Energy From the Wind

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Wind Energy

Let the wind turn the crank to produce electricy.

Windfarms are now popping up and selling electricity to the grid at around 4 cents per KWH and costs are projected to lower. Modern turbines, such as those pictured below, can achieve efficiencies of up to 40%.

Windfarms containing up to 5,000 individual wind turbines have now been created such as this facility in California (near Stockton).

Of course, the idea of a windmill as a device to turn a wheel has been around for centuries

which proliferated in Holland (a flat, windy place where Don Quixote hung out).

In the 1920's and 1930's the rotary style windmill, shown belown, became a common mixture on farms in the Midwest as a means of running a water pump

Recently, aviation technology has advanced windmill design quite a bit to produce todays's modern wind turbines:

The concept of the windfarm is now being put into practice:

Main problem with wind is its erratic nature.

Power per square meter goes as (wind velocity)³ requires good energy storage for later use.

What makes the wind blow?

Wind is the response of the atmosphere to uneven heating conditions. This creates pressure differences in the atmosphere causing the wind to blow from regions of high atmospheric pressure to low atmospheric pressure. The larger the pressure difference the greater the wind velocity.

Air pressure represents the amount of atmosphere that is pressing down on the surface of the earth at some point, as shown here:

Pressure differences yield wind (bulk motion of the air)

Local topography (mountains) can enhance or restrict the natural wind flow downslope winds off of mountain ranges represent ideal locations for wind turbines as do narrow mountain passes and river canyons such as Hood River

Large scale patterns are thus setup by the interplay of the locations of high and low pressure systems and the topology of the land leading to places in the US which are on average significantly windier than other locations. The overall capacity, in MegaWatts, in the US is large:

While wind is certainly a renewable energy source, it is also an erratic one. Energy storage is probably more critical for wind power than for any other form of alternative energy.

Basics of Wind Energy:

Kinetic Energy of wind is: 1/2 * mass * velocity²
amount of air moving past a given point (e.g. the wind turbine) per unit time depends on the velocity.
Power per unit area = KE * velocity MV² *V
So Power that can be extracted from the wind goes as velocity cubed (V³)

In essence, as shown in the above animation, the power on the windmill is proportional to the kinetic energy transfer per unit time as well as the density of the air (which is represent by the mass of the air above).
Power going as v³ is a big deal 27 times more power is in a wind blowing at 60 mph than one blowing at 20 mph

For average atmospheric conditions of density and moisture contant:

Power per sq. meter = .0006 V³

(Don't memorize .0006 V³; you will never need to know the 0.0006 part!)

velocity measured in meters per second
Power then measured in KILOwatts
1 meter per second is approximately 2 mph
How much energy is there in a 20 mph wind?
20 mph wind =10 m/s .0006 * 10³ = .0006 * 1000 = .6 KILO watts per square meter
which is 600 watts per square meter
this is identical to average solar power per square meter at our latitude.

Example Problem:

40/10 = 4 wind blows 4 times harder
4³ = 64 if a 10 mph wind gives you 100 watts per square meter then a 40 mph wind gives you 64 times more power per square meter 6400 watts per square meter
total power = 6400 watts per square meter * 2 square meters = 12800 watts = 12.8 Kilowatts this is a lot!

The above calculation is known as a scaling calculation; you simply need to scale the original conditions to the final conditions. You only need to know the v³ to do this.

Windmill Efficiency

Windmills can not operate at 100% efficiency because the structure itself impedes the flow of the wind. The structure also exerts back pressure on the turbine blades as they act like an air foil (a wing on an airplane).

In most all cases, the efficiency of the wind turbine depends on the actual wind speed. For the three blade design the efficiency curve looks like this:

Because the power goes as v³, there is no real need to optimize design for highest efficiency at highest windspeed because the power capacity in the wind will greatly exceed that which can be obtained by the generator.

Theoretical maximum efficiency is 59%
Picaresque Dutch Windmill (4=arms) = 16%
Rotary, multiblade = 30%
High speed propeller (vertical) = 42%
Two blade horizontal = 45%

Rotary type windmills have high torque and are useful for pumping water. High torque means efficient operation at low wind speeds.

High speed propeller types have low torque and are most efficient at high rotational velocities useful for generation of electricity

Example calculation:

Windmill efficiency = 42%
average wind speed = 10 m/s (20 mph)
Power = 0.0006 x 0.42 x 1000 = 250 Watts per square meter
Electricity generated is then .25 KWH per sq. meter
If wind blows 24 hours per day then annual electricity generated would be about 2200 KWH per sq. meter
But, on average, the wind velocity is only this high about 10% of the time
typical annual yield is therefore 200-250 KWH per sq. meter

To Generate 10,000 KWH annual then from a 20 mph wind that blows 10% of the time

windmill area = 10,000 KWH/220 KHW per sq. meter = 45 sq meters
This is a circular disk of diameter about 8 meters
This is not completely out of the question for some homes
Even a small windmill (2 meters) can be effective:
- 20 mph 10% of the time --> 2500 KWH annually
- 40 mph 10% of the time --> 20000 KWH annually
- 20 mph 50% of the time --> 12500 KWH annually
- 4 small windmills at 20 mph 10% of the time --> 10000 KWH annually

Wind Energy can be competitively priced:

Wind turbine technology has steadily improved
Typical capacity for a single unit is now 250-500 KW
Relatively low capital costs; very low operating costs
- Wind: 4.3 cents per KWH
- Coal: 6.2
- Photovoltaics: 16.0
- Advanced Gas Turbine: 4.6

Current Grid Connected Wind Power:

    Country/region          MW Installed
        ------------------------------------
        United States   -       1700
        Denmark         -       520
        Germany         -       330
        United Kingdom  -       145
        Netherlands     -       132
        Spain           -       55
        Greece          -       35
        Italy           -       10
        Other OECD      -       70
        India           -       50
        China           -       25

Some aggressive goals for wind power:

to install 10,000 MW of capacity in the U.S.;
to build a $4 billion domestic wind industry capable of delivering 3,000 MW annually;
to create tens of thousands of new, long-term, skilled jobs;
to achieve levelized costs below four cents per kilowatt-hour;
to make wind power a major option in achieving the nations global climate change objectives; and
to make the U.S. wind energy industry the worlds technology leader and lowest cost supplier.

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Wind Energy

Power per sq. meter = .0006 V3

Power per sq. meter = .0006 V³