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The Magnus effect is an observable phenomenon commonly associated with a spinning object moving through a fluid. A lift force acts on the spinning object. The path of the object may be deflected in a manner 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 strength of the Magnus effect is dependent on the speed of rotation of the object.
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 (soccer) and volleyball 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 airplanes.
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 shape of the foil. [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 Nikolay Zhukovsky (or Joukowski), who first analyzed the effect.
The pressure-gradient force is the force that results when there is a difference in pressure across a surface. In general, a pressure is a force per unit area, across a surface. A difference in pressure across a surface then implies a difference in force, which can result in an acceleration according to Newton's second law of motion, if there is no additional force to balance it. The resulting force is always directed from the region of higher-pressure to the region of lower-pressure. When a fluid is in an equilibrium state (i.e. there are no net forces, and no acceleration), the system is referred to as being in hydrostatic equilibrium. In the case of atmospheres, the pressure-gradient force is balanced by the gravitational force, maintaining hydrostatic equilibrium. In Earth's atmosphere, for example, air pressure decreases at altitudes above Earth's surface, thus providing a pressure-gradient force which counteracts the force of gravity on the atmosphere.
The Magnus-Force of a spinning object is the difference in pressure between opposing sides of the object scaled by the cross-sectional Area:
where is a scalar dependent on the shape and material of the rotating object, is the speed of the fluid relative to each surface and is the fluid density. [5]
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 [6] made a wind tunnel study of the Magnus effect on baseballs, and others have produced images of the effect. [6] [7] [8] [9] 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. [6] In some circumstances the causes of the Magnus effect can produce a deflection opposite to that of the Magnus effect. [9]
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.
In baseball, this effect is used to generate the downward motion of a curveball, in which the baseball is rotating forward (with 'topspin'). Participants in other sports played with a ball also take advantage of this effect.
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, , is the product of the freestream velocity, (in m/s), the freestream density of the fluid, (in kg/m3), and circulation of fluid established by the rotation, , due to viscous effects: [4]
where the vortex strength (assuming that the surrounding fluid obeys the no-slip condition) is given by
where ω is the angular velocity of the cylinder (in rad/s) and r is the radius of the cylinder (in m).
The German physicist Heinrich Gustav Magnus described the effect in 1852. [10] [11] However, in 1672, Isaac Newton had described it and correctly inferred the cause after observing tennis players in his Cambridge college. [12] [13] 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. [14] [15] [16] [17]
The Magnus effect explains commonly observed deviations from the typical trajectories or paths of spinning balls in sport, notably association football, table tennis, [18] tennis, [19] volleyball, golf, baseball, and cricket.
The curved path of a golf ball known as slice or hook is largely due to the ball's spin axis being tilted away from the horizontal due to the combined effects of club face angle and swing path, causing the Magnus effect to act at an angle, moving the ball away from a straight line in its trajectory. [20] 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.
In cricket, the Magnus effect contributes to the types of motion known as drift, dip and lift in spin bowling, depending on the axis of rotation of the spin applied to the ball. The Magnus effect is not responsible for the movement seen in conventional swing bowling, [21] : Fig. 4.19 in which the pressure gradient is not caused by the ball's spin, but rather by its raised seam, and the asymmetric roughness or smoothness of its two halves; however, the Magnus effect may be responsible for so-called "Malinga Swing", [22] [23] as observed in the bowling of the swing bowler Lasith Malinga.
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. [24]
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. [25]
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. [26]
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. [27] 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. [28]
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. [29]
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. [30] The largest deployment of the system to date is in the motor yacht Eclipse.
In physics, the Coriolis force is an inertial force that acts on objects 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.
When a fluid flows around an object, the fluid exerts a force on the object. 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 is defined to act perpendicular to the flow and therefore can act in any direction.
