# Aerodynamic and Structural Design of a 2022 Formula One Front Wing Assembly

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methodology

#### 2.1. Front Wing Design

#### 2.1.1. Design of Front Wing Baseline Configurations

#### 2.1.2. Design of 2022 Formula One Front Wing

#### 2.1.3. Design of Structural Components

#### 2.1.4. Selection of Front Wing Materials

^{3}/g) and a medium-density (4.37 kg/cm

^{3}), magnesium alloy AZ31B, which have a very low density (1.77 kg/cm

^{3}) and excellent specific modulus (25.42 GPa·cm

^{3}/g) and aluminium alloy 2024 T3, which possesses intermediate properties (specific modulus of 26.29 GPa·cm

^{3}/g and density of 2.81 kg/cm

^{3}).

^{3}), but HS40 was selected due to its higher tensile strength (4400 MPa vs. 3450 MPa). The second choice was the aramid fibre with the highest mechanical properties: Kevlar K149, which possesses an elasticity modulus of 147 GPa and a very low density (1.47 kg/cm

^{3}). Thirdly, assuming that the selected fibres have enough ultimate strength to avoid the composite breaking, the matrices were only selected according to Young’s modulus and the specific Young’s modulus: the first choice was the epoxy polymer, with a Young’s modulus of 6 GPa and a specific Young’s modulus of 4.29 GPa·cm

^{3}/g and the second selection was the thermoplastic Polyetherketone (PEK), which possesses a Young’s modulus of 4.6 GPa and a specific Young’s modulus of 3.49 GPa·cm

^{3}/g. Lastly, after all considerations and mathematical relationships needed, four composites were created with the two selected fibres (carbon and aramid) and the two selected matrices (Epoxy and PEK) with a 78.5% of fibre volume. The orthotropic mechanical properties and density of the designed composites are provided in Table 3.

#### 2.2. Fluid Conditions

#### 2.3. Mesh Design

#### 2.4. Numerical Framework

^{®}Fluent (v2019), which employs the finite volume method to solve the partial differential equations governing the fluid dynamic problem. Additionally, decoupled structural analysis were carried out with ANSYS

^{®}Mechanical (v2019), a finite element analysis solver (FEA).

## 3. Results

#### 3.1. Validation and Verification

^{®}(R2020) file developed by the author [47]. Table 6 provides a summary of the most important parameters of the grid convergence study, including the refinement ratio, the order of convergence, the asymptotic solution and the Grid Convergence Index of the two aerodynamic coefficients.

^{6}elements, the error between the lift and drag coefficients and their grid-independent values is smaller than 1% (0.067% and 0.763%, respectively). After this number of elements, the dependence between results and mesh size can be considered neglectable. Therefore, this mesh size is selected to represent the front wing. More elements would immensely increase the computational cost without any relevant accuracy improvement.

#### 3.2. Aerodynamic and Structural Analysis of Baseline Wings

#### 3.2.1. Influence of Flaps and Endplates in the Aerodynamic Performance of the Wings

^{2}), and thereby the increment in aerodynamic forces between single-element and multi-element configurations is still higher.

#### 3.2.2. Influence of Flaps and Endplates in the Structural Performance of the Wings

#### 3.3. Structural Analysis of Front Wing Components

#### 3.4. Analysis of Materials

#### 3.5. Sensitivity Analysis of Wing Structure

#### 3.6. Formula One 2022 Front Wing

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Baseline configurations: (

**a**) one-element without endplates; (

**b**) one-element with endplates; (

**c**) three-element without endplates; (

**d**) three-element with endplates.

**Figure 2.**2022 front wing attached to a 2018 Formula One car (the whole design is performed and developed by the authors).

