An electric windmill plant converts wind-driven rotor motion into electrical power. This example shows a small horizontal-axis turbine with a nacelle generator, tail vane, tower and a battery-system power path. Its calculator estimates available wind-stream power and conditional electrical output from rotor size, wind speed, air density and an entered net fraction.
Electric Windmill Plant Interactive Calculator
Explore a small wind turbine and its electrical power path. Compare wind-stream power, conditional electrical output and rotor rpm from an explicitly entered tip-speed ratio.
Equation Used
- Uniform wind and circular swept area.
- Constant entered net fraction incorporating assumed conversion losses.
- Prescribed tip-speed ratio for conditional rotor rpm.
- No power curve, storage, cut-in, high-wind cap or structural model.
Constant net fraction and prescribed tip-speed ratio. Not a measured power curve or energy-supply prediction.
Rotor, generator and electrical load
The blades turn a generator in the nacelle. The illustrated tail helps identify the aligned horizontal-axis arrangement, while the tower supports the rotor above the ground. The example electrical path shows conversion and charge control, storage and loads. It is an energy-flow overview, not a wiring diagram.
The rotor is drawn in an oblique view so the generator housing and tail remain visible behind it. Blades rotate together as rigid shapes, and the scene fits them at every entered diameter. Dimensions are labeled; tower height and construction are illustrative.
Only the rotor rotates in this model. The battery symbol identifies storage in the power path; state of charge and long-term energy supply are not calculated.
Explore size, wind and operating assumptions
Enter rotor diameter, wind speed and air density to calculate the wind power passing through the swept area. The net electrical fraction is an assumption supplied by the user and already includes aerodynamic and electrical conversion effects.
The tip-speed-ratio input specifies the rotor-speed assumption. It is blade-tip speed divided by wind speed. Changing it alters calculated rpm and the slowed animation, while the net fraction remains separately specified.
Real output requires a turbine power curve and appropriate site information. A rotor at an arbitrary tip-speed ratio does not necessarily achieve the entered net fraction. The two assumptions are not an aerodynamic design solution.
Wind-stream power and rotor speed
Swept area is A=πD²/4. Incident kinetic power is Pwind=½ρAv³, where diameter is in metres, air density in kg/m³ and wind speed in m/s. The result is watts.
Estimated electrical output is Pe=Cnet Pwind. This uses a constant net fraction, not a cut-in or rated-power curve. The ideal actuator-disk extraction ceiling is (16/27)Pwind, approximately 59.26% of incident power. That ceiling is not electrical output and does not account for drivetrain or generator losses.
Tip-speed ratio λ=(πDn/60)/v gives conditional rotor speed n=60λv/(πD) rpm. Playback uses an explicitly displayed slowdown factor so the rotor remains visible across the input range.
Default small-rotor example
A 3 m rotor has swept area approximately 7.069 m². At 10 m/s and air density 1.225 kg/m³, incident wind-stream power is approximately 4,329.5 W.
With an assumed net electrical fraction of 0.1386, output is approximately 600.1 W. At an independently assumed tip-speed ratio of 6, rotor speed is approximately 382 rpm. These values are conditional calculations, not measured turbine performance.
Doubling diameter quadruples area and power at fixed wind and net fraction. Doubling wind speed multiplies the power estimate by eight. Doubling diameter halves conditional rpm at fixed wind and tip-speed ratio.
Instantaneous power is not annual energy
The constant-fraction model excludes turbulence, wind-speed distribution, cut-in and cut-out behavior, generator limits, rated-power regulation, losses varying with operating point and downtime. It must not be extrapolated as a real turbine’s output at every wind speed.
Storage capacity, battery charge, load demand and autonomy are not calculated. Supplying a site over time requires an energy balance and a suitable power curve with site wind data. A single instantaneous power estimate cannot establish whether a cabin’s loads can be supplied over time.
Blade tolerances, guy-wire tension, maintenance intervals and equipment ratings require the documentation and engineering of a specific turbine and tower.
Electric windmill plant questions
Why does the rotor stay large when I choose a small diameter?
The drawing auto-fits the rotor to keep the blades visible. Diameter, swept area and calculated power still follow the input.
Does the battery icon show its state of charge?
No. It identifies storage in the example power path. There is no battery-energy model here.
Why does tip-speed ratio not directly change estimated power?
Power uses the separately entered net fraction. A full aerodynamic model would relate performance to operating ratio and blade design; that relationship is not included in this calculator.
Is the Betz result the amount of electricity available?
No. It is an ideal wind-energy extraction ceiling before practical conversion losses.
Does the model include high-wind limiting?
No. The cubic expression is conditional and does not include a rated-power cap or shutdown.
References
- U.S. Department of Energy, Small Wind Guidebook — turbine-system components, swept-area power calculation, battery charge control and the need for a power curve and site data.
- National Renewable Energy Laboratory, 2024 Annual Technology Baseline: Distributed Wind — rotor diameter, power coefficient and tip-speed-ratio parameters in turbine characterization.
- NREL, variable-speed wind-turbine performance analysis — the relationship between rotor operating speed, tip-speed ratio and power coefficient.
Building or designing a mechanism like this?
Explore the precision-engineered motion control hardware used by mechanical engineers, makers, and product designers.
