Ejection mechanics and trajectory of the ascospores of Gibberella zeae (anamorph Fuarium graminearum)

Since wind speed drops to zero at a surface, forced ejection should facilitate spore dispersal. But for tiny spores, with low mass relative to surface area, high ejection speed yields only a short range trajectory, so pernicious is their drag. Thus, achieving high speeds requires prodigious accelerations. In the ascomycete Gibberella zeae, we determined the launch speed and kinetic energy of ascospores shot from perithecia, and the source and magnitude of the pressure driving the launch. We asked whether the pressure inside the ascus suffices to account for launch speed and energy. Launch speed was 34.5 ms-1, requiring a pressure of 1.54 MPa and an acceleration of 870,000 g--the highest acceleration reported in a biological system. This analysis allows us to discount the major sugar component of the epiplasmic fluid, mannitol, as having a key role in driving discharge, and supports the role of potassium ion flux in the mechanism.     

Kinematics and hydrodynamics of linear acceleration in eels, Anguilla rostrata

The kinematics and hydrodynamics of routine linear accelerations were studied in American eels, Anguilla rostrata, using high-speed video and particle image velocimetry. Eels were examined both during steady swimming at speeds from 0.6 to 1.9 body lengths (L) per second and during accelerations from -1.4 to 1.3 L s(-2). Multiple regression of the acceleration and steady swimming speed on the body kinematics suggests that eels primarily change their tail-tip velocity during acceleration. By contrast, the best predictor of steady swimming speed is body wave speed, keeping tail-tip velocity an approximately constant fraction of the swimming velocity. Thus, during steady swimming, Strouhal number does not vary with speed, remaining close to 0.32, but during acceleration, it deviates from the steady value. The kinematic changes during acceleration are indicated hydrodynamically by axial fluid momentum in the wake. During steady swimming, the wake consists of lateral jets of fluid and has minimal net axial momentum, which reflects a balance between thrust and drag. During acceleration, those jets rotate to point downstream, adding axial momentum to the fluid. The amount of added momentum correlates with the acceleration, but is greater than the necessary inertial force by 2.8+/-0.6 times, indicating a substantial acceleration reaction.     

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.     

Numerical simulation of cross-country skiing

A program for numerical simulation of a whole ski race, from start to finish, is developed in MATLAB. The track is modelled by a set of cubical splines in two dimensions and can be used to simulate a track in a closed loop or with the start and finish at different locations. The forces considered in the simulations are gravitational force, normal force between snow and skis, drag force from the wind, frictional force between snow and ski and driving force from the skier. The differential equations of motion are solved from start to finish with the Runge-Kutta method. Different wind situations during the race can be modelled, as well as different glide conditions on different parts of the track. It is also possible to vary the available power during the race. The simulation program's output is the total time of the race, together with the forces and speed during different parts of the race and intermediate times at selected points. Some preliminary simulations are also presented.     

Numerical simulation of cross-country skiing

A program for numerical simulation of a whole ski race, from start to finish, is developed in MATLAB. The track is modelled by a set of cubical splines in two dimensions and can be used to simulate a track in a closed loop or with the start and finish at different locations. The forces considered in the simulations are gravitational force, normal force between snow and skis, drag force from the wind, frictional force between snow and ski and driving force from the skier. The differential equations of motion are solved from start to finish with the Runge–Kutta method. Different wind situations during the race can be modelled, as well as different glide conditions on different parts of the track. It is also possible to vary the available power during the race. The simulation program's output is the total time of the race, together with the forces and speed during different parts of the race and intermediate times at selected points. Some preliminary simulations are also presented.     

Locomotion of bluefish.

