Net force analysis during streamlined glide, dolphin kick, and front crawl at high velocities in competitive swimming : implications for optimal propulsion timing

This study aimed to identify the optimal transition velocities between streamlined glide (SL), underwater dolphin kick (DK), and front crawl (FC) during high-speed swimming. Ten elite female swimmers performed front crawl and dolphin kick trials in a long-course pool, and repeated the same motions under tethered conditions in a water flume to measure net force. Power-law fitting was applied to model net force as a function of flow velocity across the three movement conditions. The results revealed distinct patterns in the scaling coefficients <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mfenced><mml:mi>A</mml:mi></mml:mfenced></mml:math> and exponents <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mfenced><mml:mi>n</mml:mi></mml:mfenced></mml:math>, following the order: <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mi>SL</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>></mml:mo><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mi>DK</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo>></mml:mo><mml:mrow><mml:msub><mml:mi>A</mml:mi><mml:mrow><mml:mi>FC</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi>SL</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo><</mml:mo><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi>DK</mml:mi></mml:mrow></mml:msub></mml:mrow><mml:mo><</mml:mo><mml:mrow><mml:msub><mml:mi>n</mml:mi><mml:mrow><mml:mi>FC</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>. The fitted net force curves intersected at two velocities, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>U</mml:mi><mml:mrow><mml:mi>SL</mml:mi><mml:mo>-</mml:mo><mml:mi>DK</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>U</mml:mi><mml:mrow><mml:mi>DK</mml:mi><mml:mo>-</mml:mo><mml:mi>FC</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>, and for most swimmers, these intersection velocities exceeded their respective constant velocities, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mrow><mml:mi>DK</mml:mi><mml:mo>_</mml:mo><mml:mrow><mml:mrow><mml:mi>const</mml:mi></mml:mrow></mml:mrow></mml:mrow></mml:msub></mml:mrow></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mrow><mml:mi>FC</mml:mi><mml:mo>_</mml:mo><mml:mrow><mml:mrow><mml:mi>const</mml:mi></mml:mrow></mml:mrow></mml:mrow></mml:msub></mml:mrow></mml:math>. These intersection points indicate the optimal timing for initiating propulsive actions to minimise deceleration during the post-start and post-turn phases. A conceptual model was proposed to explain the phase transition strategy based on velocity-dependent net force profiles. Although individual variation was observed, most swimmers exhibited similar trends, supporting the applicability of the model. These findings provide a fluid mechanical perspective for optimising underwater strategies and may contribute to enhanced start and turn performance in competitive swimming.