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Thrust anemometer measurements of wind velocity fluctuations, spectra and stress over the sea Smith, Stuart Durnford 1966

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THRUST- ANEMOMETER FLUCTUATIONS,  MEASUREMENTS  SPECTRA  OF WIND  AND S T R E S S  OVER  VELOCITY THE  SEA  by  STUART D. B.Eng.,  M'cGILL U N I V E R S I T Y ,  A THESIS SUBMITTED THE  SMITH  IN P A R T I A L  REQUIREMENTS FOR  1962  F U L F I L M E N T OF  THE DEGREE OF  DOCTOR OF P H I L O S O P H Y  i n the Department and Institute  We  accept  this  thesis  as  of  Physics  the  of O c e a n o g r a p h y  conforming  THE U N I V E R S I T Y  to  OF B R I T I S H  September,  I <)b6  the r e q u i r e d  COLUMBIA  standard.  In presenting for  this thesis  i n p a r t i a l f u l f i l m e n t o f the  requirements  an advanced degree a t the U n i v e r s i t y o f B r i t i s h Columbia;, I  t h a t the study,  L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e  agree and  I f u r t h e r agree t h a t p e r m i s s i o n , f o r e x t e n s i v e c o p y i n g o f  t h e s i s f o r s c h o l a r l y purposes may  be  Department o r by h i s r e p r e s e n t a t i v e s .  g r a n t e d by the  Department  written  permission.  of_fH/S\Cl_  The U n i v e r s i t y o f B r i t i s h Columbia Vancouver 8, Canada  my  I t i s understood that  or p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n w i t h o u t my  Head o f  s h a l l not  this  be  copying allowed  The U n i v e r s i t y o f B r i t i s h  Columbia  FACULTY OF GBADUATE STUDIES PROGRAMME OF THE FINAL ORAL EXAMINATION FOR THE DEGREE OF DOCTOR OF PHILOSOPHY  of  STUART DURNFORD SMITH B„ Eng., M c G i l l U n i v e r s i t y , THURSDAY, SEPTEMBER 29, IN ROOM 301,  1966  1962  a t 3:30  P„M„  HEMINGS BUILDING  COMMITTEE IN CHARGE Chairman:-  I . McT. Cowan  R„ W. B u r l i n g J„ A, Jacobs P. H„ LeBlond  G. V. P a r k i n s o n G. L. P i c k a r d R. V7. Stewart  E x t e r n a l Examiner:  H. A. Panofsky  P r o f e s s o r of M e t e o r o l o g y The P e n n s y l v a n i a S t a t e U n i v e r s i t y  Supervisor:  R. W . Stewart  THRUST ANMOMETER 1_]ASUREMENTS OF WIND VELOCITY FLUCTUATIONS, SPECTRA AND STRESS OVER.THE SEA ABSTRACT A thrust anemometer was designed to measure the three components of wind v e l o c i t y fluctuations i n the atmospheric boundary layer over the surface of the sea and hence to evaluate d i r e c t l y the Reynolds stress of the wind on the sea The anemo= meter was shown to be suitable for i t s intended purpose f i r s t by wind tunnel tests and then by comparisons with spectra from measurements i n the f i e l d by cup and hot~wire anemometers. s  0  Spectra and cospectra of wind v e l o c i t y f l u c tuations were calculated by analog analysis for 32 runs of 32 min duration at the Spanish Banks experimental-site and for one run at another site<> The spectra of downwind and of v e r t i c a l v e l o c i t y fluc~ tuations were each found to be grouped closely when plotted i n normalized form.; and an empirical formula was given for the low-frequency end of the v e r t i c a l velocity spectrum., The correlation of the downwind and v e r t i c a l v e l o c i t y fluctuations was found to be -0o5 at low frequencies and to approach zero at higher frequencies. The average value of the drag coefficient of the surface of the sea for the 33 runs was .0010 and no significant variation with wind speed was observed over the range 3 to 13 m/sec*  GRADUATE STUDIES  F i e l d o f Studys  Hydrodynamics  Introduction t o synoptic oceanography I n t r o d u c t i o n t o dynamical oceanography I n t r o d u c t i o n t o chemical oceanography Introduction to b i o l o g i c a l oceanography Introduction to geological oceanography Advanced s y n o p t i c oceanography Qceanographic methods Advanced d y n a m i c a l oceanography Waves and t i d e s F l u i d dynamics Turbulence I n t r o d u c t i o n t o quantum mechanics Waves Electromagnetic theory I n t r o d u c t i o n t o meteorology Dynamic m e t e o r o l o g y  Go Lo P i c k a r d Ro W. B u r l i n g E. V. G r i l l Bo M. B a r y W» Murray G.. L„ P i c k a r d G. L* P i c k a r d R. W. B u r l i n g R. Wo B u r l i n g R. Wo S t e w a r t P„ H. L e B l o n d R. W. S t e w a r t J-. • G r i n d l a y J . Co Savage Go Mo V o l k o f f •N. Ho Thyer N. Ho Thyer  PUBLICATION  Pond, S . D . S m i t h , P . F . H a z n b l i n a n d R . W . B u r l i n g , Spectra o f v e l o c i t y a n d t e m p e r a t u r e f l u c t u a t i o n s i n t h e a t m o s p h e r i c boundary l a y e r o v e r the sea. J.Atmos.Sci*, 2 3 , 3 7 6 - 3 C 6  S.  1966.  Supervisor:  R. W. Stewart.  \'\'\  STUART D. SMITH. THRUST ANEMOMETER MEASUREMENTS OF WIND VELOCITY FLUCTUATIONS, SPECTRA AND STRESS OVER THE SEA. ABSTRACT  A  thrust  components  anemometer  of  wind  boundary  layer  evaluate  directly  sea.  the Reynolds  cup and h o t - w i r e  were  site  by a n a l o g  duration  and of  found  t o be  form,  and an  frequency  correlation fluctuations  of  found  of  the drag  coefficient runs  speed  higher  was  was  for  and in  of  velocity  to  on t h e its  then  the  by  field  Banks  fluctuations plotted  velocity  Iow  frequencies. the surface  in for  were  each  normalized the lowThe  velocity f r e q u e n c i es and  the sea  .0010' a n d n o s i g n i f i c a n t  observed.  of  The a v e r a g e of  of  experimental  spectrum.  and v e r t i c a l at  runs  The s p e c t r a  was g i v e n  -0.5  fluctuations  for thirty-two  s i t e .  when  to'be  zero  wind  at  atmospheric  the wind  tests  the Spanish  velocity  t h e downwind  approach  with  at  the v e r t i c a l  was  wind  formula  to  thirty-three  of  closely  empirical  end of  of  measurements  another  vertical  grouped  the  three  the s e a , and hence  tunnel  analysis  each  and f o r one r u n a t  downwind  the  anemometers.  and c o s p e c t r a  calculated  minutes'  from  in  t o be s u i t a b l e  wind  spectra  of  stress  was s h o w n by  to measure  fluctuations  the surface  f i r s t  with  Spectra  32  over  purpose  comparisons by  velocity  The anemometer  intended  was d e s i g n e d  value  f o r the  variation  i v  TABLE  OF  CONTENTS  ABSTRACT TABLE  OF  i i i CONTENTS  iv  FIGURES  x  TABLES  xv  ACKNOWLEDGEMENTS  xvi  1.  2.  INTRODUCTION 1.  Statement  of  2.  Motivation  3.  State  of  the  project  I . . c  2  «  3  art  THEORY 1.  V e I o c i ty a .  I ntroduc t ion  b.  Taylor's  c.  The  d.  Local  shear  k-  hypothesis flow  isotropy,  inertia!  e.  Low  frequencies  f.  Length  of  g.  Stability  h.  Wave  Turbulent  local  subrange  data  spectral  .  5  model  the  of  2.  spectra  6 equilibrium, ...  and .«  « run  7 10  analysed  and  estimates  height  s t a b i l i t y . . . 0  10  ......  12  . 0  15  fIuxes  a.  Momentum  flux  or  Reynolds  cb .  Q eu aa td r a nt d u r ew a st pe er c vt ra ap o u r H  stress  fluxes  l6 o  18 19  V  3«  3.  Indirect estimates of the s e a a.  The  b.  The d o w n w i n d method  THE  THRUST  I .  Des i g n  3«  I4..  wind  stress  on  the  surface  p r o f i l e method  velocity  19  fluctuation  spectrum •  21  ANEMOMETER  a.  Specifications  b.  Devices for measuring fluctuations  c. 2.  logarithmic  of  A history  Construction a.  Mov i ng  b.  Fixed  c.  Design  of of  ••  thrust the  Mk.  wind  velocity 23  anemometry II  thrust  ...  26  anemometer.  part  28  part of  23  29 springs  3^  Electronics a.  Differential  transformers  b.  Amplification  3  c .  Gain  33  d.  Offset  e.  Monitoring  f.  Power  g.  Frequency  modulation  h.  Direction  of  3  s w i t c h i ng voltage  1  2  33 3^4-  supply »  components  •  3k-  «•  35  ••  37  C a l i b r a t i on a.  Static  b.  Wind  calibration  tunnel  •  calibration  38 39  c.  Table  of  calibration  d.  Range  of  wind  e.  Dynamic  constants  speeds  calibration  5.  Operating  6.  C a l i b r a t i o n of, v e l o c i t y , f l u c t u a t i o n s f o r c e f I uc t u a f i o n s  7.  Calculation  8.  I . 2,  3.  procedure  of  high-frequency  a.  Effect  of  finite  b.  Effect  of  velocity  Direct-reading  MEASUREMENTS  .....  AND  stress  size of  of  response sphere  the  from  .....  sphere  ...  meter  ANALYSIS  Site Recording a .  Mean  b.  Fluctuating  A n a I og  values  .« quantities  a na I y s i s  a.  Introduction  . . « .  bo  Rs"- p G c o r d i n c ]  c.  F i I t e r i ng ' f o r  d.  Spectral  e.  Reference  f.  Computation  of  quadrature  g.  Calculation  of  spectral  h.  V e r t i c a l r o t a t i o n of c o o r d i n a t e s t i l t of a n e m o m e t e r . .. .  i.  Horizontal  o«o««*««oo*o«, *««•••«««« spectral  computation  analysis  ... . .  . . . . . . . . . . . . . . .  voltage  rotation  of  spectra  .  estimates for  coordinates  c  V I 1  j .  Analysis  k.  The s u m m a t i o n of s p e c t r a velocity products  k-.  Cup  5.  Digital  of  hot  U-wire  anemometer to  data  obtain  .  72  mean 73  anemometers  7^-  spectral  analysis  of  cup  anemometer  data  76  RESULTS 1.  Introduction  2.  Comparison of t h r u s t of downwind v e l o c i t y  81 a n d cup anemometer fluctuations  3.  Spectra  of  velocity  fluctuations  1|.  Spectra  of  downwind  velocity  5.  Spectra  of  vertical  velocity  6.  C o s p e c t r a of f I uc t u a t i ons  7»  Quadrature veIocity  and  85 •  87  fluctuations  ..  9'  fluctuations  ..  92  vertical  velocity 93  spectra  of  downwind  and  vertical  fIuctuations  8.  Covariances,  9.  Time  10.  downwind  spectra  stress  variation  Wide-band  of  .• and  drag  spectral  analysis  for  coefficients  estimates  mean  .......  Time  variation  12.  Comparisons  of  wind  between  speed  spectra  and from  turbulence the  and h o t - w i r e a n e m o m e t e r s Data from the Aruba e x p e r i m e n t a l s i t e comparison between analog and digital analyses Noise  level  SUMMARY  OF  I.  design  The  97  98  11.  \lx..  96  velocity  products  13.  95  determination  .,100  thrust 102 and I 0I4. 107  RESULTS of  the  thrust  anemometer  i09  The  performance  a.  Calibration  b.  Calculated  c.  Range  d.  Susceptibility orientation  of  of  the  thrust  anemometer «  frequency  wind  response  „  speeds to  o  errors  in  angular o  «  The  spectra  of  wind  a.  Comparison  with  cup  anemometer  b.  Comparison spec t r a  with  hot  U-wire  Comparison spectra  with  d.  Comparison analyses  between  e.  Wide-band  f.  Time  variation  of  the  spectral  estimates.  g.  Time  variation  of  the  velocity  products  h.  Noise  spectra  i.  Normalized  c.  The d r a g s e a .  .  turbulence .  anemometer 0  hot  X-wire  anemometer o  analog .  and  digital  analysis  .  spectra  c o e f f i c i e n t of  the  surface  of  the «  a.  Thrust  b.  Comparison  with  c.  Results  other  d.  The  Summary  spectra  anemometer  of  importance  measurements  .........  i n d i r e c t , methods  of  workers spectral ,>.....  ..........  o . . . .  analysis  «...  . . . . . a . .  ix APPENDICES  1,  2,  C a l c u l a t i o n of s p r i n g . c o n s t a n t s t h r u s t anemometer Plane over  wave  velocity  sphere  Transfer  5.  Computation for v e r t i c a l anemometer c o o r d i n a t e s  8.  to  analog  function  of  principles  90°  phase  report  REFERENCES  of  surface  lag  rotation  ,  13'  c i r c u i t  133  of  thrust 135  C a l i b r a t i o n and c a l c u l a t i o n f o r the h o t - w i r e anemometer,  Data  averaged 129  li..  The s p e c t r u m Banks s i t e  II  .«  Introduction  7.  Mk.  127  fluctuation  3,  6.  for  of  spectral  estimates 13&  waves  at.the-  Spanish 139  (Tables  of  the  spectral  estimates)  .  Ii+0  152  X  FIGURES  1.  The  Mk.  II  a. b.  With With  thrust  anemometer  perforated styrofOam'sphere sphere removed, showing internal  2.  S i m p l i f i e d s p r i n g and. Ii nkage mechanism f o r component of t h e Mk. II thrust anemometer  3«  a. b. c.  The The The  Mk. Mk. Mk.  anemometer  a.  As  designed  in  1963  b.  As  modified  in  1960  Dc  6.  Thrust  7.  Positive  differential  a . b. 8.  9«  10.  one  IV t h r u s t anemometer I thrust anemometer V thrust anemometer  Thrust  5o  mechanism  r e c o r d i ng  transformer  anemometer  schematic  directions  of  b I ock  diagrams  schematic  diagram  circuit  components  F o r I 96I+ a n d 1965  F o r I966  Static calibration weights on s p h e r e , Angular sphere Wind  of  thrust  anemometer  by  l9/3/'966.  r e s o l u t i o n t e s t e d by r o t a t i n g w e i g h t about h o r i z o n t a l component 2 a x i s  tunnel  placing  of  calibration 2  a. b.  F| c  vs. vs.  U U  (Upper) (Lower)  11.  R e s o l u t i o n of a n g l e s i n the w i n d tunnel  12.  a.  Measurement  b.  Relative vs.  on  Fetch  wind  iii..  The  instrument  I5.  The  recording  of  thrust  anemometer  site  location  I3«  rotation  of  direction mast platform  platform at  the  and  masts  Spanish  Banks  site  X I  |6.  The h y d r a u l i c  auxiliary  Data  by  recorded  camera  18  Cup  19  Calibration  of  cup anemometers,  20  Calibration  of  Krohn-Hite  21  Example  22.  anemometer  mast  of  oscillator  analog  a.  Calibration  b.  Data  Block  of  of  filters 0.125  f o r analog  mean  wind  circuit  I2/1|./I966.  f i l t e r s  integrator  frequency  diagram  and g r a t i n g  outputs  and computer  at  8 Hz  Hz r u n Q l spectral  velocity  analysis  23.  Profiles  21s..  Downwind s p e c t r a f o r r u n C , 3^/7/6l+, p l o t t e d f o r m f j Z S ( f ) = kjZS(k) v s . I 0 g j f a n d log^k  vs.  height in the  25.  Downwind s p e c t r a f o r r u n C, f o r m logjQ0(k) v s . log^k.  in the  26.  Spectra  for  run  El,  2242-23IIJ,,  26/6/k965  Spectra  f or  run  E2,  2 3 I14--25U-6,  26/6 i 9 6 5  28.  Spec t r a  for  run  Kl,  1528-1600,  8/5/1966  29.  Spec t r a  for  run  01,  I83O-I9O2,  l2/5/i966  30.  Spec t r a  for  run  Q2,  I902-I93i|,  12/5/1966  31 .  Spectra  for  run  03, l 9 3 l | - - 2 0 0 6 ,  12/5/1966  32.  Spectra  for  run  05, 2 3 0 8 - 2 1 1 0 ,  I2/5/1966  33.  Spe c t r a  for  run  R 1, 2238-2310, •12/5/1966  31*-.  Spectra  for  run  R2,  2310-25^2,  12/5/1966  35.  Spec t r a  for  run  R3,  21+32-00 I i i ,  1-2/5/1966  36.  Spectra  for  run  37.  Spectra  for  run  SI,  01214.-0156,  13/5/1966  38.  Spectra  for  run  S2,  0156-0228,  13/5/1966  Q  c  I  •  50/7/6I4.,  oolil-OOLIi),  plotted  13/5/1966  Spectra  for  run  F2,  29/6/1965  Spectra  for  run  F3,  29/6/1965  Spectra  for  run  Ar,  1035-1103,  The  normalized  downwind  spectra  The  normalized  vertical  spectra  The  normalized  cospectra  D r a g c o e f f i c i e n t of 32 m i n u t e s duration Time  variation  of  the  I5/2/196I4.  = sea  spectral  0  surface  from  33  wind R3  speed  (I  minute  averages)  and  direction  Wind speed c o n t i nued  (I  minute  averages)  and  direction  Wind speed continued  (I  minute  averages)  and  direction  me  variation  of  ve  o c i ty  products,  r*un  K 1  T " me  variation  of  v e  o c ' ty  produc  ts,  run  Ql  r me v a r i a t i o n  of  ve  o c * ty  produc  ts,  run  Q2  variation  of  v e  o c i ty  products,  run  Q3  r me v a r i a t i o n  of  ve  o c ' ty  p r o due t s ,  run  Q5  T me  variation  of  v e  oc  ty  products,  run  Rl  T  v a r i a t i on o f  ve  oc  ty  p r o due t s ,  run  R2  T me  va r i a t i o n  of  ve  o c ' ty  produc fs,  run  R3  T  me  variation  of  v e  oc  ty  produc  ts,  run  RI4.  T  me  v a r i a t i on  of  ve  oc  ty  produc  ts,  run  S1  variation  of  ve  oc  ty  products,  run  S2  r  T  me  me  T me  runs  of  estimates  Mean v e l o c i t y p r o d u c t s as a f u n c t i o n of f o r r u n s K l , 01, 02, Q3, Q5, R l , R2 a n d Wind  2  speed  X I I I  N o i s e s p e c t r a of U = 292 cm s e c  thrust  anemometer  in  wind  tunnel,  N o i s e s p e c t r a of U = lj.12 cm s e c " '  thrust  anemometer  in  wind  tunnel,  N o i s e s p e c t r a of U = 583 cm s e c '  thrust  anemometer  in  wind  tunnel,  N o i s e s p e c t r a of U = 825 cm s e c - l  thrust  anemometer  in  wind  tunnel,  -  1  -  I n d i r e c t d e t e r m i n a t i o n s of d e t e r m i n a t i o n s of ~ U | U ^ Comparison me t h o d s Operational  of  drag  d i g i t a l  Digital  for  wave  spectrum  Spectra  for  run  tt  tt  it  BO  it  tt  tt  Bl  ti  it  ti  B2  tt  ti  tt  tt  11  it  it  it  it  it  tt  it  El  »  tt  tt  E2  tt  ti  11  FI  tt  tt  11  F2  it  it  ti  Ar  DI  D2 D3  F3  vs.  direct  obtained  by  various  circuits  F l o w d i a g r a m of o f c o o r d i na t e s  The  2  coefficients  amplifier  program  u-«-  program  vertical  (from  for  vertical  rotation  G i l c h r i s t ,  of  J9&5)  rotation  coordinates  81+.  85. 86. 87. 88. 89.  90. 9L 92. 93.  Spectra  f o r r u n GO  IT  it  tt  Gl  it  it  it  G2  n  *!  tt  G3  II  tt  II  JO  ti  tt  tt  J1  it  V.  !!  J2  tt  It  It  it  tl  1!  tt  tl  II  J3  J5  XV  TABLES  2.1  Confidence  inervals  3.1  Frequency modulation  3.2  Thrust  1+. I  Allocation  1+.2  Calibration  for  spectral  anemometer c a l i b r a t i on c o n s t a n t s of  tape r e c o r d e r c h a n n e l s  of  filters  Thrust  A8.I  Spectra  A8.2  • "  A8.3  ,  12 37  and  degrees  freedom 5.1  estimates  ....  .......  1+1 53  of 59  anemometer r u n s for  run Kl  "  "  "  n  01  02  analysed  81+ li+l 11+2 li+3  A 8.1+  "  "  "  A8.5  "  "  "05  ll+5  A8.6  "  "  "  1.1+6  .A8.7  "  A8.8  "  "  " R3  A8.9  "  "  "  Ri+  A8.I0  "  "  "  SI  I5Q  A8.I I  "  "  "  S2  151  11  "  03  Rl R2  11+1+  11+7 1I+8  . ll+9  xvi  ACKNOWLEDGEMENTS  This  investigation  interaction University  program of  British  by  the  Defence  by  the  National  by  the  Department  Branch,  Grant  Research  this  Mk.  work  of  II  I  collaboration  in  use  of  a  tape  Mr.  R.  Loucks  of  this  Machine  Shop  anemometer. support Canada  by  of low of  the  the  speed British  to  his  the  No.  9550-09; No.  BT-HOO;  Meteorological of  the  Institute L.  A.  E.  experiment  results of  many of  in  Naval  the  of BIO  delicate  this Mines  work and  course  of  of Doe  the anemometer  the  of  supported  Grant  Office  used  Dr.  Aruba  course  Grant  Canada,  the  is  NOO|[|.-66-OOOlj/7.  Connelly  Department  of  and  and  BIO for  for the  also  digital  analysis  instrument parts  1 was  for  the  given  TechnicaI  Surveys,  BIO.  Columbia, wind  by  of  the  program  Canada,  thank  design  G.  of  Bedford  supplied  Department  British  No.  the  fabricated In  Council  Air-Sea  Oceanography,  Canada,  anemometer  for  Mr.  through  The  by  wish  who  tape.  of  the  of  This  Transport,  thrust  Oceanography.  data  Board  Grant  of  institute  5920-0, and  lent  part  Columbia.  Research  No.  was  the  Research  (U.S.A.),  The  of  formed  of  kindly  tunnel.  Columbia  Mechanical  The  carried  Engineering,  permitted  the  Computing  Centre,  out  digital  use  University of  their  University  analysis  of  cup  xv i i  anemometer  I ment Dr.  data.  am e s p e c i a l l y  from R.  D r . R.  the  while  staff  whose  this  particular analysing thrust  Dr.  work  D r . H. X-wire  services  in  Mr.  D.  of  at  Miss  1966.  has  helped  studies  but  not  hours in  of  least  Banks  on  and r e s e a r c h  in  coinciding Dobson,  site,  often  through  thank  the typing  of  this  through  I0UBC.  and  Mr. J . their  the  various  at the M r . F.  the a n a l y s i s  illustrations  without  t i m e with a  Chernock  to  at  of  thank  in  in  own p r o j e c t s .  on  to  rendered  and M r . B.  ways  wish  recording  wish  numerous  a s my  done;  and operation  their  I  been  generously  Hume  supervisor,  also  Mr. F.  and c o n s c i e n c i o u s I y  of  many  on  K.  the preparation  spent  Boston  spent  and  Last  data  encourage-  the I n s t i t u t e ,  cooperated  the Spanish  time  at  and  served  not have  the maintenance  AlIan,  willingly  could  my  I  I0UBC.  recording.  and M r . N.  expense  H . Thyer  anemometer  Garrett,  from  students  Weiler  anemometer  instruments  N.  he was a t  and graduate  help  for.guidance  W. B u r l i n g , a n d  W. S t e w a r t .  supervisor  grateful  worked of  data  the  my w i f e  summer  who h a s  manuscript  the course  Tsong,  and  o f my  I  I:  CHAPTER I .  INTRODUCTION  Statement  of  project  The o b j e c t i v e s Institute  are  (I0UBC) the  of  sea,  x  at  to measure  During  thrust  1963,  University  at  anemometer  I enrolled  the S p a n i s h borrowed  from cup and hot  On the were made the  thrust  and hot  of  Banks  these  wire  of  anemometer by c o m p a r i s o n  conditions  to o b t a i n  a preliminary  as  stress  using  and v e l o c i t y  wind s p e e d , h e i g h t  spectra  the Mk.  to  data  anemometer.  measurements  simultaneous  under idea  spectra  was  with  of cup  also  a variety of- the  of  in  the p e r f o r m a n c e  It  II  be compared  thrust  more  with  and  was  Institute  were  the  anemometer m e a s u r e m e n t s . measurements  studies  velocity  measurements,  to o b t a i n  parameters  over  thrust  It  anemometer  to d e t e r m i n e q u a n t i t a t i v e l y  turbulent  of  site  value  \undertaken  of  (196!+)  summer  These measurements  the p o t e n t i a l  basis  wire  the  from the B e d f o r d  with  to a s s e s s  of  the  Columbia  in graduate  a few measurements  (BIO).  order  British  the p e r f o r m a n c e  Oceanography spectra  of  at  t u r b u l e n c e and s t r e s s  the f o l l o w i n g  to o b t a i n  and c o - s p e c t r a  anemometer s t u d i e s  If.  ^ln September,  intended  wind  to e v a l u a t e  i tse  lOUBCi  thrust  Oceanography,  and  anemometer  of  of  variations such  atmospheric  stability.  2  Mot i va t i o n  2.  Turbulent surface force in  of  for  the  the  momentum fIux sea  is  thought  ocean c u r r e n t s ,  generation  of  (stress)  and  surface  stress,  the p a r a m e t e r s  methods  of  measuring  the  to be  the  is  critical  of  waves.  on which  it  of  it  wind on  principal  are subjects  of  driving  importance  The v a l u e depends,  the  of  and  this  the  controversy  best at  the  p r e s e n t t i m e . The wind v e l o c i t y s p e c t r a a r e of i n t e r e s t turbulence theory, d i f f u s i o n s t u d i e s , a v i a t i o n , e t c . Simultaneous of  wave h e i g h t  measurements  will  be of  of  wind  interest  fluctuations  in s t u d i e s  of  in  and  wave  generation. To m e t e o r o l o g i s t s , vapour  fIux" and  important  and  latent  and- a r e c o n s p i c u o u s  between  the  driving  global  from  direct  measurements  oceans  the o c e a n s  and  by  of  heat their  the a t m o s p h e r e  wind c i r c u l a t i o n s , is  over  course  the  the  flux  sea  are  primary  Heat  important  and water  water  equally  absence. is  of  flux  In  evaporated  source  of  prec i p i t a t i on.  Measurements are  needed.  development, less prove  However,  with  near-shore  difficulty of  of-these  value  and in  quantities Instruments  measurements  expense.  the s t u d y  in  open sea  undergoing  can  be made w i t h  These measurements of  coastal  conditions  areas.  much  should  3  3.  State  of  Most have,  the  method  are  is  more  land  valid  Another the  pf  measurements Both  of  over  the  indirect  surface  "logarithmic  3 a ) of  interpreting  height.  surface  the  This  some  boundary  infers  a better than  sea  assumptions,  fluid  method  stress  the  with  downwind,veIocity  of  wind  the  the  will  over sea.  from  and  has  direct  logarithmic be  which  stress  fluctuations,  does  indirect  of  layer  c o r r e l a t i o n with  methods  of  are  exist  among  the  various  of  on  methods the  enclosed  Such  of  the  discussed  profile in  the  wind now  the  stress  obtained  being  reported,  values  obtained.  measurements  is  from  but  a  many  The  a matter  of  debate.  Other  of  speed  atmospheric  instruments  reliability  stress  on  Section  2,  measurements  discrepancies  lively  based  on  chapter.  Direct variety  the  produce of  stress  a series  that  beeni f o u n d . t o  f o l I o w i ng  on  indirect  spectrum  method.  been  mean w i n d  for  for  wind  (Chapter  of  based  than  of  recently,  variation  method  art  estimates  until  profile"  the  sea  have  surface. of w a t e r  bodies^may  techniques  also  will  be  not  been For  used  example,  determined be  to  discussed  estimate the  using  the  average  tide  further.  slope  gauges.  k CHAPTER  THEORY  2:  '•  Ve1oc i t y  a.  Introduc  spectra  tion  Consider Assuming there  exists  a  may a l i g n  so  that  is  mean  t h e mean  we  the  U(x,t)  the process  Assuming  Let  a wind  speed  wind  x^ d i r e c t i o n  U(x,t)  =  l  have by  U|, zero  spectral  more  may  be  briefly  of  u ,  u ,  the overbar  of  (f)  0  bandwidth.  in  %  horizontal. with  ( U , 0,  height,  0),  i .e.  t h e Xj d i r e c t i o n .  upward,  and  of  velocity is  function  in  determined  coordinates.  terms  spectrum  then  fluctuation,  of  frequency  tensor  f  0jj(f)  that  J where  ij =  right-handed  the frequency  is  !..  u_) J  0  2  using  surface.  stationary  T h e X£ d i r e c t i o n  energy  def i ned so  lies  sea  invariant  that  the components  value.  the convention  A or  U£ a n d u ^ , mean  is  be v e r t i c a l l y  1  where  so  velocity  (U +  a  U ( x ) , which  direction  the coordinates  t h e mean  over  s t a t i s t i c a l l y  wind  wind  blowing  tOO  0jj(f)df,  (2.1)  o denotes  are velocity  a  time  squared  average.  per unit  of  The  dimensions  frequency  5  b.  Taylor's All  at  measurements  a fixed point.  relate  were  it will  time • v a r i a t i o n s  turbulent at  hypothesis  structure  is  t h e mean v e l o c i t y  i n the  form of  occasionally  to s p a t i a l swept  U of  past  series  be d e s i r a b l e  variations. the p o i n t  the f l o w  (Hinze,  t h e r e l a t i o n between t i m e and s p a c e  1  time  if  of  to  the  measurement  1959, P«  derivatives  h®)  is  a_  U dt  and  the downwind  per u n i t  component  distance k =  kx_»  Taylor's f »  I;  hypothesis  for  layer  is  eddies  boundary k is  e q n . 2 . 2 as length"'  radians  sec"')o  parameter.  of  sec"',  for Taylor's  (19&5)«  which kx^  is  not »  i n the s h e a r physical  the a t t i t u d e being  only  cm and U = 500 cm  The v a l i d i t y  by L u m l e y  distorted  a linear  a good a p p r o x i m a t i o n  x_ = 2 0 0  l a y e r and no p r e c i s e  intended,  is  a good a p p r o x i m a t i o n  discussed  are  this if  F o r wave numbers a t scale  in  ( 2 . 2 )  example  (cycles is  k,  7T f / U .  2  hypothesis  0.1+. Hz  number,  is  In a boundary if  of wave  f l o w of  large  the  i n t e r p r e t a t i o n of  that k is  transformation  I the  defined  from a frequency  The o n e - d i m e n s i o n a l  spectral  by to a  function  6  0..(k)  satisfies  u,Uj  the  =  relations  0  i j  (k)dk  (2.3)  o k^.j(k)  The  last  function  member  of  wave  number  to  one  another.  The s h e a r The  flow  boundary  layer  following  unit  flow in is  n,  =  since  the  lowest  assumed  a spectral  of any d e s i r e d f  and n a r e  frequency  proportional  few meters  of  the  t o be a p p r o x i m a t e d  atmospheric by t h e  assumptions:  2.  The X | d i r e c t i o n of  invariant  is  with  T h e mean  depend  T h e mean  incompressible.  or  t h e mean w i n d  x^-  is  two-dimensional, Thus  wind  only.  there  divergences speed  is  and U does  a r e no mean  i n the h o r i z o n t a l  and d i r e c t i o n a r e  time, and a s t a t i o n a r y  U = U(x )  velocity  height.  flow  on X | o r  convergences  in  k,  that  model  The f l o w  1+.  f J  i n terms  1.  3.  (2.1+)  n0 (n).  e q n . 2.1| i n d i c a t e s  may be w r i t t e n  or  c.  = f0,j(f)  state  exists.  not  local plane.  constant Thus  7  5.  The  only  body  6.  Turbulent  force  is  transports  gravity.  far  exceed  those  by  molecular  diffusion.  The  7.  These  turbulent  assumptions  the  conservation  and  Panofsky,  is  fed  at  a  of  p.  \y6h,  rate  component  A  of  the  Reynolds '  gradients  3  I  following  Buoyancy  section,  and  x^.  