer Distribution (in static/setup conditions) of about 65% and to a roll gradient equal to about 0.24 deg/g.
As you may also see, the final corners vertical stiffness has been reduced, compared to the levels suggested by Perrin itself, making the car definitely much easier to drive also on kerbs and bumpy surfaces and, in general, more predictable.
We can generally say that the vehicle, because of its design and of the setup in use, showed a pretty marked understeering tendency in corner entry, probably making even more evident the compromises accepted on the suspension design side, above all in slow speed corners. The front end is not so easy to handle, producing sometimes pretty strange reactions and generally a worse feeling than the one you could get driving an LMP2, for example (where suspension design is much less compromised). On the other hand, this has probably help to give some confidence to the driver in the corner exit phase and in fast corners.

As we already mentioned, gear ratios were also slightly changed during the “development” phase, to make the engine output more usable in corner exit in slow corners. After testing a bit, I finally came to a solution with slightly longer 2nd, 3rd, 4th and 5th gears, ending up with the following solution:

 

1st: 14/34
2nd: 16/32
3rd: 18/31
4th: 17/26
5th: 21/29
6th: 19/23
7th: 23/25

Bevel: 22/21
Crown and Pinion: 15/43

 

The vehicle model, built and set up as described, was tested in Silverstone using a very detailed track model that should eliminate the fidelity/confidence issue on this side pretty completely. The results are shown here below with graphs relating to speed, RPM, lateral acceleration and longitudinal acceleration versus driven distance.
Now, before to comment on them, I want to share a word of advice, also to avoid anybody shooting at me because of sharing wrong results.
These results refer to a simulation which, as any simulation, was performed in ideal conditions (although using a real human driver), thus excluding a long list of disturbing factors that do exist in real life (see track conditions, traffic, etc) and other important factors as tire wear, all of which have a significant influence on lap times and, more in general, on the performance of the vehicle.
Also, the data I have used to generate this model are actually derived from a car (Perrinn MyP1 project) which doesn’t exist in real life and, unfortunately, probably never will; in some cases, as we have seen, I had to derive some missing inputs, sometimes related to performance critical subsystems, see for example the engine. For other critical areas, see for example aerodynamics, the designer has only performed simulations but never tested (in a lab or on the road) any part.
This means, on one side, that the input we have given could well be wrong or, at least, different from any other existing car; this depends, as we said, on many potential data errors and, on the other side, on having no means to check how good or close all of this data is compared to, say, a real existing LMP1-L vehicle, see for example the one used by Rebellion Oreca.
Nonetheless, I think it has been an interesting exercise, also to understand how close (or how much closer) an LMP1-L car could go to the manufacturers in terms of performance and, also, which issues (setup, handling, balance, etc) such a vehicle could present.

The final lap times obtained was about 1’42’’5. Let´s look at the speed trace first.

 

speed

 

First thing to notice is that the car reaches a top speed close to 300 km/h (about 297) on the Hanger Straight and is able to drive at very high speed through the fast sections of the track (Abbey, or first right corner, where we are travel at close to 265 km/h and nearly flat out; Stowe, with a minimum speed of about 215 km/h and finally through the Maggots-Beckett section, where the relative stability helps to carry high speeds through all of the corners).
We can take a look to the lateral acceleration trace, to further understand car’s overall grip potential:

 

lat g.jpg

 

Here we can see that the vehicle is able to carry about 3gs in the two quickest corner of the track, to underline how important the aero effects are. Interesting also to notice how also in lower speed corners the car can sustain accelerations over 2gs, see for example through the Maggots-Beckett complex.
The longitudinal acceleration trace seems to confirm more or less the same trends, also giving an idea about the trusting force that our engine could produce, additionally also showing the grip potential in braking.

 

long g

 

Finally, we can take a look to the RPMs trace, at least to have an idea about the engine usage and gear ratios and to try to stimulate somebody to come back and say if and how wrong my assumptions are. As I said several times, the engine is probably the biggest question mark of the whole article and, together with aerodynamics and tires, surely a very strong performance driver.

 

rpm

 

Taking into account all the error sources we already mentioned, I even dared to compare our data and results with what happened last year in Silverstone during the first WEC Race. Pole position was signed by Porsche with a stunning 1’39’’7 average (of two drivers), but with an overall best lap of 1’39’’5; the second best non-Porsche car was the Audi, with an overall best lap of 1’40’’2 circa.  It makes no sense to analyze the LMP1-L lap times, since Rebellion was absent for the first race and the ByKolles team was surely not yet in top form; also, the fuel regulations has been changed slightly at the end of the season, as we said, probably freeing some performance potential for the non-hybrid cars. Anyway, we could try to deduce a reasonable gap, looking to the typical lap times difference between LMP1-L and LMP1-H at the end of the year: LMP1-L were typically still about 6-7 seconds slower, if we look at qualifying results of USA, Japan, China and Bahrein races; this means the typical gap between LMP1-L and the manufacturers is normally bigger than what we have obtained with our study.
In general, we should surely allow an error window to my results, to take into account effects not easy to simulate (as the ones we already mentioned, see traffic, track conditions and conditions variation, etc). In any case, also assuming a +/- 1 second tolerance for the simulation results, we still have a pretty sensible difference to what shown in 2015 by the two LMP1-L teams, in terms of performance.
This opens some possible scenarios that we can analyze: the first one is that, simply, my model is not really representative of any existing LMP1-L car: the data I used are not coming from any of these cars and there are anyway some open questions about some critical areas, like the powertrain one.
Another explanation could be that only some of the subsystem are not really performing as we would think, basing on my simulation results: my first suspect lies, again, on the engine: to be honest, I still believe that, although being realistic when looking to the BSFC values we used, the power output I assumed was probably optimistic. This could also open another discussion about the pace difference between LMP2 and LMP1-L to be expected in 2017, when LMP2 should actually get an engine with a power output of about 600hp (much more than the 500hp c.a they have now).
But we also don’t have to forget that last year LMP1-L and LMP1-H teams were using the same tire brands (Michelin, which I doubt was providing the same tires to everyone), while all of my simulations refers to a tire model based on lmp2 tire data. Incidentally, the same brand will be used in 2016 by all of the LMP1-L cars, which moved away from Michelin. We could argue that any tire model used for simulation will never really give a precise picture about the final performances of its real counterpart, but I am pretty curious to see which pace the LMP1-L cars will have in 2016 in Silverstone. Assuming my simulations are anywhere close to being correct, LMP1-L teams should be able to free some performance potential, sooner or later.
For now, what we can say is that, looking to the only 2016 lap timing results available so far (namely the results of the Prologue, held in Paul Ricard at the end of March), we see already gap reduction, with the LMP1-L cars now being closer to the LMP1-H ones, with Porsche and Rebellion being some 4 seconds away from each other and this difference further reducing to about 3 seconds if we consider Toyota and Audi.

