Take-off aerodynamics in ski jumping

The effect of aerodynamic forces on the force-time characteristics of the simulated ski jumping take-off was examined in a wind tunnel. Vertical and horizontal ground reaction forces were recorded with a force plate installed under the wind tunnel floor. The jumpers performed take-offs in non-wind conditions and in various wind conditions (21-33 m s(-1)). EMGs of the important take-off muscles were recorded from one jumper. The dramatic decrease in take-off time found in all jumpers can be considered as the result of the influence of aerodynamic lift. The loss in impulse due to the shorter force production time with the same take-off force is compensated with the increase in lift force, resulting in a higher vertical velocity (V(v)) than is expected from the conventional calculation of V(v) from the force impulse. The wind conditions emphasized the explosiveness of the ski jumping take-off. The aerodynamic lift and drag forces which characterize the aerodynamic quality of the initial take-off position (static in-run position) varied widely even between the examined elite ski jumpers. According to the computer simulation these differences can decisively affect jumping distance. The proper utilization of the prevailing aerodynamic forces before and during take-off is a very important prerequisite for achieving a good flight position.     

Take-off analysis of the Olympic ski jumping competition (HS-106 m)

The take-off phase (approximately 6 m) of the jumps of all athletes participating in the individual HS-106 m hill ski jumping competition at the Torino Olympics was filmed with two high-speed cameras. The high altitude of the Pragelato ski jumping venue (1600 m) and slight tail wind in the final jumping round were expected to affect the results of this competition. The most significant correlation with the length of the jump was found in the in-run velocity (r=0.628, p<0.001, n=50). This was a surprise in Olympic level ski jumping, and suggests that good jumpers simply had smaller friction between their skis and the in-run tracks and/or the aerodynamic quality of their in-run position was better. Angular velocity of the hip joint of the best jumpers was also correlated with jumping distance (r=0.651, p<0.05, n=10). The best jumpers in this competition exhibited very different take-off techniques, but still they jumped approximately the same distance. This certainly improves the interests in ski jumping among athletes and spectators. The comparison between the take-off techniques of the best jumpers showed that even though the more marked upper body movement creates higher air resistance, it does not necessarily result in shorter jumping distance if the exposure time to high air resistance is not too long. A comparison between the first and second round jumps of the same jumpers showed that the final results in this competition were at least partly affected by the wind conditions.     

Activities of Everyday Life with High Spinal Loads

Activities with high spinal loads should be avoided by patients with back problems. Awareness about these activities and knowledge of the associated loads are important for the proper design and pre-clinical testing of spinal implants. The loads on an instrumented vertebral body replacement have been telemetrically measured for approximately 1000 combinations of activities and parameters in 5 patients over a period up to 65 months postoperatively. A database containing, among others, extreme values for load components in more than 13,500 datasets was searched for 10 activities that cause the highest resultant force, bending moment, torsional moment, or shear force in an anatomical direction. The following activities caused high resultant forces: lifting a weight from the ground, forward elevation of straight arms with a weight in hands, moving a weight laterally in front of the body with hanging arms, changing the body position, staircase walking, tying shoes, and upper body flexion. All activities have in common that the center of mass of the upper body was moved anteriorly. Forces up to 1650 N were measured for these activities of daily life. However, there was a large intra- and inter-individual variation in the implant loads for the various activities depending on how exercises were performed. Measured shear forces were usually higher in the posterior direction than in the anterior direction. Activities with high resultant forces usually caused high values of other load components.     

Correction of the inertial effect resulting from a plate moving under low-friction conditions

The purpose of the present study was to develop a set of equations that can be employed to remove the inertial effect introduced by the movable platform upon which a person stands during a slip induced in gait; this allows the real ground reaction force (GRF) and its center of pressure (COP) to be determined. Analyses were also performed to determine how sensitive the COP offsets were to the changes of the parameters in the equation that affected the correction of the inertial effect. In addition, the results were verified empirically using a low friction movable platform together with a stationary object, a pendulum, and human subjects during a slip induced during gait. Our analyses revealed that the amount of correction required for the inertial effect due to the movable component is affected by its mass and its center of mass (COM) position, acceleration, the friction coefficient, and the landing position of the foot relative to the COM. The maximum error in the horizontal component of the GRF was close to 0.09 (body weight) during the recovery from a slip in walking. When uncorrected, the maximum error in the COP measurement could reach as much as 4 cm. Finally, these errors were magnified in the joint-moment computation and propagated proximally, ranging from 0.2 to 1.0 Nm/body mass from the ankle to the hip.     

