Engineering the race car wing: application of the vortex panel numerical method

This study examined aerodynamic properties and boundary layer stability in five cambered airfoils operating at the low Reynolds numbers encountered in motor racing. Numerical modelling was carried out in the flow regime characterised by Reynolds numbers 0.82–1.29 × 10⁶. The design Reynolds number of 3 × 10⁶ was used as a reference. Aerodynamics variables were computed using AeroFoil 2.2 software, which uses the vortex panel method and integral boundary layer equations. Validation of AeroFoil 2.2 software showed very good agreement between calculated aerodynamic coefficients and wind tunnel experimental data. Drag polars, lift/drag ratio, pitching moment coefficient, chordwise distributions (surface velocity ratio, pressure coefficient and boundary layer thickness), stagnation point, and boundary layer transition and separation were obtained at angles of attack from −4° to 12°. The NASA NLF(1)-0414F airfoil offers versatility for motor racing with a wide low-drag bucket, low minimum profile drag, high lift/drag ratio, laminar flow up to 0.7 chord, rapid concave pressure recovery, high resultant pressure coefficient and stall resistance at low Reynolds numbers. The findings have implications for the design of race car wings.     

Football boundary-layer separation via dust experiments

A method of examining the separation of the boundary layer of air from a sports ball, specifically a football, is presented. Using a ball launcher, a non-spinning football is fired into a dust cloud. A high-speed camera records the ball passing through the dust cloud. Unlike wind-tunnel methods, the dust method described here allows for the examination of the boundary-layer separation without a ball-supporting arrangement. Boundary-layer separation for speeds surrounding the drag crisis is studied. Though the general trend is for the boundary layer to separate farther back on the ball as the ball’s centre-of-mass speed increases, anomalous behaviour is seen just past the drag crisis, namely a rise in the separation angle, followed by an expected decrease.     

Experimental determination of baseball spin and lift

The aim of this study was to develop a new method for the determination of lift on spinning baseballs. Inertial trajectories of (a) ball surface markers during the first metre of flight and (b) the centre of mass trajectory near home-plate were measured in a pitch using high-speed video. A theoretical model was developed, incorporating aerodynamic Magnus-Robins lift, drag and cross forces, which predicts the centre of mass and marker trajectories. Parameters including initial conditions and aerodynamic coefficients were estimated iteratively by minimizing the error between predicted and measured trajectories. We compare the resulting lift coefficients and spin parameter values with those of previous studies. Lift on four-seam pitches can be as much as three times that of two-seam pitches, although this disparity is reduced for spin parameters greater than 0.4.     

Experimental determination of baseball spin and lift

The aim of this study was to develop a new method for the determination of lift on spinning baseballs. Inertial trajectories of (a) ball surface markers during the first metre of flight and (b) the centre of mass trajectory near home-plate were measured in a pitch using high-speed video. A theoretical model was developed, incorporating aerodynamic Magnus-Robins lift, drag and cross forces, which predicts the centre of mass and marker trajectories. Parameters including initial conditions and aerodynamic coefficients were estimated iteratively by minimizing the error between predicted and measured trajectories. We compare the resulting lift coefficients and spin parameter values with those of previous studies. Lift on four-seam pitches can be as much as three times that of two-seam pitches, although this disparity is reduced for spin parameters greater than 0.4.     

Investigation of toppling ball flight in American football with a mechanical field-goal kicker

A mechanical field-goal kicking machine was used to investigate toppling ball flight in American football place-kicking, eliminating a number of uncontrollable impact variables present with a human kicker. Ball flight trajectories were recorded using a triangulation-based projectile tracking system to account for the football’s 3-dimensional position during flight as well as initial launch conditions. The football flights were described using kinematic equations relating to projectile motion including stagnant air drag and were compared to measured trajectories as well as projectile motion equations that exclude stagnant air drag. Measured football flight range deviations from the non-drag equations of projectile motion corresponded to deficits between 9 and 31%, which is described by a football toppling compound drag coefficient of 0.007 ± 0.003 kg/m. Independent variables including impact location and impact angle orientation resulted in 15 impact conditions. We found that an impact location of 5.5 cm from the bottom of the ball maximized trajectory height and distance. At the 5.5-cm impact location, alterations in impact angle produced minimal change in football trajectory, including launch angle (range = 1.96 deg), launch speed (range = 1.06 m/s), and range (range = 0.94 m).     