To better understand if and how our results are somehow trustable, we can look in more details at the performances registered by the LMP1 cars in Silverstone in 2015 comparing them with our simulations and to the results seen by LMP1-L teams at the end of the year.
The first “quick and dirty” comparison we can do regards the maximum top speed reached in our simulation (about 297 km/h), that is pretty close to the one achieved by Porsche (300-302 km/h) but pretty much quicker than the ones of Audi and Toyota (285 km/h c.a for the Japanese and something below 280 for the Germans). This should be no surprise if we assume that, even being probably more aerodynamically efficient, the LMP1-H has less power coming from the IC engine; this should mean that, after the boost of the hybrid out of the corners is over, the car is only pushed by a less powerful engine than the one we used. A comparison between our model and real LMP1-H performances could anyway be useful to understand which delta we could expect, in order to compare it with the top speed delta between LMP1-H and LMP1-L cars in other tracks.
So, without further ado, if we look at Fuji results, we can see that, while Porsche was topping at 309 km/h c.a, the best Rebellion was able to achieve a maximum speed of about 302 km/h. We would have here a 7 km/h difference, which compares relatively good to the 5 km/h difference we have seen in Silverstone with during our simulation.
If we then look to the USA results, we even see a Rebellion on top of the best speed charts, with a maximum speed of about 301 km/h, against the 300 km/h achieved by Audi.
This shows that, at least in terms of top speed, we should be not too far off from a realistic picture.

What about other sections of the track? The only source I found to gather some information are the onboard videos you can find in Youtube about and showing portion of the WEC races: sometimes, if you are lucky enough, some of them show some telemetry data which can help to identify (at least very generally) cars performance.
Before diving into details into this, again, please keep in mind that some aspects, like for example tire wear, were not simulated during this exercise and that they could play a role in defining small differences. Moreover, some other parameters like fuel load are unknown. Finally, our model represents a car that should be slightly lighter than a LMP1-H.
Watching this video, at the 1:21:00 mark c.a, we can seat for some time onboard of the #7 Audi beside the driver Marcel Fassler. At the very beginning of this video section, we see the minimum speed inside the last chicane (Vale), being about 90 km/h (in another section of the video, around the 1:55:00 mark, the minimum speed is around 94 km/h): this compares pretty good to the 92/93 km/h we see in our simulation; a few seconds after, the Audi goes through the first very fast right corner (Abbey), with a minimum speed of about 260 km/h, which is again very close to the 262-263 km/h shown in our speed trace at the same point. Again, Fassler drives through the first right hairpin (Arena track section) with a minimum speed of about 90 km/h, which is not too far off from the 95 km/h shown by our simulation. The following left hairpin allows a minimum speed of about 83 km/h to our model, against the 80 km/h c.a of the Audi.
Afterward, the displayed data seem to stop working, not allowing for a check on the following corners. This very rough sanity check tells, anyway, that our results should not be completely off compared to the real cars.

Closing, this exercise allowed us, on one side, to explore more into details the very interesting MyP1 project, from Nicolas Perrin, analyzing a bit how the car looks like and trying to identify some key aspects, at least in some areas. Afterward, basing also on my previous experience with other similar cars, we tried to build up a simulation model of the car, assuming it was running in an LMP1-L configuration. The results we obtained has shown that, assuming the data we have used are realistic, the LMP1-L car could actually have some potential, in terms of performance, that for some reason was not yet explored. The results we obtained were also (roughly) compared to available data about LMP1 vehicle performances to double check if anything was completely off.

Hope you enjoyed it and you did it to the end without falling asleep!

Posted by: drracing | January 22, 2016

Racing Drivers and/or Simracers – New cars in Portfolio

Hi everybody and happy new year 2016!

Again long time since last i published something here.

And actually, also this one will not be a lengthy post.
I just found this article floating around the web and found it very interesting. It talks about another guy, basically with only simracing experience, who had a chance to step into a professional career (or at least try it), this time with the financial support of Mazda in the US.

This shows, once again, how driving simulation could not only help to develop driving skills and train a driver between races and tests, but also how it could be an effective school for young guns wanting to learn basics (but not only basics) before to jump in a real race car and without spending hundred thousands of euros in a real race car program.
Money will always be the biggest problem, of course. But cases like the one i am linking here seem to give some hope also to people not having a very rich dad.

There are of course things that no simulation can prepare to, see for example the physical effort that drivers need to sustain, above all when driving cars with proper downforce. And this is of course something that cannot be underestimate.
Nonetheless, simulations are getting so good to be really able to help a driver to improve himself/herself and to let a “trainer” to shape his/her skills, style and knowledge.

 

On a different note, the list of the cars i modeled in rFactor basing on real data is getting longer and longer.

Beside the already established LMP2 and LMP3 projects, during the last months i built the physics of other cars, including an LMP1 based on Perrinn data (and about which i hope i can write soon here), a new F3 model, based on Dallara F312 in F3 Euroseries spec, a mid engined GT3 car and a new LMP3 vehicle, based on real data of a lately released french race car.
This later model is actually part of the collaboration with the LMP3 team i already worked with in 2015 and that i will go on supporting also in 2016.
The results are really interesting: i cannot show too much here yet, unfortunately, but matching (thanks also to more accurate data coming from the team compared to what they had about the previous car they used) is already very very good.
About this (and somehow taking up again a topic i discussed in some previous posts), it is also interesting to see how lap times also matches with reality when working with detailed circuit models.
Because of one of my projects, i had a chance to access some laser scanned track models and test my vehicle models there. The results of using detailed vehicle models built in rFactor with such track models is above possible explanations (above all when using appropriate hardware). Beside the feedback on the steering wheel, it is also extremely interesting to analyse suspension movements with data logging and, in general, to analyze how vehicle behavior changes in comparison to a “normal” track model.
Moreover, thanks to the collaboration with a very talented guy and track modeler, i now also have access everyday to track models with an accuracy and quality comparable to that of laser scanned tracks (at least for all what concern track layout, kerbs, elevations, etc and missing only the detailed modeling of every bump which belong to laser scanning too). He developed a new method to define tracks layout, elevations, camber, etc basing on very detailed data and the results are really amazing.
This, together with some important updates to my hardware (among other things, my driving rig now has a Direct Drive Steering system and load cell pedals in place), allows realism to go another step forward, making even more interesting to evaluate car reactions not only through data analysis but also through subjective feedback.
Beside the driving feedback, it is extremely useful to have the chance to rely on accurate track models, because it allows to validate the model against real logged data without having to worry about how precisely the track is built inside the simulation.

It would be extremely interesting to have a chance to let some real drivers (beside the ones involved with the projects themselves) to test these new babies and hear their feedbacks.
Logged data matching, as i had some chances to show, is really intriguing so i am pretty confident in saying that it could be good fun, for somebody with race car driving experience, to have a try!

Next up, Renault RS01!

Posted by: drracing | November 3, 2015

Article in “24H Race Technology” + small updates

Hi everybody!

Since it is now some time I don’t write here, I thought I could just publish a small post about the latest projects I was involved with or I am still working on.

First of all, I am very very happy to tell that i wrote an article for a “real” magazine! As mentioned in the title of this entry, the magazine in question is “24H Race Technology” and, more specifically, I wrote a piece about Porsche 919 LMP1 front suspension, basing also on the analysis I already presented here about its rear one.

You can find something about this year issue of the magazine and about its content here.

In the mean time, I completed the LMP3 vehicle, at least basing on the available data. The work with the team involved in this project should probably go on, since they would like to provide the drivers with a vehicle model they can use to train for next season (basing on the data available about the new car they will drive) during the winter.
The very interesting point about this is that, potentially, they could get to know the car through simulation before than through a complete track testing program!
It would be interesting to see the impression they will get as soon as they will seat in the real car next year!

Some time ago, I also completed a first pass of an LMP1 vehicle model, mainly based on the data provided by Nicolas Perrin to the people supporting his open source project “MyP1“.
He is basically giving to everyone the chance to access more or less everything about the car, including CAD, Aero data, suspension data, etc, with the only exception being info about components/subsystems that are not yet clearly defined or that belongs to suppliers.
This include, for example, some key players of a vehicle model, like the engine torque curve and tires data, but I tried to find a workaround basing on experience and on inputs I found around on the web.

