Imagine I want to make a floating wind turbine like the Altaeros BAT, which is tethered and uses helium. What would be the best height to keep such a device deployed? I know that wind velocity decreases near the ground due to friction with the Earth's surface. Though, the density of air decreases with height, so the force of high winds aloft are lessened. Considering these issues, at what altitudes do the winds exert the most force for a tethered wind turbine to produce the most energy? Please disregard the energy required to keep the turbine afloat.
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".....the density of air decreases with height, so the force of high winds aloft are lessened." I can personally vouch for the difference between a 60mph wind at sea level, and one at 14,000 feet! However, however, the single biggest difference between the two altitudes isn't so much the force of that wind, but the consistency of that wind speed, which seems to matter most to wind generation.
Here's how a wind turbine engineer would think of this problem:
From The Engineer's Toolbox- Power generated from the wind
Theoretically power in moving air - or wind - can be calculated
P = 1/2 ρ A v^3
= 1/8 ρ π d^2 v^3
where P = power (W)
ρ = density of air (kg/m3)
A = wind mill area perpendicular to the wind (m2)
v = wind velocity (m/s)
π = 3.14....
d = wind mill diameter (m)
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1$\begingroup$ -1 This does not answer the question. $\endgroup$ Commented Jan 26, 2017 at 14:10
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1$\begingroup$ I have provided a qualification to the OP's question. A link to extensive definition of the OP's question. The equation that solves the OP's question. And the defined variables in the OP's question. The OP now has everything to generate an algorithm that plots power vs. altitude for any point on earth.... $\endgroup$ Commented Jan 26, 2017 at 14:43