Fundamental aerodynamics of the soccer ball

When the boundary layer of a sports ball undergoes the transition from laminar to turbulent flow, a drag crisis occurs whereby the drag coefficient (C _d) rapidly decreases. However, the aerodynamic properties and boundary-layer dynamics of a soccer ball are not yet well understood. In this study we showed that the critical Reynolds number (Re _crit) of soccer balls ranged from 2.2 × 10⁵ to 3.0 × 10⁵. Wind-tunnel testing, along with visualisation of the dynamics of the boundary layer and the trailing vortex of a ball in flight, demonstrated that both non-spinning and spinning (curved) balls had lowC _d values in the super-critical region. In addition, theRe _crit values of the soccer balls were lower than those of smooth spheres, ranging from ∼ 3.5 × 10⁵ to 4.0 × 10⁵, due to the effects of their panels. This indicated that the aerodynamic properties of a soccer ball were intermediate between those of a smooth ball and a golf ball. In a flow visualisation experiment, the separation point retreated and theC _d decreased in a super-critical regime compared with those in a sub-critical regime, suggesting a phenomenon similar to that observed in other sports balls. With some non-spinning and spinning soccer balls, the wake varied over time. In general, the high-frequency component of an eddy dissipated, while the low-frequency component increased as the downstream vortex increased. The causes of the large-scale fluctuations in the vortex observed in the present study were unclear; however, it is possible that a ‘knuckle-ball effect’ of the non-rotating ball played a role in this phenomenon.     

Flow analysis and aerodynamic characteristics of a badminton shuttlecock with spin at high Reynolds numbers

A badminton shuttlecock flies in a high-drag, and thus, the sport has been a subject of research from the point of view of aerodynamics. A badminton shuttlecock generates significant aerodynamic drag and has a complex flight trajectory. It also has the smallest ballistic coefficient and exhibits the largest in-flight deceleration of any airborne sporting projectile. The ballistic coefficient of a projectile is a measure of its ability to overcome air resistance in flight and is inversely proportional to deceleration. The primary objectives of this study were to measure the aerodynamic properties of feather shuttlecocks under a range of the wind speed (10–60 m/s) and pitch angle (0°–25°). In particular, measurements of aerodynamic forces were performed at high Reynolds numbers (more than Re = 210,000), and the effect of shuttlecock deformation on aerodynamic properties was also investigated, because it is presumed that the flight dynamics is affected by the deformation of the shuttlecock skirt. A shuttlecock skirt is composed of an array of diverging stems, the ends of which are at the convergent end of the skirt, joined together in an end ring. The shuttlecock rotates about its major axis in actual flight, and thus, the experiments were performed on shuttlecocks with and without rotation (spin). Furthermore, the effect of the flow passing through the gaps between the slots (stiffeners) located at the leg portion of the shuttlecock skirt on aerodynamic characteristics is demonstrated by means of a shuttlecock model without gaps, which was completely covered with cellophane tape. The free rotation rate of a shuttlecock increased with an increase in the Reynolds number, and the drag coefficient gradually decreased above Re = 86,000 for a non-rotating shuttlecock. The reduction of drag can be explained by the deformation of the skirt observed in wind tunnel experiments at high speed. In this study, for a rotating shuttlecock, a reduction of drag was not observed over a whole range of Reynolds numbers, because deformation of the skirt for a rotating shuttlecock becomes smaller than that for a non-rotating shuttlecock. However, there was no significant difference in drag coefficient between rotating and non-rotating shuttlecocks, in contrast to the difference in drag coefficient between shuttlecocks with and without gaps. The drag coefficient for a shuttlecock without gaps was significantly smaller than that for a standard shuttlecock (with gaps). For a standard shuttlecock, the air flowed through the gaps into the shuttlecock skirt, and this flow was related to high aerodynamic drag.     