I will try to share some results of the first simulations I have done and to share as much data as possible here, if time allows. It would be a very good input to start a discussion about the performance of an “LMP1 non-Hybrid” like car.
I will also try to explain more in details all the assumptions on which the data are basing and that I also had to make in order to build up the car physics.
For example, all the aero data are coming by CFD simulations, since nothing has been built yet and there was no wind tunnel testing up to now. All of this have of course an impact on the accuracy of the final results.

Last but not least, I am also building a model of a GT3 mid engine race car, basing on a good amount of data i have been able to find thanks to the help of several contacts.
Since there are so many drivers racing in one of the many GT3 championships around the world, it could be a good chance to come into contact with some of them and get a feedback about the vehicle model.
Again, I will probably write something about the results here, as soon as the model is ready and will be able to run some simulations.

More about all of this to come soon!

Posted by: drracing | August 26, 2015

How close is close enough? – Part 2

Hi everybody.

This will be a relatively short article but hopefully interesting for all the people involved with driving simulation or simply interested to it.

As the title already says, today i would like to briefly show and discuss some pictures related to one of the latest driving simulation projects i am working on. The project is not ended yet and the model is not 100% finished as well (or, to be precise, it is more or less finished in its base configuration but i would like to add more setup options for the benefit of the final user and these options are not it yet), but since it already shows good promise, i though i could show some pictures here to underline, once again, how close to real car performance you can go with a cheap commercial software like rFactor.

I will not go into the details of each graph this time and, for confidentiality reasons, i had to cover the y-axis scale of each plot, not to discover to many sensible information. I know some people don’t like it, but that’s the only acceptable way here. You will have to trust my intellectual honesty!

The car in question is an LMP3 prototype. I am building a vehicle model of this car for a team that would like to support their drivers training with some driving simulation hours.

The information available about the car are not yet complete and detailed as they were for the F3 model i used for my previous “How close is close enough” article (where i really new each detail about the car), but still complete enough to have a very good matching at the very first attempt. Together with the team, we are anyway working to find or measure all the data that are still missing and we would need to have.
Good enough, we have pretty good figures about what the guys have used until now (and, in any case, how the car was configured for the session we will use as a reference) in terms of setup, aerodynamics (although not as detailed as for the lmp2 project, for example), gear ratios etc. and about how the car looks like in terms of basic dimensions, mass distribution, suspension geometry. In a few words, the vehicle model is, relatively to this session, pretty accurate already.
As you will see looking at the pictures below, the results are already pretty good.

Next step will be collecting data also about other configurations that the team have not yet completely tested (see different aerodynamics configurations in term of wing angles, just to mention an example), but the base seems to be already pretty well established. This should make the vehicle model usable in a predictive way, to test upfront solutions they may want to use for the next race for example (at least in terms of basic things and driver preferences).

One of the most difficult areas, as always is the tires modeling.
The information the team had about them were not as detailed as the ones i had at my disposal working on the lmp2 model, for example.
We had anyway pretty good data about vertical stiffness, rolling radii and gearing effects.
For all what concerns tire forces, on the other hand, i am heavily relying on the experience i gained with LMP2 tires, which are anyway pretty similar to the LMP3 ones.

As i stressed a lot in my previous article, every simulation is nearly useless if the data we input are not accurate or even wrong, no matter how good the source code is.
Having trustable data is a key point; although then, of course, who creates the vehicle model should anyway know very well how to input this data correctly into the software and, if we speak about rFactor, this means knowing well enough the equations lying behind each subsystem model.

Unfortunately, as we already said, getting good data is sometimes very complicated. Sometimes this data doesn’t exist at all (you would be surprised to see how many teams, even at pretty high level in motorsport, don’t have or didn’t received data about their car from the manufacturers), sometimes it is very confidential and nobody really wants to share it.
In situations where you don’t get all what you want (and, in certain areas, you normally don’t get what you want!), experience can play a big role, both in understanding and estimating how certain components/systems could behave or relying on previous projects to model some of the components behavior, without having direct measurements about them.

A few word about the car. LMP3 vehicles are pretty interesting, although much simpler and slower than an LMP2. They have a reasonable amount of downforce, pretty good tires (although basically standard gt rubber) and they show a very interesting cost/performance ratio. That´s probably the most appealing aspect.
The cars are pretty slow, probably also compared to what the regulators expected, but there are some explanations (see a not too powerful engine) and probably also a pretty big margin for improvement. I am curious to see what will happen, also in terms of performance, as soon as other manufacturers will join the championship.

Let’s take a look to some plots now. As i said, i will not comment them into details, but i think, also basing on my previous article, they are pretty self explanatory.

The data (both virtual and real) refers to a lap in Imola. The virtual track is not perfect but, compared to other ones you could find on the internet, is pretty good. Track accuracy is very often one of the bottle necks to produce similar comparisons.
It is not easy to find detailed and correctly modeled tracks, so i guess tracks modeling itself is maybe so easy. That is somehow sad, since most often, also if you have enough data to validate the model you create, you cannot make a 1:1 logged data comparison, because the virtual track is too different from the real one.
In similar situations, i normally rely on a performance envelope validation (comparing for example real data to virtual one with the vehicle driving in corners with similar radius, or comparing straight and braking speed envelopes separately, etc).
This is, partially, actually better than just using only a full lap comparison and this is a face i normally follow anyway at the very beginning of the modeling face, mainly using the tools i built up in excel.
A logged data comparison is, anyway, somehow more direct and easier to understand also for the final users and that´s why it could be cool to have access to laser scanned tracks, for example.

The first plot we will look at is the vehicle speed. Real data are always the blue trace, simulated data are the red one.

Match 1

As we may see, the two traces match pretty well. There are of course some differences, including some misalignment connected to the track lengths (or, more precisely, to each track segment length), especially at the end of the lap.
In any case, the speed traces are pretty close with the main differences being in fast corners, although we still talk of pretty limited mismatches.
The reason could be, here, a slight overestimation of the downforce the car can produce, but we have to keep in mind that a driver seating in a simulator will always take more risks than what he is doing in his real car; first of all because there is no risk of any injury, or any bill to pay if you destroy the car; also, in a virtual environment, there is the possibility to try and try and try again the same track, improving every lap. In championships like LMP3, a driver has to divide his car with other drivers and this reduce his available seat time pretty significantly. Finally, driving in a simulator a fast corner is for sure less physically demanding than doing the same in a real race car, no matter how good your hardware is.
Also, one often underrated reason behind speed differences in some part of the tracks (beside, sometimes, layout or corner radii misalignment), is that a real track is changing its conditions pretty much continuously, including different level of grips just a bit out the “ideal” line, where many debris normally lie. Sometimes, this pretty much dictates where the driver has to put his wheels, also when the geometric ideal line could be another.
All of this cannot be (accurately) reproduced in a driving simulation environment and, actually, we don’t want to, since what the drivers and engineers usually look for when using a simulator is repeatability.

Let´s now look to the following plot, lateral acceleration.

Match 2

Again, the match is pretty good, a part from track misalignment in certain zones. Small differences are again visible in fast corners, maybe depending also on the driving line the virtual and the real driver had chosen. But i still think the results are pretty promising.

The same can be said about the longitudinal acceleration:

Match 3Unfortunately, the real trace is very very noisy, so you will have to extrapolate a kind of middle line to really compare this data. The trend is anyway pretty good, with the same match tendency already shown by the speed trace.

