Compute the power coefficient Cp, torque, recommended RPM and annual energy of a Savonius VAWT in real time. Vary rotor diameter and height, bucket arrangement, overlap ratio and wind speed to design small wind turbines for urban rooftops, off-grid power, water pumping or classroom demonstrations.
Parameters
Rotor diameter D
m
Rotor height H
m
Bucket arrangement
2-stage helical balances self-start and smoothness
Overlap ratio e/D
Optimum near 0.15; Cp drops away from the peak
Aspect ratio H/D
1.5–2.0 is stable; low AR increases tip losses
Wind speed V
m/s
Air density ρ
kg/m³
Application
Application drives noise limits and start-up wind
Results
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Swept area (m²)
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Cp power coefficient
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Wind power (W)
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Extracted power (W)
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Recommended RPM
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Annual energy (kWh/y)
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Savonius VAWT — Cross-section animation
Helical S-shaped buckets rotate around the vertical shaft. Blue arrows show the incoming wind; white arrows show the advancing and returning bucket velocities.
Cp–TSR curve (Savonius characteristic)
Cp comparison across bucket arrangements
Theory & Key Formulas
$$A = D \cdot H, \qquad P_{\text{avail}} = \tfrac{1}{2}\,\rho\,A\,V^{3}$$
Swept area A (projected) and wind kinetic-energy flux P_avail. ρ is air density and V the incoming wind speed.
Extracted power P_ext and power coefficient Cp. Cp_max depends on overlap ratio (peak 0.18 at 0.15) and f_arr is the bucket-arrangement factor (2-stage helical = 0.85, single = 1.0, 3-stage staggered = 0.78, twisted-S = 0.90).
$$N = \text{TSR}\cdot\frac{V}{R}\cdot\frac{60}{2\pi}, \qquad T = \frac{P_{\text{ext}}}{N\cdot 2\pi/60}$$
Recommended RPM N (TSR=0.8) and shaft torque T. R = D/2 is the rotor radius. Savonius features low TSR and high torque.
A Savonius rotor looks like a steel drum cut in half and offset to make an S. Does that thing really catch enough wind to make electricity? It looks terribly inefficient.
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Good instinct. Yes, the efficiency is poor — the theoretical Cp ceiling is around 0.20, less than half of a horizontal-axis (HAWT) rotor at 0.45–0.50. But you do not pick a wind turbine on efficiency alone. Savonius will spin in any wind direction and self-starts at 2–3 m/s. In a turbulent urban environment where wind direction shifts second-by-second, that "always-on" behaviour is more valuable than peak Cp.
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So even with a low Cp, the longer running hours pay off? I set "2-stage helical" and the panel says Cp = 0.153. Is that a good number?
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For a Savonius, 0.153 is a perfectly respectable working figure. A pure single-stage S can hit 0.18, but going helical drops you to 85% of that. In return you get continuous torque at every angle, the cogging vanishes, the start-up wind drops further, and the vibration noise into a direct-drive generator falls dramatically. For a rooftop unit, Cp = 0.153 is exactly the trade you want.
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The tool says "TSR = 0.8". The HAWT articles I read mention TSR = 7. What is going on?
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TSR is the tip-speed ratio, the bucket tip speed divided by wind speed. Savonius is drag-driven: once the tip moves faster than the wind, the advancing bucket loses its pushing force. So peak Cp lands at TSR ≈ 0.8–1.0. Lift-driven propellers need TSR = 6–8 to reach the right angle of attack. At 6 m/s wind a 1.2 m Savonius spins around 76 RPM; a propeller of the same size would be near 760 RPM. Low RPM is awkward for off-the-shelf generators but ideal for pumps or classroom rigs.
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The annual energy is 85 kWh/y. How big is that in human terms — does it power a house?
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Not even close. A typical household uses 4,000–5,000 kWh/y, two orders of magnitude more. A small Savonius is realistic for an LED street light (100–150 kWh/y), a single outdoor camera, or a Wi-Fi repeater. And the 85 kWh/y figure assumes a 20% capacity factor — real urban rooftops usually deliver half of that, 40–60 kWh/y. You store the harvest in a battery and use it during peak hours.
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So to power a house with wind you really need a tall HAWT, not a Savonius on the roof?
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Exactly. A 3 m-rotor HAWT can supply a household, but planting one in a residential area triggers fights over noise, visual impact and low-frequency vibration. The Savonius wins because it is small, quiet and omnidirectional. The right framing is "auxiliary, educational or decorative power". Hybrid setups with solar — sun by day, wind at night and on cloudy days — are increasingly common.
Frequently Asked Questions
Savonius is a drag-type machine. The advancing bucket is pushed by the wind, but the returning bucket also moves against the wind and produces negative torque. The net torque is small, and the theoretical upper-bound Cp is only around 0.20. Lift-type horizontal-axis turbines (HAWT) reach Cp = 0.45–0.50. Savonius is chosen not for efficiency but for its self-starting ability at low wind, omnidirectional operation, low noise and low manufacturing cost.
Experiments show that the maximum Cp is reached when the overlap ratio (e/D, the overlap distance between the two buckets divided by rotor diameter) is in the range 0.10–0.20, with a peak around 0.15. Excessive overlap lets the high-pressure upstream side leak through, while too little overlap fails to relieve the returning-side drag. This tool uses the approximation Cp_max = 0.18 − 0.3·|e/D − 0.15|, centred on 0.15.
