The interactive animation illustrates the forces acting in the rotor plane of a wind turbine. These forces account for a large part of the loads to which a rotor is subjected.
The magnitude of the tangential force can be continuously adjusted via a controller. The tangential force arises from the lift generated when the wind strikes the rotor blades. Additional forces are also shown, including the enormous resultant total force, which results from the sum of all acting forces.
Instructions for Use
After starting the application, you can view the animation in full-screen mode. To do this, click on “View” and then on “Full screen”:
To exit full screen mode, press the Esc key.
Description of the Animation
The following forces are visualised:
- Tangential force FT
- Weight force FW
- Resulting force FRes
- Centrifugal force FC
- Total force FTot
- Motive force FMot
The tangential force results from the lift force (not shown in the animation) that is generated on the rotor blades. The tangential force can be seen as the component of the lift force that is visible when looking at the rotor plane. The lift force or the tangential force depends on the wind speed, the angle of attack of the rotor blades and the rotational speed.
The weight force is caused by the weight of the rotor blades. This force is always directed downwards.
The tangential force and the weight force together form the resulting force FRes.
If the centrifugal force is also added, the resulting force is the total force FTot.
The total force changes during one rotation and can deform the rotor blade. The magnitude of the total force is an important constraint that must be taken into account when designing a rotor blade.
The motive force FMot is the effective component of the total force on which the acceleration of the rotor depends.
The magnitude of the motive force also changes during a rotation. There may also be cases where the motive force is temporarily opposite to the direction of rotation.
The animation only shows the forces that can be displayed when looking at the rotor plane. The rotor blades must also withstand the force exerted by the wind flowing in from the front. This force is not shown in the animation.
Physical Background: How Does the Tangential Force Arise?
The rotor blades of a wind turbine are shaped like aerofoil profiles – similar to aircraft wings. When wind flows over the blade, the air moves faster across the curved upper surface than along the flatter lower surface. According to Bernoulli’s principle, this speed difference creates a pressure difference: lower pressure on the upper surface, higher pressure on the lower surface. The result is an aerodynamic lift force perpendicular to the direction of airflow.
This lift force does not act in the rotor plane, but at an angle to it. When decomposed into components, two forces emerge:
- The tangential force (FT) – the component in the rotor plane that drives the rotation
- The thrust force – the component perpendicular to the rotor plane, pushing against the tower (not shown in this animation)
The tangential force shown in the animation is therefore the “useful” portion of the aerodynamic lift – the part that actually makes the rotor turn. Its magnitude depends on the wind speed, the angle of attack of the blade, and the rotational speed. The related animation Aerodynamic Lift illustrates this relationship in detail.
Why Does the Load Change During One Rotation?
One of the most important insights the animation provides is that the forces on a rotor blade are never constant – they change continuously as the blade moves through its circular path. This is primarily due to the interaction between the tangential force, the weight force and the centrifugal force:
- Blade at the top (12 o’clock position): The weight force pulls the blade downward, away from the hub. It acts in the same radial direction as the centrifugal force – both point outward. The tangential component of the weight force opposes the direction of rotation, reducing the net motive force.
- Blade at the bottom (6 o’clock position): The weight force still acts downward, but now the blade is below the hub. The tangential component of the weight force now supports the direction of rotation. The motive force reaches its maximum.
- Blade at the side (3 or 9 o’clock position): The weight force acts perpendicular to the blade’s radial direction, causing a bending load rather than directly aiding or opposing rotation.
The result is a cyclically varying total force that the blade experiences with every single revolution. This cyclic loading is the central engineering challenge in rotor blade design.
Practical Relevance: Material Fatigue and Service Life
The cyclic load variation described above has a direct consequence for the structural integrity of rotor blades: material fatigue. Every revolution subjects each blade to a complete load cycle – tension, compression, and bending alternate continuously.
A modern wind turbine rotates approximately 10–20 times per minute. Over a typical service life of 20–25 years, this adds up to roughly 100 million to 500 million load cycles (108–109). For comparison, an aircraft wing experiences far fewer load cycles during its entire operational life.
