Magnus effect

The Magnus effect, demonstrated on a ball. Lines V represent the wind velocity, and the arrow F represents the resulting force towards the side of least pressure.

The Magnus effect is the phenomenon whereby a spinning object flying in a fluid creates a whirlpool 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.^[1]

Importance

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 airplanes.

History

German physicist Heinrich Magnus described the effect in 1852.^[2] However, in 1672, Isaac Newton had described it and correctly inferred the cause after observing tennis players in his Cambridge college.^[3][4] In 1742, Benjamin Robins (1707-1751), a British artillery engineer, explained deviations in the trajectories of musket balls in terms of the Magnus effect.^[5][6]

Principle

When a body (such as a sphere or circular cylinder) is spinning in a fluid, it creates a boundary layer 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 fluid close to the body is a little greater than V on one side and a little less than V on the other. This is because the induced velocity due to the boundary layer surrounding the spinning body is added to V on one side, and subtracted from V on the other. In accordance with Bernoulli's principle, where the velocity is greater the fluid pressure is less; and where the velocity is less, the fluid pressure is greater. This pressure gradient results in a net force on the body, and subsequent motion in a direction perpendicular to the relative velocity vector (i.e. the velocity of the body relative to the fluid flow).^[7]

Calculation of lift force

The Kutta–Joukowski theorem relates the lift generated by a right cylinder to the speed of the cylinder through the fluid, the density of the fluid, and the circulation.

The following equations demonstrate the manipulation of characteristics needed to determine the lift force generated by inducing a mechanical rotation on a ball.

F = lift force

ρ = density of the fluid

ω = angular velocity

r = radius of the ball

V = velocity of the ball

A = cross-sectional area of ball

l = lift coefficient

The lift coefficient l may be determined from graphs of experimental data using Reynolds numbers and spin ratios. The spin ratio of the ball is defined as ((angular velocity * diameter) / ( 2 * linear velocity)).

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 is commonly used to explain the often mysterious and commonly observed movements of spinning balls in sport, especially association football, table tennis, tennis,^[8] volleyball, golf, baseball, cricket and in various paintball marker brands.

The undesirable curved motion 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.^[9] Back-spin on a golf ball causes a vertical force that counteracts the weight of the ball a little, and allows the ball to remain airborne a little longer than would be the case if the ball were not spinning. This allows the ball to travel farther than it would if it were not spinning (about its horizontal axis).

In table tennis the Magnus effect is observable because of the small size and low density of the ball. An experienced player can place a wide variety of spins on the ball. Table tennis rackets usually have outer layers made of rubber to give the racket maximum grip on the ball to facilitate spinning.

However, the Magnus effect is not responsible for the movement of the cricket ball seen in swing bowling,^[10] 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 back-spin on a fired BB which will greatly increase its range, utilizing the Magnus effect in a similar manner as in golf.

In paintball the Magnus effect is used in one of the Tippmann paintball barrels, specifically the Flatline barrel. When a paintball is fired through the barrel it is lifted, giving the paintball a backspin, reducing the parabolic travel of fired paint, while increasing range. The use of these barrels has been frowned upon, seeing as how the backspin would reduce the speed of the ball lessening the chance of the ball breaking on impact, as well as reducing consistency. There are also various markers or aftermarket "undershot" bolts for markers that direct propellant gas at the base of the paintball in order to achieve the desired backspin.

In external ballistics

The Magnus effect can also be found in advanced external ballistics. Firstly, a spinning bullet in flight is often subject to a crosswind, 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 traveling. 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. (yaw of repose)

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 impacted because the Magnus effect acts on the bullet's center of pressure instead of its center 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 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 center 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 center of pressure is ahead of the center of gravity, the effect is destabilizing, if the center of pressure is behind the center 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. ^[11]

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 guidelines.^[12]

The iCar 101 project uses the Magnus effect in a roadable aircraft design. ^[13]

See also

• Flettner airplane
• Kite types
• Coandă effect
• Ball of the Century
• Rotor Ship

Notes

1. ^ Clancy, L.J., Aerodynamics, Section 4.6
2. ^ G. Magnus (1852) "Über die Abweichung der Geschosse," Abhandlungen der Königlichen Akademie der Wissenschaften zu Berlin, pages 1-23. See also: Gustav Magnus (1853) "Über die Abweichung der Geschosse, und: Über eine abfallende Erscheinung bei rotierenden Körpern" (On the deviation of projectiles, and: On a sinking phenomenon among rotating bodies), Annalen der Physik, vol. 164, no. 1, pages 1-29.
3. ^ Isaac Newton, "A letter of Mr. Isaac Newton, of the University of Cambridge, containing his new theory about light and color," Philosophical Transactions of the Royal Society, vol. 7, pages 3075-3087 (1671-1672). (Note: In this letter, Newton tried to explain the refraction of light by arguing that rotating particles of light curved as they moved through the aether as a rotating tennis ball curves as it moves through the air.)
4. ^ Gleick, James. 2004. Isaac Newton. London: Harper Fourth Estate.
5. ^ Benjamin Robins, New Principles of Gunnery: Containing the Determinations of the Force of Gun-powder and Investigations of the Difference in the Resisting Power of the Air to Swift and Slow Motions (London: J. Nourse, 1742). (On page 208 of the 1805 edition of Robins' New Principles of Gunnery, Robins describes the experiment in which he observed the Magnus effect: A ball was suspended by a tether consisting of two strings twisted together, and the ball was made to swing. As the strings unwound, the swinging ball rotated, and the plane of its swing also rotated. The direction in which the plane rotated depended on the direction in which the ball rotated.) See also: Tom Holmberg, "Artillery Swings Like a Pendulum..." in "The Napoleon Series". Available on-line at: http://www.napoleon-series.org/military/organization/c_velocity.html . See also: Steele, Brett D. (April 1994) "Muskets and pendulums: Benjamin Robins, Leonhard Euler, and the ballistics revolution," Technology and Culture, vol. 35, no. 2, pages 348-382.
6. ^ Newton's and Robins' observations of the Magnus effect are reproduced in: Peter Guthrie Tait (1893) "On the path of a rotating spherical projectile," Transactions of the Royal Society of Edinburgh, vol. 37, pages 427-440.
7. ^ Clancy, L.J., Aerodynamics, Figure 4.4
8. ^ Lord Rayleigh (1877) "On the irregular flight of a tennis ball," Messenger of Mathematics, vol. 7, pages 14-16.
9. ^ Clancy, L.J., Aerodynamics, Section 4.5
10. ^ Clancy, L.J., Aerodynamics, Figure 4.19
11. ^ NASA - Lift on rotating cylinders
12. ^ Magenn Power Inc Website
13. ^ iCar 101 roadable aircraft

References

• Watts, R.G. and Ferrer, R. (1987). "The lateral force on a spinning sphere: Aerodynamics of a curveball". American Journal of Physics 55 (1): 40. doi:10.1119/1.14969. 
• Clancy, L.J. (1975), Aerodynamics, Pitman Publishing Limited, London ISBN 0 273 01120 0

External links

• Analytic Functions, The Magnus Effect, and Wings at MathPages
• The Magnus Effect: or, Why do cricket balls swing and curveballs curve?
• How do bullets fly? Ruprecht Nennstiel, Wiesbaden, Germany
• How do bullets fly? old version (1998), by Ruprecht Nennstiel
• Anthony Thyssen's Rotor Kites page
• Has plans on how to build a model
• Harnessing wind power using the Magnus effect
• Technion Researchers Observe Magnus Effect in Light for First Time