A biomechanical model of the foot: the role of muscles,tendons, and ligaments

A biomechanical model of the foot is developed and analyzed to determine the distribution of support under the metatarsal heads, the tension in the plantar aponeurosis, and the bending moment at each of the joints of the foot. This model is an extension of our earlier work to include the role of muscles, tendons, and ligaments. Two cases are presented: in the first the center of gravity of the body is over the mid foot, and in the second, the center of gravity is anterior, over the metatarsals, and no support is provided by the heel. The model shows the extent to which the muscles reduce the force in the supporting ligaments at each of the joints and decrease the tension in the plantar aponeurosis, and that this effect is more pronounced when the center of gravity of the body is moved forward.     

The influence of foot position on standing balance

To test the hypothesis that variations in foot position would significantly affect standing balance, we studied ten normal subjects on a Kistler force platform which measured the travel and center of pressure displacement. With the feet together there was substantially more mediolateral (ML) travel than with the axes of the feet 15, 30 or 45 cm apart and the mean ML position of the center of pressure was displaced toward the right; there was no consistent effect on anteroposterior (AP) travel or position. As the right foot was placed 10 and 30 cm forward or back, the least amount of ML and AP travel occurred with the feet even or at 10 cm either direction; the mean AP and ML position moved toward the foot which was placed more posteriorly. Of the five foot angles ranging from toes-out 45 degrees to toes-in 45 degrees, the extent of ML and AP travel was lowest in the toes-out 25 degrees position and greatest in the toes-in 45 degrees position; the mean AP and ML position was farthest forward and to the right with toes-in 45 degrees. These findings have implications for the prosthetic replacement of the lower limbs, sports, ergonomics and postural sway studies.     

An estimation of center of gravity from force platform data

A general, dynamic relationship between the data obtained from a force platform, center of gravity of the body on the platform and the time rate of change of moment of momentum of the body about its center of gravity was derived from principles of dynamics for a system of particles. The derived equations are useful for processing and interpreting the force platform data. Displacement and path of center of gravity of human body during standing on one foot and level walking were estimated by using the derived equations. An estimation of the time rate of change of moment of momentum of the body was also obtained. A biomechanical interpretation of point of application of the resultant of ground reactions was presented.     

Hydrodynamic Analysis of C-start in Crucian Carp

The kinematics of turning maneuvers of startled Crucian Carp (Carassius auratus) are presented. All escape response observed are C-type fast-starts. The position of the center of mass and the me,merit of inertia of the fish are calculated. The results show that the position of the center of mass is always at 35% of the length of the fish from the head and the position of the center of mass and rroment of inertia can be considered unchanged during C-start of Crucian Carp. Hydro-dynamic analysis of the C-start is given based on the kinematics data from our experiments. The C-start consists of three stages. In stage 1, the tail fin of fish rapidly flaps in one direction, and a large moment acts on the fish‘s body, which rotates around the center of mass with an angular acceleration. In stage 2, the tail fin flaps more slowly in the opposite direction at slower speed, the fish‘s body rotates around the center of mass with angular deceleration and the center of mass of the fish moves along an are. In stage 3, the moment approximately equals zero, the fish‘s body stops rotating and the center of mass the moves along a straight line.     

