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.     

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.     

Explosive lower limb extension mechanics: An on-land vs. in-water exploratory comparison

During a horizontal underwater push-off, performance is strongly limited by the presence of water, inducing resistances due to its dense and viscous nature. At the same time, aquatic environments offer a support to the swimmer with the hydrostatic buoyancy counteracting the effects of gravity. Squat jump is a vertical terrestrial push-off with a maximal lower limb extension limited by the gravity force, which attracts the body to the ground. Following this observation, we characterized the effects of environment (water vs. air) on the mechanical characteristics of the leg push-off. Underwater horizontal wall push-off and vertical on-land squat jumps of two local swimmers were evaluated with force plates, synchronized with a lateral camera. To better understand the resistances of the aquatic movement, a quasi-steady Computational Fluid Dynamics (CFD) analysis was performed. The force-, velocity- and power-time curves presented similarities in both environments corresponding to a proximo-distal joints organization. In water, swimmers developed a three-step explosive rise of force, which the first one mainly related to the initiation of body movement. Drag increase, which was observed from the beginning to the end of the push-off, related to the continuous increase of body velocity with high values of drag coefficient (C_D) and frontal areas before take-off. Specifically, with velocity, frontal area was the main drag component to explain inter-individual differences, suggesting that the streamlined position of the lower limbs is decisive to perform an efficient push-off. This study motivates future CFD simulations under more ecological, unsteady conditions.     

A computational study of the aerodynamic performance of a dragonfly wing section in gliding flight

A comprehensive computational fluid-dynamics-based study of a pleated wing section based on the wing of Aeshna cyanea has been performed at ultra-low Reynolds numbers corresponding to the gliding flight of these dragonflies. In addition to the pleated wing, simulations have also been carried out for its smoothed counterpart (called the 'profiled' airfoil) and a flat plate in order to better understand the aerodynamic performance of the pleated wing. The simulations employ a sharp interface Cartesian-grid-based immersed boundary method, and a detailed critical assessment of the computed results was performed giving a high measure of confidence in the fidelity of the current simulations. The simulations demonstrate that the pleated airfoil produces comparable and at times higher lift than the profiled airfoil, with a drag comparable to that of its profiled counterpart. The higher lift and moderate drag associated with the pleated airfoil lead to an aerodynamic performance that is at least equivalent to and sometimes better than the profiled airfoil. The primary cause for the reduction in the overall drag of the pleated airfoil is the negative shear drag produced by the recirculation zones which form within the pleats. The current numerical simulations therefore clearly demonstrate that the pleated wing is an ingenious design of nature, which at times surpasses the aerodynamic performance of a more conventional smooth airfoil as well as that of a flat plate. For this reason, the pleated airfoil is an excellent candidate for a fixed wing micro-aerial vehicle design.     

Aerodynamic investigation of the thermo-dependent flow structure in the wake of a cyclist

The main purpose of this study was to assess the influence of the environmental temperature on both the aerodynamic flow evolving around the bicycle and cycling power output. The CFD method was used to investigate the detailed flow field around the cyclist/bicycle system for a constant speed of 11.1 m/s (40 km/h) without wind. In complement, a mathematical model was used to determine the temperature-dependent power output in the range [−10; 40 °C]. The numerical investigation gives valuable information about the turbulent flow field in the cyclist's wake which evolves accordingly the surrounding temperature. A major result of this study is that the areas of overpressure upstream of the cyclist and of underpressure downstream of him are less extensive for a temperature of 40 °C compared to −10 °C. The results suggest that the aerodynamic braking effect of the bicycle is minimized when the air temperature is high, as a lower air density results in a reduction in drag on the cyclist. This study showed that the power required to maintain a constant speed is reduced when the temperature is high, the reason being a lower aerodynamic resistance.     