We can finally take a look to the RPM plot:

Match 4This latest graph confirms, on one side, the right engine and drag forces behavior and, on the other side, also that the rear tires rolling radius and circumference are constantly correct both at high and low speed (so with both low and high downforce compressing the tires and both high and low centrifugal tire expansion).

Again, if you consider how cheap the investment for such a software is, it is pretty amazing to see how accurate the results you could obtain are.
Also, i am more and more convinced about how useful an rFactor based simulator could be, at least for driver training. It is not a case, i guess, if many professional simulation centers use it as a base for their business.

Posted by: drracing | July 20, 2015

The Joy of Yaw Moment Diagrams

Hi everybody!

Today I will finally go back to more “vehicle dynamics” related topics, after the digression I had with my two latest articles.

Before to go into details about the object of today’s article, I am happy to share some good news about my upcoming driving simulation projects.
I have some close contacts with some teams, beside the LMP2 one I am supporting already. That means that, hopefully (and if time allows), I will model some new cars in a driving simulator environment for some professional teams/drivers, to be used mainly for driver training and for some basic setup investigations and, maybe, for some sensitivity study.
One of these teams is racing with Sportcars too, taking part to ELMS, but not in LMP2. The second one is running some cars in an OEM supported spec series here in Europe, using a very new product with very interesting performance, more or less between an GT3 and a DTM.
Two very interesting cars, anyway, that will hopefully give the same pleasure I had working on the LMP2 model.
More to come!

What about today’s topic?
Well, it is anyway partially connected to the above projects and to the LMP2 one, since I started looking into it when developing a tool for a preliminary vehicle modeling/performance validation, before to run the car model in a driving simulation environment. This follows more or less the same line I explained in the “LMP2 car modeling – first Steps – Tire data scaling” post, where I described a simple tool I developed to initially validated the tire models/data coming from the sources with a simple steady state cornering simulation.

What we will discuss today is the construction and the use of a Yaw Moment Diagram, with a procedure which is, somehow, an extension of what I used for the steady state cornering simulation.
Before going into details about it, I want to state clearly here that I am no long time expert about Yaw Moment Diagrams or Milliken Moments method in general. There are people out there who know about them much more and much deeper than me (beside, of course, Mr Milliken) and who used them to setup and developed race car already since long. It would be actually cool if some of these guys would want to comment what I am writing here. So if you know any of them, please share this link!
Yaw Moment Diagrams are anyway such an interesting topic (and, potentially, a useful tool) that I could not stop myself from trying to develop a usable Excel tool to plot them and extract some usable results/metrics, in order to describe car/model behavior and cornering performances.
Beside the chance to use this tool also for vehicle modeling, it was also a very interesting exercise: I learnt a lot both during the building process and finally also using the tool for some basic simulation.

Let’s proceed step by step.
First of all, what is a Yaw Moment Diagram and where do they come from?
First time I personally learnt about them was reading Milliken&Milliken “Race Car Vehicle Dynamics”, which was initially published in 1995, if I remember correctly (although I read it much later, of course!). The Yaw Moment Diagrams and, in general, the Milliken Moment Methods (also called Force-Moment Method) were used anyway already many years before, transferring to cars a typical aeronautical approach to stability and control studies. And, as we will see, stability and control are some of the features of a vehicle that can be investigated with this method and are, otherwise, difficult to describe and quantify.
A Yaw Moment Diagram is basically a plot which has lateral acceleration on the horizontal axis and Yaw Moment on the vertical one. To be precise, actually several versions exist with the Yaw Moment and/or lateral acceleration normalized on car mass and wheelbase, but the basic concept stays and that is what I will discuss here (following pictures have been taken from “Race Car Vehicle Dynamics”).

YMD Milliken
The original approach to build up such a diagram was based on a constrained vehicle test, with a car (or a car scale model) running on a flat belt and locked by two cables, one at the front of it (at a certain and known distance from the CG) and one approximately at the CG. The vehicle would be then put to several Body Slip Angles (Beta, β) while its front wheels would be steered at several Steering Angles (Delta, δ) through sweeps of one and the other, measuring each time (for example through load cells on the cables) the Lateral Force at the CG (Cornering Force) and the Yaw Moment (Force at the front cables times its distance from the CG). The following picture is, again, taken from “Race Car Vehicle Dynamics”:

YMD Milliken 2
Beside the possibility to build such a diagram through constrained testing, the Force Moment approach makes potentially very easy to investigate cars behavior through steady state simulations where, for each Beta value, a Delta one is picked up and Lateral Forces (and, if interested, self-aligning torques) produced by the tires are calculated.
This means, we can immediately estimate the lateral acceleration and the Yaw Moment acting on the vehicle.
As a consequence, since we investigate the vehicle status for several combinations of Beta and Delta, the Diagram itself gives a very clear picture of how the vehicle behaves more or less in its complete operational window (and inside the given boundaries, depending, for example, on speed and/or downforce).
The Yaw Moment is actually the main player here, since it enables us to study features of the vehicle and of its behavior that is normally not possible to study in steady state conditions (where, for steady state, we mean steady state cornering, so constant lateral acceleration and net Yaw Moment equal to zero).
What is extremely interesting about this method is that, with a steady state approach, we can take a look to some typical “transient” treats of car behavior: since we investigate mainly situations where the Yaw Moment is not equal to zero, we can really take a look at what the car can do in transients and how big is the available Yaw moment to make the car turn, stabilize it or control it.

I will not go into the details about how the diagram itself is built, with the meaning of each line (above all the boundary ones), since it is explained pretty deeply and with much more competence in “Race Car Vehicle Dynamics”, chapter 8.
Looking to a Yaw Moment Diagram we can anyway immediately recognize two main groups of lines: constant Delta lines and constant Beta ones. The constant Beta lines are cutting the first and third quadrant and could be more or less straight. The constant Delta ones, are normally curved and, near the origin, they normally point downward for positive lateral accelerations. Of course, everything depends on the sign conventions in use and on the tire model formulation.
The sign convention I used, again, sticks pretty much to what is shown in “Race Car Vehicle Dynamics”. That means, in a right corner, lateral acceleration and cornering forces are positive, slip angles are negative. The self-aligning torques that arises in such a situation (and with the tires not yet at the limit) are anticlockwise oriented and negative. In general, Mz is positive when clockwise oriented (picture, again, taken from RCVD).

