Search

The flow instability in a precessing spheroid is a fundamental subject of fluid mechanics and is also important in geophysics because Earth is precessing. There are at least three instabilities: elliptical, shearing, and conical shear. Theory predicts the dominance of the latter in a regime that depends on the spin rate and container's ellipticity. Laboratory experiments that perfectly support the theory are presented.

The following considers drag measurements of baseballs with backspin (spin axis horizontal and normal to trajectory) and gyro spin (spin axis parallel to trajectory) orientations. Balls were propelled through still air in a laboratory setting at 36 m/s and spin ranging from 1250 rpm to 1750 rpm. Balls were projected with backspin and gyro spin in the two- and four-seam orientations. Speed and position sensors measured the speed and location of the balls at three locations from which the coefficient of drag and lift were found. Drag was observed to depend on spin rate, spin axis and seam orientation. The largest and smallest coefficient of drag was found with the gyro four-seam and two-seam spin orientation, respectively. Drag was observed to correlate with seam height with back spin, but not with gyro spin. Lift was observed for baseballs with back spin, but not with gyro spin.

A Frisbee with a mass of 0.21 kg, diameter of 0.27 m and moment of inertia (MOI) of 0.002 kg·m2 was instrumented with a triaxial gyroscope. The Frisbee was thrown at low angular velocities as the measurement limit of a single gyroscope was at 6.065 rps. The angular velocities of the triaxial gyroscope were analysed to study the attitude of a Frisbee before and after release. The angular velocities measured were post-processed and the following data were obtained: spin rate at release—3.9–6.14 rps; user-induced peak torque—0.483–0.9 Nm, and peak angular acceleration—204–358 rad/s2; and power input 7.53–19.56 W. The Frisbee wobbled at release which decreased during the flight due to a damping effect. This affected the spin decay, the reduction of wobble lead to a reduced drag force and thus to a smaller spin decay, which was initially 1.12–0.31 rev/s2 and then asymptoted to 0.11–0.01 rev/s2.

A pitcher’s action, when delivering a fastball, was analyzed from the data provided by a smart baseball. The spin rate at the release of the ball was merely 15.7 rps, however, the peak torque was excessively high, namely 0.396 Nm. The reason why the pitcher was not able to translate the torque entirely to angular kinetic energy and this to the spin rate was that the spin axis changed its direction suddenly three times when moving across the ball’s surface. This resulted in angles between torque and angular velocity vectors of greater than 90°, high precession and precession torque, and negative spin torques, causing a very low efficiency (5.4%) and a slow spin rate at the release of the ball.

This study measured 1) the speed and spin differences between the old celluloid versus new plastic table tennis balls at pre ball-table impact and post ball-table impact when projected with topspin at 7.56 m.s-1, and investigated 2) the effect this has on the kinematic responses of 5 elite versus 5 sub-elite players’ forehand topspin in response to topspin and backspin. Plastic balls were lower in both speed and spin at pre and post ball-table impact compared with celluloid balls but the magnitude of change in speed and spin for each ball material differed. During flight before impact, plastic balls lost 3.98% more speed and 1.24% more spin than celluloid balls. Post ball-table impact, plastic balls showed a greater speed increment (0.69%) and smaller spin decrement (0.19%) than celluloid balls. Differences in players’ kinematic responses to the different ball materials were found only when players returned backspin shots. Players supinated their rackets more by 2.23% at ball-racket contact and produced 3.37% less ball spin when returning plastic compared with celluloid balls; an indication of an early adaptation to the lower spin rate of plastic balls. The lack of differences in kinematic response to topspin may be due to the similar changes in speed and spin of both types of balls at ball-table impact. It is not known if a higher initial ball projection velocity would evoke differences in movement responses from the players post ball-table impact but could be explored in future studies.

