# A MODELLING METHOD FOR DISCRETE LOW SAMPLMG FREQUENCY TEMPORAL SERIES ON THE EVALUATION OF INTRACYCLIC SWIMMING SPEED FLUCTUATIONS

### Abstract

Profiles of intra-cycle swimming speed fluctuations has been widely used as a high informative parameter on swirn~ningb iomechanics. Methods described in Iiterature can be divitled on: (i) frec swimming and (ii) linked swimming approaches. Linked swimming methods allow high sampling frequencies. NevertheIess, they present the disadvantage of mechanical links between the swimmer and the registration device. In the other hand, free swirmni~lgm ethods (eg. film ar~ti video methods) (nay allow CG stirdres, but tliey are very tirne consuming and low interactive if we consider high sampling frequencies. Interactivity with training, llowever. call be improved. if we can use a modelling method that can respect the phenomena cyclical characteristics. and requiring low sampling frequencies than, for instance, Fourier time series. 111 this paper, a method of discrete intra-cycle velocity fl~~ctuatioan alysis with reduced sampling frequencies is described. The method was used over velocity/time series obtained from intermittent light-trace photographic evaluation, and consists in a transformed polynomial repression to the estili~ationo f the first and last dependent temis of the regression equation (equal initial and final velocities and instantaneous accelerations). Three consecuti\re breaststroke cycles, sampled with a 5Hz frequency, were superimposed in accordance with a cycle period (T). estimated from the time interval between two consecutive absolute minimllnls. Optimised estimates of X r l l degree , polynomial coefficients were performed using Marqua1.t (1963) algorithm (Srutpul>hic.s 5.1. ) in successive trial and error regressions. with different T values, until rL maximum vi~lutw: as achieved. 011ceT was calculated. bl and bl = bg were also calculateti according to specially dcl-ived ecluations: 1-1 b, = -1x(I -l)biTl-l l . ~ and ' 1=2 i=l I The culves were derived and integrated (PC-hl~lrl~3l.h1 .3 in order to assess instantaneous and mean values of \,elocity and ac.celeration in ;~nd betoeen minir~~uamn d ~nasimlims ucct'ssivr velocity peak poiiits. Mean Ihorizcntal resultant impulses per phase were also estimated. Subjects Lvere 13 P o r t ~ ~ g ~ ~ e s top-level breast~trokersR. esults pointed o ~th~att: (i) mean minim~~vmel ocit!, associated with the recovery of the legs (V I ) \\.;IS .10 (k.035) 1n.s-1: (ii) mean maximal velocity associated with the Ies Lick (V2) \\,as 1.43 (f.039) tii.s-r: ( i i i ) I I I C ~ I1I1 linin1u:li i~ltc~.illedii~vttt' l~cit); ~sso~i;~t\veidtl l the tr,~nsitionp li;~se between leg and arm strokes (V3) \\(as 1 .O7 (k.0271 m.s- 1: [iii) mean pe;~h velocity associated with thc arm stroke (V 1) was 1.26 (k.O.78) ~ns-1:(i v) mean acceleration and ~.esultanitm pulse between V I ;~ndV 2 ~vere3 .03 (rt.i!-I) m.s-2 and 61.40 (k3.726) Ns: (v) betueen V2 and V i were - 1 .OX n1.s-2 and -2 1 . 1 ; (f3.478) Ns: (vi) betwern V3 ;~nci V-l \\.ere .h9 (k.0X-l) n1.s-2 ;~nrl 11.32 j f 1.853) Ns ;~nd( \!ill het\\/een V1 and V I \vrlt. -1.24 (+.02h) 111s-2a nd 5 I . I3 (f.962) Ns.
Section

Modelling / Simulation

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