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“Twisted” or the Magnus effect

Everyone saw how on football or tennis the ball flies along an incredible trajectory. What force makes a flying ball describe zigzags?

This effect was discovered by the German physicist Heinrich Magnus in 1853. The essence of the phenomenon is that the ball, when rotating, creates around itself a vortex motion of air. On one side of the object, the direction of the vortex coincides with the direction of the flowing stream and the velocity of the medium on this side increases. On the other side of the object, the direction of the vortex is opposite to the direction of flow, and the velocity of the medium is reduced.

This difference in velocities generates a transverse force, which changes the trajectory of the flight. The phenomenon is often used in sports, for example, special hits: top-spin, a dry sheet in football or a Hop-Up system in airsoft.

The Magnus effect is well illustrated in this video. Thrown from a high altitude vertically down basketball, which was given a spin, changes the trajectory and for a while flies horizontally.



The Magnus effect was demonstrated on one of the dams in Australia. The basketball was first dropped from it, flew almost straight down and landed at the intended point. Then the ball was dropped from the dam a second time, while slightly twisting it (by the way, with the effect of Magnus often face players when filing “twisted” balls).

In this case, the object behaved unusually. Video with a demonstration of the physical phenomenon was posted on YouTube hosting, literally in a couple of days, collecting more than 9 million views and almost 1,5 thousand comments.

Fig. 1 1 – boundary layer


Moving forward (nonrotating) with relative velocity V0, the cylinder flows around a laminar flow, which is not vortex (Fig. 1b).

If the cylinder rotates and simultaneously moves translationally, the two surrounding streams are stacked on each other and create the resulting flow of flow (Figure 1c).

When the cylinder rotates, the liquid also moves. The motion in the boundary layer is vortex; it is composed of a potential motion, onto which rotation is superimposed. At the top of the cylinder, the direction of the flow coincides with the direction of rotation of the cylinder, and from the bottom – opposite to it. The particles in the boundary layer above the cylinder are accelerated by the flow, which prevents the separation of the boundary layer.

From below, the flow inhibits movement in the boundary layer, which contributes to its separation. The detachable parts of the boundary layer are carried away by the flow in the form of vortices. As a result, the circulation of velocity around the cylinder occurs in the same direction as the cylinder rotates. According to the Bernoulli law, the pressure of the liquid on the upper part of the cylinder will be less than the lower one.

This leads to the appearance of a vertical force, called the lifting force. If the direction of rotation of the cylinder is reversed, the lifting force also reverses direction.

In the Magnus effect, the force F0 is perpendicular to the flow velocity V0. To find the direction of this force, the vector must be rotated by 90 ° relative to the velocity V0, in the direction opposite to the rotation of the cylinder.


The Magnus effect can be observed experimentally with a light cylinder sliding down an inclined plane.

Scheme of a rolling cylinder

Fig. 2

After rolling along the inclined plane, the center of mass of the cylinder moves not along the parabola, as the material point would move, but along the curve going under the inclined plane.

If we replace the rotating cylinder with a vortex (rotating column of liquid) with intensity J = 2Sw, then the Magnus force will be the same. Thus, a force perpendicular to the relative velocity of motion V0 acts on the moving vortex from the side of the surrounding fluid and is directed to the side determined by the above mentioned rule of rotation of the vector.

The Magnus effect is interrelated: the direction and velocity of the flow, the direction and angular velocity, the direction and the resulting force. Accordingly, it is possible to measure and use force or measure flow and angular velocity.

The dependence of the result on the effect has the following form (the Zhukovsky-Kutta formula):


FR = JrV0,


where J is the intensity of motion around the cylinder;

r is the density of the liquid;

V0 is the relative flow velocity.


Restrictions on the manifestation of the physical effect: providing a laminar flow of liquid (gas) above the object with a lifting force directed upwards.

The effect was first described by the German physicist Henry Magnus in 1853.

He studied physics and chemistry for 6 years – first at the University of Berlin, then another year (1828) in Stockholm, in the laboratory of Jöns Berzelius, and later in Paris with Gay-Lussac and Tenar. In 1831, Magnus was invited lecturer in physics and technology at the University of Berlin, then was a professor of physics until 1869. In 1840 Magnus was elected a member of the Berlin Academy, from 1854 he was a corresponding member of the St. Petersburg Academy of Sciences.

Magnus tirelessly worked all his life on the most varied issues of physics and chemistry. As a student (1825), he published his first paper on the self-ignition of metallic powders, in 1828, discovered the name platinum salt (PtCl 2NH3) named after him. In 1827-33 he studied mainly chemistry, then worked in the field of physics.

Of these, research on the absorption of gases by blood (1837-45), over the expansion of gases from heating (1841-44), over the elasticities of water vapor and aqueous solutions (1844-54), over thermoelectricity (1851), electrolysis (1856) , the induction of currents (1858-61), the thermal conductivity of gases (1860), the polarization of radiant heat (1866-68), and the issue of the heat of color of gases (since 1861).

Magnus is also known as a teacher; from his laboratory came out most outstanding modern German physicists, some Russian scientists also worked there.

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