952524.fig.009
Now we should ask ourselves the (probably) most important question: why a Yaw Moment Diagram and the metrics we can derive from it could be so important/helpful to understand how a car behaves and what is happening in certain situations.
It is pretty easy to understand that, the first very basic info that such a diagram can give is the maximum lateral acceleration that the vehicle can achieve in its test conditions (see speed/downforce in place, for a car with significant downforce, among other things like any longitudinal force/weight transfer, for example; longitudinal forces are ignored here, for the time being), both in trimmed (net Yaw moment N equal to 0) and untrimmed condition (N not equal to zero).
How far away is the car from a trimmed condition when achieving its maximum lateral acceleration also tells us immediately what the car is doing at the limit in terms of over/understeering tendency (although this terminology could probably be not really telling much, here); this point can also help to understand why an ideally neutral car would produce the maximum cornering performance, at least in steady state: the maximum lateral acceleration would be then achieved in a trimmed condition (N = 0). Such a situation would anyway lead to other “issues”, as we will see.
Using the sign conventions above, if the maximum lateral accelerations (we talk about positive lateral accelerations, here, so right corner) is achieved with a net negative Yaw Moment in place, the car is stable or tends to push at the limit: the vertex at the far right of the diagram seats below the Ay axis and the distance from it is an indication about how “understeering” the car is (or, in better terms, how stable it is).
In such a situation, what is happening is that the front tires saturate before the rear ones, and cannot produce any (or nearly any) Yaw Moment anymore (or, anyway, the yaw moment they produce is smaller in magnitude than the stabilizing one produced by the rear tires). The net yaw moment is negative, meaning that the portion that the rear tires cornering forces are still able to produce overcomes the one coming from the front tires cornering forces, resulting in the car re-aligning itself: to use a proper language, we should say that the car is stable, more than understeering, since what is actually happening is that the Yaw Torque still available if the Ay further increase over the trimmed condition tends to steer the vehicle back, not to further rotate it.
The opposite is happening, if the maximum lateral acceleration is achieved with a net positive yaw moment in place. In this situation, the rear tires saturate before the front ones and the vehicle is unstable.
This explains why, ideally, a neutral car is able to corner faster in a nearly steady state condition: the right peak of the diagram would sit on the horizontal axis and the four tires would be saturated simultaneously, producing the maximum achievable grip exactly in steady state condition. On the other hand, anyway, such a behavior would leave the driver without any mean to further change vehicle’s path, since both the front and rear tires have nothing more to give.
All of the above is, of course, only an ideal situation, since the Yaw Moment Diagram itself is, in the real world, changing continuously its shape and dimensions depending on speed (downforce), tire conditions and temperatures, longitudinal acceleration, etc. This idealized approach is anyway useful to understand certain phenomena and to describe car behavior in certain situations.

This brings up another very important point about the Yaw Moment Diagram, which is the concept itself of over and understeer. This discussion could become philosophical, I will do my best to avoid that, here.
Anyway, there is, there has always been and there will always be a very complex discussion about how to define understeer and oversteer and, even more complicated, how to measure, using the available (measured) data, how much a vehicle understeers or oversteers when driven on track by a real driver.
The truth is that, most of the theory behind the concepts of understeer and oversteer (covered again deeply in “Race Car Vehicle Dynamics”) has been developed under the hypothesis of the tires being in their linear range (where cornering forces are roughly proportional to slip angles) and using the bicycle model approach.
Under these assumptions (which are seldom verified with a race car cornering at the limit) one of the most known and used way to quantify if a car has understeer or oversteer (and this is advocated by several race car authors/engineers and also shown in RCVD) is to compare if the used steered angle is bigger or smaller than the so called Ackermann Steering Angle or Ideal Steering Angle (Wheelbase divided by corner radius). The truth is that, most of the times, you cannot do much else on the track when looking data, sometimes mainly because of lack of other information (it happens very often to me, to even have no yaw rate channel in my data).
Beside that, you always have to rely on driver feedback, since a good driver will always try to drive around a “problem” and find a way to use the car as good as possible, also when it doesn’t really handle properly; this means that, often, he will somehow “hide” the problem itself, making difficult to objectively evaluate it looking to the data: he will, anyway, inevitably be slower when the car is not giving him/her the right “feeling” or not exploring its full potential. And that’s why, often, good drivers prefers slightly understeering cars, although it could not be the best choice about performance: this behavior simply make them easier to push at the vehicle limit, even if this limit seats a step lower as where it could be.
Anyway, the above described approach to quantify how much understeer your vehicle has is formally incorrect, since a good driver will probably most of the times corner in a condition where the tires are not operating in their linear range anymore. All the linearity assumptions fall off and the approach itself becomes practically wrong (unless it could still be useful, when we don’t have anything better, and I have been happy to use it for several years).
It is clear, anyway, that, at least when developing a simulation tool, we should aim for something “better” (or formally more correct) and try to develop “weapons” that can tell us more about our car’s behavior, not only a comparison between Ackermann and real steering angle.
The Yaw Moment Diagram could well be one of these weapons, above all when backed with proper testing and calibrated with good and trustable driver feedback.
The idea should be to create some reference numbers/situations where we know the driver is happy and performance is good and identify which metrics are important and which values we should target for. This is what Claude Rouelle would call a “magic number”. As his other “magic numbers”, see for example Total Lateral Load Transfer Distribution, it should help us to identify when and why the car is performing as its best, to try to reproduce these conditions when needed.
Of course, the YMD should not be the only tool to be used, here: a race engineer has to look anyway to many other things when setting up a car, beside the pure cornering (see straights, for example!).
Anyway, when correctly developed, it could give a much better picture of how the car performs in corners than using only TLLTD, allowing for example to assess the influence of speed and downforce levels and distributions or a change of tires and to predict more realistically what to expect in terms of balance and stability.
Going back to the understeer/oversteer discussion, as I said, we actually should not speak about understeer and oversteer anymore, when working in the non-linear range of tires, at least not in the way we are used to think about it in their linear range (typical assumption for road cars investigations). This point has been analyzed already in RCVD, where the authors suggest to use the terminology “push” (for a car that tends to go straight in a corner) or, on the other side, “loose” (for a car where the rear axle tends to overcome the front one).
This is very much connected also to the concepts of stability and controllability, which are normally very difficult to define and equally difficult to quantify, at least for a running car.

The latest point that we need to discuss about the metrics we can extract from a YMD is the already mentioned stability and controllability.
Controllability is meant here as the ability of the driver to direct the vehicle as he/she desires or, in other terms, to have the power to control the direction of the vehicle through the steering wheel, creating a certain net Yaw Moment.  Consequently, to study if and in which extent a vehicle is controllable, we will look at how the Yaw Moment changes with respect to the steering inputs.
Stability normally refers to how the vehicle reacts to input and disturbances: a system in general is said to be unstable when, following an input or a disturbance, it doesn’t tend to recover its initial conditions but tends to diverge.
Since, as we saw, a racing car operates mainly as a non-linear system (at least at its limit), investigating stability and control-ability is pretty complex and, as I said, is very complicated to really quantify them objectively, above all when analyzing track data (since the driver has also a very profound influence on how the vehicle behaves, because his/her input directly dictates also the reactions that we can look at).
Being both stability and control-ability so strong related to the forces that the tires produce (which, as we saw, depend directly on Beta and Delta), we can understand why the Force Moment Approach (originally thought on the base of constraint testing) could give so many information about them, allowing to study the action that the vehicle can “offer” to the driver to control its path or to stabilize itself.
What is interesting to notice is that, as we mentioned, when the front tires have saturated and cannot produce any more force, the lateral acceleration could still increase (as a result of the forces produced by the rear tires) but the driver has lost its control on the vehicle path through the steering wheel. The vehicle would anyway be stable and, probably, easier to handle for many drivers.
It is then interesting to investigate how a certain vehicle/setup/tires combination performs in terms of stability and control-ability when the lateral acceleration is starting to increase (for example at the beginning of a corner) or when it has reached its maximum (or its steady state maximum value). In both cases, we will mainly look at how the Yaw Moment change with respect to the two main drivers for tire forces creations, Beta and Delta.
After this long (and hopefully not too boring) introduction, let’s now take a look at how the tool was practically built up.
As for the previous steady state cornering tool, Excel Solver and loop computing are doing here the whole computational work.
The vehicle model is a four wheel one; lateral load transfer is considered, although I am not looking into the effects of roll and heave on suspension geometry and wheel angles: although I am considering the effect of load traasnfer on final tires vertical loads, I am not looking at the effects of suspension movements.
Downforce is also considered, playing a key role in defining each wheel’s final vertical load. Static camber can also be considered (since I am using a Pacejka formulation to extract tire forces), but, for the time being, I am assuming it equal to zero, since I would anyway not consider its variation due to roll or heave. The wheels are supposed to always be perpendicular to the road for this simplified simulation.
I am also assuming a parallel steer setup or, more precisely, I am assuming that both the wheels on each axle are experiencing the same slip angles (so also no toe at the moment), using the bicycle model approach to calculate them based on Beta and Delta at each iteration.
Moreover, in a first iteration, I didn’t consider the tires self-aligning torque but then I inserted them in a second step. We will take a look at their effect on the diagram shape and on the results.
Summarizing, the assumptions we are considering are:

