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

The Magnus effect is the name given to the physical phenomenon whereby a spinning object creates a whirlpool of rotating air or liquid about itself. On one side of the object, the motion of the whirlpool will be in the same direction as the windstream that the object is exposed to. On this side the velocity will be increased. On the other side, the motion of the whirlpool is in the opposite direction of the windstream and the velocity will be decreased. The pressure in the air is reduced from atmospheric pressure by an amount proportional to the square of the velocity, so the pressure will be lower on one side than the other causing an unbalanced force at right angles to the wind. This is a product of various phenomena including the Bernoulli effect and the formation of boundary layers in the medium around moving objects.

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.

This is not the only way of describing the Magnus force. The separation of the turbulent boundary layer of the flow from the ball 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 reason for 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). At smaller Reynold's numbers (slower speed, smaller ball, or higher viscosity), a reverse Magnus effect occurs. 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.

It is often referred to in the context of explaining otherwise mysterious but commonly observed movements of spinning balls in sport, especially tennis, volleyball, golf, baseball, association football (soccer) and cricket. The sport in which the effect is perhaps most starkly observed is table tennis, mostly due to the ball being very small and low in density. An experienced player can place a wide array of spins on the ball, the effects of which are an integral part of the sport itself. Table tennis bats usually have outer layers made of rubber to give the racket maximum grip against the ball to facilitate spinning.

Contrary to what some think, the Magnus effect is not responsible for the movement of a cricket ball seen in swing bowling, although it does contribute to the motion known as drift in spin bowling.

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

Example Equation

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

V = velocity of the ball

A = crossectional area of ball

Cl = lift coefficient

The lift coefficient is very dependent on the spin ratio ( (angular velocity*diameter)/(2* linear velocity) ) of the ball. Lift coefficient may be determined from graphs of experimental data using Reynolds number and spin ratio. Typical lift coefficients of a smooth ball range from 0.2 to 0.6 for spin ratios ranging from 0.5 to 4.5.

The Magnus effect in external ballistics, also known as 'spin drift'

Another context where the Magnus effect can be found is advanced external ballistics. A spinning bullet in flight is often subject to a sideways wind. In the simple case of horizontal wind, depending on the direction of rotation, the Magnus effect causes an upward or downward force to act on the projectile, affecting its point of impact. Even in a complete calm, with no sideways air movement at all, a real bullet will experience a small sideways wind component. This is because real bullets have a yaw motion that causes the nose of the bullet to point in a slightly different direction from the direction in which the bullet is actually traveling. This means that the bullet is "skidding" sideways at any given moment, and thus experiences a small sideways wind component.(yaw of repose) All in all, the effect of the Magnus force on a bullet is not significant when compared to other forces like drag. However, the Magnus effect has a significant role in bullet stability because the Magnus force does not act upon the bullet's center of gravity, but the center of pressure. This means that there is a Magnus force that affects the yaw of the bullet. The Magnus effect will act as a destabilizing force on any bullet with a center of pressure located ahead of the center of gravity, while conversely acting as a stabilizing force on any bullet with the center of pressure located behind the center of gravity. The location of the center of pressure depends on the flowfield structure, in other words, depending on whether the bullet is in super-sonic or sub-sonic flight. What this means in practice depends on the shape and other attributes of the bullet, in any case the Magnus force greatly affects stability because it tries to "twist" the bullet along its flight, twisting it either towards the axis of flight (stabilizing) or away from the axis of flight (destabilizing).

Flying Machine

Many ideas using this effect involve flying machines, as incorporating the lift from a rotating cylinder at the front of a wing would allow for flight at lower horizontal speed. [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 was yellow, consisted of a fan-like rotator generating the Magnus effect, and lifted with only a few feet of forward movement.

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.

References

• Watts, R.G. and Ferrer, R. (1987). "The lateral force on a spinning sphere: Aerodynamics of a =American Journal of Physics" 55 (1): 40.

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

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