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					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
    radiation (smog, inversion).
                      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
Impact radius of wind measures
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
            over a 40m neighbourhood road
            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
             wide neighbourhood road
             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
            neighbourhood road without
            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
            ensemlbe roads.
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
                               Added amplitudes
                       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
     300m neighbourhood    road           30     500
      1km district         road           40    1000
      3km urban            highway        60    2500
     10km local            highway        70    5000
     30km regional         highway        80   10000
    100km metropolitan     highway      100    25000

				
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