What is the Magnus effect and how to calculate it:

The Magnus effect uses principals from Bernoulli's equation. Bernoulli's equation states that if the velocity of a moving fluid increased, the pressure must decrease. (at ideal conditions, constant elevation)

Bernoulli's equation with constant elevation:

P+(1/2)dv^2= C   ......(eq.1)

In solving for P we get:

P=C-(1/2)dv^2   ......(eq.2)


P =Pressure

d=The flowing fluid of constant density

v= Velocity of the fluid

C= constant

From Equation 2 we can see that pressure on the system is reduced when velocity is increased.

This is how an airplane wing creates lift.  Air is forced to travel a longer distance over the top of the wing than the air underneath.  The air above the wing is being forced to cover a greater distance in the same amount of time as the air passing under the wing.  This in turn means that the velocity of the air above the wing is greater than that passing under. This velocity difference leads to a pressure difference, high pressure under the wing, low pressure above the wing.  This difference in pressures causes lift.

The Magnus Effect

Spinning objects traveling through a viscus fluid act much like an airfoil (airplane wing)

       Spinning object

First described in 1852 by Heinrich Magnus, the Magnus effect is a force generated by a spinning object traveling through a viscus fluid.  The force is perpindicular to the velocity vector of the object.  The direction of spin dictates the orientation of the Magnus force on the objecc.  The orientation of the force can change but it is important to remmeber that it is always perpindicualr to the direction of fluid.

Like an areofoil the rotation of the object forces some air to take a longer path around the spinning object.  This air moves faster to cover the greater distance around the object in the same amount of time.  The image above shows a ball rotating clockwise, we can see that the airstreams are pulled under the ball by its rotation.  The resulting Magnus force is in the downward direction perpindicular to the direction of the air.

The force of the Magnus effect can be calculated with the following equation:

Fm = S (w × v)

Fm =the Magnus force vector

w= angular velocity vector of the object

v=Velocity of the fluid (or velocity of object, depends on perspective)

S= air resistance coefficient across the surface of the object

Once Fm is found we can use the basic kinematic equations to predict the characteristics of spinning objects in flight. 

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