1.7 Energy From Wind

Question 1

Describe two differences, other than the axis orientation, between Vertical Axis
Wind Turbines (VAWT) and Horizontal Axis Wind Turbines (HAWT).
1: {2}
2: {2}

Answer 1

VAWT can operate with wind in any direction {1} whereas HAWT must yaw to face into
the wind {1}.
VAWT can operate at low wind speeds {1} whereas HAWT requires higher wind speeds
{1}.
VAWT rotates at a low RPM {1} whereas HAWT rotates at higher RPM {1}.
VAWT is less noisy than HAWT {1} and has less vibration than HAWT {1}.

Question 2

Describe two differences between Vertical Axis Wind
Turbines (VAWT) and Horizontal Axis Wind Turbines (HAWT). {2}

Answer 2

Any two from;
• A VAWT can operate with wind in any direction whereas HAWT must yaw to
face the wind.
• VAWT can operate at low wind speeds whereas HAWT requires higher wind
speeds.
• VAWT rotates at low RPM whereas HAWT rotates at higher RPM.
• VAWT has rotor in vertical direction; HAWT has rotor in horizontal direction.
• VAWT is less noisy than HAWT.
• VAWT has less vibration than HAWT. {2}

Question 3

I the box provided in the figure above clearly label the Component X. {1}

Answer 3

X – Wind Turbine Tower.

Question 4

Fig. 2 below shows a typical horizontal axis wind turbine.
Complete Fig. 2 labelling X and Y. {2}

Answer 4

X; Gearbox {1}
Y: Generator {1}

Question 5

Fig. 3 shows a typical horizontal axis wind turbine. Identify the shaded area
which has been labelled A in Fig. 3. {1}

Answer 5

Swept area {1}

Question 6

Fig. 1 below shows a typical horizontal axis wind turbine. Complete Fig. 1 by
labelling X and Y. {2}

Answer 6

X: Nacelle – must be named correctly. {1}
Y: Anemometer – must be named correctly. {1}

Question 7

Calculate the wind speed required to produce
17,280 joules of energy from 540 kg of air. {3}

Answer 7

K.E = 1/2 mv2 {1}
17280 = 0.5 x 540 x v2
.v2 = 17280/ (0.5 x 540) {1}
= 64
.v = 8 m/s {1}

Question 8

Calculate the wind speed required to produce a maximum
theoretical energy of 15,680 joules from 640kg of air. Show your working out in
the space below. {3}

Answer 8

K.E = 1/2 mv2
15680 = 0.5 x 640 x v2 {1}
.v2 = 15680/ (0.5 x 640) {1}
.v2 = 49
.v = 7 m/s {1}

Question 9

For a HAWT turbine calculate the maximum theoretical energy available from
580 kg of air passing through the turbine with a speed of 11 m/s. Show your
working out in the space below. {2}

Answer 9

K.E = 1/2 mv2
K.E = 0.5 x 580 x 11^2 {1}
K.E = 35090 J {1}

Question 10

Calculate the maximum theoretical energy available to the wind turbine at the
quarry if the available wind speed is 27 m/s and the mass of air going through
the turbine is 2400 kg. {3}

Answer 10

K.E = 1/2 mv2 {1}
K.E = 0.5 x 2400 x 27^2 {1}
K.E = 1200 x 729
K.E = 874 800 J {1}

Question 11

The energy present in 860 kg of air moving at a particular wind speed is 43000
J. Calculate the wind speed of the 860 kg of air.
Show your working out in the space below. {3}

Answer 11

K.E = 1/2 mv2 {1}
43000 = 0.5 x 860 x v2
43000 / (0.5 x 860) = v2 {1}
100 = v2
10 m/s = v {1}

Question 12

Define what is meant by the term Betz Limit when applied
to a wind turbine and explain how it is related to power efficiencies achievable
by wind turbines in the real world. {4}

Answer 12

The maximum amount of the winds kinetic energy that a HAWT can convert to
mechanical energy turning a rotor. {1}
Betz calculated this at 59.3% of the kinetic energy from the wind. {1}
Most modern turbines however can only concert 35 – 45% of the winds energy
to electricity. {1}
Because of the energy losses in gear boxes etc. {1}

