# Numerical Investigation of the Hydrodynamic Characteristics of 3-Fin Surfboard Configurations
## 1 Introduction  
Surfboard fins are one of the major performance drivers in modern surfing. Their performance relies on their construction material and the fin template (outline) used. In recent years, fin companies have worked closely with professional surfers and surfboard shapers to test different designs and gain a competitive edge. A variety of different fins on the market is convenient for those who can trial different fins, but it makes it difficult for the average surfer to determine the differences between sets based exclusively on opinions and promotional content. In the past 20 years, computational fluid dynamics (CFD) has become an advanced tool used in many sports, including surfing. An early study by [PERSON] et al. presented a comparison of the drag forces from filleted and un-filledted board connections [1]. This study uses a laminar flow model to find the fin drag. Despite producing similar trends to turbulent models, [PERSON] et al. recognised this model under-predicts drag forces due to slower velocity conditions. More recent studies use steady Reynolds-averaged Navier-Stokes (RANS) equations to solve the flow. A study by [PERSON] et al. is the first to present multiple fins simulated using a turbulence model [2]. This study compared the performanceof three- and four-fin configurations. The CFD simulations utilised the k-\(\varepsilon\) turbulence model to solve flow across the angles of attack (AOA) 0 to 45\({}^{\circ}\). The results presented used the lift and drag coefficients to identify significant performance differences between the configurations and linked these coefficients to surfing terminology. It found the three-fin configuration to be more beneficial in regular surfing, stating higher lift would provide greater manoeuvrability, while the four-fin configuration would be more suited to big-wave surfing, where stability is the focus. Recent studies have refined both the computer-aided design (CAD) models and CFD methods to accurately represent real-world parameters. A study from [PERSON] et al. assessed a typical thruster fin configuration in detail [3]. This study reviewed the performance of all three fins individually and as a system. The simulation uses the k-\(\omega\) shear-stress transport (SST) turbulence model to solve a flow of 5 m/s across the fins at 0 to 45\({}^{\circ}\). A similar study from [PERSON] et al. investigated the fin positioning of a four-fin configuration using a similar k-\(\omega\) SST turbulence model [4]. Both these studies investigated not only steady-state flow but also presented transient flow field data, identifying vortex shedding phenomena at high angles and the wake interaction between fins. There are limited studies where experimental data are used to validate CFD results; the only two experimental studies to the authors' knowledge have been on single fins due to size, speed, and lab limitations with appropriate flumes. [PERSON] presented the lift and drag force measurements from flow tank testing on various bio-inspired fin designs [5]. The predicted CFD results show less variation between templates compared to the experimental data; however, both datasets produced similar trends for lift and drag. [PERSON] and [PERSON] also studied the effect of the Reynolds number on the lift and drag coefficients of a simplified fin using cavitation tunnel testing [6]. The fin template in this study was adopted into CFD simulation by [PERSON], [PERSON], and [PERSON] [7]. These CFD simulations produced lift and drag coefficient trends that closely match with the experimental results presented by [PERSON] and [PERSON] at small AOAs. Due to the variety of fin profiles used in the literature, the results from studies often have different coefficient magnitudes but similar trends. Many of the recent numerical studies have used a combination of these experimental results and other numerical studies to validate their results by recognising the similarities in lift and drag trends across multiple AOAs [2; 3; 4].