Issue #161, June / July 2014

Intermediate

- Intermediate

**Wind turbine design** encompasses multiple disciplines, but perhaps the most important—and often the least understood, even by would-be turbine designers—is fluid dynamics. Understanding the physics laws that govern wind power, presented here, can help consumers make wise wind turbine technology choices.

The purpose of a wind turbine is to convert kinetic energy (energy of a moving mass) of the wind into electrical energy. Energy *conversion* is common to all machines because they must obey the law of energy conservation—energy cannot be created or destroyed, but only changed from one form to another. For example, your car converts the chemical energy stored in fuel (if it’s an electric car, batteries) to kinetic energy, moving it down the road. A wind turbine also obeys this law when it extracts the kinetic energy in the wind and converts it to electrical energy.

The amount of kinetic energy in any moving mass is calculated with this equation:

**Kinetic energy = 1/2 × mass × velocity ^{2}**

For wind energy, the velocity in the equation is wind speed. The mass is for a particular volume of air. Consider the example of wind blowing through an open window. The illustration describes how a volume of the air passing through the window relates to window area, wind speed, and time. This makes sense if you consider that the larger the opening, the harder the wind is blowing, and the longer the window is open, the more air volume will flow through it.

The mass of this volume of air is arrived at by multiplying the volume by the air density. Putting this all together, we write our equation for wind energy as:

**Kinetic energy = 1/2 × air density × area × wind speed ^{3} × time**

Although a wind energy system’s final objective is to generate energy, it is more convenient to describe its size in terms of power. The relationship between power and energy is a simple one—energy is power multiplied by time. This is why power is defined in watts and energy in watt-hours. The terms *power* and *energy* are often confused and even used interchangeably in casual discussions, but in a technical analysis, it is important to make the distinction.

If we are interested in the power in the wind, we divide the energy by time. This gives us the governing equation for power available in the wind passing through an area as:

**P _{wind} = 1/2 × air density × area × wind speed^{3}**

We see that the amount of wind power is dependent on three variables. The first is *air density*, a quantity defined by Mother Nature, over which we have no real control. Another is *swept area*, that is, the projected area perpendicular to the wind that the turbine intercepts. One thing is clear from the equation: everything else being equal, a larger swept area can generate more power.

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