A modified blade element theory for estimation of forces generated by a beetle-mimicking flapping wing system

We present an unsteady blade element theory (BET) model to estimate the aerodynamic forces produced by a freely flying beetle and a beetle-mimicking flapping wing system. Added mass and rotational forces are included to accommodate the unsteady force. In addition to the aerodynamic forces needed to accurately estimate the time history of the forces, the inertial forces of the wings are also calculated. All of the force components are considered based on the full three-dimensional (3D) motion of the wing. The result obtained by the present BET model is validated with the data which were presented in a reference paper. The difference between the averages of the estimated forces (lift and drag) and the measured forces in the reference is about 5.7%. The BET model is also used to estimate the force produced by a freely flying beetle and a beetle-mimicking flapping wing system. The wing kinematics used in the BET calculation of a real beetle and the flapping wing system are captured using high-speed cameras. The results show that the average estimated vertical force of the beetle is reasonably close to the weight of the beetle, and the average estimated thrust of the beetle-mimicking flapping wing system is in good agreement with the measured value. Our results show that the unsteady lift and drag coefficients measured by Dickinson et al are still useful for relatively higher Reynolds number cases, and the proposed BET can be a good way to estimate the force produced by a flapping wing system.     

Aerodynamics of cyclist posture, bicycle and helmet characteristics in time trial stage

The present work is focused on the aerodynamic study of different parameters, including both the posture of a cyclist's upper limbs and the saddle position, in time trial (TT) stages. The aerodynamic influence of a TT helmet large visor is also quantified as a function of the helmet inclination. Experiments conducted in a wind tunnel on nine professional cyclists provided drag force and frontal area measurements to determine the drag force coefficient. Data statistical analysis clearly shows that the hands positioning on shifters and the elbows joined together are significantly reducing the cyclist drag force. Concerning the saddle position, the drag force is shown to be significantly increased (about 3%) when the saddle is raised. The usual helmet inclination appears to be the inclination value minimizing the drag force. Moreover, the addition of a large visor on the helmet is shown to provide a drag coefficient reduction as a function of the helmet inclination. Present results indicate that variations in the TT cyclist posture, the saddle position and the helmet visor can produce a significant gain in time (up to 2.2%) during stages.     

Aerodynamic study of time-trial helmets in cycling racing using CFD analysis

The aerodynamic drag of three different time-trial cycling helmets was analyzed numerically for two different cyclist head positions. Computational Fluid Dynamics (CFD) methods were used to investigate the detailed airflow patterns around the cyclist for a constant velocity of 15 m/s without wind. The CFD simulations have focused on the aerodynamic drag effects in terms of wall shear stress maps and pressure coefficient distributions on the cyclist/helmet system. For a given head position, the helmet shape, by itself, obtained a weak effect on a cyclist’s aerodynamic performance (<1.5%). However, by varying head position, a cyclist significantly influences aerodynamic performance; the maximum difference between both positions being about 6.4%. CFD results have also shown that both helmet shape and head position significantly influence drag forces, pressure and wall shear stress distributions on the whole cyclist’s body due to the change in the near-wake behavior and in location of corresponding separation and attachment areas around the cyclist.     

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.     

On optimal running downhill on skis

In the paper the problem of the minimum time schuss is discussed. The skier is modelled as a point mass moving on the slope. The profile of the slope may be represented by any given function. Initial and final conditions are given. The control function is the aerodynamic drag of the skier's body. Miele's method is applied for the optimum control problem stated in such a manner. The nature of the optimal solution is independent of the slope shape.     

How Could Beetle＇s Elytra Support Their Own Weight during Forward Flight？

The aerodynamic role of the elytra during a beetle＇s flapping motion is not well-elucidated, although it is well-recognized that the evolution of elytra has been a key in the success of coleopteran insects due to their protective function. An experimental study on wing kinematics reveals that for almost concurrent flapping with the hind wings, the flapping angle of the elytra is 5 times smaller than that of the hind wings. Then, we explore the aerodynamic forces on elytra in free forward flight with and without an effect of elytron-hind wing interaction by three-dimensional numerical simulation. The numerical results show that vertical force generated by the elytra without interaction is not sufficient to support even its own weight. However, the elytron-hind wing interaction improves the vertical force on the elytra up to 80%; thus, the total vertical force could fully support its own weight. The interaction slightly increases the vertical force on the hind wind by 6% as well.     

Determination of the drag coefficient of a toroidal plasma vortex in air

Forces acting on toroidal vortices in an unbounded medium (plasma vortices in air and vortex rings in air and water) are investigated. A solution to the equations describing such votrices is obtained. It is shown that this solution satisfactorily agrees with experiment. Based on the experimental results and the solution obtained, the drag coefficient C _x of such vortices is found. For the same Reynolds numbers, the value of C _x may be much less than the drag coefficient of a drop-shaped axisymmetric body (0.045), which is known to be the best streamlined object.     

