Thoughts

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==== Terawatts of Windpower, Global Calming, and a New Role for Meteorologists ====


//Presented as a seminar in May 1, 2008//  {{ ::windsem.pdf |}}

=== Total Available Solar and Wind Power ===
{{:globalcalming:EnergyCubes_sm.png}}

The above figure is [[http://en.wikipedia.org/wiki/Image:Available_Energy-2.jpg | from the Wikipedia]], 
but with an additional annotation indicating the flux density derived using the total surface area
of the Earth, $5.1 \times 10^{14} \mathrm{m}^2$.  

Most of us could easily calculate the numbers for solar power
using knowledge of the solar constant and the fraction of solar radiation reaching the surface.
Deriving the number for available wind power might require more effort.  Before we attempt such a derivation,
notice that global consumption is 4% of the available wind power.  This fact alone implies that powering a large portion of
human energy needs with wind power could alter weather and climate, and not just within
certain regions near where the extraction is occurring.

== Derivation of Available Wind Power ==

Here is a simple way to estimate wind power availability:

{{:globalcalming:WindAvail_sm.png}}

== A Very Large Wind Turbine ==

Here is an image of a [[http://www.treehugger.com/files/2006/08/largest_wind_tu.php | 5 MW wind turbine]] being erected.  The rotor diameter is  $2R = 126$ meters.

{{:globalcalming:repower_5m_2.jpg}}

Imagine a tube of air of radius $R$ approaching the turbine.  The rate of kinetic energy moving through the tube is 
$ \frac{1}{2} \pi R^2 \rho V^3$. 



 A [[http://en.wikipedia.org/wiki/Wind_turbine#Potential_turbine_power | wind turbine]] can capture up to 40% of this kinetic energy, at the ideal windspeed for which it was designed.  This amount of power defines the //capacity// or //nameplate// of the wind turbine.  In operation, windspeed is not ideal all the time, so production is typically about 30% of capacity.  

This 5 MW example turbine will produce at capacity in 12.5 m/s windspeed (using $\rho=1\ \mathrm{kg} \ \mathrm{m}^{-3}$). In practice, it will produce about 1.66 MW. When operating at peak capacity, this wind turbine will be removing 388 W m<sup>-2</sup> from the disc intercepted by the blades.  Coincidentally, the most efficient (and expensive) photovoltaics can also extract power at a  [[http://en.wikipedia.org/wiki/Solar_cell#Watts_peak | similar flux density ]] of 400 W m<sup>-2</sup>.  But despite all the structural mass and strength of a wind turbine, wind power is cheaper than photovoltaic power.

  
== A Very Large Wind Array ==

Imagine a slightly smaller turbine with 3 MW capacity and 1 MW production.  Suppose we construct an array with spacing of 1 km.  That allows for 1 W m<sup>-2</sup> extraction from the wind. (A denser array would decrease the windspeed too much; the investment in more wire and access roads to produce 1 km spacing is worthy).  Suppose we want to produce 16 TW.  We need 16 million wind turbines, and
an array 4000 km by 4000 km. 

== A Very Large Wind Hole ==

The atmosphere has a column mass density close to 10<sup>4</sup> kg m<sup>-2</sup>.  Using the typical windspeed of
U=10 m s<sup>-1</sup>, the column kinetic energy density is  5.0 x 10<sup>5</sup> J m<sup>-2</sup>.  In 10<sup>5</sup> seconds, or just
over one day, 1.6 x 10<sup>18</sup> Joules would be extracted from the atmosphere if the extraction rate is 16 TW.  That is equivalent to extracting all the wind, in the entire depth of atmosphere, in an area 1800 km by 1800 km - //every day//.

=== Resource needs ===

== steel ==
Company documents for the [[http://www.vestas.com/Admin/Public/DWSDownload.aspx?File=%2fFiles%2fFiler%2fEN%2fSustainability%2fLCA%2fLCAV90_juni_2006.pdf|  Vestas V90-3.0 MW ]] cite a combined weight of 256 tons for the tower, nacelle and rotor.  Most of this weight is steel, and more steel will be needed for the foundation. 
Let's work with an easy number of 0.1 kg of steel per Watt of generation capacity, and also assume a 25 year lifetime for the wind turbine and tower.  To produce 16 TW we need 50 TW capacity in operation, and about 2 TW of capacity demolished, recycled and installed every year.  We therefore need 2x10<sup>11</sup> kg of steel per year.  Current annual global steel production is 8x10<sup>11</sup> kg (requiring .5 TW for production).  Thus we anticipate needing 1/4 of the world steel production, and at least .125 TW to produce that steel, to sustain 16 TW of wind power production. 

As an American you will need about 30 kW capacity to supply your //total// power needs of 10 kW.
That works out to be 3000 kg of steel committed in wind turbines, on your behalf.  This weight is
equivalent to that of the [[http://en.wikipedia.org/wiki/Hummer| Hummer]] automobile.  
 