1. Pressure previously measured on the body surface of swimming bluefish were resolved into their backward vectorial components to allow calculation of profile drag. It was 0.18 kg at a speed of 1.8 m/sec. Tangential drag was calculated as if for a thin plate of an area equal to that of the fish. It was 0.08 kg at 1.8 m/sec. Net drag, 0.26 kg, was the sum of profile and tangential drag. 2. Thrust and drag also were calculated from the changes of acceleration measured during steady swimming, assuming that thrust took place only during the acceleration phase, whereas drag occurred during both acceleration and deceleration. This drag was 0.08 kg at a speed of 1.1 m/sec. It is compatible with the drag of 0.26 at 1.8 m/sec calculated from profile and tangential drag provided drag varies as the square of velocity. 3. The force required to produced maximal acceleration was measured during a scare. It was calculated to be 6.9 kg at a peak acceleration of 3 g. 4. The compression strength of th vertebrae was found to be approximately 20 kg per cm2, or roughly three times the force encountered during maximal acceleration. This safety factor of 3 would be reduced when the back was curved, or if opposing groups of muscles were under tension. 5. The finding that a bluefish can accelerate at 3 g and that the vertebral column is strongg enough to withstand this force indicates that the muscles and body structure of a bluefish would be able to withstand the force of gravity if the fish were otherwise equipped for terrestrial life. This fish may have evolved these strengths simultaneously with land animals. It is speculated that other fish may have evolved some degree of strength to overcome inertia and drag during aquatic locomotion, and this evolution may have been a prelude to terrestrial locomotion.     

On Higher Ground: How Well Can Dynamic Body Acceleration Determine Speed in Variable Terrain?

Introduction

Animal travel speed is an ecologically significant parameter, with implications for the study of energetics and animal behaviour. It is also necessary for the calculation of animal paths by dead-reckoning. Dead-reckoning uses heading and speed to calculate an animal’s path through its environment on a fine scale. It is often used in aquatic environments, where transmission telemetry is difficult. However, its adoption for tracking terrestrial animals is limited by our ability to measure speed accurately on a fine scale. Recently, tri-axial accelerometers have shown promise for estimating speed, but their accuracy appears affected by changes in substrate and surface gradients. The purpose of the present study was to evaluate four metrics of acceleration; Overall dynamic body acceleration (ODBA), vectorial dynamic body acceleration (VDBA), acceleration peak frequency and acceleration peak amplitude, as proxies for speed over hard, soft and inclined surfaces, using humans as a model species.

Results

A general linear model (GLM) showed a significant difference in the relationships between the metrics and speed depending on substrate or surface gradient. When the data from all surface types were considered together, VeDBA had the highest coefficient of determination.

Conclusions

All of the metrics showed some variation in their relationship with speed according to the surface type. This indicates that changes in the substrate or surface gradient during locomotion by animals would produce errors in speed estimates, and also in dead-reckoned tracks if they were calculated from speeds based entirely on a priori calibrations. However, we describe a method by which the relationship between acceleration metrics and speed can be corrected ad hoc, until tracks accord with periodic ground truthed positions, obtained via a secondary means (e.g. VHF or GPS telemetry). In this way, dead-reckoning provides a means to obtain fine scale movement data for terrestrial animals, without the need for additional data on substrate or gradient.     

The correlation of segment accelerations and impact forces with knee angle in jump landing

Impact forces and shock deceleration during jumping and running have been associated with various knee injury etiologies. This study investigates the influence of jump height and knee contact angle on peak ground reaction force and segment axial accelerations. Ground reaction force, segment axial acceleration, and knee angles were measured for 6 male subjects during vertical jumping. A simple spring-mass model is used to predict the landing stiffness at impact as a function of (1) jump height, (2) peak impact force, (3) peak tibial axial acceleration, (4) peak thigh axial acceleration, and (5) peak trunk axial acceleration. Using a nonlinear least square fit, a strong (r = 0.86) and significant (p < or = 0.05) correlation was found between knee contact angle and stiffness calculated using the peak impact force and jump height. The same model also showed that the correlation was strong (r = 0.81) and significant (p < or = 0.05) between knee contact angle and stiffness calculated from the peak trunk axial accelerations. The correlation was weaker for the peak thigh (r = 0.71) and tibial (r = 0.45) axial accelerations. Using the peak force but neglecting jump height in the model, produces significantly worse correlation (r = 0.58). It was concluded that knee contact angle significantly influences both peak ground reaction forces and segment accelerations. However, owing to the nonlinear relationship, peak forces and segment accelerations change more rapidly at smaller knee flexion angles (i.e., close to full extension) than at greater knee flexion angles.     

