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James G. Hay

There have been few attempts to synthesize the knowledge gleaned from the study of cyclic human locomotion and, specifically, to determine whether there are general laws that describe or govern all such forms of locomotion. The purpose of this paper was to test the hypothesis that, when a human participant performs multiple trials of a given form of cyclic locomotion at a wide range of speeds (S) and without constraint on cycle rate (CR) or cycle length (CL), the relationships of CR vs. S and CL vs. S have the same basic characteristics as do those for any other form of cyclic locomotion. Data were gathered from published and unpublished sources. For each participant and form of locomotion, CR-vs.-S and CL-vs.-S relationships were plotted on a common scattergram with S on the abscissa and both CR and CL on the ordinate. Analysis of data collected on 49 participants and 12 forms of locomotion showed that, for every combination of participant and form of locomotion considered (excluding combinations involving simulated locomotion), the relationships of CR vs. S and CL vs. S had the same basic characteristics. These relationships were quadratic in form with CR-vs.-S concave upward and CL-vs.-S concave downward. The factor that made the greater contribution to increases in S was a function of S, with CL the primary factor at low S and CR the primary factor at high S. In short, the results obtained provided unequivocal support for the hypothesis of the study. The basic CR-vs.-S and CL-vs.-S relationships observed for forms of actual locomotion were also observed for some, but not all, of the forms of simulated locomotion examined.

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James G. Hay

The purposes of this study were to determine the frequency with which triple jumpers used hop-dominated, balanced, and jump-dominated techniques to achieve their best distances in Olympic competition; whether the use of one of these techniques generally yielded greater actual distances than did the use of the others; and how the actual distances achieved by specific athletes were related to the way in which they distributed their efforts through the three phases. Data were collected at the 1996 Olympic Games in Atlanta. About half the competitors used a hop-dominated technique. Balanced and jump-dominated techniques were just as effective as hop-dominated techniques. Four of the top eight finishers tended to use hop percentages that were longer than the optimum for them.

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James G. Hay

The purpose of this study was to determine whether elite long jumpers make use of a visual control strategy during the final four strides of their approach. Analysis of existing film records revealed that all subjects adopted a visual control strategy at some point during their final strides. Data for the last four strides were insufficient to permit the actual point to be identified in most cases. A second study was undertaken to determine the location of this point and whether it is a function of the error accumulated during the preceding phase of the approach. The performances of 19 subjects were recorded over the last 8–10 strides of the approach. On average, the subjects adopted a visual control strategy on the 5th-last stride. The point at which this strategy was adopted was apparently unrelated to the error in the accuracy of striding up to that point.

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Bing Yu and James G. Hay

The purposes of this study were (a) to determine the magnitude of the angular momentum elite triple jumpers possess during each of the three phases of a triple jump, and (b) to identify those components of the angular momentum that are closely related to the actual distance of the triple jump. Angular momentum about each of three orthogonal axes at the takeoff of each of the last stride, hop, step, and jump was computed from the smoothed 3-D coordinate data of 21 body landmarks and joint centers and normalized to body mass (mb) and standing height (hb). Linear and nonlinear regression analyses were conducted to examine the relationships between angular momenta and actual distance. The results suggested that the estimated optimum magnitude of this side-somersaulting angular momentum is 0.0069 mb hb 2 kg · m2 · s-1 toward the side of the free leg, that the side-somersaulting angular momentum needed at the takeoff of the step should be obtained during the support phase of the hop; and that the change in the side-somersaulting angular momentum during the support phase of the step should be minimized.

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Timothy J. Koh and James G. Hay

The motions of the landing leg preceding the support phases of the hop, step, and jump, thought to be important in the triple jump, are described. Film analysis of 16 elite male triple jumpers competing in the 1986 and 1987 TAC (U.S. national) Championships showed that backward sweeping, or “active,” landings were used prior to each support phase. A mathematical model showed that muscle action reduced the forward horizontal velocity of the landing foot during each landing. There were no statistically significant correlations of measures of landing leg motion with measures of performance. The landing prior to the jump phase was less active than the two preceding landings. However, the elite athletes in the present study were much more active in this landing than athletes of lesser ability. There was also some indication among the subjects of this study that activeness in this landing was associated with long triple jumps. Thus, activeness in this landing appears to be desirable but very difficult to achieve and/or use effectively.

