magnus-effect

Like many sports, the gameplay in football can be strongly affected by the ball’s spin. Corner kicks and free kicks can curve in non-intuitive ways, making the job of the goalie much harder. These seemingly impossible changes in trajectory are due to airflow around the spinning ball and what’s known as the Magnus effect. In the animation above, flow is moving from right to left around a football. As the ball starts spinning, the symmetry of the flow around the ball is broken. On top, the ball is spinning toward the incoming flow, and the green dye pulls away from the surface. This is flow separation and creates a high-pressure, low-velocity area along the top of the ball. In contrast, the bottom edge of the ball pulls dye along with it, keeping flow attached to the ball for longer and creating low pressure. Just as a wing has lift due to the pressure difference on either side of the wing, the pressure imbalance on the football creates a force acting from high-to-low pressure. In this case, that is a downward force relative to the ball’s rightward motion. In a freely moving football, this force would curve its trajectory to the side. (GIF credit: SkunkBear/NPR; original video: NASA Ames; via skunkbear)

I recently built a plane which uses the magnus effect to  produce lift. It is build out of 2 mm and 3cmfoam. I tested it with rudder and elevator but the elevator was not as efficient as it would be on a normal plane. It has a speed range from very slow to moderate walking speed. I think I will give that design another chance and build one with landing gear.

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Spinning an object in motion through a fluid produces a lift force perpendicular to the spin axis. Known as the Magnus effect, this physics is behind the non-intuitive behavior of football’s corner kick, volleyball’s spike, golf’s slice, and baseball’s curveball. The simulation above shows a curveball during flight, with pressure distributions across the ball’s surface shown with colors. Red corresponds to high pressure and blue to low pressure. Because the ball is spinning forward, pressure forces are unequal between the top and bottom of the ball, with the bottom part of the baseball experiencing lower pressure. As with a wing in flight, this pressure difference between surfaces creates a force – for the curveball, downward. (Video credit: Tetra Research)

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A remote control plane that gives up rigid wings, and instead, rotary wings that take advantage of the Magnus effect are utilized… Truly unique, and an incredible sight.

The physics of pitching a baseball

Recently, I stumbled on a story about New York Yankees pitcher Freddy García. In april of 2011, García was pitching against the Toronto Blue Jays. In the top of the 5th, Garcia threw this pitch to batter Juan Rivera. Now to the casual baseball observer, you might think this was just was an exception throw, which it was, but then move on to the rest of the game. However, to the folks who watch these events carefully, there was something unusual about this pitch. So unusual in fact, that there existed at the time no physical explanation for that observed movement of a baseball.

There are a number of forces acting on a pitch. The most basic ones we can initially think of are 1) the forward force given to the ball by the pitcher and 2) the force of gravity. The less force a pitches gives to the ball, the longer it will take the ball to arrive to the catcher and the more time gravity will have to accelerate the ball toward the ground.

Typically, to get movement on a baseball that deviates from this gravity dependant sinking, a pitcher will alter his grip to deliver the pitch with different kinds on spin it. This spin alters the way air flows around the ball as it heads toward the catcher. This 3rd force, caused by the the Magnus Effect, tells us that there will be a force on the ball perpendicular to the axis of rotation. If a pitcher throws a 4-seam fastball with enough backspin, the magnus force be greater then the force of gravity (at least over the 60 feet 6 inches between the pitchers mound and the catcher) and cause the ball to rises up on the batter. This is due to how air flows around a spinning ball. Much like how the wing of an airplane alters airflow, the spinning ball causes differences in air pressure around in, resulting in a new force component.

These three forces are all well and good for explaining most movement on a baseball, but they dont explain García’s pitch. There is only a small amount of backspin on a relatively slowly thrown ball, which explains why gravity has time to pull it down. However, the ball cuts to the pitchers left, while the Magnus effect would predict rightward motion due to its spin. So what’s going on??

Australian physicist (and apparent baseball and cricket enthusiast) Rod Cross discovered an explanation for this effect by testing polystyrene balls, which are lighter and show exaggerated movements. In his paper published in American Journal of Physics earlier this year, Rod demonstrated how the seam of a cricket ball, along with surface difference that accumulate during a game, affect the movement of the ball when bowled.

But a cricket ball has its seam straight down the middle, while a baseball has its seam in a figure eight pattern. So how are the two connected? If you watch the original video of García’s pitch closely, you’ll notice that the axis of rotation of the ball is such that the smooth face of the ball is always toward the axis of rotation (top left of ball). Most of the time this isn’t the case, and the ball rotates in a way to average out its smoothed and seamed faces. Because of that, this effect is almost never observed.