Flight dynamics of the screw kick in rugby

This paper describes the aerodynamic forces and the flight trajectory for the screw (spiral) kick in rugby. The screw kick is defined as that which causes the ball to spin on its longitudinal axis. The aerodynamic forces acting on a rugby ball spinning on its longitudinal axis were measured in a wind tunnel using a six-component strut type balance. It was found that the drag, the lift and the pitching moment depend on the angle of attack, while the side force (Magnus force) depends on both the spin rate and the angle of attack in the range where the wind speed lies between 15 and 30 m s^-1 and the spin rate is between 1 and 10 revolutions per second. Moreover, the flight trajectory was obtained by integrating the full nonlinear six degrees of freedom equations of motion on the basis of aerodynamic data. In a simulation, a ball spinning on its longitudinal axis tended to hook toward or away from the touchline even if the velocity and angular velocity vectors were parallel to the touchline. The direction of the hook depends on the direction of the angular velocity vector. The initial direction of the hook depends on the relationship between the flight path angle and the pitch angle as well as the direction of the angular velocity vector.     

The effect of surface geometry on soccer ball trajectories

Two different measurement techniques are used to examine the effect of surface geometry on soccer ball trajectories. Five professional players are observed using high-speed video when taking curling free kicks with four different soccer balls. The input conditions are measured and the average launch velocity and spin are found to be approximately 24 m/s and 106 rad/s. It is found that the players can apply more spin (~50%) on average to one ball, which has a slightly rougher surface than the other balls. The trajectories for the same four balls fired at various velocities and spin rates across a sports hall using a bespoke firing device are captured using high-speed video cameras, and their drag and lift coefficients estimated. Balls with more panels are found to experience a higher lift coefficient. The drag coefficient results show a large amount of scatter, and it is difficult to distinguish between the balls. Using the results in a trajectory prediction programme it is found that increasing the number of panels from 14 to 32 can significantly alter the final position of a 20 m-curling free kick by up to 1 m.     

基于STAR-CCM+的帆板帆翼空气动力性能数值模拟

利用计算流体力学软件STAR-CCM+对奥运会比赛用帆板及帆船帆翼的空气动力性能进行了数值模拟,得到了不同攻角下的帆翼在粘性流场下的数值模拟结果和相应的升力系数及阻力系数。对不同攻角下的升力系数和阻力系数计算结果与实验结果进行了对比,通过比较可以看出利用STAR-CCM+软件能够快速有效地预报帆翼空气动力性能和流场。     

Wind tunnel measurement and flow visualisation of soccer ball knuckle effect

Wind tunnel experiments were conducted, in particular focusing on slow unsteady variations of aerodynamic forces as a potential cause of the knuckle effect of a new soccer ball (Teamgeist) under non-spinning condition. The experiments included simultaneous measurements of the drag, the side force and the surface pressure on a ball surface, and the tuft visualisation to investigate the flow field behind a ball. Of particular interest was the erratic nature of the knuckle effect resulting from the unsteady movement of vortical wake structure in the supercritical Reynolds number regime. A simple 2-D numerical simulation of the ball flight trajectory was performed by taking into account the unsteady side force data measured in the present experiments.     

Modelling the flight of a soccer ball in a direct free kick

This study involved a theoretical and an experimental investigation of the direct free kick in soccer. Our aim was to develop a mathematical model of the ball's flight incorporating aerodynamic lift and drag forces to explore this important 'set-play'. Trajectories derived from the model have been compared with those obtained from detailed video analysis of experimental kicks. Representative values for the drag and lift coefficients have been obtained, together with the implied orientation of the ball's spin axis in flight. The drag coefficient varied from 0.25 to 0.30 and the lift coefficient from 0.23 to 0.29. These values, used with a simple model of a defensive wall, have enabled free kicks to be simulated under realistic conditions, typical of match-play. The results reveal how carefully attackers must engineer the dynamics of a successful kick. For a central free kick some 18.3 m (20 yards) from goal with a conventional wall, and initial speed of 25 m x s(-1), the ball's initial elevation must be constrained between 16.5 degrees and 17.5 degrees and the ball kicked with almost perfect sidespin.     