Bionic Research on Fish Scales for Drag Reduction

To reduce friction drag with bionic method in a more feasible way,the surface microstructure of fish scales was analyzed attempting to reveal the biologic features responding to skin friction drag reduction.Then comparable bionic surface mimicking fish scales was fabricated through coating technology for drag reduction.The paint mixture was coated on a substrate through a self-developed spray-painting apparatus.The bionic surface with micron-scale caves formed spontaneously due to the interfacial convection and deformation driven by interfacial tension gradient in the presence of solvent evaporation.Comparative experiments between bionic surface and smooth surface were performed in a water tunnel to evaluate the effect of bionic surface on drag reduction,and visible drag reduction efficiency was obtained.Numerical simulation results show that gas phase develops in solid-liquid interface of bionic surface with the effect of surface topography and partially replaces the solid-liquid shear force with gas-liquid shear force,hence reducing the skin friction drag effectively.Therefore,with remarkable drag reduction performance and simple fabrication technology,the proposed drag reduction technique shows the promise for practical applications.     

Dynamics of the in-run in ski jumping: a simulation study

A ski jumper tries to maintain an aerodynamic position in the in-run during changing environmental forces. The purpose of this study was to analyze the mechanical demands on a ski jumper taking the in-run in a static position. We simulated the in-run in ski jumping with a 4-segment forward dynamic model (foot, leg, thigh, and upper body). The curved path of the in-run was used as kinematic constraint, and drag, lift, and snow friction were incorporated. Drag and snow friction created a forward rotating moment that had to be counteracted by a plantar flexion moment and caused the line of action of the normal force to pass anteriorly to the center of mass continuously. The normal force increased from 0.88 G on the first straight to 1.65 G in the curve. The required knee joint moment increased more because of an altered center of pressure. During the transition from the straight to the curve there was a rapid forward shift of the center of pressure under the foot, reflecting a short but high angular acceleration. Because unrealistically high rates of change of moment are required, an athlete cannot do this without changing body configuration which reduces the required rate of moment changes.     

The influence of track compliance on running

A model of running is proposed in which the leg is represented as a rack-and-pinion element in series with a damped spring. The rack-and-pinion element emphasizes the role of descending commands, while the damped spring represents the dynamic properties of muscles and the position and the rate sensitivity of reflexes. This model is used to predict separately the effect of track compliance on step length and ground contact time. The predictions are compared with experiments in which athletes ran over tracks of controlled spring stiffness. A sharp spike in foot force up to 5 times body weight was found on hard surfaces, but this spike disappeared as the athletes ran on soft experimental tracks. Both ground contact time and step length increased on very compliant surfaces, leading to moderately reduced running speeds, but a range of track stiffness was discovered which actually enhances speed.     

Protein friction exerted by motor enzymes through a weak-binding interaction.

Recently Vale et al. (1989, Cell 59, 915-925.) reported an observation of the one-dimensional Brownian movement of microtubules bound to flagellar dynein through a weak-binding interaction. In this study, we propose a theoretical model of this phenomenon. Our model consists of a rigid microtubule associated with a number of elastic dynein heads through a weak-binding interaction at equilibrium. The model implies that (1) the Brownian motion of the microtubule is not directly driven by the atomic collision of the solvent particles, but is driven by the thermally-generated structural fluctuations of the dynein heads which interact with the microtubule; (2) dynein heads through a weak-binding interaction exert a frictional drag force on the sliding motion of the microtubule and the drag force is proportional to the sliding velocity the same as in hydrodynamic viscous friction. This protein friction, with such viscous-like characteristics, may well play a role as a velocity-limiting factor in the normal ATP-induced sliding movement of motile proteins.     

On the potential of lower limb muscles to accelerate the body's centre of mass during walking

