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Vertical Axis Wind Turbine (VAWT) Cp Design Simulator

Explore the Cp(λ) curve, output power, solidity and annual energy of Darrieus H-rotor, φ-type, Savonius and helical vertical axis wind turbines. Designed as a quick-look tool for residential, rooftop and other urban small-wind concepts.

Parameters
VAWT type
Sets the peak Cp and optimal TSR for the selected family
Rotor radius R
m
Rotor height H
m
Blade count N
Blade chord c
m
Wind speed V_∞
m/s
Tip speed ratio λ
λ = ωR/V. Darrieus is optimal around 4; Savonius around 0.8
Results
—
Swept area A (m²)
—
Tip speed (m/s)
—
Output P (kW)
—
Power coefficient Cp
—
Solidity σ
—
Annual energy (kWh)
—
VAWT plan view — rotor rotation and wind

Top-down view of the rotor. Blue arrows are the free-stream wind; red vectors show lift and orange shows drag at each blade. Blade color tracks Cp / Cp,peak (green → orange → red).

Cp vs TSR (curves per type)
VAWT vs HAWT power (same swept area)
Theory & Key Formulas

$$P = \tfrac{1}{2}\,\rho\,A\,V_\infty^{3}\,C_p,\qquad \mathrm{TSR}=\lambda=\frac{\omega R}{V_\infty},\qquad \sigma=\frac{N\,c}{2\pi R}$$

P: output power [W], ρ: air density (1.225 kg/m³), A: swept area (2RH for a VAWT), V_∞: free-stream wind speed [m/s], C_p: power coefficient (Betz limit 16/27 ≈ 0.593), λ: tip speed ratio, σ: solidity, N: blade count, c: blade chord, R: rotor radius.

$$C_p(\lambda)\approx C_{p,\mathrm{peak}}\left[1-\left(\frac{\lambda-\lambda_{\mathrm{opt}}}{\lambda_{\mathrm{opt}}}\right)^{2}\right]_{+}$$

Empirical Cp(λ) approximation: parabolic around the optimal TSR. Typical values are Darrieus H-rotor C_p,peak ≈ 0.43 at λ_opt ≈ 4, and Savonius C_p,peak ≈ 0.18 at λ_opt ≈ 0.8.

Vertical Axis Wind Turbines (VAWT) — Cp Design for Darrieus and Savonius

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"Vertical axis" wind turbine — that's the kind that spins around an upright axis, not like a normal propeller, right? What's actually different?
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Good catch. A normal wind turbine is the propeller-shaped HAWT — Horizontal Axis Wind Turbine — with the rotor shaft horizontal. A VAWT has the shaft vertical, so the rotor is standing up. The big practical win is that it accepts wind from any direction without having to yaw the whole rotor around. HAWTs have to track the wind; VAWTs just spin. That's why they're attractive on city rooftops, where the wind direction is changing every few seconds. You can also put the generator on the ground, which makes maintenance much easier, and tip speeds are low so they're quieter.
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If they're that good, why isn't every wind farm using them? Why do I always see propellers in big fields?
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Efficiency. The Betz limit caps any rotor at Cp = 16/27 ≈ 0.593. A modern HAWT reaches 0.45-0.50, hitting about 85% of Betz. A good Darrieus VAWT tops out near 0.40 — about 70% — and a Savonius is only 0.18, around 30% of Betz. For wide open land or offshore, scaling up an efficient HAWT gives much cheaper electricity per kWh. VAWTs make sense where you care less about peak efficiency and more about installability, low noise, and tolerance to gusty multi-directional wind: residential, rooftop, building-integrated, and floating offshore.
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The "VAWT type" selector has Darrieus and Savonius. What's actually different between them?
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They spin on different physics. A Darrieus uses airfoil-shaped blades and runs on lift — the same effect that holds up an aircraft wing. That lets it spin fast and reach Cp around 0.40. Its sweet spot is TSR ≈ 4. A Savonius is just two half-cylinder buckets facing opposite directions, and it runs on the drag difference between the side that catches wind and the side that lets it slip past. Simple, self-starting, high torque — but its optimal TSR is only 0.8 and the efficiency is less than half. The classic compromise is a hybrid: a small Savonius core gives starting torque to a Darrieus, which then takes over for high-efficiency running.
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What about the helical one — Quietrevolution? Those twisted rotors you sometimes see on top of city buildings?
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Exactly those. A straight-bladed Darrieus H-rotor has a problem: each blade meets a different angle of attack every quarter turn, so the torque pulses heavily through one revolution. That pulsing causes vibration and noise. Twisting the blades around the circumference — that's what "helical" means — staggers the angles so that some part of every blade is always at its optimal incidence. The result is a smoother torque, less vibration and less noise. Quietrevolution's QR5 is the textbook example. Peak Cp is slightly lower than a straight H-rotor (about 0.35), but for rooftop installs near residents it's almost always the practical choice.
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Default output is about 2.1 kW. Is that enough to power a typical house?
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Good question. 2.1 kW is the instantaneous output at 8 m/s wind, not the average. The annual energy card shows about 4,600 kWh, which assumes a 25% capacity factor — i.e. equivalent to running at rated power for one quarter of the year. A typical Japanese or European household uses 4,000-4,500 kWh per year, so on paper it covers a house. The catch: real urban mean wind speeds are often below 4 m/s, and power scales as V³. At V_mean = 4 m/s the actual annual energy can drop to roughly an eighth of this estimate. The "one house" claim only holds in genuinely windy spots — a rural rooftop with a measured 6+ m/s mean. Always run a real on-site wind measurement before you commit to a small wind project.