Measurements of drag and lift on tennis balls in flight

Measurements are presented of drag and lift on new tennis balls in flight. Two video cameras were used to measure the velocity and height of the balls at two positions separated horizontally by 6.4 m. The balls were fired from a ball launcher at speeds between 15 and 30 m/s and with topspin or backspin at rates up to 2,500 rpm. Significant shot-to-shot variations were found in both the drag and lift coefficients. The average drag coefficient was 0.507 ± 0.024, independent of ball speed or spin, and lower than the value usually observed in wind tunnel experiments. The lift coefficient increased with ball spin, on average, but significant lift was observed even at very low spin. The latter effect can be attributed to a side force arising from asymmetries in the ball surface, analogous to the side force responsible for the erratic path of a knuckleball in baseball.     

Modelling the flight of a soccer ball in a direct free kick

This study involved a theoretical and an experimental investigation of the direct free kick in soccer. Our aim was to develop a mathematical model of the ball's flight incorporating aerodynamic lift and drag forces to explore this important 'set-play'. Trajectories derived from the model have been compared with those obtained from detailed video analysis of experimental kicks. Representative values for the drag and lift coefficients have been obtained, together with the implied orientation of the ball's spin axis in flight. The drag coefficient varied from 0.25 to 0.30 and the lift coefficient from 0.23 to 0.29. These values, used with a simple model of a defensive wall, have enabled free kicks to be simulated under realistic conditions, typical of match-play. The results reveal how carefully attackers must engineer the dynamics of a successful kick. For a central free kick some 18.3 m (20 yards) from goal with a conventional wall, and initial speed of 25 m·s^?1, the ball's initial elevation must be constrained between 16.5° and 17.5° and the ball kicked with almost perfect sidespin.     

The Magnus effect and the American football

The aerodynamics of an American NFL football during an end over end kick were investigated utilizing a custom rotating apparatus and large-scale wind tunnel. Non-rotating lift and drag coefficients were measured and agree well with previous data from other athletic balls and a smooth sphere. The rotation effect on an American football increased both the lift and drag coefficients more dramatically than what has been seen with symmetrical objects over a wide range of rotational rates. The results from this study can be used to more accurately predict the flight trajectory of an end over end kick, and help optimize the balance between kick velocity and rotational speed for a given kicker’s leg strength.     

Direction of spin axis and spin rate of the pitched baseball

In this study, we aimed to determine the direction of the spin axis and the spin rate of pitched baseballs and to estimate the associated aerodynamic forces. In addition, the effects of the spin axis direction and spin rate on the trajectory of a pitched baseball were evaluated. The trajectories of baseballs pitched by both a pitcher and a pitching machine were recorded using four synchronized video cameras (60 Hz) and were analyzed using direct linear transform (DLT) procedures. A polynomial function using the least squares method was used to derive the time-displacement relationship of the ball coordinates during flight for each pitch. The baseball was filmed immediately after ball release using a high-speed video camera (250 Hz), and the direction of the spin axis and the spin rate (omega) were calculated based on the positional changes of the marks on the ball. The lift coefficient was correlated closely with omegasinalpha (r = 0.860), where alpha is the angle between the spin axis and the pitching direction. The term omegasinalpha represents the vertical component of the velocity vector. The lift force, which is a result of the Magnus effect occurring because of the rotation of the ball, acts perpendicularly to the axis of rotation. The Magnus effect was found to be greatest when the angular and translational velocity vectors were perpendicular to each other, and the break of the pitched baseball became smaller as the angle between these vectors approached 0 degrees. Balls delivered from a pitching machine broke more than actual pitcher's balls. It is necessary to consider the differences when we use pitching machines in batting practice.     