Quantification of lower limb muscle function during gait or other common activities may be achieved using an induced acceleration analysis, which determines the contributions of individual muscles to the accelerations of the body's centre of mass. However, this analysis is reliant on a mathematical optimisation for the distribution of net joint moments among muscles. One approach that overcomes this limitation is the calculation of a muscle's potential to accelerate the centre of mass based on either a unit-force or maximum-activation assumption. Unit-force muscle potential accelerations are determined by calculating the accelerations induced by a 1 N muscle force, whereas maximum-activation muscle potential accelerations are determined by calculating the accelerations induced by a maximally activated muscle. The aim of this study was to describe the acceleration potentials of major lower limb muscles during normal walking obtained from these two techniques, and to evaluate the results relative to absolute (optimisation-based) muscle-induced accelerations. Dynamic simulations of walking were generated for 10 able-bodied children using musculoskeletal models, and potential- and absolute induced accelerations were calculated using a perturbation method. While the potential accelerations often correctly identified the major contributors to centre-of-mass acceleration, they were noticeably different in magnitude and timing from the absolute induced accelerations. Potential induced accelerations predicted by the maximum-activation technique, which accounts for the force-generating properties of muscle, were no more consistent with absolute induced accelerations than unit-force potential accelerations. The techniques described may assist treatment decisions through quantitative analyses of common gait abnormalities and/or clinical interventions.     

Mathematical multi-scale model of the cardiovascular system including mitral valve dynamics. Application to ischemic mitral insufficiency

The aim of this research is to propose a small intestine model for electrically propelled capsule endoscopy. The electrical stimulus can cause contraction of the small intestine and propel the capsule along the lumen. The proposed model considered the drag and friction from the small intestine using a thin walled model and Stokes' drag equation. Further, contraction force from the small intestine was modeled by using regression analysis. From the proposed model, the acceleration and velocity of various exterior shapes of capsule were calculated, and two exterior shapes of capsules were proposed based on the internal volume of the capsules. The proposed capsules were fabricated and animal experiments were conducted. One of the proposed capsules showed an average (SD) velocity in forward direction of 2.91 ± 0.99 mm/s and 2.23 ± 0.78 mm/s in the backward direction, which was 5.2 times faster than that obtained in previous research. The proposed model can predict locomotion of the capsule based on various exterior shapes of the capsule.     

An estimation of drag in front crawl swimming

Propulsive arm forces of twelve elite male swimmers during a front crawl swimming-like activity were measured. The swimmers pushed off against grips which are attached to a 23 m tube at 0.8 m under the water surface. The tube was fixed to a force transducer. Since at constant speed, mean propulsive force equals mean drag force this method also provides the mean active drag on a moving swimmer. The mean propulsive force at a speed of v = 1.48 m s-1 appeared to be 53.2 +/- 5.8 N which is two to three times smaller than what is reported by other authors for active drag but which is in agreement with values reported for passive drag on a (towed) swimmer who is not moving. Discrepancies with indirect active drag measurements are discussed.     

Mechanics of Undulatory Swimming in a Frictional Fluid

The sandfish lizard (Scincus scincus) swims within granular media (sand) using axial body undulations to propel itself without the use of limbs. In previous work we predicted average swimming speed by developing a numerical simulation that incorporated experimentally measured biological kinematics into a multibody sandfish model. The model was coupled to an experimentally validated soft sphere discrete element method simulation of the granular medium. In this paper, we use the simulation to study the detailed mechanics of undulatory swimming in a “granular frictional fluid” and compare the predictions to our previously developed resistive force theory (RFT) which models sand-swimming using empirically determined granular drag laws. The simulation reveals that the forward speed of the center of mass (CoM) oscillates about its average speed in antiphase with head drag. The coupling between overall body motion and body deformation results in a non-trivial pattern in the magnitude of lateral displacement of the segments along the body. The actuator torque and segment power are maximal near the center of the body and decrease to zero toward the head and the tail. Approximately 30% of the net swimming power is dissipated in head drag. The power consumption is proportional to the frequency in the biologically relevant range, which confirms that frictional forces dominate during sand-swimming by the sandfish. Comparison of the segmental forces measured in simulation with the force on a laterally oscillating rod reveals that a granular hysteresis effect causes the overestimation of the body thrust forces in the RFT. Our models provide detailed testable predictions for biological locomotion in a granular environment.     