equations  for  thermal  air  of  from  energy  density  the  kinetic  - p u ~ u T on a I 3  mean  (Lumley ,  p  flow  this  energy  forces,  to  energy  energy  by  mean  flow.  the  1  feed  of  energy to  the  3  turbulent  stress  isindependent  simplified  In  72).  redistribute  components.  to  U.U-^U/^x-,  -p of  lead  stress  mechanical  a  l>p U|  shear  among  be  into  a l l  the  action Pressure  the  velocity  discussed  in  or  t h e -^p  out  of  a u_^  3  a component f r i c t i o n  of  dissipate  This shear of  flow  and  d.  model over  assumption  surface of  turbulent  of  energy  the and  7  the  is a '  a  energy, energy  sea  in  reasonably  uniform n  and  solid  describing is  momentum  not  all good  the  must  of  three  viscous  components.  approximation  boundary,  certain  which  forces  flow  over  because take  but  the  the  of  place  to accuracy  f l u i d  the  interchange  between  wind  waves.  Local  isotropy,  subrange  local  equilibrium,  and  the  inertial  8  The (Hinze, ppi  KoImogoroff pp.  1959,  79"85,  theory  is  the  Lumley  (81-200;  I62-163)  of  based  on  inertia! and  the  subrange  Panofsky,  following  196I4., three  assump t i ons:  I.  Turbulent  energy  is  characteristic  of  gradients  viscous  (and  small-scale the  mean  smaller  turbulence  flow.  The  scales  information motion  is  the  is  and  largest  eddies  and  necessarily  was  passed  to  pressure the  lower et  a l ,  a  of  its  1963)  for  isotropy though  from  loss  of  of  the  the  the  in  scale  larger  directional  small  scale  structure  the  As  the  energy  is  scales  the  effect  of  smaller  redistributes reducing  the  mean  of  anisotropic.  and  the  of to  the  shear  energy  effect  of  flow  among the  generation.  logarithmic  limit  by  greatest  at  energy  Velocity  by  components,  anisotropy  of  numbers  flow.  are  negligible  determined  fluctuations  three  For  was  smaller  and  wave  mean  dissipation)  accompanied  even  at  large-scale  cascade  local  assumed  generated  boundary  isotropy  has  layer  been  (eqn.  estimated  2.15),  a  (Pond  at  (2.5)  2. time  Smaller  scale  motions  and o c c u r as scales, though larger  have  scale  shorter  motions  c h a r a c t e r i s t i c  were  constant.  9  This  is  the  steady  a  number-" are  turbulent  there  large  small  enough  number  part  numbers  the  governing rate  £  equilibrium  or  local  for  for  s u f f i c i e n t l y  range  local  viscous  This of  a  of  wave  isotropy  numbers to  dissipation  inertial  the  of  subrange  locally  high  is  isotropic  which  exist  of  Reynolds  but  energy the  range  yet  to  small of  be wave  wave  a  region  the  and  local  flow  exists  enough  negligible.  In  of  state.  For  3.  assumption  the  of  motion  local are  isotropy  the  wave  viscosity  In  the  number  the  parameters k,  the  inertial  dissipation  subrange  the  ^ effect is  a  of  the  function  suitably  viscosity only  dimensioned  0,,(k)  where  K',  measured  of  the value  =  £(cm  negligible,  2  sec  — 5  combination  K ' £  universal of  is  0.1+8  2  /  3  k ~  5  /  /  3 )  and  of  k(cm  these  0^{k)  -1  ).  (cm ' sec 5  The  only  is  (2.6)  5  Kolmogoroff (Pond  and  et  constant,  al,  has  a  1963).  The R e y n o l d s n u m b e r Re = U L / w i s a r a t i o o f the inertial to viscous forces in the f l o w , where u is the dynamic v i s c o s i t y a n d L is a Iength t y p i c a I of t h e mean f l o w . For our investigations if U * 7 0 0 cm s e c , L = x - 200 c m , a n d t h e kinematic viscosity of a i r y = 0.1 5 c m s e c , a typical Reynolds number i s Re ~ I0 which is thought to be sufficient for t h e e x i s t e n c e of an inertial subra nge. -  1  3  2  C  _  l  —2 )  10  Isotropy components preferred be  then  of  the  determines spectral  direction  the  the  values  tensor.  different  of  Since  the  other  there  velocity  can  components  Isotropy  results  0 2 2  the  Low  in  ( k )  at  lower  horizontal at  U  and  where  =  0||(k)oc k  ^3 0 | |  l°7)  P»  this  reduces  ( k )  ( 2  regarding  frequencies  are  5 to  low  has  found  10 t i m e s  boundary  Length  It  ( k )  1959,  ,(k) - k^, ,(k)/dk] .  predictions  has  (1965)  frequencies  small  ^33  =  2 2  =  (Hinze,  -  to  8 )  f r e q u e n c i es  Pond  f.  must  (2.7)  relation  subrange  Theoretical spectra  the  = ^33^)  ( k )  Inertial  0  e.  no  uncorreIated.  0 I J . U ) = 0, i + j  in  be  of  that  the  less  0  ]  lower  the  forms  the  detailed.  , ( f )oc f  than  of  even  I4..5U/2 Tr x ^ .  sea  surface,  the  s t a b i l i t y  at Near  must  0^{f)  the  be  frequencies.  of  data  run  been  direction  and  assumed 6  are  constant  of  spectral  that  the  mean  wind  during  any  particular  estimates  speed data  11  run.  This  may  by  selecting  in  the  of  steady  limit  for  As a  the  that  for  a  frequency k'  =  as  in  our  of  freedom  record. find, S0%  duration  chance  stationary  is  the  period  of  example, being  at  least  only  10  cycles,  O.I4.9  and  corresponds f i l t e r  is  of  that  the if  within  used  cycles estimates  21-25)  (pp.  with  of  at  of  we +  a  the  complete  desire of  30%  in  show  each  about  freedom.  half-octave  cycle,  the has  the  frequency on  fewer  estimates  chi-square  estimate  a  frequency  Thus  bandwidth  if,  is  used,  (2.9)  one  number  I .60 times to  of  during  fT.  lj.0 c y c l e s the  degrees  discussed  f i n i t e  spectral  chi-square,  f i l t e r  =  be  octave  as  process  be  accuracy.  are  Tukey  (f/2)T  tables  there  and  2  the  reasonabIe  Blackman Gaussian  the  low  thus  bandwidth) a  a  and  =  equals  of  will  minutes,  32  impose  approximation  as  record  distributed  must  case  of  data,  However,  decreases  k'  of  of  persist  f  r e l i a b l e .  From  for  between  T  analysis,  f '  satisfactory  typically  estimates  (effective  2T  Since  conditions  are  a  stretches  available,  frequency  less  to  measurements.  spectral  given  become  on  runs  which  achieved  suitable  section  lengths  in  be  cycles  true =  ha I f - h o u r  of  degrees  in  the  distribution  an the  estimate true  record. an  f  number  S0%  0.01  record.  have  there  change  Hz  to  values,  If  value.  we  of  when  there are  lying  This  latter a  Table  an  h a l f 2.1,  12  abbreviated  from  the'extent the  of  spectral  number the  of  Blackman  the  estimate.  "true"  range  and  Table  2.1:  or a  of  This  chance  of  Confidence  of  5 10 20 30  estimates  will  the  not  confidence  simultaneous  between  different  our  analyses  of  of  . S0%  for  the  same  same  data.  same  conditions  of  speed  and  d i r e c t i o n .  $1 j ,  confidence fractions  confidence c  '  ^33*  a  n  c  intervals of  the  l  hypothetical  intervals n  o  ^  for  ^° the  cospectral  *  n  apply e  -I.18  the  accurate  the  n  -1.30  -I.26  0.920-1.081 0.9I+3-1.057  of  estimates.  spectral  comparisons phenomena It  or  relates  long-term  steady-state  only  cospectrum  cospectra  22)  confidence  500 1000  under  a  p.  O.873-I.I39  measurements wind  (1958,  0.73 0.75 0.82  average of  mean  a  to  this  interval  sample  data  of  200  making  the  the  Estimates  Tukey  our f i n i t e  These  of  below  and  intervals  measurements  of  of  chance  \0%  50 100  prevent  between  a  i+o  O.69-1*3k  of  function  freedom  0.32-1.85  sizes  fractions  Spectral  Degrees  0.1+9-1 .60 0.62-1 .1+2  The  a  lists  22)  above.  for  0. 1 0 - 2 . 0 8 0.26-1 . 9^4-  k  as  lying  Blackman  interval  3  is  value  lying  confidence  80%  freedom  its  from  is  There  Intervals  Abbreviated  Degrees  interval  spectral  p.  (1958,  interval  freedom.  long-term  10%  Tukey  confidence  S0%  degrees  and  are  to  the  spectra The  somewhat  larger  13  g.  S t a b i l i t y  In  addition  to  water,  atmospheric  effect  the  function  mean  wind  s t a b i l i t y  spectral  or  values.  p r i n c i p a l l y  of  speed  and  height  density  The  air  temperature  above  gradient  density  P  pressure  T,  may is  a  the  a  and  humi d i t y .  Under or  f a l l s  adiabatic  will  undergo  exactly  match  This  called  is  gradient  or  its  g  is  specific  If  the  of  find  i t s e l f  will  experience  given will  also  in  will  air  fluctuations  g/c  p  -  at  a  a  to  turbulent Other  indirectly tend  damp  to  of  and  air  is  for  Io"^  x  of  gravity  which  which  its  the  - I  rises  will  new  surroundings.  temperature  dry  a i r ,  °Ccm"'  and  C p  is  the  pressure.  of  lass  air  dense  buoyancy out  which than  f o r c e .  vertical  fluxes  and  components inhibited  distribute  of  change  that  rate  parcel  restoring  tend  to  constant  surroundings  speed. be  lapse  -g/cp,  v e r t i c a l  wind  -  parcel  s t a b i l i t y ,  acceleration  dl/dx^y  reducing  =  a  temperature  temperature  adiabatic  heat  conditions  a  neutral  dT/dx^  where  conditions  of  its  will  own  These  turbuI ent  wind  stress  turbulent  because  energy  rises  and stable motion, for  a  motion  pressure  among  the  components.  'if  d T / d x ^ - g / c p ,  itself  In  more  dense  upward.  These  vertical  turbulent  particular motion to  follow  equal of  to  will  the mb  1000  amount  we  be  use  Other  at  to  and  will  all  the  rises tend  will  tend  and  stress  at  In  the  adiabatic  balloon  increase  for  a  the 0,  discussion which  pressure  succeeding  find  turbulent  temperature,  y  will  to  to  of  enhanced.  temperature,T  corresponding  which  components  potential  d i f f e r s  air  fluxes,  indirectly  actual  and  of  conditions  motion,  speed.  also  parcel  surroundings  unstable  wind  will  a  levels  lapse  is  level  by  an  rate,  J000 mb ©  The  use  effect  of  =  T  +  ( 1 / P  I  Jp  potential  on  the  gradient.  in  potential  and  c  temperature  s t a b i l i t y our  a  of  the  ) d p  takes  Info  account  atmospheric  measurements,  actual  p  over  temperature  a  5  m  the  pressure height  range,  differences  d i f f e r  for  our  by  o only  the  .05  C  The  effect  flux  ,  which  is  of  negligible  s t a b i l i t y  Richardson  may  be  most  of  expressed  in  purposes.  terms  of  number  trfu^dU/cix^  which  is  thermal w h e r e o(y  the  ratio  processes is  the  of to  energy  that  produced  produced  c o e f f i c i e n t  of  by  thermal  (or  absorbed)  mechanical expansion  by  processes, of  air  in  15  0  Another  s t a b i l i t y  is  ratio  the  giving  a  difference  similar  Richardson  1* -  is  negative  positive  for  the  in  gradient  measurements increase  of  of  of  in  zero  for T  neutral, is  a  the  and  absolute  KeIvin.  humidity and  with  s t a b i l i t y ,  humidity.  100%  (2.10)  5  conditions.  degrees  variation  density  stable,  unstable  temperature  The  for  number  g  5  which  of  T (AU/Ax )2  ""(dU/dx )2  d  indication  At  relative  20  o  C  height  may  but  have  and  humidity  we , 76O  has  also made  mm Hg the  affect no  an  same  effect  0 on  density  some  stabi  as  Ii  wind  humidity  temperature  of  2.61  C  gradients  in may  temperature.  Under  have  an  as  large  gradients  in  determining  the  make  only  an  approximate  evaluation  wind  speed  height  can  expect  stress  in  s t a b i l i t y  alone.  effective  height  determined  of  to  terms Over of  quantity  waves  on  of land  the  surface  empirically  corresponding effect  increase  ty.  Wave  We of  an  conditions  effect  h.  as  wind  for over  and  remaining  roughness, a  given water  turbulence  atmospheric parameter  which  location. is  wave  and  may  the  be  The  height,  stress  is  is  but far  the from  16  simple  and  will  period  and  velocity  wind  speed,  topography wave  stress  2,  of  the and  Turbulent  waves  duration,  being that  account  over  and  studied.  depends on  the  The  the  water  for  the  significantly  than  over  on  underwater  itself,  land  over  X  of  the  a  =  turbulent X  =  X  +  x  suitably  lower  under  which  component  under  u^  flux per  long  of  a  unit  time  property  volume,  T  of  the  having  instantaneous  The  average  a.  Momentum  an  of  volume,  the (5 Vj , a  -  x.  If  our  this  upward)  flux  or  Xu^  X  the  be  the  has  of  flux  Reynolds  quantity where  quantity  assumptions  vertical  vertical  flux  air  (2.11)  (positive  the  Let  wind  otherwise  Xdt  "  fluctuations  wind,  the  (surface  o  and  height,  the  mobility  of  water  The  fIuxes  concentration  average  wind-driven and  also  investigation.  cond i t i ons .  Consider of  of  area  probably  observed  s i mi I a r  considerable  direction  crests,  current)  bear  a  zero  of  =  is  is  by  vertical average  this  xu^  advected  velocity  value,  property a  the  is  turbulent  then  Xu^» flux,  stress  downwind  downwind  momentum  velocity  per  component  unit  17  V|  =  U +  U | .  horizontal  do  is  so  the  form  u  quantity  wind  transport  stress  of  is  u  (2.12)  5  the  vs.  3  downward  Reynolds  which  integrating f0,.Af) I  average  or  -Pa ,  =  l5  the  by  the  momentum  T  This  Then  In  e  we  wish  area f, '  to  under  noting  evaluate,  a  spectrum  and  we  will  pIotted  in  that  100  u , u  3  J^.jUJdf  =  0  =  II  ^ ,  3  (  f  )  d  (  ,  n  5  e  )  f  fjZS, (f)d(ln f) 5  f  where  f^  beyond find  and  which  (Chapter  measurements f  H  =  8  low  are  is  U|  5) of  that  is  low  and  high  negligible.  in  our  velocity  frequency  Empirically,  observations  fluctuations  frequency  f i n i t e ,  frequency,  frequency  f 0 j ^( f ) <  f [0|  required  fj#||(f)  |(f  f )~\  negligible  at  of  frequency  f|_,  must  f0^(f)  and  because  become the  suitable  f0j^(f)  lowest  decreasing at  L  to  we  limits  we  will  .  require  extend  up  to  about  Hz.  The Since  f^  (2.I3)  e  of 2  very below  m  the ust  low  is  less  eventually must  nearby also  f$|^(f)  even  horizontal  decrease  is  defined.  decrease  decrease  frequencies.  which  easily  and  with faster  boundary, will  Determination neglibible,  18  must  be  length  left of  to  run  measuring  required and  Uj  Wind  observation.  u^  stresses  dimensionless  for  at  a  may  drag  This  wind  in  turn  stress  determines  the  determinations  by  point.  be  compared  in  terms  of  a  c o e f f i c i e n t  (2.1)+) where  we  height which mast  will  of is  was  5 a  m  a r b i t r a r i l y '  (The  few  not  the  mean-wind  percent  tall  use  speed  higher,  enough  to  mean  is  wind  at  a  height  commonly  permit  speed  used  at of  measurements  at  m,  10  but  a  our 10  m  h e i g h t .)  A a  wind  " d i r e c t "  discussed  stress  measurement  measurement, in  the  contrast  to  following  section,  which  measurements  but  no  such  b.  Quadrature  resolved  method  be  the  part  f-^Sf tof + i S f  on is  the being  i t s e l f  attempted  components  frequency  of  water  the  at  referred methods  are  would the  more be  as  be  i n d i r e c t .  more  present  u  ;  where  which  of  velocity  components. lies  ^8f«f,  so  in  the  Let 1  fluctuations Uj' ( f , 8 f ,  frequency  range  that M S f  u  to  to  direct, time.  spectra  the  into  is  U|U^  in  Stress  Consider  from  j'(f,6f,t)u;'(f,Sf,t)  =  0-. , ( f ) d f .  to t)  be  19  If  a  phase  lag  of  TT/2 is  components  by  quadrature  spectrum  applied  introducing 0.  a  time  ,-«-(f)  is  to  one  lag  the  J~J  of  defined  of  by  1  velocity  then the  the  relation  nf+^&f  u. ' ( f , 6 f , ( t - T j j ) ) u j ' ( f , 6 f , t )  =1  j*(f )df.  |  (2.15.) The  information  contained  in  0|^""  _  and  can  2 conveyed  by  phase  angle  to  zero  be  gravity  degree  c.  Heat  surface momentum but  water  3.  a.  for  The  to  are  water  flux  Indirect  heat  great  site flux  are  a  The  Iogarithmic profile  of  and  of  and  two  water  will  near  more  of  p r o f i Ie mean  may  be  ~ 2  a n c  be  '  a  expected  ir/2  for  signals  a  expresses  related.  fluxes  the  estimation  sea  the  vapour  the  meteorology.  be  reported will  be  future.  distant  wind  at  to  measurements  in  which  mutually  importance  flux  ^13""" )  +  motion  of  are  measurements  the  The  turbulent  they  2  ($13  =  (0| ^"7'0| 3)  vapour  of  heat  Banks  '  coherence  which  of  vapour  tan  purely  fluxes  direct  Spanish  =  and  101 ^ I  coherence  wave.  the  The  a  also  in  made  sea  Only this at  paper, the  Measurements  prospect.  stress  on  the  surface  method  wind  of  velocity  vs.  height  is  of  20  logarithmic  for  a i r  Lumley  and  simpIe  derivafion:  of  Panofsky  (  neutral  density  103)  1961|., p .  The  gradient  give  the  over  land.  following  ratio  u»-  dU/dx  has  the  5  dimension*  characteristic equal  to  of  length Z  K(x^ +  q  )  length, is  Z  characteristic  of  has  empirically  been  found  in  height.  where  the  and  Hence  is  q  neutral  a  surface.  a i r  we s e t  roughness  this  only ratio  length  The von Karman  to  the  constant  K  O.lj.0.  be  Hence,  u*  =  K ( x  5  +  z )dU/dx 0  5  = 0.ij.0dU/d( I n x ^ ) .  Integra  ting,  U  Then  u-» m a y  logarithmic (At  our  The profiles density  (2.16)  site  =  (u*/K)  be  determined  velocity Hamblin  profile if  ln[(x  there  +  (I9&5)  ) / z  0  may  using has  be  adequate  s t r a t i f i c a t i o n .  z  directly  profile  method is  5  0  ] .  from  slope  e q n . 2.16  found  z <l  extended knowledge  However,  the  Q  of  where  the z  Q  « x ^ .  cm.)  to  n o n - 1 o g a r i thm-i c  of  the  determinations  atmospheric of  21  s t a b i l i t y  for  the  paper  not  good  are  Accordingly, velocity  method  profiles as  b.  downwind  In  enough  this  plotted  The  measurements  U  vs.  the  which  to  be  j u s t i f y  will are  to  be  discussed such  applied  nearly  a  this  treatment.  only  straight  in  to  those  lines  when  Inx^.  velocity  inertial  f I u c t u a t i 'on* m e t h o d  subrange  0, ,(k) = K'£ 2 / / V 5 / 5 . where We  the  assume  turbulent and  Kolmogoroff  constant  that  height  at  energy  Panofsky,  any is  196^-,  equal p.  to  120,  (2.  (Pond  K"=0.It-8  et  a l ,  1963),  the  rate  of  production  its  rate  of  dissipation  eqn.  6)  of (Lumley  It.2),  (2.17)  and  that  Iogarithmic  the  approximation dissipation  at  which  dU/dx  Then  least  x  we  =  p r o f i l e  over  are  the  law range  considering  is of  a  valid height  occ.urs, from  at  which  the  eqn. 2.l6,  u  - ;:  2  =  (K  2  /  5  /K')k /5 5  X  5  2/3^  |  (  (  |  <  )  = (0.]|0 Vo.W)(2rTx /u) 2/  2/5  3  We  use  the  notation  u-:c-  for  indirect  f /5 J 5  j2  i|(f)  estimates  ( 2  of  -"- R . J . Taylor (I955> S o m e o b s e r v a t i o n s o f wind v e l o c i t y a u t o c o r r e l a t i o n s in the lowest layers of the a t m o s p h e r e . Aus t . J . P h y s . , 8, 535" was a m o n g the f i r s t to r e p o r t the extension of the Kolmogoroff law t o w a v e n u m b e r s at which marked a n i s o t r o p y was present. He a l s o estimated u-"-^ u s i n g structure functions, by a m e t h o d equivalent to the downwind s p e c t r u m m e t h o d .  23  CHAPTER  I.  ANEMOMETER  S p e c i f i c a t i ons  For sea  measurement  surface and  over  u^  the  must  the  In 13  THRUST  DesIgn  a.  U|  THE  3:  m sec""'  be  frequency  be  in  seen  The depends  where  the  velocity  f  wind I  of  run  desired,  anemometer  design.  We  Then  under  typical  this  corresponds  b.  Devices  A  at  for  number  velocity  this  of  the  components the  surface,  f^.  to  ,  f  interval  negligible  above  on  ranged  from  u. m a b o v e to  be  the  about  to  3  water, Hz,  8  the  as  will  5«  length  velocities  flux)  fluctuation point  proved  confidence  Vertical  a  (momentum  speeds  from  frequency,  to  at to  L  required  Chapter  lowest on  range  heights  maximum  stress  determined  case, and  wind  turbulent  frequency  our  of  will  to  at  may  does  U =  not  500  of  2  analysed and  on  directly  take to  wavelength  height  be  recorded  a r b i t a r l l y  maximum a  be  but  conditions a  which  =  1000 of  m are  cm  over  the affect  .0039 s e c I  -  ' ,  km.  expected  to  frequency.  measuring  wind  techniques  fluctuations.  Some  are of  velocity  used these  to  fluctuations  measure  will  be  Hz•  wind discussed  be  2k  in  this  section.  The  rotating  meteorological anemometers  for  momentum  frequencies resolve  related fine to  to  wire,  wind  water, about  wire  cooling  component  of  wind  the by  called  desired using an  and  boundary  Pond,  Pond  1965;  small  frequency momentum  by  response  airborne  In  the  suitably This been  layer a l ,  1966;  of  far  the in  bent  or  of  cup  the  an  for  on  current.  and  a  the  sensor  The  broken  of  may  that  shock,  be in  a  technique in  et  yield  a  required  in  the  I9&3;  a l ,  Hasse,  or  the  wires  (Pond  readily  signal  to  used  laboriously by  purpose.  responds  hot  1966 j  not  extremely  It  standard  sea  do  this  an  u^)  oriented is  few  to  perpendicular (uj  a  e l e c t r i c a l  wind  Weiler,  excess  only  anemometers  required  of  desired  only  successfully  over  measurements.  easily  are  lightest  response  respond  Since  components  has  dimensions  flux  are  et  they  of  the  heights  velocity  "X-wire".  work  at  electrical  two  familiar even  produces  effect  an  tunnel  wires  vanes  by  a  frequency  Hz.  anemometer  atmospheric  The  I  heated  and  high  since  d i r e c t i o n ,  the  determined probe  the  is  However,  measurements  below  hot  wire  the  the  wind  The  lack  flux  above  anemometer  instrument.  cup  meters  cup  1966). highfor  calibrated contaminated  dust.  acoustic  anemometer,  variations  in  the  speed  of  25  sound in  a  along phase  advantage with  the  while root  wire  tried  be  vibrations the  spurious  and  are  but wave  the  to  shows  these  M.  Miyake  of  force  and  of  speaker  occur  in  the  promise  are  other  work an  in  Japan  components  into the  as  three  velocity  Its  response  is  non-linear,  sphere  proportional  to  the  square  our  appeared well  as  d i f f i c u l t y  by  Also, may  causing This studies.  Soviet  the  Union  United  force  on  States.  an  components,  and  components  may  the of  to  can  anemometer  the  wind  of  at  turbulence  in  the  geometry.  required.)  calculated. being  of  University  signals  in  and  square  spurious  spectra.  used  path,  its  to  microphone,  resolves  sphere  the  from  This  wind  linearly  response  noise  is  the  sound  to  acoustic  and  widely in  the  anemometer the  measured  anemometer rough  of  has  result  varies  sensitive  acoustic  more  development  Iy  a Iong  f l u c t u a t i o n s . but  great  which  calculated  being  height  It  frequency  of  an  microphone  proportional  the  framework  anemometers  thrust  veIocity is  a  signal.  unfortunately  overcome  peaks  aerodynamicaI from  (Dr.  to  shift  readily  velocity  of  under  The  wind  is  separation  instrument Acoustic  by  wind  phase  setting  site  influenced  doubtless  a  Further,  sounds.  experimental  vertical  received  disadvantage  Washington  speaker  voltage  anemometer  the  a  the  of  v e l o c i t y .  has  vary  of  producing  hot  reflected  be  from  component  acoustic It  path  shift of  the of  a  force  on  v e l o c i t y .  be  the  26  The until  thrust  now  a  fragile  than  is  less  in  the  Indicator  a  and  would  sphere  frequency  response  relatively  c.  A  Co.,  The  (1965)  as  the  thrust  not  have  quite  as  used  at  compact  two-component this  year  by  thrust  anemometer  was  Institute  of  a  hollow,  spherical  styrofoam  into  displacements  transformers. proportional sphere. roughness  linkage  These to  the  Experiments in  the  and of  high  I0UBC.  State  the  with  Hole  Dr.  Engineering  cores  shell  which of  e l e c t r i c a l  three  spheres  varying  Institute  E.  Doe  It  (BI0).' " ; :  inside  which'  wind  d i f f e r e n t i a l  signals  of  Massachusetts  A.  resolve  components of  L.  Oceanographic  Oceanography  springs  produce three  Woods  by  Bedford  force  University,  developed  and  mechanical  m  anemometry  Institute  a  Wind  C a l i f o r n i a .  York  are  e  good  National  New  of  and  thrust  Solid  at  consists  far  probe  (30«5  larger  instrument  introduced  of  wire  14-151 D y n a m i c  Model  considerably  Pasadena,  history  hot  Although  three-component  Corporation  has  diameter)  Science  available  Flow  was  a  and  ca!ibraiion„  commercially  Anemometer  developed  It  variable  A  recently  instrument.  less  Vector  a  untried  sturdy  anemometer,  is  r e l a t i v e l y  from  A  anemometer  wind  of  force  on  degrees  the of  Technology's  * A thrust a n e m o m e t e r was a l s o built by G.L. L y n d e and F.W. Stapor (1952, M . S c . T h e s i s , M a s s . I n s t . Technology, Unpublished manuscript.) Its larger size w o u l d make i t u n s u i t a b l e f o r our measurements. Doe's ''. development (1963) independent. The NESCO thrust anemometer (M.H. Norwood, A . E . C a r i f f e and V.E. Olszewski, J . Appl. Meteorol., In p r e s s . ) resembles that o f W . H . R e e d a n d J . W . L y n c h (1965, J . A p p l . M e t e o r o I . , 2, I4.I2) . w  a  s  Another instrument, the a n e m o c I i n o m e t e r , uses pressure taps d r i l l e d in a sphere to o b t a i n performance very s i m i l a r to that of the t h r u s t anemometer. (A. Martinot-Lagarde, A. Fauquet and F.M. Frenkiel, 1952: The IMFL a n e m o c I i n o m e t e r — an i n s t r u m e n t for the investigation of a f l u c t u a t i n g velocity vector. Rev. Sci. I n s t r u . , 23, 661 -666; G.W. Thurtell and C B . Tanner, 1965• M o m e n t u m t r a n s p o r t measurement in the atmospheric surface layer with the anemoc!inometer. D e p t . of S o i l S c i e n c e , U. o f W i s c o n s i n , Unpublished manuscr i p t.)  27  Low-Speed  Meteorological  Massachusetts aerodynamic than  showed  noise  dimpled  The  Mk.  II  designed  and  built  differs  system penalty  in  the  I  Mk.  voltage  a  or  by  the  which  sphere  Mk.  transducers  Doe  the  permitted  The eight of  sitting  required  from on  minutes  Mk. a  of  analysis  four  were  data  of  at  a  drag  lower  coefficient  (Figure  I0UBC the  at  in  electronic  the  the  cm  instead  of  At 7  c  in  a  I9&3.  slight tor  m  dispIacement-to-  direct  of  BIO  author.  direct  place  was  I)  author  by  considerable  model  I  one  foot  thin  relatively  measurements  in  has  current  ordinary  d i f f e r e n t i a l  simplification  of  procedure.  original  wires  of  H i l l ,  sphere  variable  DCDT-050  (Sanborn  transformers operating  (9*6 use  transformers)  Round  spheres.  and  designed  a  at  principally  I  differential  the  less  used  diameter  anemometer)  a  knobbed  Dr.  was  Tunnel  perforated  and  instrument  from  used,  that  level  smooth,  It  Wind  diameter  tubes.  complicated  recorded  produced  these  (Figure  data  with  Its  3b) steel  under  hoop  adjustment, it  way  suspended b y  electronic  and  satisfactory  is  was  at  system  but  analysis results. BIO  as  instead  several of  5  Further this  is  wr i t t e n .  When internal  the  sphere  linkage  is  is not  in  place  on  accessible  these for  anemometers,  adjustment.  if  their  28  repairs must was  are  later  needed be  designed  external but  the  cemented with  a  in  by  construction  completed  replaced  the  model  This of  was  these  arrangement  designed were  N.S.,  by  Dr.  in  in  February  A  Doe  Mk. The  by  for  be  instrument  to  three  2.  Construction  of  the  a.  Moving  other  with  and  in  and  "  C  s  in  single  transducers  in  tie  wires,  its It  w.as  more  Two  Co., one  was  used  Caribbean  Sea,  work.  development  rigid a  one  anemometer  author.  this  under  new  transducers.  and  the  I ater  a  a  the  a  three  Engineering  5 )  to  to  poor.  wires  Doe  reported  end  its  be 2)  Aruba  (Figure  thrust  because  University,  off  fastened  at  sphere  Dr.  