Wave drag on human swimmers
Introduction
Swimmers and vessels travelling on the water's surface generate waves which form a wake behind them. When travelling at high speed, as measured by the Froude number (Fr), a large proportion of the drag on surface vessels is due to the energy required to create these waves (Van Manen and Van Oossanen, 1988). Elite swimmers also travel at high Fr numbers and the aim of this paper is to give the results of fundamental research which demonstrates that wave drag is the largest component of the drag they experience when at the surface.
There are three main types of drag on surface vessels; viscous or skin friction drag, form drag associated with the turbulent wake of the vessel and wave drag. Wave drag is due to the energy required to create the transverse and divergent waves which lie within a 39° sector behind the vessel. The drag is dependant on the ratio of its speed to that of a water wave with a wavelength equal to the vessel's length, i.e. the Froude numberwhere V=vessel speed, g=9.81 m s−2, L=length of the vessel. A typical total drag curve for a vessel is shown in Fig. 1. Above the drag increases rapidly due to the increasing importance of wave drag. Drag curves may display “bumps” at particular speeds due to constructive and destructive interference of the waves generated at each change in cross-section of the hull. Around , the vessel's speed matches that of a wave which has a wavelength equal to the length of the vessel. This is the so-called “hull speed”, the maximum that can be achieved as a displacement vessel. The drag increase is typically less rapid above , as the vessel generates hydrodynamic lift, reducing its displacement as it rises to a planing condition. A 1.8 m tall elite swimmer at 1.8 m s−1 has , and with arms extended to a total length of 2.3 m, has , thus wave drag would be expected to constitute a large proportion of their total drag.
Several attempts have been made to quantify wave drag on swimmers. Vorontsov and Rumyantsev (2000) suggested that 5% of drag was due to waves at 2 m s−1. Toussaint et al. (2002) used the Measurement of Active Drag (MAD) system measurements to estimate that wave drag had a greater contribution, 21% at 1.9 m s−1. Wilson and Thorp (2003) used power law fits to estimate that wave drag contributed between 10% and 20% of active drag at 1.0 m s−1 and between 35% and 45% at 2.0 m s−1. Lyttle et al. (1998) towed 40 swimmers using a pulley system at velocities from 1.6 to 3.1 m s−1 and depths between the surface and 0.6 m. They found that drag was 20% lower at 0.6 m depth than at the surface when towing at 2.2 m s−1.
A deeply immersed solid body towed horizontally does not generate surface waves and drag is mainly due to skin friction and form drag. Viewed from a perspective moving with the body, the effect of the body is to force fluid to flow around it, distorting the flow near the body. In some regions, the distortion increases velocities and in others reduces velocities relative to the undisturbed flow, with the size of the velocity distortions decreasing with distance from the body. When the body moves close enough to the water's surface for the distorted flow to impinge on the surface the pressure changes, due to the Bernoulli effect, associated with the distortion cause both depressions and elevations in the water's surface above the body. These in turn create a wave wake and thus the body begins to experience wave drag. The closer the body is to the surface, the larger the depressions and elevations, leading to greater wave drag. Wave drag is an additional drag experienced near the surface which is not present when deeply immersed, thus total drag would be expected to increase as the body approaches the surface. Wave drag is typically assumed independent of skin and form drag and thus the difference between the total drag measured when towed near to or at the surface and the drag when deeply immersed is an estimate of the drag due to waves.
Section snippets
Measurements
The measurements were made in a 2.5 m wide, 1.5 m deep flume with a 10 m long working section capable of water speeds up to 3 m s−1. The towing rig consisted of a forward strut joined to a horizontal towing rod in series with a load cell. To keep it horizontal, the rod passed through a frictionless sleeve in a rear strut (Fig. 2). The mannequin was attached to the rod 1 m behind the rear strut to reduce the effect of the flow around the struts on the mannequin. Underwater observations of the
Drag curves
The drag–velocity curves in Fig. 3 show the increased drag with velocity. The curves from tow depths of 1.0–0.8 m are very similar, indicating weak interaction with the surface. A drag curve for the fully immersed mannequin was estimated by averaging the drag for towing depths 1.0–0.8 m at each velocity (the average is shown in Fig. 7). At 0.4 m depths and above drag rapidly increases, with drag at some velocities up to 2.4 times that when the mannequin was fully immersed at the same speed.
The
Discussion
The drag curves and contour plots generally show increasing drag as the mannequin approaches the surface and it is important to determine the cause of this additional drag. Research on vessels shows that wave drag becomes increasingly more important with speed (Van Manen and Van Oossanen, 1988), also, wave drag on an immersed body increases as it approaches the surface. Thus the low-speed drag curves for all tow depths should coincide and at higher speeds should fan out above the fully immersed
Conclusions
The measurements show that total drag increases rapidly as the mannequin is towed at depths shallower than 2.8 chest depths (∼0.7 m), at some velocities reaching up to 2.4 times the drag when the mannequin is fully immersed. Near or at the surface the reduced wetted surface and a similar form wake size suggest that the large increase in drag near the surface is unlikely to be due to skin or form drag. The upward and then downward curvature above 2.0 m s−1 (Fr=0.42) of the near surface drag curves
Acknowledgments
We thank Speedo International for the use of the mannequin constructed by CyberFX, USA.
References (9)
- et al.
Fluid Mechanics
(2002) - et al.
The effect of depth and velocity on drag during the streamlined glide
Journal of Swimming Research
(1998) The wave-resistance of a ship
The Philosophical Magazine
(1898)Marine Hydrodynamics
(1977)