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.     

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.     

Characteristics of the early flight phase in the Olympic ski jumping competition

Early flight phase (approximately 40 m) of the athletes participating in the final round of the individual large hill ski jumping competition in Salt Lake City Olympics was filmed with two high-speed pan & tilt video cameras. The results showed that jumpers' steady flight position was almost completed within 0.5s. The most significant correlation with the length of the jump was found in the angle between the skis and body (r=.714, p.001 at 1.1s after the take-off). This particular phase seemed to be important because the ski angle of attack was also related to the jumping distance at the same phase. Although the more upright ski position relative to flight path resulted in longer jumping distance, the winner of the competition had significantly lower ski position as compared to the other good jumpers. This may be due to the high altitude (>2000 m) of the ski jumping stadium in this competition. Because of the low air density, the aerodynamic forces were also low and this probably caused less skillful jumpers to lean too much forward at this phase. Maintenance of speed seemed to be emphasized in this particular competition.     

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.     

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.     

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.     

EMG activities and plantar pressures during ski jumping take-off on three different sized hills.

Different profiles of ski jumping hills have been assumed to make the initiation of take-off difficult especially when moving from one hill to another. Neuromuscular adaptation of ski jumpers to the different jumping hills was examined by measuring muscle activation and plantar pressure of the primary take-off muscles on three different sized hills. Two young ski jumpers volunteered as subjects and they performed several trials from each hill (K-35 m, K-65 m and K-90 m) with the same electromyographic (EMG) electrode and insole pressure transducer set-up. The results showed that the differences in plantar pressure and EMGs between the jumping hills were smaller than expected for both jumpers. The small changes in EMG amplitudes between the hills support the assumption that the take-off was performed with the same intensity on different jumping hills and the timing of the gluteus EMG demonstrates well the similarity of the muscle activation on different hills. On the basis of the results obtained it seems that ski jumping training on small hills does not disturb the movement patterns for bigger hills and can also be helpful for special take-off training with low speed.     

Optimal compliant-surface jumping: a multi-segment model of springboard standing jumps

A multi-segment model is used to investigate optimal compliant-surface jumping strategies and is applied to springboard standing jumps. The human model has four segments representing the feet, shanks, thighs, and trunk-head-arms. A rigid bar with a rotational spring on one end and a point mass on the other end (the tip) models the springboard. Board tip mass, length, and stiffness are functions of the fulcrum setting. Body segments and board tip are connected by frictionless hinge joints and are driven by joint torque actuators at the ankle, knee, and hip. One constant (maximum isometric torque) and three variable functions (of instantaneous joint angle, angular velocity, and activation level) determine each joint torque. Movement from a nearly straight motionless initial posture to jump takeoff is simulated. The objective is to find joint torque activation patterns during board contact so that jump height can be maximized. Minimum and maximum joint angles, rates of change of normalized activation levels, and contact duration are constrained. Optimal springboard jumping simulations can reasonably predict jumper vertical velocity and jump height. Qualitatively similar joint torque activation patterns are found over different fulcrum settings. Different from rigid-surface jumping where maximal activation is maintained until takeoff, joint activation decreases near takeoff in compliant-surface jumping. The fulcrum-height relations in experimental data were predicted by the models. However, lack of practice at non-preferred fulcrum settings might have caused less jump height than the models' prediction. Larger fulcrum numbers are beneficial for taller/heavier jumpers because they need more time to extend joints.     

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.     

The EMG activity and mechanics of the running jump as a function of takeoff angle.

To characterize the electromyographic (EMG) activity, ground reaction forces, and kinematics were used in the running jump with different takeoff angles. Two male long jumpers volunteered to perform running jumps at different approach speeds by varying the number of steps (from 3 to 9) in the run-up. Subject TM achieved a greater vertical velocity of the center of gravity (CG) at takeoff for all approach distances. This jumping strategy was associated with greater backward trunk lean at touchdown and takeoff, a lesser range of motion for the thigh during the support phase, more extended knee and ankle angles at touchdown, and a more flexed knee angle at takeoff. Accompanying these differences in kinematics, TM experienced greater braking impulses and lesser propulsion impulses for the forward-backward component of the ground reaction force. Furthermore, TM activated mainly the rectus femoris, vastus medialis, lateral gastrocnemius, and tibialis anterior, while if rarely activated the biceps femoris from just before contact to roughly the first two-thirds of the support phase. These results indicate that TM used a greater takeoff angle in the running jump because he enabled and sustained a greater blocking effect via the coordination patterns of the muscles relative to the hip, knee, and ankle joints. These findings also suggest that the muscle activities recorded in the present experiment are reflected in kinematics and kinetics. Further, the possible influence of these muscle activities on joint movements in the takeoff leg, and their effect on the vertical and/or horizontal velocity of the jump are discussed.     

