Related Resources: calculators

Magnus Effect Calculator and Formula for Ball

Fluids Engineering and Design
Engineering Physics

Magnus Effect Calculator and Formula for Ball

The Magnus effect is the observed effect in which a spinning ball curves away from its principal flight path. In football, when a footballer strikes a ball off center, a spin force is applied. From the side the ball was struck, the motion of the ball is opposed by a drag force. Now, if we consider the opposite side of the ball, the result of the spin and drag force is the sum of their magnitude as both travel in the same direction. The asymmetry of force creates a pressure differential. This causes the ball to veer towards the region of low pressure; the side of the ball opposing the initial contact point.

Fig. 1. Forces on a spinning baseball in flight. The drag force F_D acts in the -v direction, the Magnus force F_m acts in the ω x v direction, and the force of gravity F_G acts downward.

When a spinning baseball travels through the atmosphere, it experiences the force of gravity in addition to the drag and Magnus forces, F_D and F_M, as shown in Fig. 1. Conventionally the magnitudes of these forces are parametrized as

Magnus force can be described with the following equation

Eq. 1
F_M = 1/2 · C_L · ρ · A · v²

Eq. 2
A = π · R²

Eq. 3
S = R ω / v

Declarations

A = cross sectional area of ball
F_D = Magnus force (lift)
ρ = air density (1.23 kg / m³ )
v = velocity
ω = angular velocity of ball (rpm)
R = radius
S = slip factor
C_D = drag coefficients

Figure 2, Experimental results for C_L

Download: The effect of spin on the flight of a baseball ( Free membership minimum required )

Related:

• Polar Mass Moment of Inertia About Axis A-A and B-B of Common Shapes
• Mass Moment of Inertia Equations
• Estimated Motor and Transmission Inertia and Drive Requirements
• Gear Drive Motor Mass Moment of Inertia Equation

Credits:

The effect of spin on the flight of a baseball
Alan M. Nathan
Department of Physics
University of Illinois