Aerodynamic effects play an important part in any sport where the ball experiences significant periods of free flight. This article investigates the aerodynamic forces generated when a football is spinning quickly to generate swerve and more slowly to generate more erratic flight. The work reports on the application of an experimental method that measures the aerodynamic loads on a non-spinning, slowly spinning and fast spinning football, using a phase-locked technique so that orientation-dependent and steady ‘Magnus’ forces can both be determined. The results demonstrate that the orientation-dependent aerodynamic loads, widely seen in non-spinning data in the literature, surprisingly persist up to the highest spin rates reported. When predicting ball flight, it is generally assumed that at low spin rates a quasi-static assumption is acceptable, whereby forces measured on a non-spinning ball, as a function of ball orientation, apply for the spinning case. Above an arbitrary spin rate, the quasi-static ass...

This paper is about the ball trajectory analysis of a multimode cricket bowling machine. The bowling machine is used to provide training for batsmen by emulating bowler's behaviour. This, in turn, reduces the risk of injuries experienced by bowlers. The experiments were divided into three groups namely ball velocity, bowling distance, and ball spin rate. For ball velocity under three machine speed settings, the measured data between dry and wet ball showed a difference in magnitude but with similar consistency. The optimal wheel pressure to produce the best dry ball velocity among those tested was 6.25 psi. The effect of speed ratio on the ball velocity was also observed from the measured velocity data where the ball velocity increase, as wheel's rotational velocity increases, peaked at 2000 rpm before decreasing. From the comparison between measured bowling length and line to that of calculations, the suitable drag coefficient value was 0.4 for estimating the ball trajectory. From the analysis, ball wetness, wheel pressure, and speed ratio were determined to be important in evaluating the performance of the cricket bowling machine.

The implication of small amounts of cohesion within relatively small rubble pile asteroids is investigated with regard to their evolution under the persistent presence of the YORP effect. We find that below a characteristic size, which is a function of cohesive strength, density and other properties, rubble pile asteroids can enter a "disaggregation phase" in which they are subject to repeated fissions after which the formation of a stabilizing binary system is not possible. Once this threshold is passed rubble pile asteroids may be disaggregated into their constituent components within a finite time span. These constituent components will have their own spin limits -- albeit potentially at a much higher spin rate due to the greater strength of a monolithic body. The implications of this prediction are discussed and include modification of size distributions, prevalence of monolithic bodies among meteoroids and the lifetime of small rubble pile bodies in the solar system. The theory is then used to place constraints on the strength of binary asteroids characterized as a function of their type., Accepted for publication in Icarus

In seam bowling, the spin vector precesses rapidly into the torque vector, thereby crossing from one hemisphere to the other once torque is imparted onto the ball. However, the spin axis reaches the torque vector only at large times. If the spin axis does not coincide with the pole of the ball, the seam wobbles and introduces another roughness element. Thus, if the seam is angled toward the smooth side (for half a period per spin revolution) then the flow is turbulent on both sides of the ball and the aerodynamic side force decreases and vanishes, thereby disturbing the swing. The aim of this study was to investigate how accurate is the placement of the spin axis at release of the ball. A smart cricket ball instrumented with three high-speed MEMS gyroscopes was used for this purpose and the data of four spin bowlers were analysed. It was found that the spin axis can under- and overshoot the optimal position of the ball as well as deviate off the pole. The spin rates recorded were 15-20 rps produced by peak torques of 0.29-0.39 Nm. The deviation of the spin axis correlated with the torque, indicating that too much torque imparted onto the ball worsens the accuracy of bowling. Undershooting the optimal position is due to equal torques imparted by index and middle fingers. The optimal position of the spin axis can be achieved if the middle finger is closer to the seam than the index. This causes an overshooting torque vector and allows the spin axis to be placed at the pole of the ball at release.

