CFD in Formula 1: what is it for? And how does it work?

The acronym CFD stands for "Computational Fluid Dynamics". A CFD software makes it possible to study the airflow that laps the surfaces of a single-seater, and it does so by giving a numerical solution to the infamous Navier-Stokes equations. This set of differential equations, in fact, is known not to have (yet) an "analytic" solution: in fact, if we apply the common laws of mathematical analysis, we wouldn’t come to a solution, especially for complex geometries such as those of a racecar!

How does a CFD software work?

What a good CFD code does, then, is iteratively estimate the solution with the lowest possible uncertainty. In these conditions we can say that "convergence" has been obtained, in the presence of which we can consider valuable the figures of air pressure and air velocity obtained in each point of the bodywork.

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As you will understand, the degree of detail that one seeks even before approaching CFD is indisputably too high: the bodywork, just like any body, is a "continuum" ... And as such, we could potentially consider it as a set of infinite points! If we think, then, that 1 cm³ of air contains 26,000,103,515,625,000,000 molecules – yes, you read that right – it is unthinkable to avoid any kind of simplification of the problem.

What can we do to simplify our fluid dynamics problem?

First of all, over the years sets of equations have been developed with various degrees of simplification with respect to the aforementioned Navier-Stokes equations: an example is the RANS (Reynolds Averaged Navier-Stokes) approach, in which we operate an averaging which only qualitatively takes into account the effects of turbulence. If, on the other hand, we wanted to study the turbulence phenomenon itself in more detail – which we could explore in the future – it would be useful to use the LES (“Large Eddy Simulation”) approach, which is more effective in predicting the behavior of vortex structures.

On the other hand, in terms of the geometry of the single-seater, the discretization process called "meshing" comes to help us: each portion of the car bodywork is divided into more or less small cells, usually cubic or hexahedral in shape, without losing the characteristic aspects of the complete single-seater shape…

Meshing of a Formula 1 single-seater

The skill of those who perform a good mesh lies right here: to find the right compromise between precision and simplicity of the modeling. Indeed:

• Greater precision means more accurate results, and therefore the possibility of leading the aerodynamic development of the car towards the right direction;
• Greater simplicity, on the other hand, means reducing calculation times and costs: in modern Formula 1, where budget and resources are limited, this is certainly an important aspect!

In fact, for over a year the technical regulations have required the 10 teams to have different availability of resources at their disposal: the hours amount, both for CFD simulations and for wind tunnel testings, is recalculated every 6 months in order to rebalance the performance across the field. By doing so, teams in technical crisis have the opportunity to recover, while those ahead will hardly be able to extend their performance advantage!

To date, the resources mentioned are divided as follows:

	Coefficiente	Runs in galleria del vento	Numero Items utilizzabili alla CFD
Red Bull	0.63	202	1260
Ferrari	0.75	240	1500
Mercedes	0.80	256	1600
Alpine	0.85	272	1700
McLaren	0.90	288	1800
Alfa Romeo	0.95	304	1900
Aston Martin	1.00	320	2000
Haas	1.05	336	2100
Alpha Tauri	1.10	352	2200
Williams	1.15	368	2300

Ok, but after having delved into the operational aspects of a CFD analysis, what can we extract after the long calculation hours?

Lift vs Drag

The two most important data that can be extracted from a CFD analysis are the figures of aerodynamic load ("downforce", or "negative lift") and aerodynamic drag, values that both refer to the entire car bodywork. Far more important, however, is the distribution of these two quantities with respect to each macro-area of the single-seater: this helps to understand which components generate more performance, and therefore in which it is more profitable to invest in research and development.

Right now, this generation of ground effect cars sees 55% of the total aerodynamic downforce generated by the underfloor and the diffuser altogether! This explains why in 2022 the technical battle at the top between Red Bull and Ferrari was played out with aerodynamic updates right in the underfloor area…

Aerodynamic efficiency

In principle, the aim of aerodynamic engineers is to increase downforce and reduce drag: the ratio between these two quantities, often denoted by L/D, is called "aerodynamic efficiency". As the aerodynamic efficiency of a design increases, one can be reasonably confident of its competitiveness.

Shape optimization

Coming back to CFD, the iterative cycle does not end with the analysis of the results obtained, but continues with a shape optimization process: the same software, "learning" from the previous simulations which modifications had the greatest impact on performance, re-shapes the external bodywork surface within the regulatory limits – which since last year define certain volumes that cannot be exceeded.

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When a result close to (or, why not, superior to) the target figures is achieved, the aerodynamic department validates the shapes of the car we see on the track; subsequent refinements lead to update packages during the season, but only in case they actually prove to be better than the baseline.

Correlation between CFD, wind tunnel and track

Speaking about track performance, an aspect often – and rightly – mentioned is correlation, a term that indicates repeatability and consistency between the results of the wind tunnel, track and CFD itself.

On the correlation matter it is better not to seek for easy savings: if the platform that hosts the fluid dynamics calculations is powerful and efficient but provides different answers from what the track says, it soon turns into a disadvantage rather than an asset!

When this happens, the protocols in force in the teams – and common sense, after all – dictate that the aerodynamic development program has to be halted until the simulation models of each analysis tool are perfectly calibrated, in order to ensure a robust correlation.

What else?

In this article we wanted to explain what lies behind the universe of computational fluid dynamics, trying to capture as many aspects as possible; however, there are issues correlated to the topic (see turbulence) that deserve to be further explored: the comments section is at your disposal for any request, question or consideration!