# What is the Magnus Effect and How Does it Work

### What is the Magnus Effect and how Does it Work?

ScientiaThe 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.

In terms of ball games, topspin is defined as spin about a horizontal 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 airfoil (see lift force) with a circulation which is generated by the mechanical rotation, rather than by airfoil action.

The Magnus effect is named after 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.

Ok, so there is a very brief description of the Magnus Effect; however, it will probably help if you see a video of it happening. Hopefully you will think this is as awesome as I do.

### The Physics Behind the Magnus Effect

A valid intuitive understanding of the phenomenon is possible, beginning with the fact that, by conservation of momentum, 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 vice versa. 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 Magnus effect, depicted with a backspinning cylinder or ball in an airstream. The arrow represents the resulting lifting force. The curly flow lines represent a turbulent wake. The airflow has been deflected in the direction of 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 just 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.

##### Ok…Now for the hardcore

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, the density of the fluid, \rho, and the strength of the vortex that is established by the rotation, G:[4]

where the vortex strength is given by

where ω is the angular velocity of spin of the cylinder and r is the radius of the cylinder.

### Practical Uses of the Magnus Effect

##### Magnus Effect and Sport

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 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.

### Magnus Effect and 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 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 affects the amount of drag, how the bullet behaves upon impact, and many other factors. The stability of the bullet is affected[citation needed] because the Magnus effect acts on the bullet’s centre of pressure instead of its centre of gravity. 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.

### Magnus Effect and Flying Objects

Whilst this is theoretically and actually physically possible, there are a numerous amount of other factors that come into play when you are attempting to achieve lift from the surface of Earth. One main factor is air resistance. Although some people have managed to build small aeroplanes that use the Magnus effect to gain flight; commercially this is not overall feasible….at the moment anyway.

### Magnus Effect and Ship Propulsion

A rotor ship, or Flettner ship, is a ship designed to use the Magnus effect for propulsion. To take advantage of this effect, it uses rotorsails which are powered by an engine. The Magnus effect is a force acting on a spinning body in a moving airstream, which acts perpendicularly to the direction of the airstream. German engineer Anton Flettner was the first to build a ship which attempted to tap this force for propulsion.

Flettner’s spinning bodies were vertical cylinders; the basic idea was to use the Magnus effect. These types of propulsion cylinders are now commonly called Flettner rotors.

His first idea was to produce the propulsion force by using a belt running round two cylinders. Later Flettner decided that the cylinders would be better rotated by individual motors, thus avoiding power losses from the main engine. Flettner applied for a German patent for the rotor ship on 16 September 1922.

Assisted by Albert Betz, Jakob Ackeret and Ludwig Prandtl, Flettner constructed an experimental rotor vessel, and in October 1924 the Germaniawerft finished construction of a large two-rotor ship named Buckau. The vessel was a refitted schooner which carried two cylinders (or rotors) about 15 metres (50 ft) high, and 3 metres (10 ft) in diameter, driven by an electric propulsion system of 50 hp (37 kW) power. In 1926, a larger ship with three rotors, the Barbara, was built by the shipyard A.G. Weser in Bremen.

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