Influence of the postion of crew members on aerodynamics performance of two-man bobsleigh

Bobsleigh aerodynamics has long been recognised as one of the crucial performance factors. Although the published research in the area is very limited, it is well known that the leading nations in the sport devote significant resources in research and development of sleds' aerodynamics. However, the rules and regulations pose strict design constraints on the shape modifications aiming at aerodynamics improvements. The reason for that is two-fold: (i) safety of the athletes and (ii) reduction of equipment impact on competition outcome. One particular area that has not been looked at and falls outside the current rules and regulations is the influence of the crew positioning and internal modifications on the aerodynamic performance. The current study presents results on numerical simulation of the flow in the cavity underpinned with some experimental measurements including flow visualisation of the air circulation around the bobsleigh. A simplified computational model was developed to assess the trends and its results validated by windtunnel tests. The results show that crew members influence the drag level significantly and suggest that purely internal modifications can be introduced to reduce the overall resistance drag.     

Effect of forward trunk inclination on joint power output in vertical jumping

It is commonly accepted that vertical jump performance is a good indicator of maximal joint power. Some studies, however, have indicated that knee joint power output in the vertical jump is limited due to forward trunk inclination early in the push-off. The aim of this experimental study was to investigate the effect of forward trunk inclination on joint power output in vertical jumping. A group of 20 male subjects performed maximal vertical countermovement jumps from stance while minimizing the contribution of arm swing by holding their hands on their hips (arms akimbo). They also performed maximal jumps while holding the trunk as upright as possible throughout the jump, still holding the arms akimbo. Jump height, joint kinematics (angles), and joint kinetics (torque, power) were calculated. Jump height of vertical jumps while holding the trunk upright was 10% less than in normal jumps. Hip joint power was decreased by 37% while knee joint power was increased by 13%. Ankle joint power did not change. These results demonstrated that maximal jump performance does not necessarily represent maximal power of each individual joint. The implication is that jump performance may well be a good representation of overall joint power; it is, however, not an accurate measure to evaluate maximal individual joint power as part of contemporary training and rehabilitation methods.     

They seem to glide. Are there aerodynamic effects in leaping prosimian primates?

Leaping primates often assume a horizontal position while airborne. When the limbs are spread out in such maneuvers, skin folds between the upper limbs and the trunk are exposed. This has led to the assumption that the animals make use of aerodynamic forces for either gliding, steering, or braking before the landing. In terms of physics, aerodynamic lift or aerodynamic drag can cause the described effects. As coefficients of lift and drag are unknown for flying primates, we have calculated those values that give the animals either a 5% gain or loss in leaping distance. These turn out to be in the range of values for cylinder-shaped "blunt" (unstreamlined) bodies. A significant influence of aerodynamic forces on the flight path can therefore be assumed. The smaller-bodied species (e.g., galagos) are more strongly influenced by their great surface areas. Although frontal areas scale positively allometrically with respect to body mass, air speed gains importance in the larger-bodied species (e.g., sifakas). They cover absolutely greater distances and have the higher takeoff velocities. The actual importance of lift and drag cannot be derived from our theoretical calculations but must be determined experimentally.     

Morphologic and Aerodynamic Considerations Regarding the Plumed Seeds of Tragopogon pratensis and Their Implications for Seed Dispersal

Tragopogon pratensis is a small herbaceous plant that uses wind as the dispersal vector for its seeds. The seeds are attached to parachutes that increase the aerodynamic drag force and increase the total distance travelled. Our hypothesis is that evolution has carefully tuned the air permeability of the seeds to operate in the most convenient fluid dynamic regime. To achieve final permeability, the primary and secondary fibres of the pappus have evolved with complex weaving; this maximises the drag force (i.e., the drag coefficient), and the pappus operates in an “optimal” state. We used computational fluid dynamics (CFD) simulations to compute the seed drag coefficient and compare it with data obtained from drop experiments. The permeability of the parachute was estimated from microscope images. Our simulations reveal three flow regimes in which the parachute can operate according to its permeability. These flow regimes impact the stability of the parachute and its drag coefficient. From the permeability measurements and drop experiments, we show how the seeds operate very close to the optimal case. The porosity of the textile appears to be an appropriate solution to achieve a lightweight structure that allows a low terminal velocity, a stable flight and a very efficient parachute for the velocity at which it operates.     

