# Magnus effect

The Magnus effect , named after Heinrich Gustav Magnus (1802–1870), is a fluid mechanics phenomenon that describes the transverse force ( force ) experienced by a rotating round body ( cylinder or sphere ) in a flow. The effect was described 100 years before Magnus by Benjamin Robins , who suspected the cause in the rotation of the sphere. Magnus, on the other hand, was the first to succeed in giving a physical explanation of the effect.

## history

Visualization of the Magnus effect in the flow channel

Magnus provided evidence of the phenomenon purely experimentally in 1852 and thus recognized the cause of the orbital deviation of rotating projectiles. Inspired by the deviation of the trajectory of tennis balls, it was not until 1877 that Lord Rayleigh succeeded in theoretically justifying the effect. He attributed the discovery and explanation of the phenomenon to Magnus, although it was described by Robins about 100 years earlier. It was not until 1959 that Briggs expanded the previously valid explanation of the phenomenon solely via the Bernoulli relation by including the boundary layer theory , which was primarily developed by Ludwig Prandtl at the beginning of the 20th century . Work on the perfection of bullet shapes with regard to the Magnus effect and in connection with the Haackschen Ogive continued into the 21st century .

## principle

### The classic since Magnus

A rotating body ( cylinder or ball ) is deflected at right angles to the direction of flow V.

Magnus was the first to explain the effect using the Bernoulli equation , which establishes a relation between the pressure and velocity fields of a flow that is free of friction, viscosity and eddies. In order to describe the experimentally found velocity field, Magnus superimposed two velocity fields: the symmetrical flow around a non-rotating cylinder and the eddy-free circulation flow around a cylinder rotating in still air. Where the streamlines are close together, the speed is higher than elsewhere. In sum, the flow velocity on the side of the cylinder that rotates with the flow is greater than on the other side and, according to Bernoulli, the pressure is lower, so that the cylinder experiences a force at right angles to the flow direction.

Robins demonstrated the effect with the help of spherical projectiles from muskets , the barrels of which were slightly curved to the side. As a result, the ball in the barrel rolls laterally on the outer side with respect to the lateral bend of the barrel, and the ball is given a twist around the vertical axis. After leaving the barrel, the ball is clearly deflected to the side.

This explanation for the Magnus effect is successful in the sense that it can still be found today in the standard physics literature for the general case of dynamic lift . As a very special application of the energy law , the Bernoulli relation does not describe cause and effect, but only a functional relationship between the speed and pressure fields .

### Extensions when including the boundary layer and viscosity

Lyman Briggs (1959) extended Magnus' theory to include the influence of the boundary layer. Only here does a circulation flow arise through friction on the spherical surface. At the same time, the air on the side of the sphere facing away from the flow is released from the boundary layer ( boundary layer detachment ). This creates a flow outside the boundary layer that satisfies the Bernoulli relation.

If the sphere does not rotate, the separation of the boundary layers occurs symmetrically. The Magnus effect arises from the fact that, when the ball rotates, the boundary layer separates later on the side of the ball on which the flow is aligned with the direction of rotation of the ball. This gives the flow an impulse in the direction of the side of the ball that rotates against the flow. The counterforce to this is the lateral deflection force of the ball. This is illustrated by the sketch on the right: The flow hits the ball from the right and is deflected upwards - i.e. accelerated. The counterforce to this is the downward force on the ball.

## Useful examples

Flettner rotor as a ship drive

The following examples of deflected missiles are often associated with the Magnus Effect. In all cases, however, different effects occur at the same time. It is not obvious to what extent the Magnus Effect plays a role.

The effect can be tested interactively in the Magnus House in Berlin , and a board explains the process:

## literature

• G. Magnus: About the deviation of the projectiles, and: About a striking phenomenon in rotating bodies. In: Annals of Physics and Chemistry. Vol. 28, published by Johann Ambrosius Barth, Leipzig 1853, pp. 1–28. ( Full text in google book search)
• G. Magnus: About the deviation of the projectiles and about a striking phenomenon in rotating bodies. In: The progress of physics in 1853. Vol. 9, Berlin 1856, pp. 78–84. ( Full text in google book search)
• Ludwig Bergmann, Clemens Schaefer, Thomas Dorfmüller, Wilhelm T. Hering: Textbook of Experimental Physics. Vol. 1: Mechanics, Relativity, Warmth. de Gruyter, 1998, ISBN 3-11-012870-5 , p. 545 ff. ( Fluid mechanical forces on rotating bodies in the Google book search)
• Jearl Walker: The Flying Circus of Physics. Oldenbourg Wissenschaftsverlag, 2007, ISBN 978-3-486-58067-9 , pp. 92-94. ( Examples of Magnus Effect in Google Book Search)
• Thorsten Kray: Investigations into the flow processes in rotating smooth balls and soccer balls. Dissertation. University of Siegen 2008, online at d-nb.info, accessed on January 24, 2017 (PDF; 9.8 MB).

## Individual evidence

1. Gustav Magnus: About the deviation of the projectiles, and: About a striking phenomenon in rotating bodies. From the treatise of the Royal Academy of Sciences in Berlin for 1852, in: Annalen der Physik und Chemie. Volume LXXXVIII, No. 1, Berlin 1853, online at Uni-Jena.de, accessed on January 24, 2017 (PDF; 1.46 MB).
2. Magnus, 1852: "Robins, who first tried to explain the deviation in his Principles of Gunnery , believed that the deflecting force was generated by the bullet's own rotation, and this is currently widely believed."
3. Lord Rayleigh: On the irregular flight of a tennis ball. In: Scientific Papers. I, 344, pp. 1869-1881.
4. ^ Benjamin Robins: New principles of gunnery. Hutton, London 1742.
5. HM Barkla, LJ Auchterlonie: The Magnus or Robins effect on rotating spheres. In: Journal of Fluid Mechanics. Vol. 47, Issue 3, Cambridge June 1971, pp. 437-447, doi : 10.1017 / S0022112071001150 , online at Cambridge.org, accessed January 24, 2017.
6. Magnus, 1852: "Even though since Robins one has tried very differently to explain how a deviation of the projectile could occur through such a rotation, even the efforts of Euler and Poisson should not succeed in this."
7. Magnus 1852, p. 6: "Small wind vanes, which were very mobile, were used to indicate the changes in pressure that took place in the air flow during the rotation of the cylinder [...] If the cylinder was not rotated, both vanes took the direction of the airflow. As soon as the cylinder began to rotate, however, on the side where it was moving in the same direction with the air current, the plume turned towards the cylinder, while on the other, where the movement of the cylinder and the air current took place in the opposite direction , was averted. As a result, there was less air pressure on that side and greater air pressure on this side than in the state of rest. "
8. See also: RG Watts, R. Ferrer: The lateral force on a spinning sphere. In: Am. J. Phys. 55 (1), 1987, p. 40, doi : 10.1119 / 1.14969 .
9. For example: Lexicon of Physics. Spektrum, Akad. Verlag, Heidelberg 1999, ISBN 3-86025-293-3 .
10. ^ PA Tippler: Physics. Spektrum, Akad. Verlag, Heidelberg / Berlin / Oxford 1994, ISBN 3-86025-122-8 .
11. ^ Lyman J. Briggs: Effect of Spin and Speed ​​on the Lateral Deflection (Curve) of a Baseball; and the Magnus Effect for Smooth Spheres. In: American Journal of Physics. Vol. 27, Ed. 8, November 1959, p. 589, doi : 10.1119 / 1.1934921 , online at AAPT, accessed on January 24, 2017.