# Wind

Document Sample

```					Wind
Mass of atmosphere

500km air above 1m2
that is 10 000kg
At earth’s surface it equals approx.
10m x 1m2 =10m3 water
Air density and pressure
Part icles                           6
Density                          6
Pressure
6                                             1 10                                         1 10
1 10
5                             50. km              5                        50. km              5                      50. km
1 10                                                 1 10                                         1 10
10. km                                       10. km                                     10. km
4                                                   4                                            4
h 1 10                                               h 1 10                                       h 1 10
i      3                                             i     3                                      i     3

m

m
1 10                                                 1 10                                         1 10
100                                                  100                                         100
10                                                10                                           10
1                                                 1                                            1
0            2            4                       0       1            2                       0      0.5         1
particles . m
3                                      i                                           P
i
i
3                                     bar
10
25                                       kg . m

Density decreases from ample 1kg to 1g/m3 at 50km height.
So, aeroplanes meet less resistance the higher they fly (until 20km),
but propellers and wings will work less as well.
Temperature(height)
6
Temperature
1 10                                             200
5                              50. km
1 10
Stratosphere     10. km                    0
4
h 1 10                                         H                    Ionosphere
i     3
m

1 10                                             100
Troposphere               km                   Mesosphere
100
50
10                                                           Stratosphere
10
1                                          0
0   500        1000    1500                100   0           100      200
T
i                                         T1 ( H ) (celcius)
K (kelvin)

Weather takes place in troposphere.
Expanding (cooling) clouds stop raising as soon as their temperature
equals their environment, sometimes loosing moist as rain.
Air, heated by Earth’s surface sometimes stop clouds cooled by nocturnal
Wind force
Wind force (= air mass x velocity/sec);                              3000

on a surface of 1m2 it’s ‘pressure’;
2500
air mass = density x air content;
air content = surface x air length;                                  2000

air length = velocity x sec.

Newton
force ( velocity ) 1500

Velocity occurs two times in the formula                             1000

for wind force, so force increases                                    500
parabolically by
square of velocity.                                                      0
0   10   20         30   40   50
velocity
m/sec
Wind force(velocity2)
velocity
f orce mass                    mass      density  content
time

content     length  surf ace length        velocity  time

velocity
f orce( velocity)     density  velocity  time  surf ace
time

2
f orce( velocity  surf ace  density  surf ace velocity
)
Wind energy(velocity3)

energy       f orce length       length       velocity  time

2                                            kg
energy       density  surf ace velocity  velocity  time                         
density  1.290           ef f icienc y  .18
3
m
3
energy ( velocity  surf ace time  ef f icienc y)  ef f icienc y density  surf ace time  velocity

       m            2                                 5
energy  5.4          314 m  year  .19  1.062 10 kWh
      sec                            
3                                               5
E ( vg O)  2  vg  O          E ( 5.4 340)  1.071 10
Measures can be token on the level of
•   national choice of location (R=100km)
•   regional choice of location (R= 30 km)
•   arrangement of rural areas; form of conurbations (R= 10 km)
•   local choice of location (R= 10 km)
•   form of town and town edge (R= 3 km)
•   lay-out of districts and district quarters (R= 1 km)
•   allotment of neighbourhoods and neighbourhood quarters (R= 300 m)
•   allotment, urban details and ensembles divided in 4 hectares (R= 100 m)
•   buildings (R= 30m), and
•   the micro climate, important for humans, plants and animals (R= 10m).
Wind velocity
Power, dispersion, comfort
Measuring year average
potential wind velocity
Measuring wind
Wind stations register gusts of more than 5 seconds duration.

All measurements are averaged for one hour
resulting in the ‘hour average wind velocity’.

From these hour averages a year average can be calculated, the
‘year average wind velocity’.
Standard wind
Obstacles around the wind station introduce a deviation by which
these data are not immediately applicable in other locations of that
region.

Correction into a ‘standard ground roughness 3’ (grass land) and a
standard height of 10 metre produces the ‘year average potential
wind velocity’.

From that year average potential wind velocity one can calculate
back the year average wind velocity of neighbouring locations on
different heights and roughness using local ground data
(roughness classes).
Data lost in the average
However, in the year average wind velocity some data are lost
relevant for energy use, potential energy profit, dispersion of air
pollution and comfort of outdoor space as impact of different wind
velocities.

Firstly we miss a specification of wind direction and a statistical
distribution into different wind velocities throughout the year.

Secondly we miss how often special velocities occur.

So, we have to go back to the sources of ‘distributive frequency
division of the hour average wind velocity per wind direction,
reduced to 10 metre height above open ground’ per wind station.
