Magnus effect

The Magnus effect is the phenomenon whereby a object spinning in a fluid creates a whirlpool of fluid around itself, and experiences a force perpendicular to the line of motion and away from the direction of spin. 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. 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 some flying machines.

German physicist Heinrich Magnus first described the effect in 1853, but according to James Gleick ^[1] Isaac Newton described it and correctly theorised the cause 180 years earlier, after observing tennis players in his Cambridge college.

Principle

The separation of the turbulent boundary layer of the flow from the object is delayed on the side that is moving in the same direction as the free stream flow, and is advanced on the side moving against the flow. The flow is deflected toward the side moving against the flow, and this momentum change in the flow is balanced by a momentum change in the object in the opposite direction. When boundary layers make the transition from laminar to turbulent, they separate later (the separation point moves downstream). This is the purpose of the dimples on a golf ball: they energise the boundary layer, inducing turbulence which helps to reduce pressure drag due to late flow separation (see drag).

A reverse Magnus effect occurs at smaller Reynold's numbers (slower speed, smaller ball, or higher viscosity). When the boundary layer on the side moving with the flow is laminar and the boundary layer on the side moving against the flow is turbulent, the turbulent boundary layer separates later, deflecting the flow toward the side moving with the flow, resulting in a force in the opposite direction as the Magnus effect.

Calculation of lift force

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

{F}={1 \over 2}{\rho }{V^{2}Al}

F = lift force

$\rho$ = density of the fluid

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&nbsp* 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 tennis, volleyball, golf, baseball, football (soccer) and cricket.

The sport where the effect is most striking is table tennis because of the small size and low density of the ball. An experienced player can place a wide variety of spins on the ball, which is an integral part of the sport. 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, although it does contribute to the motion known as drift in spin bowling.

In external ballistics

The Magnus effect can be found in advanced external ballistics. First a spinning bullet or missile in flight is often subject to a crosswind. If the crosswind is exactly perpendicular, the Magnus effect causes an upward or downward force on the bullet. This force can cause an observable deflection in the bullet's flight.

Even in calm air, a bullet experiences a small sideways wind component due to yaw motion. This causes the nose of the bullet to point in a slightly different direction from the direction in which the bullet is traveling (i.e., the bullet is "skidding" sideways at any given moment, and thus experiences a small sideways wind component). (yaw of repose)

The effect of the Magnus force on a bullet is usually insignificant compared to forces such as aerodynamic drag. However, it greatly affects the bullet's stability because it acts on the bullet's center of pressure but not its center of gravity. Thus it affects the yaw angle of the bullet: it tends to twist the bullet along its flight path, either towards the axis of flight (stabilizing) or away from the axis of flight (destabilizing). It is destabilizing if the bullet's center of pressure is ahead of the center of gravity, and stabilizing if the center of pressure is behind the center of gravity. The location of the center of pressure depends on the flowfield structure, which depends on the bullet's speed (super-sonic or sub-sonic), shape, density and surface features.

In flying machines

Many flying machines incorporate use of the Magnus effect by generating lift with a rotating cylinder at the front of a wing that allows flight at lower horizontal speeds. [1] (Flettner rotor plane)

A remote controlled prototype was featured on the DIY network show, "Radio-Control Hobbies" that used the Magnus effect as the primary lift and thrust mechanism. It consisted of a fan-like rotator generating the Magnus effect which allowed it to lift off after traveling only a few feet forward.^{[citation needed]}

A series of prototypes were built of a design called FanWing. Wind-tunnel tests were conducted in 1998 by Pat Peebles at the University of Rome.

A patent was filed by Fred Ferguson in the 1980's for an airship which used the Magnus effect as its primary lift and propulsion.

The Rotor and UFO kites use the Magnus effect for lift.

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.{{cite journal}}: CS1 maint: multiple names: authors list (link)

^ Gleick, James. 2004. Isaac Newton. London: Harper Fourth Estate.

External links

[1] Gleick, James. 2004. Isaac Newton. London: Harper Fourth Estate.

[1]