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.     

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.     

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.     

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 effects of wind and posture on the aerodynamic performance during the flight stage of skiing

Numerical simulation is conducted to evaluate the wind and posture effects on the aerodynamic performance of a skier during the flight stage. Both steady and unsteady models are applied on a 2D geometry. Using the Fluent code, the fundamental equations of fluid flow are solved simultaneously. In particular we focus on the influence of wind speed and direction on aerodynamic forces with several different postures of the skier in steady modeling. For a chosen case, the unsteady models are used to predict the transient characteristics of streamline distributions and aerodynamic forces. It is found that the skier's postures, wind speed, and direction play a significant role. The wind condition affects the pressure force (the form drag) on the skier and makes it a resistance or thrust regarding wind directions. The optimized posture with a minimization of resistance under a facing wind is determined as a moving-forward body of the skier. The unsteady modeling reveals that the wake around the skier and aerodynamic forces are strongly dependent on time. This initial study not only provides a qualitative and theoretical basis for the athletes to understand the effects of wind and postures, and then to optimize their postures according to the wind condition during the flight stage of skiing, but also builds the foundation for the systematic study of skiing process with more advanced CFD models in the future.     

Ski jumping takeoff in a wind tunnel with skis

The effect of skis on the force-time characteristics of the simulated ski jumping takeoff was examined in a wind tunnel. Takeoff forces were recorded with a force plate installed under the tunnel floor. Signals from the front and rear parts of the force plate were collected separately to examine the anteroposterior balance of the jumpers during the takeoff. Two ski jumpers performed simulated takeoffs, first without skis in nonwind conditions and in various wind conditions. Thereafter, the same experiments were repeated with skis. The jumpers were able to perform very natural takeoff actions (similar to the actual takeoff) with skis in wind tunnel. According to the subjective feeling of the jumpers, the simulated ski jumping takeoff with skis was even easier to perform than the earlier trials without skis. Skis did not much influence the force levels produced during the takeoff but they still changed the force distribution under the feet. Contribution of the forces produced under the rear part of the feet was emphasized probably because the strong dorsiflexion is needed for lifting the skis to the proper flight position. The results presented in this experiment emphasize that research on ski jumping takeoff can be advanced by using wind tunnels.     

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.     

Using physical models to study the gliding performance of extinct animals

Aerodynamic studies using physical models of fossil organisms can provide quantitative information about how performance of defined activities, such as gliding, depends on specific morphological features. Such analyses allow us to rule out hypotheses about the function of extinct organisms that are not physically plausible and to determine if and how specific morphological features and postures affect performance. The purpose of this article is to provide a practical guide for the design of dynamically scaled physical models to study the gliding of extinct animals using examples from our research on the theropod dinosaur, ?Microraptor gui, which had flight feathers on its hind limbs as well as on its forelimbs. Analysis of the aerodynamics of ?M. gui can shed light on the design of gliders with large surfaces posterior to the center of mass and provide functional information to evolutionary biologists trying to unravel the origins of flight in the dinosaurian ancestors and sister groups to birds. Measurements of lift, drag, side force, and moments in pitch, roll, and yaw on models in a wind tunnel can be used to calculate indices of gliding and parachuting performance, aerodynamic static stability, and control effectiveness in maneuvering. These indices permit the aerodynamic performance of bodies of different shape, size, stiffness, texture, and posture to be compared and thus can provide insights about the design of gliders, both biological and man-made. Our measurements of maximum lift-to-drag ratios of 2.5-3.1 for physical models of ?M. gui suggest that its gliding performance was similar to that of flying squirrels and that the various leg postures that might have been used by ?M. gui make little difference to that aspect of aerodynamic performance. We found that body orientation relative to the movement of air past the animal determines whether it is difficult or easy to maneuver.     