Cross-correlations of center of mass and center of pressure displacements reveal multiple balance strategies in response to sinusoidal platform perturbations

Compared to static balance, dynamic balance requires a more complex strategy that goes beyond keeping the center of mass (COM) within the base of support, as established by the range of foot center of pressure (COP) displacement. Instead, neuromechanics must accommodate changing support conditions and inertial effects. Therefore, because they represent body's position and changes in applied moments, relative COM and COP displacements may also reveal dynamic postural strategies. To investigate this concept, kinetics and kinematics were recorded during three 12 cm, 1.25 Hz, sagittal perturbations. Forty-one individual trials were classified according to averaged cross-correlation lag between COM and COP displacement (lag(COM:COP)) and relative head-to-ankle displacement (Δ(head)/Δ(ankle)) using a k-means analysis. This process revealed two dominant patterns, one for which the lag(COM:COP) was positive (Group 1 (n=6)) and another for which it was negative (Group 2 (n=5)) . Group 1 (G1) absorbed power from the platform over most of the cycle, except during transitions in platform direction. Conversely, Group 2 (G2) participants applied power to the platform to maintain a larger margin between COM and COP position and also had larger knee flexion and ankle dorsiflexion, resulting in a lower stance. By the third repetition, the only kinematic differences were a slightly larger G2 linear knee displacement (p=0.008) and an antiphasic relationship of pelvis (linear) and trunk (angular) displacements. Therefore, it is likely that the strategy differences were detected by including COP in the initial screening method, because it reflects the pattern of force application that is not detectable by tracking body movements.     

The importance of being light: aerodynamic forces and weight in ski jumping

Many contemporary world class ski jumpers are alarmingly underweight and several cases of anorexia nervosa have come to light. Athletes strive for low body weight because it gives them a major competitive advantage. In order to stop this hazardous development, changes to the regulations are being discussed, and the International Ski Federation and the International Olympic Committee wish to be proactive in safe guarding the interest of the athletes and their health.This study of ski jumping uses field studies conducted during World Cup competitions, large-scale wind tunnel measurements with 1:1 models of ski jumpers in current equipment and highly accurate computer simulations of the flight phase that include the effects due to the athlete's position changes.Particular attention has been directed to the design of a reference jump that mirrors current flight style and equipment regulations (2001), and to the investigation of effects associated with variation in body mass, air density, and wind gusts during the simulated flight. The detailed analysis of the physics of ski jumping described here can be used for the investigation of all initial value and parameter variations that determine the flight path of a ski jumper and will form a reliable basis for setting regulations that will make it less attractive or even disadvantageous for the athlete to be extremely light.     

Surface EMG and torsion measurements during snow skiing: laboratory and field tests

The relationship between mean rectified EMG (MREMG) measured with surface electrodes and the longitudinal torsion of the lower extremity was investigated in laboratory and snow skiing experiments. Linear regression of the MREMG from the gluteus medius and the peroneus longus with the torsion measured at the foot in the laboratory tests showed that torsion can be predicted with correlation coefficients greater than 0.95 and with a standard deviation less than 5 Nm over all knee flexions and weight bearing. A similar correspondence between MREMG and torsion during skiing does not exist. MREMG is dominantly correlated to posture and body position control functions in skiing. During falling, during ski binding release, and during possible injury sustaining situations, the MREMG was always relatively large, but it was not distinguishable from that associated with smaller torsion of the lower extremity.     

Flow over a ski jumper in flight: Prediction of the aerodynamic force and flight posture with higher lift-to-drag ratio

Large eddy simulations (LESs) are performed to study the flow characteristics around two flight posture models of ski jumping. These models are constructed by three-dimensionally scanning two national-team ski jumpers taking flight postures. The drag and lift forces on each component of a ski jumper and skis (head with helmet and goggle, body, arms, legs and skis) and their lift-to-drag ratios are obtained. For the two posture models, the drag forces on the body, legs and skis are larger than those on the arms and head with helmet and goggle, but the lift forces on the body and skis are larger than their drag forces, resulting in high lift-to-drag ratios on the body and skis and low lift-to-drag ratio on the legs. We construct simple geometric models, such as the circular cylinder, sphere and thin rectangular plate, predicting the drag and lift forces on each component of a ski jumper and skis, and validate them with those obtained from LES. Using these geometric models, we perform a parametric study on the position angles of flight posture for higher total lift-to-drag ratio. The flight postures obtained increase the total lift-to-drag ratios by 35% and 21% from those of two base postures, respectively. Finally, LESs are performed for the postures obtained and show the increases in the total lift-to-drag ratios by 21% and 16%, respectively, indicating the adequacy of using the simple geometric models for finding a flight posture of ski jumping having a higher lift-to-drag ratio at low cost.     

