Magnus Force Calculator
Calculate Magnus force on spinning cylinders in fluid flow using the Kutta-Joukowski theorem
Calculate Magnus Force
Radius of the spinning cylinder
Length of the spinning cylinder
Angular velocity of cylinder rotation
Velocity of fluid flow around the cylinder
Magnus Force Results
Method: Kutta-Joukowski theorem
Parameters: ω = 20.00 rad/s, f = 3.18 rev/s, ρ = 1.225 kg/m³
Force Analysis
Example: Flettner Rotor Ship
Ship Propulsion System
Application: Flettner rotor for wind propulsion
Cylinder radius: 0.5 m
Cylinder length: 10 m
Angular velocity: 20 rad/s
Wind speed: 10 m/s
Air density: 1.225 kg/m³
Calculation Steps
1. Rotational speed: v_r = ω × r = 20 × 0.5 = 10 m/s
2. Vortex strength: G = 2πr × v_r = 2π × 0.5 × 10 = 31.42 m²/s
3. Magnus force: L = ρ × ℓ × v_free × G
4. L = 1.225 × 10 × 10 × 31.42 = 3,848 N
Magnus Effect Applications
Baseball Pitching
Curveball, slider, and knuckleball
Flettner Rotors
Wind-assisted ship propulsion
Table Tennis
Topspin and backspin shots
Soccer Free Kicks
Curved ball trajectories
Key Formulas
Kutta-Joukowski theorem
Vortex strength
Rotational speed
Angular velocity
Understanding the Magnus Effect
What is the Magnus Effect?
The Magnus effect is a phenomenon where a spinning object moving through a fluid experiences a force perpendicular to both its direction of motion and axis of rotation. This occurs due to the pressure gradient created by the interaction between the object's rotation and the fluid flow.
Physical Mechanism
- •Cylinder rotation creates velocity difference on opposite sides
- •Bernoulli's principle creates pressure gradient
- •Net pressure difference generates Magnus force
- •Force direction follows right-hand rule
Kutta-Joukowski Theorem
L = ρ × ℓ × vfree × Γ
where Γ = 2π × r × vr
- L: Magnus force (N)
- ρ: Fluid density (kg/m³)
- ℓ: Cylinder length (m)
- vfree: Free stream velocity (m/s)
- Γ: Circulation strength (m²/s)
- r: Cylinder radius (m)
- vr: Rotational speed (m/s)
Note: The alternative formulation L = 2πr²ρℓωvfreeis mathematically equivalent and often preferred for engineering calculations.
Factors Affecting Magnus Force
Geometry
- • Cylinder radius (squared effect)
- • Cylinder length (linear effect)
- • Surface roughness
- • End effects
Fluid Properties
- • Fluid density
- • Viscosity (Reynolds number)
- • Compressibility effects
- • Temperature effects
Motion Parameters
- • Free stream velocity
- • Rotation rate
- • Spin ratio (vr/vfree)
- • Flow direction