The Aerodynamic Cost of Head Morphology in Bats: Maybe Not as Bad as It Seems

At first sight, echolocating bats face a difficult trade-off. As flying animals, they would benefit from a streamlined geometric shape to reduce aerodynamic drag and increase flight efficiency. However, as echolocating animals, their pinnae generate the acoustic cues necessary for navigation and foraging. Moreover, species emitting sound through their nostrils often feature elaborate noseleaves that help in focussing the emitted echolocation pulses. Both pinnae and noseleaves reduce the streamlined character of a bat’s morphology. It is generally assumed that by compromising the streamlined charactered of the geometry, the head morphology generates substantial drag, thereby reducing flight efficiency. In contrast, it has also been suggested that the pinnae of bats generate lift forces counteracting the detrimental effect of the increased drag. However, very little data exist on the aerodynamic properties of bat pinnae and noseleaves. In this work, the aerodynamic forces generated by the heads of seven species of bats, including noseleaved bats, are measured by testing detailed 3D models in a wind tunnel. Models of Myotis daubentonii, Macrophyllum macrophyllum, Micronycteris microtis, Eptesicus fuscus, Rhinolophus formosae, Rhinolophus rouxi and Phyllostomus discolor are tested. The results confirm that non-streamlined facial morphologies yield considerable drag forces but also generate substantial lift. The net effect is a slight increase in the lift-to-drag ratio. Therefore, there is no evidence of high aerodynamic costs associated with the morphology of bat heads.     

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.     

A potential role for bat tail membranes in flight control

Wind tunnel tests conducted on a model based on the long-eared bat Plecotus auritus indicated that the positioning of the tail membrane (uropatagium) can significantly influence flight control. Adjusting tail position by increasing the angle of the legs ventrally relative to the body has a two-fold effect; increasing leg-induced wing camber (i.e., locally increased camber of the inner wing surface) and increasing the angle of attack of the tail membrane. We also used our model to examine the effects of flying with and without a tail membrane. For the bat model with a tail membrane increasing leg angle increased the lift, drag and pitching moment (nose-down) produced. However, removing the tail membrane significantly reduced the change in pitching moment with increasing leg angle, but it had no significant effect on the level of lift produced. The drag on the model also significantly increased with the removal of the tail membrane. The tail membrane, therefore, is potentially important for controlling the level of pitching moment produced by bats and an aid to flight control, specifically improving agility and manoeuvrability. Although the tail of bats is different from that of birds, in that it is only divided from the wings by the legs, it nonetheless, may, in addition to its prey capturing function, fulfil a similar role in aiding flight control.     

Optimization of ski jumper's posture considering lift-to-drag ratio and stability

An optimization analysis of a ski jumper's posture has been performed to improve the lift-to-drag ratio, and to examine aerodynamic stability to ensure flight control and safety. Three-dimensional Reynolds-averaged Navier-Stokes equations were discretized using finite volume approximations for the flow analysis, and the shear stress transport k-ω turbulence model was used for a turbulence closure. The Airfoil theory and principles of aircraft stability were used to examine the stability mechanism. Two ski jumper posture angles were chosen as design variables through a preliminary test, and the lift-to-drag ratio was used as an objective function for the optimization problem. Thirteen design points within design spaces are selected by Latin hypercube sampling. In order to predict the objective function values in the design space, the Kriging model was constructed using the numerical results on the design points. By the sequential quadratic programming, the optimal point was found from the constructed the Kriging model. The Kriging model predicted the objective function value at the optimum point with a 1.1% error compared to the value obtained by numerical analysis. The optimum design showed a considerable lift-to-drag ratio improvement compared to the reference design.     

Anatomy and histochemistry of hindlimb flight posture in birds. I. The extended hindlimb posture of shorebirds

Birds utilize one of two hindlimb postures during flight: an extended posture (with the hip and knee joints flexed, while the ankle joint is extended caudally) or a flexed posture (with the hip, knee, and ankle joints flexed beneath the body). American Avocets (Recurvirostra americana) and Black‐necked Stilts (Himantopus mexicanus) extend their legs caudally during flight and support them for extended periods. Slow tonic and slow twitch muscle fibers are typically found in muscles functioning in postural support due to the fatigue resistance of these fibers. We hypothesized that a set of small muscles composed of high percentages of slow fibers and thus dedicated to postural support would function in securing the legs in the extended posture during flight. This study examined the anatomy and histochemical profile of eleven hindlimb muscles to gain insight into their functional roles during flight. Contrary to our hypothesis, all muscles possessed both fast twitch and slow twitch or slow tonic fibers. We believe this finding is due to the versatility of dynamic and postural functions the leg muscles must facilitate, including standing, walking, running, swimming, and hindlimb support during flight. Whether birds use an extended or flexed hindlimb flight posture may be related to the aerodynamic effect of leg position or may reflect evolutionary history. J. Morphol., 2008. © 2008 Wiley‐Liss, Inc.     

