Savonius Wind Turbine: Principles, Power Equation, and Design Optimization
Introduction
The Savonius wind turbine is a vertical-axis wind turbine (VAWT) that operates on the principle of drag difference rather than aerodynamic lift. Invented by Finnish engineer Sigurd J. Savonius, it is widely known for its simplicity, self-starting capability, and ability to operate in low and turbulent wind conditions.
While it is not suitable for large-scale power generation, the Savonius turbine is extremely valuable for small power applications, urban environments, and educational and experimental setups.
Working Principle
A Savonius turbine consists of two or more curved blades, typically half-cylinders, mounted vertically on a rotating shaft.
When wind flows across the rotor:
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The concave side of the blade experiences high drag
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The convex side experiences lower drag
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The difference in drag forces produces a net torque
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The rotor rotates regardless of wind direction
Because it relies on drag rather than lift, the turbine starts rotating at very low wind speeds.
Key Characteristics
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Vertical-axis configuration
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Omnidirectional wind acceptance
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Drag-based operation
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High starting torque
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Low rotational speed
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Quiet operation
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Simple construction
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Low maintenance
These properties make the Savonius turbine particularly suitable for rooftop installations and hybrid renewable systems.
Power Available in Wind
The power contained in moving air is given by the standard wind power equation:
P_wind = 0.5 * rho * A * V^3
where:
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P_wind = power available in wind (watts)
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rho = air density (kg/m^3), typically 1.225
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A = swept area of the turbine (m^2)
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V = wind speed (m/s)
Power Extracted by a Savonius Turbine
A turbine can extract only a fraction of the available wind power. This fraction is expressed using the power coefficient (Cp).
P = 0.5 * rho * A * V^3 * Cp
For Savonius turbines:
Cp ≈ 0.15 to 0.25
This is significantly lower than lift-based turbines but acceptable for low-speed, high-torque applications.
Swept Area of a Savonius Rotor
Unlike horizontal-axis turbines, the swept area of a Savonius rotor is rectangular, not circular.
A = H * D
where:
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H = rotor height (m)
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D = rotor diameter (m)
Using a circular area formula is incorrect for vertical-axis turbines.
Final Power Equation (Design Equation)
Substituting the swept area:
P = 0.5 * rho * H * D * V^3 * Cp
This is the working power equation used for Savonius turbine design and sizing.
Tip Speed Ratio (TSR)
The tip speed ratio indicates how fast the blade tip moves relative to wind speed.
TSR = (omega * R) / V
where:
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omega = angular speed (rad/s)
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R = rotor radius (m)
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V = wind speed (m/s)
For Savonius turbines:
TSR ≈ 0.8 to 1.2
This low TSR explains the turbine’s high torque and low rotational speed.
Example Power Calculation
Assume:
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Rotor height H = 1.2 m
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Rotor diameter D = 0.8 m
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Wind speed V = 6 m/s
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Air density rho = 1.225 kg/m^3
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Power coefficient Cp = 0.20
P = 0.5 * 1.225 * 1.2 * 0.8 * 6^3 * 0.20
P ≈ 32 watts
This illustrates why Savonius turbines are best suited for small-scale power generation.
Design Optimization of Savonius Turbines
Although efficiency is inherently limited, careful design optimization can significantly improve performance and reliability.
1. Overlap Ratio
The overlap ratio is defined as:
Overlap ratio = e / D
where:
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e = overlap distance between blades
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D = rotor diameter
The overlap allows airflow from the advancing blade to reduce negative torque on the returning blade.
Optimal range:
e / D ≈ 0.15 to 0.18
Too little overlap causes poor starting torque.
Too much overlap causes excessive leakage and power loss.
2. Aspect Ratio
The aspect ratio is defined as:
Aspect ratio = H / D
where:
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H = rotor height
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D = rotor diameter
Aspect ratio affects flow uniformity, end losses, and structural behavior.
Recommended range:
H / D ≈ 0.8 to 1.2
Lower values increase end losses.
Higher values increase structural bending and vibration.
3. Helical (Twisted) Blades
In a helical Savonius turbine, the blades are twisted along the height of the rotor, typically by 60 to 120 degrees.
Advantages:
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Smoother torque output
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Reduced vibration
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Lower noise
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Improved bearing life
Optimal twist:
Helical twist ≈ 90 degrees
Helical designs slightly reduce peak torque but significantly improve usable, continuous power.
Combined Optimized Design Parameters
A well-optimized Savonius turbine typically uses:
Overlap ratio (e/D) ≈ 0.15 – 0.18
Aspect ratio (H/D) ≈ 0.9 – 1.1
Helical twist ≈ 90 degrees
Such designs can achieve:
Cp ≈ 0.22 – 0.25
which is close to the practical maximum for drag-based turbines.
Limitations
Despite optimization, Savonius turbines remain limited by:
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Inherent drag losses
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Flow separation
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Counter-drag on returning blades
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Wake interference
They are not suitable for large-scale power generation.
Applications
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Rooftop wind systems
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Battery charging
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Water pumping
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Ventilation
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Hybrid solar-wind systems
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Educational demonstrations
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Urban and low-wind environments
Conclusion
The Savonius wind turbine is not designed for maximum aerodynamic efficiency, but for robust, low-speed, high-torque energy extraction. When properly optimized using overlap ratio, aspect ratio, and helical blades, it becomes a highly reliable solution for small-scale and urban renewable energy applications.
