Magnus effect - AbsoluteAstronomy.com

The Magnus effect is the phenomenon whereby a spinning object flying in a fluid

Fluid

In physics, a fluid is a substance that continually deforms under an applied shear stress. Fluids are a subset of the phases of matter and include liquids, gases, plasmas and, to some extent, plastic solids....

creates a whirlpool

Whirlpool

A whirlpool is a swirling body of water usually produced by ocean tides. The vast majority of whirlpools are not very powerful. More powerful ones are more properly termed maelstroms. Vortex is the proper term for any whirlpool that has a downdraft...

of fluid around itself, and experiences a force perpendicular to the line of motion. 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 aerofoil action.

In many ball sports, the Magnus effect is responsible for the curved motion of a spinning ball. The effect also affects spinning missiles, and is used in rotor ships and Flettner aeroplanes

Flettner airplane

A flettner or rotor airplane is an airplane that has no wings but instead uses the Magnus effect to create lift. Thus it is similar to the Flettner rotor used in a Rotor ship...

History

German

Germany

Germany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...

physicist

Physicist

A physicist is a scientist who studies or practices physics. Physicists study a wide range of physical phenomena in many branches of physics spanning all length scales: from sub-atomic particles of which all ordinary matter is made to the behavior of the material Universe as a whole...

Heinrich Magnus described the effect in 1852. However, in 1672, Isaac Newton

Isaac Newton

Sir Isaac Newton PRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived."...

had described it and correctly inferred the cause after observing tennis

Tennis

Tennis is a sport usually played between two players or between two teams of two players each . Each player uses a racket that is strung to strike a hollow rubber ball covered with felt over a net into the opponent's court. Tennis is an Olympic sport and is played at all levels of society at all...

players in his Cambridge

Cambridge

The city of Cambridge is a university town and the administrative centre of the county of Cambridgeshire, England. It lies in East Anglia about north of London. Cambridge is at the heart of the high-technology centre known as Silicon Fen – a play on Silicon Valley and the fens surrounding the...

college. In 1742, Benjamin Robins

Benjamin Robins

Benjamin Robins was a pioneering English scientist, Newtonian mathematician, and military engineer.He wrote an influential treatise on gunnery, for the first time introducing Newtonian science to military men, was an early enthusiast for rifled gun barrels, and his work had substantive influence...

, a British artillery engineer, explained deviations in the trajectories of musket balls in terms of the Magnus effect.

Principle

When a body (such as a sphere or circular cylinder) is spinning in a viscous

Viscosity

Viscosity is a measure of the resistance of a fluid which is being deformed by either shear or tensile stress. In everyday terms , viscosity is "thickness" or "internal friction". Thus, water is "thin", having a lower viscosity, while honey is "thick", having a higher viscosity...

fluid, it creates a boundary layer

Boundary layer

In physics and fluid mechanics, a boundary layer is that layer of fluid in the immediate vicinity of a bounding surface where effects of viscosity of the fluid are considered in detail. In the Earth's atmosphere, the planetary boundary layer is the air layer near the ground affected by diurnal...

around itself, and the boundary layer induces a more widespread circular motion of the fluid. If the body is moving through the fluid with a velocity V, the velocity of the thin layer of fluid close to the body is a little greater than V on the forward-moving side and a little less than V on the backward-moving side. This is because the induced velocity due to the boundary layer surrounding the spinning body is added to V on the forward-moving side, and subtracted from V on the backward-moving side. One explanation of the Magnus effect is since there is more (forward) acceleration of air on the forward-moving side than the backward-moving side, there is more pressure on the forward-moving side, resulting in a perpendicular component of force from the air towards the backward-moving side. This layer of spinning air, however, is very thin, and it is more likely that most of the Magnus effect is due to the earlier detachment of the air flow on the forward-moving side

Flow separation

All solid objects travelling through a fluid acquire a boundary layer of fluid around them where viscous forces occur in the layer of fluid close to the solid surface. Boundary layers can be either laminar or turbulent...

, which results in a diversion of the flow (acceleration of air) with a perpendicular component towards the forward-moving side, coexisting with an opposing aerodynamic force with a perpendicular component towards the backward-moving side.