Comparing aerodynamic efficiency in birds and bats suggests better flight performance in birds

Flight is one of the energetically most costly activities in the animal kingdom, suggesting that natural selection should work to optimize flight performance. The similar size and flight speed of birds and bats may therefore suggest convergent aerodynamic performance; alternatively, flight performance could be restricted by phylogenetic constraints. We test which of these scenarios fit to two measures of aerodynamic flight efficiency in two passerine bird species and two New World leaf-nosed bat species. Using time-resolved particle image velocimetry measurements of the wake of the animals flying in a wind tunnel, we derived the span efficiency, a metric for the efficiency of generating lift, and the lift-to-drag ratio, a metric for mechanical energetic flight efficiency. We show that the birds significantly outperform the bats in both metrics, which we ascribe to variation in aerodynamic function of body and wing upstroke: Bird bodies generated relatively more lift than bat bodies, resulting in a more uniform spanwise lift distribution and higher span efficiency. A likely explanation would be that the bat ears and nose leaf, associated with echolocation, disturb the flow over the body. During the upstroke, the birds retract their wings to make them aerodynamically inactive, while the membranous bat wings generate thrust and negative lift. Despite the differences in performance, the wake morphology of both birds and bats resemble the optimal wake for their respective lift-to-drag ratio regimes. This suggests that evolution has optimized performance relative to the respective conditions of birds and bats, but that maximum performance is possibly limited by phylogenetic constraints. Although ecological differences between birds and bats are subjected to many conspiring variables, the different aerodynamic flight efficiency for the bird and bat species studied here may help explain why birds typically fly faster, migrate more frequently and migrate longer distances than bats.     

A wing-assisted running robot and implications for avian flight evolution

DASH+Wings is a small hexapedal winged robot that uses flapping wings to increase its locomotion capabilities. To examine the effects of flapping wings, multiple experimental controls for the same locomotor platform are provided by wing removal, by the use of inertially similar lateral spars, and by passive rather than actively flapping wings. We used accelerometers and high-speed cameras to measure the performance of this hybrid robot in both horizontal running and while ascending inclines. To examine consequences of wing flapping for aerial performance, we measured lift and drag forces on the robot at constant airspeeds and body orientations in a wind tunnel; we also determined equilibrium glide performance in free flight. The addition of flapping wings increased the maximum horizontal running speed from 0.68 to 1.29 m s?1, and also increased the maximum incline angle of ascent from 5.6° to 16.9°. Free flight measurements show a decrease of 10.3° in equilibrium glide slope between the flapping and gliding robot. In air, flapping improved the mean lift:drag ratio of the robot compared to gliding at all measured body orientations and airspeeds. Low-amplitude wing flapping thus provides advantages in both cursorial and aerial locomotion. We note that current support for the diverse theories of avian flight origins derive from limited fossil evidence, the adult behavior of extant flying birds, and developmental stages of already volant taxa. By contrast, addition of wings to a cursorial robot allows direct evaluation of the consequences of wing flapping for locomotor performance in both running and flying.     

