Calculator Inputs
Formula Used
Wind power density is the available wind power per unit swept area: WPD = ½ · ρ · E[v³]
- ρ is air density in kg/m³.
- v is wind speed in m/s.
- E[v³] is the cube moment of wind speed.
If a Weibull distribution is selected, the cube moment becomes: E[v³] = c³ · Γ(1 + 3/k)
Optional turbine estimates use Pₐᵥₐᵢₗ = WPD · A and Pₑ = Pₐᵥₐᵢₗ · Cₚ · η, where A is rotor swept area.
How to Use This Calculator
- Select a wind model: single speed or Weibull parameters.
- Choose an air density method suitable for your site data.
- Optionally enter rotor diameter or swept area for power estimates.
- Adjust Cₚ and η to match expected performance.
- Click Calculate to show results above the form.
- Use Download CSV or Download PDF to export.
Example Data Table
| Wind Speed (m/s) | Air Density (kg/m³) | Wind Power Density (W/m²) | Category (Typical) |
|---|---|---|---|
| 4 | 1.225 | 39.2 | Low resource |
| 6 | 1.225 | 132.3 | Moderate |
| 8 | 1.225 | 313.6 | Good |
| 10 | 1.225 | 612.5 | Very good |
| 12 | 1.225 | 1058.4 | Excellent |
These values assume steady speed and standard density. Real sites vary by turbulence, shear, and seasonal patterns.
Wind Power Density Guide
1) What wind power density means
Wind power density (WPD) is the rate of wind energy available per square meter of rotor swept area. It is expressed in watts per square meter (W/m²) and is a practical way to compare sites without selecting a turbine first. Higher WPD generally supports higher annual energy production when other conditions are similar.
2) The key relationship: speed cubed
WPD follows WPD = ½·ρ·E[v³], so wind speed matters more than most inputs. If speed doubles, v³ increases by eight times. For example, at standard density (1.225 kg/m³), 6 m/s yields about 132 W/m², while 10 m/s yields about 613 W/m².
3) Air density and why it changes
Air density (ρ) depends on pressure, temperature, and altitude. A common reference is 1.225 kg/m³ at sea level near 15°C and about 1013 hPa. Warm air or high elevation reduces density and lowers WPD for the same wind speed. Using measured pressure and temperature improves comparisons between seasons.
4) Using Weibull parameters for long-term wind
Wind is not constant, so long-term assessments often model variability with a Weibull distribution. This calculator uses E[v³] = c³·Γ(1 + 3/k), where k controls spread and c sets scale. Typical k values range from about 1.5 to 3.0 for many locations.
5) From WPD to turbine power estimates
Available wind power over a rotor area is Pₐᵥₐᵢₗ = WPD·A. Electrical output is lower because turbines cannot capture all wind energy. Aerodynamic performance is represented by Cₚ, capped by the Betz limit (0.593). Real turbines often operate around 0.35–0.45 at optimal conditions.
6) System efficiency and realistic losses
The drivetrain, generator, power electronics, and availability reduce delivered energy. Many small-to-medium systems use overall efficiencies around 0.85–0.95 depending on design and maintenance. This calculator lets you include a combined η to reflect these losses when estimating daily and yearly energy.
7) Interpreting WPD categories with data
As a simple rule of thumb, WPD under ~200 W/m² is often considered low, 200–400 W/m² moderate, and above ~400 W/m² increasingly attractive for utility-scale projects. These thresholds depend on turbine size, hub height, wake effects, and grid economics. Use the example table to sanity-check your results.
8) Measurement height, shear, and uncertainty
Wind speed increases with height due to wind shear, so hub-height data is more relevant than rooftop measurements. Local terrain, roughness, and turbulence also influence performance. Treat WPD as a screening metric, then refine with site measurements, hub-height extrapolation, and energy yield modeling.
FAQs
1) What is a good wind power density value?
Many projects target more than about 400 W/m² at hub height. Smaller turbines can work at lower values if costs are low, winds are steady, and the load is well matched.
2) Should I use single speed or Weibull inputs?
Use single speed for quick checks or a measured average. Use Weibull when you have long-term statistics, because the distribution captures variability that strongly affects the cube of speed.
3) Why does temperature change my result?
Temperature changes air density. Warmer air is less dense, so the same wind speed contains less power. Using pressure and temperature gives a more realistic site-to-site comparison.
4) What values are reasonable for Cₚ and η?
For screening, Cₚ around 0.35–0.45 is common. Use η around 0.85–0.95 for combined electrical and mechanical losses. Keep Cₚ below 0.593 to respect the Betz limit.
5) Does rotor diameter affect wind power density?
No. WPD is per square meter and is independent of rotor size. Rotor diameter affects total available power and energy because it changes swept area, not the WPD itself.
6) Why is wind power density better than average wind speed?
Average speed hides variability. Because power scales with v³, occasional higher winds contribute disproportionately. WPD captures this effect directly when you use E[v³] or a Weibull model.
7) Can I use this for offshore and high-altitude sites?
Yes, as a first estimate. For high altitudes, use the altitude and temperature option. Offshore sites often have higher, steadier winds; still account for air density, turbulence, and turbine availability.