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• Author: Scott P. McLean
• Journal of Applied Biomechanics
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## A Mathematical Model of Competitive Swimming in Pools with Currents

Swimmers may be placed at a disadvantage when water in a pool is actively circulated during competition. This circulation may produce currents in specific lanes which add to a swimmer’s speed in one direction and subtract from it in the other direction. This article presents a mathematical model of swimming in a lane with a current. It predicts that even small currents can add significantly to a swimmer’s race time. The effects of the current will not equal out over an even number of lengths swum because the swimmer always loses more time swimming against the current than he or she gains from swimming with the current. Mathematical simulations of races of various distances show that the losses in time can range from 100ths of a second in a 100-m sprint to several seconds in the longer distances. Since circulating water may create currents only in specific lanes, some swimmers may be placed at a disadvantage compared to others. A simple solution to the problem of currents is suggested.

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## Buoyancy, Gender, and Swimming Performance

This study investigated the relationship of gender and buoyancy to sprint swimming performance. The center of buoyancy (CB) and center of mass (CM) were measured using reaction board principles. Performance was evaluated as the time needed to complete the middle 13.7 m of a 22.9-m sprint for kicking and swimming trials. Nineteen female swimmers (mean ± SD, 21.9 ± 3.2 years) had significantly more body fat (24.1 ± 4.5%) than 13 male swimmers (21.7 ± 4.2 years, 14.8 ± 5.0%). Males swam and kicked significantly faster (p < .01) than females. Percent body fat, upper body strength, the distance between the CB and CM (d), and the buoyant force measured in 3 body positions all met the criteria for entrance into a regression equation. When gender was not controlled in the analysis, these variables accounted for 70% of the variance in swim time (p < .008). When gender was controlled in the analysis, these variables accounted for 45% of the variance in swim time (p = .06). Percent body fat accounted for the largest amount variance in both regression analyses (39%, p < .001; 18%, p = 0.02, respectively). Upper body strength accounted for 14% of the variance in swim time (p = .006) when gender was not controlled but only 4% when gender was controlled (p = .27). The distance d as measured in a body position with both arms raised above the head was the buoyancy factor that accounted for the greatest amount of variance in swim time (6% when gender was not controlled, p = .06, 10%; when gender was controlled, p = .07). Percent body fat, d, and the buoyant force accounted for no significant amount of variance in kick time. These data suggested that a swimmer’s buoyancy characteristics did have a small but important influence on sprint swimming performance.

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## Addition of an Approach to a Swimming Relay Start

Ten male collegiate swimmers (age = 20.2 ± 1.4 years, height = 184.6 ± 5.8 cm, mass = 82.9 ± 9.3 kg) performed 3 swimming relay step starts, which incorporated a one or two-step approach, and a no-step relay start. Time to 10 m was not significantly shorter between step and no-step starts. A double-step start increased horizontal takeoff velocity by 0.2 m/s. A single-step together start decreased vertical takeoff velocity by 0.2 m/s but increased takeoff height by 0.16 m. Subjects were more upright at takeoff by 4°, 2°, and 5° in the double-step, single-step apart, and single-step together starts, respectively, than in the no-step start. Entry angle was steeper by 2°, entry orientation was steeper by 3°, and entry vertical velocity was faster by 0.3 m/s in the single-step together start. Restricting step length by 50% had little effect on step starts with the exceptions that horizontal velocity was significantly reduced by 0.1 m/s in the double-step start and vertical takeoff velocity was increased by 0.2 m/s in the single-step together start. These data suggested that step starts offered some performance improvements over the no-step start, but these improvements were not widespread and, in the case of the double-step start, were dependent on the ability to take longer steps.

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## Relationship of Pelvis and Upper Torso Kinematics to Pitched Baseball Velocity

Generating consistent maximum ball velocity is an important factor for a baseball pitcher’s success. While previous investigations have focused on the role of the upper and lower extremities, little attention has been given to the trunk. In this study it was hypothesized that variations in pelvis and upper torso kinematics within individual pitchers would be significantly associated with variations in pitched ball velocity. Nineteen elite baseball pitchers were analyzed using 3-D high-speed motion analysis. For inclusion in this study, each pitcher demonstrated a variation in ball velocity of at least 1.8 m/s (range: 1.8–3.5 m/s) during his 10 fastball pitch trials. A mixed-model analysis was used to determine the relationship between 12 pelvis and upper torso kinematic variables and pitched ball velocity. Results indicated that five variables were associated with variations in ball velocity within individual pitchers: pelvis orientation at maximum external rotation of the throwing shoulder (p = .026), pelvis orientation at ball release (p = .044), upper torso orientation at maximum external rotation of the throwing shoulder (p = .007), average pelvis velocity during arm cocking (p = .024), and average upper torso velocity during arm acceleration (p = .035). As ball velocity increased, pitchers showed an increase in pelvis orientation and upper torso orientation at the instant of maximal external rotation of the throwing shoulder. In addition, average pelvis velocity during arm cocking and average upper torso velocity during arm acceleration increased as ball velocity increased. From a practical perspective, the athlete should be coached to strive for proper trunk rotation during arm cocking as well as strength and flexibility in order to generate angular velocity within the trunk for maximum ball velocity.

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## Relationship of Biomechanical Factors to Baseball Pitching Velocity: Within Pitcher Variation

To reach the level of elite, most baseball pitchers need to consistently produce high ball velocity but avoid high joint loads at the shoulder and elbow that may lead to injury. This study examined the relationship between fastball velocity and variations in throwing mechanics within 19 baseball pitchers who were analyzed via 3-D high-speed motion analysis. Inclusion in the study required each one to demonstrate a variation in velocity of at least 1.8 m/s (range 1.8–3.5 m/s) during 6 to 10 fastball pitch trials. Three mixed model analyses were performed to assess the independent effects of 7 kinetic, 11 temporal, and 12 kinematic parameters on pitched ball velocity. Results indicated that elbow flexion torque, shoulder proximal force, and elbow proximal force were the only three kinetic parameters significantly associated with increased ball velocity. Two temporal parameters (increased time to max shoulder horizontal adduction and decreased time to max shoulder internal rotation) and three kinematic parameters (decreased shoulder horizontal adduction at foot contact, decreased shoulder abduction during acceleration, and increased trunk tilt forward at release) were significantly related to increased ball velocity. These results point to variations in an individual's throwing mechanics that relate to pitched ball velocity, and also suggest that pitchers should focus on consistent mechanics to produce consistently high fastball velocities. In addition, pitchers should strengthen shoulder and elbow musculature that resist distraction as well as improve trunk strength and flexibility to maximize pitching velocity and help prevent injury.