Bernoulli's principle is a key concept in fluid dynamics that relates pressure, speed and height. Bernoulli's principle states that an increase in the speed of a fluid occurs simultaneously with a decrease in static pressure or the fluid's potential energy. The principle is named after the Swiss mathematician and physicist Daniel Bernoulli, who published it in his book Hydrodynamica in 1738. Although Bernoulli deduced that pressure decreases when the flow speed increases, it was Leonhard Euler in 1752 who derived Bernoulli's equation in its usual form.
In fluid dynamics, a vortex is a region in a fluid in which the flow revolves around an axis line, which may be straight or curved. Vortices form in stirred fluids, and may be observed in smoke rings, whirlpools in the wake of a boat, and the winds surrounding a tropical cyclone, tornado or dust devil.
The Coandă effect is the tendency of a fluid jet to stay attached to a convex surface. Merriam-Webster describes it as "the tendency of a jet of fluid emerging from an orifice to follow an adjacent flat or curved surface and to entrain fluid from the surroundings so that a region of lower pressure develops."
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. These are collectively known as aircraft attitude, often principally relative to the atmospheric frame in normal flight, but also relative to terrain during takeoff or landing, or when operating at low elevation. The concept of attitude is not specific to fixed-wing aircraft, but also extends to rotary aircraft such as helicopters, and dirigibles, where the flight dynamics involved in establishing and controlling attitude are entirely different.
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.
In fluid mechanics, the pressure-gradient force is the force that results when there is a difference in pressure across a surface. In general, a pressure is a force per unit area across a surface. A difference in pressure across a surface then implies a difference in force, which can result in an acceleration according to Newton's second law of motion, if there is no additional force to balance it. The resulting force is always directed from the region of higher-pressure to the region of lower-pressure. When a fluid is in an equilibrium state, the system is referred to as being in hydrostatic equilibrium. In the case of atmospheres, the pressure-gradient force is balanced by the gravitational force, maintaining hydrostatic equilibrium. In Earth's atmosphere, for example, air pressure decreases at altitudes above Earth's surface, thus providing a pressure-gradient force which counteracts the force of gravity on the atmosphere.
An aircraft stabilizer is an aerodynamic surface, typically including one or more movable control surfaces, that provides longitudinal (pitch) and/or directional (yaw) stability and control. A stabilizer can feature a fixed or adjustable structure on which any movable control surfaces are hinged, or it can itself be a fully movable surface such as a stabilator. Depending on the context, "stabilizer" may sometimes describe only the front part of the overall surface.
In ball sports, topspin or overspin 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.
Stability derivatives, and also control derivatives, are measures of how particular forces and moments on an aircraft change as other parameters related to stability change. For a defined "trim" flight condition, changes and oscillations occur in these parameters. Equations of motion are used to analyze these changes and oscillations. Stability and control derivatives are used to linearize (simplify) these equations of motion so the stability of the vehicle can be more readily analyzed.
The Kutta–Joukowski theorem is a fundamental theorem in aerodynamics used for the calculation of lift of an airfoil translating in a uniform fluid at a constant speed large enough so that the flow seen in the body-fixed frame is steady and unseparated. The theorem relates the lift generated by an airfoil to the speed of the airfoil through the fluid, the density of the fluid and the circulation around the airfoil. The circulation is defined as the line integral around a closed loop enclosing the airfoil of the component of the velocity of the fluid tangent to the loop. It is named after Martin Kutta and Nikolai Zhukovsky who first developed its key ideas in the early 20th century. Kutta–Joukowski theorem is an inviscid theory, but it is a good approximation for real viscous flow in typical aerodynamic applications.
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 the 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.
This glossary of aerospace engineering terms pertains specifically to aerospace engineering, its sub-disciplines, and related fields including aviation and aeronautics. For a broad overview of engineering, see glossary of engineering.
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.
The Plymouth A-A-2004 is a rotor aircraft inspired by the Flettner rotor, a type of rotor that uses the Magnus effect to produce lift. Built specifically for Zaparka in 1930 by three anonymous American inventors, this aircraft showcased the innovative use of the Magnus Effect in aviation, leading to successful flights over Long Island Sound
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