Magnus effect
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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. 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.
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, association 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 bats usually have outer layers made of rubber to give the racket maximum grip on the ball to facilitate spinning.
Contrary to what some think, 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.
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.
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[edit] 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 = cross-sectional area of ball
- Cl = lift coefficient
The lift coefficient is dependent on the spin ratio ( (angular velocity*diameter)/(2* linear velocity) ) of the ball. The Lift coefficient may be determined from graphs of experimental data using Reynolds numbers and spin ratios. Typical lift coefficients of a smooth ball range from 0.2 to 0.6 for spin ratios ranging from 0.5 to 4.5.
[edit] The Magnus effect in external ballistics, also known as 'spin drift'
The Magnus effect can be found in advanced external ballistics. A spinning bullet in flight is often subject to a sideways wind. In the simple case of horizontal wind, the Magnus effect causes an upward or downward force that depends on the direction of the wind which affects the projectiles point of impact. Even in completely calm air, a bullet will experience a small sideways wind component. This is because 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 such as 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 the Magnus force 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, it depends 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 path, twisting it either towards the axis of flight (stabilizing) or away from the axis of flight (destabilizing).
[edit] Flying Machine
Many flying machines incorporate this idea 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.
[edit] See also
[edit] 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.
- ^ Gleick, James. 2004. Isaac Newton. London: Harper Fourth Estate.
[edit] 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