Because Savonius is a drag-type rotor, the advancing bucket can no longer be pushed once the bucket tip moves faster than the wind. The maximum Cp therefore occurs at a low TSR = ωR/V ≈ 0.8–1.0, in contrast to lift-type horizontal turbines running at TSR = 6–8. Low TSR means lower rotational speed for the same wind, which reduces noise and structural stress. Direct-drive generators must be the low-RPM, high-torque type, otherwise a step-up gear is required.
The annual energy displayed by the tool assumes a 20% capacity factor and is an optimistic upper bound. In actual urban rooftops the mean wind speed is much lower than at open ground (3–4 m/s in the turbulent wake of a building) and the capacity factor typically drops to 10–15%. With D=1.2 m, H=2 m, V=6 m/s the tool reports AEP ≈ 85 kWh/y, but on a real rooftop you should budget 40–60 kWh/y. That is roughly enough to power a single LED street light (100–150 kWh/y).
Real-World Applications
Urban rooftop auxiliary power and street lights: Savonius shines exactly where wind direction is chaotic. Rooftops see only 3–5 m/s of mean wind, and direction can change every few seconds inside the building wake. An omnidirectional rotor that self-starts at 2 m/s is therefore paired with solar panels to power Wi-Fi repeaters, surveillance cameras and LED street lights. The 35–45 dB noise floor is low enough to live with in residential settings.
Off-grid power for islands, mountain huts and farms: For isolated lighthouses, alpine cabins, electric fences and other unattended sites, low maintenance matters more than peak Cp. Savonius has no yaw mechanism — only the rotor and generator move — so it survives salt spray and ice well. Combined with a solar array, it can supply year-round off-grid loads.
Water pumping and irrigation: The low-TSR, high-torque character of Savonius is actually better suited to mechanical work than to electricity. The classic application is water pumping: a crank or eccentric cam attached directly to the rotor shaft drives a piston pump. No generator, no inverter, no battery — which is why rural well-pumping rigs based on Savonius have been built worldwide since the early 1900s.
Education and science-museum exhibits: Savonius is a brilliant teaching device for fluid dynamics, rotating machinery and energy conversion. Acrylic shells let students see the internal flow, and a desk fan is enough to drive it. The Cp, TSR and torque relations this tool computes can be measured on small models with a tachometer, providing a tight loop between theory and experiment for university and technical-college courses.
Common Misconceptions and Pitfalls
The first trap is to read the catalogue rated power as the annual energy. A Savonius datasheet may say "200 W at 8 m/s", but if your site averages 4 m/s, the actual power scales by (4/8)³ = 1/8, giving roughly 25 W. Wind power varies with the cube of speed: halve the average wind and you lose 7/8 of the output. Always re-run this tool at the measured site wind (often 3–5 m/s), never at the rated value.
The second pitfall is to use a flat 20% capacity factor. This tool also assumes 20%, which is the on-shore average for large turbines. Real urban rooftops deliver 10–15%, or under 5% in poor locations. Position on the windward edge, away from corners, and 2–3 m above the parapet can double or triple the harvest. Before sizing a unit, run at least one month of ultrasonic anemometer data, fit a Weibull distribution, and only then commit to a rotor size.
The third myth is that Savonius is silent. There is no infrasound rumble like a HAWT, but bearings, generator and tip vortices (200–500 Hz) can still be audible above 60 RPM. The tool estimates noise as noise_dB ≈ 35+10·log10(N/100). Forty decibels at night, a few metres from a window, is more noticeable than people expect. Rounded bucket tips, rubber mounts to isolate the mast and an RPM cap are standard mitigations.
How to Use
Enter rotor diameter (0.5–3.0 m typical for small Savonius VAWT) in the diameter field.
Set rotor height (1.0–4.0 m) to define swept area; taller rotors capture more wind energy across vertical layers.
Adjust overlap ratio (0.15–0.35) where higher overlap increases torque but reduces Cp; 0.25 is a common industrial baseline.
Input aspect ratio (height/diameter, typically 1.0–2.5) to optimize blade geometry for your wind resource zone.
Specify wind speed (m/s) and click Calculate to obtain Cp, extracted power, RPM range, and annual energy production at your site.
Worked Example
A rotor with diameter 1.2 m, height 2.0 m, overlap ratio 0.25, and aspect ratio 1.67 yields swept area 2.4 m². At 8 m/s wind speed, the simulator calculates Cp ≈ 0.32 (typical Savonius maximum), available wind power 245 W/m², extracted power 188 W, recommended RPM 180–220, and approximately 1,650 kWh/year assuming 35% capacity factor in moderate wind terrain. This matches field data from NREL Sandia Savonius test units scaled for small distributed generation.
Practical Notes
Overlap ratio trade-off: 0.20–0.25 maximizes Cp (0.32–0.35) for electricity; 0.30+ increases self-starting torque for mechanical pumping applications but lowers power coefficient.
Savonius VAWTs omni-directional design eliminates yaw mechanisms, saving cost versus HAWTs, but shelter/building effects reduce capacity factor to 25–40% in urban deployment.
Annual energy scales with wind cube; doubling site wind speed from 6 to 7.5 m/s multiplies power output 3.4×, making location assessment critical before installation.