A method for the assessment of area-elastic surfaces

Modeling a Viscoelastic Gymnastics Landing Mat during Impact

Landing mats that can undergo a large amount of area deformation are now essential for the safe completion of landings in gymnastics. The objective of this study was to develop an analytical model of a landing mat that reproduces the key characteristics of the mat-ground force during impact with minimal simulation run time. A force plate and two high-speed video cameras were used to record the mat deformation during vertical drop testing of a 24-kg impactor. Four increasingly complex point mass spring-damper models, from a single mass spring-damper system, Model 1, to a 3-layer mass spring-damper system, Model 4, were constructed using Matlab to model the mat's behavior during impact. A fifth model composed of a 3-layer mass spring-damper system was developed using visual Nastran 4D. The results showed that Models 4 and 5 were able to match the loading phase of the impact with simulation times of less than 1 second for Model 4 and 28 seconds for Model 5. Both Models 4 and 5 successfully reproduced the key force-time characteristics of the mat-ground interface, such as peak forces, time of peak forces, interpeak minima and initial rates of loading, and could be incorporated into a gymnast-mat model.

Video Analysis of the Deformation and Effective Mass of Gymnastics Landing Mats

INTRODUCTION

Landing mats that undergo large area deformation are now essential for the safe completion of landings in gymnastics. The aim of this study was to determine the effective mass, shock transmission time, and deformation characteristics of a mat during impacts using high-speed video and to improve the accuracy of measuring foot-mat contact forces during landing. For validation, the same variables need to be accurately assessed using accelerometer and force plate data.

METHODS

A 24-kg impactor with an attached accelerometer was dropped onto the sample mat from various heights. The surface deformation of the mat was recorded using high-speed video, and force data were obtained from a force plate beneath the mat.

RESULTS

The maximum vertical deformations were between 0.088 and 0.118 m, with corresponding volume deformation estimates ranging from 0.030 to 0.044 m3. The delay between accelerometer and force plate readings at initial contact was approximately 7 ms. The delay between peak acceleration and peak force was 3 ms. The peak acceleration calculated from the video data was within 2.5% of that recorded via the accelerometer. The effective mass of the mat being accelerated corresponded to forces that ranged from 481 to 930 N, up to 12% of the peak force.

CONCLUSIONS

The acceleration estimates obtained from high-speed video were combined with the effective mass estimates from the volume calculation to give peak calculated forces at the bottom of the mat to within -1.1 to +3.7% of the force recorded via the force plate. The use of high-speed video can be used to give data of sufficient accuracy for measuring foot/mat contact forces in gymnastics landings.

Simulation of the influence of sports surfaces on vertical ground reaction forces during landing

In many biomechanical analyses, the vertical ground reaction force (GRF) is measured by force plates. However, if force plates are fixed on elastic surfaces, the force signals have low-frequency oscillations superimposed. The question arises, as to whether this oscillation results from the response of the athlete to the surface properties or from the fixation of the force plate on the elastic surface. For the simulation of the vertical GRF, a mechanical model was developed that combines three submodels representing the surface, the athlete and the force plate. The simulations were carried out for landings on concrete and wooden elastic surfaces, without and with the force plate, respectively. Comparison of the two surfaces showed that, on the elastic surface, the passive peak of the vertical GRF was lower and was reached later than on the concrete surface. Thus a lower force rate was possible during the landing on the elastic surface (concrete: 186 body weight per second; wooden: 164 body weight per second), which can reduce the risk of damaging the joint cartilage. The simulations also showed that the time course of the GRF was changed by a rippling effect when the force plate was fixed on the elastic surface. The rippling was not the result of a change in the athlete's movements, because the parameters of the athlete submodel were not changed. The rippling induced by the force plate hinders the analysis of the GRF time course involving the real peak force and the force rate.

Simulation of the Vertical Ground Reaction Force on Sport Surfaces during Landing

The surface-athlete interaction is discussed as one possible factor in overuse injuries, as the ground reaction force does not depend only on the athlete’s movement during surface contact but also on the mechanical properties of the playing surface. Since it is extremely difficult to measure the ground reaction force on an area-elastic surface, two damped linear-spring models were combined to calculate both the vertical ground reaction force on area-elastic surfaces and their deformations during the athlete’s landing from a jump height of 0.45 m. The athlete model consists of 4 segments (feet, shanks, thighs, and rest of the body) and the surface model consists of 5 segments each connected (a) to the concrete and (b) to each other via an additional imaginary segment. While the connections to the concrete were kept constant, the surface mass and the connections between the segments were varied in order to consider different degrees of area-elasticity of the simulated surfaces. With this approach it was shown that both the passive and active maximum of the vertical ground reaction force depend only on the maximum deformation of the surface, whereas the force rates vary greatly for identical maximum deformations. It appears that these differences increase with increasing maximum deformation. Therefore, in constructing area-elastic sport surfaces, the maximum deformation allowed should be as large as would coincide with other functions the surface must fulfill. Subsequently, the surface mass interacting with the athlete during landing should be large and the damping properties between these mass-segments should be very small.

Assessment of the mechanical properties of area-elastic sport surfaces with video analysis

Mechanical properties of a surface are assumed to be of importance with respect to injuries, comfort, and performance in sport. For a better understanding of the factors that do influence the etiology of injuries as well as comfort, a method was developed to compare mechanical characteristics of wooden area-elastic indoor surfaces. The method was based on video analysis of markers mounted on the surface during tests using human subjects performing movements. The method provided information concerning deflection, area-elasticity, and vibration. With the proposed methodology it was possible to detect differences with respect to these variables in differently built wooden sport surfaces. The accuracy of the analysis was greater than 0.1 mm. The results show that it was possible to use the proposed methodology in the assessment of the area-elastic wooden sport surfaces. This information may be at help in understanding the relation between surface characteristics and surface-related injuries, comfort, and possible fatigue.