:: Magnus effect ::



I guess you have played table tennis before? Well, then you will have played also the top spin, giving the table tennis ball a fast rotation around its axis additional to the forward motion. It can be seen that the ball is devitated from a just ballistic curve, meaning that only the gravitational force would be acting on the ball. The ball trace curvature is either enhanced or weaken, depending on the sense of rotation of the ball. Have you ever asked yourself what this additional force comes from? Well, I did not, until I heared from the Magnus effect. The Magnus effect uses the fact that every unsymmetrical body exposed to oncoming flow will have a lift force perdendicular to the flow. The value and the sign of the lift force is determined by the so-called circulation. The circulation is the mathematical  projection of the velocity vector close to the boundary onto the boundary itself. Now you will say that a table tennis ball is purely symmetrical, so why should it experience a lift force? A non-rotating table tennis ball is symmetrical for the flow and will not experience a lift force, but a rotating ball is asymmetrical for the flow. It will therefore experience a lift force, the direction depends on the sense of rotation but will always be perpendicular to the oncoming flow. This observation is called Magnus effect and is valid for any rotating, symmetrical body (e.g. cylinder).


I designed an experiment to prove the Magnus effect acting on table tennis ball (see picture above). A table tennis ball is equipped with a metal axis right through its center line. One end of this axis is connected with a small electrical engine, which was fixed to a metal frame. The frame has the shape of an 'U', surrounding the table tennis ball. The other end of the table tennis ball axis was suspended with the frame as well. To make it clear, the frame carries the ball and the engine and is clinged to one end of a precise scale. Maybe you want to ckeck this sketch to get the right picture. The weight of the frame with the engine and the ball is calibrated. Then the whole apparatus is put into the stream of a ventilation. The ball will keep its horizontal position. If one puts eletrical power to the engine so that the ball rotates, one can see that the ball is deviated from its original horizontal position, either up or down depending of the sense of rotation. This proves the acting Magnus effect.

     The Magnus effect finds application in varies technical systems, e.g. even in a sailing boat. Maybe you have seen pictures of boats with toll cylinders on deck, wondering for what they are good for. Well, these cylinders are rotating and acting like sails for the boat. One can find some nice animations related to the Magnus effect, one of them is the following:

Another "illustration" of the Magnus effect is the following picture: It was send to me by Thomas Klein after hours of studying for a fluid dynamic exam, especially regarding the complex potential flow functions (the flow around a rotating cylinder can be mathematically represented by a superposition of three complex functions: a parallel flow, a source and a sink (giving a dipol)):