**Figure 3.**Examples of wing structural designs: (

**a**) wing structure with high-density ribs; (

**b**) ribs with implemented circular holes; (

**c**) wing structure with high-density spars; (

**d**) ribs with high thickness.

**Figure 6.**Distribution of pressure in the lower surface of (

**a**) one-element without endplates; (

**b**) one-element with endplates; (

**c**) three-element without endplates; (

**d**) three-element with endplates.

**Figure 9.**Z-Position of the trailing edge along with spanwise direction in (

**a**) one-element without endplates; (

**b**) one-element with endplates; (

**c**) three-element without endplates; (

**d**) three-element with endplates.

**Figure 10.**Increment in weight (

**a**) and reduction in deformation (

**b**) according to the structural configuration.

**Figure 13.**Pressure distribution in the three elements of the 2022 F1 front wing at sections: (

**a**) 0.05 s; (

**b**) 0.95 s.

**Table 1.**2022 FIA Formula One Technical Regulations [7].

Parameter | Articles |
---|---|

Front Bodywork | Art. 3.6.1, Art. 3.9.9 and Art. 3.11.5 |

Front Wing Airfoils | Art. 3.9.1 |

Front Wing Endplates | Art. 3.9.2 and Art. 3.9.5 |

Front Wing Tip | Art. 3.9.3 |

Front Wing Diveplane | Art. 3.9.4 |

Front Wing Assembly | Art. 3.9.6 |

Materials | Art. 15.3.1, Art. 15.3.2, Art. 15.3.3 and Art. 15.3.4 |

Coordinate Systems, Reference Surfaces and Reference Volumes | Art. 2.9.1, Art. 2.9.2, Art. 2.9.3, Art. 2.9.4, Art. 2.11.1, Art. 2.11.2, Art. 2.11.3, Art. 3.4.1, Art 3.4.2, Art 3.4.3, Art. 12.1.4, Art. A.9, Art. A.12, Art. A.21, Art A.22, Art. A23, Art. A24, Art. A25 and Art. A26. |

**Table 2.**Features of bidimensional three-element F1 front wing achieved by Gorostidi et al. [11].

Feature | Symbol | Value | Units |
---|---|---|---|

Airfoil | S1210 | - | - |

Chord of Main Element | ${c}_{1}$ | 250 | mm |

Chord of Primary Flap | ${c}_{2}$ | 125 | mm |

Chord of Secondary Flap | ${c}_{3}$ | 62.5 | mm |

Attack Angle of Main Element | ${\alpha}_{1}$ | 3 | ° |

Attack Angle of Primary Flap | ${\alpha}_{2}$ | 6 | ° |

Attack Angle of Secondary Flap | ${\alpha}_{3}$ | 9 | ° |

Gap between elements 1 and 2 | ${g}_{12}$ | 19.43 | mm |

Gap between elements 2 and 3 | ${g}_{23}$ | 16.27 | mm |

Overlap between elements 1 and 2 | ${o}_{12}$ | 29.87 | % |

Overlap between elements 2 and 3 | ${o}_{23}$ | 35.46 | % |

Distance to the Reference Plane | ${h}_{RP}$ | 75 | mm |

Distance to the Floor | $h$ | 160 | mm |

Property | HS40-Epoxy | HS40-PEK | K149-Epoxy | K149-PEK | |
---|---|---|---|---|---|

Density | $\rho $ | 1.73 | 1.71 | 1.46 | 1.44 |

Longitudinal Young’s Modulus | ${E}_{1}$ | 354.0 | 353.7 | 118.8 | 118.5 |

Transversal Young’s Modulus | ${E}_{2}$ | 28.5 | 22.1 | 25.8 | 20.4 |

Flow Condition | Symbol | Value | Units |
---|---|---|---|

Fluid Density | $\rho $ | 1.225 | $\mathrm{kg}/{\mathrm{m}}^{3}$ |

Fluid Temperature | $T$ | 288.15 | $\mathrm{K}$ |

Aospheric Pressure | $p$ | 101325 | $\mathrm{Pa}$ |

Dynamic Viscosity | $\mu $ | 1.8 × 10^{−5} | $\mathrm{Pa}\xb7\mathrm{s}$ |

Streamwise Air Velocity | $u$ | 105 | $\mathrm{m}/\mathrm{s}$ |

Spanwise Air Velocity | $v$ | 0 | $\mathrm{m}/\mathrm{s}$ |

Surface | Boundary condition | Value | Units | Description |
---|---|---|---|---|

Inlet | Velocity-inlet | (105, 0, 0) | m/s | Normal to boundary |

Turbulence Intensity | 0.3 | % | ||

Turbulent Viscosity Ratio | 10^{−7} | - | ||

Outlet | $\mathrm{Pressure}\text{-}\mathrm{outlet}(\nabla p$) | (0, 0, 0) | Pa/m | Allows for recirculation |

