The following animation illustrates the forces acting on the rotor of a wind turbine in the rotor plane. The various force components and their vector addition are displayed dynamically during rotation.
Links
Description of the Animation
The animation shows a simplified wind turbine rotor with three blades in a top-down view. Pressing the Start button initiates the rotation, with the forces acting on the rotor blades being continuously updated.
The following forces are illustrated:
- Gravitational Force FG (blue): The weight of the rotor blade, always acting vertically downward
- Tangential Force FU (gray): Tangential component of the aerodynamic lift force
- Centrifugal Force FF (purple): Radially outward inertial force caused by the rotation
- Resultant Force FRes (green): Vector sum of gravitational force and tangential force
- Total Force FTotal (orange): Vector sum of the resultant force and centrifugal force
- Driving Force FDrive (yellow): Tangential component of the total force
Interactive Controls
The checkboxes on the right side allow individual forces and auxiliary elements to be shown or hidden:
- Individual force vectors (FG, FU, FF, FRes, FTotal, FDrive)
- Parallelograms: Show the graphical vector addition using the force parallelogram method
- Connection Lines: Dashed auxiliary lines between the total force and the driving force
The parallelograms visualize the step-by-step addition:
- FG + FU = FRes (green parallelogram)
- FRes + FF = FTotal (orange parallelogram)
Physical Background
The tangential force results from the aerodynamic lift generated when the wind strikes the rotor blades. It is the effective component of the lift force in the rotor plane and depends on the wind speed, the pitch angle of the rotor blades, and the rotational speed. In this animation, the tangential force is assumed to be constant.
The gravitational force acts due to the weight of the rotor blades and is always directed downward. During rotation, the position of the rotor blades relative to the direction of gravity changes continuously.
The centrifugal force acts radially outward and arises from the rotation of the rotor. It is proportional to the square of the angular velocity and the mass of the rotor blade.
The total force FTotal is the vector sum of all acting forces. It changes continuously in both magnitude and direction over the course of one revolution and can cause deformation of the rotor blade. The magnitude of the total force is a critical design parameter that must be considered in the structural design of a rotor blade.
The driving force FDrive is the tangential component of the total force — the projection of the total force onto the direction of rotation. It determines the acceleration and the torque of the rotor. The magnitude of the driving force also varies during one revolution. In certain positions, the driving force may temporarily oppose the direction of rotation.
Simplifications in the Animation
The animation only depicts the forces that are visible in the rotor plane when viewed from above. In reality, the rotor blades must also withstand the force exerted by the wind flowing from the front (thrust force). This axial force component is not shown in this animation.
The tangential force is assumed to be constant in this animation. In reality, it varies depending on the wind speed, turbulence, and the position of the rotor blade.
Practical Significance
- Rotor Blade Design: The alternating loads determine material selection and dimensioning
- Fatigue: Cyclic loading from periodically changing forces can lead to material fatigue
- Performance Optimization: The driving force determines the torque and thus the power output
- Control: Modern wind turbines adjust the pitch angle of the rotor blades to optimize loading conditions