Vehicle Dynamics: Lap Time Simulation.
Updated: Jul 20, 2020
As technology has progressed over the decades and advancements in computer technology haven made, automotive engineering is a discipline that has reaped the benefits. The miniaturisation and digitisation of sensors has allowed a whole new world of data to be gathered and analysed around vehicle behaviour.
Powertrain control sensors lead the way in the digitisation of control systems. Chassis sensors soon followed - measurement of damper displacements, translational and rotational accelerations, temperatures, steering angles and a whole range of other parameters have allowed engineers to develop a complete picture of the cars steady state character through real time observation, importantly giving insight it’s response to dynamic and transient situations.
With the advent of computer simulations; FEA, CFD etc, the opportunity to use mathematical models to predict natural phenomena produced great advancements in their respective fields. Vehicle dynamics theory has long since derived the equations of cornering. The next logical step for automotive engineering was then to start to explore opportunities to build mathematical models of vehicles.
Over the years, the accuracy of these models has improved greatly through developments within multi-body dynamics software, allowing every link, joint, structural member, spring and damper in the real system to be simulated with their own relative movements, compliances and damping rates.
At this stage, even highly non-linear components and their influence on vehicle behaviour, such as tyre models are developed enough to use for analytical purposes.
So here we are today, where in modern automotive engineering and motorsport, vehicle dynamics simulation is one of the most important elements of vehicle development. Starting at the design concept stages and running through right until the end of the last race of a season.
General dynamic simulations can be used during automotive development to assess a concept’s basic character and reaction to things like constant radius corners (understeer gradients), step steer events (stability & balance) and even abuse cases such as curb strikes and potholes to understand component loadings and frequency responses.
What i’d like to focus on here though is the rise of lap time simulations in a motorsport application as a means to really hone in on the optimum setup of a vehicle platform analytically, generating virtual data on it’s response to input measured in the same manner as physical chassis sensors.
There are really two main ways in which these simulations are used to prepare a car for a race or test.
Scenario #1. It can be tasked with the objective of understanding lap time sensitivity to certain elements of the car performance. Something which may be useful in deciding which elements of the car to focus development efforts on - the aero package or the mechanical grip to name an example.
This can also be super useful when in the concept development phase of a design, when you’re making choices on the basic architecture of the car. It will at some point be logical to investigate the question “At this track, is the fastest lap time more dependent on downforce, drag, tyres, suspension setup, engine power or weight?”
Scenario #2. Once a complete model of the vehicle has been built and correlated from real data gathered on a previous run at that particular track, simulations can be used to fine tune setup.
This kind of study would start with a question like “What combination of adjustments to my setup will give me the fastest lap”
For example; you may have damper settings, ride springs, front/rear wing adjustments and ride heights available to play with to dial in a race trim. With simulation software, you can evaluate all the possible combinations of those variables analytically to understand the combination that provides the best result for a specific KPI (Key Performance Indicator).
KPIs can be lap time, lateral acceleration or, with a narrower view, down to small details such as corner exit acceleration etc.
Let’s say there were 5 settings for each of the variables listed above, thats a total of 78125 (57) simulation runs that can be assessed by the software. It doesn’t take long to see the cost and time advantages of simulation vs manually completing laps in the car!
Where the latter style of vehicle dynamics simulation looks at combinations of setup parameters to lead you to the best setup with respect to your particular KPI without consideration the relative weighting of their influence, the former method is more precise - studying the sensitivity of the KPI to a particular parameter and enabling you to better understand what’s happening to the chassis from a theory.
At this point, you’d struggle to find a high level race team who aren’t using simulations as part of their day-to-day, especially so during the season as part of preparation before practice, qualifying and race events.
The optimal setup for a particular circuit is a constantly moving goal post. Changing weather and other ambient conditions can call for a very different approach throughout the race weekend, so it’s vital that we as race engineers are precise with our approach - where the benefits of an analytical, qualitative approach are essential.
So let’s get into the practical side of vehicle dynamics simulations and demonstrate with some lap time sims of the above two scenarios. I’ll take you through the process.
Dynamics simulations have seen mainstream use since the early 2000s through various software packages. I’m using VI-grade, which is used widely throughout automotive and motorsport disciplines.
So, the first thing to be aware of, as ever with simulation is the concept of good data in = good data out. A representative car model is essential.
Suspension hard points, CoM locations, kinematics and compliance, aeromaps, torque maps are all fairly straightforward to implement mathematically, but most importantly and with most difficulty - tyre models must be accurate in order to increase the correlation of simulated data with measured data.
Being a visco-elastic component with hysteresis, tyres are notoriously tricky to model as there are so many variables that dictate their frictional coefficient at any given moment. Normal force, temperature, surface quality, moisture, inflation pressure, are all some of the variables that create a very non-linear problem. These have always been traditionally one of the big issues with correlation of simulation to reality, although improvements have been made in recent times, and will continue to be made.
Either way, once you have your vehicle model you’re ready to start simulating.
For starters let’s look at a simple lap-time sensitivity study.
Normally, the first task you’d perform is to correlate your simulated data with real data, it’s unlikely that they would immediately mirror each other, so it can be a case of trial and error; going back to simulation setup to adjust correction factors and scales for parameters such as frictional coefficients and so on.
Once a level of correlation has been reached (±5%), we can label this the reference, or base setup and begin with the main simulations.
I’m going to add 10% to each value and record the % change in lap time that follows.
Here are our chosen chassis parameters, with their initial and new values;
So for each of the parameters a simulation was run on an arbitrary circuit and compared to the base value.
The software works with an iterative approach, so it will simulate a run of the track using performance limits established through an initial quasi-static simulation, if it reaches an an unfeasible state in a particular corner, determined by either excessive deviation from a pre-defined driver path, or excessive wheel slip (lateral and horizontal?), the relevant tractive, braking or cornering factors are scaled back until feasibility is met.
Once this process is repeated over an entire lap, the simulation is complete!
Here’s an example of the solved base configuration:
Now, the data is ready to analyse.
In the same way as real data taken from a car after a run, the software allows post-processing of the results. Data can be displayed in user configured plots; histograms and maths channels can be configured to show any relationships you’d like, importantly, data can be overlaid so you can compare datasets from different runs/simulations.
Ultimately, the data shows you everything, but another useful feature is the capability to visualise the lap using 3D graphics. Visualising car behaviour is another tool that can be used to understand what the data is telling you combined with physically seeing what the car is doing.
Below, we’re looking at a comparison between the base car and the car with the wider track width, it’s easy to see that the larger track width is producing a larger peak lateral acceleration (reduced total lateral weight transfer), the ghost car confirms that!
So, the final results?
This platform, on this track is clearly most sensitive to vehicle weight and CoM height. Minimum weight is usually set by regulations, and once the platform is designed and built, you’ll struggle to make big changes to CoM position, but it at least highlights the significance of getting it right. Around +150kg of weight added nearly 3s to the lap time!
The track surface here was perfectly smooth, so the spring and damper rates aren’t doing much to influence lap times, any change here would appear to be due to their influence on management of weight transfer during the lap.
Interestingly, the lap time wasn’t so sensitive to aero performance, perhaps indicating that the track heavily features low speed corners. On the high speed straights, the drag penalty outweighs the gains in terms of lateral acceleration. Regardless, on a car with not so much downforce to begin with, +10% isn’t actually a significant change to normal force on the tyres. All useful information gained.
Of course i’m just trying to demonstrate concepts so this isn’t such an in depth experiment. For example if you changed the longitudinal CoM position you’d likely also change spring, damper and ARB rates, as well as your tyre width to accommodate the change. For these purposes though it’s a nice demonstration tool.
On to scenario #2.
As discussed earlier, it’s more useful/practical for race engineers to optimise setup for an event via running numerous lap simulations with a large number of different setup combinations, investigating a number of factors (setup variables in our case) in a full-factorial design and outputting the data with reference to a chosen KPI.
More often than not this will be lap time, but for example maybe you’d want to chose a setup conducive to a strong corner exit acceleration to gain an advantage over your competition preceding a long straight. With this, you have the freedom.
It unlocks a wealth of strategy considerations that would be really quite tricky or even impossible to dial in without some form of analytical approach!
Let’s run through the process.
In all honesty, to run a practical simulation with just three options for 8 factors would be 6561 separate simulations, which my office computer is not quite equipped to run in a decent time frame just now (vehicle dynamics simulations do have cloud based solutions with much greater computing power, but i don’t have access to that for this article). Instead i’ll run a simpler study of just 81 :-).
VI-grade uses simple scaling factors for this kind of analysis, so i’m going to scale each factor by -0.5 and +0.5 relative to base setup and run the study.
Visualised, this creates the following experimental design:
What the above plot allows you to do is visualise how the experiment will run. I’m a visual learner so i often find plots like this to be helpful. It’s also interactive, which allows you to examine a KPI i.e. lowest lap time and trace it back, even highlighting which variant it is.
So, it was a draw between variant 78 and variant 81 in terms of laptime, but that doesn’t mean the handling characteristics are the same, so some further conditions must be taken into account, as a quick addition, i added peal lateral and yaw accelerations.
In addition to this mini data analysis, most lap-sim softwares offers a level of post-processing. Drawing from many in-built data channels and user configurable maths channels to get into some complex relationships. Below, you can see the comparison between the two variants, same overall lap time, but clearly a different approach to the driving character and sector times!
There can be many inputs behind this behaviour and as a driver, reasons you may prefer one setup after another, but that’s not for today. The scope of this article isn’t a dynamic analysis.
This is an example of when there are ‘caveats’ to be understood in order to apply the technology effectively. For example the results from lap time don’t immediately take into account things like driver preference or indeed drivability.
The simulation does not inherently understand the driver’s perception of ‘handling’, which certainly can’t be neglected unless you’re looking to produce a car that the driver has no confidence in.
Perhaps an effective measure of balance is the understanding of a chassis’ static margin, which relates the magnitude of the moment arm between the CoM and the resultant of lateral forces generated during cornering, known as the neutral steer point. Configuration of a maths channel would be appropriate here in order to investigate.
Ultimately the subjective, human element is still valid input in any setup and simulation results can’t blindly be taken from the program and implemented. An experienced hand is still needed.
With that i hope I’ve introduced those of you that were unaware, or wanted to learn a little more around lap simulations within modern motorsport.
Where is simulation going in the future? Effort is usefully focused on improving factors that are more complex to model. Things like exact driver paths, tyre models, brake performance modelling, damper hysteresis and other non-linear variables in performance are all things that if improved, will provide stronger correlation between measured and simulated data so we can expect progress to be made there.
There has also been a lot of focus recently on DiL simulation, which incorporates a real driver into the simulation as it is completed real-time. Compared to the script used in most programs, this provides a much more representative scenario, in which real driving styles and techniques can be used and valuable subjective feedback gained.
Expect the importance and reliance of vehicle dynamics and lap time simulation to only increase!
Thanks to VI-grade for their involvement in this article.