Diphasic modelling of vertical flow filter

Wastewater treatment quality in vertical flow filter fed intermittently depends on the oxygen renewal capacities. Convective transport by the air phase is one source. Diphasic modelling has been shown to be an efficient tool to describe complicated movement of air and water during a feeding sequence and thus to estimate the convective dioxygen income. However, earlier numerical works do not describe the full complexity of the system, like the seepage front existing at the interface with the drain, and are limited to one scenario. In this paper, we introduce an adaptation of an existing diphasic numerical model to the specificity of vertical flow filter with a particular emphasis on the choice of boundary and initial conditions. Completely different behaviour was observed as ponding does or does not occur. Taking into account the influence of air also enables us to understand a phenomenon like early seepage at the bottom due to air pushed downward and reduction of infiltration speed linked to air compression in the top layers. We investigate relationships between the feeding parameters and the quantity of dioxygen entering the porous media by convection. Hydraulic loading rate does not seem to affect the quantity of dioxygen entering by convection. Increase of the daily hydraulic augments the dioxygen income. However, this phenomenon seems limited as it tends towards an asymptotic value. The number of flushes per day has a contradictory impact: it reduces the income of dioxygen per flush but have a positive impact over a day. Finally we initiate a benchmark of simulation scenarios, which might be a basis for model comparison and experimental validation.     

Solving the chemical master equation for monomolecular reaction systems analytically

The stochastic dynamics of a well-stirred mixture of molecular species interacting through different biochemical reactions can be accurately modelled by the chemical master equation (CME). Research in the biology and scientific computing community has concentrated mostly on the development of numerical techniques to approximate the solution of the CME via many realizations of the associated Markov jump process. The domain of exact and/or efficient methods for directly solving the CME is still widely open, which is due to its large dimension that grows exponentially with the number of molecular species involved. In this article, we present an exact solution formula of the CME for arbitrary initial conditions in the case where the underlying system is governed by monomolecular reactions. The solution can be expressed in terms of the convolution of multinomial and product Poisson distributions with time-dependent parameters evolving according to the traditional reaction-rate equations. This very structured representation allows to deduce easily many properties of the solution. The model class includes many interesting examples. For more complex reaction systems, our results can be seen as a first step towards the construction of new numerical integrators, because solutions to the monomolecular case provide promising ansatz functions for Galerkin-type methods.     

A deterministic model of the vertical jump: implications for training

Increasing vertical jump height is a critical component for performance enhancement in many sports. It takes on a number of different forms and conditions, including double and single legged jumps and stationary and run-up jumps. In an attempt to understand the factors that influence vertical jump performance, an extensive analysis was undertaken using the deterministic model. Once identified, practical training strategies enabling improvement in these factors were elucidated. Our analysis showed that a successful vertical jump performance was the result of a complex interplay of run-up speed, reactive strength, concentric action power of the take-off leg(s), hip flexors, shoulders, body position, body mass, and take-off time. Of special interest, our analysis showed that the concentric action power of the legs was the critical factor affecting stationary double leg vertical jumps, whereas reactive strength was the critical component for a single leg jump from a run-up.     

The effectiveness of resisted movement training on sprinting and jumping performance

Resisted movement training is that in which the sports movement is performed with added resistance. To date, the effectiveness on enhancing sprint speed or vertical jump height had not been reviewed. The objectives of this review were to collate information on resisted training studies for sprinting and vertical jumping, ascertain whether resisted movement training was superior to normal unresisted movement training, and identify areas for future research. The review was based on peer-reviewed journal articles identified from electronic literature searches using MEDLINE and SPORTDiscus data bases from 1970 to 2010. Resisted sprint training was found to increase sprint speed but, in most cases, was no more effective than normal sprint training. There was some evidence that resisted sprint training was superior in increasing speed in the initial acceleration phase of sprinting. Resisted jump training in the form of weighted jump squats was shown to increase vertical jump height, but it was no more effective than plyometric depth jump training. Direct comparisons between resisted jump training and unresisted normal jump training were limited, but loaded eccentric countermovement jump squat training with unloaded concentric phase and eccentric landing was shown to generate superior results for elite jumpers. More prospective studies on resisted sprint training are required along with monitoring both kinematic and kinetic adaptations to fully determine any underlying mechanisms for any improvements in sprint speed. Based on the available data, the benefits and superiority of resisted sprint training have not been fully established. As for resisted jump training, although there are some promising findings, these results need to be duplicated by other researchers before resisted jump training can be claimed to be more effective than other forms of jump training.