York  is  BIO.  tie  Eastbourne  New  to  (Figure  by  11 I  and  f l e x i b l e  would  five  measurements  19&h,  V  of  j o i n t l y  built  Dartmouth,  force  off  attached  not  of  symmetrical  Mk.  slender,  was  IV  cut  three  resolution Mk.  be A  sphere  directional by  must  place.  hollow  transducers  its  sphere  rod  at  attached  weatherproof  housing.  The Mk. of  II the  Mk.  anemometer  part  mechanical  linkage  thrust  anemometer  Mk.  except  that  resulted  in  transformers  thrust  II  I,  and  spring  (Figure the an  use  lb) of  increase  arrangement  follows larger from  of  closely  the that  d i f f e r e n t i a l  "J .6  to  9,6  cm  in  29  the  outer  diagram of  the  the  diameter  of  the  three  movable  (c). (e)  At of  alloy each along  an  the  thin,  axis  a of  blocks  of  Two  cemented  for a  a  Figure  signIe  threaded of  a  rod  is  clamped  the  beryllium sphere  to  circles  (g)  together  close on  spacing  the  tie  are  spring  section. wire  of  (f)  two the  rod  uniform  From projects  of  the styrofoam  turned  heated  aluminum  each  carries  flat  support  of  For  (a)  a  center  shells a  simplified  constant-modulus  junction  by  a  transformer  to  and  which  perforated at  (d)  copper a  hemisphericaI  holes  rod  d i f f e r e n t i a l  low-hysteresis  fine  is  2  component.  brass  chemically-etched  styrofoam,  diameter  sphere.  (b)  C  aluminum  (h).  and  end  (d)  sphere  mm  core  Nispan  a  orthogonal  3  mechanism  iron  Wilco  clamp  the  components  each  with  of  from to  produce  density,  c i r c l e s .  b . F i x e d p a r t  The core by  rods  the  movable and  flat  differential blocks  (j),  adjusting  a  fine  after  springs  (e)  are  mounted (I)  for  r e l a t i v e  to  has  supporting  transformer a  (c),  on  its  fixed  zero core  the  been  cores  frame  clamped  sliding  the  through  anemometer  sphere,  from  transformers  screwdriver the  of  d i f f e r e n t i a l  screws  transformer  assembly  in  is  may  in  assembled.  The  clear  position  holes  suspended  ( i ) .  subframes  which  c i r c l e s ,  the  plastic  (k)  with  of  the  be  reached  sphere,  Vibration  with  even  30  damping f l u i d in  (underdamped) in  an  Figure  0.5  2)  (This  the  resonant  frequency  occurrence  3  m  32  terminated  at  instrument  mast.  the to  eight the  from A  a  lead  cover  to  moving  protects  the  sits  the  at  natural  the  on  the  12  in  arm  an  connected  to  the  Four  stubs  sphere  for  5  c  cm  rain  on  attached pass  from ON  or  to  two  the  the  of  mast  project  aerodynamic  from  or  long  I 9  m  rain,  mounted  tubes  cable  by  springs,  is  tubes  shown  fixed  out  these  anemometer  to  (not  washed  of  the  blocks  and  each  of  silicone  framework  steel  platform.  side  be  mass  fixed  which  Through  rod  vibration  stainless  wires  other  tended of  viscous  plastic  core  The  f i t t i n g  by  each  the  Hz.)  recording  the  of  diameter  m  between  to  f l u i d  al lowing  approximately  provided  mm s p a c e  attached  framework.  four  is  symmetry.  damage  when  i t i s n o t i n u s e .  c .  D e s i gn  of  spri  Although will  be  used  necessary much and make  to  in  to  spring  the  Appendix  all  the  the of  s e n s i t i v i t y  calculations before  deflection  use I  measured  decide  design  good  ngs  was  desired  linear  spring  and  for  to  be  2.1  x  10  for  of  dyne  a  cm  the  each  -1  6 calculated  anemometer it  was  construction given  electronic  range  constant  the  results,  starting  mechanical the  of  of  just  wind  system  how force,  to  DCDT's.  In  component  is  31  The +  0.05  DCDT  in  (+  s e n s i t i v i t y  output 0.127  cm)  , 5«°  is  3•  Electronics  a.  Differential  is  + and  C  are  equal  is  other  in  is  transformer  the  and  the  output  (12  v  oscillator unit,  which  iron  coil  core,  A  A  or  coil  and  and  and  to  two 5) B  their  convert e l e c t r i c a l  •  in  phase. then  toward  C,  one  coils  the  between  is  a  an  When  C  produces  by  secondary  and  opposite  between  to  driven  (Figure  but  A  used  springs  the  output  its  a  sensitive  is  phase a  the  a  of  crosses  driving is  were  the  between  toward  phase  core  to  used  of  core B  and.  The  net  zero. half  larger  is  If  or  A  or  the  the  voltage  and  output.  DCDT-050  -  of  magnitude  Sanborn  cm ')  displacement  dyne  primary  secondary  the  springs  directions  voltage  the  dominates  It  movable  displaced  of  a  voltages  d i f f e r e n t i a l core  have  opposite the  the  transformers  These  centered  with v  voltages.  in  a  -I  10  displacements  wound  for  -6 x  mechanical  a  v  transformers  Differential  o s c i l l a t o r ,  1.5  dc  or  center  primary  cylinder  2.1  of coil  cm  reverses  when  position.  In  demodulator  is  low-frequency  displacement the  that  the is  long  signal core. also  and  I.9  the  the built  in,  proportional k  J  built cm  kc into in  the  diameter.  32  The  three  electronic They  are  equipment  connected  twisted,  shielded  platform. because  d i f f e r e n t i a l  Noise  the  is  a  resistance  of  the  input  b.  Amp I i f i c a t i o n  Three  suitable able  for  with  the  Philbrick  input  adjustable  to  the  2.2  kil.  k£l)  of  from  the  of  gain  i t s e l f . cable  (four on  are  minimized  the  DCDT  in  the  only  chassis  output  comparison  dc  dc  the  3ilseries  The  with  amplifiers.  amplifiers  anemometer  amplifiers  introduced  Zeltex  a  and  (These  resistor give  dc  negligible  recently  or  v  cable  operational  signals  more  P-65AU  The  P-65  conductor  electronics  low  3  are 'the  anemometer  eight  6  is  recording.  the  in  (over  the  the  is  cable  Philbrick  boost  to  supply  impedance  in  'JO m o f  r e l a t i v e l y  the  to  by  problems  impedance  used  mounted  pairs)  power  transformers  to  are  and  are  a  level  interchange-  less  expensive  ll6B.)  each  amplifier  from  1.6  to  is  7»i+»  continuously The  nominal  -6 sensitivity for  each  at  the  component.  nominal  values  for  transverse  the  s e n s i t i v i t i e s at  the  of  of  amplifier  adjusted  amplifier  to  make  The  1.8  I  for  the  to  x  2  -  5  and  for  The  5»6  gains  downwind  components 10  is  amplifier  outputs. up  input  -  x  10  from  were  v set  dyne  v  ,  to and  3-6  the  amplifier  deviations  10  component  obtain  5  x  -I  desired -I dyne respectively  gains the  were  design  then values  33  of  spring  stiffness  and  d i f f e r e n t i a l  transformer  sens i t i v i ty .  c.  G a i n s w i t c h i n g  Gains  of  were  obtained  (The  control  in  Appendix  as  the  of  or  l6  6I4. t i m e s  switching  amplifier  operational Since  of to  the a  halving  calibrated  feedback  amplifier  signal  wind  the  levels  gains  speed,  each  step  of  wind  speed  the  r e s i s t o r s .  is  varied  value  described  approximately of  Ix. i n  gain  range.  O f f s e t v o l t a g e  voltages  approximately  mean at  by  square  Offset to  Ix.,  3.)  corresponded  d.  I,  wind  higher  finer  supplies. resistors  This  electrical  than  could  the  DCDT's,  d r i f t  offset Ten  was  their  for  were  the  used  inputs  offset  rotary  at  zero  of  +  I  v  switches  adjustment,  for  fine  the  by  to  from  to  also  used  output  component  corresponding  obtained  was  coarse  signal  fluctuations  be  derived  position  served  to  in  the  and  each  voltages  gain.  potentiometers connected  out  to  allowing  positioning  The  balance  added  speed,  adjustment  day-to-day  were  be  the  recorded  provided  a  mechanically  eliminate wind  slight  speed.  zener-reguI and  ated  chains  while  adjustment  operational  to  ten and  of turn  were  amplifiers  in  3i+  parallel  with  Was  for  each  the  schematic  used  shown  in  reduce  the  A It  was  in  This  eliminate  offset  and  such  6)  in  c i r c u i t  c i r c u i t  order  is  to  with an  the  was  used  the  DCDT's  excessive  c i r c u i t  196I1-  in  was  and  196%  and  employed  amount  a  of. dri  modified  ft  in  1966  built  into  fault.  control  having panel  parallel  Power  A v  196I4.  +  on  IOUBC  regular be  10  and  v  and  could  A  plug  be  I  v  ranges  switched  was  oscillograph the  +  also  to  one  to  was any  provided of  of  to  the  three  connect  an  the  amplifier  outputs  supply  operating  from  meter.  supply  60 a  or with  15  at  +  outputs.  oscilliscope  to  i t s e l f ,  one  (Figure  c i r c u i t  series  only  offset  diagram.  introduced  this  meter  amplifier  at  the  separate  M o n i t o r i ng  A  115  of  A  but  diagram  connected  to  f.  component,  offset  the  in  signals.  different  in  the  DCDT  complexity  transistor.  e •  the  v  zener-reguI  cycles  separate at  that  testing,  was  a ted  designed  chassis  time.  The  Battery  P-65  and  because  maintenance  unnecessary.  power  and  built no  such  operation  by  unit would  replacement  amplifiers  the  were  author was  in  available,  require  which  was  powered  felt  35  directly the  from  DCDT's  employed  g.  a  the  and  19 61+  frequency The  I  v  the  a  supplies  output  sinusoidal  voltage  of  controlled  by  Its  frequencies I,  2  and  IRIG  (intermediate  5,  7  and  is  +  .075  or,  supply  for  c i r c u i t s  signal  a  3  n  of  were  Range  i  tape  for  1270  each  A  e j  n  was  recorder. component  was  voltage-controlled  whose  amplitude  voltage  Q  the  device  constant  f  to  anemometer  output with  is  a  frequency  ,  )  the  o s c i l l a t o r s  1300, 2300  Full  scale  for  39OO H z  and  Instrumentation  used  Group)  ,  for  channels  frequency  deviation  V three  o s c i l l a t o r and  recorded  alternately,  a v a i l a b l e . for  v  6  offset  thrust  Model  respectively.  (multiplexed) tape  the  a  regulation,  going  + 0.003 e  0  The  the  is  input  f = f (I  9  of  TeledyBamics This  components  zener  low-frequency  (VCO).  center  while  for  of  before  oscillator  The  supplies,  v  stage  modulated  to  15  modulation  amplified  applied  +  second  Frequency  In  +  The  recording  by  thrust a  outputs on  a  recorded  single on  anemometer  conventional  could  i:"  be  channel  separate was  combined of  channels  originally  tape  magnetic  recorder  if  designed and  a  36  |[L.,5 (to of  be  multiplexed  the  effects  reference CP  signals  was  I965  the FM  VCO's  and  7/8  '  speeded  n  tape not  FM  e  '  c  up  of  the  factors  used  I0UBC to  the CP  and n  for IRIG  100  are  signals.  2  not  While  (n  was  some  of  the  the  three  Wave  155^4-A  designed  resulting  some  Table  in  3«'  frequency  for  loss  lists  of  the  modulation  data,  the  tape,  the  by  means  of  carriers  Analyses  Demodulators  of  196!+  (Filters) wider  set  Ampex  to  bands  signal-to-noise  bandwidths and  of  the  demodulation.  The  Figure  6.  for was  could  at  be  without  convenient  reproducing  separate  used  0, I,...,5)  =  by  recorder. in  of  and  replaced  recording  e f f i c i e n c y .  to  Ampex  channels  demodulations  This  channel  the  were  were  of  one  elimination This  shown  sake  on  available  demodulation  tape  the  multiplexed  for  with  VCO's  amplifiers  of  was  variations.  suited  Ampex  levels.  for  signals)  or  at  c i r c u i t r y  FM  signal  recorder.  seasons  playback  voltage  analysis  In  1966  all  1  by  needed  tape  reproduce of  other speed  ideally  associated  s  changing  for  the  reference  available  not  and  demodulation  Model  was  channels  Ampex  up  the  equipment  three  I  of  signal  The  for  with  instrumentation  100  FM  I I ed  c r y s ta I - c o n t r o  kHz  in  which f i r s t  speeding  was step  General 10%  was  Radio  bandwidth.  were  used,  r a t i o .  channels  used  37  Table  '3.1:  Component  Frequency  Year Used  Modulation  Frequencies Lower Center  Channel  Deviation  1  1961+  5  1.202  1.300  1.398  2 3  1961+ 196IJ.  7 IRIG 9 IRIG  2.127 3.608  2.300 3.900  2.J+73 I+.192  + 7.5% +7-5  I J Amp e x  2.025  .3.375  U-.725  + 1+0%  J4..O5  All  65-66  IRIG  (kHz) Upper  Reproduce  only  3I:  "  "  "  "  " "  " "  7f 15 30 60  h.  Direction  If of and  only  velocity  the  reversing  are  irrelevant.  components are  the  anemometer  In  6.75  tt  9.1+5 I8.9  I3.5 27 54 108  tt " "  37.8 75.6 151.2  be  be  studied,  However,  desired,  obtained  arrows  to  for  positive  deflections  in  Figure  7»  normally  points  into  positions  of  components  the  should  A  2  on and  polarity  total  force  amplifier in  the  pointer the  I966 t h e a n e m o m e t e r w a s m o u n t e d the  7.5%  components  is  voltages  directionsof  " «  fluctuations  the signal  output  of  of  11  8.1 16.2 32.I+ 61+. 8  +  on  the  wind.  its 3«  side,  base  38  !+•  Ca I i b r a t i on  Two  types  calibration  of  with  applied  force.  voltage  response  necessary, equipment  a.  but and  Static The  tested  as  expected,  of  the  was was  was  pointed  of  much  of  less for  the  positioned and  The  demanding  Static  response  was  to  in  the  not  time  strictly  and  performanee  S^.  These  =  10  In  May,  so  that  to  the  10  f  each  checks.  expressed  v dyne repeated  ,  sphere.  The  weight  as  were  2  turn were,  and  adjusted  = S^  found  in  the  sensitivities by  values  = 2 x  preiodically  1 9 6 6 \ t was  as  2  =  I.82  x  10  means of  10 v J  dyne  a check  that  -5  S  was  The  outputs  to nominal S  forces  component  applied  resistors,  J  the  downward.  -5  x  on  sensitivities  input  I x  to a p p l i e d  directly  were  c a l i b r a t i o n was  1.02  former  routine  then  proportional  performance. =  voltage  anemometer  weights  upward  S,  S|  out.  c a l i b r a t i o n determined  velocity.  used  amplifier  Static  determined  tunnel  calibration  and  2  to  placing  was  S  Wind  carried  calibration  instrument  S|,  weights  response  by  results  c a l i b r a t i o n were  _5  and  S3 =  2.01  x  10  —I v dyne  .  The  results  (March,  1966) are  shown  of in  a  typical Figure  8.  static  calibration  on  *  39  The was 2  resolution  tested  axis  the  by  and  of  the  angle  orientation. the  angular  vertical  angles  it  the  rotating  recording  weight  indicated  of  the  force  moving  tan  Over  about  (Fj/F^)  the  range is  the  components  is  Fj  In  of  30  accurate  component  and  Figure  plotted o  +  anemometer  horizontal  components.  '  resolution  of  F^  of  the  9  against  actual  within  +  winds 1°,  expected  although  o there  were  larger  errors  of  the  components  in  is  not  accessible  when  b.  Wind  tunnel  Wind sphere  done  each  occurred  once  of  was  For  the  sphere  calibration to  or  twice  or  per  recorded  at  in  is  The  is  not  in  place  carried  alignment  adjustable  repairs  various  the  wind  were  The wind  and  0  each  which  output  of  time had  made.  speeds  tunnel  to  be  This  of and  the  a  each at  Department  UBC.  calibration,  1966  out  anemometer,  season.  Engineering,  March  was  the  adjustments  orientations  Mechanical  range.  3°0  anemometer  the  cemented  time  component various  was  this  a  calibration  tunnel  new  over  Figure  IOa  shows  2 force c  =  from the  as  F/U 3  2  a  function  =  .0220  to  sphere  |8  dyne  m sec  used  of  in  ', the  U cm  .  -2  which  I966  Figure sec is  2  ,  10b  over  the  shows a  wind  speed  calibration  measurements.  range  constant  for  i+o  The  resolution  rotation  of  component the  was  the  then  which  of  winds  result  in  the  the  of  to in  c  the  this  of  f i e l d  test  was  was  At  sphere  that  the  transverse  orientation  the  range  can  by  balanced  and  the  experiments  each  was  adjustments Over  tested  horizontal  tunnel.  s e c " ' .  m  its  the  offset  653  angles  about  wind  weight  electrical set  vertical  anemometer  axis  2  effect  using  the  of  be  out  wind  of  +  speed  3O  at  0  expected,  calibration  constant  the S  2  of  3 vertical because  component of  sIight  perforations;  Indicated  after  this The  actual  =  accounts  v  J  actual  adjustment  has  been  axis  angle  was  and  in  also  the  Figure  transverse  l«67  10  10  x  for  dyne  its  in  Figure  agree  Ma  within  +  1°  made.  rotated  about  indicated angle  Mb,  or  ,  angle  The  component  the  is  vertical  plotted  c a l i b r a t i o n S2 has  v  dyne  ,  This  missing  portions  tubes  and  the  dummy  factor  was  l,lJ+  supporting  sphere  presumably  been  of  divided  against the  by  I <,09|  -1  J  the  I o0lj_,  by  the  and  -5 -  in  angle  3  horizontal  divided  x  1,92  anemometer  component  be  assymetry  S^'  shows  must  empirical of  prongs  the  correction  sphere  opposite  where them  the  are  attached. This and  1965,  In  I966  and the  correction  was  then  anemometer applied  to  for  applied was the  the to  mounted less  spheres the  used  vertical  sideways  important  and  in  196I4.  component the  horizontal  3«  1+1  transverse  c.  Table  component  of c a l i b r a t i o n  Tab I e 3-2 s h o w s constants  d.  Thrust  Run / (dyne  •15/2/61+ 2V7/6L 30/7/6k 23/7/61J, 26/6/65 29/6/65 22/7/65 23/7/65 8/5/66 12/5/66 12/5/66 13/5/66  AR  B  C D  E  F  G J  K  0  R S  Range  The  and w i n d  run analysed,  tunnel  with  calibration  adjustments  for  2 and 3 i n c l u d e d .  3»2:  Date  constants  static  f o r each  components Table  2.  Anemometer  c  Calibration  Constants  S.xICK S^'xICK S ' x l C K p ?v 3 c m ' ^ s e c ^ ) (v d y n e " ) /  • 0ll+5 20 .0294 1.96 .0270 1.92 .029k 1.96 .0228 1 .22 .0216 1 .22 .0216 I .22 .0228 1 .22 .0220 1 .02 .0220 1 .02 .0220 I .02 .0220 1 .02  of wind  maximum  G' I  z  1  ^  I v 1  3.76 3 . 7-6  -  2.97 16 2.16 1  2.1+6 2.1+6 2.1+6 I .67 1 .67 1 .67 I .67  2.16 2.16  Q  ,.081 1 .31 .327  80 2.97  2.1+6  G ' 2  16  16  2.16 1 .92  k k  1 .92 k 1 .92 k 1 .92 k  1.16 16 1 6k 16  k k k k k  speeds  weight  used  in static calibration,  dynes,  corresponds  h 70 gm o r 7  x  '0  ±  U = (F/c)  2  =  18 m s e c  j  .  t o a wind  speed  G < 3  .1073 1.96 16  4 1-6  h k k k h  1+2  Presumably higher  the anemometer  wind s p e e d s ,  encountered,  13  the mast and  other  but  even  m sec ', -  field 292  and  of in  velocity the wind  cm s e c " ' ,  those  in  the  frequencies  of  e.  Dynamic A hot  mast  will  wire  tunnel.  be  component.  the  in  strain  measured  the  the  least  lowest  on  in  the  speed,  f i e l d exceeded  a factor  These n o i s e  discussed  will  Operating  the  alignment  I)  f i e l d with  of  10  at  level  in Chapter  placed  50  c  5, S e c t i o n  to compare that  be d i s c u s s e d  on the S p a n i s h  directly  m  The r e s u l t s  II4..  of of  its  the  upwind  the  high-frequency  thrust  this  of  Banks  anemometer  dynamic  in Chapter  5»  procedure  The anemometer was  for  signals  values  by a t  in order  downwind  For  speed  d e t e r m i n e d by  Even a t  less.  Section  1|.,  in  mast.  of  anemometer was  response  5•  spectra  tunnel  anemometer  calibration  wind  even,  calibration  (Chapter  thrust  the h i g h e s t  wind s p e e d was  8 Hz and  determinations  o p e r a t e at  placed a considerable  the s p e c t r a l wind  could  equipment.  The minimum u s e f u l comparison  itself  1966 of  the  attached  measurements vertical  to an arm on the a bubble  component  3«  level In  instrument  was 19 61+  used a  n d  10  I965 and  the the  full  importance  anemometer  vertical  to  the  anemometer  and  platform.  A  when the  not  in  mast  was  eye. to  cover, use,  was  turned  to  cable  the  was  was  removed so  that  mast,  before  been  which  chassis  placed  the  had, not  connected  electronics  which  was  levelling  fixed A  the  of  over  made  the  the  the  recording  anemometer  recording  instrument  was  to  on  realized  data;  and  pointed  info  t h e w i n d .  The for  5  power  supply  minutes.  The  produce  a  suitable  average  outputs  voltages. the  outputs  ( i . e .  at  e r o  z  recorded. range  of  The recorded tape  were  This the  force on  channel moved turn.  of  on  Wind  to  zero  speed)  were  six  heights  the  d i r e c t i o n  mast at  be  the  of  to  of  platform  up  to  the  offset  recordings covered  full  were  dynamic  used.  on  the  the  sphere  Ampex  anemometer from  multiplexed  each  value  and  the  Pulses  "roving"  warm  components  because  made.  a  the  1965  force  not  to  anemometer  hot-wire  were  seventh  hydraulic  the  channels  to  using  components  often  set  and  total  could  allowed  recording  zero  with  discontinued  separate  were  196I4.  and  and  for  to  the  Simultaneous  tape,  its  of  fluctuation  recordings at  adjusted  recorder  three  anemometers  level  was  recorder.  height  output  set  tape  on  switches  some  wind  turned  gain  were  During  was  cup the and  were  CP-100 and seven  onto  at  cup  one  anemometer six  wave  being  heights  the  mast,  in  current  speed,  temperature  eiectro-mechanicaI revolutions automatic  One  were  channel on  direction time  counter  the  "roving"  readings  recorded  of  anemometer  the cup  at  one  minute  tape  was  reserved  and  anemometer  intervals  by  an  camera.  commentary  and  at  of of  of  the  the measurements,  for  a  including  mean  current  and  waves,  amplifier  gain  starting  and  ending  recording  of  voice water  level,  settings  the  various  s i gna I s ,  Calculation  6.  of  velocity  fluctuations  from  force  f I u c t u a t i ons  The sphere  magnitude  was  found  F  of in  = p CAV  the  wind  drag tunnel  = cV  2  a  wind C  =  0,220  speeds, 0.25  force be  c =  written  a  in in F,  and  the  sec  is  vector =  calibration  constant  to  diameter  be  drag  direction  coefficient. as  the  the  range  encountered,  wind,  Since this  of  and the  may  form,  (3.1)  CVV;  v e l o c i ty  cm  9,6  over  and p r e s s u r e s  dimensionless the same  the  2  temperatures  is  was  gm m  on  2  -2 where  force  components  are given  by  k5 v,  The  = F  subscript  horizontal  i  J  "  G  =  F "  2  (3.2)  2  I denotes  crosswise  a  downwind  component,  and  i  component, =  a  5  i  =  2  a  vertical  component.  A  linearizing  turbulence The of  (It  anemometer the mean  Taking  i  =  5  I  f I u c t u a t i ng  found  is  =  in  u  so  typically,  be  aligned  for  (uj  in  the  low-level  ) <0.|.U.) 2  direction  U|  2  u  5  and s p l i t t i n g  (3»t)  +  fj  =  -  the mean  F, ^  the  made  that  c ( U  ^ c ( U  leaves  to  can be  it  into  mean  and  parts,  Fj  Subtracting  that,  assumed  = U +  \lo_ V  was  wind  V|  approximation  cU  c ( U  +  2  2  + u  2  |  (  +  2  part  U j  ) ( U + u  + 2Uu,)  part  fluctuating  2Uu  )  2  +  u  2 2  +'u^ )^(U 2  +  u )  )  (3«3)  (  1+6  f,  "  2cU  u,  -  f,/2cU  U |  ,  and  Similarly,  taking  f  —  2  i  (3.4)  = 2  c(U +  and 3  u, ) u  *  2  in  (3*1)  cU,u  2  and u  2  *  f /cu,  f,  ^  c(U +  u  *  fj/cU.  3  (3«5)  2  u,)u, - cUu,  1 3  3  and 3  (3.6)  Also, f jf . = 5  *  c[(U +2Uu,+u, +u 2  c [ ( U  2  2  + 2Uu ) (  -  2 2  +u  2 5  ) ( U + u , )' -  U ](U +  u,)u  2  U J (U +2Uu, + . . . ) ^ ^ 2  2  u  5  *2cU u,u . 2  (3.7)  5  7« * C a l c u l a t i o n  a.  Effect  It  is  of  of  high-frequency  finite  shown  the surface  Fourier  frequency  =  of  in Appendix  Uj over  u.  size  of  a  sphere.  2  that  sphere  component  response  of  the average radius  Uj cos(Ukt), Q  u j c p s ( Uk t ) s i n'( k r ) / k r . 0  r, is  velocity  for a  particu  This and  component the  sphere f i r s t k  curly of  of  f  =  calculation of  the  r.  50  the  i.e.  complicated.  There  response,  during  change  wind at  seen  5,  S e c t i on  11+) .  Effect  the  response  the  wind  Suppose U  of  +  u  in  to  a  cos  is  rate  velocity the  the  velocity  sphere  it  then  passes is  flow, be  drag  which  U  =  500  =  kU/2TT,  over  cm  typical  conditions in  by  the  rough  must  lag  result  be  in  mechanism  at  more  aerodynamic  adapts  in  is  presence  only  a  the  this  unimpeded  which  a  s e c " ' ,  almost  some  will  f  average  unaffected  also  the  an  assumed  This  of  noise wind  of  the  at  to  a  additional  at  to  sphere  its  frequency noise  a  of  springs about  spectra  of  the  velocity wind sphere  velocity  spring  on  J>2  Hz,  (Chapter  sphere  change  wind  a  tunnel  moving of  the  the  relative  downstream  cot,  and  m  frequency  frequencies.  considerable  be  in  which  c  these  is  resonances  will  If  will  and  been  actual  high  as  b.  the  5  has  flow  speed,  Mechanical introduce  =  Under  that  k  indicates  perforations. to  attenuation  r  It  the  approximation  in  If  Hz.  that  number  here  response  sphere,  through  wave  overbar  radius  zero  = TT/5,  has  V  on  velocity, is  V  component  displacement  is  -  its V, V'.  is  springs then  i+8  wheres  the  spring  stiffness  the  calibration  constant  c  0.0220 d y n e  cm  -2 =  Under  the  (highest and  f  =  velocity it  8.  is  to  =  .  Differentiating,  worst  conditions  -2cUu  for  this  speed  and  highest  16 H z ,  V  2.1  x  sphere  smaller  would  measure  be  accurately  be  other  stress  found  and to  be  to  d i r e c t l y .  levelled,  particular  sin  ojt.  neglected errors  consideration  U =  1000  cm  The  effect  sec"' of  henceforth,  since  expected.  meter  possible  stress  was  frequency) u  I0"5  will  than  Direct-reading  sphere  cm  (2TTf )s i n CJ,t/K  wind  the  dyne  10  2  dS./dt  of  x  the  sec  =  2.1  of  V » =  much  It  Kj  the  mean  construct Assuming  a  thrust  the  vertical  anemometer  anemometer  force  on  the  to  be  sphere  i s  =  cVu  *  c(U  3  u,ju  +  c u , uu  l 3°  All is  that  is  averaging  required over  a  to  indicate  suitable  the  length  stress of  time,  T| ^ = which  "f^  1  f 3 u  could  k9 be  done  by  However, the  an  any  analog angular  component  F  integrator  '  =  misalignment  will  c U  2  produce  s i  a  typically,  within +  I x  the  +  Spanish  9  a  low-pass  from  the  spurious  f i l t e r .  vertical  vertical  of  force  n6  U j U ^ ^ -  then  10%  10 ^  by  5 2  -3 If,  or  or  9  we  must  within  Banks  mast  U  10  +  be  and  able  0.01°.  may  change  if  to  we  wish  know  sin9  Since  if  its  t i l t  is by  to  measure  within  estimated as  much  that as  o +  0.1  present  during  a  run,  measurements.  this  method  is  not  of  value  for  the  50  CHAPTER  I .  Si  1+:  MEASUREMENTS  accessible being  at  in  the  short  shallow tide,  mast  during  fetch,  from  for  some  advantageous  for  others,  limits  this  site  may  conditions, coastal  the  but  situations  instrumentation sea  as  south,  a  at  The 10  cm  the a  function very  diameter  water  equipment the  and  of  15)  1+0  operated. into  of  be  to  I4. m  used,  wave  a  studies.  Results  to  open  It  from  ocean  to  many  in  benefit  fetch  not  is  actually  gained  on  future a  Winds  deep  logarithmic  from  the  recorded.  on  heights  away  easil  maintenance  applicable  will  carried m  0  winds  is  certain  shows  were  at  were  ease  for  but  supported  III.)  of  d i r e c t i o n .  fetch,  signals  instruments  km  experience  13  an  disadvantage  depth  encountered.  will  wind  (Figure  as  at  tides.  70  analysis  were  by  made The  extrapolated  Figure  short  (Figure was  the  data  instruments  platform  aim  and  investigations.  scale  be  results  and  to  waves  always  the  7  such  of  a  spring  measurements  size  not  at  countered  low  were  12a).  (Figure water,  is  disadvantage  also  measurements  I0UBC  near  quite  on  the  The  interaction  site  depending work  ANALYSIS  re  Air-sea  of  AND  an  aluminum  from  by  where  I  to  5  electrical the  The  entire  mast  the  wind.  It  m  of  above  cables  to  recording  could  was  mast  held  be  rotated  upright  by  t  51  three The  guy  wires,  thrust  anemometer  horizontal  An and  arm  to  designed being the  2.  