环境风对跳台滑雪空中飞行气动特性的影响

目的:探讨环境风对跳台滑雪空中飞行气动特性的影响。方法:通过计算流体力学(computational fluid dynamics,CFD)方法数值模拟预测了不同环境风下跳台滑雪空中飞行空气动力学特性,并探究了水平方向环境风、竖直方向环境风以及侧向环境风对气动特性的影响。将跳台滑雪运动员与滑雪板看成一个多体系统,建立在空中飞行某一种普遍姿态下此多体系统的精细化三维几何模型与网格模型,采用部分时均(partially averaged Navier-Stokes,PANS)湍流模型进行数值模拟,提取多体系统的受力及力矩情况,直观地显示多体系统周围的流场信息。数值预测涉及的水平方向风风速包括-4 m/s、-2.5 m/s、-1 m/s、0 m/s、1 m/s、2.5 m/s、4 m/s等工况;竖直方向风风速包括-8 m/s、-4 m/s、-2.5 m/s、-1 m/s、0 m/s、1 m/s、2.5 m/s、4 m/s、8 m/s等工况;侧向风风速包括1.5 m/s、3.0 m/s、4.5 m/s、7.5 m/s、10.5 m/s、13.5 m/s等工况。结果:1)水平方向环境风下多体系统升力、阻力以及俯仰力矩变化明显,与风速呈现近似线性关系,同时水平逆风情况下力学特性数值结果的增长速度大于水平顺风情况下力学特性数值结果的减小速度;2)在竖直方向风速较小时(小于2.5 m/s),升力、阻力以及俯仰力矩增加缓慢,在竖直方向风速较大时(大于4 m/s),升力、阻力以及俯仰力矩开始相对快速增加,同时,竖直向上环境风使得升力、阻力、俯仰力矩增大,竖直向下环境风使得升力、阻力以及俯仰力矩减小,而且竖直向上环境风情况下增长幅度明显小于竖直向下环境风情况下减少幅度;3)侧向环境风产生偏航力、偏航力矩、翻滚力矩,同时,侧向环境风对运动员的升力、阻力以及俯仰力矩产生影响。在风速较小(小于3 m/s)时,这些力和力矩很小,在风速较大(大于4.5 m/s)时,比较明显。结论:1)水平方向环境风对跳台滑雪空中飞行气动特性的影响非常明显,相较而言,竖直方向环境风和侧向环境风对空中飞行气动特性的影响小很多,但侧向环境风的影响情况较为复杂,对多体系统产生较为明显的偏航力、偏航力矩、翻滚力矩;2)环境风对跳台滑雪空中飞行气动特性的影响机理能够为比赛临场预判与决策提供有效的辅助支持,也为运动员空中飞行稳定性控制与技术训练提供科学指导。     

Variability of impact kinematics and margin for error in the tennis forehand of advanced players

The kinematics of the racket and ball near impact in tennis forehands were studied to document typical variation in successful and unsuccessful shots, in order to determine biomechanically meaningful differences in advanced players and confirm models of groundstroke trajectories. Seven tennis players (six males and one female) were videoed from the side at 180 Hz as they performed 40 forehand drives on an indoor tennis court. Vertical plane kinematics of the racket and ball near impact were analysed for sub samples of successful and unsuccessful shots for each subject. Most racket kinematic variables were very consistent (mean CV< 6.3%) for successful shots, so bio mechanically meaningful differences in angles and velocities of the racket and ball (3° and 2 m s⁻¹) near impact could be detected between successful and unsuccessful shots. Four subjects tended to miss long and three subjects missed shots in the net that were reflected in initial ball trajectories. Mean (SD) initial trajectories for long shots were 9.8° (1.4°), while netted shots were 0.7° (1.1°) above the horizontal. The initial ball trajectories and margins for error for these subjects were smaller than those previously reported (Brody, 1987) because players tended to select mean ball trajectories close to one error than another, differing amounts of topspin, or incorrect lift and drag coefficients for tennis balls had not been published when this model was created. The present data can be used to confirm if recent models (Cookeet al., 2003; Dignallet al., 2004) more closely match actual performance by advanced players.     

High-speed video image analysis of ski jumping flight posture

Ski jumping flight posture was analyzed for achieving large flight distance on the basis of high-speed video images of the initial 40 m part of 120-m ski jumping flight. The time variations of the forward leaning angle and the ski angle of attack were measured from the video images, and the aerodynamic forces were calculated from the kinematic data derived from the images. Some correlations were investigated between the initial-speed corrected flight distance and such parameters as the angles of jumper, the initial transition time and the aerodynamic force coefficients. The result indicated that small body angle of attack was a key for large flight distance in the initial phase of flight because of small drag force, and that the most distinctive fault of beginners was too large body angle of attack and ski angle of attack leading to aerodynamic stall. Too small drag force does not give an optimal condition for large flight distance because the lift force is also too small. The ratio of the lift to the drag was larger than 0.95 for advanced jumpers.