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Atmospheric Boundary Layer Wind Shear Profile Calculator

Earth surface friction retards horizontal winds near ground level, creating a steep vertical velocity gradient (wind shear) within the atmospheric boundary layer.

Wind speed recorded at meteorological mast height.

Height of anemometer measurement mast (typically 10 m).

Hub center height of wind turbine generator.

Mathematical boundary layer shear model.

Shear exponent (typically 0.10 for offshore, 0.143 for open flat land, 0.25 for forested terrain).

Aerodynamic surface roughness length (used if Log Law selected).

Calculated Result
9.03 m/s

Hub Height Wind Speed

Wind Velocity Gain Factor

39.0%

Wind Power Density Multiplier

2.69×

Reference Height / Speed

10 m / 6.5 m/s

Target Hub Height

100 m

Calculation Breakdown

  1. Shear Scaling ModelPower Law (α = 0.143)
  2. Target Velocity: u(z)9.03 m/s
  3. Kinetic Power Multiplier: (u/u_ref)³2.69×

What Is the Atmospheric Boundary Layer Wind Shear Profile Calculator?

Wind shear describes the rate of change of horizontal wind speed with height above ground level.

Because kinetic wind power scales with the cube of velocity (v^3), taller towers capture disproportionately higher energy.

How Does the Atmospheric Boundary Layer Wind Shear Profile Calculator Work?

Applies the chosen atmospheric shear formulation (Power law or Log law).

Calculates hub height wind speed.

Computes the wind power density multiplier (u_hub / u_ref)^3.

Atmospheric Boundary Layer Wind Shear Profile Calculator Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

u(z) = u_{ref} \left(\frac{z}{z_{ref}}\right)^\alpha, \quad u(z) = u_{ref} \frac{\ln(z / z_0)}{\ln(z_{ref} / z_0)}, \quad \frac{P_{wind}}{A} \propto u(z)^3

Hellmann power law and Prandtl logarithmic profile models for vertical wind shear.

How to Use the Atmospheric Boundary Layer Wind Shear Profile Calculator

  1. Enter the reference wind speed and anemometer height.
  2. Specify the target turbine hub height in meters.
  3. Choose the shear model and enter the appropriate terrain exponent or roughness length.

Step-by-Step Example Calculation

Commercial Wind Farm Hub Height Sizing

Input Values:

referenceWindSpeedMS:6.5
referenceHeightM:10
targetHubHeightM:100
shearModel:powerLaw
powerLawAlpha:0.143
Worked Steps: Extrapolating 10 m mast wind data to a 100 m hub height 3 MW wind turbine.

Understanding Your Result

Hub wind speed indicates the effective average speed seen by the rotor swept plane.

The power density multiplier shows the exponential boost in harvestable energy due to tower elevation.

Factors That Affect the Result

  • Atmospheric stability: Nighttime stable thermal stratification dramatically increases shear exponent alpha.
  • Surface obstacles: Trees, buildings, and complex hills create high turbulence and elevated roughness length z0.

When Should You Use This Calculator?

  • Wind resource assessment (AEP estimation) and turbine micro-siting.
  • Tower structural fatigue loading analysis caused by rotor top-to-bottom wind speed disparity.

Assumptions & Limitations

  • Assumes neutrally stable atmospheric boundary layer over horizontally homogeneous flat terrain.
  • Does not model low-level nocturnal jets (LLJ).

Frequently Asked Questions

Calculation Accuracy & Reference Note

Standard IEC 61400-1 wind turbine design standard methodology.

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