A power equation for the sprint in speed skating.

An analysis of the start of the 500 m speed skating races during the 1988 Olympic Winter Games showed a remarkably high correlation between the acceleration of the skater in the first second of the sprint and the final time (r = -0.75). In this study a power equation is used to explain this high coefficient of correlation. The performance in speed skating is determined by the capability of external power production by the speed skater. This power is necessary to overcome the air and ice friction and to increase the kinetic energy of the skater. Numerical values of the power dissipated to air and ice friction, both dependent on speed, are obtained from ice friction and wind tunnel experiments. Using aerobic and anaerobic power production as measured during supra maximal bicycle tests of international-level speed skaters, a model of the kinetics of power production is obtained. Simulation of power production and power dissipation yields values of speed and acceleration and, finally, the performance time of the sprint during speed skating. The mean split time at 100 m and the final time at 500 m in these races, derived from simulation, were 10.57 s (+/- 0.31) and 37.82 s (+/- 0.96), respectively. The coefficient of correlation between the simulated 500 m times and the actual 500 m times was 0.90. From the results of this study it can be concluded that the distribution of the available anaerobic energy is an important factor in the short lasting events. For the same amount of anaerobic energy the better sprinters appear to be able to liberate considerably more energy at the onset of the race than skaters of lower performance level.     

Physiological and biomechanical comparison of roller skating and speed skating on ice

Eight well trained marathon skaters performed all-out exercise tests during speed skating on ice and roller skating. To compare these skating activities in relation to the concept of training specificity, relevant physiological (VO2, VE, RER and heart rate) and biomechanical variables (derived from film and video analysis) were measured. There were no significant differences between oxygen uptake (50.5 +/- 8.0 and 53.3 +/- 6.7 ml.min-1.kg-1), ventilation (102.4 +/- 11.2 and 116.0 +/- 11.1 1.min-1) or heart rate (174 +/- 12.2 and 176 +/- 14.5 min-1) between speed and roller skating. In roller skating a higher RER (1.16 +/- 0.1 cf. 1.05 +/- 0.1) was found. Power, work per stroke and stroke frequency were equal. Due to a higher coefficient of friction the maximal roller skating speed was lower. The effectiveness of push-off and parameters concerning the skating techniques showed no differences. In roller skating a 7.5% higher angle of the upper leg in the gliding phase occurred. It is speculated that the blood flow through the extensor muscles might be higher in roller skating. It is concluded that roller skating can be considered as a specific training method which may be used by trained speed skaters in the summer period.     

The Influence of Normal Load and Sliding Speed on Frictional Properties of Skin

The study of frictional properties of human skin is important for medical research, skin care products and textile exploi- tation. In order to investigate the influence of normal load and sliding speed on the frictional properties of skin and its possible mechanism, tests were carded out on a multi-specimen friction tester. When the normal load increases from 0.1 N to 0.9 N, normal displacement and the friction coefficient of skin increase. The friction coefficient is dependent on the load, indicating that both adhesion and deformation contribute to the friction behaviour. The deformation friction was interpreted using the plough model of friction. When sliding speed increases from 0.5 mm·s^-1 to 4 mm·s^-1, the friction coefficient increases and ＂stick-slip＂ phenomena increase, indicating that hysteretic friction contributes to the friction. The hysteretic friction was in- terpreted using schematic of energy translation during the rigid spherical probe sliding on the soft skin surface, which provides an explanation for the influence of the sliding speed on the frictional characteristics of the skin.     

Frictional properties of regenerated cartilage in vitro

Although tribological function is the most important mechanical property of articular cartilage, few studies have examined this function in tissue-engineered cartilage. We investigated changes in the frictional properties of cartilage regenerated from the inoculation of rabbit chondrocytes into fibroin sponge. A reciprocating friction-testing apparatus was used to measure the friction coefficient of the regenerated cartilage under a small load. The specimen was slid against a stainless steel plate in a water vessel filled with physiological saline. The applied load was 0.03 N, the stroke length was 20 mm, and the mean sliding velocity was 0.8 mm/s. The friction coefficient of the regenerated cartilage decreased with increasing cultivation time, because a hydrophilic layer of synthesized extracellular matrix was formed on the fibroin sponge surface. The friction coefficient of the regenerated cartilage was as low as that of natural cartilage in the early stages of the sliding tests, but it increased with increasing duration of sliding owing to exudation of interstitial water from the surface layer.     