Flight style optimization in ski jumping on normal,large, and ski flying hills

In V-style ski jumping, aerodynamic forces are predominant performance factors and athletes have to solve difficult optimization problems in parts of a second in order to obtain their jump length maximum and to keep the flight stable. Here, a comprehensive set of wind tunnel data was used for optimization studies based on Pontryagin′s minimum principle with both the angle of attack α and the body-ski angle β as controls. Various combinations of the constraints α_max and β_min(t) were analyzed in order to compare different optimization strategies. For the computer simulation studies, the Olympic hill profiles in Esto-Sadok, Russia (HS 106 m, HS 140 m), and in Harrachov, Czech Republic, host of the Ski Flying World Championships 2014 (HS 205 m) were used. It is of high importance for ski jumping practice that various aerodynamic strategies, i.e. combinations of α- and β-time courses, can lead to similar jump lengths which enables athletes to win competitions using individual aerodynamic strategies. Optimization results also show that aerodynamic behavior has to be different at different hill sizes (HS). Optimized time courses of α and β using reduced drag and lift areas in order to mimic recent equipment regulations differed only in a negligible way. This indicates that optimization results presented here are not very sensitive to minor changes of the aerodynamic equipment features when similar jump length are obtained by using adequately higher in-run velocities. However, wind tunnel measurements with athletes including take-off and transition to stabilized flight, flight, and landing behavior would enable a more detailed understanding of individual flight style optimization.     

Flight of the honeybee

Summary Drag forces and lift forces acting on honeybee trunks were measured by using specially built sensitive mechanical balances. Measurements were made on prepared bodies in good and in bad flight position, with and without legs, at velocities between 0.5 and 5m·s^-1 (Reynolds numbers between 4·10² and 4·10³) and at angles of attack between-20° and +20°. From the forces drag coefficients and lift coefficients were calculated. The drag coefficient measured with a zero angle of attack was 0.45 at 3v5m·s^-1, 0.6 at 2m·s^-1, 0.9 at 1m·s^-1 and 1.35 at 0.5m·s^-1, thus demonstrating a pronounced effect of Reynolds number on drag. These values are about 2 times lower (better) than those of a drag disc with the same diameter and attacked at the same velocity. The drag coefficient (related to constant minimal frontal area) was minimal at zero angle of attack, rising symmetrically to larger (+) and smaller (-) angles of attack in a non-linear fashion. The absolute value is higher and the rise is steeper at lower speeds or Reynolds numbers, but the incremental factors are independent of Reynolds number. For example, the drag coefficient is 1.44±0.05 times higher at an angle of attack of 20° than at one of 0°. On a double-logarithmic scale the slope of the drag versus Reynolds number plot was 1.5: with decreasing Reynolds number the relationship between drag and velocity changes from quadratic (Newton's law) to linear (viscous flow). Trunk drag was not systematically increased by the legs at any velocity or Reynolds number or any angle of attack. The legs appear to shape the trunk aerodynamically, to form a relatively low-drag trunk-leg system. The body is able to generate dynamic lift. Highly significant positive linear correlations between lift coefficient and angle of attack were determined for the trunk-leg system in the typical flight position. Lift coefficient was +0.05 at zero angle of attack (possibly attained during very fast flight), +0.1 at 5° (attained during fast flight), +0.25 at +20° (attained during slow flight) and +0.55 at 45° (attained whilst changing over to hovering). Average slope c_L was 0.66±0.07, and average profile efficiency was 0.10. Non-wing lift contribution due to body form and banking only accounts for a few percent of body weight during fast flight. A non-wing lift contribution due to the legs has been demonstrated. The legs increase trunk lift by 23–24%. Reynolds number lift effects are present but of no biological significance. Force and power calculations do not support maximum flight speeds substantially higher than approximately 7m · s^-1 relative to the ambient air. At this speed body drag attains 35% and body lift 8.4% of the body weight, and parasite power is 5% of the maximum metabolic power.Abbreviations angle of attack - A area - c drag coefficient - c_L lift coefficient - D drag - F force - L lift - P power - Q quotient - Re Reynolds number - density - dliding number - O₂ oxygen consumption - W work - v kinematic viscosity - efficiency - v velocity     

The influence of aerodynamic and biomechanical factors on long jump performance

A new analysis, based on the equations of motion, is made of the influence of aerodynamic drag on the trajectory and aerial range achieved by a long jumper. The general result is applied to a particular case, namely the world long jump record obtained by Bob Beamon at the Mexico Olympics in 1968. Calculations are also made of the influence of body height and jumping technique on overall long-jump performance. A comparison is made between the relative importance of aerodynamic and anthropometric aspects of long jump performance.     

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.