WOLFRAM SYSTEM MODELER

# MagnusForce

Component calculating the magnus force # Wolfram Language

In:= `SystemModel["EducationExamples.Physics.FreeKick.Components.MagnusForce"]`
Out:= # Magnus Force Calculation

## Magnus Force

The Magnus force is dependent on the geometry and size of the object, the density of the air, the spin factor, the velocity of the object, and the so-called Reynolds number. In this implementation, the equation describing the Magnus force has been taken from the book Physics for Game Programmers, equation 7.56 on page 194, defined as:

• FM = (1/2) ρ v^2 A CL

where ρ is the air density, v is the velocity of the ball, A is the cross-sectional area of the ball, and CL is the lift coefficient. The lift coefficient is a tricky variable to describe and is normally measured from experiments. In Physics for Game Programmers, experimental data is used to create a function to describe CL. This results in the expression:

• CL = 0.385(r*ω/v)^0.25

where r is the radius of the ball, ω is the angular velocity, and v is the velocity of the ball.

# Parameters (1)

rho Value: 1.225 Type: Density (kg/m³) Description: Density of the fluid (1.225 kg/m^3 for air)

# Connectors (1)

 frame_b Type: Frame_b

# Components (1)

 force Type: WorldForce Description: MultiBody force component applying the Magnus force

# Used in Components (1) Ball EducationExamples.Physics.FreeKick.Components Ball subject to magnus forces.