Coordination of leg muscles during speed skating

Five speed skaters of elite performance level and six speed skaters of trained level were subjected to an inverse dynamical analysis during speed skating. Push-off forces were registered by means of special skates. Myoelectric activity (EMG) of ten leg muscles and cinematographic data were recorded. Linked segment modelling yielded net joint moments and joint powers. The speed skating technique is characterized by a typical horizontal position of the trunk and a suppression of a plantar flexion during the push-off. This technique, necessary to reduce external friction, constrains the transfer of rotation in joints to translation of the mass center of the body. In spite of constrained push-off, the EMG levels of the leg muscles show a proximo-distal temporal order which to a certain extent is comparable to that previously found in an unconstrained vertical jump. This proximo-distal sequence is also reflected by the time courses of the net moment and net power output in hip, knee and ankle joints. The temporal sequence in activation levels of activated muscles is not different between elite and trained speed skaters. The difference in performance level between these groups obviously has an origin in the ability of the elite speed skaters to realise larger net joint moments. Differences in net joint moments and in kinematics result in a higher power output and a lower air frictional force for the elite than for the trained speed skaters.     

Evaluation of the superficial characteristics of articular cartilage using evanescent waves in the friction tests with intermittent sliding and loading

Articular cartilage plays an important role in the lubrication of synovial joints because of its peculiar characteristics. In this work, the frictional and superficial characteristics of articular cartilage were evaluated simultaneously during intermittent sliding and loading. The apparatus used for the analysis of the articular surface was based on the evanescent waves, where a laser light was reflected at the interface between a prism and a specimen of articular cartilage. Friction forces were measured due to the sliding of specimens on the prism. Images of reflected light were analyzed and attenuation of the reflectance was associated with the presence of collagen fibers near the interface, which interacted with the evanescent waves because of the high refractive index of these fibers. Specimens were tested in the intervals of 5.5 min with an interruption of 10 and 30 s in the sliding and loading. Results indicated a decrease in the both friction coefficient and attenuation of reflectance after the unloading. The level of reduction of the friction as well as of the attenuation of reflectance increased as the time of unloading increased. Decrease of friction after unloading was related to the decrease of collagen contents, or increase in water contents, at the articular surface, which was observed through the decrease of the attenuation of reflectance. Results indicated that the increase in the water content at the articular surface and the rehydration ability of articular cartilage after unloading could be responsible for the maintenance of friction in low levels.     

Design and verification of a simple 3D dynamic model of speed skating which mimics observed forces and motions

Advice about the optimal coordination pattern for an individual speed skater, could be addressed by simulation and optimization of a biomechanical speed skating model. But before getting to this optimization approach one needs a model that can reasonably match observed behaviour. Therefore, the objective of this study is to present a verified three dimensional inverse skater model with minimal complexity, which models the speed skating motion on the straights. The model simulates the upper body transverse translation of the skater together with the forces exerted by the skates on the ice. The input of the model is the changing distance between the upper body and the skate, referred to as the leg extension (Euclidean distance in 3 D space). Verification shows that the model mimics the observed forces and motions well. The model is most accurate for the position and velocity estimation (respectively 1.2% and 2.9% maximum residuals) and least accurate for the force estimations (underestimation of 4.5–10%). The model can be used to further investigate variables in the skating motion. For this, the input of the model, the leg extension, can be optimized to obtain a maximal forward velocity of the upper body.     