In the present review, we include a series of recent experiments in order to update and summarize the characteristics of ball spin in baseball pitching. The motion of a ball thrown by a pitcher is influenced by three forces: gravity, the drag force due to air resistance, and the lift force which deflects a ball vertically or laterally due to the Magnus effect (Magnus force). The forces acting on a baseball are influenced by the ball's translational speed and spin rate as well as the orientation of the spin axis. The lift force acting on the ball becomes greater with increases in the “spin parameter” (proportion of the spin rate and the movement speed) when the spin axis of the ball is orthogonal to the direction of movement. On the other hand, when the spin axis is located in line with the direction of the movement (so-called “gyro ball”), the drag force becomes smaller and the lift force decreases to nearly zero regardless of the spin parameter. The orientation of the spin axis also affects the direction of the lift force on the ball; that is, the lift force acts perpendicular to the cross product of the spin axis and the direction of motion. There are great variations in the spin of fastballs; both spin rate and orientation of the spin axis vary widely across individual pitchers. When the spin rate is extremely low, such as with a knuckle ball, the amount and direction of lift force changes irregularly during flight. This is caused by seams on the ball surface, which cause an unpredictable “fluttering” trajectory. The reason for the success of pitchers that can produce abnormal or unique ball spins is discussed.

In this paper are review of impact experiment to study the dynamic behaviour of sports ball during oblique and normal impacts. In previous studies, the investigation was done on the dynamic behaviour of a sports ball during oblique and normal impacts from experimental, numerical, and theoretical viewpoints. The experimental results are analysed and compared with the theories, in order to understand the dynamics behaviours based on the phenomenological occurrence. Throughout the experimental studies previously, there are results of dynamics behaviours examined by many researchers such as the coefficient of restitution, tangential coefficient, local deformation, dynamic impact force, contact time, angle of impact (inbound and rebound), spin rate of the ball, ball stiffness and damping coefficient which dependable of the initial or impact velocity.

A technique of combined experimental and theoretical determination of the functional dependence of the steady-state angular spin rate of a windwheel on the pitch angle of the blades is proposed. The technique is studied with the use of a mock-up of a vertical-axis windwheel.

While some tennis racket strings have more grip than others do, this does not guarantee that they will impart more spin to a tennis ball. Experiments with hand-held rackets are required to determine the longstanding question of how players can discern that different strings behave differently when laboratory tests indicate that they should play the same. In a previous study, we clarified the top-spin mechanism of a tennis racket by using high-speed video analysis on a tennis court for the first time. Furthermore, we improved it by using lubricated notched nylon strings. These experiments revealed that the more the main strings stretch and bend laterally, the more spin is imparted to the ball. This is due to the restoring force being parallel to the string face when the main strings spring back and the ball is released from the strings. Notched strings reduce the spin rate, but this can be effectively counteracted by employing lubricants. Furthermore, we found that imparting more spin reduces shock vibrations on the wrist during impact. The present study revealed that a ball has a 40% lower spin rate when hit with a racket with notched strings than with one with unnotched strings in the case of nylon (it had to be determined whether new strings or lubricated used strings give more spin). The experiments also showed that 30% more spin is imparted to a ball when the string intersections are lubricated by oil than when notched used nylon strings are used. Furthermore, we found that used natural gut notched strings reduced the spin rate by 70% compared to when new natural gut unnotched strings are used. We also investigated different top-spin behaviors obtained when professional and amateur tennis players hit a ball.

The present study clarifies the effects of dimples for drag and lift on a sphere with rotation. The sphere with dimples has 328 arc type dimples on its surface uniformly. The present study measures velocity distribution in wake and pressure distribution on a sphere surface, and visualizes flow around a sphere by the spark tracing method for the case in which Reynolds number Re=0.4×105-1.3×105. For the case of a smooth sphere, separation point on deceleration side shifts downstream remarkably as spin rate ratio (circumferential velocity of a sphere / free stream velocity) increases. The pressure distribution on deceleration side decreases compared to that on acceleration side. The wake becomes small and shifts opposite direction of rotation. Therefore, the drag reduces, and the lift becomes negative. For the case of a sphere with dimples, this phenomenon occurs for the case in which critical Reynolds number Re=0.5×105. The separation point on acceleration side shifts downstream, and the separation point on deceleration side shifts upstream as spin rate ratio increases for the case in which super critical Reynolds number Re=1.3×105. The pressure distribution on acceleration side decreases compared to that on deceleration side. In addition, the pressure distribution on outside dimple decreases compared to that on inside dimple. The wake becomes large and shifts direction of rotation. Therefore, the drag and positive lift increase.