a .  and  profile  s t a b i l i t y  was  of  (Figure  a  to  be  offer  measured.  platform  at  from  which  high  the  It  measured  tide.  mast  shows  the  hydraulic to  the  the  be  on  a  raised  carried  used  which  obstruction 12b  was at  from  The  could  control,  probe.  estimated.  Figure  l6),  p r o f i l e  minimal  and  cm  80  remote  velocity  temperature  could  by  thermistor  mean  submerged  iJj.).  mast  a  fully  mounted  h y d r a u I i c a I Iy  lowered  provide  were  (Figure  auxiliary  anemometer the  which  to  main  a  cup  check mast  and  atmospheric mast  was  wind  flow  relative., location  of  mast$.  Recording  Mean  A  vaIues  camera,  (usually  53 »h  operated sec)  of  automatically  time,  recorded  at the  reguIar  Interva I s  following  quant i t i es:  I . 2  Ti me . Wind  direction  at  3.  Wind  direction  relative  Ij..  Current  5.  7  6,  Temperature  9  cup  speed  and  anemometer at  platform. to  mast.  direction counter  the  top  of  just  below  surface.  readings. the  hydraulic  mast.  52  Figure  b.  17  is  reproduction  Fluctuating  An  Ampex  fluctuating could  be  its  tape  CP-100  the  speed  tape  quantities.  I  7/8  in  ranges  were  to  for  FM  Hz  The  1966  is  signals 12  an  allocation listed  in  f j ,  and  f^  respectively,  all  the  channels  of  f^  a  each FM  frame.  kc  of  I  in  6.25  kHz  +  to  record  of  Its  II4.  channels  recording  3*25  used  to  used  an  sec™'  I4.. I  were  else  were  carrier v.  for  a  by  At  recording,  recorder  + I4.O/S  the  the  direct  .  channels  196I4.  In  recorded  at  have  once; been  signals  at  works  with  the  on  multiplexed  used  anemometer  a.  or  inputs  tape  with  Ana l o g  camera  and  0  channel.  fluctuations  3*  to  for  Table  or  was  input  direct  0.2  temperature thrust  typical  modulating  frequency 625  a  frequency  of  a  recorder The  either latter  center  of  quantities  through  amplifier, of  a  thrust  channels  onto for  1965  and  anemometer 10,  channel  example,  recorded the  for  II 10.  and Not  no  simultaneously  time  of  signals  in  writing.  analysis  I n t r o d u c t i on  An voltage Analog  analog levels, analysis  computer while is  a  well  digital suited  computer to  deals  performing  the  form  with  of  numbers.  r e l a t i v e l y  53  simple brief  operations  on  introduction  Appendix  Table  a  to  long  stream  a n a I og  of  continuous  principIes  is  given  data.  A  in  3»  I:  Allocation  of  Tape Recorder  Tape  Recorder  Channels  R e c o r d i ng Mode  Signal  Channe1  None  1  None  2  Hot  wire  3  Hof  w i re  2  FM  h  Hot  wire  3  FM  5  Thrust  anemometer  fj  FM  6  Thrust  anemometer  fg  FM  7  Thrust  anemometer  f-.  FM  8  Temperature  9  None  FM.  |  FM  flucutations  None  10  Temperature  l I  None  None  12  Waves  D i rec t  Cup  Direct  '3  fluctuations  ;  anemometers  recorded  thrust  Direct  Direct  Voice  The  .  anemometer  signaIs  consisted  of  bk three  components  magnetic in  tape.  equations  analysis  was  of  force  These  fluctuations  were  ^.k,  3«5  to  resolve  a  d  n  equated 3*6.  to  The  these  in  FM  velocity  purpose  into  form  fluctuations  of  velocity  on  the  analog  spectra  and  cospectra,  Re-recording  b.  Analysis a  number  of  separating The or  original at  |6  times  dc  signal  level stage.  lasted  .  up  For by  only  The  only  fwb  treated from  the  and  I/6I4.  of  that  and  1965  separately. original were  a  was  tapes  few to  of  I  ZhfiO  often  that  to  f a c i l i t i e s the  check  encountered  in  in  FM in  c a r r i e r . sec  ',  s e c " ' , was  A  used  to  amplification  of  introduced  new  tape  each  32  at  was  .  minute  run  minute.  preserve  runs  $0  Hz)  components  and  tape,  of  'j/Q  and  or  re-recording  new  speed  four,  so  by  unmodulated  the  were  A  a  analysis  time,  time  a  signal,  vertical  there at  at  factor  of  of  speed  the  simultaneously  signals  d i f f i c u l t i e s  from  cases on  (0,02IL. t o  f i l t e r  factor  runs  played  known  most  sections  spectral  downwind  re-recorded  I96ij-  a  in  recording  level a  up  minute  were  the  by  32  short  band-pass  any  speeded  by  tapes  remove  this  speeded  selected them  wide-band  In  was  their for  sideways  were the  were,  of  course,  covariance.  re-recording component  analysed  directly  re-recordings.  re-recording  was  until  Some the  55  proper  c.  techniques  F i l t e r i n g  for  Krohn-Hite These  have  approximately frequency,  any  s h i f t .  A  applied  to  each  was  an  then  outputs  vertical  and  the  not  require  using f i l t e r s for  U£  for  i t .  were and  and  the  I  the  be  cutoff  same  center  c a l l e d  The  in  the  matching  used,  1966 one  by to  the  phase  of  an  input s h i f t ,  since  Uj  and  to  oscilloscope  the  phase  shifts  equal  but  opposite  the  line.  frequency as  used  two  other  in  for  I9&4  U£,  were  It  the  required  component  the  phase  connected  cospectra  only  in  was  an  f i l t e r ,  no  the  frequency  straight  horizontal  analysis for  were  a  for  matched  match  remaining  phase the  To  used  center  amplifiers  varying  matched  were  outputs  reduced  transverse  ti?,  at  f i l t e r s  the  displaced  ellipse on  at  trace.  was  that  the  components  the  In  wiI  lower  used.  available,  cutoffs  frequency  vertical  c o s p e c t r a I'-ana I ys is.' 1965  both  voltage  input  remained  and  and  bandwidth  setting  e l i p t i c a l  found  upper  were  0  setting  until  f i l t e r s  f .  each  f i l t e r  amount  with This  sinusoidal  produce  Ie  narrowest  particular  horizontal  band-pass  adjustab  used.  and  analysis  35^-A  -2" o c t a v e  was  downstream  to  the  sett i ng,  At  the  Model  and  discovered.  spectral  separateIy  frequencies,  f iIter  were  did  computed  matched alternately  56  Sinusoidal frequencies  voltages  in  turn  output  voltages  in  form  the  particular  of  shows  measured  in  The squared F i l t e r  3  f i l t e r  I,  lower 90° is  (A.  2)  a  is  a  phase  f i l t e r s  and  u^  (3  The  areas  planimefer.  having  the  I  and  (The  I,  the 2)  to  of  2  to  in  be  the  under  I,  the  for  a  for of  1+  Hz,  area  for  lag  phase to  gain  c i r c u i t  the  phase  not.squared of  the on  quadrature  curves  were  0  f  0  =  I. and  the  response series s h i f t e r .  because  it of  the  components  spectral  idealized  >l.5  a  of  attenuations  velocity  )  slightly  and  2  0  shifter  is  o.5f < f < l . 5 f . 0  2( f  l\.  used  an  Aj  attenuation  F i l t e r  is  these  0  2  make  shifted  phase  product  = 0 , f <o.5f ,f  A ; =  of  plotted  20,  show  2  the  characteristics  A  and  were  setting  f i l t e r  is  f i l t e r  attenuation  The  a  number  frequency ^ '  frequency-dependent  Appendix  S-  for  a  f i l t e r s  Figure  normalized  used.  respectively  at  results  setting.  response  the  and  the  against °  combination  peak  represents  2  curves  f i l t e r  f i l t e r  the  to The  ,/e. ) ou t in  scale  by  in  of  case  two  a  its  amplitude  1966,  series  shifter  combination  already  (e  f i l t e r  for  and  applied  frequency  curves  frequency  this  =  the  on  known  measured.  January,  calculated  In  2  f i l t e r  example,  were  were A. i  of  analysis.  measured "unit"  using  f i l t e r  U|  57  would  be  f  0  .  The  * , < f  where  the  If  the  is  Aj(f  f i l t e r  )  0  =  )  the  i  use  in  measured  by  (by  as  considerably bandwidths these and  were  analysis  The f i l t e r  long and  (+  10%  setting  I  i  (  f i l t e r s  two  f i l t e r s  of  of  +  be  f , Q  (It-  of  For  frequencies  2  this  (1965)  in  used,  from  less  +  used  of  series, which  using  was  A  (  and  A2  series.  (f  0  )  vary  day  2%  to  from was  in  his  the  both day  to  day  used  in  our  analysis.)  repeated I  d r i f t  day,  in  B  f i l t e r s  greatly  and  variable  reason,  procedure  in  I)  downwind  f i l t e r s ,  f i l t e r s ;  Bandwidths and  10%)  much  between  setting  | ; | .  c o e f f i c i e n t s oCj  order to  used.  frequency  cbspectrum  between  calibration  and  s s  2)  (Pond  used.  center  of  periods).  above  the  found  not  individually, 1-I-.2 f o r  the  is  0,5.  the  the  factor  (of  respects  over  a  the  fraction  )  0  =  transmission  as  ( f  2 !  B  a  of  B ^ C f ^ w a s - c a l c u l a t e d -  connecting  much  the  as  ) / A  one  at  is,  0  c o e f f i c i e n t  o  f  calculating  fluctuations  the  /  f i l t e r ,  vertical  While  )  identifies  = « , ( f  half-octave  For  o  f  bandwidth  0  a  (  attenuation  B;(f )  For  i  subscript  amplitude  Q  S  transmission  and  for  each  2  are  listed  in  Table:  were  spaced  in  a  58  geometric uniform  coverage  We  have  analysis of f  progression  is  k'  used,  T  degrees  d.  seen  using  degrees  to  freedom For  =  1920  sec.  freedom  Krohn-Hite times The  I .1+  of  computer  If)  that  32  for  bandwidth  nearly  lists  the  analog  the  of  number  frequency  minutes'  frequencies  the  to  21+00  have  output  stages  to  the  range  +  a  duration  number  of  analysed.  having  f i l t e r  desired by  directly  The  f i l t e r s  were  spectral  Accudata  adjustable  of +  the 15  v  tape and  Wide-band gain  the  fed  played  V  from  dc  10  to  steps.  boosting  removing output.  a  were  the  in  v.  recorder,  f i l t e r s .  of  range  computer, and  speed,  gain  or  100  tape  followed  preamplifier  Hz)  the  330-A  were  continuously  amplifiers  amplified  provide  estimate  of  Iso  frequency  which  (0.021+  dynamic  runs  from  Model  the  maximum  v,  spectral  original  f i l t e r s  preamplifiers,  The  to  2  computation  times  either  a  the  the  61+  Section  Table for  2  half-octave  data  at  estimate.  +  of  signals  61+  2,  of  the  of  spectra.  Re-recorded  to  1000  the  f i l t e r  fT.  of  increments  (Chapter  =  three  set  a  of  Spectral  back  of  at  of the  small  10  of  the  was  analog  band-pass were  signal dc  recorder  used to  amplifiers as  the  component  input desired  of  the  59  Table  1+.2:  Calibration for  Data frequency  Analog  of  F i l t e r s  Spectral  61+f  .0039 .0055 .0078 .0109 .0156 .022 .031 -OI4J4. .062 .088 .125 .177 .25 •35 .50 .70 1.0 I .I4.  .569 .5I4J+ .525 .532 ,546  .574 .535 .536 .550 .543  .557 -54-0 .5^0 .54-1 .51+4  computation  was  .561 .571  IO2I4.  stage  multiplying.  The  squarers  have  resistors  used and  proportional  in  Donner  non-linear  biased to  the  Model  diodes square  to of  Freedom  .555 .561  3732  P  feedback produce the  Degrees of freedom k  2  .530 .557 .570 .551+ .560 .550 .550 .567 .562 .570 .557 .567 .569 .557 .565 .56 .55, .560  128 180  next  B|  2  .530 .569 .576 .563 .566 .547 .562 .555 .562 .569 .566 .557 .561 .575 .580 .562 .569 -560  256 362 512 725  The  B  .5.3,7 .5M+ .563 .565 .575 .556 .5^8 .514.6 .570 .556 .562 .582 .599 .588 .566 .57I4.563 .570  J4..O 5.6 8.0 N.3 16.0 22.6 32 hF) 6I4. 90  l+.o 5.6 8.0 M.3 16.0  of  Analysis  B|  .25 .35 .50 .70 1.0 1 2.0  2.0 2.8  Degrees  Krohn-Hite f.ilter bandw i d t h s  Analysis frequency  f  and  .565 .558  squaring  3',8oo 5,4oo  7,700 10,800 is.Loo 19,800 30,700  and  multipliers networks an  input.  and  of  output Multiplication  is  6 0  by  the  "quarter  square"  method.  XY = i [ ( X + Y ) Multiplication If  the  signal  dynamic gain  of  turned  occasionally, new  and  These  better  operate range.  product  of  vertical  the  voltage  each  the  relay time  to  it  Sanborn  voltage models  the  integrator  the  pen  chart  vs. were  used  Each  was  for a  sweeping  a  value, The  much  The  time  larger  and  the  and  at  made of  pattern  the  chart  to  rate  integrator  purpose.)  sawtooth  a  the  a  had  outputs  outputs graph  Varian The  of  and  trace  produced as  a  the  integrator  which  used  output  bringing  assortment  across  purchased.  were  s h o r t - c i r c u i t e d  this  two  computed.  voltage.  (An  were  downwind  in  zero.  I9°6,  components, of  the  saturated  In  have  outputs.  recorders  time.  output  repeatedly  to  of  preamplifier  time.  increased  maximum  back  the  integrators  multiplier  a  fraction  but  three  accurately  amplifiers  the  were  momentarily  done  multipliers  analog  input  reached  to  of  fluctuations  Its  of  principle  integrator  output  1%  components  U2-J  be  and  computer  Dynamics  squares  and  only  computer;  than  same  ] .  2  appreciable  the  frequency  which  connected  output  The  squarer  of  integrator were  the  Philbrick  proportional reset  until  Applied  the  an  could  analog  less  velocity  Four total  up  on  dyanmlc  was  the  but  (X - Y )  squaring  level  range  was  and  -  2  the  of by  6l  integrator time  the  voltage  reset  proportional relays of  to  were  squared  mu11 i p I i  scale the  relay the  21  1 sec  number  hundredth  then  to  to  +  back  The  slope  the  integrator.  operate  and  flying  at  v  50  of  v  100  for  the  to  the  zero  line The  for  the  each  was reset integrals  integrals  of  voItages .  shows  ( v e r t i c a l ,  of  input  voltages  ed  up,  f i r e d .  adjusted  Figure voltage  built  Njj of  integrator  a  per of  typical full  small  scale)  of  in  are  of  a  v  100 30  (top  s  e  integrator  vs.  d i v i s i o n ) .  sweeps  sweep)  outputs  v  100  graphs  time  These  each  (to  i n t e r v a l .  c  to  bottom  in  phase.  in  output  (horizontal  were  read  the  as  nearest  The  Figure  four 21)  dt  where  e,-*  In  is  ej  Figure  delayed  21  a l ,  90  e  and I  phase the  and  constant  outputs  of  the  amplitude integrators  e  are  sine  waves  of  the  same  3 at  a are  frequency of  of  constant  8  Hz,  slope.  and A  62  change  of  negative and  a3  sign  in  the  analog  slope  of  the  uppermost  the  phases  respectively, negative  of  e^  relative  covariance  have to  covarances  respectively.  references  voltages  system  will  In  and  that  thrust  u^.  occupied 8  Hz  The  a  used  be  of  the  that  22  speeded run  of  21  a2  120°  and  2l|.0  signals  of  by  in  negative these  of  the  inputs  30  s  e  to  c  a  a  the  is  signal  n  up  d  the  data  sinusoidal  two  ej  a  factor  traces  e^  levels in  the  a  diagram  vary  of  so  6I4.,  frequency  of  with  the  the  12/5/1966)  not  following  were  signals  of  f i l t e r i n g  are  computing,  subsections.  and  frequency  further  block  by  o  quadrature  analog  following  the  Figures  (I83O-I902,  Ql  Integrator  discussed  Figure  the  computer  data  corresponded  indicating will  minute  of  use  calibration  the  were  period  slopes  and  for  a n e m o m e t e r v e l o c i t y f l u c u t a t i o n  These  32  the  b  21  resulting  The  in  In  advanced  positive  discussed  Figure  recorded U|  be  accounts  graph.  been  e^,  with  in  computer  of  Hz.  0,125  constant, time.  (This  chapter.)  ana Iog  computing  system.  e.  Reference  Before the sine  tape wave  voltage  each  playback  recorder of  known  output  of was  amplitude  the  tape  for  temporarily at  the  spectral replaced  f i l t e r  center  analysis by  a  frequency.  63  This  f i r s t  downwind earlier  was  and for  used  vertical the  figure  relations  between  reference al)  the  providing  a  f i l t e r s  oscilloscope cospectrum  shifts  as  A  the  described  straight-line  indicated  and  of  that  quadrature  phase  spectrum  of  of  the  spectra 1966  by "TT/2.  various  used  phases  to  It a  then  of  the  square  of  recorded entire  the  (Figure  f i l t e r i n g  and  is  in  spectra  ana I y s e d ,  of  The  some  phase  Appendix  5  phase  shifter,  and  the  sinusoidal fi I tered  of  the  of  signal  in  using  place  for  fluctuation  shown  suitable  1965  the was  that  the  this  voltage  was  inputs  at  ve I o c i t y  signals.  in-phase  cospectrum serve  mean  computed  velocity  experimentally  fluctuation  The  is  were  runs  retarded  verified  were  quadrature  downstream  c i r c u i t  voltage  the  s ys t e r n .  Computation  all  to  calibration  f i l t e r e d  mdre  phase  c a l i b r a t i o n .  corresponding  Quadrature and  component  an  sinusoidal  c o m p u t i ng  f.  on  the  conserved.  Integrals  21  equalize  f i l t e r  Lissajous  were  to  had  reference  zero  calibrate  calibration  voltages  quadrature the  covariance,  quadrature  signals  were  used  analysis  used,  which  in  computing  and  could  system. had  the  the not  Two phase  61+  shifter  input  products  e.  of  advance  these  in  two  phase  by  +  120  .  The mean  quadrature  voltages,  = A c o s (kit ± 2 r r / 3 )  and  e  = A c o s &}t,  3  were  2IT/<^ 2  N| # cc e | -»e^ = CO/2  A  3  cos(<jjt+2TT/^-7r/2)cos y j t  dt  o  A  2TT/OJ (+ d o  2  +  Their  mean  (A /2)  cos  2  products  Calculation  were  Spectral  of  N  cc e  3  spectral  estimates  _  cos  M/6  e ="i  A  s i n i»)t s i n IT/6) 'fcos u)t)dt -  -  7T/6.  1  g.  wt  cos  2  13 estimates  were  calculated  from  the  following  equations:  f *  i o  M  = M  ,N ,( N , ' B ,g , ) 2  M  M 5  f  ^ l  (  f  )  =  M  N  N  l 3  M  5  frf,,»(-)=  2  2  ( N  ( N  5  N  N  5  l 3  I3 I3"  ' B  2  ; :  ' B  (  N  "  ( N  2  2  g  g  l 3  I3  s p e c t r urn) (1+.2)  s p e c t r urn) (I4..3)  ) " '  (transverse  2  ) -  (vertical  5  , B  (downstream  2 2  ,  1  B  1  l 2  I2'  : :  g  i  g  3  r  spectrum)  (cospectrum)  l  '9|93 " )  '(quadrature  (1+.1+) (1+.5)  s p e c t r u m ) (1+.6)  wh e r e  M  =  (e'  2  )(2cS.G.U)"  2  (1^.7)  65 2 M  M  2  5  M  Bj,  B  spectral  I966 are  those  used the  with  a  =  (e' )(2c U S,S G G )"'  Nj^-"-'  are  of  listed  Bj *  B j ^ .  numbers  gain  NJJ-»- a r e  of of  data.  Nj '  integrator  S j ,  S ,  and  2  of  calibration  the  are  constant  the a m p l i f i e r  of  the  data  at  the  level  of  the  thrust  G j  and  the  re-recording  G,  Gj - G , " .  1  values  of  gains  of  are  is  used  for  the analysis g j ,  g  2  ,  increased e'  analysed,  B,  g  used  of  g^  over  volts  that  rms  at  of  I,  values  ^  2  are  ' > ^3 ' '  sweeps  the  gain  for  a  the  and c  *  same of  G|",  2  and  re-recording  wind  the  of  is  G j , G and  the mean  is  n C  s e n s i t i v i t i e s  recording  (If  I 3' ^  N  voltage  anemometer  is  integrator  during  sinusoidal  anemometer.  and N  of  the s p h e r e .  in  and U  numbers  again  thrust  G^  gain  r  may h a v e  the  calibrating  be  was  They  the  to  f °  voltage  for  components  f i l t e r s  The f a c t o r s  time  three  the  3.4  sinusoidal  and  the  The  of  100.  or  e ' .  =  5  Table  frequency.  value  the  1  preamplifier  rms  again  in  O.98  =  2  (4.10)  2  the bandwidths  ana l y s i s  the  (4.9)  5  N^,  2  are  2  center  N ,  -2  ? ?  calibrating  during  length  2  2  2  2  2, 5, 10, 20, 50,  sweeps-  cS_G.,U)  (e«  which  f i l t e r s '  N|,  )(  (1+.8)  =  and by  cS 6 U)  (e<  analysis,  data,  )(  =  a n d B j2  2  -2  velocity  recording  then  particular  frequency.  66  If  during  always  a  analysis power  frequency  f  fhe  of  the  tape  then  2,  f i l t e r  was  for  speeded  a  up  spectral  frequency  used  by  some  estimate  was  f  factor, at  times  a  this  factor.  h.  Vertical t i l t  of  anemometer made  for  the  was  an  error  the  runs  made  and  on  of  for  to  compensate  importance  of  levelling  fully the  itself +  3  realized  thrust  In  in  It  effect  of  is  to  t i l t  no  for  except  during  anemometer  the  mast.  the  A  by  that some  the  on  the  provision  expected  levelling  addition,  relative  and  anemometer  v e r t i c a l .  degrees  t i l t e d the  may  there of have  correction  cospecfrum  f0\j(f)  stress.  the  unprimed  t i l t e d  primed.  fluctuations  f ,  f^'  The  been  analysed.  anemometer are  not  mast  the  Let  coordinates  the  levelling  slightly  was  1965  and  had  making  been  of  anemoneter  I96i+  In  was  rotation  relation  Then on  on  an  the  the  coordinates.be angle  true  sphere  ' = f j cos  9  = -f|Sin9  between  the  +  +  9 ,  those  while  horizontal  of  the and  the  true  thrust coordinates  vertical  force  are  f^s i n 9  fjC0s9  force  and  velocity  fluctuations  3*h  (eqns.  3»6)  9  f  f  n  o  apply  w  '  *  2cUu.  '  *  c U u '  5  and  the  will  products  i  of  into  ^  =  u^'  =  2  velocity  spectra  os^O  |  f  are,  to  fluctuations  in  sin  +  -  spectral  terms  of  which  the  we  recorded  f ,  f |  9  +  9  -  f ,f  )sin2©  +  f | f^cos29j/2c*~U  2  s i n  2  estimates,  calculated  assuming  f j f ^ s i n  9)i+c~U  i n29)/c U 2  in  terms  of  the  zero  t i l t ,  are  2  spectra!  now  readily-  be  0  ! M  The  =  0  9  +  ijZ^sin^O  +  ^ ,  s i n 2 9  (lull)  0„cos^9  +  i|#  -  20.-.sin29  (I+.I2)  jZS  '  =  0  '  =  5 5  the  +  (f^cos^G  correct  estimates  is  coordinates,  5  the  i ( f j  seen  primed  f I uctua t ions  u  The  the  5  resolve  force  to  most  vertical  is  I  c o s  2  9 3  -  d i f f i c u l t  estimation  technique  (  to  of  use  velocity  the a  II  part  of  angle  to  sin  , )sin  0,  rotation  equal  M  2  9  2 9 •+  of  t i l t .  which  zero.  15  0  making  5  j  a  5  I  cos29  t i l t One  I,  I  Z\  correction, obvious  makes  the  average  However,  our  recordings  68  were of  purposely  force  made  of  fluctuations  components  on  the anemometer  arbitrary not  offset  applicable  At  the  voltages.  to  our  lower  6)  we w i l l  see  on  the cospectrum  frequencies  that  jZJjj(f)  of  at  low f r e q u e n c i e s  has  a  relatively  the  low-frequency  sensitive  From  to  to  and a  fj#l^(f)  were  considerations the wind  made  a  found  8)  (Appendix  of  the cospectrum.  (This  to  investigation  the effect  anemometer.) the 5, and  anemometer Section for  .0055,  6)  to  make  that  the five  0OO78,  was  For the runs 0  =  of  non-negative  cospectral  should  n o t be  without  of  the  of  with  0.0°  it  will  be s e e n  correlation  which  levelling  led  of  (Chapter  f o r eight  analysed  end  thrust  1966  Hz) is  careful  low-frequency  in  . 0 1 0 9 a n d .0156  positive.  values  the f a c t o r s  t i l t  frequencies  words,  a l l  the  one of  ^(((f)  particularly  few p o s i t i v e at  t i l t a  other  made  the average  lowest  is  I96I4- a n d I 9 6 S  the anemometer,  it  of  In  from  0^{f)  of  0\\(f)»0\j(f)  we e x p e c t  stress  in  add to  o n 0\j(f).  anemometer.  the  Section  3,  effect  fraction  of  of  therefore  that  the cospectrum  the runs of  to  see  small  effect  In  levelling  is  and the  f)  also  and the cospectrum  of  levels  o u t by  (Chapter  ( e q n . 1+.3)  estimates, some  analysed  end of  physical  contributions  is  We w i l l  large  t i l t  t h e dc  balanced  technique  0\\(f)».0jj(  0||(f).  with  data.  fraction these  This  only  (.0039,  runs  6  R, (f) 5  The  following  rotation angle  was  R ,  at  each  of  rotation  5  for  was  each  calculated  five  that  used of  to  lowest  R. ' ( f )  5 5  (f ) ] ~  to  the  determine  other  funs  '(f)0  n  5  the  vertical  analysed:  An  we  0  would  -0.5(4.15)  '(f)]"^ =  5  frequencies.  =  (k.\k)  -0.5.  =  2  make  = 0 , 3 ' ( f ) [ 0  ' ( f )  the  so  3  c r i t e r i o n  required  9(f)  0, (f)[0, , ( f ) 0  =  9  Now  take  to  '(f)  0  •5  make  I  a  =  0  in  5  (I4..I3) a n d tan 29(f ) = 0  If  29  is  between  a  small  R|j(f)  tan  angle  and  29(f) ^  ( f )[0, , ( f ) - ifi^if  we  may  tan 29(f)  assume and  0, (f)[0, ,(f)  to  -  5  a  )]"'  linear  make  ^ ( f ) ]  relation  R|3'(f)  -  [l  1  =  +  -0.5,  0.5/R, (f)] 5  (4.16)  Values were the  of  tan  averaged corrected  eqns.  i+.ll,  29(f) to  for  obtain  spectral  4«I2  the  five  tan  29  lowest  for  estimates  a  frequencies  particular  were  analysed  r u n , and  calculated  from  a n d I|..I3.  ( A 9,  digital  carry  and This  out  print is  the  computer the  rotation  results  discussed  program  in  in  of the  Appendix  was  written  coordinates, form 5«  of  to  calculate  calculate  tables  and  uw',  graphs.  70  i«  Horizontal  A  rotation  similar  misalignment horizontal  method  of  the  wind  coordinates  may  be  thrust  applied  be  those  coordinates  those  of  of  horizontal  Again  the  the  to  anemometer  d i r e c t i o n .  coordinates  transverse  of  mean  with  let  thrust  the  mean  unprimed  Then  of  for  the  anemometer  wind.  components  correct  and  the  force  the  primed  downwind  fluctuation  and are,  respectively,  f  f  where  9  is  unprimed  2  2  2  =  -f  sin9«  ( f ,  =  ( f  2  =  correct  estimates  f  2  2 2  cos  [ i ( f  9  2  2  -  angle  between  be  analysed  2  9«  +  f  (  -  f|  spectral  calculated  2cUu  2  f  2  -  f cos9'  +  2  s in9'  The p r o d u c t s  will  c o s  2  +  horizontal  =  !  +  (  which  U| u »  to  f cosQ'  coordinates.  U|'  The  ! 2  =  the  components  u »  '  !  2  s i n 2  2  s i n  2  9'  )sin29'  assuming  the  =  primed  velocity spectra  are:  f ,f s i n29  )/lj.c U  -  f •, f s i n 2 9 ' ) / c  1  2  2  2  f,f  cos29 ]/2c !  2  terms 0,  of  are  the  now  and  fluctuation  +  +  in  9'  2  into  2  estimates,  cUu *  of  9 *  !  2  2  2 U  22 U  spectral  readily  seen  be  jfl  M  '  =0  cos 9» 2  | |  +i0  sin 9' 2  2 2  +  -§-jZi s i n 2 9 « 12  (4.l'7)  71  ^22*  i ^ 2 2  =  0 ' = (i0 | 2  At  this  point  is  relatively  transverse  by  '  G  - 0  22  setting  ^1  +  |  p  introduce  a  ' "  +  2  j2i  ^ | 2  flux  S  i  n  2  9  '  (1+.I9)  cos29'  | 2  assumption  in  the  that  there  horizontal  0  ^  2  9  physical  momentum U j U  2  |2  angle  ^12*  averaged  =  0  29'  =  over  most  9' in  is  on  may  0 /(0 ]2  the  the  rotation  spectrum  spectrum  0  is  zero,  of  |  5  '(f)  =  and  f j z i  occurs  analysed.  of $  2  horizontal  2  '  small, that  |  frequency  (1+.20)  5  on  ( f ) [ f ^  because  the  on  that the  |  |  rotation  I|_.l8),  (eqn.  coordinates  r e l a t i v e l y  each  22  effect  of  at  l).J9  frequencies  is  fj*  calculated  , - i0 )  ]  0^  33  be  eqn.  important  horizontal  power  i  , )sin29'  {  spectrum  The  S  Zfjzf '(f) * o  coordinates of  2  direction,  horizontal  The  s  l i t t l e  tan  and  O  we  The  C  the  on  the  |  |  effect  downwind vertical  cospectrum  ' ( f ) / f ^  The  of  was  0  ( f ) ] ^ .  cospectrum  depends  on  2 U|  while  the  correlation horizontal  downwind R j ^(f)  is  rotation.  spectrum assumed  depends to  be  on  Uj  ,  unaffected  and by  the the  72  j .  Analysis  of  For of  hot  U-wire  and  h o t - wire  also  for  third  decided  to  analysed  to  available  not to  the  enough  functions  f 01 ^ ( f )  and  s  replaced a  f0 j  u  u  had  A  of (f)  been  For or  f0|j(f) and  of  f0| -«(f)  apparently  computed  2  f  u  u  data,  on  were  and  ;0| ""(f), u  a  it  runs data  depending  (f) on  u  u  #  was  made pass  at  each  were  uj and  f0^{f)  pass,  2 2  1966  was  f0|j(f),  fj#  few  functions  The f u n c t i o n s ei t h e r  was  in  the  f i r s t  the second «  for  equipment  data  were  It  anemometer  of  the  respectively  u  and  of  number  the  u  available  the h a l f  desired  and  anemometer  9  u ^ was computed  a  n  d  were  *0|2^)»  whether  u  2  o  or  re-recorded.  rotation  function  u  of  (f)  thrust  cospectra made  spectra  f0j  desired.  analysis  of  the  U|  hot-wire  inputs  f) 0  either  repetition  f0 (f), u  by  f0j  was  for  best  passes  Uj ,  cospectra  were  2  2  analysed,  between  f0| (f)  analog  The f i l t e r  the  u  the  two  runs  also  channels  with  frequency. and  the  equipment  had  data  measurements  examine  compute  simultaneously,  and  u  simultaneous  which  data  fluctuations  dispense  Since  1966  fjZi| -»-(f)  anemometer  Re-recording  a  the  spectra  velocity  decided  runs.  of  anemometer  measurements,  quadrature  downwind  U-wire  some  and  of  hot  2  coordinates was  dominated  also by  made  analysed  noise,  being  {f)  -  but  the  results  small  in  0  The  f0  o  were  magnitude  r  73  and  showing  analysed.  