An approximate simulation model for initial luge track design

Competitive and recreational sport on artificial ice tracks has grown in popularity. For track design one needs knowledge of the expected speed and acceleration of the luge on the ice track. The purpose of this study was to develop an approximate simulation model for luge in order to support the initial design of new ice tracks. Forces considered were weight, drag, friction, and surface reaction force. The trajectory of the luge on the ice track was estimated using a quasi-static force balance and a 1d equation of motion was solved along that trajectory. The drag area and the coefficient of friction for two runs were determined by parameter identification using split times of five sections of the Whistler Olympic ice track. The values obtained agreed with experimental data from ice friction and wind tunnel measurements. To validate the ability of the model to predict speed and accelerations normal to the track surface, a luge was equipped with an accelerometer to record the normal acceleration during the entire run. Simulated and measured normal accelerations agreed well. In a parameter study the vertical drop and the individual turn radii turned out to be the main variables that determine speed and acceleration. Thus the safety of a new ice track is mainly ensured in the planning phase, in which the use of a simulation model similar to this is essential.     

A geometrical model of speed skating the curves

The centripetal force in speed skating the curves has to be delivered by the push off force which also does the external work to maintain the speed. Based on the geometry of the speed skating oval and the sideward push off characteristics in speed skating, a mathematical model of the power output in skating the curves was deduced. The power required to follow the curve is dependent on the mean speed in the curve, the work per stroke and the radius of the speed skating oval. Measurements (by means of film and video analysis) during the 5000 m races at the European Championships for ladies (n = 16) yielded on the one hand power from the geometrical model and on the other hand power losses due to air- and ice- friction. The difference between power delivered and power lost is used by the skaters to increase their speed. The difference between predicted power and measured power used to increase the kinetic energy of c.g. was only 3% thereby providing strong support for the validity of the model. The analysis suggested that skaters who want to accelerate in the curves should increase their work per stroke. The model can be a useful tool to provide insight into this form of human locomotion and its optimization under competitive conditions.     

The Frictional Coefficient of Bovine Knee Articular Cartilage

1 Introduction Cartilage has excellent biomechanical and tri- bological properties with low friction and minimum wear in diarthrodial joints throughout the lifetime of most people, and the lifetime of articular cartilage can be 40 years or longer. This has inspired material and bionic scientists to study the mechanism of such excellent tri- bological characteristics in order to develop artificial joints. Various mechanisms have been proposed to ex- plain the remarkable low friction behavior of…     

In situ friction measurement on murine cartilage by atomic force microscopy

Articular cartilage provides a low-friction, wear-resistant surface for the motion of diarthrodial joints. The objective of this study was to develop a method for in situ friction measurement of murine cartilage using a colloidal probe attached to the cantilever of an atomic force microscope. Sliding friction was measured between a chemically functionalized microsphere and the cartilage of the murine femoral head. Friction was measured at normal loads ranging incrementally from 20 to 100 nN with a sliding speed of 40 microm/s and sliding distance of 64 microm. Under these test conditions, hydrostatic pressurization and biphasic load support in the cartilage were minimized, providing frictional measurements that predominantly reflect boundary lubrication properties. Friction coefficients measured on murine tissue (0.25+/-0.11) were similar to those measured on porcine tissue (0.23+/-0.09) and were in general agreement with measurements of boundary friction on cartilage by other researchers. Using the colloidal probe as an indenter, the elastic mechanical properties and surface roughness were measured in the same configuration. Interfacial shear was found to be the principal mechanism of friction generation, with little to no friction resulting from plowing forces, collision forces, or energy losses due to normal deformation. This measurement technique can be applied to future studies of cartilage friction and mechanical properties on genetically altered mice or other small animals.     

Constituents and pH changes in protein rich hyaluronan solution affect the biotribological properties of artificial articular joints.

