Optimal glide path during the freestyle flip turn - Lyttle, A.; Lloyd, D.; Blanksby, B.; Elliott, B. (1999)
The streamlined glide represents an integral component of the swim turn. The two determining factors that affect glide performance are the initial wall push-off velocity and the hydrodynamic drag that acts to decelerate the swimmer. This drag is related to the glide velocity, body form, degree of streamlining and the glide depth. A swimmer, through maintaining an appropriate glide depth and efficient streamline, will minimise drag and permit horizontal glide velocity to be maximised. This study aimed to determine the optimal glide path of the swimmer from the wall push-off to stroke resumption. Forty experienced, male swimmers of similar body shape, mass and height acted as subjects for the study. Drag-velocity and drag-depths curves were developed for the group based on passive drag measurements of the towed subjects at selected velocities (1.6, 1.9, 2.2, 2.5, 2.8 & 3.1 ms-1) and depths (surface, 0.2, 0.4 & 0.6 m deep). A linear fit was applied to each curve with regression values ranging from 0.85 - 0.99. A glide velocity-depth relationship was then calculated as a function of the drag force using a multiple linear regression (R2 = 0.98). A set of two differential equations were then developed given that the drag force was a function of both glide velocity and glide depth: dv = (avi + byi+ c) dt / m (1) dy = vi sinq dt (2) where dv = acceleration; vi = velocity of the swimmer; yi = glide depth; a and b = coefficients of velocity and depth from the multiple regression equation; c = constant from multiple regression equation; dt = change in time; m = mass of swimmer; dy = vertical component of swimmer`s velocity; and q = body alignment angle to horizontal. These equations were solved as a system of differential equations using trapezoid rule numerical integration with steps sizes of 1 ms. The body alignment to horizontal (q ) was used as the control variable with 11 control points set from the start to finish of the glide period. The summed horizontal velocity was then maximised by finding the optimal body alignment path using a quasi-Newton optimisation scheme. This optimisation was subject to velocity, depth and q boundary conditions. The results of the optimisation model revealed an optimal glide path based on the depth-velocity function of the passive drag force. This path indicates that swimmers should push-off the wall at approximately 0.4 m deep and maintain this glide depth for approximately 0.5 m for maximum drag reduction benefits at the faster velocities. Following this, swimmers should begin to ascend gradually for a further 0.5 m before rising more sharply to reach the surface and resume stroking at race pace.