The pattern of hammer speed during a hammer throw and influence of gravity on its fluctuations

Hammer speed at release is one of the most important factors contributing to the distance of a hammer throw. Hammer speed follows a generally increasing trend during the throw, with one fluctuation per turn. The purpose of the present paper was to quantify the influence of gravity on the speed fluctuations. Eight experienced hammer throwers were studied with three-dimensional filming methods. Instantaneous values of hammer velocity and speed were calculated from the film data. The rate of change of hammer speed due to the tangential component of gravity was computed, and integrated to calculate the accumulated contribution of gravity to hammer speed at all instants of the throw. These values were subtracted from the corresponding values of hammer speed. The amplitude of the fluctuations was reduced in the corrected speed functions, indicating a contribution of gravity to the original fluctuations. However, the fluctuations were still clearly present in the corrected speed functions, indicating the existence of other causal factors.     

Influence of the direction of the cable force and of the radius of the hammer path on speed fluctuations during hammer throwing

Hammer speed increases gradually during a throw, but this general increasing trend has one fluctuation superimposed in each turn. In some throwers, gravity and the forward translation of the system produce most of the fluctuation; in others, a marked fluctuation remains after the effects of gravity and of the forward translation of the system have been subtracted out. The remaining fluctuation could be produced through two mechanisms: (a) pulling on the hammer cable in a direction alternately ahead and behind the position of the centroid of the hammer path and (b) alternately shortening and lengthening the distance between the hammer head and the centroid of its path. Three-dimensional film analysis of eight highly-skilled throwers showed that the portion of the hammer speed fluctuation not due to gravity nor to the forward motion is produced mainly by pulling alternately ahead and behind the position of the centroid of the hammer path.     

Individualized optimal release angles in discus throwing

The purpose of this study was to determine individualized optimal release angles for elite discus throwers. Three-dimensional coordinate data were obtained for at least 10 competitive trials for each subject. Regression relationships between release speed and release angle, and between aerodynamic distance and release angle were determined for each subject. These relationships were linear with subject–specific characteristics. The subject–specific relationships between release speed and release angle may be due to subjects’ technical and physical characteristics. The subject–specific relationships between aerodynamic distance and release angle may be due to interactions between the release angle, the angle of attack, and the aerodynamic distance. Optimal release angles were estimated for each subject using the regression relationships and equations of projectile motion. The estimated optimal release angle was different for different subjects, and ranged from 35° to 44°. The results of this study demonstrate that the optimal release angle for discus throwing is thrower-specific. The release angles used by elite discus throwers in competition are not necessarily optimal for all discus throwers, or even themselves. The results of this study provide significant information for understanding the biomechanics of discus throwing techniques.     

A kinematic study of center of mass motions in the hammer throw

Eight highly-skilled hammer throwers were studied using film analysis procedures. The location and velocity of the center of mass (c.m.) of each thrower, hammer and thrower-hammer system were calculated. The vertical component of motion of all three c.m.s followed cyclic patterns with one fluctuation per turn. The fluctuation of the c.m. of the thrower was ahead of that of the hammer by approximately a third of a cycle, and this made the periods of upward vertical acceleration of the system c.m. coincide approximately with the double-support phases. In the horizontal direction, the c.m.s of the thrower and of the hammer followed roughly trochoid patterns as a result of the combination of rotation with forward displacement across the throwing circle. Their rotations were out of synchrony by approximate synchrony with the hammer, or an essentially straight trajectory. The results of this study suggest that the investigation of the hammer throw might be facilitated by the use of a quasi-inertial non-rotating reference frame that follows the general motion of the system c.m. while ignoring its fluctuations within each turn.     

Influence of environmental factors on shot put and hammer throw range

On the rotating Earth, in addition to the Newtonian gravitational force, two additional relevant inertial forces are induced, the centrifugal and Coriolis forces. Using computer modelling for typical release heights and optimal release angles, we compare the influence of Earth rotation on the range of the male hammer throw and shot put with that of air resistance, wind, air pressure and temperature, altitude and ground obliquity. Practical correction maps are presented, by which the ranges achieved at different latitudes and/or with different release directions can be corrected by a term involving the effect of Earth rotation. Our main conclusion and suggestion is that the normal variations of certain environmental factors can be substantially larger than the smallest increases in the world records as acknowledged by the International Amateur Athletic Federation and, therefore, perhaps these should be accounted for in a normalization and adjustment of the world records to some reference conditions. Although this suggestion has certainly been made before, the comprehensiveness of our study makes it even more compelling. Our numerical calculations contribute to the comprehensive understanding and tabulation of these effects, which is largely lacking today.     