  • Equal left-to-right mass distribution
  • Fixed longitudinal CG location
  • Fixed downforce (ClA) and Downforce distribution values (no ride heights and rake effects simulated)
  • Fixed Lateral Load Transfer Distribution (TLLTD, which could be calculated in the future directly from an integrated excel module, where all the setup info are input and the suspension parameters are given)
  • No suspension kinematics effect
  • Same wheel angles left to right (corner radius calculated at the CG, using the bicycle model approach)
  • Tires produces Fy; cases with and without Mz, no longitudinal forces are considered

The simulation is performed assuming a certain speed and, as a consequence, the downforce acting on the car. For each Delta and Beta combination (which defines necessarily a front and rear slip angle, using the bicycle model), the tool iterates on the lateral acceleration using Excel Solver: lateral acceleration produces weight transfer, “deciding”, together with downforce, how much vertical load acts on each tire; this vertical load is fed into the tire model to output the cornering force and the Mz that each tire produces. The iterative process goes on (changing the Ay value) until the sum of the cornering forces produced by each of the four tires is not equal to the force required to balance the car at the picked Ay. During this process, being the speed fixed, also corner radius changes, coming into play in defining the final tire forces, through the definition of front and rear slip angles with respect to Beta and Delta.
When equilibrium is found, the values are stored (Lateral Acceleration, net Yaw Moment, slip angles, etc) and a new Beta and Delta combination is picked for the next step. For this study, Beta and Delta sweep between 12 and -12 degrees, with 1 degree steps.
The diagram is then built up drawing all the constant Beta and constant Delta lines. Moreover, I calculate some metrics of interest out of the results.
The scenario I´m presenting here is a very high speed corner (240 km/h). As a consequence, downforce and downforce distribution are key players on the final results.
The following pictures show the results for a high downforce, 1000kg heavy sport car cornering at very high speed and assuming a TLLTD equal to 0.5 (no tires Mz considered for now).

YMD-no Mz-TLLTD0.5

The main metrics I am extracting are:

  • Maximum Lateral acceleration
  • Maximum Lateral acceleration in trimmed condition (N ≈ 0)
  • Yaw Moment at Maximum Lateral Acceleration (tells how far we are from a neutral setup and gives indication about stability)
  • Slip Angles, Beta, Delta and Cornering Forces values at Maximum Lateral Acceleration
  • Maximum Yaw Moment
  • Slip Angles, Beta, Delta and Lateral Acceleration at maximum Yaw Moments
  • Variation of the Yaw Moment with respect to Delta when Beta is equal to 0: should give an idea about how controllable the car is in corner entry
  • Variation of the Yaw Moment with respect to Delta when Beta is equal to the Maximum Lateral Acceleration value: should help to understand how controllable the car is at the apex or, anyway, at its maximum cornering usage
  • Variation of the Yaw Moment with respect to Beta when Delta is equal to 0: should depict how stable the car is in corner entry
  • Variation of the Yaw Moment with respect to Beta when Delta is equal to the maximum Lateral Acceleration Value: should point out how stable the car is at the apex or, anyway, at its maximum cornering usage

YMD res-no Mz-TLLTD0.5

Let’s try to understand what their meaning is and, in a second step, to see how they change if we modify something on the car or test assumptions.
The first line (“Max Ay”, measurement unit being “g”) tells us the maximum lateral acceleration the car can achieve at the test speed or, in other terms, the minimum corner radius of the path the car can follow. It gives info about the maximum cornering performance envelope the car is capable of.

The second line (“N @ Max Ay”, measurement unit being Newton-meter) gives the Yaw Moment value at the maximum lateral acceleration. As we discussed, a positive value, as in the picture, means our vehicle is unstable at the limit, with the rear axle tires saturating before the rear ones. In our case, as we will see comparing this simulation/setup to the other I tested, N is very small, pointing to a nearly neutral car at the maximum lateral acceleration. This is further confirmed looking at another metrics, namely the maximum lateral acceleration in trimmed condition (“Max Ay @ N=0”): it is in fact very close to the overall maximum lateral acceleration in our case, confirming how the car is nearly neutral at the limit or, in other terms, how close is the steady state maximum acceleration (similar condition to what we could have in a very long corner more or less at constant speed, for example, although it is a very unusual condition in a race car environment) to the overall car cornering limit.
Since the only moment where we could have a close-to-trimmed-condition situation in a corner is probably the apex, having a higher steady state acceleration should mean having an higher minimum speed in the corner, so, potentially, better lap times. Although, assuming a close-to-steady state condition for corner apex could be sometimes not completely appropriate, above all in certain “highly dynamic” racing environments, like autocross.

Beside the “only-registering” metrics, like the slip angles, Beta and Delta the car experiences at maximum lateral acceleration (you can see more or less the same data also immediately below the “Max Ay @ N=0” metric), another useful information is given by the maximum Yaw Moment achieved during the simulation (“Max N”), which gives an idea about how big is the torque at our disposal to rotate the car, for example in corner entry.
The following line (“Ay @ Max N”) indicates which lateral acceleration the car is experiencing when it is producing the biggest Yaw Moment possible.
The latest metrics we will discuss here are probably the most complex ones, being them mainly related to stability and control.
The first of them shows the variation of the Yaw Moment with respect to Delta, when Beta is equal to zero (“dN/dδ @ β=0”). Since we are looking at a snapshot of how the car could perform in the region where Beta is close to zero, we can assume that the result should be representative of how the car behaves in corner entry in terms of control (what the driver could obtain acting on the steering wheel). We are here moving on a constant Beta line, in particular on the one “β=0”: this graphically explains the positive value of this metric, basically stating that, if Beta is equal to 0 and we start acting on Delta (steering) to steer the car toward right, we produce a positive variation of the Yaw Moment, cause we initially only have a cornering force on the front tires (the rear slip angle, being Beta = 0, is at the beginning also equal to zero). It will be interesting to compare the absolute value of this metric with different setups, to see if and when it is increasing or decreasing, meaning a more or less controllable car.

The second one shows the variation of the Yaw Moment with respect to Delta, when Beta is close to its value at maximum lateral acceleration (“dN/dδ @ β Aymax”). This time, we look at a region close to the maximum lateral acceleration; thus, we could assume that this metric depicts what the car does when at the apex or, anyway, to its maximum usage in terms of lateral forces. Again, we are moving on a constant Beta line but, depending where we are in terms of tire (or axle) saturation, now the variation could even become negative, as in our case: that means that if we would try to further increase Delta’s magnitude by another degree (still keeping Beta constant), we would see the Yaw Moment decreasing. In such a situation, the front tires have lost the power to generate any Yaw Moment and, actually, increasing Delta any further (so, as a consequence, increasing the front slip angle), the tire forces generated at the front axle would decrease.
In our particular case, considering a right corner, lateral acceleration and lateral forces are positive and the Yaw Moment is positive if clockwise oriented. Delta is also positive, so what we are analyzing here is what we get when increasing it by one degree (with its variation being positive). Since the net overall Yaw Moment we get at Delta = 6 degrees is smaller than the one we have if Delta is equal to 5 degree, its variation is negative. That means that, at its cornering limit, the car is loosing the ability to be controlled through the steering wheel.
The third metric of this section is the variation of the Yaw Moment with respect to Beta, when Delta is equal to zero (“dN/dβ @ δ=0”). We are looking here at stability now and moving on a constant Delta line. Being again in the region close to the origin (Beta and Delta both close to zero), we can assume this metric shows how the car behaves in corner entry. More precisely, here we are analyzing the stabilizing effects produced mainly by the rear axle, when trying to rotate the car. Since having a positive Beta here produces a positive rear slip angle (being Delta equal to zero), the rear tires see a negative force and that produces a positive Yaw Moment and Yaw Moment variation (see sign convention picture and assumptions for reference). From a pure sign perspective, a positive Yaw Moment would create an angular acceleration “bringing” the car toward the corner, actually “destabilizing” the car or, in other words, making it turns, not realign: as I said, this is mainly the result of the sign of the rear Slip Angle and, being the behavior symmetrical, we can imagine a similar phenomenon in magnitude also in the other direction.

