The aim of the article is to determine the hydrodynamic characteristics of a swimmer’s scanned hand model for various possible combinations of both the angle of attack and the sweepback angle, simulating separate underwater arm stroke phases of front crawl swimming. An actual swimmer’s hand with thumb adducted was scanned using an Artec L 3D scanner. ANSYS Fluent code was applied for carrying out steady-state computational fluid dynamics (CFD) analysis. The hand model was positioned in nine different positions corresponding to the swimmer’s hand orientations (angle of attack and sweepback angle) and velocities observed during the underwater hand stroke of front crawl. Hydrodynamic forces and coefficients were calculated. Results showed significantly higher drag coefficient values in the pull phase, when compared with previous studies under a steady-state flow condition. The mean value of the ratio of drag and lift coefficients was 2.67 ± 2.3 in underwater phases. The mean value of the ratio of drag and lift forces was 2.73 ± 2.4 in underwater phases. Moreover, hydrodynamic coefficients were not almost constant throughout different flow velocities, and variation was observed for different hand positions corresponding to different stroke phases. The current study suggests that the realistic variation of both the orientation angles influenced higher values of drag, lift and resultant coefficients and forces.

# Search Results

### Milda Bilinauskaite, Vishveshwar R. Mantha, Abel I. Rouboa, Pranas Ziliukas and António J. Silva

### Alexandra Laurent, Annie Rouard, Vishveshwar R. Mantha, Daniel A. Marinho, Antonio J. Silva and Abel I. Rouboa

The distribution of pressure coefficient formed when the fluid contacts with the kayak oar blade is not been studied extensively. The CFD technique was employed to calculate pressure coefficient distribution on the front and rear faces of oar blade resulting from the numerical resolution equations of the flow around the oar blade in the steady flow conditions (4 m/s) for three angular orientations of the oar (45°, 90°, 135°) with main flow. A three-dimensional (3D) geometric model of oar blade was modeled and the kappa-epsilon turbulence model was applied to compute the flow around the oar. The main results reported that, under steady state flow conditions, the drag coefficient (C_{d} = 2.01 for 4 m/s) at 90° orientation has the similar evolution for the different oar blade orientation to the direction of the flow. This is valid when the orientation of the blade is perpendicular to the direction of the flow. Results indicated that the angle of oar strongly influenced the C_{d} with maximum values for 90° angle of the oar. Moreover, the distribution of the pressure is different for the internal and external edges depending upon oar angle. Finally, the difference of negative pressure coefficient C_{p} in the rear side and the positive C_{p} in the front side, contributes toward propulsive force. The results indicate that CFD can be considered an interesting new approach for pressure coefficient calculation on kayak oar blade. The CFD approach could be a useful tool to evaluate the effects of different blade designs on the oar forces and consequently on the boat propulsion contributing toward the design improvement in future oar models. The dependence of variation of pressure coefficient on the angular position of oar with respect to flow direction gives valuable dynamic information, which can be used during training for kayak competition.

### Vishveshwar R. Mantha, António J. Silva, Daniel A. Marinho and Abel I. Rouboa

The aim of the current study was to analyze the hydrodynamics of three kayaks: 97-kg-class, single-rower, flatwater sports competition, full-scale design evolution models (Nelo K1 Vanquish LI, LII, and LIII) of M.A.R. Kayaks Lda., Portugal, which are among the fastest frontline kayaks. The effect of kayak design transformation on kayak hydrodynamics performance was studied by the application of computational fluid dynamics (CFD). The steady-state CFD simulations where performed by application of the *k*-omega turbulent model and the volume-of-fluid method to obtain two-phase flow around the kayaks. The numerical result of viscous, pressure drag, and coefficients along with wave drag at individual average race velocities was obtained. At an average velocity of 4.5 m/s, the reduction in drag was 29.4% for the design change from LI to LII and 15.4% for the change from LII to LIII, thus demonstrating and reaffirming a progressive evolution in design. In addition, the knowledge of drag hydrodynamics presented in the current study facilitates the estimation of the paddling effort required from the athlete during progression at different race velocities. This study finds an application during selection and training, where a coach can select the kayak with better hydrodynamics.