Management,winter climate and plant–soil feedbacks on ski slopes: a synthesis

Owing to the increasing popularity of skiing and the upslope movement of the snow reliability line in mountain regions, more and more alpine environments are being turned into skiing areas, with strong impacts on ecosystem functions and biodiversity. Creation and management of ski slopes cause physical disturbance to soil and vegetation, while (artificial) snow supplements affect soil structure, chemistry, moisture and temperature regimes as well as shifts in snow season and growing season length. Vegetation–soil feedbacks may influence the outcome of these interactive effects on soil and vegetation, with possible consequences for soil erosion. Moreover, climate warming will lead to changing snow cover and duration, which will interact with ski slope management effects on soil and vegetation and its feedbacks. Based on a conceptual framework we review the main elements of these interactive effects on soil and vegetation on new and established ski slopes. We also set a research agenda with specific studies that could further advance our understanding of interacting ski slope management, winter climate, vegetation–soil feedbacks and ecosystem functioning. In such new investigations, alpine climate change ecology can probably learn much from the “experimental” disturbance and snow manipulations on ski slopes and vice versa.     

Individual flight styles in ski jumping: results obtained during Olympic Games competitions

From the physics point of view, the jump length in ski jumping depends on: the in-run velocity v(0), the velocity perpendicular to the ramp v(p0) due to the athlete's jumping force, the lift and drag forces acting during take-off and during the flight, and the weight of the athlete and his equipment. The aerodynamic forces are a function of the flight position and of the equipment features. They are a predominant performance factor and can largely be influenced by the athlete. The field study conducted during the Olympic Games competitions 2002 at Park City (elevation: 2000 m) showed an impressive ability of the Olympic medallists to reproduce their flight style and remarkable differences between different athletes have been found. The aerodynamic forces are proportional to the air density. Elite athletes are able to adapt their flight style to thin air conditions in order to maximise jump length and to keep the flight stable. The effects of flight position variations on the performance have been analysed by means of a computer model which is based on the equations of motion and on wind tunnel data corresponding to the flight positions found in the field. Athletes have to solve extremely difficult optimisation problems within fractions of a second. The computer simulation can be used as a reliable starting point for the improvement of training methods and gives an insight into the "implicit" knowledge of physics that the ski jumping athlete must have available for a good performance.     

Estimates of Achilles tendon moment arm differ when axis of ankle rotation is derived from ankle motion

The plantarflexor moment arm of the Achilles tendon determines the mechanical advantage of the triceps surae and also indirectly affects muscle force generation by setting the amount of muscle-tendon shortening per unit of ankle joint rotation. The Achilles tendon moment arm may be determined geometrically from an axis (or center) of joint rotation and the line of action of the tendon force, but such moment arms may be sensitive to the location of the joint axis. Using motion analysis to track an ultrasound probe overlying the Achilles tendon along with markers on the shank and foot, we measured Achilles tendon moment arm during loaded and unloaded dynamic plantarflexion motions in 15 healthy subjects. Three representations of the axis or center of rotation of the ankle were considered: (1) a functional axis, defined by motions of the foot and shank; (2) a transmalleolar axis; and (3) a transmalleolar midpoint. Moment arms about the functional axis were larger than those found using the transmalleolar axis and transmalleolar midpoint (all p < 0.001). Moment arms computed with the functional axis increased with plantarflexion angle (all p < 0.001), and increased with loading in the most plantarflexed position (p < 0.001) but these patterns were not observed when either using a transmalleolar axis or transmalleolar midpoint. Functional axis moment arms were similar to those estimated previously using magnetic resonance imaging, suggesting that using a functional axis for ultrasound-based geometric estimates of Achilles tendon moment arm is an improvement over landmark-based methods.     

Energy cost and muscular activity required for leg swing during walking.