Question 13

For a rotor diameter of this size and with a wind speed of 11m/s the maximum
available rated energy in the wind is 16.4 kW. Identify two reasons which
explain why there is an energy shortfall between the maximum energy available
in the wind and the actual rated energy output of the turbine. {2}

Answer 13

• Because a significant portion of the available wind energy has to pass
through the blades and is unavailable for energy conversion (i.e. the Betz
limit). {1}
• In addition, there will be further energy losses within the gearing and
electrical components of the turbine. {1}

Question 14

Define what is meant by the term Betz Limit when applied to a wind turbine. {2}

Answer 14

Betz Limit: The maximum amount of the wind’s kinetic energy that a HAWT can
convert to mechanical energy turning a rotor; Betz calculated this at 59.3% of
the kinetic energy of the wind. {2}

Question 15

Explain how the Betz Limit is related to power efficiencies achievable by wind
turbines in the real world. {2}

Answer 15

Most modern wind turbines can only convert 35–45% of the wind’s energy into
electricity; This is because of energy losses in gearboxes, generators, etc. {2}

Question 16

(i): Define the term ‘Rotor Collected Energy’. {1}
(ii): Give two reasons to explain why the rated energy output of a wind turbine
is lower than the rotor collected energy.
1: ____________ {2}
2: ____________ {2}

Answer 16

(i): The rotor collected energy refers to the energy in the wind utilised by the
turbine blades. {1}
(ii): The energy can be lost through inefficiencies such as energy loss between
components in the turbine. {2}
The rated energy output of a turbine can be limited by the size of the generator. {2}

Question 17

Use the Betz limit to calculate the maximum theoretical limit of kinetic energy
that can be converted by the turbine from 43000 J of wind energy.
Show your working out in the space below. {2}

Answer 17

43000 x 0.593 = 25499J {2}

Question 18

Explain the relationship between Power output and swept
area for a HAWT. {1}

Answer 18

The power output is directly proportional to the swept area. {1}

Question 19

If a turbine has a rotor diameter of 6.0m calculate the rotor
swept area for the turbine. Show your working out in the space below. {3}

Answer 19

Radius = 1/2 x diameter = 3m {1}
Swept Area = 3.14.. x r2 {1}
A = 3.14 x 3^2 = 28.27m2 {1}

Question 20

If the length of the rotor blades in a HAWT is doubled, explain by what factor
the shaded area will increase. {2}

Answer 20

A = πr 2 therefore if r is doubled the swept area will be quadrupled; {2}

Question 21

If the rotor swept area for the turbine in Fig. 1 is 50.27 m2, calculate the rotor
diameter. {4}

Answer 21

50.27 = 3.14.. x r2 {1}
R2 = 16m2 {1}
R = 4m {1}
Rotor diameter = 8m {1}

Question 22

The figure below illustrates a typical wind power curve.
Identify and explain the following annotated points on the graph;

X {2}
Y {2}

Answer 22

X; The Rated Power, Prated. {1}
This is the power limit of the electrical generator. {1}
Y: Cut on speed, Ucut-in. {1}
This is the wind speed that first causes the turbine blades to rotate and produce
power. {1}

Question 23

Explain the relationship between Power output and wind
speed for a HAWT. {1}

Answer 23

The power output increases with wind speed as Pout is directly proportional to
v3
. {1}

Question 24

Fig. 3 below shows a typical wind turbine power curve.
Explain the significance of the annotated points. {4}

Answer 24

A: Cut in speed {1}, the wind speed at which the turbine begins to turn and
generate electricity {1}

B: Cut out speed {1}, the wind speed at which the turbine stops rotating in
order to protect itself from damage {1}

Question 25

If the length of the rotor blades in Fig. 3 increases, how will the power output of the turbine change (assuming the wind speed remains constant)? {1}

Answer 25

The power output will increase {1}

Question 26

Describe how the power output of a wind turbine is affected by the following factors; (i); Air density. {1} (ii); Temperature. {1}

Answer 26

When air density is lower the power output is less or when air density is higher the power output increases. {1} When temperature is lower the turbine power output is greater or when temperature is higher the turbine power output reduces. {1}