Asphalt | No-slip moving wall | (105, 0, 0) | m/s | Enforces relative movement |

Left-Wall | Symmetry | - | - | Saves computational time |

Top-Wall | Symmetry | - | - | Verified with experimental data |

Right-Wall | Symmetry | - | - | Verified with experimental data |

Wing | No-slip stationary wall | (0, 0, 0) | m/s | Allows boundary layer build-up |

Parameter | r | p | f_{h=0} | GCI_{12} | GCI_{23} | GCI_{12}/r^{p}GCI_{23} |
---|---|---|---|---|---|---|

C_{L} | 2 | 1.5850 | 0.0655 | 2.9297 | 0.9615 | 1.0156 |

C_{D} | 2 | 1.8074 | 1.1868 | 0.2956 | 0.0843 | 1.0017 |

Material | Ribs | Spars | Skin | |||
---|---|---|---|---|---|---|

Max. Def. (mm) | Weight (kg) | Max. Def. (mm) | Weight (kg) | Max. Def. (mm) | Weight (kg) | |

Aluminium | 4.28 | 7.707 | 4.28 | 7.707 | 4.28 | 7.707 |

Titanium | 4.25 | 8.421 | 4.03 | 8.413 | 2.74 | 10.585 |

Magnesium | 4.32 | 7.234 | 4.47 | 7.248 | 6.51 | 5.778 |

Carbon–Epoxy | 4.29 | 7.228 | - | - | 2.33 | 5.738 |

Aramid–Epoxy | 4.31 | 7.095 | - | - | 4.05 | 5.234 |

**Table 8.**Weight-deformation variation gradient of the entire wing according to the sequential combination in each degree of freedom.

Parameter | i1→i2 | i2→i3 | i3→i4 | i4→i5 |
---|---|---|---|---|

∂W/∂def | ∂W/∂def | ∂W/∂def | ∂W/∂def | |

Number of ribs | 2.1736 | 1.6456 | 0.9305 | - |

Rib thickness | 3.3456 | 3.3726 | 1.9640 | - |

Rib circles | ∞ | ∞ | ∞ | ∞ |

Number of spars | 1.2502 | 1.1961 | - | - |

Spars size | 0.5920 | 0.8885 | 0.5606 | - |

Spar root width | 2.8754 | 2.4763 | - | - |

Spar head length | 1.0638 | 0.9743 | - | - |

Spar head width | 2.2526 | 1.0046 | - | - |

Skin thickness | 0.6954 | 0.6062 | 0.7233 | 0.3456 |

Spars material | 1.3632 | 1.3423 | - | - |

Ribs material | 10.9533 | 66.1858 | 18.1257 | - |

Skin Material | 0.1195 | 1.6456 | 0.9305 | - |

Parameter | Main Element | Primary Flap | Secondary Flap | |
---|---|---|---|---|

Number of ribs | 17 | 17 | 17 | |

Rib thickness | mm | 5 | 5 | 20 |

Rib circles | % | 80 | 80 | 80 |

Number of spars | 8 | 8 | 8 | |

Spars size | mm | 80 | 80 | 80 |

Spar root width | % | 10 | 20 | 20 |

Spar head length | % | 100 | 100 | 100 |

Spar head width | % | 10 | 20 | 5 |

Skin thickness | mm | 2.5 | 2.5 | 2.5 |

Spars material | Titanium R54810 | Titanium R54810 | Titanium R54810 | |

Ribs material | Aramid K149-Epoxy | Aramid K149-Epoxy | Aramid K149-Epoxy | |

Skin material | Carbon HS40-Epoxy | Carbon HS40-Epoxy | Carbon HS40-Epoxy | |

Expected Deformation | mm | 1.98 | 1.98 | 1.97 |

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**MDPI and ACS Style**

Castro, X.; Rana, Z.A.
Aerodynamic and Structural Design of a 2022 Formula One Front Wing Assembly. *Fluids* **2020**, *5*, 237.
https://doi.org/10.3390/fluids5040237

**AMA Style**

Castro X, Rana ZA.
Aerodynamic and Structural Design of a 2022 Formula One Front Wing Assembly. *Fluids*. 2020; 5(4):237.
https://doi.org/10.3390/fluids5040237

**Chicago/Turabian Style**

Castro, Xabier, and Zeeshan A. Rana.
2020. "Aerodynamic and Structural Design of a 2022 Formula One Front Wing Assembly" *Fluids* 5, no. 4: 237.
https://doi.org/10.3390/fluids5040237