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**18** 

*Portugal* 

**Modelling Propelling Force in Swimming** 

*1University of Beira Interior, Department of Sport Sciences, Covilhã 2Research Centre in Sports, Health and Human Development, Vila Real 3Polytechnic Institute of Bragança, Department of Sport Sciences, Bragança 4University of Trás-os-Montes and Alto Douro, Department of Sport Sciences,* 

Daniel A. Marinho1,2, Tiago M. Barbosa2,3, Vishveshwar R. Mantha2,4,

In the sports field, numerical simulation techniques have been shown to provide useful information about performance and to play an important role as a complementary tool to physical experiments. Indeed, this methodology has produced significant improvements in equipment design and technique prescription in different sports (Kellar et al., 1999; Pallis et al., 2000; Dabnichki & Avital, 2006). In swimming, this methodology has been applied in order to better understand swimming performance. Thus, the numerical techniques have been addressed to study the propulsive forces generated by the propelling segments (Rouboa et al., 2006; Marinho et al., 2009a) and the hydrodynamic drag forces resisting

Although the swimmer's performance is dependent on both drag and propulsive forces, within this chapter the focus is only on the analysis of the propulsive forces. Hence, this chapter covers topics in swimming propelling force analysis from a numerical simulation technique perspective. This perspective means emphasis on the fluid mechanics and computational fluid dynamics methodology applied in swimming investigations. One of the main aims for performance (velocity) enhancement of swimming is to maximize propelling forces whilst not increasing drag forces resisting forward motion, for a given trust. This chapter will concentrate on numerical simulation results, considering the scientific

Basically, numerical simulations consist of a mathematical model that replaces the Navier-Stokes equations with discretized algebraic expressions that can be solved by iterative computerized calculations. The Navier–Stokes equations describe the motion of viscous non-compressible fluid substances. These equations arise from applying Newton's second law to fluid motion, together with the assumption that the fluid stress is the sum of a diffusing viscous term (proportional to the gradient of velocity), plus a pressure term. A

forward motion (Silva et al., 2008; Marinho et al., 2009b).

simulation point-of-view, for this practical application in swimming.

**1. Introduction** 

 **Using Numerical Simulations** 

Abel I. Rouboa2,5 and António J. Silva2,4

*5University of Trás-os-Montes and Alto Douro,* 

*Exercise and Health, Vila Real* 

*Department of Engineering, Vila Real* 
