9 On the Hydrodynamics of Rowing Oars and Blade Design. 1 Introduction. 2 Theoretical Analysis. 2.1 Hydrodynamic description

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1 115 9 On the Hydrodynamics of Rowing Oars and Blade Design Abstract by Helge Nørstrud, Ernst A. Meese (March 26, 2012) A theoretical analysis is derived for the hydrodynamics of rowing from the catch part of the rowing stroke to the release. It also gives an empirical formula for the aerobic power output for athletes as function of performance time. Two oar blade designs are introduced, i.e. a commercial design for reference use and a proposed design of cubic parabolic shape. Both blades are regarded as flat plates of equal blade area. The obtained results gives the polar diagram (lift and drag coefficients versus angle of attack) for both blade designs and can conclude that the normal force on the blades are favourable higher for the new design. The theoretical results are confirmed by computational fluid dynamics (CFD) analysis. The CFD analysis give further information on the flow field details and indicates how vortex generation is related to the oar blade performance. 1 Introduction The art of rowing as bee practiced since the ancient time both in China and Egypt and was later transferred to the Viking age ( AD). The first Olympic competition in rowing was introduced in On February 2, 2012 two Norwegian men arrived in Barbados after having crossed the Atlantic in about 60 rowing days from the Canary Island. The approximate length (air distance) is 4858 km and this means that the average time over the Olympic distance of 2000 m was 36 minutes. They did not receive any Olympic medal, but earned the name of Ocean rowers. 2 Theoretical Analysis 2.1 Hydrodynamic description Figure 1 gives an overview of the geometric parameters involved in transferring the rowers power to the oar blade in order to produce a propulsive force in the rowing direction. Detailed description is found in Reference [1]. Figure 2 gives the human power output based on biomechanical data [2] and the athletic factor P(t) = A 2 /[4 ln(t)], see [3], [4], and [5]. ComputIT as, Trondheim, NORWAY, helgnoe@online.no SINTEF, Trondheim, NORWAY, ernst.a.meese@sintef.no

2 116 Chapter II. Waves and fluids Figure 1 : Rowing parameters. Figure 2 : Human power output. 2.2 Oar blade design The two oar blade designs analyzed are the commercial Big Blade and the proposed Donald and the geometries are depicted in Figures 3 and 4 respectively, along with the polar diagram which collects the hydrodynamic characteristics C L [ ] and C D [ ] versus the angle of attack α [deg]. Please note that the Donald blade shows a larger lift at α = 50 degrees as compared to the Big Blade and this indicates that Donald produces larger suction on the back of the oar blade. The performances of the two blades are further shown in Figures 5 and 6 and Figure 1 should be consulted. The normal force in Figure 6 designates the force F n as shown in Figure 1 and is the prime force for propelling the boat. 3 Numerical analysis 3.1 Method The CFD simulations were performed using an in-house code developed at CFD norway [6, 7]. In the work presented here, the code was used to solve the incompressible Euler equations, i.e., viscous forces are neglected, Å t + u ã u = 1 ρ w p. (1)

3 117 Figure 3 : Big blade characteristic. Figure 4 : Donald characteristic. Figure 5 : Drag and lift vs. angle of attack. Figure 6 : Normal force vs. oar angle. The equations are solved for the velocity vectors u and the pressure field p for given water density ρ w. Another approximation is that we assume steady state at a given angle of attack, i.e., the transient term / t is neglected. The Euler equations (1) will give a good representation of pressure distribution on the oar blades. What we will miss in the resulting force balance is the drag force due to skin friction. Skin friction is expected to be an order of magnitude smaller that the pressure forces. This assumption is supported by the results from a recent PhD

4 118 Chapter II. Waves and fluids Thesis [8] where CFD calculations including viscous effects are performed. Looking at the results in this PhD thesis, we see that the results are close to the results obtained in our work. To obtain good results, a sufficiently large computatioinal domain is needed. In Figures 7 and 9 the domains used in the present work are shown. Note that since Donald is a symmetrical shape, we simulate only half the domain, applying a symmetry condition at the cut plane. This is done to save compuational time. Details of the computational grid around the oar blades are shown if Figures 8 and 10. Care is taken to have a sufficiently fine mesh towards the edges of the blades in order to accurately capture the vortices that are generated. Figure 7: Calculation domain for simulations on Big Blade. Figure 8 : Calculation grid for Big Blade. Figure 9: Calculation domain for simulations on Donald. Figure 10 : Calculation grid for Donald.

