Savonius Wind Turbine Power Calculation
Estimate the mechanical and electrical output of a Savonius vertical axis wind turbine using rotor dimensions, wind speed, air density, performance coefficient, generator efficiency, and optional tip speed ratio for RPM and torque estimation.
Calculator
Enter your rotor and operating parameters to calculate available wind power, rotor output, electrical output, estimated RPM, and torque.
Expert Guide to Savonius Wind Turbine Power Calculation
A Savonius wind turbine is one of the most recognizable vertical axis wind turbine designs. It uses drag rather than lift as the primary driving mechanism, which makes it mechanically simple, self starting, and tolerant of turbulent or shifting wind. Those advantages make it attractive for demonstration projects, rooftop experiments, remote sensing systems, small ventilation units, and educational builds. However, the same drag based principle that gives the Savonius its reliability also limits its aerodynamic efficiency compared with lift based machines such as horizontal axis turbines or Darrieus rotors. That is why correct power calculation matters. If you estimate output too optimistically, your turbine may underperform and your electrical system may be poorly matched.
The goal of Savonius wind turbine power calculation is to move from raw wind conditions and rotor dimensions to a practical estimate of shaft power and electrical power. The calculator above follows the standard engineering approach. First, it computes the wind power crossing the swept area of the rotor. Second, it applies a power coefficient, or Cp, which represents the fraction of available wind power that the rotor can capture mechanically. Third, it applies generator efficiency so the final result better reflects usable electrical output. If you also enter tip speed ratio, the calculator estimates rotational speed and torque, which are especially useful when sizing bearings, shafts, belt drives, direct drive alternators, or permanent magnet generators.
The core formula used in Savonius turbine power estimation
The fundamental wind power equation is:
Where P is wind power in watts, rho is air density in kilograms per cubic meter, A is the swept area in square meters, and V is wind speed in meters per second. For a Savonius rotor, the projected swept area is commonly estimated as:
Here, D is rotor diameter and H is rotor height. Once available wind power is known, actual rotor output is estimated as:
Finally, electrical power is:
In the calculator, generator efficiency is entered as a percentage and converted internally to decimal form. This is a practical way to approximate losses in the generator, rectifier, wiring, and sometimes even a charge controller if you want to treat the value as an overall drivetrain efficiency estimate.
Why Savonius turbines have lower power coefficients
A Savonius rotor captures energy mainly through differential drag. One blade or cup catches the wind while the returning blade resists it. Designers reduce this negative return drag through overlap tuning, blade shaping, end plates, helical twists, shielding, and multi stage geometry. Even so, Savonius machines typically operate at lower Cp values than lift based turbines. In many small practical builds, Cp falls around 0.10 to 0.20, while well optimized designs may approach 0.24 or a bit more in ideal conditions. This lower efficiency is not necessarily a disadvantage in every use case. For low wind startup, simplicity, and operation in gusty urban flow, the Savonius can still be an excellent choice.
| Turbine type | Typical Cp range | Typical TSR range | Starting behavior | Best use case |
|---|---|---|---|---|
| Savonius vertical axis | 0.10 to 0.25 | 0.7 to 1.2 | Very strong self starting | Low speed, turbulent, simple off-grid systems |
| Darrieus vertical axis | 0.25 to 0.40 | 3 to 6 | Often needs assistance | Higher efficiency vertical axis applications |
| Small horizontal axis | 0.30 to 0.45 | 5 to 8 | Good with proper design | Maximum energy capture in cleaner wind |
Step by step interpretation of the calculator inputs
- Rotor diameter: For a Savonius, diameter directly affects swept area and therefore power capture. A wider rotor intercepts more wind, but it can also increase structural loading and inertia.
- Rotor height: Height also scales swept area. If you double height and keep all else the same, ideal available wind power doubles.
- Wind speed: This is the most important input because power scales with the cube of wind speed. A change from 5 m/s to 10 m/s increases theoretical wind power by a factor of eight.
- Air density: Lower density at higher elevation or higher temperature reduces power. Sea level standard air density of 1.225 kg/m³ is often used for baseline calculations.
- Cp: This accounts for rotor aerodynamic performance. It is the single most important design quality factor after wind speed and area.
- Generator efficiency: A rotor may produce mechanical power that never fully appears as electrical power because of generator and electrical conversion losses.
- Tip speed ratio: The ratio of blade tip speed to wind speed helps estimate RPM and torque. Savonius turbines usually run with low TSR, so they develop relatively high torque at low rotational speed.
