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Extrapolate wind speed to any hub height using the power law. Select your terrain type and instantly visualize how wind speed changes with altitude.
Shear Exponent: 0.143
Terrain: Flat / Open Terrain — Grasslands, deserts, flat plains. Higher exponents mean wind speed increases more steeply with height.
Wind shear describes how wind speed changes with altitude above the ground. Near the earth's surface, friction from terrain features like buildings, trees, and topography slows the wind. As you move higher, these frictional effects diminish and wind speeds increase. Understanding wind shear is essential for wind energy because turbines are mounted on tall towers, and the wind speed at hub height is what determines energy production.
Wind shear is typically characterized by a shear exponent (α), also called the power law exponent. A higher shear exponent means wind speed increases more dramatically with height, which is common in areas with rough terrain or dense obstacles. Conversely, open water and flat terrain have low shear exponents because there is less surface friction to slow the wind near the ground.
v₂ = v₁ × (h₂ / h₁)ᵅ
v₂ — Wind speed at the target height (the value we want to find)
v₁ — Known wind speed at the measurement height
h₂ — Target height above ground (e.g., turbine hub height)
h₁ — Measurement height (often 10 m for weather stations)
α — Shear exponent, determined by terrain roughness and atmospheric stability
The power law is the most widely used empirical model for vertical wind speed extrapolation. While it has limitations — it doesn't account for atmospheric stability changes or temperature inversions — it provides a practical and accurate first approximation for most wind energy assessments.
Surface roughness is the primary factor that determines the shear exponent. Rough surfaces create more turbulent friction in the boundary layer, which slows wind near the ground and produces a steeper speed gradient. Here are the standard shear exponent values for common terrain types:
| Terrain Type | Shear Exponent (α) | Description |
|---|---|---|
| Open Water | 0.1 | Oceans, large lakes |
| Flat / Open Terrain | 0.143 | Grasslands, deserts, flat plains |
| Agricultural | 0.17 | Farmland with low crops |
| Suburban | 0.2 | Scattered buildings, low-density housing |
| Forested | 0.25 | Dense woodland, tall vegetation |
| Urban | 0.35 | City centers with tall buildings |
Wind power is proportional to the cube of wind speed, so even a small increase in wind speed yields a large increase in energy production. For example, increasing wind speed by just 20% results in a 73% increase in available power. This is why the modern wind industry has been building taller and taller turbines — the additional cost of a taller tower is more than offset by the substantially higher energy yield from stronger, more consistent winds at greater heights. A turbine at 120 m hub height typically captures 15-25% more energy than the same turbine at 80 m, depending on the terrain and wind shear profile.
When evaluating a potential wind farm site, accurately extrapolating wind speed from the measurement height (often 10 m at weather stations) to the planned hub height (typically 80-150 m for modern turbines) is one of the most critical steps. Getting this right can mean the difference between a financially viable project and one that underperforms expectations.