Deck 10: Wind Energy

Question 1

The Royal Clipper (Figure 10.1) has a total sail area of the estimate for the total power of a large sailing ship as given in the text is reasonable.

Answer 1

The total power available is

Question 2

A wind turbine with an efficiency of velocity of 13 m/s. What is the turbine rotor diameter?

Answer 2

From equation (10.5)

Question 3

A high-speed two-blade wind turbine operates with a tip speed ratio of 14.
It produces 1.0 MWe in a 12 m/s wind. What is the rotor diameter?

Answer 3

The power is

Question 4

For a 10 m diameter wind turbine with an efficiency of 45% located on land
of roughness class 2, calculate the power produced by as a function of hub height from 20
m to 120 m for a wind velocity of 10 m/s at a height of 50 m.

Question 5

A Darrieus rotor has an area of speed ratio. What is its power output in a wind with a velocity of 20 m/s?

Question 6

A wind turbine with a 40-m diameter rotor produces 287-kW output in a 10-
m/s wind. What is its efficiency?

Question 7

A three-blade wind turbine with a 100 m rotor diameter operates with a tip
speed ratio of 10.
(a) What is the efficiency?
(b) What fraction of the Betz limit is achieved?
(c) What is the actual power output in kW for a wind speed of 11 m/s?
(d) For the wind speed in part (c), what is the actual blade tip velocity?
(e) For the wind speed in part (c), how long does it take the rotor to make one rotation?

Question 8

A Darrieus rotor with a swept area of 1000 m2 produces 240 kW output in

Question 9

Wind with a velocity of 12 m/s is incident on a three-blade wind turbine

Question 10

Estimate the ratio of wind velocity 10 km off shore the wind velocity at the

Question 11

Dresden, Germany has a population of 700,000 and a population density of

Question 12

Wind velocities are not constant throughout the day. The daily average

Question 13

A three-blade wind turbine with a rotor diameter of 50 m, produces an
output of 570 kW in a 10 m/s wind. Calculate the wind velocity after passing through the
turbine.

Question 14

(a) Two locations have the same average wind velocity. One location has a

Question 15

A home owner installs a wind turbine with a rotor diameter of 2 m to
supplement electricity from the public utility. The cost of the turbine, the associated
electronics, and energy storage system (batteries) is $10,000. If the turbine has an
efficiency of 35% and the energy is utilized and or stored at an efficiency of nearly 100%,
what is the payback period for the investment? Assume that maintenance costs are
minimal, the capital recovery factor is unity, electricity from the public utility costs $0.10
per kWh, and the wind velocity is constant at 12 m/s.

Question 16

(a) Show that for a wind turbine spacing of 3 rotor diameters crosswind
and 10 rotor diameters downwind, the power generated per unit land area for a wind farm
is independent of rotor diameter and is equal to where ρ is the air density and η is the turbine efficiency.
(b) Show that when the velocity is measured in m/s, the power per unit area is in kg/s3.
(c) Discuss the relevance of hub height on the answer to part (a).

Question 17

Consider two identical wind turbines with a hub height of 40 m, one
located in flat agricultural land and one located above a forest. What is the relative output
power for the two turbines if the wind velocity is 10 m/s at a height of 100 m in both
cases?

Question 18

(a) Consider a wind farm consisting of 10-m diameter wind turbines with

Question 19

A country would like to provide all of its residential and industrial

Question 20

A country with good wind resources decides to make a national
commitment to the development of wind energy. It is decided that 10% of the land area
will be devoted to wind energy with a goal of 1.5 kWe per-capita wind capacity. This is
roughly the electricity used by one person in an industrialized nation (Chapter 2). Two-
megawatt wind turbines with rotor diameters of 80 m (Energy Extra 10.1) are placed at the
average spacing shown in Figure 10.18. Average output based on wind conditions is 650
kWe per turbine. Estimate the maximum population density that is consistent with this
plan. Locate geographical information about Germany, Spain, India, and Denmark (all of
whom have active wind power programs), and discuss the possibility of achieving this goal
in each of these countries.