D3 Wind Energy Project

# Wind Grapher

Hub Height Wind Speed: m/s

Power Law Constant:

Hub Height: m

Turbine Diameter: m

REWS=

# User Input Plot

Velocity: m/s                   Height: m

User Saved Data:

### Plot Info:

The plot derived using power law to relate wind velocities at certain heights. To use this plot, you may choose a reference wind velocity at a height of 10m, and a power law constant. This will generate a curve indicating how the velocity profile of the wind would look like. To see the velocity at a certain point, you may place your cursor on one of the dots on the curve.

### On power law theory:

The use of power law to stipulate wind speeds at different heights is a simplified model of how wind speeds tend to behave. While it may not be as detailed as other models, which take into consideration other factors that affect wind speeds, such as temperature, or actual wind measurements, like the Monin-Obukhov similarity theory; the power law model is still a valuable tool when the measurement of wind speeds may not be required to be as accurate.

The following equation was used to make the plot: $$u(z) = u_{ref}\times(\frac{z}{z_{ref}})^p$$
In the equation above u(z) is the velocity at z height. uref is the reference velocity and zref is the height of reference. p is the most important part of this model, as it represents the power law constant. Under neutral atmospheric conditions, the power law constant may be assumed to be 17. This constant is higher in stable conditions, and lower in unstable ones. This model is a great way to estimate wind speeds at heights greater than 100m, but for heights under 100m, the use of log law is preferred.

The formula for log law may be seen bellow: $$u(z) = u_{ref}\times\frac{\\ln(\frac{z}{z_{0}})}{\\ln(\frac{z_{ref}}{z_{0}})}$$

In the formula above, the velocity at a height z is u(z). This model is calculated using a reference velocity, uref, at a reference height, zref. Unlike the previous model, where at 100m, the conditions at lower altitudes could be accounted in the power law constant, in this model z0 is used to account for the roughness length in the current wind direction.

### Power Law Calculator:

Although the interactive plot may provide a variety of data, in the case of a more specific wind measurement, you may use the form bellow to get a specific velocity measurement. In the first instance, when stipulating wind speeds under 100 meters, the log law may be used:

# Log Law Calculator

Velocity of reference: m/s

Height of reference: m

Desired height: m

Roughness length: m

Place the parameters above...

In the case of wind speed measurements of over 100m, the power law may be used to calculate this velocity bellow:

# Power Law Calculator

Reference Velocity at 10m: m/s

Desired Height: m

Power Law Constant:

Place the parameters above...

### Wind Shear Exponent Calculator:

The wind shear exponent is an essential tool to estimate the wind speeds at different heights. It may vary depending on many conditions on the surface, and the atmosphere. A good way to obtain this exponent is by comparing the wind speeds at two different heights. This can be calculated bellow:

# Wind Shear Exponent Calculator

Velocity 1: m/s

Velocity 2: m/s

Height 1: m

Height 2: m

Place the parameters above...