Calculation of Magnus force

Given the angular velocity

Angular velocity

In physics, the angular velocity is a vector quantity which specifies the angular speed of an object and the axis about which the object is rotating. The SI unit of angular velocity is radians per second, although it may be measured in other units such as degrees per second, revolutions per...

vector

and velocity

Velocity

In physics, velocity is speed in a given direction. Speed describes only how fast an object is moving, whereas velocity gives both the speed and direction of the object's motion. To have a constant velocity, an object must have a constant speed and motion in a constant direction. Constant ...

of the object, the resulting force

can be calculated using the following formula:

where

is dependent on the average of the air resistance coefficient across the surface of the object. The

denotes the vector cross product.

An example of spin ball in the air

The following equation demonstrates the lift force induced on a ball that is spinning along an axis of rotation perpendicular to the direction of its translational motion:

F = lift force

= density of the fluid

r = radius of the ball

v = velocity of the ball

A = cross-sectional area of ball

C_L = lift coefficient

Lift coefficient

The lift coefficient is a dimensionless coefficient that relates the lift generated by a lifting body, the dynamic pressure of the fluid flow around the body, and a reference area associated with the body...

The lift coefficient C_L may be determined from graphs of experimental data using Reynolds numbers and spin ratios. For a smooth ball with spin ratio of 0.5 to 4.5, typical lift coefficients range from 0.2 to 0.6.

In sport

The Magnus effect explains commonly observed deviations from the typical trajectories or paths of non-spinning balls in sport

Sport

A Sport is all forms of physical activity which, through casual or organised participation, aim to use, maintain or improve physical fitness and provide entertainment to participants. Sport may be competitive, where a winner or winners can be identified by objective means, and may require a degree...

, notably association football, table tennis

Table tennis

Table tennis, also known as ping-pong, is a sport in which two or four players hit a lightweight, hollow ball back and forth using table tennis rackets. The game takes place on a hard table divided by a net...

, tennis

Tennis

, volleyball

Volleyball

Volleyball is a team sport in which two teams of six players are separated by a net. Each team tries to score points by grounding a ball on the other team's court under organized rules.The complete rules are extensive...

, golf

Golf

Golf is a precision club and ball sport, in which competing players use many types of clubs to hit balls into a series of holes on a golf course using the fewest number of strokes....

, baseball

Baseball

Baseball is a bat-and-ball sport played between two teams of nine players each. The aim is to score runs by hitting a thrown ball with a bat and touching a series of four bases arranged at the corners of a ninety-foot diamond...

, cricket

Cricket

Cricket is a bat-and-ball game played between two teams of 11 players on an oval-shaped field, at the centre of which is a rectangular 22-yard long pitch. One team bats, trying to score as many runs as possible while the other team bowls and fields, trying to dismiss the batsmen and thus limit the...

and in paintball marker

Paintball marker

A paintball marker, also known as a paintball gun, is the main piece of equipment in the sport of paintball. Markers use an expanding gas, such as carbon dioxide or compressed air, to propel paintballs through the barrel. Some paintball players refer to the piece of equipment as a "marker" rather...

balls.

The curved path of a golf ball

Golf ball

A golf ball is a ball designed to be used in the game of golf.Under the Rules of Golf, a golf ball weighs no more than 1.620 oz , has a diameter not less than 1.680 in , and performs within specified velocity, distance, and symmetry limits...

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. Back-spin (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.

Sometimes, table tennis is played with the Magnus effect.
In table tennis, the Magnus effect is easily observed, because of the small mass and low density

Density

The mass density or density of a material is defined as its mass per unit volume. The symbol most often used for density is ρ . In some cases , density is also defined as its weight per unit volume; although, this quantity is more properly called specific weight...

of the ball. An experienced player can place a wide variety of spins on the ball. Table tennis racket

Table tennis racket

A table tennis racket is used by players in the game of table tennis. The racket is usually made from laminated wood covered with rubber on one or two sides depending on the grip of the player...

s 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

Swing bowling

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.-Physics of swing bowling:...

, although it does contribute to the motion known as drift in spin bowling

Spin bowling

Spin bowling is a technique used for bowling in the sport of cricket. Practitioners are known as spinners or spin bowlers.-Purpose:The main aim of spin bowling is to bowl the cricket ball with rapid rotation so that when it bounces on the pitch it will deviate, thus making it difficult for the...