The fourth metric is the variation of the Yaw Moment with respect to Beta, when Delta is close to its value at maximum lateral acceleration (“dN/dβ @ δ Aymax”). As for the previous one, this parameter gives us a feeling about car stability but in proximity of maximum lateral acceleration (so, again, here we look at the corner’s apex or where the maximum usage of lateral forces takes place). We move here of course on a constant Delta line, so we are only looking at the effects of Beta’s variation on Yaw Moment.
As we may see in the picture above, this metric’s value is, in our case, negative. We have to be careful about signs, here. We look at what does it bring to increase the Beta magnitude by one degree (from 5 degrees, value where we find the maximum lateral acceleration, to 6 degrees in magnitude, in this case). In particular, let’s consider now what it happens in a right turn, with positive lateral acceleration: tire forces are positive and so is the Yaw Moment if clockwise oriented, so if “turning” the car into the corner. On the other side, in a right corner and with the car close to its maximum lateral acceleration, Beta is negative and its value is here equal to -5 degrees. What happens if we increase its magnitude by another degree, bring it to -6 degrees?

The Yaw Moment (which is positive at maximum lateral acceleration, as we saw when looking to the “N @ Max Ay” metric) increases by about 55 Nm, while the Beta variation is negative. Hence, the negative value of this metric. The Yaw Moment’s increase is driven by the rate at which front and rear cornering forces change: they both decrease, switching Beta from -5 to -6 degrees, but the rear cornering forces change is bigger in magnitude than the front one, determining the net Yaw Moment’s increase.
This confirms the car tendency to instability at the limit and gives a “number” to quantify this behavior: this number is what we can use to somehow quantify if and how car behavior changes with a different setup or different assumptions.
If we consider this latest metric result with the one we got for the “dN/dδ @ β Aymax”, we can see a very interesting point. The car (or we should better say, its simplified model) is loosing its control-ability and it is also, in this particular situation (we have to remember we are, for example, ignoring the Self Aligning Torque effect at this stage), unstable. A pretty funny situation, isn’t it?
As we said, this model reaches its maximum trimmed lateral acceleration in a situation where the overall yaw moment is very close to 0; as a consequence, the maximum lateral acceleration in trimmed condition is very close to the overall maximum lateral acceleration. The vehicle is nearly neutral at the limit or, more correct, our vehicle model is, under the simplified assumptions we are considering, pretty neutral at the limit.
With such a vehicle behavior, the driver has not many means at its disposal to really control the car, although it is probably the configuration that would theoretically produce the maximum cornering performance. Anyway, the question we should ask ourselves is: can a real driver use it comfortably, fully exploring the best performance of the “car-driver” package?

It is anyway worth to remember that, what we have just analyzed is the result of the simulation where we ignored the self-aligning torques produced by the tires.

Now that we have taken a look at the meaning of the main metrics I am extracting, we can finally take a look to what happens to each of them and to the Yaw Moment Diagram itself when changing any of simulation parameters.
To follow up what I just said about the Self Aligning Torques, let’s take now a look at how the model’s behavior changes if we take them too into account.
Before to look at the bare results, just a word of warn: what I present here refers to this vehicle and, most importantly, only to the tire model I used for this study (and, here in particular, to how the Pacejka set I used depicts the tire self-aligning torques produced by the tires). Any generalization could lead to an error, since how a vehicle behaves at the limit depends of course very strongly on how its tires perform.
The picture below shows how the diagram itself looks like, if also the SAT is considered.

YMD-Mz-TLLTD0.5

And here below the results table referring to the same simulation:

YMD res-Mz-TLLTD0.5

The first thing to notice is that, although the Maximum Lateral acceleration stays the same (at least up to the second decimal), the maximum lateral acceleration in trimmed conditions drops slightly in comparison to what we have seen in the previous simulation.
This aspect is strictly connected to another very interesting metric, namely the “N @ Max Ay”, which became now negative, meaning the car is now stable at the limit. That is also confirmed, of course, by the shape of the diagram itself, with the extreme right peak now seating below the Ay axis, although only slightly.
As we already saw in other entries here, the Self Aligning Torque produces a stabilizing effect and, in this particular case, this actually means switching from a potentially unstable vehicle to a stable one.

Beside this, which is probably the most important point here, it is interesting to notice how the maximum net Yaw Moment slightly increases: if you look to the Yaw Moment signs, it is easy to understand why: in a right corner, the greatest Yaw Moment value in magnitude is actually negative and is achieved with a set of negative Beta and Delta. This is not a realistic cornering situation, as far as I know! This metric should anyway give a feeling about how big the overall Yaw Moment can be and it is nonetheless interesting to see how this value increases when adding the self-aligning torque to the game.
While the “dN/dδ @ β=0” (Control-ability in corner entry) decreases a bit (confirming how the Self Aligning Torques produce a stabilizing effect in this phase, here reducing the overall available net Yaw Moment to steer the car into the corner), it’s intriguing to see how the “dN/dδ @ β Aymax” (Control-ability at corner apex) switches from a negative to a positive value. Interesting enough, this change is strictly connected to the sign’s change of the net Yaw Moment at maximum lateral acceleration, which is now negative. That drives, practically, a negative net Yaw Moment both at the maximum lateral acceleration Delta step and at the following one, under the influence of the Self Aligning Torques produced at the corresponding slip angles by this particular tire model.
It is anyway interesting to notice how the net Yaw Moment (now being negative, as we said), is, in magnitude, still bigger at the maximum lateral acceleration Delta value as it is at the next computational step. Here, this phenomenon is driven by the SAT itself, reducing its effect and magnitude as the front slip angles increase.
So, again, the tires have actually already saturated (exactly as it was in the “no SAT” case), as we can also understand looking at the cornering forces produced at the front and rear axle, which stays exactly the same as in the previous case; what we see here is only the tires MZ effect. It is still true that, at the limit, the car is loosing the ability to be controlled through the steering wheel, as in the previous case, but here the self-aligning torque is coming over the Yaw Moments produced by the front and rear tires (which were indeed very small). The car is, as we see, effectively stable at the limit now, but still, increasing the steering angle would not produce bigger yaw moments magnitude.
Nonetheless, the sign of this metric has changed, suggesting how, in this situation, we have to be a bit more careful about our analysis and always keep in mind what the effect of each “player” could be.