Table 1

Mea-                         Velocity Still or
Class* variable
m/sec      0
E**
1 2 3 4 5 6
S
7   8
W       N TOTAL
9 10 11 12

sure-                          vk
0,5
1,5
w
348
78
10 8 11 10 12 16 14
39 43 50 51 58 72 53
16
66
15
51
9
36
13
44
14
148
618
55

ments                          2,5
3,5
4,5
15
2
59 82 98 80 97 132 111 119
88 118 133 94 118 155 160 125
86 132 136 86 124 150 170 113
84
106
110
68
84
77
79
94
87
102
1111
107
1382
1358
87
5,5             82 110 101 55 86 121 157 113    112   74   76   1158
71
6,5             74 112 82 46 71 100 163 119     109   73   76   1091
66
7,5             46 88 52 22 47 73 113 123        98   58   62    824
42
8,5             38 59 29 8 27 51 92       90     77   48   37    582
26
9,5             21 44 17 5 17 32 68       84     59   40   29    431
15
10,5             13 29 14 3 10 21 52       70     45   30   17    311
7
11,5              8 14 6 1 4 13 32         53     32   19   10    196
4
12,5              4 8 3         2 8 25     45     26   14   7     145
3
13,5              1 3 1         1 4 15     30     17   7    4     85
2
1400
12
14,5              1 2 1             1   8  20     9    4    3     49
11               1
1200                     15,5                 1              1   6  12     6    3    1     30
1000

10
800
2
16,5                                    3   8     4    3    1     19
600
400
17,5                                    2   8     4    2          16
200                     18,5                                    2   5     3    1          11
9                0                3
19,5                                    1   2     1    1           5
20,5                                        2     1                3
8                        4
21,5                                        1     1                2
7               5
22,5                                        1                      1
6                TOTAL     443 570 853 734 461 674 950 1247 1225   970 651 640 601 10000
Modelling wind velocity

C
C   1.       a. v
P( v , C, a )   a. C. v          e
Power of wind turbine
Modelling data for calculations
Fortunately the form of the graphs is higly similar to the
mathematical graph of a Weilbull probability.

C
C      1.       a. v
P( v , C, a )            a. C. v                e
‘C’ determines form, ‘a’ scale and %wind direction differs per region:
form schale % from direction (‘hours’ from North, 0 is calm or variable):
E             S           W           N total
C     a    0 1 2 3 4 5 6 7 8 9 10 11 12                             %
Beek           2,01 0,042 2 7 9 7 3 4 10 20 17 8 4 4 4                            99
Den Helder     2,00 0,014 1 6 7 8 6 5 10 13 12 10 8 8 7                          101
Eelde          1,74 0,059 3 6 8 8 7 5 9 14 14 10 7 5 4                           100
Eindhoven      1,86 0,052 8 7 8 5 6 6 7 13 16 9 6 5 4                            100
Schiphol       1,86 0,032 4 6 9 7 5 7 10 12 12 10 7 6 6                          101
Vlissingen     1,95 0,025 1 9 9 6 4 5 9 13 13 11 6 7 7                           100
The impact of parameters

C
C   1.       a. v
P( v , C, a )   a. C. v            e
Ventilation losses
Loss Schiphol and Eindhoven
Comfort
Air pollution
Regional behaviour
Windvel. 20m per roughness
Roughness islands
Lateral impacts
Dispersion
Lobe city
Lobe city
Temperature impact

'uren'
'uren'                                             250%
800                   Laagbouw                11              1
11             1           zonder                       200%                   Laagbouw
600                                                1 50
temperatuurin                 %                     Hoogbouw
10           400           2       vloed           10           1 00           2
%

200                   Hoogbouw                     50%
zonder
9              0               3   temperatuurin   9             0%                3
vloed

8                      4                           8                       4

7             5                                   7               5
6                                                   6
Lower levels of scale
Wind tunnel experiments

‘Low rise at the edge’   ‘High rise at the edge’
Green central or perpheral

‘Peripheral green’   ‘Central green’
District level
Average DCp(10) in different                    Average ventilation loss of a non airtight dwelling
configurations two times mirrored               in kWh per allotment direction if standard
around the centre.                              Northerly wind would blow from all directions .
