In sports, magnus effect causes some dramatic movement such as the banana ball and slice. Keywords drag force, magnus effect, spinning ball, baseball, nonlinear physics, mathematica 1. Magnus effect and dynamics of a spinning disc in a rarefied medium. He attempted to explain the curved path of a ball in terms of the magnus effect by calculating the magnus force from the pressure distribution of a rotating body. Impact of the drag force and the magnus effect on the. The magnus effect is the lift produced by a rotating cylinder in a uniform stream. The experimental observation by robins1, that a projectile spinning about its axis of travel experiences a transverse force lift, was refuted by euler2 purely as a. Magnus effect on a rotating soccer ball at high reynolds. When and why in some specific conditions, a flying spinning ball deflects in a direction opposite to. In the year 1877 lord john rayleigh wrote an article on the irregular. The magnus effect responsible for the anomalous curvature of spinning.
The experiment is conducted in a wind tunnel at re 0. Pdf negative magnus effect on a rotating sphere at. The magnus or robins effect on rotating spheres journal. The path of the spinning object is deflected in a manner that is not present when the object is not spinning. For a clockwise rotation of the ball, the fluid velocity relative to the surface is larger on the lower side figure 10. The magnus effect is also exploited in a number of natures designs. Moreover, the ball goes through momentfree motion, hence there is no energy due to rotation and the workenergy theorm simplifies to 23 where f m is the magnus force, f d is the drag force. Pdf negative magnus lift on a rotating sphere at around the critical. Inverse magnus effect on a rotating sphere nasaads. The planar incompressible potential flow past a spinning cylinder radius r. The coupling of the resulting rotational and translational motions can give rise to a magnus lift force that considerably extends the range of these seed pods. Negative magnus lift on a rotating sphere at around the critical reynolds number masaya muto, makoto.
In this study, we investigate the flow characteristics of rotating spheres in the subcritical reynolds number re regime by measuring the drag and lift forces on the sphere and the twodimensional velocity in the wake. We investigate the interplay of these forces on the trajectories. The magnus effect is the commonly observed effect in which a spinning ball or cylinder curves away from its principal flight path. However, for the rotating ball the greater velocity on one side causes the air pressure to be less on that side. The results of the magnus force measurements on the rotating sphere may be described by nondimensional similarity parameters. In contrast, the lift force was negative in the critical regime when particular rotating speeds were imposed. Many seed pods, including maple keys, are shaped such that they tumble as they fall figure 5a. Of these forces, only the gravitational force is conservative. Units and divisions related to nada are a part of the school of electrical engineering and computer science at kth royal institute of technology. Negative magnus effect on a rotating sphere at around the. Positive and negative magnus force on a rotating sphere at. Trajectory prediction of rotating objects in viscous fluid. The predictions show that the rotation of the cylinder suppresses the vortex development in both the steady and the unsteady flow regimes and significantly changes the flow field close to the cylinder.
This results in a force pushing the ball to that lowpressure side and so the ball curves in the air figure 2. To elucidate when and why this effect occurs, we measure the variations of the drag and lift forces on a rotating sphere and the corresponding. The motion of an arbitrarily rotating spherical projectile. This negative magnus effect was investigated in the. Experimental measurement of the magnus force on a rotating. The purpose of this study was to measure the aerodynamic force acting upon a soccer ball spun in a windtunnel test. At that time he also stated that it was not possible to give a. The influence of the magnus effect in tennis bachelors project applied mathematics december 2017. Negative magnus lift on a rotating sphere at around the. The magnus effect is an observable phenomenon that is commonly associated with a spinning object moving through the air or another fluid. Pdf inverse magnus effect on a rotating sphere semantic scholar. With this background, we are now in a position to understand how a spinning ball generates a negative magnus effect at re magnus effect at re re cr. For a rotating sphere or cylinder, the lift coefficients become negative at some specific reynolds numbers re and spin ratios. The magnus force is a force that acts upon a rotating ball when the ball moves through a fluid.
The spinning leads to a deflection in the direction. For a smooth sphere, the magnus effect was observed for ratios of spin speed to flow speed between 0. The spin of the ball will affect its trajectory through the magnus effect. Mehta 2, 3, who published most studies on sports ball aerodynamics. On drag and lift forces acting at flow past rotating bodies. Experiment of aerodynamic force on a rotating soccer ball. The deflection can be explained by the difference in pressure of the fluid on opposite sides of the spinning object. Inverse magnus effect on a rotating sphere request pdf. To elucidate when and why this effect occurs, we measure the variations of the drag and lift forces on a rotating sphere and the corresponding flow field with the. Robins explained the deviation of the trajectories of musket balls by the magnus e ect 2,3. According to the kuttajoukowski theorem, for a spinning sphere with an inviscid flow of air, the magnus force is equal to, where r is the radius of the ball. Magnus effect on a rotating sphere at high reynolds numbers. Finally, we use one of the models in an experiment to nd the. Magnus force occurs when rotating objects travel through the air with an angle between the axis of rotation.
The fullscale model of a freely rotating cylinder with the fixed axis of rotation mounted at threefifths of chord length from the leading edge of the wing is developed using solidworks. Experiments were performed using a rear sting support where the soccer ball was split into two halves that were driven by a motor inside of. Negative magnus lift acting on a sphere rotating about the axis perpendicular to an incoming flow is investigated using largeeddy simulation at three reynolds numbers of 1. Magnus effect we envision a scenario where the rotation of the ball confines the magnus force to the vertical plane. Negative magnus effect on a rotating sphere at around the critical reynolds number view the table of contents for this issue, or go to the journal homepage for more 2011 j. Yanshin, forces and moments acting on bodies rotating about a symmetry axis in a free mlecular. Effect of high rotation rates on the laminar flow around a. In particular, we prepared two types of spinning soccer balls air and motor types, measured the aerodynamic force on each, and examined the validity of the measurement method. The magnus effect on a sphere rotating perpendicular to the flow direction at reynolds numbers in the range of 68,000 force measurements and of. Flow past a rotating cylinder journal of fluid mechanics. For very low reynolds numbers, the drag force is not affected by rotation and the lift force. Magnus 1 nowadays it is known magnus effect theory. In this situation we therefore have no drag and lift force acting on the sphere.
Magnus effect combined with circulation theory is applied in designing a fullscale wing inorder to overcome main aerodynamic problems. The magnus effect on a prototype model soccer ball rotating perpendicular to the flow direction at reynolds numbers in the range of 0. Effect of freely rotating cylinder mounted near the. At a given re, the lift force is positive, negative and. A rotating sphere would experience two extremities with respect to the drag force. Magnus effect on a rotating sphere at high reynolds. On a cylinder, the force due to rotation known as kuttajoukowski lift, can be analysed in terms of the. The classical magnus effect, discussed for a sphere or a cylinder with the symmetry axis orthogonal to its velocity, is a consequence of the transverse force. The unsteady stokes flow of a couple stress fluid around a rotating sphere with slip.
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