A rotationally skew fold membrane for the spinning solar sail is discussed to examine the deployment characteristics. The membrane is characterized by double corrugation fold and is advantageous in the complete folding and compact storage. Spinning experiments with scaled models are performed to investigate the geometrical and deployment characteristics. As the result of the spinning experiments, it is indicated that the rotationally skew fold membrane is completely deployed and there is a minimum spin rate to complately deploy. The fact that the spin-direction wrapped membrane realizes quick deployment is also indicated. To investigate the dynamic characteristics, a non-dimensional similarity parameter derived with the theoretical analysis for one-dimensional Z-fold membrane is expressed by the geometrical parameters as the radius, folding pitch, material properties and spin rate. The theoretical similarity parameter is applied to the results of the spinning experiments and indicates the effect of the folding pitch of the rotationally skew fold membrane. Also the similarity parameter based on the experimental results is introduced.

The drag and lift coefficient characteristics of rotating cylinder with arc grooves is investigated. The circular cylinders with grooves have thirty-two arc grooves of different depth on the cylinder surface. Pressure of the cylinder surface is measured with the Reynolds number Re= (0.4-1.8) ×105, and rotation of 0-4500rpm.The drag and lift coefficients are calculated from pressure distribution. At Re=0.4×105, the drag coefficient CD of smooth cylinder is constant until the spin rate ratio α (α=rotating speed/uniform flow) =0.6, and CD decreases afterwards at 0.6 1.0×105.As groove depth becomes deep, CD becomes constant value as α increase. The lift coefficient CL of smooth cylinder increases as a increase.However, CL decreases to the minimum value as α further increase and CL increases again with the increase of α, CL indicated negative lift in Re>1.0×105.CL of cylinder with grooves become monotonous increases tendency in Re>1.0×105.As groove depth becomes deep, the increasing gradient of CL becomes small.

When a ball is incident obliquely on a flat surface, the rebound spin, speed, and angle generally differ from the corresponding incident values. Measurements of all three quantities were made using a digital video camera to film the bounce of a tennis ball incident with zero spin at various angles on several different surfaces. The maximum spin rate of a spherical ball is determined by the condition that the ball commences to roll at the end of the impact. Under some conditions, the ball was found to spin faster than this limit. This result can be explained if the ball or the surface stores energy elastically due to deformation in a direction parallel to the surface. The latter effect was investigated by comparing the bounce of a tennis ball with that of a superball. Ideally, the coefficient of restitution (COR) of a superball is 1.0 in both the vertical and horizontal directions. The COR for the superball studied was found to be 0.76 in the horizontal direction, and the corresponding COR for a tennis ball was found to vary from −0.51 to +0.24 depending on the incident angle and the coefficient of sliding friction.

This paper investigates how the physical characteristics of a golf club head affect its performance, with the aim of developing a superior club head. The physical characteristics investigated were the magnitude of the moment of inertia and the location of the centre of gravity. The performances were classified as the release velocity, the spin rate of the ball and the size of the uniform restitution area. In the numerical analysis, several kinds of club head were modelled with different moments of inertia and different locations of the centre of gravity. For every club head model, the ball was hit at various impact points and the release velocity, spin rate and size of the uniform restitution area were calculated. The results are as follows. The bigger the moment of inertia Izz about the vertical axis or the shallower the depth of the centre of gravity, the less side spin rate caused. Izz has more influence on the side spin rate than the depth of the centre of gravity. The shallower the depth of the centre of gravity, the more back spin rate caused. The size of the uniform restitution area increases in proportion to the increase in Izz, or in proportion to the decrease of the depth of the centre of gravity.