The validation of a portable force plate for measuring force-time data during jumping and landing tasks

The purpose of this study was to determine the reliability and validity of a portable force plate when analyzing jumping and landing tasks. Subjects performed 3 drop vertical jumps and 3 drop landings on both a standard strain gauge laboratory force plate and a portable force plate. In contrast to typical laboratory installed force plates, the portable 6-component force plate can be easily transported and used onsite at various training or data collection sites and incorporates Hall effect technology. The measured parameters included maximum force and time to maximum force for initial stance of the both tests, maximum takeoff force, and time to maximum takeoff force for the drop vertical jump. The Pearson correlation coefficients for the drop landing and the drop vertical jump for maximum force (r = 0.942, r = 0.940), time to maximum force (r = 0.891, r = 0.920) and for drop jump maximum jumping force (r = 0.971), and time to maximum takeoff force (r = 0.917) were all high and indicate that the force data collected by a resistor-type portable force plate provide similar measures to a standard strain-gauge laboratory force plate. Additionally, the within session reliability of the drop landing and the drop vertical jump measured by the portable force plate showed high interclass correlation coefficients for examined variables of 0.979 and 9.67 for maximum landing force and 0.917 and 0.920 for time to maximum landing force, respectively. The interclass correlation coefficients for the maximum takeoff force and time to maximum takeoff force during the drop vertical jump were 0.991 and 0.86. The results indicate the force and timing measurements from the portable force plate were both valid and reliable. Use of the portable force plate may facilitate methods of force measurement that can be applied out into the field and therefore a valuable tool for on site landing and jump force measurements in a variety of settings for large numbers of subjects.     

Wind and fairness in ski jumping: A computer modelling analysis

Wind is closely associated with the discussion of fairness in ski jumping. To counter-act its influence on the jump length, the International Ski Federation (FIS) has introduced a wind compensation approach. We applied three differently accurate computer models of the flight phase with wind (M1, M2, and M3) to study the jump length effects of various wind scenarios. The previously used model M1 is accurate for wind blowing in direction of the flight path, but inaccuracies are to be expected for wind directions deviating from the tangent to the flight path. M2 considers the change of airflow direction, but it does not consider the associated change in the angle of attack of the skis which additionally modifies drag and lift area time functions. M3 predicts the length effect for all wind directions within the plane of the flight trajectory without any mathematical simplification. Prediction errors of M3 are determined only by the quality of the input data: wind velocity, drag and lift area functions, take-off velocity, and weight. For comparing the three models, drag and lift area functions of an optimized reference jump were used. Results obtained with M2, which is much easier to handle than M3, did not deviate noticeably when compared to predictions of the reference model M3. Therefore, we suggest to use M2 in future applications. A comparison of M2 predictions with the FIS wind compensation system showed substantial discrepancies, for instance: in the first flight phase, tailwind can increase jump length, and headwind can decrease it; this is opposite of what had been anticipated before and is not considered in the current wind compensation system in ski jumping.     

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.     

Force platform for rats measures fore and hind forces concurrently

Animal models are commonly used to test the efficacy of impact loading regimens on bone strength. We designed an inexpensive force platform to concurrently measure the separate peak vertical impact forces produced by the fore and hindfeet of immature F-344 rats when dropped onto the platform. The force platform consisted of three load cells placed in a triangular pattern under a flat plate. Rats were dropped from heights of 30, 45 and 60 cm onto the platform so that they landed on all four feet concurrently. The peak vertical impact forces produced by the feet of the rats were measured using a sampling frequency of 100 kHz. The location of each foot at landing relative to the load cells, and the force received by each load cell were combined in a series of static equations to solve for the vertical impact forces produced by the fore and hindfeet. The forces produced by feet when rats stood on the single platform were similarly determined. The forces exerted separately by the fore and hindfeet of young rats when landing on the plate as a ratio to standing forces were then calculated. Rats when standing bore more weight on their hindfeet but landed with more weight on their forefeet, which provides rationale for the greater response to landing forces of bones in the forelimbs than those in the hindlimbs. This system provided a useful method to simultaneously measure peak vertical impact forces in fore and hindfeet in rats.     