### Daniel A. Marinho, Tiago M. Barbosa, Victor M. Reis, Per L. Kjendlie, Francisco B. Alves, João P. Vilas-Boas, Leandro Machado, António J. Silva and Abel I. Rouboa

The main aim of this study was to investigate the effect of finger spread on the propulsive force production in swimming using computational fluid dynamics. Computer tomography scans of an Olympic swimmer hand were conducted. This procedure involved three models of the hand with differing finger spreads: fingers closed together (no spread), fingers with a small (0.32 cm) spread, and fingers with large (0.64 cm) spread. Steady-state computational fluid dynamics analyses were performed using the Fluent code. The measured forces on the hand models were decomposed into drag and lift coefficients. For hand models, angles of attack of 0°, 15°, 30°, 45°, 60°, 75°, and 90°, with a sweep back angle of 0°, were used for the calculations. The results showed that the model with a small spread between fingers presented higher values of drag coefficient than did the models with fingers closed and fingers with a large spread. One can note that the drag coefficient presented the highest values for an attack angle of 90° in the three hand models. The lift coefficient resembled a sinusoidal curve across the attack angle. The values for the lift coefficient presented few differences among the three models, for a given attack angle. These results suggested that fingers slightly spread could allow the hand to create more propulsive force during swimming.

### Daniel A. Marinho, António J. Silva, Victor M. Reis, Tiago M. Barbosa, João P. Vilas-Boas, Francisco B. Alves, Leandro Machado and Abel I. Rouboa

The purpose of this study was to analyze the hydrodynamic characteristics of a realistic model of an elite swimmer hand/forearm using three-dimensional computational fluid dynamics techniques. A three-dimensional domain was designed to simulate the fluid flow around a swimmer hand and forearm model in different orientations (0°, 45°, and 90° for the three axes Ox, Oy and Oz). The hand/forearm model was obtained through computerized tomography scans. Steady-state analyses were performed using the commercial code Fluent. The drag coefficient presented higher values than the lift coefficient for all model orientations. The drag coefficient of the hand/forearm model increased with the angle of attack, with the maximum value of the force coefficient corresponding to an angle of attack of 90°. The drag coefficient obtained the highest value at an orientation of the hand plane in which the model was directly perpendicular to the direction of the flow. An important contribution of the lift coefficient was observed at an angle of attack of 45°, which could have an important role in the overall propulsive force production of the hand and forearm in swimming phases, when the angle of attack is near 45°.

### J. Paulo Vilas-Boas, Rui J. Ramos, Ricardo J. Fernandes, António J. Silva, Abel I. Rouboa, Leandro Machado, Tiago M. Barbosa and Daniel A. Marinho

The aim of this research was to numerically clarify the effect of finger spreading and thumb abduction on the hydrodynamic force generated by the hand and forearm during swimming. A computational fluid dynamics (CFD) analysis of a realistic hand and forearm model obtained using a computer tomography scanner was conducted. A mean flow speed of 2 m·s^{−1} was used to analyze the possible combinations of three finger positions (grouped, partially spread, totally spread), three thumb positions (adducted, partially abducted, totally abducted), three angles of attack (a = 0°, 45°, 90°), and four sweepback angles (y = 0°, 90°, 180°, 270°) to yield a total of 108 simulated situations. The values of the drag coefficient were observed to increase with the angle of attack for all sweepback angles and finger and thumb positions. For y = 0° and 180°, the model with the thumb adducted and with the little finger spread presented higher drag coefficient values for a = 45° and 90°. Lift coefficient values were observed to be very low at a = 0° and 90° for all of the sweepback angles and finger and thumb positions studied, although very similar values are obtained at a = 45°. For y = 0° and 180°, the effect of finger and thumb positions appears to be much most distinct, indicating that having the thumb slightly abducted and the fingers grouped is a preferable position at y = 180°, whereas at y = 0°, having the thumb adducted and fingers slightly spread yielded higher lift values. Results show that finger and thumb positioning in swimming is a determinant of the propulsive force produced during swimming; indeed, this force is dependent on the direction of the flow over the hand and forearm, which changes across the arm’s stroke.

### Daniel A. Marinho, Victor M. Reis, Francisco B. Alves, João P. Vilas-Boas, Leandro Machado, António J. Silva and Abel I. Rouboa

This study used a computational fluid dynamics methodology to analyze the effect of body position on the drag coefficient during submerged gliding in swimming. The k-epsilon turbulent model implemented in the commercial code Fluent and applied to the flow around a three-dimensional model of a male adult swimmer was used. Two common gliding positions were investigated: a ventral position with the arms extended at the front, and a ventral position with the arms placed along side the trunk. The simulations were applied to flow velocities of between 1.6 and 2.0 m·s^{−1}, which are typical of elite swimmers when gliding underwater at the start and in the turns. The gliding position with the arms extended at the front produced lower drag coefficients than with the arms placed along the trunk. We therefore recommend that swimmers adopt the arms in front position rather than the arms beside the trunk position during the underwater gliding.