# Estimating F1 Aero Coefficients with Lap Simulation

F1 aero data is always a hot topic for speculation, and while only the teams will know the real answer, I decided to take a crack at estimating F1 aero coefficients from the bit of public data that we have available.

In order to do this I used my custom MATLAB lap time simulation (LTS) tool as well as the publicly available telemetry data via the FastF1 python package. I have discussed some of the basics of my LTS tool in previous posts and have built up a modern F1 car model and a library of tracks to use.

Process:

The idea of this exercise is simple — I take the data generated from the LTS tool, compare it to the real telemetry, and adjust the LTS inputs until the results match. Specifically I focused on matching vehicle speeds. For a given lap I chose several points — a mix of high, medium, and low speed corners, as well as a DRS straight and a non-DRS straight — and iterated through the LTS inputs until the velocities at those points matched as closely as possible.

In the first round of iterations I looked only at low speed corners and adjusted tire grip coefficients, the idea being that slow corners are affected mainly by mechanical rather than aero grip. Next I adjusted lift coefficient to match medium and high-speed corners. This process was repeated, alternating tire and aero adjustments, until the average error between all test points was minimized. Finally once the cornering speeds were set, I adjusted base drag and DRS drag to match speed on the straights (I generally chose points halfway to 3/4 down the straight rather than the absolute end in order to avoid areas where the real cars are “clipping” and running out of hybrid deployment).

The initial telemetry data that I used was all pulled from Lewis Hamilton’s fastest 2020 qualifying lap. In a few cases where 2020 data was not available I used another year (COTA 2021, Interlagos 2019).

2020 Results:

The aero values below represent the lap-average coefficient as calculated from the LTS tool (note that I use frontal area = 1 m^2 for all cases):

My main takeaway from these results is that they appear to at least be “in the ballpark” of what I would expect, if a bit on the high end (there are many possible reasons for this, discussed in the “Errors” section below). The differences between the tracks seem to make some intuitive sense, with Budapest, Interlagos, and Silverstone showing the highest downforce and drag, and Monza showing the lowest.

In addition, we can compare these numbers to some of the amateur CFD that’s been published. My own rough analysis of the leaked Williams FW43b yielded CL -4.598, CD 1.746, L/D -2.634. A more in-depth analysis showed CL -5.60, CD 1.83. Both of these simulations were missing some underbody strakes and other details which would likely increase the downforce.

2022 Results:

Using the 2020 LTS model I then made several adjustments to represent the change to the 2022 regulations, including increased mass, tire diameter, and a new aero ride height map. Tire grip was not changed. The velocity matching process was then repeated using Max Verstappen’s fastest qualifying laps:

Interestingly the maximum CL decreased (Budapest 2020 CL = -7.373 to Budapest 2022 CL = -6.613) however the lower downforce tracks did not see much of a change (Spielberg 2020 CL = -6.303 to Spielberg 2022 CL = -6.293) and the minimum downforce track actually increased (Monza 2020 CL = -5.731 to Monza 2022 CL = -5.841). Of the four tracks that were repeated in 2020 and 2022, the average CL only dropped from -6.445 in 2020 to -6.351 in 2022. Drag changed very little with the average actually increasing slightly.

Some comparisons can also be made by looking at the change in lap times between 2020 and 2022:

Speed vs distance plots for a few of the tracks are below. Blue = 2020 LTS, black = 2020 telemetry, pink = 2022 LTS, red = 2022 telemetry.

Errors:

There are a number of factors which may be driving these calculated aero coefficients to be off. Among these the most likely candidates are:

• Track data – I have observed that using better quality track data generally causes the LTS to generate higher cornering speeds and faster laps. I have done my best to build decent track models and in a few cases I even ignored certain corners that I knew to be bad, but I suspect that improving the quality of the tracks by using real velocity and acceleration data would lead to overall lower CL values.
• Tire grip – If the tire coefficients or the tire load sensitivities are very wrong then the calculated CL will also be wrong. Too little tire grip would cause cause the CL to be too high and vice versa.
• Engine model – Much like tires, if the modeled engine torque curve is not good it will effect the drag coefficients. I also model one single torque curve and do not take varying hybrid deployment or clipping into account.
• Environmental factors – All LTS runs were assumed to be at standard sea level air density and with no wind. In some cases wind was actually visible in the telemetry traces as a boost in top speed on one straight followed by a decrease in top speed on the opposite straight. In these cases I generally tried to split the difference with the LTS top speed.