A drag-driven vertical-axis wind rotor whose two helical buckets are wrapped onto a sphere — or, if you stretch it, an ellipsoid. Every proportion that matters is a slider: aspect ratio, overlap ratio, twist angle, blade count, end plates and the operating tip speed ratio. Watch the swept area, power coefficient, shaft torque and torque ripple move with them, and see the shape you just described spinning from the front, the side and above. Everything starts at the optimum — change one thing and see what it costs.
| Quantity | Formula | Optimum | Current | Effect on Cp |
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The Savonius is a drag machine. Wind pushes harder on the hollow (concave) bucket coming toward it than on the round back of the bucket going away. The difference is the torque. That ceiling is low — a Savonius lives around Cp ≈ 0.20 against the 0.45–0.50 of a good lift-driven turbine — but it starts itself in almost no wind, does not care which way the wind blows, and can be built out of a split drum.
Tall and thin loses less at the ends relative to its height, so a straight Savonius wants AR ≈ 2. Wrap the same blade onto a sphere and the taper does that job for you: the optimum falls back to AR ≈ 1, which is exactly the sphere. That is why the optimum shown in the table moves when you change the profile fullness.
The gap between the two buckets lets air that has finished pushing the advancing bucket cross over and push the inside of the returning one instead of stalling. Too little and you waste that flow; too much and the buckets stop being buckets. The wind-tunnel optimum sits at 0.15, and the penalty is gentle — anything from 0.10 to 0.20 is a good build.
Twist barely moves peak power. What it does is spread each bucket's torque pulse over the height of the rotor, so the pulses overlap instead of stacking. The smoothing factor is a clean piece of maths: |sin(NΨ/2) / (NΨ/2)|. At Ψ = 180° with two buckets that is exactly zero — the torque ripple vanishes and the rotor will start from any position. That is the whole argument for the helical shape.
λ = ωR/V is how fast the bucket edge moves compared to the wind. Below the optimum the buckets are too slow and let wind through; above it, the returning bucket is fighting the air. A Savonius peaks just under λ = 1 — the tips move at about wind speed — which is why it is quiet and safe compared with a fast three-blade turbine.
Power scales with area and with the cube of wind speed: doubling D roughly doubles the power, doubling the wind multiplies it by eight. The catch with an ellipsoid is that its frontal area is only π/4 ≈ 79% of the D × H rectangle a straight rotor would sweep — you give up a fifth of the area for a shape that is stiff, self-supporting and much better looking.