Kinetic analysis of ski turns based on measured ground reaction forces

The objective of this study was to devise a method of kinetic analysis of the ground reaction force that enables the durations and magnitudes of forces acting during the individual phases of ski turns to be described exactly. The method is based on a theoretical analysis of physical forces acting during the ski turn. Two elementary phases were defined: (1) preparing to turn (initiation) and (2) actual turning, during which the center of gravity of the skier-ski system moves along a curvilinear trajectory (steering). The starting point of the turn analysis is a dynamometric record of the resultant acting ground reaction force applied perpendicularly on the ski surface. The method was applied to six expert skiers. They completed a slalom course comprising five gates arranged on the fall line of a 26° slope at a competition speed using symmetrical carving turns (30 evaluated turns). A dynamometric measurement system was placed on the carving skis (168 cm long, radius 16 m, data were recorded at 100 Hz). MATLAB procedures were used to evaluate eight variables during each turn: five time variables and three force variables. Comparison of the turn analysis results between individuals showed that the method is useful for answering various research questions associated with ski turns.     

Correlation between ground reaction force and tibial acceleration in vertical jumping

Modern electronics allow for the unobtrusive measurement of accelerations outside the laboratory using wireless sensor nodes. The ability to accurately measure joint accelerations under unrestricted conditions, and to correlate them with jump height and landing force, could provide important data to better understand joint mechanics subject to real-life conditions. This study investigates the correlation between peak vertical ground reaction forces, as measured by a force plate, and tibial axial accelerations during free vertical jumping. The jump heights calculated from force-plate data and accelerometer measurements are also compared. For six male subjects participating in this study, the average coefficient of determination between peak ground reaction force and peak tibial axial acceleration is found to be 0.81. The coefficient of determination between jump height calculated using force plate and accelerometer data is 0.88. Data show that the landing forces could be as high as 8 body weights of the jumper. The measured peak tibial accelerations ranged up to 42 g. Jump heights calculated from force plate and accelerometer sensors data differed by less than 2.5 cm. It is found that both impact accelerations and landing forces are only weakly correlated with jump height (the average coefficient of determination is 0.12). This study shows that unobtrusive accelerometers can be used to determine the ground reaction forces experienced in a jump landing. Whereas the device also permitted an accurate determination of jump height, there was no correlation between peak ground reaction force and jump height.     

Jumping without using legs: the jump of the click-beetles (Elateridae) is morphologically constrained

To return to their feet, inverted click-beetles (Elateridae) jump without using their legs. When a beetle is resting on its dorsal side, a hinge mechanism is locked to store elastic energy in the body and releases it abruptly to launch the beetle into the air. While the functional morphology of the jumping mechanism is well known, the level of control that the beetle has over this jumping technique and the mechanical constraints governing the jumps are not entirely clear. Here we show that while body rotations in air are highly variable, the jumps are morphologically constrained to a constant “takeoff” angle (79.9°±1.56°, n = 9 beetles) that directs 98% of the jumping force vertically against gravity. A physical-mathematical model of the jumping action, combined with measurements from live beetle, imply that the beetle may control the speed at takeoff but not the jumping angle. In addition, the model shows that very subtle changes in the exact point of contact with the ground can explain the vigorous rotations of the body seen while the beetle is airborne. These findings suggest that the evolution of this unique non-legged jumping mechanism resulted in a jumping technique that is capable of launching the body high into the air but it is too constrained and unstable to allow control of body orientation at landing.     

Spatial and temporal coordination of traction forces in one-dimensional cell migration

ABSTRACT

Migration of a fibroblast along a collagen fiber can be regarded as cell locomotion in one-dimension (1D). In this process, a cell protrudes forward, forms a new adhesion, produces traction forces, and releases its rear adhesion in order to advance itself along a path. However, how a cell coordinates its adhesion formation, traction forces, and rear release in 1D migration is unclear. Here, we studied fibroblasts migrating along a line of microposts. We found that when the front of a cell protruded onto a new micropost, the traction force produced at its front increased steadily, but did so without a temporal correlation in the force at its rear. Instead, the force at the front coordinated with a decrease in force at the micropost behind the front. A similar correlation in traction forces also occurred at the rear of a cell, where a decrease in force due to adhesion detachment corresponded to an increase in force at the micropost ahead of the rear. Analysis with a bio-chemo-mechanical model for traction forces and adhesion dynamics indicated that the observed relationship between traction forces at the front and back of a cell is possible only when cellular elasticity is lower than the elasticity of the cellular environment.