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The Magnus effect is the commonly observed effect in which a spinning ball (or cylinder) curves away from its principal flight path. It is important in many ball sports. It affects spinning missiles, and has some engineering uses, for instance in the design of rotor ships and Flettner aeroplanes.
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In terms of ball games, topspin is defined as spin about an axis perpendicular to the direction of travel, where the top surface of the ball is moving forward with the spin. Under the Magnus effect, topspin produces a downward swerve of a moving ball, greater than would be produced by gravity alone, and backspin has the opposite effect. Likewise side-spin causes swerve to either side as seen during some baseball pitches, e.g. slider. The overall behaviour is similar to that around an aerofoil (see lift force) with a circulation which is generated by the mechanical rotation, rather than by airfoil action.
The Magnus effect is named after Heinrich Gustav Magnus, the German physicist who investigated it. The force on a rotating cylinder is known as Kutta–Joukowski lift, after Martin Wilhelm Kutta and Nikolai Zhukovsky (or Joukowski), who first analyzed the effect.
Physics
An intuitive understanding of the phenomenon comes from Newton's third law, that the deflective force on the body is no more or less than a reaction to the deflection that the body imposes on the air-flow. The body "pushes" the air down, and the air pushes the body upward. As a particular case, a lifting force is accompanied by a downward deflection of the air-flow. It is an angular deflection in the fluid flow, aft of the body.
In fact there are several ways in which the rotation might cause such a deflection. By far the best way to know what actually happens in typical cases is by wind tunnel experiments. Lyman Briggs made a definitive wind tunnel study of the Magnus effect on baseballs, and others have produced interesting images of the effect. The studies show a turbulent wake behind the spinning ball. The wake is to be expected and is the cause of aerodynamic drag. However there is a noticeable angular deflection in the wake and the deflection is in the direction of the spin.
The process by which a turbulent wake develops aft of a body in an air-flow is complex but well-studied in aerodynamics. It is found that the thin boundary layer detaches itself ("flow separation") from the body at some point and this is where the wake begins to develop. The boundary layer itself may be turbulent or not; this has a significant effect on the wake formation. Quite small variations in the surface conditions of the body can influence the onset of wake formation and thereby have a marked effect on the downstream flow pattern. The influence of the body's rotation is of this kind.
It is said that Magnus himself wrongly postulated a theoretical effect with laminar flow due to skin friction and viscosity as the cause of the Magnus effect. Such effects are physically possible but slight in comparison to what is produced in the Magnus effect proper. In some circumstances the causes of the Magnus effect can produce a deflection opposite to that of the Magnus effect.
The diagram at the head of this article shows lift being produced on a back-spinning ball. The wake and trailing air-flow have been deflected downwards. The boundary layer motion is more violent at the underside of the ball where the spinning movement of the ball's surface is forward and reinforces the effect of the ball's translational movement. The boundary layer generates wake turbulence after a short interval.
On a cylinder, the force due to rotation is known as Kutta–Joukowski lift. It can be analysed in terms of the vortex produced by rotation. The lift on the cylinder per unit length, F/L, is the product of the velocity, v (in metres per second), the density of the fluid, ρ (in kg/m3), and the strength of the vortex that is established by the rotation, G:
where the vortex strength is given by
where s is the rotation of the cylinder (in revolutions per second), ω is the angular velocity of spin of the cylinder (in radians / second) and r is the radius of the cylinder (in metres).
Applying this same relationship to a sphere, results in the following vector equation for the Magnus force on a ball:
because the force is mutually perpendicular to the velocity and the axis of rotation.
History
German physicist, Magnus, described the effect in 1852. However, in 1672, Isaac Newton had described it and correctly inferred the cause after observing tennis players in his Cambridge college. In 1742, Benjamin Robins, a British mathematician, ballistics researcher, and military engineer, explained deviations in the trajectories of musket balls in terms of the Magnus effect.
In sports
The Magnus effect explains commonly observed deviations from the typical trajectories or paths of spinning balls in sport, notably association football, table tennis, tennis, volleyball, golf, baseball, cricket and in paintball marker balls.
The curved path of a golf ball known as slice or hook is due largely to the ball's spinning motion (about its vertical axis) and the Magnus effect, causing a horizontal force that moves the ball from a straight line in its trajectory. Backspin (upper surface rotating backwards from the direction of movement) on a golf ball causes a vertical force that counteracts the force of gravity slightly, and enables the ball to remain airborne a little longer than it would were the ball not spinning: this allows the ball to travel farther than a non-spinning (about its horizontal axis) ball.
In table tennis, the Magnus effect is easily observed, because of the small mass and low density of the ball. An experienced player can place a wide variety of spins on the ball. Table tennis rackets usually have a surface made of rubber to give the racket maximum grip on the ball to impart a spin.
The Magnus effect is not responsible for the movement of the cricket ball seen in swing bowling, although it does contribute to the motion known as drift and dip in spin bowling.
In airsoft, a system known as hop-up is used to create a backspin on a fired BB, which will greatly increase its range, using the Magnus effect in a similar manner as in golf.
In paintball, Tippmann's Flatline Barrel System also takes advantage of the Magnus effect by imparting a backspin on the paintballs, which increases their effective range by counteracting gravity.
In baseball, pitchers often impart different spins on the ball, causing it to curve in the desired direction due to the Magnus effect. The PITCHf/x system measures the change in trajectory caused by Magnus in all pitches thrown in Major League Baseball.
The match ball for the 2010 FIFA World Cup has been criticised for the different Magnus effect from previous match balls. The ball was described as having less Magnus effect and as a result flies farther but with less controllable swerve.
In flying machines
Some flying machines have been built which use the Magnus effect to create lift with a rotating cylinder at the front of a wing, allowing flight at lower horizontal speeds. The earliest attempt to use the Magnus effect for a heavier-than-air aircraft was in 1910 by a US member of Congress, Butler Ames of Massachusetts. The next attempt was in the early 1930s by three inventors in New York state.
The iCar 101 project suggests the use of Flettner rotors in roadable aircraft design to combine compactness and increased lift potential.
Ship propulsion and stabilization
Rotor ships use mast-like cylinders for propulsion. The effect is used in a special type of ship stabilizer consisting of a rotating cylinder mounted beneath the waterline and emerging laterally. By controlling the direction and speed of rotation, strong lift or downforce can be generated. The largest deployment of the system to date is in the motor yacht Eclipse.