# Numerical Investigation of the Hydrodynamic Characteristics of 3-Fin Surfboard Configurations

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## Abstract

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## Featured Application

**This study builds on the fundamental understanding of surfboard fin design. This research identifies quantitative performance differences between the fin parameters used by surfers. These results aim to help both fin designers and surfers tailor fin choices to specific surfing styles/waves.**

## Abstract

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Fin Design

#### 2.2. Optimised Design (Wave Condition)

#### 2.3. Numerical Methods

^{−3}.

#### 2.4. Fluid Domain

^{3}and viscosity of 0.001003 kg/(m.s). There is a wide range of speeds a surfer can reach on a wave; however, speeds recorded using an inertial sensor in a study by Gately et al. show the average speed during standard manoeuvres (cutback/bottom turn) of 6.8 ± 1.7 m/s [9]. Therefore, the flow velocity at the inlet was set at 7 m/s. In water, flow is incompressible for low-speed applications. The effects of water chop have been ignored and ideal conditions were assumed to simplify each simulation. The Reynolds number, Re, is 7.73 × 10

^{5}and calculated using

^{3}), V is the free stream velocity (ms

^{−1}), L is reference length (m), μ is dynamic viscosity (kg/ms). The reference length (L) is the chord length of the foil at the base of the fin. For external fluid flow, the critical Reynolds number is (Re

_{cr}= 5 × 10

^{5}); therefore, the flow is turbulent [14].

#### 2.5. Mesh Generation

^{−6}m or 0.0032 mm, with 20 layers at a growth rate of 1.2. The calculated Y+ on the fin surface is shown in Figure 4; the maximum value on the fin wall is 1.37 and the minimum is 0.025. The area of red in the contour originates from the surfboard wall, not the fin wall itself.

#### 2.6. Numerical Error and Uncertainty Estimation

#### 2.7. Validation

## 3. Results and Discussion

#### 3.1. Baseline Fin

#### 3.2. Template Comparison

#### 3.3. Optimisation Results

#### 3.4. Shortcoming

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 3.**(

**a**) Computation surface grid. Inset: fin wall and surrounding inflation layers; (

**b**) standard surfboard fin plug configuration, showing lift and drag directions (dimensions in mm unless otherwise stated).

**Figure 7.**Baseline performance, primary axis: L/D ratio; secondary axis: ${C}_{L}$ and ${C}_{D}$; X-axis: AOA.

**Figure 8.**Turbulent kinetic energy in the wake region of baseline set (y = 50 mm) at various A0A. (

**a**) 0°; (

**b**) 5°; (

**c**) 10°; (

**d**) 15°; (

**e**) 20°; (

**f**) 30°.

**Figure 9.**Lift and drag coefficient versus AOA. (

**a**) Baseline vs. large-rake vs. small-rake; (

**b**) baseline vs. large-base vs. small-base.

**Figure 10.**Turbulent kinetic energy in the wake region of rake fin designs (y = 50 mm). (

**a**) Small-rake at 20°; (

**b**) large-rake at 20°; (

**c**) small-rake at 30°; (

**d**) large-rake at 30°.

**Figure 11.**Baseline vs. large-depth vs. small-depth. (

**a**) Lift and drag coefficients; (

**b**) lift and drag forces.

**Figure 13.**Turbulent kinetic energy in the wake region of fin designs at AOA 30 (y = 50 mm). (

**a**) Baseline; (

**b**) large-rake; (

**c**) final design.

Template Name | Rake (°) | Base Length (mm) | Depth (mm) | Foil Centre | Foil Side | 3-Fin Reference Area (mm^{2}) |
---|---|---|---|---|---|---|

Baseline | 33.7 | 111 | 115 | NACA 0006 | Half NACA 0012 | 21,994.9 |

Large-Rake | 37 | 111 | 115 | NACA 0006 | Half NACA 0012 | 22,804.8 |

Small-Rake | 28 | 111 | 115 | NACA 0006 | Half NACA 0012 | 21,268.3 |

Large-Base | 33.7 | 119 | 115 | NACA 0005 * | Half NACA 0005 * | 23,453.7 |

Small-Base | 33.7 | 100 | 115 | NACA 0014 * | Half NACA 0014 * | 20,039.9 |

Large-Depth | 33.7 | 111 | 121 | NACA 0006 | Half NACA 0012 | 23,617.5 |

Small-Depth | 33.7 | 111 | 105 | NACA 0006 | Half NACA 0012 | 19,788.5 |

Optimised | (Side: 39) (Centre: 30) | 111 | (Side: 115) (Centre: 100) | NACA 0006 | Half NACA 0012 | 20,388.2 |

Mesh | Number of Elements | Time (h) | Lift Force (N) | ${\mathit{C}}_{\mathit{L}}$ |
---|---|---|---|---|

Coarse (M5) | 1,164,030 | 0.19 | 501.1528 | 0.6200 |

M4 | 2,500,329 | 0.60 | 496.0812 | 0.6137 |

Medium (M3) | 6,284,662 | 2.55 | 489.3098 | 0.6054 |

M2 | 11,720,165 | 4.96 | 485.0050 | 0.6000 |

Fine (M1) | 18,296,932 | 7.93 | 484.2851 | 0.5991 |

Mesh | $\mathbf{Error}\left|{\mathit{E}}_{\mathit{n}}\right|$ | GCI |
---|---|---|

M3 | 6.40 × 10^{−3} | 7.99 × 10^{−3} |

M2 | 1.07 × 10^{−3} | 1.34 × 10^{−3} |

M1 | 1.79 × 10^{−4} | 2.24 × 10^{−4} |

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**MDPI and ACS Style**

Crameri, S.; Collins, P.K.; Gharaie, S. Numerical Investigation of the Hydrodynamic Characteristics of 3-Fin Surfboard Configurations. *Appl. Sci.* **2022**, *12*, 3297.
https://doi.org/10.3390/app12073297

**AMA Style**

Crameri S, Collins PK, Gharaie S. Numerical Investigation of the Hydrodynamic Characteristics of 3-Fin Surfboard Configurations. *Applied Sciences*. 2022; 12(7):3297.
https://doi.org/10.3390/app12073297

**Chicago/Turabian Style**

Crameri, Sam, Paul K. Collins, and Saleh Gharaie. 2022. "Numerical Investigation of the Hydrodynamic Characteristics of 3-Fin Surfboard Configurations" *Applied Sciences* 12, no. 7: 3297.
https://doi.org/10.3390/app12073297