Estimating propulsive forces—sink or swim?
Introduction
The most popular procedure for the estimation of hand forces in swimming uses a combination of kinematic data derived from underwater video analysis and hydrodynamic lift and drag force coefficients for the hand/forearm obtained from laboratory experiments (Berger et al., 1995; Schleihauf, 1979). The procedures of Schleihauf (1979) and Berger et al. (1995) determined lift and drag coefficients using series of tests that were performed with hand/forearm models immersed in various orientations in an open water channel under steady flow conditions. The force exerted by the hand/forearm on the water was determined by using the measured force and standard hydrodynamic equations (1), (2) to calculate the coefficients of lift (CL) and drag (CD) for known orientations of the hand, relative to the flow of the water:
These coefficients have been used in subsequent studies to calculate propulsive lift and drag forces (Eqs. (3), (4)) from underwater three-dimensional video analysis of the swimming strokes (Schleihauf et al., 1988)where FL is the lift force, FD is the drag force, ρ is the density of water; ν is the relative velocity between the hand and water, and A is the largest possible projected area of the hand (Prandtl and Tietjens, 1934).
The applicability of the quasi-static lift and drag coefficient values obtained by Schleihauf (1979) and Berger et al. (1995) to the non-steady conditions in real swimming has recently been questioned (Lauder and Dabnichki, 1996; Pai and Hay, 1988; Toussaint et al., 2002). Hydrodynamic forces in swimming are dependent on two important effects associated with an immersed accelerating segment, vortex shedding and added mass effects (Childress, 1981). The testing protocols that have been previously used to obtain lift and drag coefficients ignore these effects, and although studies have attempted to improve the accuracy of such protocols (Lauder et al., 2001), the problem remains. Recently, the use of computational fluid dynamics (CFD) to model the propulsive forces generated by the hand and forearm has been introduced (Bixler and Riewald, 2002). This approach offers some benefits in terms of the ability to run a number of simulations, which otherwise might be costly through experimental techniques. However, the problem of simulating unsteady flow conditions remains. Bixler and Riewald (2002) replicated force coefficients for the hand and forearm that had been determined experimentally (Berger et al., 1995; Schleihauf, 1979), an important first step in the use of CFD techniques to solve the problem, but concede that simulation of unsteady flow conditions presents a greater challenge.
Direct measurement of hydrodynamic forces in swimming is perhaps the most appropriate approach to investigating the problem (Lauder et al., 2000). The purpose of the present study was to investigate the appropriateness of hydrodynamic force estimation in swimming as calculated by the quasi-static approach. This was to be achieved through the comparison of shoulder torque profiles calculated from hydrodynamic drag forces estimated by using the quasi-static approach with direct measurements of propulsive force profile using an instrumented mechanical arm.
Section snippets
Methods
The study was conducted in two stages. The first stage consisted of the design, construction and calibration of a full-scale mechanical arm, capable of replicating an underwater stroke partially representative of the underwater phase of the front-crawl stroke and measuring the shoulder torque profile due to the hydrodynamic resistance on the arm during this phase. The second stage consisted of filming the mechanical arm in a full-scale environment using a three-dimensional underwater filming
Results
If the hand is the major contributor to propulsive force generation in swimming (Schleihauf, 1974), the profile of shoulder torque for the direct measurement and the quasi-static approach should be similar. The comparisons of shoulder torque profile as calculated by the quasi-static approach with the shoulder torque profile as measured by the mechanical arm for each elbow angle setting are shown in Fig. 2, Fig. 3, Fig. 4, Fig. 5. Clear differences are evident in the profiles presented. Given
Discussion
The reliability of the direct measurement of shoulder torque was high across repeated trials (±4.5 N m). The mean measurement error expressed as a percentage of the peak torque, was 1.7% across trials. With regard to the mechanical measurement of hydrodynamic forces, only Berger et al. (1995) has reported on the level of error. For their model, used to estimate lift and drag coefficients, the error in the mean measurements of lift and drag force was reported as being ‘less than 10%’. Clearly, the
Conclusion
In conclusion, the mechanical arm was shown to produce a controlled movement pattern, which is reliable and accurate to within ±1° for repeated trials and ±2.3° across different trials. The shoulder torque measurement was also shown to be reliable and accurate to within ±1.22 N m, over a range from 0 to 70 N m.
Differences in torque profiles for the quasi-static approach and the direct measurement of shoulder torque indicated that the quasi-static approach might greatly underestimate the
Acknowledgements
The mechanical arm model was designed and constructed in collaboration with the Department of Exercise and Sport Sciences, Manchester Metropolitan University, in consultation with the Department of Prosthetics and Orthotics, University of Salford.
References (17)
- et al.
Hydrodynamic drag and lift forces on human hand/arm models
Journal of Biomechanics
(1995) - et al.
Analysis of a swimmer's hand and arm in steady flow conditions using computational fluid dynamics
Journal of Biomechanics
(2002) - et al.
Improved accuracy and reliability of sweepback angle, pitch angle and hand velocity calculations in swimming
Journal of Biomechanics
(2001) - et al.
Determining propulsive force in front crawl swimming: a comparison of two methods
Journal of Sports Sciences
(1999) - et al.
Statistical methods for assessing agreement between two methods of clinical measurement
Lancet
(1986) Mechanics of Swimming and Flying
(1981)- et al.
Relationships among anthropometric and stroking characteristics of college swimmers
Medicine and Science in Sports and Exercise
(1986) - et al.
A proposed mechanical model for measuring propulsive forces in front crawl swimming