Regarding the two following metrics in the list, what we see is that the “dN/dβ @ δ=0” (Stability at corner entry) increases, under the effect of the Self Aligning Torque (as we could already expect), confirming the car is now more stable compared to the previous case of study, while the “dN/dβ @ δ Aymax” (Stability at corner apex) further decreases (or, in other terms, increases its magnitude still being negative): again, here we need to be careful with the signs and with the effects produced by the Self Aligning Torque.
If we still consider a right corner, as we did in the above explanation about this metric, we already saw how the net Yaw Moment produced by the tire forces is positive and increases its magnitude switching from the maximum lateral acceleration Beta’s step (-5 degrees in our case) to the following one (-6 degrees), determining, because of the negative variation of Beta, a negative value for this metric.
In particular, we saw how both front and rear tire forces decrease, when switching Beta from -5 to -6 degrees, but the rear tire forces ones do it at a higher rate, leading the Yaw Moment to increase.

Now, we have to consider inside this picture also the effect of the self-aligning torque: it makes the net Yaw Moment at both Beta’s steps negative, with a bigger magnitude at -5 degrees as what we have at -6.
Hence, we see again the effect of tire saturation, now also on the self-aligning torque. Since the net Yaw Moment is negative at both the two steps, we have a positive variation, which leads again to the negative value of this metric.
An interesting point coming out of this analysis is that it seems to be possible, with and without considering the self-aligning torques, to understand what is going on with tire saturation by looking to the sign of this “variation” metrics.
Nonetheless, I would not jump to conclusion too quickly, when interpreting the diagram. I would not exclude that engineers with more experience about this topic could maybe extract their takings quicker and easier than me.
In any case, the interpretation process itself can teach a lot about car behavior in general and about this particular simulation in particular.

We can now take a look at what happens to the Diagram and the relative metrics as a consequence of a setup change. We can analyze, for example, how the vehicle behavior changes if we increase the TLLTD value from 50% to 60% (that could be, for example, the result of a stiffer front antiroll bar or softer rear one, or a suspension geometry change that moved the Lateral Load transfer distribution toward the front, for example reducing the Roll center height at the rear or increasing it at the front).
The setup change we are looking at here is pretty substantial and it is not something you would want to do so lightly on the track. This should anyway help to better see how and how much such a modification could change our model’s behavior and balance and the Yaw Moment diagram’s shape and its metrics.
From now on, the Self Aligning Torque of each tire will always be considered.

So, without hesitating any further, here below is how the YMD itself looks like after the above described change:

YMD-Mz-TLLTD0.6
And below you can see the results table referring to the same case:

YMD res-Mz-TLLTD0.6

The first thing we see is a very slight decrease of maximum lateral Acceleration: although slightly, the setup change effectively reduce car’s cornering potential (actually both in trimmed and untrimmed conditions); moreover, the maximum lateral acceleration is now achieved at a bigger Delta value, as we could expect from a setup change that should increase the understeering tendency.
This later point is also confirmed by the diagram’s extreme right vertex position (or, looking at the table, from the “N @Max Ay” metric), which now seats lower compared to the previous case (the “N @Max Ay” has now again a negative value, as for the previous simulation, but a bigger magnitude, confirming how the vehicle has now become more stable).
While the overall maximum Yaw Moment doesn’t change significantly, we see a pretty sensible reduction of the maximum lateral acceleration achievable in trimmed conditions: this is directly connected to how the diagram itself moved toward a more stable behavior, consequently making the extreme right peak to slide downward and making its interception with horizontal axis to move more on the left.

What is happening to the “Variation” metrics?

First thing we see is that the “dN/dδ @ β=0” (Control-ability in corner entry) is further reducing, confirming how the vehicle became more stable (here, this means less available net Yaw Moment to steer the car). The “dN/dδ @ β Aymax” metric (Control-ability at corner’s apex) is, on the other hand, further increasing compared to the case with 50% of Lateral Load Transfer distribution at the front and Self Aligning Torque considered. Again, beside the pure number, it is interesting to notice how, again, the net Yaw Moment shows negative values at both the maximum lateral acceleration Delta and at the following step, with the latter showing a slightly smaller magnitude. Beside this, the Yaw Moment magnitude is anyway significantly greater than in the 50%TLLTD case (-300Nm vs -1600Nm c.a).

Its negative value in a right corner indicates an aligning torque. Interesting enough, here it is clear that the front tires have saturated, while this is not the case for the rear ones: between the two steps, we can clearly see a reduction in front lateral forces, while the rear are still (slightly) increasing. The car is clearly understeering and, to gain control-ability, the only way would be to reduce the cornering speed: any further increase of the steering angle produces only a further reduction of the front tire forces.

The following two metrics also confirm the same tendency. The “dN/dβ @ δ=0” (Stability at corner entry) one, has an higher value than in the previous case, confirming how the tire forces that the rear tires produce in corner entry can be bigger and help to further keep the vehicle stable in this phase.

The “dN/dβ @ δ Aymax” (Stability at corner apex) line, on the other hand, has again a negative value, which increased in magnitude in comparison with the previous simulation. As in the previous case, here the overall net Yaw Moment is negative and its magnitude decreases if we increase Beta by one degree (from its maximum lateral acceleration value to the bigger one). Being N negative in both steps, what happens here means, again, a reduction of the overall aligning moment when increasing Beta. In any case, still being the vehicle stable, this seems to indicate that, increasing Beta, we loose some of the self-aligning effect and, in other terms stability. This makes physically sense, since our Beta’s change practically produces a growth of both front and rear slip angles (lateral acceleration is close to its maximum, here) and, while the front axle’s cornering force stays nearly the same because of front SA change, the rear axle one decreases more significantly, reducing its stabilizing effect.

This closes our analysis about what happens and how the diagram changes for a certain setup change we put in place on our car (in our case, we are pretending this has produced a switch in Total Lateral Load Transfer Distribution from 50% to 60% at the front axle).
As we have seen, if, on one hand, looking to the diagram and reading the metrics gives an immediate understanding of some of the reactions that we could expect when changing any parameter on the car, a more detailed analysis of the simulation results could anyway show important information that should not be taken for granted.
In any case, the Yaw Moment diagram could be implemented as a more completed method to classify and predict what to expect in terms of balance, control-ability and stability when changing a certain setup parameter.
Of course, as for each and every simulation we could perform, the better and more detailed is the data we can access, the more reliable are the results we can expect. What seem to be anyway necessary, at least at the stage I personally am with my knowledge about this topic, is a kind of “validation period” during which the engineer can cross check driver feedback to the results shown by the diagram, at least to identify which is the “right” window where the car should be for the package (driver-vehicle) to work at its best.

One interesting point about this is the possibility to understand and study in more detail car reactions in both low and high speed corners: here below you can see two pictures of the resulting diagrams with the vehicle in the 50% TLLTD configuration cornering at very low and medium-low speed (I purposely didn’t change the diagram scale to let you see how much smaller it gets, compared to the previous ones).

YMD-Mz-TLLTD0.5-Low Speed

YMD res-Mz-TLLTD0.5-Low med Speed

The insight we could gain from this approach would be at its best if, as I said, we could access detailed and reliable information about the car and a well validated tire model.
Some of the data/assumptions that we ignored for this article but could very beneficial to have and implement are:

  • Proper suspension geometry model, above all with regards with roll and ride height variation
  • Complete aeromap, including effects of front and rear ride heights
  • Any non-linear suspension behavior, like the effects of bump stops of any kind

In any case, also if detailed data are not available, I still think “something is better than nothing”. Such a tool could still be useful, even if we don’t have access to detailed info or we have to guesstimate some of the values we need for our models.
Beside the availability of useful results, the building process of such a tool can still teach a lot about vehicle dynamics in general and about your car in particular.

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