Worked example using realistic numbers
Assume a small Savonius rotor has a diameter of 1.2 m and a height of 2.0 m. The swept area is 2.4 m². If wind speed is 8 m/s and air density is 1.225 kg/m³, then available wind power is:
If the rotor has a Cp of 0.16, rotor mechanical power is approximately 120.4 W. With generator efficiency of 85 percent, the estimated electrical output is around 102.3 W. This result is useful because it immediately shows the difference between the large amount of energy flowing through the wind stream and the much smaller amount that can be captured and converted by a small drag based turbine. Many hobby builders expect several hundred watts from compact Savonius rotors at moderate wind speeds, but physics and Cp limits often bring real output much lower.
How RPM and torque are estimated
Rotational speed can be estimated from tip speed ratio using the relation between blade tip speed and rotor circumference. For a rotor of diameter D, the approximate RPM is:
Once RPM is known, angular velocity can be found and torque can be estimated from:
This is particularly useful for direct drive systems. Savonius turbines tend to produce lower RPM than many alternators prefer, so gearing or custom low speed generators are often required. The advantage is that shaft torque can be relatively high, especially during startup or at low speed operation. For pumping, mechanical agitation, or simple battery charging through a proper generator match, that can be beneficial.
Real world performance factors that reduce output
- Turbulence: Rooftops, trees, parapets, and nearby buildings create swirling flow that can dramatically reduce net energy capture.
- Poor siting: A perfectly built rotor in bad wind performs worse than an average rotor in clean wind.
- Mechanical losses: Bearings, misalignment, seals, belts, and couplings reduce shaft power delivered to the generator.
- Generator loading mismatch: If electrical loading is too heavy at startup, the turbine may stall. If too light, energy extraction may be poor.
- Unrealistic Cp assumptions: Marketing claims sometimes exaggerate performance. Conservative estimates are safer for design.
- Air density variation: Hot weather and high altitude reduce available wind power.
- End effects and geometry limitations: Simple barrel designs may not match the performance of carefully optimized helical or end plate equipped rotors.
Typical air density values and effect on power
Air density can alter expected output by a meaningful margin. Standard sea level air is commonly taken as 1.225 kg/m³. At moderate elevation or on hot days, density drops, reducing both available wind power and turbine output. The table below shows how much available wind power crosses a 2.4 m² swept area at 8 m/s under different density conditions.
| Condition | Approx. air density (kg/m³) | Available wind power at 8 m/s on 2.4 m² area | Change vs 1.225 kg/m³ |
|---|---|---|---|
| Cold dense air near sea level | 1.30 | About 798.7 W | +6.1% |
| Standard sea level | 1.225 | About 752.6 W | Baseline |
| Warm conditions | 1.15 | About 706.6 W | -6.1% |
| Higher elevation or hot air | 1.00 | About 614.4 W | -18.4% |
How to choose a realistic Cp for your design
If you have no measured performance data, a Cp value of 0.15 to 0.18 is a practical starting range for many small Savonius designs. Use the lower end if the rotor is a basic two bucket build, poorly optimized, or expected to run in rooftop turbulence. Use the middle to upper end if the machine includes end plates, optimized overlap, smoother blade geometry, and better mechanical integration. For concept studies or investor facing estimates, be careful with values above 0.20 unless you have test data from a controlled experiment or a reputable published source. Conservative modeling protects the credibility of the project.
Best practices for accurate Savonius power calculation
- Measure wind speed at hub height rather than relying only on regional averages.
- Use local air density where possible, especially for mountain or desert sites.
- Estimate annual energy, not just peak power, because average production matters more than occasional bursts.
- Model system losses honestly, including rectifier drop, controller losses, battery charging inefficiency, and cable losses.
- Compare calculated values with real test data after installation and refine Cp and efficiency assumptions.
When a Savonius turbine is the right choice
A Savonius rotor is often selected when simplicity and starting torque matter more than absolute efficiency. It can be a good fit for educational experiments, hybrid vertical axis concepts, low speed ventilation, signage, art installations, sensor platforms, and small charging systems in places where wind is variable and direction changes frequently. It is less ideal when the sole objective is maximizing kilowatt hours per square meter of swept area. In that case, a well designed horizontal axis turbine usually wins.
Authoritative resources for deeper study
For reliable background on wind energy fundamentals, turbine performance, and small wind system design, review these authoritative sources:
- U.S. Department of Energy Wind Energy Technologies Office
- National Renewable Energy Laboratory wind research
- U.S. Department of Energy guide to planning a small wind electric system
Final takeaway
Savonius wind turbine power calculation is straightforward in formula but highly sensitive to assumptions. Wind speed, swept area, and air density define the raw energy flowing through the rotor. Cp determines how much of that energy your Savonius can capture mechanically. Generator efficiency determines how much becomes usable electricity. By combining these values carefully, you can produce a realistic estimate rather than a marketing number. Use the calculator above to test design scenarios, compare rotor sizes, evaluate how higher wind speed changes output, and understand why proper siting is often more important than minor geometry tweaks. In small wind design, accurate assumptions are the foundation of better results.