Wind Energy Concepts

Wind Energy Reference Manual
Part 1:
Wind Energy Concepts

Unit Abbreviations

m = metre = 3.28 ft.
s = second
h = hour
W = Watt
HP = horsepower
J = Joule
cal = calorie
toe = tonnes of oil equivalent
Hz= Hertz (cycles per second) 10^-12 = p pico = 1/1000,000,000,000
10^-9 = n nano = 1/1000,000,000
10^-6 = µ micro = 1/1000,000
10^-3 = m milli = 1/1000
10³ = k kilo = 1,000 = thousands
10⁶ = M mega = 1,000,000 = millions
10⁹ = G giga = 1,000,000,000
10¹² = T tera = 1,000,000,000,000
10¹⁵ = P peta = 1,000,000,000,000,000

Wind Speeds

1 m/s = 3.6 km/h = 2.187 mph = 1.944 knots
1 knot = 1 nautical mile per hour = 0.5144 m/s = 1.852 km/h = 1.125 mph

Wind Speed Scale

Wind Speed at 10 m height Beaufort Scale
(outdated) Wind

m/s knots

0.0-0.4 0.0-0.9 0 Calm

0.4-1.8 0.9-3.5 1 Light

1.8-3.6 3.5-7.0 2

3.6-5.8 7-11 3

5.8-8.5 11-17 4 Moderate

8.5-11 17-22 5 Fresh

11-14 22-28 6 Strong

14-17 28-34 7

17-21 34-41 8 Gale

21-25 41-48 9

25-29 48-56 10 Strong Gale

29-34 56-65 11

>34 >65 12 Hurricane

Roughness Classes and Roughness Lengths

The roughness class is defined in the European Wind Atlas on the basis of the roughness length in metres z₀, i.e. the height above ground level where the wind speed is theoretically zero. ln is the natural logarithm function.

if (length <= 0.03) class = 1.699823015 + ln(length)/ln(150) if (length > 0.03) class = 3.912489289 + ln(length)/ln(3.3333333)

You may use the calculator below and enter either the roughness length or the roughness class.
Do not use the calculator until this page and its programme have loaded completely.

Roughness Class Calculator

Roughness length in m
= Roughness class

Roughness Classes and Roughness Length Table

Rough-
ness Class

Roughness
Length m

Energy Index
(per cent)

Landscape Type

0

0.0002

100
Water surface

0.5

0.0024

73
Completely open terrain with a smooth surface, e.g.concrete runways in airports, mowed grass, etc.

1

0.03

52
Open agricultural area without fences and hedgerows and very scattered buildings. Only softly rounded hills

1.5

0.055

45
Agricultural land with some houses and 8 metre tall sheltering hedgerows with a distance of approx. 1250 metres

2

0.1

39
Agricultural land with some houses and 8 metre tall sheltering hedgerows with a distance of approx. 500 metres

2.5

0.2

31
Agricultural land with many houses, shrubs and plants, or 8 metre tall sheltering hedgerows with a distance of approx. 250 metres

3

0.4

24
Villages, small towns, agricultural land with many or tall sheltering hedgerows, forests and very rough and uneven terrain

3.5

0.8

18
Larger cities with tall buildings

4

1.6

13
Very large cities with tall buildings and skycrapers

Definitions according to the European Wind Atlas, WAsP.
For practical examples, see the Guided Tour section on Wind Speed Calculation.

Density of Air at Standard Atmospheric Pressure

Temperature
° Celsius

Temperature
° Farenheit

Density, i.e.
mass of dry air
kg/m³

Max. water
content
kg/m³

-25

-13

1.423

-20

-4

1.395

-15

5

1.368

-10

14

1.342

-5

23

1.317

0

32

1.292

0.005

5

41

1.269

0.007

10

50

1.247

0.009

15

59

1.225 *)

0.013

20

68

1.204

0.017

25

77

1.184

0.023

30

86

1.165

0.030

35

95

1.146

0.039

40

104

1.127

0.051

*) The density of dry air at standard atmospheric pressure at sea level at 15° C is used as a standard in the wind industry.

Power of the Wind **)

m/s

W/m²
m/s
W/m²
m/s W/m²

0

0

8

313.6

16

2508.8

1

0.6

9

446.5

17

3009.2

2

4.9

10

612.5

18

3572.1

3

16.5

11

815.2

19

4201.1

4

39.2

12

1058.4

20

4900.0

5

76.2

13

1345.7

21

5672.4

6

132.3

14

1680.7

22

6521.9

7

210.1

15

2067.2

23

7452.3

**) For air density of 1.225 kg/m³, corresponding to dry air at standard atmospheric pressure at sea level at 15° C.
The formula for the power per m² in Watts = 0.5 * 1.225 * v³, where v is the wind speed in m/s.
Warning: Although the power of the wind at a wind speed of e.g. 7 m/s is 210 W/m², you should note, that the average power of the wind at a site with an average wind speed of 7 m/s typically is about twice as large. To understand this, you should read the pages in the Guided Tour beginning with the Weibull Dustribution and ending with the Power Density Function.