To investigate the metabolic cost and muscular actions required for the initiation and propagation of leg swing, we applied a novel combination of external forces to subjects walking on a treadmill. We applied a forward pulling force at each foot to assist leg swing, a constant forward pulling force at the waist to provide center of mass propulsion, and a combination of these foot and waist forces to evaluate leg swing. When the metabolic cost and muscle actions were at a minimum, the condition was considered optimal. We reasoned that the difference in energy consumption between the optimal combined waist and foot force trial and the optimal waist force-only trial would reflect the metabolic cost of initiating and propagating leg swing during normal walking. We also reasoned that a lower muscle activity with these assisting forces would indicate which muscles are normally responsible for initiating and propagating leg swing. With a propulsive force at the waist of 10% body weight (BW), the net metabolic cost of walking decreased to 58% of normal walking. With the optimal combination, a propulsive force at the waist of 10% BW plus a pulling force at the feet of 3% BW the net metabolic cost of walking further decreased to 48% of normal walking. With the same combination, the muscle activity of the iliopsoas and rectus femoris muscles during the swing phase was 27 and 60% lower, respectively, but the activity of the medial gastrocnemius and soleus before swing did not change. Thus our data indicate that approximately 10% of the net metabolic cost of walking is required to initiate and propagate leg swing. Additionally, the hip flexor muscles contribute to the initiation and propagation leg swing.     

An investigation of rugby scrimmaging posture and individual maximum pushing force

Although rugby is a popular contact sport and the isokinetic muscle torque assessment has recently found widespread application in the field of sports medicine, little research has examined the factors associated with the performance of game-specific skills directly by using the isokinetic-type rugby scrimmaging machine. This study is designed to (a) measure and observe the differences in the maximum individual pushing forward force produced by scrimmaging in different body postures (3 body heights x 2 foot positions) with a self-developed rugby scrimmaging machine and (b) observe the variations in hip, knee, and ankle angles at different body postures and explore the relationship between these angle values and the individual maximum pushing force. Ten national rugby players were invited to participate in the examination. The experimental equipment included a self-developed rugby scrimmaging machine and a 3-dimensional motion analysis system. Our results showed that the foot positions (parallel and nonparallel foot positions) do not affect the maximum pushing force; however, the maximum pushing force was significantly lower in posture I (36% body height) than in posture II (38%) and posture III (40%). The maximum forward force in posture III (40% body height) was also slightly greater than for the scrum in posture II (38% body height). In addition, it was determined that hip, knee, and ankle angles under parallel feet positioning are factors that are closely negatively related in terms of affecting maximum pushing force in scrimmaging. In cross-feet postures, there was a positive correlation between individual forward force and hip angle of the rear leg. From our results, we can conclude that if the player stands in an appropriate starting position at the early stage of scrimmaging, it will benefit the forward force production.     

Curvature facilitates prey fixation in predatory insect claws

Insects show a large variety in prey capture strategies, with a correspondingly large diversity in predatory adaptations. We studied a specific type of predatory claws, these can for example be found in praying mantis species. The claw is closeable over its entire length and the prey is fixed between the femur (upper arm) and the tibia (lower arm) of the insect leg. The morphology of these predatory claws is diverse. Some species have straight claws covered with spines, while other species have smooth, curved claws. We have studied the mechanics of this femur-tibia type of predatory insect claws, by making a physical model, eventually trying to explain why in some insect species the claws are curved instead of straight. The main results are (1) when comparing curved claws to straight claws, curvature leads to a strong reduction of forces driving the prey away from the pivoting point, thereby reducing the need for friction generating structures. (2) In the curved claw model a position exists where the resulting force on the prey is exactly zero. This is because the normal forces on the femur and tibia are opposed, and in line. At this position the prey is perfectly clamped and not driven out of the claw. This feature does not exist in straight claws. (3) In the curved claw, the prey cannot be placed at a position further than a certain maximum distance from the pivoting point. Near this maximum position, the resulting force on the prey reaches high values because moment arms are near zero. (4) Between the zero position and the maximum position the resulting force is directed toward the pivoting point, which stabilizes prey fixation.     

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.