Calculating the Effect of Wind Power

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Buying a wind turbine for your home might seem like a great idea on the surface, but before you take the leap, there are a few things you should know about how wind power calculations are made. The first thing that you must understand is that there are two different calculations made for wind power – the theoretical maximum and the real-world  potential.  Let’s start with the theoretical value.

Making the Theoretical Calculation

Wind energy calculations are made by taking the kinetic energy of the system. This requires knowing two things – the mass of the air running through the system and the speed at which it is moving.

The formula for kinetic energy is X = ½ Mass x Velocity2.

While air doesn’t have much mass, it does have some, and we know its density at sea level – 1.23kg/m3.

To figure out the mass of the air that is being moved through the turbine system we need to make the following calculation: Mass = Velocity x Area x Density or Mass = Velocity x Area x 1.23kg/m3.

The area of the turbine is a simple calculation of the circumference of the area swept by blades – π x r2.

The potential power generated by a turbine can then be determined by substituting Velocity x Area x 1.23kg/m3 for Mass in the original equation. Making the equation for potential wind power:

Potential Power = 0.5 x π Blade Length2 x Wind speed x 1.23kg/m3

Remember, this calculation is dependent on your home being situated at sea level. If you are not at sea level, which is true for about half the population, you will need to consult an air density calculator like the one offered by Denysschen Corporation.

Actual Performance

The theoretical power presented in the prior calculation is actually a measurement of the total kinetic energy attributed to the wind. The turbine extracts energy by slowing the wind down. It cannot extract all the energy from the wind or the blades would cease to rotate. The calculation for the actual maximum energy extraction is known as Betz Law. It is a very extensive mathematical formula that was developed in 1919 by German physicist Albert Betz. This law states that no turbine can ever exceed 59.3% efficiency. Practical performance is generally in the range of 70-80% of the Betz number or 41% to 47% of total theoretical value.

To determine your watt potential, take the results from the equation in the theoretical section and multiply it by 47%.

Mitigating Factors

Wind turbines on the current market do not produce electricity unless there is a consistent wind speed of at least 10 mph. In urban areas and areas lower than 90 ft from the ground, sustained winds of this speed are relatively rare. New wind lens technology is currently in development that may reduce needed wind speeds to around 5 mph. If this happens, wind turbines will become a viable alternative for urban home owners.

 

After doing the calculations, do you think wind energy is worth the cost to you? What if wind lens technology were available?

 

  • Ollie Shough

    This widespread occurance of wind is what makes wind power such a promising technology. Those familiar with facts about wind energy know that over 50% of the United States can be used for effective wind generated power. The great thing about wind power is that it is renewable. We will never run out of wind!