Free · Energy scenarios
Horizontal and Vertical Wind Power with Losses
Compare swept-area wind power, conversion losses, mean delivered power, rotor speed and torque in two rotor geometry scenarios.
- Formula & worked example
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Calculator inputs
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How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
Private by default
Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.
Formula and method
area ≈ 28.274334; kinetic power ≈ 8.8668311; efficiency ≈ 23.163746; power with losses ≈ 2.0538902; revolutions per minute ≈ 152.78875; torque ≈ 128.36814; revenue ≈ 0.30808353.
Available power = ½ρAv³; delivered fraction = Cp × (1−each stated loss); rotor angular speed = tip-speed ratio × wind speed / rotor radius. Revenue is hourly gross electricity receipts.
Worked example
Enter these known values and leave the other values blank.
- Turbine type
- Horizontal Axis Wind Turbine (HAWT)
- Blade length
- 3 m
- Wind speed
- 8 m/s
- Air density
- 1.225 kg/m³
- Turbine efficiency
- 30 %
- Wake losses
- 10 %
- Mechanical losses
- 5 %
- Electrical losses on turbine
- 2 %
- Electrical losses (transmission)
- 5 %
- Time out of order
- 3 %
- Tip Speed Ratio (TSR)
- 6
- Electricity tariff
- 0.15 USD / kWh
- Sweep area
- 28.3 m²
- Available wind power
- 8.867 kW
- Output power before losses
- 2.394 kW
- Real efficiency
- 23.164 %
- Output power with losses
- 2.054 kW
- Revenue
- 0.31 USD / hrs
- Revolutions per minute
- 152.8 RPM
- Torque
- 128.37 N·m
Assumptions and limitations
- Horizontal-axis swept area is πr², with blade length as rotor radius. The vertical-axis scenario uses a rectangular projected area equal to diameter times height.
- Wind speed and air density are constant inputs, not a weather forecast. Cubing average wind speed generally differs from averaging cubed wind speed.
- The power coefficient is bounded by the exact ideal Betz value 16/27. Loss and downtime fractions range from zero to one. Multiplying independent factors is an assumed loss model.
- Downtime scales the delivered power as an availability average. Torque from that power is therefore a corresponding average reference, not an instantaneous stopped-rotor torque.
- The retained 1.225 kg/m³ density is an illustrative near-standard sea-level value, not a universal atmospheric property.
- Cost inputs are scenario values. Currency conversion choices retain the captured exchange snapshot, rather than live exchange rates; enter all costs in one currency for an internally consistent comparison.
- The calculation assumes the entered operating conditions are constant for the stated comparison period. It does not predict weather, site suitability, construction performance, taxes, financing or maintenance.
- Keep known inputs fixed with locks; clear the unknown before solving an inverse. Singularity or insufficient known inputs can leave results incomplete.
Common questions
Are the outputs a site-specific forecast?
No. They apply the stated algebraic model to supplied conditions. A real installation or building needs measured operating data and a broader engineering or cost assessment.
How are currency choices handled?
They use a fixed captured conversion snapshot. They do not retrieve current prices or exchange rates.
References
Bookify adds explicit model-domain checks: The ideal open-current power coefficient cannot exceed exactly 16/27. Rotor diameter must be positive. Rotor height must be positive.