LMP2 Car Setup Optimization
Please enjoy the 2-minute summary gallery below, or scroll further to explore my work in greater detail
I believe that change is not something to be simply dealt with; rather, change is something to take charge of and make into your own opportunity. The 2020 COVID-19 pandemic shook the world, and I went into quarantine with my family for over 5 months. I consider myself lucky to have been blessed with all that time alone in a position free of responsibility. This time was mine to make the most of, and this is one of the significant projects I undertook during that period.
On April 9th, Danny Nowlan, Director of ChassisSim Technologies, announced the launch of the ChassisSim Online Race Engineering Competition. In this competition, for a small entrance fee you were given a vehicle and circuit model, as well as a temporary license of ChassisSim, good for 100 simulations. The car in question was an LMP2 race car, pictured below, running on the Circuit 24 Hours of Le Mans. Competitors are free to adjust the setup of the car within a set of regulations, and whoever could achieve the fastest lap time in 100 iterations would win a cash prize. My friend Derek Moore and I decided to team up and tackle this project together (Spoiler alert, in case you don't read to the end - we finished quite well!). On this page you will learn about some tools that I developed to aid in our work, as well as a summary of the tuning decisions we made together to optimize our lap time.
The Ligier JS P217 as replicated in the model provided to entrants.
Before using our limited reserve of simulations, we agreed to use the provided parameters to understand as much about the vehicle as possible. Anything we learn could help inform where to begin with setup changes.
The first thing I did was to create a suspension setup table based on the parameters provided in ChassisSim. This would enable us to visualize the effects that suspension adjustments have on overall vehicle characteristics. The baseline setup is pictured in the table below. Some initial details that stood out were the differences in ride frequency and damping ratio. Another significant detail was the 63% front static lateral load transfer distribution, which is significantly higher than the front weight distribution (46%). It is discrepancies such as these that can point us in the right direction to determine where to focus our setup changes.
In addition, Derek used his custom kinematics software to evaluate the front and rear suspension pickup points. A brief evaluation showed that the sign of the front camber gain rate was opposite to that of the rear, and the front end was gaining positive camber over bump. This was a fast catch that could have potentially cost several precious runs to uncover.
Finally, ChassisSim included aero maps for lift, drag, and center of pressure as a function of front and rear ride height. This created an opportunity for a head start on setting ride heights for maximum aero performance without having to use a single simulation run! Starting from a framework initially developed for the vehicle tradespace analysis project, I was able to create a tool to evaluate the suspension and aerodynamic interactions of the car.
Aero Platform Optimization
As mentioned earlier, included in the vehicle parameters were ride height maps allowing me to track various aerodynamic characteristics:
Another important set of information was a bump-profile provided for the track. This enabled me to capture the spectral density of the track surface:
Taking the parameters from the setup sheet I built earlier, I simulated the vehicle using a 4 degree of freedom ride model (unsprung masses, body height, pitch angle). By capturing the partial differentials of the aero maps, I was able to linearize the change in downforce, drag, and pitch moment at any single operating point. These effects could be represented as spring elements, and incorporated into the ride model. Using a state space representation, I was then able to simulate the model travelling over the above track surface at a constant speed, constructing frequency response plots from the output signals:
The frequency outputs that I tracked were front and rear tire load, downforce, drag, and aero moment over the rear axle. By repeating the simulation over the full range of track speeds expected, I could construct a 3D map of the frequency response over the full range of vehicle operating conditions:
With all of the information put together, a graphic like the one below can be generated in seconds, making an easy visualization tool with which to compare different setups (again, the image below is for the baseline vehicle):
In order to maximize tire grip it is critical to minimize normal load variation - in other words, the amplitude of oscillation in the frequency response. As a general metric, the total volume under the 3-D response surfaces can be used as an indicator of the total load variation, which results in tire grip loss. This opens up an optimization opportunity to minimize the volume under the response surfaces. As a design exploration, I created a multi-objective optimization problem using ModeFRONTIER. The optimization objectives were to:
1) Maximize total downforce
2) Minimize total drag
3) Minimize aero moment (aka center of pressure) variation
4) Minimize tire load variation
5) Minimize aero balance offset from CG (as a starting point - optimal aero balance may be determined later).
The overall optimization workflow is pictured below:
With so many optimization objectives, it is impossible to come up with a single solution that meets all of them. However, I was able to utilize the ModeFRONTIER post-processing tools to get a visualization of the relationships between the tradeoffs, and create a set of design options from there.
For example, the visuals below demonstrate a trade-off between downforce and aero balance. Lowering static ride height and increasing rake, generally, increases the overall downforce produced, at the expense of a forward-biased center of pressure that could induce high speed oversteer balance.
Static rake angle (y) versus static ride height (x), colored by total amount of downforce produced.
Static rake angle (y) versus static ride height (x), colored by aero balance offset.
The relationship can also be seen in the figure below, where configurations with high downforce correlated with configurations with high aero balance error.
Aero balance variation (y) versus aero balance offset (x), colored by downforce produced.
Another trend can be seen above, where the aero balance variation has minimums at each end of the design space. This can also be seen in the graphic below. It seems that keeping the car at one extreme end of the setup spectrum will maintain a higher consistency.
Static rake angle (y) versus static ride height (x), colored by aero balance variation
Let's introduce spring, damping, and grip into the picture as well now. The figure below supports the intuition that softer ride rates increases mechanical grip at the wheel, by minimizing tire load variation over bumps. Damping effects are comparatively smaller.
Rear damping ratio (y) versus rear ride frequency (x), colored by rear tire load variation
These mechanical grip requirements, however, are at direct odds with downforce goals. This is because the high rake, low ride height setups require stiff spring rates in order to maintain a minimum ride height. The plot below is a good visualization of this trade-off. The lower donwforce range on the left side of the graph is not very relevant, as those are simply poorly configured and low-performing setups. As the graph moves to the right, however, there is a distinct trend where increasing downforce comes at the expense of increased tire load variation. This also correlates with the increased suspension stiffness, which is indicated by the color of the dots.
Tire load variation (y) versus downforce produced (x), colored by front suspension frequency.
The competition specifies a minimum dynamic ride height of 10 mm measured at the front. Since this is at odds with the low-ride height, high-rake conditions to maximize downforce, this drives the need for a high enough front suspension frequency to keep the front end off the ground. Since the rear end is not held to such constraints, the optimizer immediately converged to the softest frequency allowed. Similarly, front damping had a reasonable mid-range spread, while rear damping converged to the lowest possible.
Rear suspension frequency (y) versus front suspension frequency (x), colored by iteration count
Rear damping ratio (y) versus front damping ratio (x), colored by iteration count
One output I did not mention yet is drag. This is because even though tradeoffs do exist in minimizing drag, the sensitivity is much lower. Increasing downforce comes at the cost of increasing drag, but all being told, the total variation in drag among the most realistic design solutions is no more than +/- 1%. With much more drastic tradeoffs elsewhere, it did not make sense to focus too much effort on minimizing drag.