Energy Talk!

lion_sim_bob asked:


Rows of wind-powered generators are used in various windy locations to generate electric power. Does the power generated affect the speed of the wind? Would locations behind the windmills be windier if the windmills weren’t there? Discuss this in terms of energy conservation.

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2 Responses to “Energy conservation as it relates to windmills?”

1. jjjcmzzt Says:
   October 7th, 2007 at 9:24 pm

   I’m guessing it would because the windmill is spinning when the wind hits it so ya i’m guessing it probably does slow it down.

2. pp_314156 Says:
   October 9th, 2007 at 4:50 am

   Do you mean energy conservation, or the conservation of energy?

   The first wind turbine will extract power from the moving air stream, and since energy is conserved (neither created or destroyed), the downstream air will have less energy. The energy of the moving air mass is proportional to the velocity, therefore velocity (aka air speed) will decrease.

   The power available from a horizontal axis mill (they look like airplane propellers) is:

   Power in watts = (1/2) x (air density) x (swept area) x (wind velocity) cubed. Sorry, it isn’t easy to type formulas in these boxes.

   air density is 1.23 kg/m3 at sea level
   swept are in square meters
   wind velocity in meters per second

   The theoretical limit to efficiency (called the Betz limit) is 59.26%. Real world generators will extract less energy than this. You could use this for the sake of example, and then work backwards to see how much slower the wind immediately behind the first would be. The energy in front of the mill = the energy extracted by the mill + the energy behind the mill.

   Have fun with the math.