The and is  of  no They  in  spectra  graphically  may  be  be  in  contributions range  to  velocity form  included  in  the  hot-wire  anemometer  obtain  fj#j . ( f )  vs.  Chapter  mean  velocity  j(f )  df  to  integral  the f^  d(ln  to  will  the  be  presented  These  area  products  are  under  them  products:  (2.3)  (f)  f)  are  negligible  outside  a  f^,  ,f UTuT * J  J f  '  Z'  f  1  fJZf. . ( f ) J.  H  will  be  seen  ana l y s e d , the  of in  from  calculation  f^  of  =  lk.2\)  L and  Chapter f^  f) e  fjeij , ( f ) 6 ( l n f )  H  r  Determination  d( In  1  L  of 6  .OO39 U|  2,  6.  (1966),  Weiler  velocity  logigf.  because  p f ^ .  from  from  mean  fluctuations  graphs  J%j  spectra  6.  spectra  the  other  be  estimates,  spectral  integrable to  not  the  of  of  =  frequency  therefore  did  of  the  related  as  e  calibration  of  LTTUT =  If  tr nds  Appendix  summation  The  to  of  computation  The  said  will  method  outlined  k.  consistent  u^  f^  is  that Hz  to  2  and  left  the  to  range =  8  Hz  U | U ^ from  observation. of  It  frequencies  is our  suitable data  at  for the  Ik  Spanish  Banks  summation spectral  f0j.(f)  is  s i t e .  equivalent  estimates vs.  frequency  is  f  coordinates drag  k»  Cup  p  / f  will  be  starting total  was  350  cm.  on  anemometer  shaft on  a  The  v e r t i c a l  surface  a  the  graphs  increment  rotation  of  to  of  of  = O.3I4.6.  of  UJUJ  the  sea.  calculation  the  the  the  e  The  cup  was  a  anemometer cups  ends  photocell  is  in  spacings  SO,  and  70,  the  on  90  top  of and  of  weighs  shutter,  interrupted  A  and once  a  hot  so  that  up  wire  were or  seventh  down  cup  mast.  7  beam  per  were,  anemometers  vane  assembly  only  them cm,  the  cranked  hydraulic  an  levels  bottom  d i r e c t i o n  of  six  110  also  be  manufactured  between and  recording. the  at  and  and  could  consists which  a  wind  which data  mounted  plastic  which  probe  of  30,  mounted  anemometers,  assembly  start  anemometers,  were  between  cup  wave  an  cup  vertical  bottom,  separation  the  conical  in  Associates,  the  anemometers,  A  after  between  on  S ( i n f)  and  light-weight  water. at  the  before  lines  analysis  2  of  integration  anemometers  the  mounted  our  used  an  interpolating  2 ,  =  c o e f f i c i e n t  Thornthwaite  above  In  _ |  from  straight  estimates  Sensitive, by  n  change to  with  log.Qf.  Spectral  the  The  9> m  of  of It  three s i t s  light  revolution.  on  a  shining  75 Electrical cable  to  pulses the  from  platform  electro-mechanical  A  cup  IOUBC  anemometers  on  one  by  I+.90  spacing  kHz  using  of  to  minimize  to  u t i l i z e  outputs  a  single  seven  of  The  the be or  summed may  be  when  into  than  and  them I  the  response cm o f  sec I  I  to  to  due  the  low to  pulses  gate  1  a  drive  by  from  tape.  seven  the  seven This  3.30, 1+.02 The  frequencies  was  to  distortion  tiarmonic Each  of  multiplexed  for  cup  selected  the  and  seven  signal  separately.  was  o s c i l l i a t o r s  respectively.  internal  respond  for  Figure  shows  |8  anemometer  an  at  m of  a  passed.  can wind  a i r  of  to  pulses;  to  is  be  the  the  the  cups  Assuming  500  required  to  of  results  change  of  cup  manufacturer's  considered  speed  of  frequencies  instantaneous  have  they  lag  f r i c t i o n  up  According  to  a i r  0.05 about  to  built  .81, 2.22, 2.70,  inertial  constant  of  the  and  magnetic  c i r c u i t  Hz.  response,  passage  by  used.  exponential of  I  monitored  inertia  60  carried  amplified  bandwidth.  were  allows  of  adjacent  these  more  are  designed  pulses  anemometers  o s c i l l a t o r  low  are  record  '1.1+9,  of  gated  two-thirds  speed  the  available  s p e c i f i c i a t i o n s , a  to  intermoduI a t i o n  anemometers slightly  was  channel  between  22$  may  recording,  for  they  c i r c u i t  at  h a v i ng . f r e q u e n c i e s and  where  staff  accomplished  photocells  counters.  multiplexing  technical  the  in  in wind  an to  have  a  cm s e e " " ' . complete  one  time The  7  revolution which  can  Cup  of be  a  the  where of  true  error  in  our  Engineering agree  is  1966,  required  this  be  they  is  the  smallest  interval  of  Department  of  one  are to  with  were  of  same  UBC  shown  and  determine  the  supplied  test, in  the  the  small  this  cup  type  anemometers  type.  were  results by  19.  p r o f i l e s ,  checked  Mechanical  the  conducted  Figure  higher  different  anemometers of  speed  wind  of  All  the  Consequently,  important^  used.  those  such  are  cup  they  wind  of  were  tunnel  at  mean  instruments  the  wind  a  measurement  if  that  decelerate.  indicate  differences  serious  the  disadvantage they  the  measurements  in  the  than  In  velocity  closely  results  A p r i l ,  wind  calibrations  periodically  The  rapidly  characteristics  The  to  have  value.  could  response used  more  small  and  recorded.  fluctuating  than  cups,  anemometers  accelerate in  the  6  by  were  manufacturer. the  author  Precise  ve I o c i t y  found  in  c a l i b r a t i o n  differences  with  confide nee.  5•  Digital  Our  spectral  principal  measurements valuable measuring  was  reason  to  by-product spectra  analysis  of  find was  of  for the  cup  making mean  having  downstream  an  anemometer  cup  wind  anemometer  speed,  independent  wind  data  velocity  but  a  method  of  fluctuations.  77 Measurements displaying magnetic  were the  tape  average  recorded  number as  a  were  over  of  photographs  pulses.  each  calculated,  by  Bnemometer  cup  series  velocities  intervals  of  either  of  and  a  of  counters  revolutions,  in  series  either of  or  on  case  equal  d i g i t a l a n a l y s i s  time was  indicated.  The was  digital  performed  spectral  by  the  of  British  Columbia  of  Program  BMD  UCLA, at  a  I  9 61+,  pp.  number  of  estimates  at  method  that  is  If equal  the  02T  a  analysis,  Computing (Health )  of  at  Centre.  A  Sciences w  a  used  s  to  a  number  of  frequencies  t the  Fourier  and  consists of  time,  anemometer the  compute  Tukey  of  N  velocities  and  n  lags  frequencies  of  the  F a c i l i t y ,  spectra!  computed.  (1958?  are  version  a u t o c o v a r i a nee s  transform, were  data  University  modified  Computing  By  Blackman  cup  computer  lags.  record  then  70I4-O  IBM  1+59-11-81  of  intervals  analysis  The  P« 53) »  averaged  used  spectral  in  over  the  estimates  are  f  The  highest  frequency, number  of  (Blackman  =  i/2nt,  frequency determined  degrees and  of  Tukey,  i  =  0 , l , 2 . . . n ,  f  =  l/2t  by  the  freedom p.  112)  is  the  Nyquisf  folding  sampling  interval  t.  for  spectral  estimate  each  The is  78  k = 2(n/N The  program  spectrum  by  and  a  last  weighting estimate  used  hanning. smoothed  the  smoothing  (At  except  estimate  the  O.i+6, s o  (BMD 0 2 T ) includes  on  and  single  that  each  spectral  Q»5k-»  by  frequencies, by  1/3)  -  the  total  spectral  estimate,  assigned  contains  considerable  low-frequency estimate,  which  may  a  energy  be  or  of  The  plot  hanned  onto  expected  to  first  and  was  of  have  last  the frequency  zero,  often  variations  f0||(f).  the  central  weighted  of  lowest  long-term  we  the  summation  frequency  when  is  the  f i r s t by  and  0.23  the  the  obtained  estimate  unaffected.)  vanishes  energy  At  energy  was  by  neighbouring  was  but  side  summing.  estimates  speed,  estimate  each  spectral  wind  frequency  of  next an  in  Some  of  this  spectral  anomalously  high  vaIue.  For problem  any of  spectral  aliasing  considerable  energy  fluctuations  at  this  velocities  averaged  sense  from  Noise  in  is  be  the  involving  over  turbulent higher  the  Introduced,  than  is  however,  by  there  Nyquist  out  by  intervals  aliasing  veIocI ty  the is  velocity  the  filtered  no  data  Although  wind  sampling  There  frequency  discrete  considered.  automatically  samples.  higher  is  must  frequencies  frequency,  instantaneous  program  in  our and the  folding use not  of of  usual  fIuctuations .  the  recording  of  only  79 integral To  numbers  estimate  recorded being too  the  anywhere  is  of  The  of  this  of  has  revolution  probability  the  noise,  revolutions  from  cup  suppose  equal  too  anemometer the  probability  high  distribution  that  rotors.  to  P(x)  of  revolution of  error,  this  then  P(x)  The  revolutions  effect  number  low.  x,  of  mean  nearest  =  square  noise  integral  P  09  level  number  of  P(x)  =  introduced  0  elsewhere.  by  revolutions  2 x  J  --k^x&k;  I,  rounding  =  J  the  is  2 P(x)dx  to  2  x  dx  =  1/12  revolution  o Typically  the  revolutions  counting  and  the  2 to  be  interval  mean  square  to  signal  x-30  level  will  be  found  U|  ~  0.01  U  The  .  signal  level  will  then  be  2 ~  0.01(900)  =9  revolutions  approximately  this  noise  spectrum, the  direct  will  \% be  of  the  folded  affecting  higher The  and  total or  the  energy.  aliased  principally  noise  the  onto  will  amount  The  spectrum  the  measured  spectral  estimates  of  at  frequencies.  spectral  estimates  comparison  from  the  also  required  our  include  2  2 x  will  thrust to  definitions  with  f0||(f)  anemometer bring of  the  were  the  multiplied  computed  records. digital  spectral  A  by  by  analog  factor  results  functions.  f  of  into  to  permit  methods 2TT line  was with  80  The tunnel  c a l i b r a t i o n  (Figure  linearly spectra the  computed  force  analysing  of  the  shows  proportional  v a l i d i t y  relate  19)  of  from the  to the  anemometers  that  their  wind  speed.  cup  to  anemometer  rotation  in  data.  wind  rate  records  approximations  velocity  the  is  Comparisons  anemometer  linearizing  fluctuations  thrust  cup  with will  made  fluctuations  test to  when  81  CHAPTER  RESULTS  5:  I n t r o d u c t i on  I .  One of  of  the  measurements  most  r e l i a b l e  made  with  with  p r i n c i p l e s .  Comparisons  between  fluctuations  of  velocity  the  and  validity  assumption  from  of  thrust  the  for  force  the  analysis  techniques.  The  performance  U-wire  are  vertical a  hot  compared  spectra  X-wire  Spectra fluctuation duration are  are  each,  calculated  variation  of  the  records  averages.  are  These  of  of  eight  data  to  make  and  analog  the  and  An is  hot and  from  of  velocity 32  minutes'  c o e f f i c i e n t s  example  of  the  shown,  as  are  spectral  the  of  drag  hypothetical up  and  thrust  records  estimates our  our  Horizontal  components  spectra.  relating  results  the  of  compared.  Stress  1966.  velocity  and  the  cup demonstrate  anemometer  from  different  linearizing  to  spectra.  also  from  spectral  our  of  cospectra  these  intervals  f i n i t e  terms  from  the  thrust  the  in  confidence  of  of  analysed  for  and  these  of  records  fluctuations  cospectra  made  computed  anemometer  validity  to: c o m p a r e  spectra  anemometer,  anemometer  and  the  is  the  employing  thrust  in  and  judging  devices  c a l i b r a t i o n  relating  fluctuations  .using.  downwind  of  instrument  measurements  anemometer  others  an  ways  estimates  time  for  long-term  backbone  of  this  thesis.  82  A  wide-band  closely the  the  velocity  spectral  spectral  analysis  and  computation  of  of  products  velocity  Eight  runs  confidence For  other  vertical Chapter Eight and i n  in  Section  3h  runs  Append i x  and  analysis  of  of  did  at  rejected.  such  the  and  were  applied  another  we  orientation  coordinates  f  on  method  of'  which  confidence  in  to  of  the  for  time  have of  would  variation  considerable  the not  instrument. be  calculated the  this  seventeen  anemometer comparison same  duration  on  short-cut  for  discussed  shows  23  Iogarithmic  noted  a the  Figure  heights  check  a  summation  as  spectral  chapter,  such  j u s t i f i e d ,  runs  in  analysis.  and are  spectra presented  8.  analysed  them  for  thrust  the  are  provides  duplicates  shown•«,  directional  where  from  Examples  analysed  of  cospectra  over  are  products  calculated  a  stress.  rotations  such  This  offers  were  the  runs,  I4.,  One  wind  velocity  products  estimates.  analysis  for  of  sea Ie. the not  the  This  is  of  made  profiles each  a  with  run,  it  wind  plotted  often  r e l i a b l y .  recording  why  of  anemometers  but  operate  time  is  from  different a  site  digital  is  spectral  data.  Cup  mast,  run  many  of  velocity against  were  averaged height  mounted  happened  that  Irregular  at one  on  a  six or  operation  and  doubtful  data  were  the  p r o f i les  have  fewer  more was  than  83  six  points.  For a  convenience  letter  and  sequence  or  analysed  are  date, x  mean  and  3  t i l t of  the  f  wind at  of  the  =  8  DI,  D2,  is  of  the  of  5»l, the  as  well  thrust as  13  The the  in  runs  time, height  ca I cu I a ted' ver t i ca I  drag  c o e f f i c i e n t  summation  from  will  are  anemometer  by  (f)  assigned  letter  gives  the  The  and  been  same  which  f0  l i s t e d ,  has  intervals.  calculated  cospectrum  Ql,  runs this  F2,  Q2,  m sec on  the  '  at same  of  be  f  =  of  the Hz  .OO39  L  discussed  and  in  the  Q5.  drag  most It  mean  in  The  of  m  run  R2  were  sec Rl  profiles  from ',  of  m  then a  runs  for  the  method  to  showed  (2238) for  runs  p r o f i I es  7  are  selected  p r o f i l e  speed  on  some  for  interesting  wind  3  and  those  crooked  is  height  c o e f f i c i e n t  dropping  about  start  day.  and  logarithmic  time, to  Rl  vs.  straight  p r o f i l e s ,  The  the  velocity  are  the  i+b) .  Q5 (2110)  23)  J2,  G3,  the  (12/5/66)  variations run  by  Q3  wind  straight  F3,  sea  of  (Figure  Section  day  unusual  profiles  scale  the  for  later  short  at  sea  determinations  6,  10  the  -also  F l ,  (Chapter  of  U  the  anemometer.  r e l a t i v e l y  D3,  surface  end  of  by  Table  height,  Hz  Only  indirect  on  in  thrust  logarithmic  not.  only  with  run  8.  Some  to  5  minute  32  those  speeds  anemometer  H S e c t i on  a  listed  surface  thrust to  number;  separated  IL  ?  9  a  each  s  e  c  are  note  that  some '  at  the  increasing short Rl,  R2,  time R3  81+  Table  5•' •  Thrust  Anemometer  Runs  Analysed  Wind T i me  Date  d ir ' cm  Ar  BO Bl B2 C DI D2  D3 El  1 0 3 5 ' •I 103 15/2/61+ l8J+k -1932 2T+/7/61+ 2 0 0 0 ' •2032 21+/7/6I+ 2 0 3 2 . -2 I 01+ 21+/7/61+ 102k' •1112 30/7/61+ I 8 2 k -I856 23/7/61+ I 8 5 6 ' •1928 23/7/61+ 1928- •2000 23/7/61+ 221+2- •231k 26/6/65  E 2 23I1+. -23k6 F I 2 0 1 7. -201+9 F 2 201+9. -2121 F3 2121-2153 GO 11+53- -1525 G I 1 5 5 5 ' -I627 G2 1627. -1659 G3 1659- •1731 jo 1 3 0 4 -1336 Jl ll+OO -11+32 J 2 11+32- •150k J 3 I SOli- •I536 Jl+ -1536- -1608 J5 1 6 0 8 -161+0 K 1528' -1600 01 1 8 3 0 -1902 Q2 1 9 0 2 -193k 03 1 9 3 k -2006 05 2 0 3 8 . •2110 R l 2 2 3 8 -2310 R 2 2 3 1 0 -23I+2 R 3 231+2- -00 I k  26/6/65 29/6/65 29/6/65 29/6/65 22/7/65 22/7/65 22/7/65 22/7/65 23/7/65 23/7/65 23/7/65 23/7/65 23/7/65 23/7/65 8/5/66 12/5/66 12/5/66 12/5/66 12/5/66 12/5/66 12/5/66 12/5/66 -OOl+b 13/5/66 Rl+ 00I1+' -0156 13/5/66 51 0 1 2 k 5 2 OI56' -0228 13/5/66  sec  81+0  k92 82 92 570 I+25 337 375 971  9kk  335 320 3,1 3 3l+l  k 327 583 50 51 500 517 1+90 702 828 668 917 1013 1069 1 il+o 100I+ 892  cm  sec  -I  n  deg.  9 cm d e g .  090 760 3.56 .001 61+* 250 150 1.76 .00086 .74 .00052 21+3 133 23k Ik3 5.4o .00139 110 220 .03 .00090 288 11+7 288 11+1+ .00 .00161 311 ll+l 7.01 .00096 276 213 1.93 .00127 276 210 0.62 .00112 258 90 2 . 0 2 .00138 26k I 10 1.01 .00092 258 120 1.33 . 0 0 0 8 1 .00071 256 2I+1 ,OOOc37 253 250 260 265 1+.I0 .00060 260 2 7 0 5.81+ .00068 27O 2l+2 1 .l+o.OOO83 260 206 2.0I+ . 0 0 0 9 0 256 200 2.82 ^00089 250 202 3.26 .00093 256 203 2.38 .00105 250 207 1+.36 .00099 251 1+22 0,0 .00102 260 1+13 0.0 .00109 2l+6 1+01 0.0 .00127 233 383 0,0 .00091 233 331 0.0 .0011+9 262 2f+5 0.0 ; 001 o k 266 225 0,0 .00087 266 202 0.0 .001 il+ 27O I85 0.17 .00083 269 I58 l .56 .00089 271 155 1.58 .00082 ;  m  from  .0109  to  8 Hz  8  and  Rjj. a r e q u i t e  Q2, ' 03  a  n  anemometer  2,  system  Comparisons downwind  (Run  C,  of  of  mean the  the  220  thrust  level.  ±  )  ,  for  made  runs  to  Ql,  the cup  time.  and cup anemometer  in  time  from  spectra  the thrust  a n d f rom  a  cup  The t h r u s t  of.  was  wind  570  anemometer  anemometer  anemometer  cup anemometer  T h e mean  anemometer (u|  those  were  i  anaIysed.  2 fluctuation,  n.o c h a . n g . e s  30/7/61+)  cm a n d t h e  water  from  fluctuations  overlapping  were  shape  intervening  thrust  I021+-III2,  (1039-1150) height  in  of  in  f h o u ch  velocity  Records  the  even  05,  d  different  5  at  speed  cm s e c  '  190  cm  U at and  was  at  a  above  the  level  t h e rms  - I ' was  60  cm s e c  .  The wind  direction  0 was 10  110 sec  .  Average  intervals  counter  In  the d i g i t a l spectral  values  of  Figures  105  the  calculated numbers  fj#||(f)  groups  points  degrees.  spectral  estimates  2l+ a n d 25,  seven  wind  speeds  from  of  during  photographs  revolutions  of  successive of  a  the cup  rotor.  obtain  former  were  displaying  anemometer  in  horizontal  of  have  have  analysis,  a t 1+0  been  plotted  as  the remaining  five,  are plotted  degrees  of  lags  frequencies.  while  21  1+0  were  The f i r s t  triangles estimates,  as  freedom  used  squares. and the  to five  i n averaged The latter,  86  Spectral digital  estimates  f i l t e r  for  the  me t h o d • o f . , B I a - c k m a n are  plotted  hanning  at  as the  estimates  obtained  by  in  lag  f 01  IogjQ0jj(k)  vs.  25  have  spectra of  the  is  very  accuracy  recording data  of  was  and  vs.  This  method  spectral  I  150)  and  avoids  estimate  frequencies  octave  " p i l o t "  approximate  spectrum  I og | g f in  in  and  and  than  •  and  of  basically  two  25,  result  gives  were  is  an  been  we  but  form  form  taken  is  in  between  less  Figure the  two  v e r i f i c a t i o n  measuring,  cup  his  the  have  important  The  c i r c l e s in  lines  different  (I965)»  as  and  where  Agreement  this  has  2l+  straight  techniques.  Hamblin  plotted  The l a t t e r  The  -5/3  is  Figure  Figure  close,  by  the  1+5, hi  = f0|j(f)/k.  computing  taken  corrected.  -I  by  a  pp.  lower  discrepancies.  slopes  using  analysis.  I 0 g1Q(k) M  to  to  anemometer  = 2rrf/U a n d 0 ( k )  sensitive  This  down  |( f )  (1958,  Tukey,  frequency  type  thrust  form  k  the  and  lowest  IO53-M25  period  crosses.  spectral  The  comp.u t e d : man.ua I I y  anemometer  analysis  pub I i she d , ( P o n d  has  been  e_t_ a_[,  1966).  Another anemometer and  comparison  spectra  23ll4.-23!+6,  Figures  26a  and  pulses  recorded  out  I4..69  at  was  26/6/65) 27a. on  second  between  cup  anemometer  and  (22l+2-23ll|  made  for  runs  El  and  E2  and  the  results  are  shown  For  digital  magnetic intervals  tape  analysis were  using  a  cup  counted Hewlett  thrust  in  anemometer and  printed  Packard  Model  87  5262A  counter  lags  25  and  computed. four of  averages  height  is  the  spectrum  3.  of  downwind  at  the  are the  these  is  good  26  Kl,  02,  Ql,  to  to  as  l+l  Q3,  Autocovariances frequencies  five  single  having  significant  are  the  as  of  open  on  degrees  l6l  with  into  Thrust  spectral  each  hanning,  energy  digital  which  this  Ar  respectiveIy  fluctuations  show  the  Rl,  Q5,  Iog j Q f  (Hz).  coordinates out  to  The  u  ( f ) ,  prime  either  adjust  anemometer  f 0  A  in  for  orientation  symbols  f 0  f0  M  ^22  used  ' ( f )  '  (f)  the  spectra  R2,  form  R3,  of  indicates  vertical the  spreads  estimate.  and  cospectra  SI,  RI4.,  S2,  or  that  for  the the  a  between  mean  wind  various  (cm  has  the  runs  F3, -2  sec  rotation  horizontal,  difference and  f0j.(f)  for  F2,  2 and  and  c i r c l e s ;  high  plotted  use  and  spectra.  Anomalously  c  were  variation  plotted  at  estimates  32  low-frequency  frequency  velocity  Figures  25  frequency  attributed  of  No  spectra  low  at  estimates,  lowest  very  Spectra  EI,E2,  in  agreement  estimates  plotted  five  observed  printer.  estimates  were  over  562A  respectively.  anemometer again  Model  spectral These  freedom  some  and  )  vs,  of been  carried  thrust  d i r e c t i o n .  spectral  functions  ares  88 f0  (f),  f0  3 5  '(f)  f0|z(f),  f0  |  '(f)  5 3  3  f0, *(f)  ;  5  f0  (f)  f0 j j ( f ) m e a s u r e d anemometer.  u  •FJZ5. I  (f)  Cospectrum downwind  U  of  using  thrust  velocity  hot  and  wire  hot  wire  fluctuation  measurements. f0.  » ( f )  Quadrature  spectrum  of  thrust  and  h o t w i r e .  For  runs  E l ,  rotations  through  R2  a  a n d R3  carried  involved, a  run.  shift of  A  to  make  aligned since  z  =  to  =  0.  make  9'  wind  For =  direction  mean  wind  direction  solid  of  triangle  frequency  to  caption the  run,  the  F o r runs an Ql  angle the  Some  9'  Q5,  was was  luck  shifted  because  would  Nl,  mast  good  often  rejected  vertical  was  during  excessive  make  interpretation  d i f f i c u l t .  inverted  the  run  0 ° .  the  results  made.  through  were  The  x^  rotation ^ *  SI,S2&Ar  were  runs  interpolated  of  9  0  mean  dimensionless  date  angle  Rl+,  data  relating or  FJ>,  Many in  the  an  F2,  horizontal  out  accurately  E2,  scale  frequency the  of  t h e mean  thrust  to  the  the  value  scale  of  k x , = 2Trfx,/U,  height  each  marks  of  of  the  wind  anemometer  speeds and  UV  < x  ^)=Q  normalized  where  thrust  the figures  \ og ^ ( {  U  is  anemometer..  lists  U at at  the a  the  time  and  height  height  of  5  m  T  89  above  the  rotation the is  water, of  coordinates  surface the  of  For  each  The also  shown.  are  in  shown  Run was so  that  and  9'  =  31)  9  show  anemometer Section of  d i r e c t i on .  u  ( f )  °t  of  a  vertical  coefficient  R^  from  of  of  the  runs  e q n . 2.10.  the symbols  used,  this  further  1  is  with  was  one  The  are  chapter.  and t a n "  with  12  32)  to a  made  be  this j ) u  28.  the  anemometer  wind  direction  to  study  be  the  (Figures.30  thrust  and  discussed  correct  the h o r i z o n t a l  of  described  horizontaI to  of  are  (jZSj  1  a n d Q3  between  again  was  fjZSj^Kf)  a .qua)i t a t i ve  Q2  fjZMf)  fluctuations.  Section  Figure  Runs  (Figure  the anemometer  in  estimates  comparisons  -11.1°)  velocity  f o r which  in  between  anemometer  the h o r i z o n t a l  used  spectra,  =  of  made  spectrum  7)  spectral  F o r r u n QS (9  (^  portion  aligned  the  downwind  discussed 1  is  U-wire  quadrature  d  be  29)  It  comparison  of  tan"  lower  of  n  will  angles  0°.  coordinates  alignment  !  downwind  12.  and  the  f o r some  number  a  spectra  (Figure  variation  Section  0  the  accurately  time in  Q l ,  listed  and hot  (  the f  28)  f0 |(f)  These  Phase  Also  (Figure  of  chapter.  and the drag  analysed,  anemometer  cospectrum  direction,  figur e.  run Kl  measurements  9,  Richardson  functions  I i s t ed on  wind  the s e a .  difference  spectral  thrust  t h e mean  hot-wire in  rotation the wind  90  For extent  r u n Rl  of  spectral  t h e Q0°/o estimates  averages. other  (Figure  appropriate  on  fjZf||(f)  Figure  spectral  since  the  were  confidence  intervals  as  same are  of  those  confidence  for  same  r u n Rl  at  \0%  Horizontal made  f o r runs  respectively. highest  mean  analysed. to  have  this in  this  ti Ited wind.  case,  calculated. effect For  was  runs  SI  and  and a  The  make  and  for  different  are  again  estimates These  from  are estimated  15*0°  and  3l+» 35  and  to  ')  9)  could  before and  during not of  17•5°  of  at the  runs  course  r e l i e d  coordinates  9 = 0,17°, rotation  the  morning  the  be  were  36)  was  the f o l l o w i n g  r u n Rl+ w a s  S 2 , (OI2I+-OI56  runs  the  frequencies.  rotation  C p L$> l o w e r  the  t o 1+1  26  spectral  cm s e c  (positive  vertical  of  minutes,  I3/5/1966)  1285  levelling  the  estimates.  observed  back  (Figures  which  downwind  frequencies.  these  Rl+ ( F i g u r e s  =  shown).for  32  0' = 2 0 , 1 ° ,  (  was  The a n g l e to  t h e same  spectral  speed  The mast  strong  for  RI4. (0014.-OOI4.6,  Run wind  been  the  R3  duration,  the  fractions  analysed  the  long-term  t h e same  errors,  rotations  R2,  at  are completely  be  of  t h e same  e  show  relating  (not  the appropriate  and a n a l y s i s  than  r  runs  experimental less  intervals a  bars  hypothetical  (not shown)  pf  intervals  vertical  interval  estimates  the  fractions  ' y ,  n  to  33  other  inclusive)  the  o  confidence  The c o n f i d e n c e  spectra  Further,  33)  and  than  of  on was its a f t e r .  0156-0228, I3/5/1966)  91  which  started  calculated values  of  minutes  38  angles CQ  of  19$  and  and  F3  after  t i l t  the  1.56°  were lower  27$  end  of  run  Rlj.,  1.58°,  and  respectively  the  making  before  the  rotation  t h a n a f t e r .  Runs low  wind  thrust  F2  speeds  anemometer  are  the  hot  X-wire  9  1.01°  =  be  only  Run  anemometer  as  at in  in  Figure vs.  of  log  the  been  (kx  1 0 3  ) »•»  thrust  plotted,  overlapping. composite  plot  a The  c  m  i+0) s e c  are  which  are '  respectively)  overlap  in  because time  VerticaI•  have  this  marginally  included  (1966).  made  -  at  been  for they  with  the  rotations  made.  These  will  chapter.  with  a  different site  and  thrust  will  be  velocity  fluctuation  to  2k  I4.I  composite mean  plot  of  speed  Only  A  few  points  had  At  the  higher  wave  this  spectra  are  plotted  .  wind  anemometer.  of  d  experimental  velocity  F i gures  is  n  I3«  downwind  L\2a  but  of  was  different  downwind  c i r c I es  12  J4.I )  Section  of  3'3  Weiler  Section  a  a  respectively  (Figure  Spectra  The  of  1.33° in  Ar  discussed  available  analyses and  and  320  =  39  recording,  ones  discussed  I4..  (U  (Figures  the to  I og U  £f 0 ^  was  eleven be  1966  omitted  numbers  dimensionless  at  (f)  the  height  runs  x  3  have  because  analysed  downwind  U"2J  of  the  spectral  -» T h e s p e c t r a may a l s o b e n o r m a l i z e d a g a i n s t u* as on p. 119, in a c c o r d a n c e with the Monin-Obukhov s i m i l a r i t y t h e o r y . They a l s o o r i g i n a t e d the use of the kx^ abscissa. 2  92  function plotted  kx, = 3  but  is as  closely in  Figure  At  lower  tend  to  fetch  or  wave  there  that  some  has  is  )  more  at  the  high  with  the  a  a  slope  broad  of  -2/3.  When  peak  near  are  more  scattered,  frequency.  parameter  enters against  at log  visibly  low  1  Q  k  less  frequencies,  appropriate  points  decreasing  other  stability)  l|.2b) s h o w s  (Figure  be  numbers  decrease  I o g j Q( f 0 j | ( f ) U  to  lj.2a  and  0.005.  indicates  but  grouped,  (such  as,  The  perhaps,  frequencies. instead  of  scatter  at  indicating  dimensionless  scatter  A  plot  of  logj^kx^) low  that  frequencies k x ^ may  frequency  at  the  cease lower  f r e q u e n c i e s . "*  5.  Spectra  The  33  observed  A  in  to  above  (Figure  or  is  plot  at  frequencies  high  low  plotted  At  as  frequencies f0  (f)  the  f) U  less  I966 r u n s  eleven  vertical  velocity  )  vs.  l o g ^ ^ x ^ )  of  the  points  than  that  for  The n o r m a l i z e d  at  of  is  in  is  shown  in  the  lower  frequencies  t h e downwind  vertical  the  spectra  spectra  302-317) .  spectra  are  A similar resultwas obtained over l a n d by Estimating the l o n g i t u d i n a l wind spectrum ground. Quart. J . R. M e t . S o c .  (I965,  upright  f0||(f).  for  The s c a t t e r  I|2a).  are  t o I4.I .  dimensionless  much  spectra  J J  I o g j Q( f 0 ^ (  I4.3.  analysed  26  while  composite  form  Figure  Figures  cross  velocity  velocity  f0..(f), 1 l  normalized the  vertical  vertical  triangles f0,,(f)  of  peaked  S. Berman near the  93  near  kx., = 3  2.  At  low  frequencies  spectra  are  approximated  on  the  log-log  plot  of  (kx^^O.l) 3 by  the  Figure  the  normalized  straight The  I4.3.  line  vertical  of  equation  slope of  +  this  I line  is  Iog, (f0 o  or,  since  f0 j(f)  Cospectra  6.  The  5  5  since  stress  the  measure. of  the  out  as  values  f0|z'  the  eight  9  0.0°  =  The It  is  have  runs and  no  |  and  )  =  ( k x  5  )  -  most  2.7  is  5  a  IV,  f 0 | 55(f)  is  required  very  to  function  the  set  wind  out  sensitive  out.  Section  R l ,  (5.1)  fluctuations  spectral  For  rotation  The  .  to  measurements  1966  carried  plotted.  is  velocity  originally  is  coordinate  Chapter been  we  -3  10  x  proportional  in, t h e  levelling  I .8  important  which  only  =  vertical  f0|^(f)  rotation  as  0  const  Kl,QJ, Q2, Q3, Q5,  function  negative,  l o g  and  surface  measurements in  2  integral  careful  outlined  U  5  the  Unfortunately,  s u f f i c i e n t l y 1965  is  its  anemometer  and  ) / ( k x  5  downwind  sea  =  kx^^Ckx^),  cospectrum  analysed, on  ( k x  of  5  =  3  k x ^  (f)U" ) 2  5  3h,  best R2  has a r  >d  and  196J4.  been  results  R3  t i l t  was  the  the  to  carried  rotated are  for  from  which  required.  seen for  to  be  positive  relatively wind  f l a t .  stress.  It  94  falls of  to  i| to  zero  high  just  Hz,  8  anemometer the  at  below  response.  high-frequency  again  l i t t l e  of  frequency  range  suitable data  value  runs  lower  speed  and  R| (f)  be  with  t i l t  ^  44  =  five  is  it  if  lies  we  wished  then  be  ^  very  the is  z  a  longer  analyse  more  sfationarity  that  since  to  a  analysed  below  .0039  that  is  Hz  8  indicating  fortunate,  would for  and  covers  at  d i f f i c u l t  (cons tant  to  wind  the  cospectral of  the  lowest  2  i  P  s  |  o  M  estimates  anemometer  (f)«f0  principal  average  correlation t  t  e  d  c o e f f i c i e n t against  l o g ^ f  for  eight  0.0°.  add f r a c t i o n s  The  This  and  thrust  adequately  cospectrum  analysis  and  of  v i c i n i t y  frequency  values,  required  3 ^ 1 |^33^"  f0  the  lowest  the  d i r e c t i o n ) .  $|  =  The  to  f|_.  the  requirements  Figure  5  and  for  would  our  In  to  our  limit  analysis  the  small  in  of  frequencies,  satisfy  runs  energy  in  the cospectrum  At  to  usually  upper  our  of  f|_|.  falls  the  the  Thus  end  s u i. t a b I e • v a I u e . f o r f0\j{f)  frequency,  value  3  5  at  of  f0  M  R|^  frequencies  low  particularly frequencies,  sensitive where  (f)  e f f e c t ' o f  of  are  t i l t  (f)  the anemometer  t o f0^{f)  for is  of  the  and to  eight  - 0 . 5 , and  best  for  the  f0  runs  )  is  5  (f).  at  other  thus  the runs,  95  where a  the  levelling  vertical  value  when  Section  3  n  the  rotation  was  averaged and  eqn.  Quadrature  7.  of  thrust  anemometer  applied  to  over  these  five  i+. IJ4.)  •  spectra  of  make  downwind  was  Rjz'  uncertain,  equal  frequencies  and  vertical  as  inverted  to  this  (Chapter  1+,  velocity  f I u c t u a t i ons  Quadrature in  Figures  spectra  to  26  The  38. for  triangles  In than  in  the  general  the  the  plotted  phase  runs  lower  cospectra  are  Kl  angle  and  portions  quadrature fJ0j^(f)  Rl+  of  tan is  and  do  ' (f  not  Ri+ I85  (Figure cm  trough  3^),  above  at  frequency  the  thrust  waves  f^j^*(f) make  A  is  and  peak  cm  above  spectrum also 38).  Relatively  •  an  to  large  run  a  in  was m  in  shallow The  runs  lesser  phase  I  Kl  in  the  at  are  less  peak  extent at  In  2  a  Run  height  of  peak-to-  quadrature  water  SI  ) «  typical  (Figure  R3,  angles  36.  important  f0\j*  approximately  absent.  present  and  is  For very  is  be  appears  This 7)  +  to  inverted  2 ~  anemometer  estimated  Hz,  0,25  lj.22  of  spectrum 37  coherence  (Appendix  quadrature  35»  the  amplitude,  spectrum  height  to  as  and  28  2 contribution  0\j*/f0\z.)  plotted  Figures  spectra  triangles  and  the  wave  28),  at  this in  in  the  run  peak  the S2 R2  higher  a in  the  quadrature (Figures (Figure  3k)  •  frequencies  96  analysed  are  vibration  possibly  of  the  Because shifter  of  used,  accurate  response  anemometer  the  the  than  in  and  of  certain  its  c h a r a c t e r i s t i c s  quadrature  that  to  for  the  other  of  supports.  of  analysis  modes  the was  analog  phase  slightly  spectral  less  functions.  The  o high  gain  of  the  (Appendix  1+)  greatly  discontinuity  90  in  The was  computed  by  of  8 u.u* 1  Except  for  values  fiZi  =  0.346  the  eight  '(f)  of  runs  the  of  any  step  or  c o e f f i c i e n t s  and  the  vertical  cospectral  v e l o c i t i e s estimates,  Hz  (1+.2I )  f0.(f).  £ .0039  0  frequency  effect  drag  downwind of  low  signal.  and  summation  at  the  recorded  stresses  covariance  s h i f t e r  amplified  the  Covariances,  8.  phase  5  with  9  cospectrum  =  0.0  have  o' ,  the  been  rotated  used  for  the  13 covariance, In  stress  and  all  these  cases  larger  after  r o t a t i o n .  anemometer relative of  to  accurate The  mean  wind  9  drag  was  positive This  must  have  been  the  mast  in  levelling  drag  had  at  a  and  mounted  not of  at  the  height  of  a  I965,  been  c a l c u l a t i o n s .  the  indicates  1964 a n d  c o e f f i c i e n t  speed  c o e f f i c i e n t  covariance  that  the  positive when  the  was  thrust angle  9  importance  r e a l i z e d .  surface 5  m  was  above  based the  on  water,  the  97  Cn  A  mean  wind  would by the  only  a  few  eight  points)  a  m height  reduction  of  cent.  was  It  coefficients and  plotted  which  wind  value  reported  10  OV  speed  The  scatter  is  greater  9»  variation  and at  squared  frequencies  1902, 9 = l,  signals  analog  This  which  figure  computer  signals  minute  yield  averaged  by  a  approximately an  exponential  was  which,  f0  low-pass I minute, drop  at  0.5  Hz.  shown  when  (f).  the the  end  the  (Iarge for  all  deviation wind  speeds.  having  of  run  of the  the over  from  which  the  and  and  be  also  J2  been  constant may  run  whole  has>  time  run  this  the  t  (I85O-  f i l t e r e d  signal a  f0^{t)  Ql  for  directly are  f i l t e r e d  obtain  because  each  effect  to For  averaged  Here  f i l t e r  and  lower  averaged  selected  Also  ,  half-octave  constructed  output.  multiplied run  was  No  observed.For  standard  the  the  were to  at  listed  estimates  shows  O.OO39  from  12/5/1966),  0°.  spectral  which  II, .  I  .00027.  (I4. p a g e s )  is  0.001  0.0010,,with  I4.6  Figure  are  C  is  and  coefficients  runs  of  is  used,  height.  rotation  n  li+)  extrapolate  coordinate  it  Figure  to  no  runs  of  drag  not  m  in  thirty-three  Time  commonly  thirty-three  against  with  more  decided to  for  required  average  is  the  profiles  variation  the  (2.  .  10  velocity  5»l  runs  at  per  drag  significant  and  in  measured  Table  -u juzU^  speed  result  The in  =  of  seen in  an  in  9=0.  98  exponential  rise  lines  the  30  on  arbitrary  and  The  the  start.  graph.  d i f f e r  time  frequencies,  et  The  from  as  may  be  is  greatest  expected  of  freedom.  Both  history  at  any  frequency,  peaks  to  troughs  v a r i a b i l i t y . time  those  frequency  10.  At  variations  while  at  to  the  the  to  energy  the  lower a  number  very  higher  Hz  0.125  next.  lowest  indicates  recognizably  for  greater  and  of  similar ratio  higher  similar  d i f f e r  uj  mean  spectral  of time the  features,  greatly  in  the  than  and  velocity  analysis  was  carried  velocity  Ix. H z .  u u^ (  is  of  (0.0039  analysis  products  greater in  of  frequencies  wide-band  contained  frequencies  show  analysis  velocity  is  cospectrum  the  occupies  entirely  the  the  have  but  are  to  at  run  from  one  next.  addition  mean  energy  a l l  from  functions  frequencies  the  fluctuations,  the  lower  Wide-band  In  in  scales  frequency  degrees  given  minute  32  vertical  one  v a r i a b i l i t y  The  A at  products  velocity to  l+.O. H z )  out.  Negligible  fluctuations  negligible  frequencies  for  at  portion below  of  O.OO39  Hz.  A in  majority  f0||(f)  frequencies  with  of  the  spectra  decreasing  analysed,  analysed  frequency  indicating  that  at  showed the  there  a  reduction  lowest is  often  a  gap  99 in  the wind  velocity  at  the Spanish  fluctuation  Banks  site  spectrum  and making  for  fj_ i n t h e c a l c u l a t i o n  of  for  analysis  relatively  speed  and d i r e c t i o n  occurrence and  (uju^)  The spectra check of  of  this  velocity  the entire  with  much  spectral  spectral  less  with  (u| ) , 2  2  If  wind  ( u / )  against  be c a l c u l a t e d affords  effort  selection  mean  plotted  and this  analysis.  estimates  plot,  runs,  Ie'choice  to the frequent  shows  may a l s o  computed,  on a n a l y s i s  47  best  a suitab  constant  contributed  Figure  products  this  O.OOJj. H z  The d e l i b e r a t e  Uj .  may h a v e  for the eight  2  Iog jgf  with  gap.  previously  between vs.  of runs  around  than  a a  2  U^.  from the  useful repetition  we i n t e r p o l a t e  straight  lines  o n a n f0. . ( f )  then , 00  J^,j(f)d(ln f)  V7T=  e  4  Hz  - Z f0, ,(f)6(ln f)  (4.21)  e  .0039  where  6( I n  in our analysis  n J_ r o o t s (u  f)  2  ) , 2  I  J  (u_ ) ?  -k  a n d (u u _ )  '5  calculated  by s u m m a t i o n  Figure  and the d i f f e r e n c e s  47»  wide-band The be  values wind  calculated  u ju ^ u s i n g  of  t h e mean  between  2.12  from  are also  square products  shown  the summation  in and  negligible.  t h e mean  a n d 2.l4.  The  velocity  !  the spectra  t o be  0.346.  =  g  T| ^ a n d t h e d r a g  directly  eqns.  of  are seen  stress  = iln 2  c o e f f i c i e n t CQ velocity  However,  can  product  experience  shows  100  that  for  used, the  measurement  it  is  important  spectrum  spectral  for  the  analysis of  stress  I I.  variation  Figures cup  for  runs  Kl,  El,  and  S2.  For  runs  been  plotted  (The  height,  158  and  runs  SI  and  S2  were  sampled  at  Figures  5'  ~~2  2  c  U|  <  ,  Q5, of  I  u  c —  2  or  Rl,  R2,  minute  frequency  u  S2  2  ,  u^  and  to  measured  R2,  at  I minute  Ri|,  R3,  two  by  intervals, SI  heights  similar  are  have  time  thrust  wind  anemometer a t J4.78  directions  c  for  m  shown  intervals.  square  is  runs  averaged as  fluctuations  by  a  from O.OO39  denote  quantities  vertical from  Kl,  one  to  of  the  Q2,  a  Q3, filter  time.  t o 1+ H z .  while  scales  Ql,  low-pass  a function  average,  differ  Rl,  lines  I minute  The  reliable  I minute  the  t h e mean  and  turbulence  very  The  U | U ^for  and S 2 ,  covered  Q5,  dotted  of  data.  over  at  end  anemometer,  velocities,  are  method  3  constant,  is  and  ,  the  obtain  and  have  The  t ° 6 l show c  overbar  arbitrary,  to  lines  «  of  velocities  approximately  a  runs.  seen  experimental  low-frequency  our  Q3,  respectively.)  denotes  minute  of  averaged  and  c m  to  wind  SI  solid  the  speed  02,  overbar  32  show  and  are  time  used  wind  Ql,  Rlj., SI  range  most  the  tilt  necessary  50  155  2  u  of  E2,  and  variation.  effect  of  anemometers  with  examine  from  J4.8 t o  the  stress  to  wea  estimates  Time  of  The  The  curly  straight  averaged  over  in  figures  these  next.  In  entire  fact,  are  101  the  thrust  anemometer  response  sensitivity  is  proportional  sensitivity  of  the  fluctuation  products  thrust is  is  to  non-linear  the  wind  and  its  speed.  Thus  anemometer  to  the  velocity  proportional  to  the  square  the  of  the  2 mean  wind  velocity,  s e n s i t i v i t y JL  U  and  2  to  that  U  ,  Conversely,  velocity  for  the  fluctuations  velocity  products  hot-wire  is  is  proportional  proportional  -1 U u  ,  Thus are  y  some  apparent  attributed  opposite  to  discrepancies  changes  non-linearities  anemometer  responses  to  of  in  mean  the  between wind  thrust  and  Uj  speed  and  to  2  <  hot  to  §nd  wire  v e l o c i t y .  2 The a  section  The  where  spectrum  high of  hot-wire  and  the  was  0  u  signal  noise ( f )  not  Q2isclearly  The  section  spectral  for  u  appears  computed shown  re-recording  run  u  in  of  the  this  affected  by  this  two  this  minute the runs  variations  averaging  surface much  affected  of  time the  shorter by  in  time  sea than  was  pulse  was  graphs not  shows  recording. anomalously  anemometer  pulse  of in  —  near  the  end  u^  signal  for  of  Figure  53«  counted  in  the  3  indicate  U|U*.  calculating  barely  those  variations  A  5&)  run*  time used  the was  lower  t The  (Figure  run  33«  thrust  the  Rl  dominate  Figure  in  for  to  for  seen  analysis  run  long  analysed of  e  .  ,•>  ti|Uz,  that  the  enough would  be  the  stress and  32 on  that  seriously  102  Comparisons  12.  wire  run  anemometer  fj#  cospectrum  the  f0,  (f)  between  I u  indicates  low  would speed  Hz,  at  this  vanish.  The  the  and  Figure  two  If  the  smaller 7  in  sec"',  m  is  phase  than  expected phase  to  50  28)  increases  phase  quadrature  analysis  55,  u  positive  For there The  is  hot  runs again U-wire  angle)  where  02  and  close  as  extended  Q3  a  only  agreement  2  signal  and  between 50  cm  spectral of  the  the  in  the  of  f0 ^ ^(f) )  3«5  is  seen  (lower  portion  u line  shows  frequency, Hz.  We  leads  in  f0||(f) of  but  the  take phase.  193J4.-2OO6,  ahead  of  hot-wire  frequency  l  two  spectra.  separation  (solid  to  (I902-I93I4.  was  u  increasing  U-wire  anemometer  cm  cospectrum  expected  with  the  of  t a n ~ ' ( f 0 , -"-/ f 0,  shift  instruments  same  result  by T T / 2 a t  the  were  two  either  the  anemometer  cospectrum  the  f0^{f)  Further,  the  thrust  agreement  spectra,  the  correlation, be  the  instruments  having  frequency  calculated  f0| "  hot-  U-wire of  thrust  l of  and  hot  upwind  analysed.  U-wire  that  a  downwind  fluctuations  instruments leading  to  thrust  satisfactory  fluctuations.  of  anemometer and  of  frequencies  but  wind  very  measurements  different  two  the  directly  all  measurements the  from  8/5/1966)  cm  shows  28  identical  properties  50  at  measurements  At  operated  two  (f),  reported  (1528-1600,  Figure  the  recording  Kl  was  anemometer.  and  spectra  anemometers  During  between  between  12/5/66)  and  and  50  fj# c  (f). m  103  above f^I  the  (f)  thrust  falls  indicating velocity  a  runs  limit,  cm a b o v e  lie  about  not  much  SI  the  two  signals  above  were  cm s e c  '  X-wire  thrust  anemometer.  for  lower  a  the wind  Computations  the  and  fjZf (f) u  discrepancy hot-wire  and  and 2122-2206)  and  29/6/1965)  (Figures for  speeds,  vertical  and  39  comparison 320 a n d  for operation of  in  of  of  their  1966).  F2 a n d F 3  limit  beyond  cm a h e a d  between  suited  Hz.  confidence  and 2121-2153,  ideally  I  OI56-O228,  fj#||(f),  (2039-2122  run K l ,  above  The v a l u e s  Weiler,  runs  not  jO  cospectrum  the two  depleted less  found  19^51  because  the  of  been  (201+9-2121  instruments  0  were  the for  between  anemometer.  analysed  at  was  (Pond,  hot  than  frequencies  batteries  has  runs  (012X4.-0156 a n d  the values  than  runs  were  at  a n d S2  thrust  anemometer  These  I|_0).  coherence  again  larger  were  frequencies  The h o t - w i r e  Simultaneous  readings  these  have  the  3°$  in  For  a n d we t h e r e f o r e  measurements  thrust  lower  reduction  calibration.  other  at  the h o t - w i r e  13/5/66)  50  off  fluctuation  During  normal  anemometer.  of  of  313  the  r o t a t i o n s (of  Oi  1.01  a n d 1.33  in  the accurate  step noise  in  ) were  the  which  in  rotation.  calculations  since  levelling  re-recording  energy  coordinate  required  were  of of  turn  on  the  thrust  have  introduced  may h a v e  affected  and  the  confidence  anemometer.  r u n F3  Stress  based  we d i d n o t  A  low-frequency the  drag .c o e f f i c i e n t  frequency  range  .0109  to  8  Hz  for.run  F3.  Despite discrepancy cospecfrum above  0.5  these in  d i f f i c u l t i e s ,  run  has  F2  is  that  values  This  probably  is  anemometer  response  f a l l i n g  c o r r e l a ted  noise  low  The  13.  downwind  Data  The site  is  from  analog  readily  experimentaI  but  it  one  thrust  was  made  not  for  typical  lable  of  and  experiment  the  lee  of ' A r u b a  a  in  this  s i t e  Only  28  was  the  may  be  minutes  data Dr.  or  of  and  a  sand  A.  equivalent were  frequencies.  well.  si te  and  comparison  at  Banks  experimental our  conditions.  Fortunately  IO35-IIO3, Doe  of  comm.).... a  a at  With  instruments development,  of  The  the  of  tip  limited  ours  in  available,  Mk.  anchor about  of  the  wave  surface but  IV  platform  taut  fetch  15/2/196J4.)  Bedford  floating  number  to  of  undergoing  E.  on  spit  high  since  (Ar,  (pers.  by  presence  analyses  run L.  the  agree  sea  mounted  data  thrust  s t i l l  deep  Carribbean.  of  of  Spanish  conducted  shallow  indication  speeds  are  of  s t a b i l i z e d  The  of  was  an  purposes  Oceanography  anemometer  anchored  by  frequencies  digital  our  anemometer at  experimental  methods  anemometer  avai  Institute  and  the  serious  X-wire  spectra  accessible  excellent  is  Aruba  only  thrust  than  off  wind  vertical  the  and  thrust  at  and  between  the  smaller  Hz.  the  this  lines.  3  km  in  island heights, roughness. is  not  105  s i g n i f i c a n t l y density but  no  gradient  Dr.  Doe  adjustments.  i.e.  velocity  components  3«5°  v e I o c i ty  zero .  have  our  speed  The  w  a  s  in  3*56°  was  The  analog  and  the  and  close  techniques.  were eqn.  by  is  points  A  was  original  a  are  to  to  compared  be  v e r t i c a l  at  omitted  noise  A  may tape  vertical  our in  of  the  possible  recording.  v e r i f i c a t i o n  had  coordinate  Some  according  for  force  re-recorded  for  force  linearized,  average  B.C.  BIO  covered  was  v e r t i c a l  the  at  Total  from  compensating  spectra  stable,  being  response  make  indicated  atmospheric  performed  comm.).  Esquimalt,  not  the  was  3.2,  data  The  available.  calculated  the  digital  few  is  anemometer  to  agreement A  marginally  be  (pers.  found  introduced  of  to  data  the  Laboratory,  fluctuations  rotation  runs.  anemometer  to  analysis  Naval  been  Loucks  according  of  Pacific  R.  this  components  rotation  For  of  recorded,  zero  other  measurement  Mr.  were  the  estimated  analysis and  components  than  was  quantitative  Digital by  shorter  method.  Figure  both  J+l,  analysis  because  of  overlapping.  The  most  prominent  spectra  from  f$l|(f)  at  low  frequencies  found  data  was  absent  the  Banks  the  two  difference  si t e s  from  was  between  that in  Aruba  the most  wind  decrease of  data.  the  velocity in Spanish  106  Spectral the  downwind  well  with  wind  speeds.  .0109  to  runs  ana  for  component  those  8  at  The  Hz)  the  largest spectra  frequencies. frequencies  59$  The are  minutes be  of  Aruba  data  than  the  C  component  and  above  Hz  si te  the  0.1  for  for agree  comparable  «0016J4.  =  n  average  recording  analysis  and  did  not  computer  calibration  between  to  was  or  (analog,  for  all  ahead which  not  the  error  are  the  the  the  there  of  the  time  a  out  of,the  level  was  at  start  of  dc  f0^{f)  a  data band-pass  level,  intended  but  for  and  analog analog  account  spectra  not  least  wide-band  to  low  start  Re-recording  two  at  lowest  were  the  believed  and  component  signal  originally  this.  analog  at  at  dc  balance  have  between  step  Usually  during could  values  a  average out.  the  downstream  analog  recorded  f i l t e r  differences  in  the  analysed,  re-recording  the  higher  attributed  balanced  the  Banks  c o e f f i c i e n t  higher  successfully  to  frequencies  Spanish  ;  appear  where  run  v e r t i c a l  discrepancies  re-recording  10  at  drag  is  the  Iysed.  The digitaI  levels  for  at  higher  frequencies.  In was  the  already  recording  v e r t i c a l  component  approximately  did  not  low  frequencies  the  latter  may  occur.  r e f l e c t also  have  zero  sjgnal and  Large the  high  the  this  average  problem  cospectral values  adversely  of  affected  level  in  values  r e at  f$||(f), the  these and  accuracy  107  of  our  calculation  of  the  t i l t  angle  The  0.  close  agreement  ,o between 3 . 5 °  our  to  vertical  make  u^  =  fortuitous  in  end  analog  of  that  the  our  summed  only  •at  lower  '4«  view  to  level  using  Figures At are  for to  less  than  by  for  the  the  lowest  the  Hz  the  must  we  technique  8  8  the  the  at  at  be  is  low  of  of  yet  frequency be  applicable The  because  rotation partly  the  cannot  s i t e s .  were  sure without  cospectrum  our  was  d i f f i c u l t i e s  and  and  component speed, higher  the  cable,  the  the  1966 the  same  results  are  shown  the  spectral  the  f i e l d  at  wind  noise at  2000.  higher  latter  for  equal  been  comparable (The  former  frequencies  speeds.)  approximately  data.  by  less,  and  wind  f i e l d  have  10  the  electronics,  rotations  in  between  for  with  Engineering  computed  coordinate  Hz  speeds  method,  used  were  data,  wind  MechanicaI  levelling  levels  were  four  UBC  spectra  No  of  wind  sphere  the  which  factors  at  made  f i e l d  vertical  component  Also,  other  to  same  65.  frequencies  speeds  on  the  component  62  from  in  recorder  used  but  d i f f i c u l t i e s  rotation  were  tunnel  method  our  and  determination  anemometer  Velocity  3.So  frequencies.  thrust  tape  of  gratifying  .0109  Recordings  and  of  data  from  Noise  is  spectrum*  v e r t i c a l  modification  the  0  rotation  the  in made. levels  wind is at  downwind  Force in  and  analog  all  fluctuations three  108  directions, therefore noise  and  smaller  velocity  The  the  than  by  noise  a  at  that  anemometer  of  the  about  32  in  the  noise Hz  which  may  been  of  the  wind  subject wind  to  a  some  tunnel.  observed major  A that  in  e l e c t r i c a l  the  sphere,  noise  of  no  spectra .  and  Hz- a n d  sideways  four.  the  accuracy  less.  aligned  were  Th i s  in  the  of  shows  d i r e c t i o n  cospectra  the  show  mechanical sphere  p a r t i a l l y would  other  on by  its  was  not  sharp  peaks  spectra,  at  springs.  occur the  which  peaks  vibration  vibrations  not  hand,  large  in  mast  of  the may  this  Hz  |6  was  the These  the  floor  f i e l d have  duplicated  below  at  in  been the  were  probably  not  shut  showed  noise.  with  the  wind  noise  from  the  anemometer, cab I e,  was  mechancial in  within,  spectra  made  recorder  fluctuations  I 1.3  and  measured  recording  tape  the  motion  the  v e r t i c a l  approximately  correctly  which  Since  source  and  of  tunnel On  velocity  tunnel.  excited  i n s t a l l a t i o n .  the  vanished  indicate  frequency  noise  of  of  of  was  spectra  resonant have  factor  frequencies  wind  .The  those  cospectra  analysis the  downstream  the  negligible. vibration,  wind  tunnel  tunnel  Aerodynamic and  actual  account  for  off  electronics,  noise  of  velocity the  measured  109  CHAPTER I .  SUMMARY OF RESULTS AND CONCLUSIONS  6;  The d e s i g n  of  Two t h r u s t  for  this  Reynolds the  of  of  were d e s i g n e d  over  to p e r m i t  the wind  to measure  flucutations  the s e a . direct  which a c t s  in  The  the  motivation  measurement on  the  of  the s u r f a c e  of  sea. The Mk.  the Mk.  I  II  anemometer  thrust sphere  components  of  (Doe,  containing  force  IV anemometer, the  closely  anemometer  perforated  Mk.  layer  chiefly  stress  anemometer  wind v e l o c i t y  boundary  was  thrust  anemometers  t h r e e components atmospheric  the  into of  I9&3),  a mechanism  three e l e c t r i c a l  which  linkage  but  outside  the s p h e r e .  Accessibility  repairs  is  the expense  The Mk.  II  at  and e l e c t r i c a l  anemometer was  demonstrated  to be s u i t a b l e  Measurements  using  performance  is  the Mk.  equally  the  for  for  of  to  hollow  resolve  signals. has  a  three The  similar  transducers are adjustment  I0UBC and  intended  IV anemometer  satisfactory.  a  of  or  compactness..;  used at its  design  having  two were b u i l t ,  sphere,  gained  follows  was  purpose.  indicate  that  its  I 10  2.  The  performance  a.  Calibration  The  Mk«  s u i t a b Ie the  sea  and  and  thrust  anemometer  anemometer  for  has  been  shown  measurement  of  wind  anemometer  to  forces  to  be  stress  a  over  surface,  response  weights.  of  the  was  the  response tested  anemometer  analysed,  turbulence  of  The  directions  level  the  thrust  II  Instrument  The using  of  and  was  levels  in  to  in  in  of  various  a  wind  tunnel.  the  wind  tunnel  found the  winds  was  speeds  The was  below  tested  noise  recorded  to  be  well  the  field  at  corresponding  observed wind  speeds,  b.  Calculated  The  frequency  response  fluctuations  was  of  a  50  Hz  for  calculation the 32  sphere. Hz  which  c.  was  The  A  also  proved  Range  of  of  to  of  the  response  thrust  expected  wind  speed  the  average  anemometer  to  fall  of  5  m  to s e  c  velocity  mechanical  resonance  well  the  be  wind  above 8  zero  to at  velocity a  based  ',  frequency on  over  the  at  frequency  required  a  surface  upper  of  of  frequency  Hz,  speeds  calibration  coefficient  of  the  sphere  used  was  111  found  by c a l i b r a t i o n  a range  of  wind  highest  wind  speeds  speed  13 m s e c " ' ,  this  measurements  at  anemometer The by  the  noise  with  Three analysed. very  three  normal  have  d.  times  apparently been  as  being that  results  more s t r o n g l y measured  high  by a  in  the  as  by  a f f e c t e d by  an  from  m  recordings  below  s  e  c  '  of  the  were  coefficient  spectral  its  at  third  levels had a  vertical these  spectrum  spectra  results.  the  orientation  thrust  anemometer  cospectrum  tilt  response  3  The  None  in a n g u l a r  the measured  linear  had  expected.  of  recording  and a drag  but  If  determined  were w e l l  below  reported  response  is  the  just  noise.  was  built.  field.  spectrum  to e r r o r s  in  be  spectra  another  the  were d e s i r e d ,  the  in s p e c t r a  dominated  The s q u a r e - l a w speed  speeds  downwind  included  in  Since  Banks  low speed  tunnel  wind  Susceptibility  wind  could  a wind  in  over  than a d e q u a t e .  wind s p e e d s  Noise  expected, while  appearing  more  speeds.  One r e s u l t e d  much as  about  at  m sec"'.  |8  must d o m i n a t e  encountered  runs  is  springs  which  to be c o n s t a n t  the S p a n i s h  performance at  low wind  levels  at  limit  stiffer  the anemometer  spectral  was  upper  of  tunnel  from 3 to  measured  level  sufficiently  a wind  much h i g h e r  with  limit  in  of  f0^{f)  the anemometer  (sonic)  or  to  than  square-root  I  response should  (X-wire)  be  levelled  required affect of +  for  the by  1.5°  present  an  measured  thus  seen  f$22^)  vertical a  r  least  vertical  alignment  some  the  were  vertical  analysed  orientation. R, (f) 3  the  =  -.5  vertical  rotation,  into the  be  SI  t i l t by  and  anemometer  l\. t i m e s  the  of  was  0,2°  (Run  L $ S2).  