Engineers use so-called S-N curves (also known as Wöhler curves) to predict how many load cycles a material can withstand at a given stress amplitude before failure. Rotor blades are typically constructed from glass-fibre or carbon-fibre reinforced composites, which offer an excellent strength-to-weight ratio and good fatigue resistance. Despite this, the cyclic loading remains the primary factor limiting a blade’s service life.
Orders of Magnitude: Real-World Numbers
Abstract force diagrams become much more tangible with concrete numbers. Here are some typical values for a modern 3 MW onshore wind turbine with a rotor diameter of approximately 120 m:
- Blade mass: approx. 12,000–15,000 kg per blade
- Weight force per blade: approx. 120–150 kN (equivalent to the weight of about 10–12 cars)
- Rotational speed: approx. 10–15 revolutions per minute
- Tip speed: up to 80 m/s (approx. 290 km/h)
- Centrifugal force per blade: approx. 300–600 kN at rated speed
- Blade length: approx. 60 m – longer than the wingspan of an Airbus A380
These numbers illustrate why the interplay of forces shown in the animation is so critical: even seemingly small percentage changes in the tangential force can translate into load variations of tens of kilonewtons at the blade root.
Which Forces Are Not Shown – and Why?
The animation deliberately focuses on the forces visible in the rotor plane – the plane in which the blades rotate. However, a rotor blade in operation is subject to additional significant forces that act perpendicular to this plane:
- Thrust force (axial force): The wind pushes against the rotor disc from the front. This thrust force is the largest aerodynamic load on the turbine and must be absorbed by the tower and foundation. On a 3 MW turbine, the thrust force can reach 300–500 kN at rated wind speed. Because this force acts along the rotor axis (perpendicular to the rotor plane), it cannot be represented in the 2D front view shown in the animation.
- Gyroscopic forces: When the nacelle yaws (rotates horizontally to follow changing wind directions) while the rotor is spinning, gyroscopic effects create additional bending moments on the blades and the main shaft.
- Turbulent and gusty loads: Real wind is not uniform. Wind shear (the increase in wind speed with height) means that a blade at the top of its arc experiences stronger wind than at the bottom, adding further cyclic variation beyond what is shown in the animation.
Understanding which forces are shown and which are omitted helps put the animation in the right context: it provides a clear picture of the in-plane loads, while the full structural analysis of a rotor blade must also account for the out-of-plane forces described above.
Scaling Effects: Small vs. Large Wind Turbines
The force relationships shown in the animation change dramatically as wind turbines are scaled up. This is one of the central challenges of modern wind energy engineering:
- Weight force scales with volume (proportional to the cube of the blade length), while the aerodynamic forces scale with area (proportional to the square of the blade length). This means that as blades get longer, their weight grows faster than the forces that drive them – the so-called square-cube law.
- A small turbine (e.g. 50 kW, blade length ~8 m, blade mass ~50 kg): The weight force is almost negligible compared to the aerodynamic forces. The cyclic load variation due to gravity is minimal.
- A large offshore turbine (e.g. 15 MW, blade length ~110 m, blade mass ~50,000 kg): The weight force per blade exceeds 500 kN. The cyclic bending caused by gravity with each revolution becomes the dominant fatigue driver – far more significant than in smaller turbines.
This scaling effect explains why modern large turbines require advanced materials such as carbon-fibre composites, sophisticated structural designs, and active load control systems (such as individual pitch control) to manage the enormous cyclic loads. When observing the animation, consider how dramatically the force vectors would differ if the blade were ten times longer and a thousand times heavier.
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Overview and Download
| Title | Forces on the rotor of a wind turbine |
| Target Audience | Teachers and lecturers |
| Platforms | Microsoft® Windows® Apple® Macintosh® (version-dependent) |
| Features | Full-screen mode Lossless scaling Large screens and projectors supported |
| License | Freeware |
| Download | Contact |
Contributors
C. Hein, S. Rikowski
Sources
- Authoring tool (control elements supplied): Adobe Animate