Energy and Human Ambitions on a Finite Planet, 2021a

12 Wind <strong>Energy</strong> 196
17. In a way similar to Figure 12.5, replicate the statement in the text
that the fraction of l<strong>and</strong> covered per rotor area is 0.65% if turbines
are separated by 15 rotor diameters along one direction <strong>and</strong> 8 rotor
diameters along the cross direction.
18. Check that the units of Eq. 12.3 43 indeed are equivalent to Watts 43: . . . essentially ρv 3
per square meter (W/m 2 ).
19. Provide a clear explanation of why the area under the blue curve
in Figure 12.6 compared to the area of the whole rectangular box
is an appropriate way to assess the capacity factor of the depicted
wind farm?
20. What capacity factor would you estimate for the wind farm performance
depicted in Figure 12.6? In other words, what is the
approximate area under the curve compared to the entire box area,
as explored in Problem 19? An approximate answer is fine.
21. Referring to Figure 12.7, examine performance at 5 m/s <strong>and</strong> at
10 m/s, picking a representative power for each in the middle of
the cluster of black points, <strong>and</strong> assigning a power value from the
left-h<strong>and</strong> axis. What is the ratio of power values you read off the
plot, <strong>and</strong> how does this compare to theoretical expectations for
the ratio going like the cube of velocity?
22. Figure 12.7 surprisingly has all the information required to deduce
the rotor diameter! The turbine appears to produce 1,400 kW when
the wind velocity is 10 m/s, <strong>and</strong> we also know it appears to operate
at ε 0.44. What is the rotor diameter?
23. Considering that wind turbines are rated for the maximumtolerable
wind speed around 12 m/s, <strong>and</strong> tend to operate at
about 30% capacity factor, how much average power 44 would a
100 m diameter turbine operating at 45% efficiency be expected to
produce?
24. Table 12.2 shows Germany having more than twice the wind
capability as Spain, yet each gets 8.3% of its power from wind.
What do you infer the difference to be between the countries?
44: Hint: compute power at 12 m/s then
apply capacity factor
Hint: no external research necessary: what
do the numbers mean?
© 2021 T. W. Murphy, Jr.; Creative Commons Attribution-NonCommercial 4.0 International Lic.;
Freely available at: https://escholarship.org/uc/energy_ambitions.