Here is a 1997 document citing [[http://www.windpower.org/media(444,1033)/the_energy_balance_of_modern_wind_turbines,_1997.pdf | 0.1 kg of steel per Watt of generation capacity ]] (for 1.65 MW tower). 
== copper ==
[[http://www.infra.kth.se/fms/utbildning/lca/projects%202006/Group%2007%20(Wind%20turbine).pdf | Life cycle assessment of a wind turbine]] divulges that the Vestas V90-3.0 MW has as 8.5 ton generator, of which 35% is copper.  This gives a number very close to 1 gram of copper per Watt of generating capacity (from the generator alone).  50 TW of wind power capacity requires 50 Tg of copper just for generators. [[http://www.pnas.org/cgi/content/abstract/103/5/1209 | Metal stocks and sustainability ]] states that the USGS estimates total recoverable copper on Earth to be 1000 Tg.  (400 Tg has been mined so far, and presumably most is in use).  So 5% of all the world's copper, currently in use and potentially mined, is needed just for the generator component.  (Yes, we do have a copper supply problem looming: [[http://en.wikipedia.org/wiki/Peak_copper | peak copper]]).

== money ==

According to Table B-11 in [[ http://www.20percentwind.org/20p.aspx?page=Report |  "20% Wind Energy by 2030" (US)]], in 2010 the capital cost for a shallow offshore installation in class 5 winds would be
 \$2,300 per kW capacity. The capacity factor is stated to be .45 (too good to be true?). So the cost is 
\$5,100 per kW of production. An American's total energy needs are 10 kW or 88 MWh per year.   A turbine typically lasts 25 years.  So an American can purchase ''their entire energy needs, both direct and indirect'' for \$51,000 capital investment, every 25 years.  Or, if your are paying 7.5% interest on the investment, you would be paying $3825 per year on interest.  Table B-11 also implies ''fixed O&M costs'' of \$333 and ''variable O&M costs'' of \$1494, for a total of $5652.  This implies a cost \$0.064 per kWh.  This is slightly lower than the \$0.080 per kWh on a typical electric bill.  

So the calculation here is consistent with the statement that wind energy is competitive with the cheapest source of electricity: coal power.  The \$5652 per year implies you are using wind generated electricity to heat your home, which is not cost-effective.  You would probably rather use solar thermal energy for that purpose.  But keep in mind your \$5652 buys ''all'' your energy needs, both direct and indirect. Examples of indirect energy use are: mining and food production done for you, the energy needed for your steel and concrete production and transport, and so on.  Though \$5652 is lot of money, keep in mind that you currently pay a lot for indirect energy costs in all your purchases.
 
=== Projections for Wind Power 2020-2050 ===

These projections are more modest than the 16 TW examples above. Keep in mind that,
in generating electricity, fossil fuel energy consumption is 2 to 3 times the electrical energy
production (the rest of the energy being lost as waste heat).  So, coincidentally, the fossil fuel offset provided by wind energy is close to the capacity of the wind turbine.

The following figure shows various //production// projections;  //capacity// would need to be about 3 times as large:

{{:globalcalming:WindProjections.png}}

  * 2007 (year end) U.S. Capacity: [[http://en.wikipedia.org/wiki/Wind_power#Utilization_of_wind_power | 16.8 GW]], producing about 5.6 GW
  * 2007 (year end) Global Capacity: [[http://en.wikipedia.org/wiki/Wind_power#Utilization_of_wind_power |93.8 GW]], producing about 31.3 GW
  * 2010 World Wind Energy Association: [[http://www.wwindea.org/home/index.php?option=com_content&task=view&id=167&Itemid=43 |160 GW ]] capacity, producing about 53 GW
  * 2020 Shell ''Blueprint'' global production projection: 290 GW production 
  * 2020 Lester Brown's ''Plan B'' (global): 3000 GW capacity, producing about 1000 GW  
  * 2030 DOE [[ http://www.20percentwind.org/20p.aspx?page=Report |  "20% Wind Energy by 2030" (US)]]: ~300 GW capacity, producing about 132 GW 

=== Environmental Impacts of Wind Farms ===

== Traditional Environmental Impact Concerns ==
Not everybody thinks wind farms are desirable (and for some very good reasons):
  * [[http://www.savewesternny.org/index.html | Wind Farm Madness ]]
  * [[http://www.aweo.org/ProblemWithWind.html | A problem with wind power ]]
  * [[http://www.wvmcre.org/ | Mountain Communities for Responsible Energy ]]
== Weather impacts of a simulated 10 GW wind farm within Oklahoma ==
Somnath Baidya Roy, Steve Pacala and Robert L. Walko (2004) [[ http://www.agu.org/pubs/crossref/2004/2004JD004763.shtml | Can Large Windfarms Affect Local Meteorology? ]] J. Geophys. Res.-Atmos.  VOL. 109, D19101. 

This article emphasizes the effects //within the wind farm itself//.

== Climate impacts of 10 TW of wind farms in a GCM ==
David W. Keith, Joseph F. !DeCarolis, David C. Denkenberger, Donald H. Lenschow, Sergey L. Malyshev, Stephan Pacala and Phillip J. Rasch (2004):[[ http://www.ucalgary.ca/~asadams/keith2004.pdf | The influence of large-scale wind-power on global climate.]] Proceedings of the National Academy of Sciences, 101, p. 16115-16120.

== Simulations with WRF ==

Three years after this page was constructed, at last, with help from my colleagues, we have completed our [[https://www.researchgate.net/publication/231078334_The_effect_of_a_giant_wind_farm_on_precipitation_in_a_regional_climate_model#fullTextFileContent |The effect of a giant wind farm on precipitation in a regional climate model ]].  Here is a [[https://12characters.net/saga/ | figure dump ]].