The relationship between the coefficient of friction and pH value or protein constituents of lubricating fluid, together with viscosity, were studied within a bearing surface model for artificial joint, ultra-high molecular weight polyethylene (UHMWPE) against stainless steel (SUS), using a mechanical spectrometer. Four lubricants were tested in this study: sodium hyaluronate (HA), HA with albumin, HA with gamma-globulin, and HA with (L)alpha-dipalmitoyl phosphatidylcholine ((L)alpha-DPPC). The coefficient of friction between UHMWPE and SUS in HA with albumin or HA with gamma-globulin varied from 0.035 to 0.070 depending on angular velocity and pH. The coefficient of friction in HA or HA with (L)alpha-DPPC varied from 0.023 to 0.045 depending on angular velocity and pH. The variation in pH for HA with albumin had a large effect on the coefficient of friction at low range of angular velocity with viscosity independence. The variation in pH for HA with gamma-globulin had a large effect on the coefficient of friction with viscosity dependence at high angular velocity. The addition of (L)alpha-DPPC showed a small effect on the coefficient of friction at low angular velocity. This study confirms that the presence of albumin in the lubricant promotes pH dependence and viscosity independence of the tribological properties at low speed while the presence of globulin promotes pH and viscosity independence at low speed and promotes pH and viscosity dependence at high speed in the lubrication of UHMWPE against SUS. This study supports the clinical hypothesis that the effect of constituents and pH changes in periprosthetic fluid for the lubrication is a clue toward resolving many complications after total joint replacement.     

Physical Factors Influencing Pleasant Touch during Tactile Exploration

Background

When scanning surfaces, humans perceive some of their physical attributes. These percepts are frequently accompanied by a sensation of (un)pleasantness. We therefore hypothesized that aspects of the mechanical activity induced by scanning surfaces with fingertips could be objectively associated with a pleasantness sensation. Previously, we developed a unidimensional measure of pleasantness, the Pleasant Touch Scale, quantifying the pleasantness level of 37 different materials. Findings of this study suggested that the sensation of pleasantness was influenced by the average magnitude of the frictional forces brought about by sliding the finger on the surface, and by the surface topography. In the present study, we correlated (i) characteristics of the fluctuations of frictional forces resulting from the interaction between the finger and the surface asperities as well as (ii) the average friction with the sensation of pleasantness.

Results

Eight blindfolded participants tactually explored twelve materials of the Pleasant Touch Scale through lateral sliding movements of their index fingertip. During exploration, the normal and tangential interaction force components, f_N and f_T, as well as the fingertip trajectory were measured. The effect of the frictional force on pleasantness sensation was investigated through the analysis of the ratio f_T to f_N, i.e. the net coefficient of kinetic friction, μ. The influence of the surface topographies was investigated through analysis of rapid f_T fluctuations in the spatial frequency domain. Results showed that high values of μ were anticorrelated with pleasantness. Furthermore, surfaces associated with fluctuations of f_T having higher amplitudes in the low frequency range than in the high one were judged to be less pleasant than the surfaces yielding evenly distributed amplitudes throughout the whole spatial frequency domain.

Conclusion

Characteristics of the frictional force fluctuations and of the net friction taking place during scanning can reliably be correlated with the pleasantness sensation of surfaces.     

Experimental evaluation of the power balance model of speed skating.

Prediction of speed skating performance with a power balance model requires assumptions about the kinetics of energy production, skating efficiency, and skating technique. The purpose of this study was to evaluate these parameters during competitive imitations for the purpose of improving model predictions. Elite speed skaters (n = 8) performed races and submaximal efficiency tests. External power output (P(o)) was calculated from movement analysis and aerodynamic models and ice friction measurements. Aerobic kinetics was calculated from breath-by-breath oxygen uptake (Vo(2)). Aerobic power (P(aer)) was calculated from measured skating efficiency. Anaerobic power (P(an)) kinetics was determined by subtracting P(aer) from P(o). We found gross skating efficiency to be 15.8% (1.8%). In the 1,500-m event, the kinetics of P(an) was characterized by a first-order system as P(an) = 88 + 556e(-0.0494t) (in W, where t is time). The rate constant for the increase in P(aer) was -0.153 s(-1), the time delay was 8.7 s, and the peak P(aer) was 234 W; P(aer) was equal to 234[1 - e(-0.153(t-8.7))] (in W). Skating position changed with preextension knee angle increasing and trunk angle decreasing throughout the event. We concluded the pattern of P(aer) to be quite similar to that reported during other competitive imitations, with the exception that the increase in P(aer) was more rapid. The pattern of P(an) does not appear to fit an "all-out" pattern, with near zero values during the last portion of the event, as assumed in our previous model (De Koning JJ, de Groot G, and van Ingen Schenau GJ. J Biomech 25: 573-580, 1992). Skating position changed in ways different from those assumed in our previous model. In addition to allowing improved predictions, the results demonstrate the importance of observations in unique subjects to the process of model construction.     