0                                                0
0,2                                                     150
11                    1
0,15                                              11     140
1
130
10         0,1                  2
10                                 2
120
0,05
110
9               0                       3
9              100                      3

8                              4                       8                               4

7                    5                                   7                   5
6
6
configuration 1    peripheral low rise                  configuration 1
configuration 2    peripheral high rise                 configuration 2
configuration 3    peripheral green low                 configuration 3
configuration 4    central green low                    configuration 4
Low and high rise on the edge

250                                                                           250

Ventilatieverlies in kWh
200
Ventilatieverlies in kWh

200

150                                                                           150

100                                                                           100

50
50

0
0
0                 500             1000
0      200    400    600    800       1000
Afstand vanaf de stadsrand in m
Afstand vanaf de stadsrand in m
Green peripheral or central
250
250

200
Ventilatieverlies in kWh

200

Ventilatieverlies in kWh
150
150

100
100

50
50

0
0
0      200    400    600    800       1000
0      200    400    600    800       1000
Afstand vanaf de stadsrand in m
Afstand vanaf de stadsrand in m
Neighbourhoods and trees
Measure points 1(186kWh),
6(190kWh), 7(190kWh),
9(163kWh), 15(197kWh) and
32(182kWh) score high by wind
without trees. Measure points
5(145kWh), 17(143kWh) and
29(150kWh) get wind over a
much wider district road (80 to
100m) with 6m heigh trees. The
local importance of trees in
large urban spaces is indicated
here. The difference is approx.
40 or virtually 1500kWh.
Neighbourhoods and trees
In configuration 2 measure
points 7(147kWh), 11(170kWh)
en 14(131kWh) lie on a 40m
without trees. Measure point 14
scores low because it is shelterd
by 22m high high rise buildings
on the other side of the road.
The low rise minimum measure
point 10(116kWh) lies on 10m
wide ensemble streets. The
maximum in measure point
25(180kWh) is most likely
explained by its position on the
edge of the used model.
Neighbourhoods and trees
In configuration 3 here not
visible measure point
27(150kWh) lies on a 40m wide
trees. Measure points
18(152kWh), 15(150kWh) and
16(143kWh) score
approximately equaly high lying
on a 70m wide district road with
trees. Minima 17(116kWh) and
19(116kWh) get wind from a
backyard lying on 10m wide
Neighbourhoods and trees
In configuration 4 measure point
18(194kWh) scores extremely
high. It gets wind from 300m
wide open green area in the
centre of district quarter. Even
district road trees do not help
much on this location.
Measure point 19(143kWh) lies
on a small street, but that is the
first street behind the green
behind measure point
18(194kWh), and that is still
apparent there.
Repeating hectare allotments

point

line

angle

court
Court and high rise allotments
0                                             0
7500                                          3100
11                      1                     11                 1
7000                                          3050
6500                                10                           2
10                                2                     3000
6000
2950
5500
9             5000                        3   9             2900                   3

8                                4            8                           4

7                      5                      7                 5

6                                             6

Hof 1       Hof 2                             Hoek 1,2
Lijn 6
Hof 3       Hof 4                             Lijn 8,9
Hof 5                                         Punt 9,10
Point and line allotments

1
1
7500                                       7500
12                 2
7000                                  12                2
7000
6500                                       6500
11                            3
11                              3
6000                                       6000
5500                                       5500
10             5000                    4
10             5000                      4

9                            5
9                              5

8                 6
8                6
7
7

Punt 1,2,6                                 Lijn 1,2
Punt 3,4,5                                 Lijn 5
Lijn 6
Punt7                                      Lijn 7
Building level
Vibration in the air
Movement of air is measured as wind
when it is moving into one direction longer
than 5 seconds. When it is flowing back in
the next 5 seconds it is not even counted
in wind statistics.
It would have a vibration time of 5 sec
with a frequency f of 1/5 = 0.2 vibrations
per second or 0.2Hz (hertz).
Sound
Vibrations in the air from 16 Hz (vibrations
per second) to 20 000 Hz are accepted by
our eardrums as sound.
Vibrations slower then 16Hz are called
infrasonic, faster then 20 000Hz
ultrasonic.
Notes

Any next octave doubles the frequency.
An octave is subdivided in 12 notes (named a, ais or
bes, b, c, cis or des, d, dis or es, e, f, fis or ges, g, gis).
Because 21/12 = 1.0594630944, the frequency of any
next key is a factor 1.0594630944 higher then the
previous one.
So you can calculate the frequency of any note
(n=0…87) by f(n)=27.5 x 1.0594630944n.