In this paper, the effects of the physical characteristics of a golf club head are investigated on its performance in order to develop a superior club head. Here the physical characteristics are the magnitude of the moment of inertia and the depth the center of gravity. And the performances are the release velocity, the spin rate of the ball and the size of the uniform velocity ratio. In the numerical analysis, several kinds of club head are modeled with different moment of inertia and depth of the center of gravity. For every club head model, the ball is hit from various impact points, and the release velocity, the spin rate and the size of the uniform velocity ratio are calculated. The results are as follows. When the moment of inertia increases, the spin rate decreases and the release velocity increases. The size of the uniform velocity ratio also increases. When the moment of inertia about the horizontal axis or the one about the vertical axis increases, the width in vertical direction or the one in horizontal direction increases, respectively. When the ball hits at the heel side or toe side, the bigger the depth of the center of gravity is, the bigger the spin rate is. The sensitivities of the physical characteristics of club head on the performance, also, can be obtained.

Shear banding is considered as localized necking where multiple solutions can exist on the necking plane comprising the boundary between the shear band and its surroundings. Therefore, shear banding is identical with localized necking though it is investigated under plane strain. On the necking plane the discontinuity of velocity gradient can be permitted. Hill and Hutchinson [J. Mech. Phys. Solids, 23 (1975), 239-264] investigated shear band without considering the discontinuity, but their method is methodically equivalent to that which takes into account the discontinuity. In previously published analyses of shear banding, it is assumed that the regions separated by the necking plane keep contact each other during the onset of shear banding, and the equilibrium of forces is maintained on the plane. However, it is proven that this assumption cannot provide useful information for determining the deformation when shear banding begins to occur. Furthermore, the assumption does not allow the formation of a common boundary condition imposed on both regions separated by the necking plane. When shear banding occurs, the spin rate of the regions differs because of multiple solutions. The criterion for determining the occurrence of shear banding can be deduced by imposing a rigid spin to make the spin rates identical. It is found that this criterion agrees with one of the universal criteria obtained from considering the occurrence of multiple solutions under the common boundary condition on the surface of a body.

We report a new flow control method for centrifugal microfluidic systems; CO2 is released from on-board stored baking powder upon contact with an ancillary liquid. The elevated pressure generated drives the sample into a dead-end pneumatic chamber sealed by a dissolvable film (DF). This liquid incursion wets and dissolves the DF, thus opening the valve. The activation pressure of the DF valve can be tuned by the geometry of the channel upstream of the DF membrane. Through pneumatic coupling with properly dimensioned disc architecture, we established serial cascading of valves, even at a constant spin rate. Similarly, we demonstrate sequential actuation of valves by dividing the disc into a number of distinct pneumatic chambers (separated by DF membranes). Opening these DFs, typically through arrival of a liquid to that location on a disc, permits pressurization of these chambers. This barrier-based scheme provides robust and strictly ordered valve actuation, which is demonstrated by the automation of a multi-step/multi-reagent DNA-based hybridization assay.

The equations of motion for a ball moving in a vertical plane are used to calculate flight paths for a typical golf ball subjected to a variety of launch conditions, spin rates, atmospheric parameters, and wind fields. Time histories of the ball's velocity, flight-path angle, height, range, and spin rate between tee and first impact illustrate that lift induced by the ball's spin has a significant effect on driving range, actually causing the flight-path angle to increase during the first few seconds of flight. While light winds have the expected effects, heavy tailwind is shown to spoil the carry of the ball. Linearized sensitivity analysis indicates that wind uncertainty is an important contributor to impact range and time uncertainty.

