The Effects of Air on the Balls  - Bernouilli's Principle and Magnus Effect

Bernouilli's Principle

The Bernouilli's Principle expresses the conservation of energy in the fluid.

"If all the forces acting on the fluid are conservatives, the total energy per unit volume remains constant".

When the fluids moves in the horizontal direction only, this principle will be:

Kinetic Energy per unit volume (1/2 density x square of velocity)  + Potential energy per unit volume associated with the pressure (p) = const.

In a horizontal pipe, the greater velocity, the lower the pressure, and conversely. This effect is used to produce the lift of an airplane. The design of wing profile is so that the air has a greater velocity above the wing surface than bellow it, which produces a lower pressure above. This results in a net resultant upward force E.

Magnus Effect

This effect was studied experimentally by Magnus in 1853. Impressing a rotation (spin) in a ping-pong ball, by example, the air effects cause sideways forces, which produces curve or drop balls or rising balls. These forces will move the ball faster on one side than the other, making the ball a curve. This effect is named "Magnus Effect" and is responsible by the switch of the ball of tennis or ping-pong launched  "with effect", to spinning rapidly about your own edge and result a net force named "Magnus Force" (fig.2), This force is similar to the force E in Bernoulli's Principle (fig. 1).

Figure 2 - Magnus Effect

Examples: Magnus Effect in a ping-pong match with the team (fig. 3a and 3b)
 

Figure 3a - Value of vertical acceleration approximatelly: 13,6 m/s2. Magnus Force is downward (-y). See this image in avi

Figure 3b - Value of vertical acceleration approximatelly: 8.7 m/s2. Magnus Force is upward (y). See this image in avi