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Category Physics & Science

Configuration

Turbine Model (Preset)

Geometry & Efficiency

Rotor Diameter (m)

Efficiency (%)

Environment Conditions

Wind Speed (m/s)

Advanced Atmosphere (Altitude/Temp)

Instant Power 0 kW

Annual Energy (Est.) 0 MWh/yr

Revenue (@ $0.12) $0 /year

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0 Homes Powered continuously

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0% Cap. Factor Efficiency Metric

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0 km EV Range / Hour

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About

Accurate wind energy estimation is the cornerstone of any renewable energy project, from micro-grid residential setups to gigawatt-scale offshore farms. However, the standard power formula is often insufficient for real-world application because it assumes standard atmospheric conditions. This tool bridges the gap between theoretical physics and engineering reality.

Unlike basic calculators, this engine adjusts for Air Density (ρ) variances caused by altitude and temperature - a critical factor since air density drops by approx. 3% for every 1000 meters of elevation. It also visualizes the Power Curve, illustrating the non-linear relationship between wind speed and electrical output, bounded by the Cut-In, Rated, and Cut-Out speeds.

We use the Betz Limit as a theoretical ceiling but apply realistic Power Coefficients (C_p) found in modern horizontal-axis turbines. This tool is essential for energy analysts, landowners, and engineers assessing site viability and projected Annual Energy Production (AEP).

Formulas

The mechanical power captured by the turbine is calculated using the aerodynamic power equation, corrected for environmental variables:

P = 12 ⋅ ρ ⋅ A ⋅ v³ ⋅ C_p

1. Area Calculation:

A = π ⋅ (D2)²

2. Air Density Correction (Ideal Gas Law):

ρ = P₀R_specific ⋅ T ⋅ exp(−g ⋅ M ⋅ hR ⋅ T)

Where h is altitude, T is absolute temperature (Kelvin), and g is gravity. We approximate this density lapse rate for the final power output.

Reference Data

Parameter	Symbol	Standard Value (Sea Level)	Impact on Output
Air Density	ρ	1.225 kg/m³	Linear (1:1). Denser air = more power.
Wind Velocity	v	Variable	Cubic (v³). 2x speed = 8x power.
Rotor Radius	r	Variable	Squared (r²). 2x radius = 4x power.
Betz Limit	Limit	59.3%	Theoretical maximum efficiency.
Real Efficiency	C_p	35% - 45%	Mechanical and aerodynamic losses.
Roughness Class	z₀	0.0002 - 1.6	Surface friction reducing wind speed at hub height.
Cut-In Speed	v_in	3.5 m/s	Minimum speed to overcome inertia.
Rated Speed	v_rated	11 - 15 m/s	Speed at which max generator capacity is reached.

Frequently Asked Questions

Instantaneous power is what the turbine generates right now based on current wind speed. Rated power is the maximum output the generator can handle (usually achieved around 12-14 m/s). If wind exceeds this speed, the turbine pitches its blades to cap power and prevent damage.

Thinner air contains less mass per unit volume, meaning less kinetic energy is transferred to the blades. A turbine in Denver (high altitude) produces approximately 15-20% less energy than the exact same turbine in San Francisco (sea level) at the same wind speed.

AEP assumes the wind doesn't blow at a constant speed all year. We use a Rayleigh Distribution (a subset of Weibull) based on the average wind speed to statistically predict how many hours the wind spends at each velocity, summing the total energy produced over 8760 hours (one year).

Standard commercial turbines have a "Cut-Out" speed (usually 25 m/s). Beyond this point, the braking system engages to stop rotation immediately. This is a safety mechanism to prevent catastrophic structural failure due to centrifugal forces.