accuracy seen  RL\) a n d  accurate  to  a  L e v e I I i ng  s u f f i c i e n t l y  as  less  a l l  an  at  t i l t  to  for  our  the  sand,  to  spectra  to  were  the  Chapter  I4., S e c t i o n s  only  but  such  permit  also  would  coordinates  for  as  ,0156  to  Hz  in  mast,  out  angular  =  0  the  criteria  .OO39  from  of  fjZi^tf)  not  anemometer,  carry  and  sturdier  would  and  the  gives  instruments.  rotations  on  levelling,  horizontal run  other  for  The  suitable  data  calculate  based  downwind  mean  a  over  correct  frequencies  a  the  of  horizontal  discussed  of  in  course  devised  the  by  and  fftj^if)  misalignment.  changes  advantage  and  and  controlled  the  rotation  use  angular  be  to  spectra  strongly,  by  can  These  The  thrust  transverse  during  anemometer  suitable  and  tolerance  Methods  on  of  direction  thrust  A  stress  (Runs  affected  e  spectrum  wind  probe,  to  thrust  approximately  wind  23$  The  purposes.  The  while  with  X-wire  about  is  0,1°  anemometer.  12  the  a  reduce  for  horizontal 3  N  piling  better  Hz  and  driven  levelling the  3' •  of  hazard  of  loss  the  of  mast  by  because to  equipment  it  tidal was  the wind  that  being  importance  if  the  thrust  anemometer  3.  The  a.  Comparison Close  from  C,  calibration,  to  to  check  b.  a  frequency  falling of  8 Hz.  cup  anemometer  with  spectra response  f r o m cup  technique  in  The  0.1  Hz,  at  which  of with  thrust Figure  thrust  was  velocity  records  the  linearizing  spectra was  anemometer  and 28)  not  extended sufficient  detected  between  spectra  hot  U-wire  tested  anemometer  a wind speed  shift  be  performance.  U-wire  Kl,  of  and  only  the  will  downwind  validity  anemometer  response phase  of  cup  between  of  disturbance  measurements  The  (run  undue  anemometer  analysis  fluctuations off  and  hot  been r e j e c t e d  design  between s p e c t r a  the  of  against  spectra  verified  agreement  anemometer  velocity  with  used.  has  cause  stress  turbulence  has  carried  desired.  high-frequency  Comparison  Close  wind  are  it  Mast  wind  frequency the  might  of  analog  approximations up  accurate  anemometer  El, E2)  this  are  logs  However,  measured.  comparisons  thrust  (runs  more  spectra  floating  currents.  felt  flow  when  the  of up  7  the  to m  to a  signals  downwind  sec"',  No  frequency from  the  wk  two  anemometers,  was  consistent  in  space  of  calculated  with  the  two  signals  from  measure  identical  c.  the  Comparison  The  unfortunately is  thrust  the  the  the  cospectra  rotation loss  noise 2.1$  of  of at  and  (.OOllli. run  hot  at  very  few  loss  of  F2  wind  limit The  2  and  speeds  for  from  above  X-wire  0.5  Hz.  vs.  .00092  for  run  However,  the  thrust  thrust  of  drag F2  higher  the  anemometer  .001 |8  anemometer wind  momentum response  with  the  runs  f a l l s  '  of  n  by  (after either  correlated  accounts  c o e f f i c i e n t s and  '»  c  signals  of  This  e  measurements,  affected  presence  X-wire  cent  be  the  higher  s  30$»  as  to  else  m  were  1+0)  these  much  appear  at  3  8  as  both  and  measurements  coordinates)  better  39  above  spectra  by  the  X-wire  Figures  anemometer  be  that  s e n s i t i v i t y  Hz  separation  between  anemometer  L\6%  per  hot  thrust  or  the  Hz,  spectra  of  frequencies  to  and  just  useful  cospectra  f0|^(f)  FJ,  2  fluctuations.  anemometer  downwind  to  of  to  demonstrated  thrust  for  thrust  the  response  F3)•  thought  X-wire  up  cospectrum  velocity  between  from  with  because A  instruments  (runs  lower  frequencies  comparison  a  with  made  that  expected  downwind  anemometer.  indicate at  two  spectra  frequencies  instruments.  comparisons  anemometer  which  that  at  for  vs.  for  these  .00081  runs  for  performance  speeds  flux  is  at  high  and  only  missed  by  the  is a the  frequency.  115  d.  Comparison  The  analog  f0^(f)  spectra  comparison data  for  Chapter  e ,  run 5,  The  closely  the  an  range  the  where  Time  for  mean  .0039  to  with  (Figure  spectral of  of  the  f i l t e r e d  was  f0|j(f)  to  1+6).  expected  the  cycles  data  f0\^(f)  on  of  the  discussed  This  of  in  was  of  less  results  a  over  further  used,  not  the  and  offers  quantities  of  desired.  of  variation  products  f0^(f)  variation  even  was  a  estimates  velocity  (degrees  over  summation  large  is  low-frequency  greater  by  technique  made  and  products,  produced  spectral  half-octave  cospectrum  1+7).  interpretation  the  run,showed  velocity  analysis  study  the  v e r t i c a l  v e r i f i e d  been  obtained  analysis  rapid  spectral  of  the  analysis  has  1+ H z ,  those  qualitative  complete  was  digital This  the  averaged  of  1+1),  A  As  f0^{f)  for  lysis  spectra  obtain  used  analyses  I3«  from  variation  digital  technique  independent  comparable  on  and  cospectra  (Figure  ana  p o s s i b i l i t y  data  and  Section  analysed  check  of  Ar  analog  analysis  analysis  frequency  f.  with  Wi d e - b a n d  the  between  for  which  run  Ql  components, freedom) with  steady  in  time. than  in  was  time  were (Figure  with the The the  fewer  duration  116  downwind the  spectrum  history  similar.  of  the  next  at  the  lower  g.  Time  of  time  at  the  higher  variation  of  study  during  the  runs  showed  relatively  during  h.  1966  was a  the  62  the  signal  i,  Norma I i z e d  runs  analysed 0,05  was Uj  made  2  ,  one  analysed,  was  frequency  but  not  products  of  " o  the  2  u^ror  u  51  6l)«  to  u  for  the  variation  ,  u^  2  and  The  unsteadiness,  similar  If0  1u  and  show  65  anemometer of  but  time  u|u^  cross-product  the  various  f c  in  variation components  that  in  a  field  the  wind  measured  tunnel  are  noise  levels  well  below  measurements.  spectra  normalized  Iog  -  from  frequency  run.  and  levels  form  kx  similar  but  spectra  thrust  The  frequency,  particular  velocity  greater  otherwise  Figures of  was  (Figures  particular  Noise  any  frequencies  the  products  time  at  particular  frequencies.  velocity  in  the  any  variation  qualitative  A  at  fluctuations  The  to  f0j|(f)  downwind  (f)U~  1 1  (Figure had  a  I  vs. l\2a)  slope  spectra  log. (kx_) 1u n  These  , of  -2/3  were j  had at  examined  in  for  the  eleven  a  broad  peak  the  higher  the 1966  near  frequencies  117  analysed.  This  Kolmogoroff below  that  more  theory  for  the  Inertial  peak  the  points  the  that  showed than  indicating for  same  the  parameters  spectra logj^k  the  of  indicating on  Is  the  a  that  than  The  U,  kx^  vertical  is  k  (or  were  the  spectrum and  by  the  At  frequencies  scattered, must  x^.  depend  The  plotted  normalized  against  l o g ^ k x ^ ) ,  (Figure  i|2b)  a p p r o p r i ate f r e q u e n c y  low-frequency  spectra  more  when  against  not  predicted subrange.  f)  grouping  plotted  normalized  as  low-frequency  closer  when  slope  were  downwind  normalized  parameter  spectrum.  in  a  similar  —2 way log  and  were  .(kx_) IU 3  we  (Figure  j r  plotted see  near the  kx  by  not  the  law  because to  of  remain has  the  do the  to  33.  this  (1964.,  with  168,  p.  which  vs.  spectra Figure  v e r t i c a l  0.3,  3  5»3)  spectrum  falls  among  shown.  at  spectra the  not  unlike grouped  a  of- +  t.  do  not  show  high-frequency  extend  inertial  closely slope  )  n  x_/X=  normalized  that,  I o g , ( f J2L-, ( f ) U "  normalized  vertical  reach  is  form  Comparing  peaks  they  of  the  Panofsky  behaviour  fea't/ure  graph  peak  normalized  expected  points  and  •  corresponds  frequencies  A  in  ij-3)  frequency  power  probably  the  =2  higher  The line  Lumley  that  3  examined  to  at At  end,  enough  subrange.  vertical t.he  high  straight-  spectra  downwind the  which  was  spectra,  the  tow-frequency  end  k x ^ ^ O . l  the  and  normalized  118  vertical  spectra  kx 0 3  It of  (kx  3 5  (Those  extend  to  as  universal  This of  small  wind  result  tunnel  may  for  velocity  own side  corresponds  dimension our  (2D =  x «  In number  of  120,000  our  x,,  while  of  the  the  velocity  t  h  for  lie  (5.1)  may  above  e  x /D 3  =  nor may  of  end be  are  the  is  of  not  are  they  prove  to  the  (I965)  be  spectrum with  is  for  the  using  translated  tunnel  paper  same do  compared  vertical  our  the  atmospheric s t a b i l i t y .  rectangular  wind u^  on  spectra  ( I 96I4-)  ours,  dimension  of  and  as  results  cm)  I V-I4.3 o f  vertical  Comte-Bellot  x.^  (3-D  the  function  |8  f r i c t i o n  Figure  of  Her  ( 2 H = 21+0 c m ) The  2  to  a  These  notation.  10 -3  x  Panofsky  eqn.  by  1.8  low-frequency  measurements  into  and  kxj  fluctuations  anemometers.  narrower  be  the  hot-wire our  of  and  l"he"constanf" i n or  =  normalized,  Lumley  values  approximated  whether  when  in  be  const  seen  will,  one,  vertical  be  shown  normalized.) a  to  to  ) =  3  workers  line.  seen  )/(kx U  5  remains  other  were  here  the  test  section  (her  x,)  corresponds  to  U-*.  at  a  O.OI4.O t h e  Reynolds  curve  _2  M  3 3  (k)u-"-  appears  at  kJZf (k)/(<x u-::33  To  relate  3  the  low )  thrust  frequency =  to  approach  the  (6.1)  I .0  anemometer  line  results  (Figure  )  H9  to  this,  we  note  that  U  u-»  1 average, of  our  at  I4.3  IV-I4.3.  the  level  that  Figure  Figure but  so  wind  at  high  by  simply  adding  we  obtain  the  ^he tunnel  the  peak  in  from  thrust  the  alarmingly  the  4..  The  a.  Thrust  wind  very  Figure  No with 13  of  of  the  lie  drops  the  absence  Our  constant 1.8,  is  value  the  near  off  kxz.  surface  much  for  in  faster  inertial eqn.  is  6;T  -  not  eqn.  the  2  =  spectral  an  which  of  )  Comte-Be I Io t ' s  of  given  scales  of  the  anemometer  wind  of  normalized  determinations  surface  thrust mean  of  l o g j Q ( f jZJ^ ^ ( f ) U  0  and  2  6.1  two  '*  experiments.  of  the  sea  of  the  drag  measurements  direct  the  the  I"  lower  data  the  _  curves  0.6)  different  c o e f f i c i e n t  Thirty-three  cospectra  from  5  equivalent  a  tunnel.  anemometer  c o e f f i c i e n t  vs.  anemometer  the  drag  has  on  -  3  both  indicating  different  considering  of  curve  (0.25  frequency,  subrange  against  peaks  = 0,0010  ~-u,u-,Ur  sea  by  summation  measurements  speed  at  a  height  the  drag  were of  5  of  plotted in  m  45.  significant  wind  speed  m sec"'  = 0.0010 coefficient The  of  was  the and  than resu  variation observed  of over  observations. the this  I ts  of  Aruba  run  average. C.  the The  had  a  This  Elderkin  c o e f f i c i e n t  range average  61$  from  value  higher  difference  (1966,  3  Ph.D.  to was  drag is  believed  Thesis,  U . of  Washington) under neutral conditions over sagebrush desert give a v a l u e of I .4. f o r e q n . 6.1, although he f o u n d higher turbulence l e v e l s a n d a CQ o f .006 invariant with wind speed.  120  to  be  of of  s i g n i f i c a n t  and  experimental  to  sites,  be  associated  i . e .  fetch,  with  wave  the  differences  height,  and  depth  water.  b.  Comparison  The  with  indirect  logarithmic  methods  profile  method  (Chapter  2,  Section  3a)  2 was  used  F3,  G3,  graphs  to  estimate  J2, of  against  Rl  U  which  In  x^  (Figure  in  relationship  and  indirect  a  majority  larger  The  which  not  of  than  Figure  methods  does  had  runs  The  the  be  results  obtained  consistent  The  by  FI,  are  line  if  results  estimates  D3,  F2,  straight-Iine  straight  equivalent.  indirect  D2,  D I ,  relatively  23).  and  would  direct  downwind  66  were  give  the  the  ten  R2  the  clearly  for  and  vs.  -U|U^  u-"-  the  indicates direct  p r o f i l e  for this  plotted  our  method  data,  method  and  are  ones.  velocity  fluctuation  spectrum  method 2  (Chapter  2,  D | ,  D2,  R2,  R3  the  direct  much the  D3, and  more  Section  3b)  was  used  FI,  F3,  G3,  J2,  Rlj.,  methods  and  the  estimates consistent  estimates In  F2,  from  Figure are  67a  -U|U^  with  the drag-  compared  -«- T h e e f f determination important in will produce 20% in the s p  of  results  the  to  estimate  Kl, are  in  Ql, again  Figure  direct  logarithmic  those  from  for  Q3, Q5,  plotted 66.  estimates  from  runs Rl,  against  These  p r o f i l e  c o e f f i c i en t s  with  Q2,  u*  than  are are  method. both  direct  indirect  determinations.  ect of unstable or s t a b l e s t r a t i f i c a t i o n in the of u-» by t h e p r o f i l e m e t h o d is p a r t i c u l a r l y light winds. A Richardson number of o n l y -.10 an e r r o r of 7 ° $ ; i n t h e p r o f i l e m e t h o d b u r only ectrum method. '(Panofsky, Pers. comm.) 2  121  (I966)  Weiler  found  that  the  downwind  velocity  2 fluctuation his  direct  larger  method  gave  determinations  than  difference  those lies  from  in  p o s s i b i l i t i e s  are  may  f a l l  than  the  strongly  off  more  hot-wire than  fluctuations  from  anemometer  needed.  Results  Direct the  surface  workers. relative the  of  noise  of  was  with  are is  of  these runs  .0010  (1966) His  as  than  already  records.  The  spectral  levels. response  frequencies,  that  response  or  more  from  probes.  Only are at  temperature  Further of  the  wind  used  analog  a  c o e f f i c i e n t  reported  by  thrust  by  of  CQ  various  confused,  and  the  various  methods  are  few  recent  results  will  in  Figure  67b.  shown Spanish  and  drag  somewhat  measurements  mean  were  affected  the  the  s t i l l  debate.  and  be  such  u-»  workers  sea  of  anemometer  s i t e .  may  of  anemometer  high  high-frequency  picture  thrust  Banks  by  at  being  here,  Weiler  expected  of  quoted  variation  thrust  of  merits  coefficient  the  determinations  The  subjects  that  other  the  which  anemometer  vibration  of- the  c.  - u j u^,  measurements  investigation is  of  estimates  higher-frequency  expected or  higher  thrust  the  Two  that  L\£>%  there  Banks was  no  the  For  average  be  33 drag  significant  speed.  an  X-wire  analysis  anemometer and  at  integration  the  Spanish  over  the  122  cospectrum  were  1+,  3.  Section  in  time  X-wire than  with  For runs  from  F2  for  two  and are  the  comparison  conditions  similar  the  measurements  those  these  very  investigation  wind  duration  value  speed  at  a  drag  m sec"'  I  with  method. u  2  1  (-u  1  speed  They u^)~  no  possible  average  drag  which  50%  is  is  runs.  required.  measurements  Sea  from  13  anemometers.  significant  of  runs  of  The  variation  (1966),  using  coefficient  varying  linearly  •0019  (I963) also  at  1+.0  For  the  eight  1+7)  the  average  significant  Baltic  but  best  anemometer  Volkov  at who  report  which  2  3  from  and  to  Sheppard  0.00150,  direct  hot-wire  and  the  difference  the  from  respectively  The  thrust  report  overlap  with  observed.  Zubkovski report  with  the  this  over  .0007  is  is  of  (1966)  c o e f f i c i e n t  minutes'  average  e_t__a_J_  for  is  which  Chapter  measurements  under  runs  average  5  made  in  c o e f f i c i e n t s  anemometer not  runs  higher  1+6%  X-wire  the  drag  and  drag  anemometer.  higher  the  the  2l+%  described  Weiler's  thrust  10  Hasse  those  the  for  Further  F3,  were  coefficient than  of  thrust  runs  to  a  m s e c " ' ,  used  the  values  in  of  speed  2  anemometer  value with  of  this  wind  with to  runs  with  speed  is  is  .0008  agreement p r o f i l e  ratio  m sec  ratio  anemometer  from  close  the  linearly  of  sonic  logarithmic  decrease  thrust  trend  10  a  2.5  increasing 2.2 9  and  observed.  a t  9  0.0° no The  m  wind  s  e  c  (Figure  I2J differences higher  in  values  the of  drag  uj  coefficients  than  at  therefore  Spanish  — p ~ Our  values  calculated f^  report upper  Uj  Hz over  2  limit  instrument analysis over f^  to  in  f^  1+  =  Hz.  on  and  the  technique.  It  Most  can  of  limit  have  a  large  also  response  often  d i f f i c u l t  intervals,  workers  frequencies  frequency  lower is  other  range  the  frequency  particular  were  2  arbitrary  depending  different  -  2  an  used  Banks.  (u. ) a°hd ( - u . u , ) f o r F i g u r e 1+7 I 15 arbitrary frequency limits, from  between  .0039  =  of  indicate  to  of  since  the on  the  the  depending  compare  effect  with  on  the  results  choice  the  of  value  of  2~ (uj be  ) .  A  2  (u^  better  ) ,  which  2  choice  of  f. L  indication should  since  significant  energy  (Figure  to  1+3)  dimensionless  d.  The  and  seen  horizontal,  mean  wind  s i t e . f by  have  speed  Typical -  which  0.1 the  f 0 ( f )  is  at  low  a  very  uniform  turbulence much  less  peaked,  levels  strongly  does  not  frequencies, shape  might  when  on  the  contain  and  appears  expressed  in  parameters.  importance  We  depend  55  have  of  Hz.  of  that  spectral  spectral  are  functions  and  height,  correlations It  is  analysis  at  levels,  principally least  were  d i f f i c u l t  correlation  could  both  be  at  Rj^(f) to  of  the =  frequency, Spanish  -.5  imagine  much  vertical  a  larger  at  Banks  frequencies  mechanism in  magnitude  121+  than  this.  reported  Therefore,  here  must  Alternately, reported double for  if  here,  those  the drag  much  larger  be a c c o m p a n i e d  spectral the drag  reported  levels  drag  by h i g h e r  c o e f f i c i e n t  is  cannot  to  levels.  those  be more  and an a p p r o x i m a t e established.  than  spectral  are comparable  c o e f f i c i e n t s  here,  c o e f f i c i e n t s  than  upper  limit  The m a j o r i t y  of  to reported  values  reported  here,  Hasse.  of  CQ a r e e q u a l ^ o r  and none  a r e much  (1906),about  lower,  greater  lower.  than  those  The values  a r e among  the  of  lowest  reported. Examination reveal be two  at  signals limits  Another of  a glance  d i f f i c u l t  .these  d i f f i c u l t  in  the t h r u s t  t i It  of  5.  Summa r y  a.  A  thrust  making  velocity  an. e r r o r  the thrust  anemometer  measurements fluctuations,  to  +  I,  of  some  and which  investigation  and is  of  should  values  which  were  of  indicated.  positive  results,  can  otherwise  the c o r r e l a t i o n  in analysis  anemometer  physically  leading  might  not exceed  the occurrence  to e x p l a i n  for.  must  and c o s p e c t r a  which  f o r example  be e x c e e d e d is  spectra  inconsistencies  by d e f i n i t i o n  considerations  of  the v e l o c i t y  to detect;  example  R|3^f)  of  were  among  the  corrections  anemometer,  was d e s i g n e d of  three  and hence  with  the  components of  wind  of  intention wind  stress,  over the  125  sea.  Calibrations  thrust  anemometer  in  a  wind  tunnel  be  suitable  for  32  minutes'  duration  should  indicated  that  its  the  intended  purpose.  b.  Thirty-three  Spanish were  Banks  analysed  runs  of  experimental  site  into  and  spectra  196i+,  in  I  cospectra  made  9&5  by  a  n  the  '9^6  d  an  at  analog  techni que.  c.  The  thrust  anemometer  is  a  suitable  instrument  for  of direct to  a  measurements ReynoIds  few  meters  demonstrated cospectra d.  T"he  surface  e.  of  drag  p r o f i Ie  surface  from  value sea  of  for  variation  of  at  of  heights  the  velocity  sea.  spectra  measurements  by  the  drag  c o e f f i c i e n t  these  runs  was  C  =  n  from  one  This  was  and  other  .  of  this  parameter  with  methods  were  also  to  instruments.  of  the  0010^. mean  No  wind  observed.  indirect  c o e f f i c i e n t .  produced  f.  those  the  the  comparison  average  was  Two  above  by  with  significant speed  stress  A  much  The  better  downwind  results  used  velocity  than  did  calculate  spectrum  the  the  method  logarithmic  method.  Composite  plots  fluctuation  spectra  principally  of  of  the  showed  frequency,  downwind these mean  and  vertical  quantities  wind  speed,  to and  be  velocity functions  height  above  126  the  water.  constant a t  i ow  for  The the  data  suggest  spectrum  f requenc i es.  of  that  there  vertical  may  be  velocity  a  universal  fluctuations  127  APPEND i X  I:  CALCULATION THRUST  The a)  of  under  deflection  length a  L  force  f  SPRING  CONSTANTS  ANEMOMETER  d  and  OF  of  a  FOR  THE Mk.  II  .  simple  cantilever  cross-sectional  moment  spring  of  (sketch  inertia  I  is  d = fL /3ql 5  where  q  deflect  is  Young's  in  an  S  width a = .635  modulus.  shape c m  >  The. f l a t  (sketch  the  q =  19  x  cross-section  10  have  b =  .OO76  dyne  cm  .  3o  the  stiffness  Simple  a.length cm a n d  2L  Figure =  of  cantilever  2)  1.03  cm,  Young's  T h e moment  of  inertia  is  X| = a t r / 1 2 = 2.3 x 10 and  (e,  -2  II modulus  b) , ;  thickness  springs  the  flat  spring.  cm " 4  spring  b.  Flat  is  cantilever  cIamped  at  both  spring ends  of  128  The sketch  beryllium  b.  They  copper  have  a  tie  wires  radius  r  also  deflect  ,0089  =  cm,  as  in  moment  of  i nert i a  I  = TTrVk = k.92 x I 0 "  2  cm *" 1  9  I I and  Young's  of  a  tie  modulus  wire  k  of  q  x  12  length  =  2L  dyne  10 0,80  = f / 2 d = 3ql/2|_5 _  £  The  displacement  of  two  flat  and  springs  constant  =  the  core  four  -2  fie  cm  0 < 2  rod  cm  3  j 6 Q  one  wires,  d  y  This  flat to  =  is  2k  of  tie  total  + lik2  regarded  certain  springs  the  stiffness  e  c  m  -\  and  the  deflects  total  spring  is  k  length  n  component  _ j  6  because  The  is  x  of  .  and  the  2  only  spring  wires)  =  l  as  x  1  an  dimensions  were tie  s t i f f n e s s .  t  not wires  0  d  V  n  e  c  m  ~  approximate (thickness  closely  *  calculation, of  flat  controlled.  contribute  about  springs,  The  equally  129  APPENDIX  PLANE  2:  WAVE  OVER  In  Chapter  frequency  Section  3»  component  of  average  velocity  the  surface  of  the  org i n  proof  an  =  stated  "Ja  wind  (here  that  velocity  for  a  Fourier  fluctuation  denoted  by  a  sphere  of  radius  imaginary  u j  foilows  Consider U j ( x j , t )  =  wind  This  Uj  transverse elements  AVERAGED  curly  Uj cos(Ukt) Q  overbar) r  over  centered  at  is  Uj  U.  FLUCTUATION  SPHERE  the  The  VELOCITY  (i  of  a  Q  c o s ( U k t ) s i n ( k r ) / k r .  0  .  single  spectral  cos(kX| may =  be  Z\  area  -  either  which a  plane  3)  at  Ukt)  angle  velocity is  component  advected  longitudinal  wave.  9  from  r  cos9  (i  Take the  Xj  by =  l)  the  mean  or  c i r c u l a r axis  so  that  2 dA  =  2 -ftr  sin9d9  u. ( t )  and  =  x^  J  A  =  U-J-QCOSUXJ  -  Ukt)dA  A  ~  2 pv =  u^/h/nr  I  (cos  kXj  cos  Ukt  +  (2Tfr =  =  In  applying  u.  10  cos  Ukt  u.  cos(Ukt)  this  result  10  j j  -cos(kr  2  cos9)  sin  kx  sin  Uk  sin9)dQ  d(cos9)  sin(kr)/kr  to  the  thrust  anemometer  it  mus  150  be  assumed  it  causes  that l i t t l e  measurements the  sphere  the  sphere  is  disturbance  so to  highly the  of  air  flow  through,  have  yet  been  made.  perforated  flow  of  a i r .  around  or  in  the  that No wake  of  131  APPENDIX  3:  The  INTRODUCTION  basic:  of  extremely  an  input  in  Figure  is  negligible,  Z j  and  unit  high  e  =  -Ae  provided network  _  that is  By  and  Q  to  using  performed, amplifier.  Z|  e  It  feedback  the  ij  is  a  dc  =  input  i  amplifier  connected  impedance  amplifier  current  s e,  -  Q  e  o e  e  "  s  / e j . e  and  the  Some  band-pass  The  The ~  s  Z  as  Q  shown  current  must  flow  with  i j  n  through  -  e  ) / Z  0  0  -  'A) <v - e ^ A e , ) "  effect  gain  reversed. and  Philbrick  each  Analog many  analog  feedback  called  an  and  operations  which  and  At  e,  the  resistors  c i r c u i t s  -5  amplifier,  of  is  operational of  of  fo "  0.  amplifier  r e s p e c t i v e l y ) .  (I965)  o(< e , U  mathematical  a  Paynter  s  various  amplifier  is  (e  networks  e ,  signal  =  s  various  dc  d  e )/Z|  maintain  a  and  -  A » e  are  c  (9,  -A.  is  and  s  o Z,  2  same  computer  gain, a  PRINCIPLES:  Q  0  Z  analog  and  the  ANALOG  Z .  Z  for  Z|  Assuming  i I =  but  an  negative  impedance 68.a.  of  TO  an  in  two  integrator  stage  techniques  may  be  operational  used  sums  capacitors  the are  this  program  inputs  e|  (Figure  sign  of  and 68.b,  the  discussed  by  I0UBC c o n s i s t s  of  others.  computer  at  132  30  operational  current  i.  =  amplifiers 10  amp.  of  gain  A  =  2  x  10'  and  input  133  APPENDIX  TRANSFER  k:  The  phase  operational  FUNCTION  shifter  amplifier,  OF  90°  PHASE  LAG  network,  incorporating  is  in  shown  Figure  CIRCUIT  an  68c.  We  use i  standard  notation  indicating  and  the  a  for  phase  input  c i r c u i t  analysis,  lead  of  90°.  impedance  is  Zj  The  with  j  feedback  I / j 10 C  +  =  (-1)^  impedance  is  •  to 500 The Cj  10  =  c i r c u i t jif  and f o  parameters  C  £ o  =  e,  0.1  =  Q  ^jf.  Z,  RQ/J<*>CQ  these  0  conditions  second  when  adjusting  f •  R  for  of  frequencies  need  be  The  gain of  was  included  was  found  be  the  was  that  from  of 1.8  used  equal  of  in  and  satisfied  range  may  kept  R|  0  o  0  frequencies  not  setting  is  The  is  o  u4/2w»l/2nR C  =  to  phase  dependent  the B| * 2  .^k-f)^ RQ  = I44  function  M£l,  is  0  0  l/ooC  C « C,. R I'  I  (R + l/jw C HR, + l/JWC, J  o  0-  =  transfer  U + l/j0^ C )(ju)C R  =  where  The  _  =  R|  are:  f i l t e r -  R. at  0  "  o  l/oOC .  =  1  + C /C, j  (  0  all  n  The  f i r s t  frequencies,  = .036  Hz  and  the  adjustment  to  but  if  the  Hz, gain  of  a  the  of  wider  the  of  third  continuous 128  / J * "J  f  by  Rj range  phase  shifter  unity.  shifter on  at  frequency,  bandwidth  0„98B J ^ •  any  A  particular and  this  c a l i b r a t i o n .  slight  shift  effect It  toward  lower was  frequency  neglected.  of  the  quadrature  f i l t e r  characteristi  135  APPENDIX  5:  COMPUTATION ANEMOMETER  A to  digital  apply  a  spectral  estimates  correcting discussed  for in  DO  loops  the  repetitions  (FR(I)) CROSS  and (-»-),  beginning f0||(f), one by  run the  angle  were  of  the  use and  time.  of the  (A)  t i l t  of  DO  the  (-),  read  were  loops  corrected  records,,  the  at  (0)  the  and  were  processed  then  calculated  .  DOWN  r u n . n a m e , a n d . ...  in  va I u e s f 0 . . ' ( f ) ,  f a c i l i t a t e  frequency  (+),  once,  as  variables  to  for  fj#  accomplished the  '(f)  t i l t  and  fjZT  ' ( f ) ,  15  35-  .  IV  analog  anemometer  DOT in  which  to  FORTRAN  u j u^. The  values The  using  program  read  1 1  and  THRUST  Subscripted  run, while (f)  f0  the  39*  The c o m p u t a t i o n s  three  OF  data  . The v a l u e s  BLANK  where  written  anemometer  throughout  symbohs  and  ROTATION  coordinates  Ix., S e c t i o n  computer  f0^(f) a  of  calculations.  VERT  was  of  thrust  effect  used  group and  at  rotation  Chapter  and  program  from  the  VERTICAL  COORDINATES  computer  vertical  FOR  before  IBM  results chart  second  70I+O are  and  half  and of  of  after  the  70  is  program  rotation  UBC  presented  Figure  the  Computing  and  printed graphed  Centre  in  Appendix  8.  a  printout  of  was  Figure the  the  spectral  the  latter.  used. 69  is  program.  The a  flow  136  APPENDIX  6:  CALIBRATION ESTIMATES  The wire  output  anemometer  proportional object  of  relating  to  the  the  THE  the  SPECTRAL  ANEMOMETER  Model  is  fluctuating  voltage  a  velocity to  e  balance  to  vs.  