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 the Columbia Gorge:



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 and we will assess this capacity later.

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 practice, wind farms do not take advantage of this physics but they could )
  

  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 (in units of Kilowatts) 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
• 1 meter per second is approximately 2 mph

  
  
  
  How much power 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
  

Example Problem:

In your back yard the average wind speed is 10 mph which yields 100 watts per square meter. If the wind blows 40 mph, how much power does a wind mill of 2 square meters generate?
1. 40/10 = 4 wind blows 4 times harder

2. 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

3. total power = 6400 watts per square meter * 2 square meters = 12800 watts = 12.8 Kilowatts this is a lot! but we have not yet factored in efficiency.

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:

The maximum efficiency of 44% is reached in a 9 m/s wind (18 mph) and falls sharply at higher wind speeds. For a reasonable range of winds, the average effiency is around 20%,

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
• 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

Basic Wind Router Design:

Important Economies of Scale have been realized which we can leverage later.

Note that research suggests it may be feasible to have unit capacity in a horizontal wind turbine as large as 20 MW. This would make a huge difference on overall wind scalability. But there are serious research issues with materials design and vertical turbulence (the rotor diameter would be about 250 meters) that need to be overcome first.

Some direct benefits from wind energy besides electricity generation:

• Revitalizes rural economies
• creates jobs
• promotes cost-effective energy production (e.g. low levelized costs)
• improves sustainability
• reduces air pollution (avoids the construction of a fossil plant)
• generates no waste or need for waste storage
• supports agriculture (multi use of land underneath)

  Modern Wind Turbines: