WOLFRAM SYSTEM MODELER

MagnusForce

Component calculating the magnus force

Diagram

Wolfram Language

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

Information

 

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.