		Wind Energy Reference Manual Part 1: Wind Energy Concepts
		Unit Abbreviations
		m = metre = 3.28 ft. s = second h = hour W = Watt HP = horsepower J = Joule cal = calorie toe = tonnes of oil equivalent Hz= Hertz (cycles per second)		10^-12 = p pico = 1/1000,000,000,000 10^-9 = n nano = 1/1000,000,000 10^-6 = µ micro = 1/1000,000 10^-3 = m milli = 1/1000 10³ = k kilo = 1,000 = thousands 10⁶ = M mega = 1,000,000 = millions 10⁹ = G giga = 1,000,000,000 10¹² = T tera = 1,000,000,000,000 10¹⁵ = P peta = 1,000,000,000,000,000
		Wind Speeds
		1 m/s = 3.6 km/h = 2.187 mph = 1.944 knots 1 knot = 1 nautical mile per hour = 0.5144 m/s = 1.852 km/h = 1.125 mph

Wind Speed Scale
Wind Speed at 10 m height		Beaufort Scale (outdated)	Wind
m/s	knots	Beaufort Scale (outdated)	Wind
0.0-0.4	0.0-0.9	0	Calm
0.4-1.8	0.9-3.5	1	Light
1.8-3.6	3.5-7.0	2
3.6-5.8	7-11	3
5.8-8.5	11-17	4	Moderate
8.5-11	17-22	5	Fresh
11-14	22-28	6	Strong
14-17	28-34	7	Strong
17-21	34-41	8	Gale
21-25	41-48	9	Gale
25-29	48-56	10	Strong Gale
29-34	56-65	11	Strong Gale
>34	>65	12	Hurricane

Roughness Classes and Roughness Lengths The roughness class is defined in the European Wind Atlas on the basis of the roughness length in metres z₀, i.e. the height above ground level where the wind speed is theoretically zero. ln is the natural logarithm function. i`f (length <= 0.03) class = 1.699823015 + ln(length)/ln(150) if (length > 0.03) class = 3.912489289 + ln(length)/ln(3.3333333)` You may use the calculator below and enter either the roughness length or the roughness class. Do not use the calculator until this page and its programme have loaded completely.
Roughness Class Calculator Roughness length in m = Roughness class
Roughness Classes and Roughness Length Table
Rough- ness Class	Roughness Length m	Energy Index (per cent)	Landscape Type
0	0.0002	100	Water surface
0.5	0.0024	73	Completely open terrain with a smooth surface, e.g.concrete runways in airports, mowed grass, etc.
1	0.03	52	Open agricultural area without fences and hedgerows and very scattered buildings. Only softly rounded hills
1.5	0.055	45	Agricultural land with some houses and 8 metre tall sheltering hedgerows with a distance of approx. 1250 metres
2	0.1	39	Agricultural land with some houses and 8 metre tall sheltering hedgerows with a distance of approx. 500 metres
2.5	0.2	31	Agricultural land with many houses, shrubs and plants, or 8 metre tall sheltering hedgerows with a distance of approx. 250 metres
3	0.4	24	Villages, small towns, agricultural land with many or tall sheltering hedgerows, forests and very rough and uneven terrain
3.5	0.8	18	Larger cities with tall buildings
4	1.6	13	Very large cities with tall buildings and skycrapers
Definitions according to the European Wind Atlas, WAsP. For practical examples, see the Guided Tour section on Wind Speed Calculation.

Density of Air at Standard Atmospheric Pressure
Temperature ° Celsius	Temperature ° Farenheit	Density, i.e. mass of dry air kg/m³	Max. water content kg/m³
-25	-13	1.423
-20	-4	1.395
-15	5	1.368
-10	14	1.342
-5	23	1.317
0	32	1.292	0.005
5	41	1.269	0.007
10	50	1.247	0.009
15	59	1.225 *)	0.013
20	68	1.204	0.017
25	77	1.184	0.023
30	86	1.165	0.030
35	95	1.146	0.039
40	104	1.127	0.051
*) The density of dry air at standard atmospheric pressure at sea level at 15° C is used as a standard in the wind industry.

Power of the Wind )**
m/s	W/m²	m/s	W/m²	m/s	W/m²
0	0	8	313.6	16	2508.8
1	0.6	9	446.5	17	3009.2
2	4.9	10	612.5	18	3572.1
3	16.5	11	815.2	19	4201.1
4	39.2	12	1058.4	20	4900.0
5	76.2	13	1345.7	21	5672.4
6	132.3	14	1680.7	22	6521.9
7	210.1	15	2067.2	23	7452.3
*) For air density of 1.225 kg/m³, corresponding to dry air at standard atmospheric pressure at sea level at 15° C. The formula for the power per m² in Watts = 0.5 1.225 * v³, where v is the wind speed in m/s. Warning: Although the power of the wind at a wind speed of e.g. 7 m/s is 210 W/m², you should note, that the average power of the wind at a site with an average wind speed of 7 m/s typically is about twice as large. To understand this, you should read the pages in the Guided Tour beginning with the Weibull Dustribution and ending with the Power Density Function.

Wind Energy Reference Manual Part 1: Wind Energy Concepts

Wind Energy Reference Manual
Part 1:
Wind Energy Concepts