Check out the man himself explaining it:

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Almost everyone has tried skipping rocks across the surface of a pond or lake. Here Professor Tadd Truscott gives a primer on the physics of rock skipping, including some high-speed video of the impact and rebound. In a conventional side-arm-launched skip, the rock’s impact creates a cavity, whose edge the rock rides. This pitches the rock upward, creating a lifting force that launches the rock back up for another skip. Alternatively, you can launch a rock overhand with a strong backspin. The rock will go under the surface, but if there’s enough spin on it, there will be sufficient circulation to create lift that brings the rock back up. This is the same Magnus effect used in many sports to control the behavior of a ball–whether it’s a corner or free kick in soccer or a spike in volleyball or tennis. (Video credit: BYU Splash Lab/Brigham Young University)

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Physics students are often taught to ignore the effects of air on a projectile, but such effects are not always negligible. This video features several great examples of the Magnus effect, which occurs when a spinning object moves through a fluid. The Magnus force acts perpendicular to the spin axis and is generated by pressure imbalances in the fluid near the object’s surface. On one side of the spinning object, fluid is dragged with the spin, staying attached to the object for longer than if it weren’t spinning.  On the other side, however, the fluid is quickly stopped by the spin acting in the direction opposite to the fluid motion. The pressure will be higher on the side where the fluid stagnates and lower on the side where the flow stays attached, thereby generating a force acting from high-to-low, just like with lift on an airfoil. Sports players use this effect all the time: pitchers throw curveballs, volleyball and tennis players use topspin to drive a ball downward past the net, and golfers use backspin to keep a golf ball flying farther. (Video credit: Veritasium)

BackSpin in Tennis And Golf

In racquet sports and golf, backspin (also known in racket sports as slice or underspin), is a shot such that the ball rotates backwards (as though rolling back towards the player) after it is hit. This direction of spin imparts an upward force that lifts the ball (see Magnus effect). While a normal hit bounces well forward as well as up, backspin shots bounce higher and less forward. Backspin is the opposite of topspin.

In racket sports, the higher bounce imparted by backspin may make a receiver who has prepared for a different shot miss or mis-hit the ball when swinging. A backspin shot is also useful for defensive shots because a backspin shot takes longer to travel to the opponent, giving the defender more time to get back into position. Also, because backspin shots tend to bounce less far forward once they reach the opposite court, they may be more difficult to attack. This is especially important in table tennis because one must wait for the ball to bounce before hitting it, whereas in tennis the opponent may volley the ball.

In golf, a well-struck shot will result in a large amount of backspin that will carry the ball higher into the air and farther. Backspin also helps with distance control, as if there is enough backspin, the ball will “check” if it lands on the putting surface, and sometimes even creep backwards (in the opposite direction that the ball was flying) upon landing.

TopSpin: The Physical Explanation , Lift Force, and The Magnus Effect

Topspin on a shot imparts a downward force that causes the ball to drop, due to its interaction with the air (see Magnus effect). In racquet sports, it can be generated by hitting the ball with an up-and-forward swing, with the racquet facing below the direction it is moving. A topspin shot is the opposite of the slice; topspin itself is the opposite of backspin.

One way of explaining the Magnus effect is that - because of the rotation and the fact that air acts as a viscous or “sticky” substance on the surface of the ball, a stream of air in the wake of the ball is being ejected upwards. As a reaction to this, the ball is pushed downwards.

Often Bernoulli’s principle is used to explain the topspin effect, as the difference in speed between ball surface and air is greater on the top of the ball. For example, if the air flowing past the bottom of the ball is moving faster than the air flowing past the top then Bernoulli’s principle implies that the pressure on the surfaces of the ball will be lower below than above. In other words, since there is more air friction occurring on the top surface of the ball compared to the bottom, this differential causes a greater pressure to be applied on the top of the ball, resulting in the ball being pushed down.

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.

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. leg break.

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.

It is named for 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.


A fluid flowing past the surface of a body 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 surface force parallel to the flow direction. If the fluid is air, the force is called an aerodynamic force. In water, it is called a hydrodynamic force.

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

F/L= \rho V G,
where the vortex strength is given by

G = 2 \pi \omega r^2,
where ω is the angular velocity of spin of the cylinder and r is the radius of the cylinder.

German physicist Heinrich Gustav 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.


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.

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.