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Toshimasa Yanai and James G. Hay

The purpose of this study was to test the hypothesis that, in human running at a given speed, runners select the combination of cycle rate (CR) and cycle length (CL) that minimizes the power generated by the muscles. A 2-D model of a runner consisting of a trunk and two legs was defined. A force actuator controlled the length of each leg, and a torque actuator controlled the amplitude and frequency of the backward and forward swing of each leg. The sum of the powers generated by the actuators was determined for a range of CRs at each of a series of speeds. The CR and CL vs. speed relationships selected for the model were derived from a series of CR and CL combinations that required the least power at each speed. Two constraints were imposed: the maximum amplitude of the forward and backward swing of the legs (±50°) and the minimum ground contact time needed to maintain steady-state running (0.12 sec). The CR vs. speed and CL vs. speed relationships derived on the basis of a minimum power strategy showed a pattern similar to those reported for longitudinal (within-subjects) analyses of human running. The anatomical constraint set a limit on the maximum CL attainable at a given speed, and the temporal constraint made CL decrease at high speeds. It was concluded that the process for selecting CL-CR combinations for human running has characteristics similar to the process for solving a constrained optimization problem.

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John A. Miller Jr and James G. Hay

The horizontal jumps at the 1985 TAC (U.S. national) Championships in Indianapolis were filmed as part of the Elite Athlete Project of the U.S. Olympic Committee. Jumps by Willie Banks and Mike Conley were especially outstanding and, because of this as well as some excellent performances by the third and fourth place finishers, an analysis of the jumping techniques used by the top four finishers was conducted. Its purposes were (a) to determine selected kinematic data for a world record triple jump, and (b) to compare these data with corresponding data for previous performances by the same athlete and for performances by other elite triple jumpers. A comparison of the phase distances and phase ratios for the 1985 TAC jumps with those for the best analyzed jump by Banks, Conley, and Joyner at some previous meets revealed that, as they increased their effective distances, all three decreased the emphasis they placed on the step phase. The best athletes seem to use a “pawing” (or active) landing prior to takeoff into the step phase and a “blocking” landing prior to takeoff into the jump phase.

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Yi-Chung Pai and James G. Hay

The purpose of this study was to determine the validity of the quasi-static assumption—that fluid forces exerted under unsteady flow conditions are equal to those exerted under similar steady flow conditions—in the case of a cylindrical model oscillating in a vertical plane about a transverse axis normal to the flow. The findings indicated that the quasi-static approach is applicable only to cyclic motions with low frequencies and small accelerations. For swimming motions that involve high frequencies and high accelerations, like those that occur in competitive swimming, the vortex shedding effect and the added mass effect must be taken into account if accurate values are to be obtained for hydrodynamic forces.

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Timothy J. Koh and James G. Hay

The motions of the landing leg in the final three strides of the approach in the long jump are described, as are the relationships of these landing leg motions with performance. Film analysis of 19 elite male long jumpers competing in the 1986 and 1987 TAG (U.S. national) Championships showed that backward sweeping, or “active,” landings were used in each stride considered. However, the landing in the last stride was less active than those in the two preceding strides. A mathematical model showed that muscle action reduced the forward horizontal velocity of the landing foot in each landing. There were no statistically significant correlations of measures of landing leg motion with measures of performance. However, there was some indication that landing leg motion plays a role in lowering the center of gravity in the second-last stride and that this lowering increases the distance of the jump. There was also some indication that placing the landing foot well forward of the body at the end of the last stride benefits the distance of the jump, perhaps by promoting the development of vertical velocity during the support phase of the jump. This appears to be more important than minimizing the loss in horizontal velocity during the support phase of the jump.

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James G. Hay and John A. Miller Jr.

The purposes of this study were (a) to describe the techniques used by elite triple jumpers and (b) to determine which characteristics were significantly related to the officially recorded distance of the jump. The subjects were the 12 finalists in the Triple Jump at the 1984 Olympic Games. Two motion-picture cameras placed with their optical axes at right angles to the runway were used to record the performances of the subjects. Means and standard deviations of the variables identified in a theoretical model and correlations between these variables and the distance of the jump were computed. Correlation of the distances achieved in each of the phases with the official distance of the jump suggested that, although the hop and jump phases made greater percentage contributions to the official distance than did the step phase, they accounted for only small amounts of the variance in that distance. Significant correlations of other independent variables with the distance of the jump suggested that the more the athlete's resources are expended prior to the jump phase and the more vertical his effort at takeoff into the jump, the better is the final result.