# Magnus effect

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The Magnus effect is an observable phenomenon that is commonly associated with a spinning object moving through air or another fluid. The path of the spinning object is deflected in a manner that is not present when the object is not spinning. The deflection can be explained by the difference in pressure of the fluid on opposite sides of the spinning object. The Magnus Effect depends on the speed of rotation.

## Contents

The most readily observable case of the Magnus effect is when a spinning sphere (or cylinder) curves away from the arc it would follow if it were not spinning. It is often used by football players, baseball pitchers, and cricket bowlers. Consequently, the phenomenon is important in the study of the physics of many ball sports. It is also an important factor in the study of the effects of spinning on guided missiles—and has some engineering uses, for instance in the design of rotor ships and Flettner aeroplanes.

Topspin in ball games is defined as spin about a horizontal axis perpendicular to the direction of travel that moves the top surface of the ball in the direction of travel. Under the Magnus effect, topspin produces a downward swerve of a moving ball, greater than would be produced by gravity alone. Backspin produces an upwards force that prolongs the flight of a moving ball. [1] Likewise side-spin causes swerve to either side as seen during some baseball pitches, e.g. slider. [2] The overall behaviour is similar to that around an aerofoil (see lift force), but with a circulation generated by mechanical rotation rather than airfoil action. [3]

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, [4] after Martin 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 a reaction to the deflection that the body imposes on the air-flow. The body "pushes" the air in one direction, and the air pushes the body in the other direction. In particular, 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.

Lyman Briggs [5] made a wind tunnel study of the Magnus effect on baseballs, and others have produced images of the effect. [5] [6] [7] [8] The studies show that a turbulent wake behind the spinning ball causes aerodynamic drag, plus there is a noticeable angular deflection in the wake, and this deflection is in the direction of spin.

The process by which a turbulent wake develops aft of a body in an airflow is complex, but well-studied in aerodynamics. 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, and that 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. [5] In some circumstances the causes of the Magnus effect can produce a deflection opposite to that of the Magnus effect. [8]

The diagram above 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: [4]

${\displaystyle {\frac {F}{L}}=\rho vG,}$

where the vortex strength is given by

${\displaystyle G=(2\pi r)^{2}s=2\pi r^{2}\omega ,}$

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).

## History

The German physicist Heinrich Gustav Magnus described the effect in 1852. [9] [10] However, in 1672, Isaac Newton had described it and correctly inferred the cause after observing tennis players in his Cambridge college. [11] [12] 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. [13] [14] [15] [16]

## In sport

The Magnus effect explains commonly observed deviations from the typical trajectories or paths of spinning balls in sport, notably association football, table tennis, [17] tennis, [18] volleyball, golf, baseball, and cricket.

The curved path of a golf ball known as slice or hook is largely due 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. [19] :§ 4.5 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 ball not spinning about its horizontal axis.[ citation needed ]

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 conventional swing bowling, [19] :Fig. 4.19 although it may be responsible for "Malinga Swing" [20] [21] and 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 greatly increases its range, using the Magnus effect in a similar manner as in golf.

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. [22]

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. [23]

## In external ballistics

The Magnus effect can also be found in advanced external ballistics. First, a spinning bullet in flight is often subject to a crosswind, which can be simplified as blowing from either the left or the right. In addition to this, even in completely calm air a bullet experiences a small sideways wind component due to its yawing motion. This yawing motion along the bullet's flight path means that the nose of the bullet points in a slightly different direction from the direction the bullet travels. In other words, the bullet "skids" sideways at any given moment, and thus experiences a small sideways wind component in addition to any crosswind component. [24]

The combined sideways wind component of these two effects causes a Magnus force to act on the bullet, which is perpendicular both to the direction the bullet is pointing and the combined sideways wind. In a very simple case where we ignore various complicating factors, the Magnus force from the crosswind would cause an upward or downward force to act on the spinning bullet (depending on the left or right wind and rotation), causing deflection of the bullet's flight path up or down, thus influencing the point of impact.

Overall, the effect of the Magnus force on a bullet's flight path itself is usually insignificant compared to other forces such as aerodynamic drag. However, it greatly affects the bullet's stability, which in turn affects the amount of drag, how the bullet behaves upon impact, and many other factors. The stability of the bullet is affected, because the Magnus effect acts on the bullet's centre of pressure instead of its centre of gravity. [25] This means that it affects the yaw angle of the bullet; it tends to twist the bullet along its flight path, either towards the axis of flight (decreasing the yaw thus stabilising the bullet) or away from the axis of flight (increasing the yaw thus destabilising the bullet). The critical factor is the location of the centre of pressure, which depends on the flowfield structure, which in turn depends mainly on the bullet's speed (supersonic or subsonic), but also the shape, air density and surface features. If the centre of pressure is ahead of the centre of gravity, the effect is destabilizing; if the centre of pressure is behind the centre of gravity, the effect is stabilising. [26]

## In aviation

Some aircraft have been built to use the Magnus effect to create lift with a rotating cylinder instead of a wing, allowing flight at lower horizontal speeds. [4] 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. [27]

## Ship propulsion and stabilization

Rotor ships use mast-like cylinders, called Flettner rotors, for propulsion. These are mounted vertically on the ship's deck. When the wind blows from the side, the Magnus effect creates a forward thrust. Thus, as with any sailing ship, a rotor ship can only move forwards when there is a wind blowing. The effect is also 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. [28] The largest deployment of the system to date is in the motor yacht Eclipse.