Notes and Octaves
Harmonic Intervals
Music notes, intervals
Music notes                                                                 Harmonic intervals

stamtonen
m/sec velocity v   factor           keybord                                  seconds      thirds    fourths      fifths   sixths
340     1,0594630944                                         secundes     tertsen   kwarten      kwinten   sexten

0,688          493,883   50       b1     b1     b1
0,729          466,164   49       bes1   ais1
0,773          440,000   48       a1     a1     a1              stemtoon     klein^      rein^       rein^
0,819          415,305   47       as1    gis1
0,867          391,995   46       g1     g1     g1
0,919          369,994   45       ges1   fis1
0,974          349,228   44       f1     f1     f1                           groot^                           groot^
1,031          329,628   43       e1     e1     e1                                       rein^
1,093          311,127   42       es1    dis1
1,158          293,665   41       d1     d1     d1                           klein^                  rein^
1,227          277,183   40       des1   cis1
1,300          261,626   39       c1     c1     c1              centrale c
1,377          246,942   38       b      b      b               secundes     tertsen   kwarten      kwinten   sexten
1,459          233,082   37       bes    ais
1,545          220,000   36       a      a      a                 groot^                                      klein^
1,637          207,652   35       as     gis
1,735          195,998   34       g      g      g                 groot^     groot^                  rein^
1,838          184,997   33       ges    fis
1,947          174,614   32       f      f      f                 groot^               overmatig^
2,063          164,814   31       e      e      e                 klein^     klein^
2,186          155,563   30       es     dis
2,316          146,832   29       d      d      d                 groot^
2,453          138,591   28       des    cis
2,599          130,813   27       c      c      c                 groot^     groot^      rein^       rein^    groot^
Scales
Span of music
Overtones
7                                                          7
5 10                                                       5 10

A
0
                                                             
A . sin
L                              A . sin
i      
0                                       i      i          0
i                                             i
A
0
7                                                          7
5 10                                                       5 10
0   0.65   1.3    1.95   2.6                               0   0.65   1.3    1.95   2.6
                                                          
2.                                                        2. 
Supposition of tones
1

sin(  )
0
sin( f.  )

1
0          2       4               6       8       10

2. 

2

sin (  )    sin ( f.  ) 0

2
0          2       4               6       8    10

2. 
From sound to noise
Amplitude and power of sound
Power/m2
The power/m2 of a sound wave (called intensity
‘I’ and expressed in W/m2) depends on
amplitude A, frequency f, air density  (normally
1.290kg/m3), and travel speed c (normally
340m/sec) according to
I =  x (2 x  x f x A)2 x c/2.
So, in normal  and c conditions power
depends on amplitude A and frequency f
according to I = 8658 x (f x A)2.
Distance
A speaking voice produces 10-5 W.
A globe with a radius of 28cm has a surface of 1m2.
So, at 28cm distance that voice has a power of 10-5
W/m2.
It is composed by adding 8658*(f x A)2 for every
frequency and its accompanying amplitude in the voice.
A piano produces maximally 0.2W/m2 and if it would be
produced by tone c only the amplitude should be
0.0000367m.
For an exended symphony orchestra and a loudspeaker
the figures would be 5W/m2 (A=0.0000183m) and
100W/m2 (A=0.00082m).
Intensity(frequency, amplitude)
3
1000                                             1 10

100

10

I( f , 0.0000820 )                               I( f , 0.0000820 )              1

0.1
I( f , 0.0000183 )
W/m2

I( f , 0.0000183 )

W/m2
500                                               0.01
I( f , 0.0000367 )                               I( f , 0.0000367 )
0.001
I( f , 0.0000003 )                               I( f , 0.0000003 )     4
1 10
5
1 10
6
1 10
0                                                    7
1 10
2000   4000                                              0   2000   4000
f                                                            f
Hz                                                           Hz
Intensity (W/m2) and dB
A logarithmical representation shows the range
from soft to loud better.
Dividing the intensity by a standard of 10-12
W/m2 (comparing it with that standard) we get
positive logarithms from 0 to 14 only, starting
with what is just audible.
Multipying it by 10 we get a useful range of
decibells (dB) from 0 to 150.
From intensity to dB
160                                                       160

I( f , 0.0000820 ) 140                                    I( f , 0.0000820 ) 140
10. log                                                   10. log
12                                                        12
10                                                        10

I( f , 0.0000183 ) 120                                    I( f , 0.0000183 ) 120
10. log                                                   10. log
12                                                        12
10                                                        10
dB

dB
100                                                       100
I( f , 0.0000367 )                                        I( f , 0.0000367 )
10. log                                                   10. log
12                                                        12
10                                                        10
80                                                        80
I( f , 0.0000003 )                                        I( f , 0.0000003 )
10. log                                                   10. log
12                                                        12         60
10            60                                          10

40                                                        40                3 4
0   2000   4000                                           10           1
100 1 10 10

f                                                            f
Hz                                                           Hz
Audibility
dB(A): what we think to hear
From dB to dB(A)
Traffic
noise
Traffic

radius served urban area             m width    mv/h
30m residential      path           10      30
100m residential      street         20     100