Question 27

Explain one factor that is critical in determining the hub height of a wind turbine. {2}

Answer 27

Visual impact of the turbine {1} which is dependent on size of turbine/ tower and topography of the surroundings {1}

Question 28

A local quarry owner has applied for planning permission to install a Horizontal Axis Wind Turbine. The Planning Service has requested that the hub height of the turbine be lowered Discuss two reasons why this will have a detrimental impact on the power output of the turbine. 1: _________________________ {2} 2: _________________________ {2]

Answer 28

Wind speed is higher as height increases from ground level. Wind velocity has a crucial impact on the power output of the wind turbine. A larger hub height will allow for a larger blade diameter and therefore a larger swept area giving a greater power output. A higher hub height prevents the air flow from becoming disturbed by any obstructions such as trees or buildings. {4}

Question 29

Outline two critical factors that must be taken into account when determining the hub height for a wind turbine installation. {2}

Answer 29

Any two from; • Wind resource assessment of the site. {1} • Topography of the site. {1} • Size of the turbine / blade length. {1} • Visual impact of the turbine. {1}

Question 30

A turbine has a mass of 10 tonnes. In the space below, show that is the blade length is doubled the new mass of the turbine will be 80 tonnes. {4}

Answer 30

Existing mass (10 tonnes) is proportional to R3 {1} 2R then new mass (X) proportional to (2R) ^3 {1} = 8R^3 {1} If R = 10 tonnes then 2R = 80 tonnes {1}

Question 31

A wind turbine has a mass of 9 tonnes. Show that, if the blade length doubles, the new mass of the turbine will be 72 tonnes. Show your working out in the space below. {3}

Answer 31

Existing mass (9 tonnes) proportional to cube of blade length {1} 2R = new mass proportional to (2R)^3 = 8R^3 {1} 9 x 8 (or 2^3) = 72 tonnes {1}

Question 32

John is considering a wind turbine to power his home. Describe two ways in which the performance of his turbine could be influenced by each of the following factors; {6} 1 – Blade length; 2 – Strength of materials; 3 – Siting requirements;

Answer 32

Blade length; {2} Any 2 from; • Longer blades could generate more power than short blades due to larger swept area. • Longer blades may need stronger wind speeds to generate power. • Longer blades can increase the stresses within the turbine. Strength of materials; {2} Any 2 from; • Lightweight balde materials may be too weak and may break. • Stronger, heavier blades need stronger wind speeds to generate power. • Composite materials can provide a good mix of strength and weight. • Turbine blades need to resist corrosion / rust. Siting requirements; {2} Any 2 from; • Exposed locations provide stronger, more consistent wind. • Obstacles (buildings / trees) can reduce performance. • Hills facing towards prevailing winds can improve performance.

Question 33

Explain how blade length and strength of materials affect turbine performance. Blade length: ______________________ {2} Strength of materials ________________ {2}

Answer 33

Blade length: Longer turbine blades have a greater swept area so can harness more wind power, increasing turbine performance. {1} They may require higher cut-in wind speeds unless they are composed of lightweight/composite materials. {1} Strength of materials: Strong materials are required to withstand the forces acting on the turbine blades. {1} Stronger blades may be heavier and may need higher cut-in speeds to generate power which will reduce the efficiency/performance of the turbine. {1}

Question 34

Define the term ‘wind survival speed’. {1}

Answer 34

The maximum wind speed that a turbine is designed to withstand before sustaining damage.

Question 35

State what is meant by the wind survival speed of a wind turbine. {1}

Answer 35

The maximum wind speed that a turbine is designed to withstand before it will sustain damage {1}

Question 36

Wind turbines are designed with a range of power control systems. Name one power control system used in wind turbines. {1}

Answer 36

Yawing. {1}

Question 37

Describe the purpose of the Yaw mechanism. {2}

Answer 37

Yaw mechanism ensures; • Rotor faces the wind at all times. {1} • Maximum energy extraction. {1}

Question 38

Explain the function of yawing in the context of a wind turbine. {2}

Answer 38

Where the turbine is turned to face into the wind in order to extract maximum energy from it. {2}