Declining track and field performance trends in recent years in the Austrian best results 1897-2019

Objectives:Plateauing of world records in sports has been suggested to reflect the limits of human physiology. Possible explanations include reduced doping or declining popularity that may even lead to a decrease in human performance. Such a decrease, however, has not yet been observed. We hypothesized that rather than a performance plateau, performance has recently declined.Methods:Fifteen athletic disciplines of the Austrian annual rankings were analyzed by regression statistics and the average best performance of the last 20 years compared to earlier periods.Results:The best performances occurred between 1980–1999 and were on average 2.56% (men) and 1.67% (women) better than between 2000–2019. This attenuation was significant in men in 200 m, 800 m, 1500 m, 10 km, long jump, javelin throw (p<0.05), high jump, pole vault, discus throw, shot put and hammer throw (p<0.001); and in women in 400 m, long jump, discus throw (p<0.05) and high jump (p<0.001). The greatest performance declines were observed in the men’s shot put (9.11%) and hammer throw (11.44%).Conclusions:The Austrian track and field annual best results show a performance decline following a peak, instead of a plateau. Future studies should address the causes and whether this also applies to other sports and countries.     

A model of optimal voluntary muscular control

Summary In the absence of detailed knowledge of how the CNS controls a muscle through its motor fibers, a reasonable hypothesis is that of optimal control. This hypothesis is studied using a simplified mathematical model of a single muscle, based on A. V. Hill's equations, with series elastic element omitted, and with the motor signal represented by a single input variable.Two cost functions were used. The first was total energy expended by the muscle (work plus heat). If the load is a constant force, with no inertia, Hill's optimal velocity of shortening results. If the load includes a mass, analysis by optimal control theory shows that the motor signal to the muscle consists of three phases: (1) maximal stimulation to accelerate the mass to the optimal velocity as quickly as possible, (2) an intermediate level of stimulation to hold the velocity at its optimal value, once reached, and (3) zero stimulation, to permit the mass to slow down, as quickly as possible, to zero velocity at the specified distance shortened. If the latter distance is too small, or the mass too large, the optimal velocity is not reached, and phase (2) is absent. For lengthening, there is no optimal velocity; there are only two phases, zero stimulation followed by maximal stimulation.The second cost function was total time. The optimal control for shortening consists of only phases (1) and (3) above, and is identical to the minimal energy control whenever phase (2) is absent from the latter.Generalization of this model to include viscous loads and a series elastic element are discussed.     

A comparison of kinematics between overarm throwing with 20% underweight, regular, and 20% overweight balls

The aim of this study was to compare the kinematics in throwing with a regular weighted handball with 20% lighter and heavier balls in female experienced handball players. In total, eight joint movements during the throw were analyzed. The analysis consisted of maximal angles, angles at ball release, and maximal angular velocities of the joint movements and their timings during the throw. Results on 24 experienced female team handball players (mean age 18.2 ± 2.1 years) showed that the difference in ball weight affected the maximal ball velocity. The difference in ball release velocity was probably a result of the significant differences in kinematics of the major contributors to overarm throwing: elbow extension and internal rotation of the shoulder. These were altered when changing the ball weight, which resulted in differences in ball release velocity.     

A three-dimensional analysis of overarm throwing in experienced handball players

The aim of this study was to investigate the contribution of upper extremity, trunk, and lower extremity movements in overarm throwing in team handball. In total, 11 joint movements during the throw were analyzed. The analysis consists of maximal angles, angles at ball release, and maximal angular velocities of the joint movements and their timing during the throw. Only the elbow angle (extension movement range) and the level of internal rotation velocity of the shoulder at ball release showed a significant relationship with the throwing performance. Also, a significant correlation was found for the timing of the maximal pelvis angle with ball velocity, indicating that better throwers started to rotate their pelvis forward earlier during the throw. No other significant correlations were found, indicating that the role of the trunk and lower limb are of minor importance for team handball players.     