Lubrication mode analysis of articular cartilage using Stribeck surfaces

Lubrication of articular cartilage occurs in distinct modes with various structural and biomolecular mechanisms contributing to the low-friction properties of natural joints. In order to elucidate relative contributions of these factors in normal and diseased tissues, determination and control of lubrication mode must occur. The objectives of these studies were (1) to develop an in vitro cartilage on glass test system to measure friction coefficient, mu; (2) to implement and extend a framework for the determination of cartilage lubrication modes; and (3) to determine the effects of synovial fluid on mu and lubrication mode transitions. Patellofemoral groove cartilage was linearly oscillated against glass under varying magnitudes of compressive strain utilizing phosphate buffered saline (PBS) and equine and bovine synovial fluid as lubricants. The time-dependent frictional properties were measured to determine the lubricant type and strain magnitude dependence for the initial friction coefficient (mu(0)=mu(t-->0)) and equilibrium friction coefficient (mu(eq)=mu(t-->infinity)). Parameters including tissue-glass co-planarity, normal strain, and surface speed were altered to determine the effect of the parameters on lubrication mode via a 'Stribeck surface'. Using this testing apparatus, cartilage exhibited biphasic lubrication with significant influence of strain magnitude on mu(0) and minimal influence on mu(eq), consistent with hydrostatic pressurization as reported by others. Lubrication analysis using 'Stribeck surfaces' demonstrated clear regions of boundary and mixed modes, but hydrodynamic or full film lubrication was not observed even at the highest speed (50mm/s) and lowest strain (5%).     

Freezing and melting water in lamellar structures.

The manner in which ice forms in lamellar suspensions of dielaidoylphosphatidylethanolamine, dielaidoylphosphatidylcholine, and dioleoylphosphatidylcholine in water depends strongly on the water fraction. For weight fractions between 15 and 9%, the freezing and melting temperatures are significantly depressed below 0 degree C. The ice exhibits a continuous melting transition spanning as much as 20 degrees C. When the water weight fraction is below 9%, ice never forms at temperatures as low as -40 degrees C. We show that when water contained in a lamellar lipid suspension freezes, the ice is not found between the bilayers; it exists as pools of crystalline ice in equilibrium with the bound water associated with the polar lipid headgroups. We have used this effect, together with the known chemical potential of ice, to measure hydration forces between lipid bilayers. We find exponentially decaying hydration repulsion when the bilayers are less than about 7 A apart. For larger separations, we find significant deviations from single exponential decay.     