Frequently Asked Questions

A VAWT has its rotor axis perpendicular to the ground, so it needs no yaw control and tolerates the turbulent, shifting winds typical of urban roofs. The generator and gearbox sit at ground level, which makes maintenance easier, and the tip speeds are lower so the acoustic signature is quieter. The trade-off is efficiency: a good Darrieus reaches Cp ≈ 0.40 and a Savonius only ≈ 0.18, while modern utility-scale HAWTs reach Cp 0.45-0.50. Darrieus rotors also struggle to self-start and place pulsating fatigue loads on the blades. VAWTs win in niches: residential, building-integrated and floating offshore.
Darrieus rotors run on lift, prefer TSR ≈ 4-5 and reach Cp ≈ 0.35-0.43 — high speed, high efficiency, but poor self-start, often paired with a Savonius for starting torque. Savonius rotors run on drag at TSR ≈ 0.8 with Cp ≈ 0.15-0.20 — low speed, low efficiency, but high torque and reliable self-start, ideal for pumps, ventilators or as a starter stage. Use Darrieus when energy yield matters most, Savonius when reliability and starting matter, and helical (Quietrevolution-style) rotors when you need a quiet, low-vibration design for the city.
Solidity is σ = Nc / (2πR). Darrieus types want σ ≈ 0.1-0.25, while Savonius wants σ ≈ 1.0 (buckets covering half the perimeter). Too high a solidity on a Darrieus lowers the optimal TSR and causes blade-to-blade interference and stall, dropping Cp. Too low and the lift per swept area is insufficient. This tool issues a warning when σ deviates more than ±50% from the recommended value (0.15 for Darrieus/helical, 1.0 for Savonius); tune blade count N and chord c to land back in the sweet spot.
Measured urban wind speeds are typically 30-50% lower than the figures published by weather stations, and flow separation around buildings drops the effective wind further. Below an annual mean of 4 m/s the economics of small VAWTs are poor and real annual energy falls well below the figure this tool reports (which assumes a 25% capacity factor). Mount the rotor at least 2D (two rotor diameters) above the roof and keep a clear distance from nearby obstacles. Noise is lower than for HAWTs, but resonance and inverter buzz can still be issues — plan for anti-vibration mounts and low-frequency mitigation. Compliance with IEC 61400-2 (and local small-wind guidelines) is effectively required.

Real-World Applications

Residential and small wind: Examples include the Aeolos-V 1 kW, Windspire 1.2 kW and Quietrevolution QR5 6 kW — rooftop or garden-mounted VAWTs aimed at homeowners. In suburban areas with a mean wind of about 5 m/s they are typically paired with solar PV in off-grid or self-consumption installations. Installed cost is higher per kW than a small HAWT, but low noise and a small visual footprint make them much easier to permit on residential land.