Force, velocity and energy flow during the overarm throw in female handball players

The overarm throw of 56 female handball players was analysed cinematographically. The time courses of the ball velocity, the force on the ball, the energy flow to the ball as well as the velocities of wrist, elbow and hip were calculated. The mean ball velocity at release was 17.2 m s-1. The major part (73%) of the work on the ball appeared to be done in the last 50 ms of the throw. It is shown that high maximal segmental velocities are important pre-requisites for an optimal flow of energy to the ball during that last phase of the throw. The consecutive actions of body segments from larger proximal segments to the relatively smaller distal segments seem to be connected to intrinsic muscle properties and to a flow of energy from proximal to distal segments.     

Strain-dependent cross-bridge cycle for muscle. II. Steady-state behavior.

Quantitative predictions of steady-state muscle properties from the strain-dependent cross-bridge for muscle are presented. With a stiffness of 5.4 x 10(-4) N/m per head, a throw distance of 11 nm, and three allowed actin sites/head, isometric properties and their dependence on phosphate and nucleotide levels are well described if the tension-generating step occurs before phosphate release. At very low ATP levels, rigorlike states with negative strain are predicted. The rate-limiting step for cycling and ATP consumption is strain-blocked ADP release for isometric and slowly shortening muscle. Under rapid shortening, ATP hydrolysis on detached heads is the rate-limiting step, and the ratio of bound ATP to bound ADP.Pi increases by a factor of 7. At large positive strains, bound heads must be forcibly detached from actin to account for tension in rapid extension, but forced detachment in shortening has no effect without destroying isometric attached states. Strain-blocked phosphate release as proposed produces modest inhibition of the ATPase rate under rapid shortening, sufficient to give a maximum for one actin site per helix turn. Alternative cross-bridge models are discussed in the light of these predictions.     

Rapid and accurate estimation of release conditions in the javelin throw

We have developed a system to measure initial conditions in the javelin throw rapidly enough to be used by the thrower for feedback in performance improvement. The system consists of three subsystems whose main tasks are: (A) acquisition of automatically digitized high speed (200 Hz) video x, y position data for the first 0.1-0.2 s of the javelin flight after release (B) estimation of five javelin release conditions from the x, y position data and (C) graphical presentation to the thrower of these release conditions and a simulation of the subsequent flight together with optimal conditions and flight for the sam release velocity. The estimation scheme relies on a simulation model and is at least an order of magnitude more accurate than previously reported measurements of javelin release conditions. The system provides, for the first time ever in any throwing event, the ability to critique nearly instantly in a precise, quantitative manner the crucial factors in the throw which determine the range. This should be expected to much greater control and consistency of throwing variables by athletes who use system and could even lead to an evolution of new throwing techniques.     

A method to determine the displacement velocity field in the apical region of the Arabidopsis root

In angiosperms, growth of the root apex is determined by the quiescent centre. All tissues of the root proper and the root cap are derived from initial cells that surround this zone. The diversity of cell lineages originated from these initials suggests an interesting variation of the displacement velocity within the root apex. However, little is known about this variation, especially in the most apical region including the root cap. This paper shows a method of determination of velocity field for this region taking the Arabidopsis root apex as example. Assuming the symplastic growth without a rotation around the root axis, the method combines mathematical modelling and two types of empirical data: the published velocity profile along the root axis above the quiescent centre, and dimensions of cell packet originated from the initials of epidermis and lateral root cap. The velocities, calculated for points of the axial section, vary in length and direction. Their length increases with distance from the quiescent centre, in the root cap at least twice slower than in the root proper, if points at similar distance from the quiescent centre are compared. The vector orientation depends on the position of a calculation point, the widest range of angular changes, reaching almost 90°, in the lateral root cap. It is demonstrated how the velocity field is related to both distribution of growth rates and growth-resulted deformation of the cell wall system. Also changes in the field due to cell pattern asymmetry and differences in slope of the velocity profile are modelled.     

