WOLFRAM SYSTEM MODELER

MagnusForce

Component calculating the magnus force

Diagram

Wolfram Language

In[1]:=
SystemModel["EducationExamples.Physics.FreeKick.Components.MagnusForce"]
Out[1]:=

Information

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

Description: Coordinate system fixed to the component with one cut-force and cut-torque (non-filled rectangular icon)

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.