.

In airsoft

Airsoft

Airsoft is a sport in which participants shoot round non-metallic pellets launched via replica firearms.Gameplay varies in style and composition but often range from short-term skirmishes, organized scenarios, military simulations, historical reenactments, to competition target shooting events...

, a system known as Hop-Up

Hop-Up (Airsoft)

The term Hop-up, short for High Operation Power Up, describes the back-spin put on airsoft pellets and BB's to increase their range and accuracy via Magnus effect. Hop-up acts somewhat like the rifling on the barrel of a firearm, but without the increase in horizontal accuracy...

is used to create a back-spin on a fired BB

BB gun

BB guns are a type of air gun designed to shoot projectiles named BBs after the birdshot pellet of approximately the same size. These projectiles are usually spherical but can also be pointed; those are usually used for bird hunting. Modern day BB guns usually have a smoothbore barrel, with a bore...

, which will greatly increase its range, using the Magnus effect in a similar manner as in golf.

In baseball, the spin of a baseball from a pitch influences the air running by a ball, creating low air pressure on one side of the ball; the ball will tend to curve toward the direction of low-pressure side of the ball.

The Magnus effect can be a hindrance to a sport-player when it is not anticipated. For example, a novice golf player may intend to hit a straight shot, but fail to do so because of not anticipating the effects of a spinning ball in air. Experienced players can however use the Magnus force to obtain intentional results.

In external ballistics

The Magnus effect can also be found in advanced external ballistics

External ballistics

External ballistics is the part of the science of ballistics that deals with the behaviour of a non-powered projectile in flight. External ballistics is frequently associated with firearms, and deals with the behaviour of the bullet after it exits the barrel and before it hits the target.-Forces...

. Firstly, a spinning bullet in flight is often subject to a crosswind

Crosswind

A crosswind is any wind that has a perpendicular component to the line or direction of travel. In aviation, a crosswind is the component of wind that is blowing across the runway making landings and take-offs more difficult than if the wind were blowing straight down the runway...

, which can be simplified as blowing either from 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 is pointing in a slightly different direction from the direction in which the bullet is travelling. In other words, the bullet is "skidding" sideways at any given moment, and thus it experiences a small sideways wind component in addition to any crosswind component.

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 an observable deflection in the bullet's flight path up or down, thus changing 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 effects 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

Center of mass

In physics, the center of mass or barycenter of a system is the average location of all of its mass. In the case of a rigid body, the position of the center of mass is fixed in relation to the body...

. 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 stabilizing the bullet) or away from the axis of flight (increasing the yaw thus destabilizing 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 stabilizing.

In flying machines

Some flying machines use the Magnus effect to create lift with a rotating cylinder at the front of a wing that allows flight at lower horizontal speeds. The earliest attempt to use the Magnus Effect for a heavier than air aircraft being in 1910 by a US member of Congress, the next attempt was in the early 1930s by three inventors in New York state.

Magenn Power Inc created a lighter-than-air high altitude wind turbine called MARS that uses the Magnus effect to keep a stable and controlled position in air. MARS meets FAA and Transport Canada

Transport Canada

Transport Canada is the department within the government of Canada which is responsible for developing regulations, policies and services of transportation in Canada. It is part of the Transportation, Infrastructure and Communities portfolio...

guidelines.

The iCar 101 project uses the Magnus effect in a roadable aircraft design.

2010 FIFA World Cup Match Ball

The match ball for the 2010 FIFA World Cup

2010 FIFA World Cup

The 2010 FIFA World Cup was the 19th FIFA World Cup, the world championship for men's national association football teams. It took place in South Africa from 11 June to 11 July 2010...

has been criticised for the different Magnus effect to previous match balls. The current ball is described as having less Magnus effect and as a result flies further but with less controllable swerve. Additionally, some say that the ball's Magnus effect varies depending upon the axis on which it spins.

In Astronomy

Many astronomical objects (planets, galaxies etc.) have both rotational (spinning) and linear (moving) motions in space. The Magnus force should in principle be acting on astronomical objects. There have been arguments indicating that Magnus effect works on planets and galaxies.

External links

The source of this article is wikipedia, the free encyclopedia. The text of this article is licensed under the GFDL.