Optimal discus trajectories

A general 3-D dynamic model for men's and women's discus flight is presented including precession of spin angular momentum induced by aerodynamic pitching moment. Dependence of pitching moment coefficient on angle of attack is estimated from experiment. Numerical integration of 11 equations of motion for nominal release speed v₀=25 m/s and axial spin p₀=42 rad/s also requires 3 other release conditions; initial discus flight path angle β₀, pitch attitude θ₀, and roll angle φ₀. Optimal values for these release conditions are calculated iteratively to maximize range and are similar for both men and women. The optimal men's trajectory and range R=69.39 m is produced by the strategy β₀=38.4°, θ₀=30.7°, and φ₀=54.4°. Initial angular velocities except spin are chosen to minimize wobble but an optimal initial spin rate p₀=25.2 rad/s exists that also maximizes range. Optimal 3-D range exceeds that predicted by 2-D models because, although angle of attack and lift are negative initially, 3-D motion allows advantageous orientation of lift later in flight, with tilt of the axis of symmetry from vertical becoming much smaller at landing. Optimal strategies are discontinuous with wind speed, resulting in slicing and kiting strategies in large head and tail winds, respectively. Sensitivity of optimal range is largest to initial β₀ and least to φ₀. Present calculations do not account for dependence of initial release angle or spin on release velocity or among other release conditions.     

Architectural gear ratio and muscle fiber strain homogeneity in segmented musculature

In the segmented axial musculature of fishes and amphibians, the patterns of muscle fiber shortening depend on both the orientation of muscle fibers relative to the long axis of the body as well as the distance of fibers from the neutral axis of bending (vertebral column). In this study we use the relatively simple architecture of salamander hypaxial muscles to explore the separate and combined effects of these morphological features on muscle fiber strains during swimming. In Siren lacertina the external oblique (EO) muscle has more obliquely oriented muscle fibers and is located further from the neutral axis of bending than the internal oblique (IO) muscle. To examine the effect of muscle fiber angle on strain patterns during swimming, we used sonomicrometry to quantify architectural gear ratio (AGR=longitudinal strain/fiber strain) in these two hypaxial muscles. By comparing the muscle fiber strains and shortening velocities of the EO and IO during swimming, we test whether variation in mediolateral position of the muscle layers is counteracted by their differences in AGR. We find that despite substantial differences in mediolateral position, the EO and IO undergo similar fiber strains and shortening velocities for a given amount of axial bending. Our results show that variation in muscle fiber angle acts to counteract differences in mediolateral position, thereby minimizing variation in muscle fiber strain and shortening velocity during swimming. These results highlight the significance of both muscle architecture and muscle moment arms in determining the fiber strains required for a given movement.     

A linear canal-otolith interaction model to describe the human vestibulo-ocular reflex

A control systems model of the vestibulo-ocular reflex (VOR) originally derived for yaw rotation about an eccentric axis (Crane et al. 1997) was applied to data collected during ambulation and dynamic posturography. The model incorporates a linear summation of an otolith response due to head translation scaled by target distance, adding to a semi-circular canal response that depends only on angular head rotation. The results of the model were compared with human experimental data by supplying head angular velocity as determined by magnetic search coil recording as the input for the canal branch of the model and supplying linear acceleration as determined by flux gate magnetometer measurements of otolith position. The model was fit to data by determining otolith weighting that enabled the model to best fit the data. We fit to the model experimental data from normal subjects who were: standing quietly, walking, running, or making active sinusoidal head movements. We also fit data obtained during dynamic posturography tasks of: standing on a platform sliding in a horizontal plane at 0.2 Hz, standing directly on a platform tilting at 0.1 Hz, and standing on the tilting platform buffered by a 5-cm thick foam rubber cushion. Each task was done with the subject attending a target approximately 500, 100, or 50 cm distant, both in light and darkness. The model accurately predicted the observed VOR response during each test. Greater otolith weighting was required for near targets for nearly all activities, consistent with weights for the otolith component found in previous studies employing imposed rotations. The only exceptions were for vertical axis motion during standing, sliding, and tilting when the platform was buffered with foam rubber. In the horizontal axis, the model always fit near target data better with a higher otolith component. Otolith weights were similar with the target visible and in darkness. The model predicts eye movement during both passive whole-body rotation and free head movement in space implying that the VOR is controlled by a similar mechanism during both situations. Factors such as vision, proprioception, and efference copy that are available during head free motion but not during whole-body rotation are probably not important to gaze stabilization during ambulation and postural stabilizing movement. The linearity of the canal-otolith interaction was tested by re-analysis of the whole body rotation data on which the model is based (Crane et al. 1997). Normalized otolith-mediated gain enhancement was determined for each axis of rotation. This analysis uncovered minor non-linearities in the canal-otolith interaction at frequencies above 1.6 Hz and when the axis of rotation was posterior to the head. Received: 11 March 1998 / Received in revised form: 1 March 1999     