5 Results Similar to what was done for the theoretical analysis as shown in Figure 5, we may calculate the pressure coefficient at the blade and integrate to find the lift and drag coefficients for each blade at several angles of attack. An example of the pressure coefficient distribution over the blades both on the suction and pressure sides are shown in Figures 11 an 12. Figure 11: Pressure coefficient C p on the suction (left) and pressure (right) side for Big Blade at an angle of attack of α = 45.5 from behind. Figure 12: Pressure coefficient C p on the suction (left) and pressure (right) side for the Donald oare blade at an angle of attack of α = 45.5 from behind. The resulting lift and drag coefficients for the two oar designs from the CFD simulations are shown in Figures 13 and 14 respectively. Comparing to the result from the theoretical analysis in Figure 5, we see that there are differences in the amplitude between the theoretical analysis and the CFD analysis. However, trends and positions of extremal points fit very well between the two approaches. Figure 13: Lift coefficient for Donald and Big Blade as a function of angle of attack. Figure 14: Drag coefficient for Donald and Big Blade as a function of angle of attack.

6 120 Chapter II. Waves and fluids Figure 15 : Calculated force normal to the oar blade. These curves can be translated into the force normal to the oar blade, i.e. the force felt by the rower. In Figure 15, the force is shown for the Big Blade and Donald designs as functions of the position in the rowing stroke from catch to release. Position in the stroke is given as the oar angle θ, i.e. the angle between the oar and the rowing direction (see Figure 1). Again comparing with the results from the theoretical analysis (Figure 6), we see a good match between the two methods of analysis. Although there is a difference in amplitude of about 25% between the results from the theoretical analysis and the CFD analysis, both analyses show that the Donald design exerts a larger normal force that the Big Blade design. The Donald design was selected for study due to its well known qualities in vortex generation. Using CFD analysis, it is easy to visualize the vortices that are generated. In Figures 16 and 17, flow lines are shown for three different angles of attack for the two designs. What can be seen is that the Donald design has well defined and concentrated vortices for the angles of attack from the front of the oar. For Big Blade, the vortices are less defined, although towards the end of the stroke (angle of attack from behind) the oposite situation may be observed. 4 Conclusions The proposed Donald oar blade is based on the generation of vortex flow primary on the suction side of the blade. This is supported by the visualisation of the results from the CFD simulations. Similar flow patterns are observed on other oar blades,

7 121 Figure 16: Flow lines for the Big Blade design at three angles of attack, from top to bottom: 8.9, 42.5, and 42.5 from behind. Colors on the surface represent the pressure coefficient C p on the suction side of the blade. Figure 17: Flow lines for the Donald design at three angles of attack, from top to bottom: 8.9, 42.5, and 42.5 from behind. Colors on the surface represent the pressure coefficient C p on the suction side of the blade. but the Donald blade exhibits larger forces due to the consentrated vortex. Both a theoretical and a CFD analysis has been performed on the proposed Donald oar blade with the commercial oar Big Blade as a reference. The two methods of analysis show the same trends and give the same conclusions, although there is a moderate difference in amplitude of the force exerted on the oar blade between the two methods. Finally, the Vikings showed early talents in both ship design (e.g the Oseberg ship built around 820 AD) and in oar shaping (see photo in Figure 18) without any CFD analysis.

8 122 Chapter II. Waves and fluids Figure 18: Viking roing oars (Foto: Eirik Irgens Johansen, University of Oslo, Museum of Cultural History). References [1] H. Nørstrud. Teoretisk strmningsanalyse av roårer (in norwegian). CFD norway report 213:1998, October [2] P. Webb, editor. Bioastronautics Data Book [3] H. Nørstrud. Aerodynamisk analyse av sykkelrytter (in norwegian). Norsk Teknologisk Tidskrift, 1:63, [4] H. Nørstrud, editor. Sport Aerodynamics. Springer, Wien, New York, [5] N.H. Secher and S. Volianities, editors. Rowing, Handbook of Sports Medicine and Science. Blackwell Publishing, [6] I.J. Øye. On the Aerothermodynamic effects on Space Vehicles. PhD thesis, NTNU, Trondheim, [7] E.A. Meese. Numerisk strømningsanalyse av roårer (in norwegian). CFD norway Report 221:1999, [8] A.L. Coppel. A Computational Fluid Dynamic Investigation of Rowing Oar Blades. PhD thesis, University of Birmingham, 2010.