Influence of translocation track on the motion of intra-axonally transported organelles in human nerve

The mechanism by which organelles are transported bidirectionally in axoplasm is still unknown; however, evidence of a key role for microtubules in many nonmammalian models has been established. We have observed common or shared tracks within the axoplasm of human nerves along which multiple organelles of varying size and shape are bidirectionally transported. Organelles traveling anterogradely and retrogradely were visualized by video-enhanced differential interference contrast optics and analyzed with the aid of computer-image-processing techniques. Speeds of translocating organelles were determined at eight to 16 translocation points along a path or "track." Each translocation speed was plotted against its corresponding position on the track to develop a "speed/position diagram." Regardless of mean organelle speed or direction of motion, organelles sharing a common track exhibited similar patterns of "speeding up" and "slowing down" relative to position along the track. Speed position data for organelles translocating the local axonal region of a common track showed no unique patterns (not different from a uniform distribution, p less than 0.05). The unique speed/position patterns exhibited by common tracks were not necessarily related to the patterns of other tracks in the immediate vicinity (distance between tracks of less than 0.50 micron). These findings suggest that there are "common tracks" shared by organelles moving retrogradely and anterogradely; both the organelles and the "track" associated with its translocation play a role in the resultant motion of that organelle; the influence exerted by a common track on the motion of an organelle results in a pattern of speed changes related to position along the track.     

Upper body accelerations during planned gait termination in young and older women

Transitory tasks, such as gait termination, involve interactions between neural and biomechanical factors that challenge postural stability and head stabilization patterns in older adults. The aim of the study was to compare upper body patterns of acceleration during planned gait termination at different speeds between young and older women. Ten young and 10 older women were asked to carry out three gait termination trials at slow, comfortable and fast speed. A stereophotogrammetric system and a 15-body segments model were used to calculate antero-posterior whole-body Center of Mass (AP CoM) speed and to reconstruct the centroids of head, trunk and pelvis segments. RMS of three-dimensional linear accelerations were calculated for each segment and the transmission of acceleration between two segments was expressed as a percentage difference. Older women reported lower AP CoM speed and acceleration RMS of the three upper body segments than young women across the three speed conditions. A lower pelvis-to-trunk attenuation of accelerations in the transverse plane was observed in older compared to young women, and mainly in the medio-lateral direction. As possible explanations, older women may not need to reduce acceleration as young women because of their lower progression speed and the subsequent acceleration at upper body levels. On the other hand, older women may prioritize a decrease in the whole body progression speed at expense of the involvement of upper body segments. This limits the attenuation of the accelerations, particularly in the transverse plane, implying an increased dynamic unbalance in performing this transitory task.     

A contact model to simulate human–artifact interaction based on force optimization: implementation and application to the analysis of a training machine

Musculoskeletal multibody models are increasingly used to analyze and optimize physical interactions between humans and technical artifacts. Since interaction is conveyed by contact between the human body and the artifact, a computationally robust modeling approach for frictional contact forces is a crucial aspect. In this contribution, we propose a parametric contact model and formulate an associated force optimization problem to simultaneously estimate unknown muscle and contact forces in an inverse dynamic manner from a prescribed motion trajectory. Unlike existing work, we consider both the static and the kinetic regime of Coulomb’s friction law. The approach is applied to the analysis of a leg extension training machine with the objective to reduce the stress on the tibiofemoral joint. The uncertainty of the simulation results due to a tunable parameter of the contact model is of particular interest.     

Sprinting with banked turns

Bank angle effects can attenuate peak running speed on the order of 10%. Experimental and theoretical results are presented here to quantify this phenomenon over a wide range of bank angles theta b and turn radii R. Experimentally, eleven subjects ran on a 34 m long plywood test track with variable radius and bank angle to sample the (R, theta b) space. From another study, ten subjects are borrowed to examine the theta b = 0 degrees case in greater detail. Various gait parameters were measured from high-speed film, and after parallax correction, compared with the theoretical predictions. The theory is a simple two-parameter constant force model requiring only the effective ankle pulley ratio beta and the runner's top speed vm. A closed-form dimensionless solution is presented for the speed ratio (v/vm) as a function of the radius number (Rg/v2) and the bank angle theta b. Agreement between theory and experiment is limited by experimental scatter. For twenty different subjects and twelve different combinations of R and theta b, the apparent ankle pulley ratio is beta = 0.27 +/- 0.22 based on 128 separate trials. Applications are discussed briefly for the design of indoor and outdoor running tracks. The theory allows a calculation of foot force, bone force, and tendon tension for the general case of arbitrary maximum speed, turn radius and bank angle.