A model of the nystagmus induced by off vertical axis rotation

A three-dimensional model is proposed that accounts for a number of phenomena attributed to the otoliths. It is constructed by extending and modifying a model of vestibular velocity storage. It is proposed that the otolith information about the orientation of the head to gravity changes the time constant of vestibular responses by modulating the gain of the velocity storage feedback loop. It is further proposed that the otolith signals, such as those that generate L-nystagmus (linear acceleration induced nystagmus), are partially coupled to the vestibular system via the velocity storage integrator. The combination of these two hypotheses suggests that a vestibular neural mechanism exists that performs correlation in the mathematical sense which is multiplication followed by integration. The multiplication is performed by the otolith modulation of the velocity storage feedback loop gain and the integration is performed by the velocity storage mechanism itself. Correlation allows calculation of the degree to which two signals are related and in this context provides a simple method of determining head angular velocity from the components of linear acceleration induced by off-vertical axis rotation. Correlation accounts for the otolith supplementation of the VOR and the sustained nystagmus generated by off-vertical axis rotation. The model also predicts the cross-coupling of horizontal and vertical optokinetic afternystagmus that occurs in head-lateral positions and the reported effects of tilt on vestibular responses.     

A cross-bridge model that is able to explain mechanical and energetic properties of shortening muscle.

The responses of muscle to steady and stepwise shortening are simulated with a model in which actin-myosin cross-bridges cycle through two pathways distinct for the attachment-detachment kinetics and for the proportion of energy converted into work. Small step releases and steady shortening at low velocity (high load) favor the cycle implying approximately 5 nm sliding per cross-bridge interaction and approximately 100/s detachment-reattachment process; large step releases and steady shortening at high velocity (low load) favor the cycle implying approximately 10 nm sliding per cross-bridge interaction and approximately 20/s detachment-reattachment process. The model satisfactorily predicts specific mechanical properties of frog skeletal muscle, such as the rate of regeneration of the working stroke as measured by double-step release experiments and the transition to steady state during multiple step releases (staircase shortening). The rate of energy liberation under different mechanical conditions is correctly reproduced by the model. During steady shortening, the relation of energy liberation rate versus shortening speed attains a maximum (approximately 6 times the isometric rate) for shortening velocities lower than half the maximum velocity of shortening and declines for higher velocities. In addition, the model provides a clue for explaining how, in different muscle types, the higher the isometric maintenance heat, the higher the power output during steady shortening.     

Actomyosin-ADP States, Interhead Cooperativity, and the Force-Velocity Relation of Skeletal Muscle

Despite intense efforts to elucidate the molecular mechanisms that determine the maximum shortening velocity and the shape of the force-velocity relationship in striated muscle, our understanding of these mechanisms remains incomplete. Here, this issue is addressed by means of a four-state cross-bridge model with significant explanatory power for both shortening and lengthening contractions. Exploration of the parameter space of the model suggests that an actomyosin-ADP state (AM^∗ADP) that is separated from the actual ADP release step by a strain-dependent isomerization is important for determining both the maximum shortening velocity and the shape of the force-velocity relationship. The model requires a velocity-dependent, cross-bridge attachment rate to account for certain experimental findings. Of interest, the velocity dependence for shortening contraction is similar to that for population of the AM^∗ADP state (with a velocity-independent attachment rate). This accords with the idea that attached myosin heads in the AM^∗ADP state position the partner heads for rapid attachment to the next site along actin, corresponding to the apparent increase in attachment rate in the model.