## Related Research Articles

An aircraft is a vehicle that is able to fly by gaining support from the air. It counters the force of gravity by using either static lift or by using the dynamic lift of an airfoil, or in a few cases the downward thrust from jet engines. Common examples of aircraft include airplanes, helicopters, airships, gliders, paramotors and hot air balloons.

In physics, the Coriolis force is an inertial or fictitious force that acts on objects that are in motion within a frame of reference that rotates with respect to an inertial frame. In a reference frame with clockwise rotation, the force acts to the left of the motion of the object. In one with anticlockwise rotation, the force acts to the right. Deflection of an object due to the Coriolis force is called the Coriolis effect. Though recognized previously by others, the mathematical expression for the Coriolis force appeared in an 1835 paper by French scientist Gaspard-Gustave de Coriolis, in connection with the theory of water wheels. Early in the 20th century, the term Coriolis force began to be used in connection with meteorology.

A fluid flowing around the surface of an object exerts a force on it. Lift is the component of this force that is perpendicular to the oncoming flow direction. It contrasts with the drag force, which is the component of the force parallel to the flow direction. Lift conventionally acts in an upward direction in order to counter the force of gravity, but it can act in any direction at right angles to the flow.

Flight dynamics is the science of air vehicle orientation and control in three dimensions. The three critical flight dynamics parameters are the angles of rotation in three dimensions about the vehicle's center of gravity (cg), known as pitch, roll and yaw.

Aircraft flight control surfaces are aerodynamic devices allowing a pilot to adjust and control the aircraft's flight attitude.

External ballistics or exterior ballistics is the part of ballistics that deals with the behavior of a projectile in flight. The projectile may be powered or un-powered, guided or unguided, spin or fin stabilized, flying through an atmosphere or in the vacuum of space, but most certainly flying under the influence of a gravitational field.

Swing bowling is a technique used for bowling in the sport of cricket. Practitioners are known as swing bowlers. Swing bowling is generally classed as a subtype of fast bowling.

The Focke-Wulf Triebflügel, or Triebflügeljäger, literally meaning "thrust-wing hunter", was a German concept for an aircraft designed in 1944, during the final phase of World War II as a defence against the ever-increasing Allied bombing raids on central Germany. It was a vertical take-off and landing tailsitter interceptor design for local defense of important factories or areas which had small or no airfields.

A helicopter pilot manipulates the helicopter flight controls to achieve and maintain controlled aerodynamic flight. Changes to the aircraft flight control system transmit mechanically to the rotor, producing aerodynamic effects on the rotor blades that make the helicopter move in a deliberate way. To tilt forward and back (pitch) or sideways (roll) requires that the controls alter the angle of attack of the main rotor blades cyclically during rotation, creating differing amounts of lift (force) at different points in the cycle. To increase or decrease overall lift requires that the controls alter the angle of attack for all blades collectively by equal amounts at the same time, resulting in ascent, descent, acceleration and deceleration.

Coaxial rotors or coax rotors are a pair of helicopter rotors mounted one above the other on concentric shafts, with the same axis of rotation, but turning in opposite directions (contra-rotating). This rotor configuration is a feature of helicopters produced by the Russian Kamov helicopter design bureau.

In ball sports, topspin is a property of a ball that rotates forwards as it is moving. Topspin on a ball propelled through the air imparts a downward force that causes the ball to drop, due to its interaction with the air. Topspin is the opposite of backspin.

P-factor, also known as asymmetric blade effect and asymmetric disc effect, is an aerodynamic phenomenon experienced by a moving propeller, where the propeller's center of thrust moves off-center when the aircraft is at a high angle of attack. This shift in the location of the center of thrust will exert a yawing moment on the aircraft, causing it to yaw slightly to one side. A rudder input is required to counteract the yawing tendency.

Transverse flow effect is an aerodynamic effect encountered when a helicopter moves through the air.

A Flettner rotor is a smooth cylinder with disc end plates which is spun along its long axis and, as air passes at right angles across it, the Magnus effect causes an aerodynamic force to be generated in the direction perpendicular to both the long axis and the direction of airflow. The rotor sail is named after the German aviation engineer and inventor Anton Flettner, who started developing the rotor sail in 1920s.

Hop-up is the backspin put on airsoft pellets and BBs to increase their range via the Magnus effect.

The yaw system of wind turbines is the component responsible for the orientation of the wind turbine rotor towards the wind.

Flight dynamics is the study of the performance, stability, and control of vehicles flying through the air or in outer space. It is concerned with how forces acting on the vehicle determine its velocity and attitude with respect to time.

A rotor wing is a lifting rotor or wing which spins to provide aerodynamic lift. In general, a rotor may spin about an axis which is aligned substantially either vertically or side-to-side (spanwise). All three classes have been studied for use as lifting rotors and several variations have been flown on full-size aircraft, although only the vertical-axis rotary wing has become widespread on rotorcraft such as the helicopter.

A falling leaf is an aerobatic maneuver in which an aircraft performs a wings-level stall which begins to induce a spin. This spin is countered with the rudder, which begins a spin in the opposite direction that must be countered with rudder, and the process is repeated as many times as the pilot determines. During the maneuver, the plane resembles a leaf falling from the sky; first slipping to one side, stopping, and then slipping to the other direction; continuing a side-to-side motion as it drifts toward the ground.

The physics of a bouncing ball concerns the physical behaviour of bouncing balls, particularly its motion before, during, and after impact against the surface of another body. Several aspects of a bouncing ball's behaviour serve as an introduction to mechanics in high school or undergraduate level physics courses. However, the exact modelling of the behaviour is complex and of interest in sports engineering.

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