Building-integrated wind (BIWT) on high-rises: Helical VAWTs on the rooftops of tall city buildings double as a visible architectural statement. The Bahrain World Trade Center and London's Strata SE1 tower are well-known examples. Designers can exploit local flow acceleration around the building (the "venturi" effect), though strong turbulence makes site-specific wind simulation essential.

Floating offshore VAWTs (FOWT-VAWT): Research projects such as DeepWind in the EU, the Swedish SeaTwirl, and the AeroGenerator concept place large VAWTs on floating platforms. A low center of gravity is forgiving in waves, and key maintenance can happen near sea level rather than at hub height. Mainstream Renewable Power and similar developers have explored 5-10 MW class concepts.

Hydro and tidal cross-flow turbines: The VAWT concept transfers naturally to underwater turbines: Darrieus-style cross-flow water turbines are used in river and tidal applications. Verdant Power's East River trial in New York and Andritz Hydro's cross-flow units are representative. With water being roughly 800× denser than air, the same torque is produced at much smaller dimensions.

Common Misconceptions and Pitfalls

The biggest myth is that "the nameplate rating equals the actual annual energy". A "1 kW VAWT" only hits 1 kW at its rated wind speed, typically 11-12 m/s. Annual mean winds inland are 3-4 m/s and even coastal sites are usually 5-6 m/s. Because power scales with V³, at a mean of 5 m/s the rotor delivers only 8-10% of rated power. The annual energy figure in this tool is similarly optimistic — it assumes a 25% capacity factor, which is rarely achieved in real urban sites without proper anemometer measurements.

Next: the idea that "more solidity gives more torque so it must be better". That holds for a drag-driven Savonius (σ ≈ 1 is correct), but on a lift-driven Darrieus pushing σ above ~0.3 destroys performance. Adjacent blades disturb each other's flow, the rotor stalls, the optimal TSR drops and peak Cp collapses. The textbook answer is N = 2-3 blades with a reasonable chord. N = 5-6 is rarely used except for structural reasons. This is why the tool flags a warning when σ drifts more than ±50% from the recommended value.

Finally, the belief that "buildings concentrate the wind so my rooftop turbine will out-perform". Local flow acceleration is real near building corners, but it comes with violent separation, turbulence and vertical shear. Cp drops sharply and the blades take heavy fatigue loads, shortening life. For a rooftop install, lift the rotor at least 2D (two rotor diameters) above the roof surface and verify that nearby penthouses, towers and stacks do not feed turbulence into the rotor disk. Use CFD or a wind-tunnel test up front to pick a location where turbulence intensity stays below ~18%.

How to Use

  1. Enter rotor radius (m) and height (m) to define the swept area—a Darrieus H-rotor with R=1.5m and H=3m yields A=9m²
  2. Specify number of blades (typically 2–3 for H-rotor) and blade chord (0.15–0.25m for small turbines) to calculate solidity σ
  3. The simulator computes Cp(λ) across the tip-speed ratio range, displays peak power coefficient, and integrates annual energy output using Rayleigh wind distribution at your site's mean wind speed

Worked Example

A Savonius-hybrid VAWT with R=0.8m, H=2m, 3 blades, chord=0.18m and mean wind speed=8m/s: Swept area A=3.2m², solidity σ≈0.27, Cp peak≈0.38 at λ≈2.1, tip speed=16.8m/s, output power≈1.8kW. Annual energy production≈9,200kWh with capacity factor ~58%. A pure Darrieus (Cp≈0.42) on the same site yields ~10,600kWh annually.

Practical Notes

  1. H-rotor Darrieus turbines reach Cp=0.40–0.45 but require careful blade geometry; Savonius hybrids sacrifice efficiency (Cp≈0.28–0.35) for low-speed torque and self-starting
  2. Solidity above σ=0.35 increases Reynolds number and drag; offshore installations typically target σ≈0.20–0.30 for optimal Cp curve shape
  3. Verify site wind speed distribution—Rayleigh assumption valid for flat terrain; mountainous regions require Weibull fitting for accurate annual energy forecasts