Forces and stresses acting on fusion pore membrane during secretion

To assess the forces and stresses present in fusion pore during secretion the stationary convective flux of lipid through a fusion pore connecting two planar membranes under different tensions was investigated through computer simulations. The physics of the problem is described by Navier-Stokes equations, and the convective flux of lipid was evaluated using finite element method. Each of the membrane monolayer is considered separately as an isotropic, homogeneous and incompressible viscous medium with the same viscosity. The difference in membrane tensions, which is simulated as the pressure difference at two ends of each monolayer, is the driving force of the lipid flow. The two monolayers interact by sliding past each other with inter-monolayer frictional viscosity. Fluid velocity, pressure, shear and normal stresses, viscous and frictional dissipations and forces were calculated to evaluate where the fusion pore will deform, extend (or compress) and dilate. The pressure changes little in the planar sections, whereas in the toroidal section the change is rapid. The magnitude of lipid velocity peaks at the pore neck. The radial lipid velocity is zero at the neck, has two peaks one on each side of the pore neck, and diminishes without going to zero in planar parts of two monolayers. The peaks are of opposite signs due to the change of direction of lipid flow. The axial velocity is confined to the toroidal section, peaks at the neck and is clearly greater in the outer monolayer. As a result of the spatially highly uneven lipid flow the membrane is under a significant stress, shear and normal. The shear stress, which indicates where the membrane will deform without changing the volume, has two peaks placed symmetrically about the neck. The normal stress shows where the membrane may extend or compress. Both, the radial and axial normal stresses are negative (extensive) in the upper toroidal section and positive (compressive) in the lower toroidal section. The pressure difference determines lipid velocity and velocity dependent variables (shear as well as normal axial and radial stresses), but also contributes directly to the force on the membranes and critically influences where and to what extent the membrane will deform, extend or dilate. The viscosity coefficient (due to friction of one element of lipid against neighboring ones), and frictional coefficient (due to friction between two monolayers sliding past each other) further modulate some variables. Lipid velocity rises as pressure difference increases, diminishes as the viscosity coefficient rises but is unaffected by the frictional coefficient. The shear and normal stresses rise as pressure difference increases, but the change of the viscosity coefficients has no effect. Both the viscous dissipation (which has two peaks placed symmetrically about the neck) and much smaller frictional dissipation (which peaks at the pore neck) rise with pressure and diminish if the viscosity coefficient rises, but only the frictional dissipation increases if the frictional coefficient increases. Finally, the radial force causing pore dilatation, and which is significant only in the planar section of the vesicular membrane, is governed almost entirely by the pressure, whereas the viscosity and frictional coefficients have only a marginal effect. Many variables are altered during pore dilatation. The lipid velocity and dissipations (viscous and frictional) rise approximately linearly with pore radius, whereas the lipid mass flow increases supra-linearly owing to the combined effects of the changes in pore radius and greater lipid velocity. Interestingly the radial force on the vesicular membrane increases only marginally.     

Validation of a biodynamic model of pushing and pulling.

Pushing and pulling during manual material handling can increase the compressive forces on the lumbar disc region while creating high shear forces at the shoe-floor interface. A sagittal plane dynamic model derived from previous biomechanical models was developed to predict L5/S1 compressive force and required coefficients of friction during dynamic cart pushing and pulling. Before these predictions could be interpreted, however, it was necessary to validate model predictions against independently measured values of comparable quantities. This experiment used subjects of disparate stature and body mass, while task factors such as cart resistance and walking speed were varied. Predicted ground reaction forces were compared with those measured by a force platform, with correlations up to 0.67. Predicted erector spinae and rectus abdominus muscle forces were compared with muscle forces derived from RMS-EMGs of the respective muscle groups, using a static force build-up regression relationship to transform the dynamic RMS-EMGs to trunk muscle forces. Although correlations were low, this was attributed in part to the use of surface EMG on subjects of widely varied body mass. The biodynamic model holds promise as a tool for analysis of actual industrial pushing and pulling tasks, when carefully applied.     

Translational friction of rigid assemblies of spheres: Derivation and application of new hydrodynamic interaction tensors

In connection with our goal of calculating by practical methods the frictional properties of biopolymers from surface shells composed of spheres, we have investigated by the method of reflections the low-Reynolds-number hydrodynamic interaction between two unequal-sized spheres in translation. Previous results, in which the velocities were used as independent variables and which have the form of truncated infinite power series, were substantially extended. By inversion of the power series, new power series with better convergence properties were obtained. Equivalence of these inverted power series with those previously reported based on the method of reflections, when forces are used as independent variables, was demonstrated, and the solutions were again substantially extended. Applying the Lagrange interpolation to data generated from exact theories for the hydrodynamic inteaction between two spheres, it was demonstrated that the various forms of the method of reflections do not just give reasonable power series, but actually yield optimal ones. These findings constitute a unification of diverse approaches and show methods of interconversion of results. On the basis of the power series obtained, a set of new hydrodynamic interaction tensors for two unequal spheres were derived. While the new tensors described the case of two unequal spheres with considerably more accuracy than those previously reported, direct application of these tensors to objects composed of more than two spheres revealed some unexpected problems resulting from overcorrection in the fourth-order term. However, when the tensors were preaveraged over all orientations of the multisphere object, a formula for the scalar translational friction coefficient was obtained that outperformed all but the most involved earlier approaches. It thus constitutes an improved and practical solution to the problem of computing translational friction coefficients of objects describable by a surface shell of many spheres, such as proteins.