The objective of this study was to develop a finite-element (FE) model which could accurately simulate the behaviour of golf impacts, and to investigate the effect of a shaft on the clubhead upon the rebound of a ball, by conducting FE analysis on a ball colliding with a simplified club. The clubs were constructed by holding simplified clubheads by a locking ring fitted onto a steel shaft. The clubheads were designed based on the mass, volume and position of the centre of gravity (CoG) of commercial clubheads, so as to enable a typical golf impact. Three circular, hollow, titanium alloy bodies of constant mass, with increasing loft angles, were manufactured. FE models with linear elasticity of the clubs, which consisted of the clubheads, a locking ring and a shaft, were constructed. The FE model of the ball consisted of 8-node solid elements, and the material model was expressed as a hyper-elastic/viscoelastic model. Impact experiments were also conducted for comparison to confirm the accuracy of the FE models. The results of the impact simulations closely matched the experimental results. Impact behaviour was analysed by varying the impact point of the ball colliding with the full clubs and the lone clubheads and then comparing the ball/club and ball/clubhead collision results. The differences between the two most extreme values for the rebound angle and spin rate tended to be smaller in the club impact cases than in the clubhead impact cases. This tendency was estimated to depend on the relationship between the shaft position and the loft angle/CoG of the clubhead.

The effects of a time-dependent angular velocity upon the vibration of a rotating Euler beam are presented. It is assumed that the angular velocity can be expressed as the sum of a steady-state value and a relatively small periodic perturbation. Equations of motion are derived for a beam oriented parallel to the spin axis. Terms with time-dependent coefficients appear in the equations of motion due to the nonconstant spin rate resulting in a nonautonomous system possessing parametric instabilities. A perturbation technique called the KBM method is used to derive general expressions for approximate solutions and instability region boundaries. A simple perturbation function is assumed for the purpose of illustrating the use of the derived general expressions.

This investigation is concerned with the determination of effects of elastic deformation on the stability of a rotating satellite composed of two elastically connected, inertially identical, unsymmetrical rigid bodies. Following a stability analysis, examples are presented to demonstrate effects of elasticity on vehicle motion, to illustrate various types of instability, and to point out that the performance of the system can be highly sensitive to dimension and spin rate changes.

This paper describes the hysteresis in the aerodynamic properties of a discus near to its stalling angle. Wind tunnel tests were carried out with a full-size woman's discus. The experimental aerodynamic data D, L and M were obtained from wind tunnel tests as functions of the angle of attack and the spin rate. It was found that the drag, lift and pitching moment coefficients, CD CL and CM, increase with increasing the angle of attack up to a stalling angle of 28-30°. Beyond the stalling angle, CL and CM decrease suddenly and abruptly with increasing angle of attack. On the other hand, recovery from the stall does not occur at the same stalling angle of 28-30° when the angle of attack decreases from the stall state; recovery actually occurs at 25°. The CL -α (angle of attack) curve is almost the same when the angle of attack is less than 24°. Therefore, hysteresis occurs near the stalling angle.

In the study, offsets, products of inertia, tip-off errors, and nominal spin rate were varied to find the relative importance of each on the accuracy of the mission. Since no requirements have been placed on maximum or minimum apogee altitude acquired from the final initial conditions agreed upon, a parametric study was made showing the relative effect of varying each parameter. Assumptions have led to suggested tolerances on the controlled parameter.

The basic principles behind cricket ball swing have been understood by scientists for years1–3; however, there has been only one published account of experiments on cricket ball swing4. Through a combination of flow visualization and measurements of surface pressures on a cricket ball, the individual parameters responsible for producing swing have been investigated. An accurate correlation between swing, seam angle, spin rate and flow speed was obtained in the more realistic projection tests where spinning cricket balls were projected into a wind tunnel5. For a ball to swing well, it should be released at a speed of between 15 and 30 m s−1 with the seam inclined at about 20° incidence and the ball spinning steadily along the seam at about 11 rev s−1. The present experiments do not support the popular view that swing increases in damp or humid conditions. In particular, measurements show that the cricket ball seam does not swell in such conditions.