I  velocity  cause  U,  d i r e c t l y and  conversion  depends  fluctuations curve  a  on the  which  hot-  H W B 2  fluctuations,  obtain  fluctuations  velocity  HOT-WIRE  OF  Corporation  is  velocity  along  CALCULATION  Flow  wind  c a l i b r a t i o n  Small move  to  mean  FOR  bridge  voltage  The I.  of  AMD  the  constant  fluctuations  the  wire  current  operating  may  be  u.  point  taken  as  linear.  u  The  effect  order  and  (d^/de)  =  of  =  of  l/R  be  w  Law  =  (A'  where  Rg  oCis  +  is  are  a  states  The  steady  state  resistance  Values  9  W  that in -  the  air 9  ).  resistance  of  thermal  used.  wire  is  of  Qu/dl)  of  second  and  of  required,  B'U*)(9  the  in  neglected.  temperature  dQ/dt  and  variations  may  King's wire  (dU/^I)(dl/ae)e  resistance  remaining  at  of  heat  temperature  The  the  resistance  wire  at  c o e f f i c i e n t  non-linear  conditions  rate  terms  are  loss 9g R  from is of  the  temperature of  the  a  wire  9g  metal  negligible.  Under  137  I R 2  w  =  (A•  A  +  +  B'U )(R 2  w  -  R ) " ' g  or  1 since  R  w  =  and  Rg  BU  can  2  be  considered  to  be  constants.  Differentiating,  dl/dU  =  Calibration  B/1+.IU  of  the  2  wire  current  I  in  a  wind  tunnel  2 a  series  which  is To  of  a  velocities straight  determine  known  wire  of  and  line the  of  wire  p e a k - t o - r p e a k the  U results slope  B  a  plot  and  resistance  amplitude  resulting  in  peak-to-peak  ±  I  vs.  intercept  a  was  2i  of  through  voltage  E'  U  2  A.  square-wave sent  at  was  current the measured.  Then  =2 i / E ' where  was  calculated  bridge  hlH, I  practice using osciI  from  (BN)  E'~was  either Ids6ope.  an  and  the  resistance  measured osciI  settings  on  of  ratio  playback  Ioscope  or  the  a  of  hot-wire  (RR) a  =  tape  photograph  /  R w  anemometer R g  «  In  recording of  an  138  The  result  u  =  of  calibration  is  K ' e i  K'  where may  is  I  be  =  the  81iU /BE' 2  measured  computed  =  u  the  same  way  current.  Spectral  estimates  from  f0 (f) in  wire  (N /N')(e' K')/(6" g (BW)) 2  2  2  u  as  were  the  thrust  is  the  mean  to  a  anemometer  spectral  —5 estimates. wave  Here  voltage  frequency computer  f,  an  applied G"  is  the  preamplifier  integrator during  e'  sweeps equal  square  f i l t e r  of  bandwidth  re-recording gain  during  interval  a of  r a t i o . data  run  caIibration  N  BW  set  gain  and  g  is  the  number  u  and  calibration  N'  the  signal.  is  sine at  the of  number  139  APPENDIX  7:  THE  SPECTRUM  BANKS  Wave probe  in  heights an The  70  less,  km  or  Figure  were  waves  7'  measured  measurements  a  WAVES  as  on  f0 (f) speed  a  AT  THE  SPANISH  capacitive  described  limited wind  vs.  w  wind  using  usually  depended  shows  at  c i r c u i t  were  and  a  SURFACE  SITE  o s c i l l a t o r  (1965)*  OF  of  by  spring  log|Qf U =  by  G i l c h r i s t  the  fetch  and  d i r e c t i o n .  for  600  wave  of  G i l c h r i s t ' s  cm s e c  and  a  0 wind  direction  of  102  .  The s p e c t r u m  satisfies  the  relation (f)df  where from  is the  results  the  mean in  the  wave  height  water  level.  form  winds  peaked  the  peak  at  a  of  the  closer  spectrum  is  expected  features  in  comparison  peaked  Typical 3 of  cm a t  13m  a  and  (f)  to  s e c " ' •  of  0.5  Hz,  of  a  shows  D  displacement  the  same  The s p e c t r u m  remain  is  while the  Hz.  In  strong  expected  the  shape  same.  Its  to of  west be  at  the  wave  principal  with  wind  spectra  is  that  not  vary  greatly  in  frequency.  wave  amplitudes  3  m  is  10  0,25 to  as  10 g , _ f .  spectrum  does  speed  vs.  wave  peak-to-trough  wind  7'  O'w  frequency  frequencies  sharply  I  cm m e a s u r e d  Figure  I 0 g._0 A  sharply  in  sec  '  to  I.5  m  it  ranged in  a  west  is  from wind  APPENDIX  DATA  8:  Tables cm  s e c "  2  A 9 * I to  for  2  and  S2  5.  Vertical  runs  runs  was  spectral  coordinates,  J3,  jl+..and  described The  D3, J5 in  El,  a  r  used  Q3,  Q",  Rl,  been  estimates)  estimates R2,  R3,  discussed for  the  in  computer  range  of  the  the  frequencies  3  graphs  F l ,  three  and  after  19^5  F3,  F2,  The  after  vertical  runs  GO,  and  Ar,  BO,  Gl, G2,  computer  of  rotation Bl,  G3, JO,  program  B2,  Jl,  was  6. on  the  graphs  0  f0,,'(f)  A  f0  *  f0,  graph are  SI  Chapter  printouts  are:  '(f)  3 3  ; 3  (O ?  The  in  Rl+,  last  ( f 0 | j , ^ 3 5 , t0| )  respectively.  symbols  spectral  have  \9bl+  the  Appendix  spectral  the  digital  e  and  E2,  the  hand,  before  for  Q2,  of  coordinates  by  f0|z'),  3 3  D2,  Ql,  of  93  estimates  list  These  out  to  12  f0 ',  (f0|l',  DI,  Kl,  rotation  carried  (Tables  A9.M  respectively.  Figures  of  REPORT  is  listed  from in  -500 the  to  2000  column  cm  -2 sec  adjacent  , to  and the  gra ph. Some  of  been  discussed  runs  are  comment.  these  similar  in  runs  (Ar,  Chapter in  5«  character  El,  E2,  F2,  The  spectra  and  do  not  F3) for  have the  require  already remaining individual  J2,  Table  A8•I:  it I  f Hz  .0039 .0055 .0078  .0109 .0156 .022  Spectra  cm  2  96 I 0i|. 192 279 296 631 693 636 545 506 430 545 310 289 215 176 153  'P 72 55  f0  I  sec  for  -2  33  Run  ff6  21  "3  • 17 • 35 £3 80 116 152  70 101 116  133 •171 168 11+8  J  182 203 2J+1 233 262 272 265 290  •119  o  5  • 81 54 29  0  194  133 118  + + +  4 12 6 5  282  + -  5 1 1  f^  1 12 102 165  + 2 -22  -38  -58 -62 -24 --11  t -21 - 9 0  228  138  ft 13'  • 23  ho  , 5  Kl  +  I  +  5  +  5  %  479 606 655  n  592 495 411 560 322 286 206 176 148 115 86 86  $ 45  lu  65 78 150 245  rl!  8 5.68 591  54p 524 457 574 529  :.2 -22 +  1  + 17 25 57 57 2.  147  60 6$ 66  96 69  54 60  257 212  55 11 0 2  Table  A8.2:  f  f0  Hz  cm  .0039 .0055 ,0078  397 563 765  .0109 .OI56  .022 .051  .0kl+ .062  .088 .125 .177 .25 .35 .50 .70 I .0 I. 4 2.0 2.8 I4-.O 5.6  8.0 3 16.0  II.  Spectra  M  2  -2  for  f0  2 2  Run Ql  ^35^,3  tf, * 3  sec  114-60 13 8I41517 1373 1190 1080 892 76k 718 638 606 1+23 395 5' 287 206 170 134 99 1  189  22 0 88 126 1I4-T 11+9 kJl 251 277 337  - kj ^  •  - 82 -li+5  -211 -253 -301 -250 -255 -262 -223 • 168 -176 -11+8 -136 -123  ill :ll ill 311 292 276 231+ 249 716  0 10 8 6 0  1+0  5 2  % 21+ 10 21+  56 67 36 17 3 21  Table  f H-  Spectra  A 8 . 3 :  f0 cm  2  399 575 650 631 838 1029 1355 M 10 IO3I4. 888 770 712 oko 549  A  285 261 198 155 125 83 150  - 2  for  33  Run  fjZf  Q 2  13  fjZf  13  *0.  sec  .19  %  • 76 -122 -223 -264 -202 •248 -235 -250 • 190 -156 -201 -152 -116 • -  45 27 21 12 6 2 2 0  •10 13 57 0 -27 •52 •36 -27 -64 •43  -26 -24 2 16 10  522  PI  6o4 816 1017 924 963 752  15 ?  570 4o4  439 330 255 221 182 0  ok 8k 74  52k 492 426 58k 883 980 824 701 674 574 504 411 296 219 187 81 42 23 10 6 4 0 2  9? 158 139 50 26 56 60 49 42 114 35  Table  A8.1+.:  Spectra  f  f0 2  Hz  cm  .0039 .0055 .0078 .0109 .0156 .022  21+8 359 802  .051 .ou4 .062  .088 .125 .177 •25 .35 .50 .70 1.0  I.It-  2.0 2.8  l+.o  8.0 M.3 16.0  818 957 885 6I+3 605 378 356 353 256 21+8 225 195  \jk  134  119 106 112 250  sec  -2  for  33  111-  36 53 52 10I+ 111 110 126 180 215 265 307  3k7 3kl  337  2I3 3I3 1315  Run  f]0  Q5  13  • 35 • 50 •122 •155 • 99 -160 -206 •152 -152 -I 18 • 88 - 81 - 79 -107 •  • • • • •  68 1+1. 29 15 5 5  I 55  f0  13"'  3k  >20  k7  56 39  ~i -23 - 3 -52 -28 -51 -52 -l -17 3  1'75  <"820 7l+2  fee  •65 0 8  928 677 £7 j 558 •505 277 227  ll  161+  1 1:3 72  10  15 r~  l  3 2  .2. 34  Table  A8.5r  Hz  .0039 .OO55 .OO78 .0109 - .OI56 .022 .031 .Okl+ .062  .088  Spectra  cm^sec"  458 741 1155 1273 1238 876 81+6 121+2 868  .125  .177 •25 .35 .50 .70 I .0  1.4 2.0  2.8 1+.0 5.6 8.0 11.3 16.0  I 61+ I  ll+  100 76  58 87  Run  Q5  2  321).  \k  960  5  869 835 122 1060 885 853 792 562  35 50 65 103  kl ,. k i+22 36l 26l 232 198  for  81  a,  1+1+9 337 327 270 250 228 212 209 11+9 195 185  2  3k  llil  169 196 215  234 270  283 311 321 289  258 232 200 202 179 168 61 210  - 36 - 97 -126 -I 18 -108 -105 -132 -201+ -114-7  -1+2 -ll+3 -152 -129 -115 -  68  -- 36 ^ - 26 - 12 - 1 1 - 3 - 8 3 1+5  -73-30 0 26 - 5 -l  I  -15 -18 -29 ~% -38 -20 - 5 13 2 z  k  Table  A8.6:  f0,  f  Hz  cm  .0039 .0055 .0078 .0109 .0156 .022 .031 .  Spectra  o  J  A  .062 .088 .125 .177 .25 .35 .50 .70 1.0 1.4 2.0 2.8 4.0 5.6 8.0 11.5 16.0  2  <0 sec  -2  for  33  Run  Rl  fjzf 13  • 31 - 72 • 123 -133 -163 -206 -192 -232 -258 -214 -18; -238 -205 "151  -122 - 61 • 44 - 21  :I  10 11 37  13''  -58 5 15 92 58 27 -19 -29 0 .30  -43 -6 - 3 3  Table  A8.7:  Spectra  f o r Run  f  fjzh i f # 2 2  Hz  cm s e c  x  f  $35  R2  f  0i5  *$\y*  2 - 2  621 736 1081 829 955 1358 1913 2107 182I4. 1683 1333 1369 12I4.2 I 166 986  888 7)4.2 1107 1551 1524 1357  554  1232 915 1025 871 1065 1097 1581 1050 I 125 1000  r+71  765  362 286 21 I 177 2l|5  ?687 3  753 . 729 650  5  m 12  11 -39 -50  •4 •2 •39 -26 -29 •25 • 5  Table  A8.8:  Spectra  f  fjzf,, »  Hz  cm sec"'2  ,0039 .0055  .OO78 ,0109  .OI56 *022 .031  ,062 .088 .125 .177 .25 .35 .50 .70 1,0  1.4 2.0 2,8.  4.0 5.6 8.0 11.3 16.0  f0  2 2  for  '  Run  ^33  R3  t0i3  ^13*  2  799 666 I 196 2624 2327 1809 2231 2839 2588 2308 1988 1792! 1707 1536 1250 1053 936 821 679  in 315 262 298  1124 854 1081 896 1426 1157 14^6 1378 1638 1692 1317  1492  1562  1421 1438 1261 1669 1794 1455 1180 1020 98 59, 612  • 14 - 32 - 97 -229 -200 -I69 -215 -258  25.. 5 22  44 2  -374  -24.! 0 •409 -377  -240 -276 -343 -304 -259  -194 -150 - 92 - 48 -  !7 7  52 90 176 101 8? 38 22 16 27  Table  A8.9:  Spectra  f  fjZJ-,,'  Hz  cm^sec"^  .OO3.9 .0055 .OO78 .0109 .OI56 .022 .031  .0%.  .062 .088 .125 .177 .25 .35 .50 .70 I .0  1.4 2.0 2.8 4.0 8.0 11.3 16.0  824 1061  1945 22J+2 3274 2980 2462 2603 2231 2036 1968 1816 1785 1681 1591 1310 1111 918  pk 60k  492 324 26 29,  fj2J  for  2 2  '  718 1+76 715 1065 1307 1351 llj-95 1561 1 173 ION  961 I36O 1299 11+07  1526 2332 171 I 1 447 1^36 1001 1017 590 625  Run  ^33'  10 12 19  ko 50 56  ?? 156  19'  25 55 75 692 656 693 692 785 821 770 733 754 582 769 359  RI4.  f0, « 5  •  2  9  - 45 -106 -160 •140 -210 -179 -249 •297 -296 •335 -234 -261 -258 •266 •253 -18 •17 •I 30 -  fJZf,^  90  - 44 - 21 9 - 20 50  48 -2. 6^ 162 124 49  _33 18 -67 -19 32  150  Table  A8•10:  Spectra  f  fJZl,,  Hz  cm^sec"^  .0039 .0055 ,0078 .0109  .OI56  ,022  .051  .00+ .062  .088 .125 .177 .25 • 35 .50 .70 .0  .4  2.0 2.8 4.0 5.6 8.0  11.3 16.0  f033«  361 61I4. 1063 823 1213 1187 1278 161+8 1617 1796 1201+ I 130 1050  434 576  1093  51+1  101+6 834 815 686  III 1+00  5?'I  248 21 29  for  13 12 18 21+ 32  81  11+5 2ll+  550 608 629 §53 659 522 610 532 503 592 1315  Run  f013«  SI  f0| 5  f0  f0,  u  ll  68  8  102 -176  74  1474  -212 •229 •259 .238  14 15 48  1887  •177 •222 -223 -205 -207  61  13  -161+  •177 -160 -127  :2 •  16 16 11 59  P  134 100  69 2 2 3  2  38 32  u  f0|u""  555 819 1635 1151 1650  135 0  \%  104 0 81 146  1845 1731 1651 i486 1689 1502 1392 145I I 163 1027 9  2,  2  784 592 635 436 340 290  213 188 143 150  -  3 13  151 Table  A8.ll:  f Hz  .0039 .0055 .0078 .0109 .0156 .022  Spectra  f0l  2  cm s;ec 662 8614. 770 533 506 890 151J+ 1215 993 762 80I4. \\l 715 715 559 550 459 390 313 262 201 158 i44  252  fjZf 33  for  Run  fjzj,« 3  S2  f0,-::3  fjZf  u  fjZf,  f0,  -p cL  12 18 17 22 26 70 69 76 105 150 271 345 325 355 395 422  - 30 - 73 - 56  - 1+4 • V -187 -200 -165 •177 •150 -113 -113 • l 36 •Il8 -. 86  3§3 4oo  :il  368 4o6 448  • 32  8 3  -29 5 54 52 14 23 55 66 57 27 •10 - 8 •25 •19  2156 1321 814 805  724  1257 1897 1675 ..48 1076 1208 1169 1090 1070 988 980 782 743 657 51 431 413 307 2  3>  198  765 735 373 385 W  143 •  12+3  l 172 803 755 625 657 647 632 517 359 219 125 63 45  3 5  ^  • § - 38 25 9  ll 81 85 11 1 102 43 35 3 20  152  REFERENCES  Blackman, R. B . a n d J , W. T u k e y , 1958s The Measurement Power S p e c t r a , D o v e r , . N e w York, 1 90 P P •  of  C o m t e - B e I I o t , G . , I9&5: Ecoulement turbulent entre,deux parois paralle'les. (Turbulent f l o w b e t w e e n two parallel boundaries.) Publications S c i e n t i f i q u e s et Techniques d u M i n i s t e V e d e I ' A i r , N o . lj.1 9, P a r i s , ~~ France. " Doe,  :  L . A . E . , 1963s A three-component thrust anemometer for studies of v e r t i c a l transports above the sea surface. Report BIO-63-I, Bedford I n s t i t u t e of Oceanography, Dartmouth, N.S. (Unpublished manuscript.)  Hamblin, P . F , , 1965: Cup anemometer wind observations over t h e s e a . M.Sc. t h e s i s , Department of Physics, University of B r i t i s h Columbia. (Unpublished manuscript.) H a s s e , L . , K. B r o c k s , M. Dunckel and U. G B r n e r , 1966: Eddy: flux measurements at sea... BeitrBge zur Physik der A tmosph'are« (in press.) Health  Sciences  U.S.A.  Programs, Hess,  Computing  F a c i l i t y ,  (W. J. D i x o n ,  G . D.  585  PP•  and H. A.  turbulent  Los  Angeles,  Biomedical  Computer  -  Panofsky,  energy  UCLA,  E d . ) , I9"4,  near  1966:  the ground.  The budget Quart.  of  J .Roy.  M e t . S o c , 92, 277-280. Hinze,  J .  0 . , 1959°  U.S.A., G i l c h r i s t , Ph.D.  580  I9&5:  TurbuIence .  The d i r e c t i o n a l  thesis,.Department  British  McGraw-Hill,  Columbia.  of  spectrum.of Physics,  (Unpublished  and  H.  A,  Panofsky,  196I4.:  Turbulence  waves. of  manuscript.)  The S t u r c t u r e  Wi I e "y~,  ocean  University  Lumley, J . L . , I9&5* Interpretation of time measured in high-intensity shear flows. Fluids, 8, IO56-IO62.  Atmospheric  New Y o r k ,  pp.  spectra Phys. of  of  New Y o r k ,  239 P P «  P a y n t e r , H . M , , I965: A Palimpsest on t h e E l e c t r o n i c Analog A r t . George A, P h i l b r i c k Researches Inc., D e d h a m , M a s s , 02026, U . S . A , , 27O p p .  153  Pond,  S., 1965s Turbulence spectra in the atmospheric boundary layer over the s e a , Ph.D thesis, Department of P h y s i c s , U n i v e r s i t y o f B r i t ! s h .Co I u m b i a . (IOUBC Manuscript Report N o , 19, U n p u b l i s h e d Manuscript.)  - — ,  R.  W.  Stewart  spectra  in  a n d R.  the wind  20, 319-324. — - ,  S .  D.  Smith,  Spectra  of  P.  F.  VeIocity.  in  the atmospheric  J .  A fmos . S c i .  W.  Burling,  over  waves.  Hamblin  and  1963s  R.  W.  and"temperature boundary  25,  Turbulence  J . Atmos.  Burling,  9  1966:  fluctuations  layer'over (July,  S c i .  the s e a .  1966)  Sheppard, P . A . , 1963° Distribution of wind speed, temperature a n d humid!ty !n a i r f l o w i n g over water. I.U.G.G., August B e r k s ley., C a l i f o r n i a . (Verbal paper.) • • •- •- • •  1963?  Weiler, H. S . , I966: D i r e c t measurements of s t r e s s and spectra of t u r b u l e n c e i n t h e boundary layer over the sea. Ph.D. thesis, Department of P h y s i c s , University of British Columbia. (Unpublished manuscript.) Zubkovski, S . L, a n d Y u . A . V o l k o v , I966: Direct measurements of«certain characteristics of atmospheric turbulence in the boundary layer. (in press, U.S.S.R.)  F I G U R E 1. a . WITH PERFORATED STYROFOAM SPHERE  THE Mk I I THRUST ANEMOMETER b . WITH SPHERE REMOVED, SHOWING INTERNAL MECHANISM  FIGURE 2. a. core r o d d. s p r i n g  clamp  g. a l u m i n u m j.  plastic DCDT  circle  S I M P L I F I E D SPRING AND LINKAGE MECHANISM FOR ONE COMPONENT OF THE Mk I I THRUST ANEMOMETER, c. S a n b o r n DCDT-050 d i f f e r e n t i a l b. transformer core transformer f . .007" d i a m e t e r Be-Cu w i r e e. f l a t s p r i n g spring h. s t y r o f o a m sphere i . f i x e d frame  mounting b l o c k f o r  k. s l i d i n g DCDT  subframe f o r  1. a d j u s t i n g s c r e w f o r p o s i t i o n o f s l i d i n g s u b f r a m e a n d DCDT  FIGURE 3.  (a) THE Mk IV THRUST ANEMOMETER  (b) THE Mk I THRUST ANEMOMETER  (c)  THE Mk V THRUST ANEMOMETER.  WIND  FORCE  WIND  FORCE  H X  •JO  LINKAGE,  SPRINGS  c  c  LINKAGE,  CO H  SPRINGS  >  MECHANICAL DEFLECTION  1  1  o o a  s m  DCDT's  1  _ > ?z  z m 2 o  o o o  o -4  H  H  LOW-FREQ.  CABLE  1  OFFSET  o *n c/> m  VOLTS  1  1  1  1  m r  2© m  w  • r  'f  -  m o  1 l  1  ©  H  AMPLIFIERS  1  m H m vo CABLE  SIGNALS  1  z  0  m  1  m 2 O  O O  GAIN  o  < r  > H  I  VARIABLE  a) o z o  DC  •  AMPLIFIERS  0)A  O z o  •  *5  CO  1  V C O ' s  1  1  FM  1  FM  TAPE  RECORDER  SIGNALS  TAPE  FIGURE  4.  RECORDER  THRUST (a)  As  (a)  ANEMOMETER designed  in  (b)  RECORDING 1963  BLOCK  (b)  As,  DIAGRAMS modified  1966  Green Demodulator »B  and  —O Output  Fi Her  O Yellow  Displacement  FIGURE  5.  D C  DIFFERENTIAL  TRANSFORMER  SCHEMATIC  rn rm  DIAGRAM  IM l€32 45v  ...  6v,0.5<x  iir  ANEMOMETER  ,1,1 I 1,1,1 * l * l , lAIBCPlElFlGlHl  INPUT FROM CABLE  FIGURE 6.  OUTPUT TO TAPE R K .  ,1 , I • I • I |S I 3 | Z\ J  THRUST <\NEMOMETER SCHEMATIC CIRCUIT  FIGURE 7.  P O S I T I V E DIRECTIONS OF COMPONENTS. a. f o r 1964 a n d 1965 b. f o r 1966  ,  1  1  1  1  r  x X  OUTPUT (volts,gain I)  FIGURE  8.  &  STATIC CALIBRATION OF THRUST ANEMOMETER BY PLACING WEIGHTS ON SPHERE, 1 9 / 3 / 1 9 6 6 .  1  •  -  180  -  120  1  '  ;  1  '  I  i  |  i  |  i  I  INDICATED 8  A  -  -  / *  60 /*  Ac -  0  y/  --60  --I20  -  -  J* MEASURED 0  r  * /  1  FIGURE  -120  9  -60  .  1  0 —t—  1  60 J .  i„  120 , i  •  ,  180  ANGULAR RESOLUTION TESTED BY ROTATING WEIGHT OF SPHERE ABOUT HORIZONTAL COMPONENT 2 AXIS.  H o r i z o n t a l s c a l e i s measured angle, v e r t i c a l s c a l e i s i n d i c a t e d angle 9 = t a n " ( F g / F ^ . 1  FIGURE 10. WIND TUNNEL CALIBRATION, a; F-^ v s . U (upper). b. c v s . U (lower). 2  1  1  i  t*  i  r-30  8 (indicated)  /  A  -  /  -20  -20  -10  -io  A  X  10  20  -30  /  ^(indicated)  A  -io-  X  -20  -10 x  /  X -X  /  >  */ -10  </  30-  -30  B  -20  -20-  -  30  6  10  20  9  30  t  / /  -10-  -20-  -30-  i  i  FIGURE 11. RESOLUTION OF ANGLES ON ROTATION OF THRUST ANEMOMETER IN THE WIND TUNNEL. a. VERTICAL ANGLES b. HORIZONTAL ANGLES  9 9'  FIGURE 1 2 .  a. MEASUREMENT S I T E b . RELATIVE LOCATION OF PLATFORM AND MASTS  1 p  CD/  AUXILIARY ROVER  O  MAIN  MAST  N  I1  0  /  MAST  - 4 9 ° 171' N  H 0  PLATFORM r — 1I—H  1 •  \ \ U-— 1  20m  123° I44' W  1  FIGURE 13  FETCH VS WIND,DIRECTION AT THE SPANISH BANKS SITE  FIGURE 14  FIGURE 15  THE RECORDING  PLATFORM  FIGURE 16. THE HYDRAULIC AUXILIARY MAST  FIGURE 17. DATA RECORDED BY CAMERA  FIGURE 19. CALIBRATION OF CUP ANEMOMETERS  12/4/1966  Bars show range of values for 10 different anemometers in revolutions per minute.  FIGURE 2 0 .  C A L I B R A T I O N OF KROHN-HITE F I L T E R S AT f o = 4 H z .  F I L T E R 1.  A  1  F I L T E R 2.  A  2  F I L T E R 3.  A^  F I L T E R 4.  A *A X  2  ©  2  X  <^2  V  ^ l * =.1462  B j * =.585  ^  od  B *=.560  2  2  =.1422 =.6706  L 2  *=-  0 9 7 8  =.569 B  2  1 2  =.576  N11  Mill-  N  33  •t• ; J J;  J!!  N 13 i:; i'  \  ;:;>  ni:  \  v-  / // 7 • • 7  rr  L  y ."i....  :::!  /  1  • j %m  N * "13  I  %*e dt  1 :\...  % w•H to a  3  FIGURE 21. EXAMPLE OF ANALOG INTEGRATOR OUTPUTS CALIBRATION OF FILTERS AND COMPUTER AT 8 H z .  1. in phase  2. e advanced 1  120°  3  240°  If  b. DATA FREQUENCY 0.125 Hz RUN Q l  FM REPRODUCE TAPE PLAYBACK (OR REFERENCE S I N E WAVE.)  FORCE OR V E L O C I T Y COMPONENT  Ul \ OCTAVE SPECT RAL FILTER  FREQUENCY COMPONENT DC PREAMP •  WIDE -BAND AMPL I F I E R  t  SQUARE  SQUARE  90° PHASE LAG  SQUARE  9MULTIPLY  MULTIPLY  INTEGRATE  CHART RECORDER  f 0  22  (f)  FIGURE 2 2 .  f 033 ( ) f  f  011  () f  f 0  13  (f)  SPECTRAL ESTIMATES  BLOCK DIAGRAM FOR ANALOG S P E C T R A L A N A L Y S I S .  f 0 * 13  (f)  FIGURE  2S  PROFILES  OF  MEAN  WIND  VELOCITY  vs  HEI^HTj  -5  -3  -4  -I  -2  log k  FIGURE 24. DOWNWIND SPECTRA FOR RUN C, 30/7/64 . PLOTTED IN THE FORM f0(f)=k0(k) VS. L 0 G f and L 0 G k. 1 0  1 0  LEGEND: O  T h r u s t anemometer, z=220cm, analog a n a l y s i s , 1024-1112.  •  Cup anem. No. 2, z=190cm, l a g type d i g i t a l a n a l y s i s , 1039-1150  A F i v e p o i n t averages f o r above. X Cup anem. No. 1, z=170cm, p i l o t d i g i t a l a n a l y s i s 10531125.  -5  -4  -3  -2  -I  log k no  FIGURE 25. DOWNWIND SPECTRA FOR RUN C, 30/7/64 PLOTTED IN THE FORM LOG 0(k) VS. LOGlok. lo  LEGEND: O  Thrust anemometer, z=220cm, analog analysis, 1024-1112.  •  Clip anem. No. 2, z=190cm, lag type digital analysis, 1039-1150.  A  Five-point averages for above.  •yt Cup anem. No. 1, z=170cm, pilot digital analysis 10531125.  f 0n(f) cm  z  <3>  sec ^ ^ o  •  O A  • G  -2000  o  • G  o A\  •  ?  • o  o  o 0  ^  1000  o  10G  1 0  -1  F I G U R E 2 6 a . DOWNWIND SPECTRA f 0 ( f ) . f o r RUN E l , 2242-2314, 26/6/1965. , THRUST ANEMOMETER © CUP ANEMOMETERS U = 9 7 1 cm s e c - 1 • 1. x = 2 0 6 cm U = 1 0 6 2 cm s e c A 3. x =' 2 8 6 cm AVG. WIND DIRECTION 276° § 4. x = 356 cm ^ 5 . X 3 = 446 cm 0 6. X 3 = 556 cm 1 1  3  1  5  3  3  f  f 0 (f) cm  -  2  sec  -2  o  2000  o  O o  O O  O <  x  1  1000  O O O X  x  X  x  X  &  &  A  &  A  O  A  o  A A A a  A  •  ^  A  A  •  •  • •  * o  A  *  G  A  •  • • • • E J O G J G J Q  V  V  •  •  V  57  •  •  •  _ -500 -2  L0G  1 0  I  J _  FIGURE 26b. C = U = U = x = AVG. D  5  3  THRUST ANEMOMETER SPECTRA FOR RUN E l  2242-2314, 26/6/1965. .0012 7 971 cm s e c 1062 cm s e c " 213 cm 0=193° WIND DIRECTION 2 76°  9 = 1.93*  - 1  1  O f Xf A f Qf V f  0-n' (f)  (f) 03 ' (f) 013' (f) 0 * (f) 02 2  3  13  f  f 0 n (f) '? -2 cm' s e c  2000  G  Oo  a  Oo  o  ©  G  °  o o o  o  o  U 500  L0G  -2  _L  i  T  DOWNWIND SPECTRA f0n (f) FOR RUN E2, 2314,2346, 26/6/1965. THRUST ANEMOMETER © CUP ANEMOMETERS U = 943 cm s e c - 1 © 2. x 3 = 226 cm U5= 1032 cm s e c " B 4. X 3 = 346 cm AVG. WIND DIRECTION 276° 5. x = 436 cm 6. Yg = 546 cm FIGURE 27a.  1  Q  3  1 0  f  f  0(f) sec 2  cm^  _  -  2000  ©  ©  0 O  O  ° G  0  O  O  1°  * x  *  x  * x  x  x  x  x  x  &  *  * O  8  x  o |  A  A A  A  Q  A -  •  y  U  Q  D  Q  Q  Q  Q  Q  *  ?  Q  Q  ^  y  O  -500  -2  _L  V  L_  I  FIGURE 2 7 b . =  .00112  THRUST ANEMOMETER SPECTRA FOR RUN E2 '"14-2346,26/6/1965.  IT = 9 4 3 cm s e c U = 1032 cm s e c " x = 203 cm 9 = 0.62° AVG. WIND DIRECTION 276° - 1  1  5  3  L0G  -1  f 0 f f f f  n  (f)  O  0 (f) X 0 '(f) & 0 «(f) • 0 *(f) v 22  3 3  13  1 3  10  f  ft£(f>  cirf sec  o  2  .8  - 600  u  f f  fl  f  f f f f  8 -400  ti  fl  8  o  (J  - 200  •1  *  *  V  • Q  - -2 0 0  •  B  * •  FIGURE 2 8 . SPECTRA FOR RUN K l 1528-1600  z  8/5/66  = .00102  U = 702 cm s e c -  = 422 cm  U  AVG. WIND DIRECTION 251°  - + 5 0 °  © o a  o  _ f _ L  D  PHASE ANGLE  9  5  = 0.0°  t a n " ( 0 */0 ) V t a n - ( 0^*/0i ) * 1  1  13  * **  1  = 707 cm s e r  12 u  -2  ^ kl y  • og,'of  °  i_  8'i  0  a  -2  C  f  fl  * * '* * * * * V  f  fl  A  *  (f) O A. 033 ( > %3 ( ) • fg*(f) (f) u 01U (f) 01U*(f) '*  t) O  8  fl  0U  0  log f l0  1  T" o  o crrfsec*  o  FIGURE 2 9 . SPECTRA FOR RUN Q l 1 8 3 0 -1902 12/5/66 cD = .00109  o  U  = 9.525 m/sec 9.76 m/sec 5 z = 413 cm .16 d = 9 = 0.0° AVG. WIND D I R E C . 260° U  =  R  1200  o  f f f f f  o _800  o  o  9 x  o x x o o  0 (f) 0 (f) 033 (f) 013 ( f ) 013*Cf) U  22  G X CD  f#(f) cm sec 2  FIGURE 30 SPECTRA FOR RUN Q2 1902 -1934 12/5/66 D = .00127  2  C  U  = 8.45 m/sec 8.68 m/sec 5 = z = 401 cm .19 d e = 0.0° AVG. WIND DIREC. 246° U  H200  R  =  d  o o3  8  0  u  o f 011 (f) f 0u (f) f 0iu (f)  o o  - 800  o  U  o  n A « o  f 013 (f) f 013*(f) f 0 *(f)  J  fl  8 fl )400  f 033 c n  (j)  0  A  ° A  A A  A  A  *  A  fl  n  k  a  o  fl *  fl  A  lu  (J fl  o u  ** * * * * * * *  fl  u  8  a  T  f*<f>  FIGURE 31 SPECTRA FOR RUN Q3 1934-2006 12/5/66 C = .0091  sec  —  D  U U z R  - 1200  d  8.28 8.31 383 .14  m/sec m/sec cm cm  e  —  ••- 0 . 0 ° AVG. WIND DIREC  o  233°  O  o  o  = = .= =  5  R fl  f 0?3 f 013 f 0u ?iu * 013*  0  •  U D  f  o fl © (J (J fl  f  0iu*  0  O 0  o  So n • 1  L 0  o "  "  •  A  A• • V  •  ^  h-200 -2 L_  A  A  /.)  0  A 0  fl  •  •  ^  a  y © ©  n  0  A  0  A  •  A  y © 0 tl t)0 O ^ O  0  * * * * * * * * *  A  A  A  A  A  «  B  I $  *  • J2_  0  _1_  iog.of  (  (  f*<f>  crrfsec  FIGURE 32 SPECTRA FOR RUN Q5 2308 -2110 12/5/66 C = 00149  2  D  V  0  o +  1200  O  5  =  R  0  4-  = 6.68  m/sec 6.91 m/sec z = 331 cm -.24 d e = 0.0° e» = -11.1° AVG. WIND DIRECTION 233° U  4 O  800  =  0  f 0, "11 < ) 033 ( ) f 013 ( ) f  f  9  f  0  f  f  t  ^ ( f )  f 0 *(f^ 13  0  O  A  o + 6 -400 A  A  A A A  Q  m  •  0  0  A  m  A  A  A  A i t r,  0  A  A  ^ ©  L_  JL  2  ©  •  •  •  Q  • • •  £3  ^ V • •  --200 -2  4A 4"T A 40 A  -I  0 JL  g  0  , + 0  Q • CO  fog.of i_  j -  f*cf> sec  2000  (>  o  <>  o  -1000  T  -  I I 5f  1  <>  o <D  A  A  A  A 1  Q  n  v  •  v ^  V  •  •  •  -2  D  U  U5 =9.76  m/sec  • • • • 0  'og.o  f  II  f  m/sec  z = 245 cm R =.146 AVG. WIND D I R E C T I O N 2 6 2 d  Q  r  FIGURE 3 3 . SPECTRA FOR RUN R l 2238-2310 12/5/66  = .00104  =9.17  •  g ;g§ as  y v  -I  i_  C  •  •  y  9 = 0.0'  jJJ (f)  f 013 (f) f 0 *(f) 13  A  • *  v e r t i c a l b a r s show 80% c o n f i d e n c e i n t e r v a l  f</>(f) 2  -2  cm sec  + o  1500  o +  © +  o +° o +  +  +  u  +  o  o  1-500  A  A  -A-  A  A  A  °  A  •V—"9—<r  •  A  ^  V  A  A  o o o _  A  -PT  •  A  +  • I  8  +  • •  B  ^  g  • a  • • a  •  Q  ^  --500  log, f 0  -I  -2 L_  0  FIGURE  34.  SPECTRA FOR RUN R 2 , 2 3 1 0 - 2 3 4 2 , 1 2 / 5 / 1 9 6 6 . U = 1 0 1 3 cm s e c " U = 1 0 9 4 cm s e c - 1 z = 225 cm R = .048 C = .00087 _ e'= 20.1° AVG. WIND DIRECTION 1  5  0  ,  +  f f  • S7  D  -  F  A  d  9  O  0  266°  0rT 0 ' 0 22  33  f.0 f  1 3  0 * 13  () f  (f) (f) (f)  (f)  5  S  ~  -a—E  -  1  n  1  — i — —  1  r  f^tf) cm s e c 2  °  2  o  o  o  o  o  1-2000  O  O  +  °  +  +  O  +  +  +  +  +  o  + ©  +  +  +  tiooct +  O  •+  © . o  &  A  A O  A  A  V  ^  •  (j O  ^ •  Q  •  •  Q  •  -2 r  Q  •  -i  I  L  C = .00114 U = 1069 cm sec-1 U5 = 1206 cm sec-1 z = 202 cm Rd = .032 AVG. WIND DIRECTION 266  • _ •  0  b  Q  •  o  . f 0 '(f) f 0 2*( ) 11  f  2  = 0.0° 0'= +15  •  I_l  D  ,  V  I  FIGURE 35. SPECTRA FOR RUN R3 2432-0014 12/5/66  f 0 3 3 (f) f 0 (f)  0  l g  f  A  .  .A  &  A A  ° Q -\  A O  +^  +  0 *(f) 13  _ o + A  •  9  •  r cm sec 2  r  2  _ 2000  -§ l  -  +  2  t*  O  +  00  +  +  A  A  A  A  A  A  A  O  V I  V  3  A  A  ^  A  A  A  „ A  A  ^  A  ^  A  •  •  •  •  •  O  •  E  •  Q  •  * « • • •  •  FIGURE 36. SPECTRA FOR RUN R4P014-0046, 13/5/66 U= 1140 cm s e c f 0u' ( f ) O U5=1285 cm s e c " f 022* (f) + 9 = 0.17° z = 185 cm f 033' ( f ) A e » - 17.5° C =.00083 f 0 (f) • AVG. WIND DIREC. f 0 * (f) V PHASE ANGLE (LOWER PORTION OF FIGURE.) t a n (0i3*/013) V 1  1  D  - 50"  13  o  2  7  0  13  - 1  ^7  0~  -9-  -2  -I  0  log f l o  TJ-B-  —  I  f<frf>  u  crrfsec U h 1500  o  2  u  U  U  o n  u fl ft ° ft  n o  U  u  FIGURE 37. SPECTRA FOR RUN S I 0124-0156 13/5/66 U = 1004 cm s e c 9=1.5t U5= 1114 cm s e c z = 158 cm CD = .00089 AVG. WIND DIRECTION 269' LEGEND AS BELOW  ftp  - 1  o  n  2  A 0  - -200  Q  o a  0  A  *  a  A  A  2  - u u  8  - 1000  o n 8  ft':  u  •  .•  *  ?  a  •  0  $ -6 a  l o g  A  1  i  6  a  f  011  (f)  'Eif 013'( ) V f 0i *( ) ftf 0iu ( ) U f 0U ( f ) * f 01U*(f) f  f  3  f  u  u o n  88  »I I »  e ° • o 2, Q, JL J  'o  Of  o o n o n o A  •f;'f  a  •  T  o © n n  -500  •  n  Q  a  2  FIGURE 3 8 . SPECTRA FOR RUN S2 0156-0228 13/5/66 U = 892 cm s e c - 1 9 = 1.58' U5= 974 cm s e c - 1 z = 155 cm Cp =.00082 AVG. WIND DIRECTION 271°  f^(f) crrfsec  ft  ft  A  T  i  o  -I  -2 i_  1  A  * „ * * *  A  Q 0  - 1  F- 500  u  0 EI  •  • Q  °0 L  a o  e  § ?g °  u A O  o o n -o- -a—B-4  o cm sec 2  40 2  h 150  i! •  o o  •  J00  ^  W  G  y  U  U  U  8 « 8  I lit  I 'e g,  •  f  1.5  '°9  i.5  iofl ;  f | 0  9 •  FIGURE 39. SPECTRA FOR RUN F2, 29/6/1965. THRUST ANEM. X-WIRE, U-WIRE. 2049-2121 2039-2122 "5C U = 320 cm sec-1 z = 110 cm , LEGEND AS BELOW C = . 00092  o  O 2  cm sec  -2  -150  o  u  o - 100  FIGURE 40. SPECTRA FOR RUN F3, 29/6/1965. J = 313 cm s e c z - 120~ cr THRUST ANEM. X-WIRE, U-WIRE 2121-2153 2122-2206 G f 0 i i (f) • U -50 A f (f) A  INSERT (UPPER RIGHT) EXTENDS GRAPH TO HIGHER FREQUENCIES.  <4>  - 1  O ^n=  f 013 ( f )  .'0Q083J  • s—-  t<  S A  A &  FIGURE 4 1 . SPECTRA FOR RUN A r , 1 0 3 5 - 1 1 0 3 , 15/2/1964 C = .00164 ( A n a l o g , .0109-8 c y c l e s ) .0016 ( D i g i t a l , .005-7 c y c l e s ) . .0020 ( D i g i t a l , dc-7 c y c l e s ) U •= 840 cm s e c - 1 z = 760 cm WIND DIRECTION 090°  f'0(f)  m /sec  8  D  o  LEGEND  3000  ANALOG ANALYSIS (6=3.56°)  ©  DIGITAL ANALYSIS 0=3.5°)  o  f f 022'(f) . f 033'(f) f 013'(f)  A  B  • e X  A  2000 © o  -1000 x  #x *  °  ©  x  o o A£*  X ^ A 5  AA ^AA  A  h-50(P-2  A  A  A  ,  -,i  »  0  log,/  1  FIGURE 42 3.  Kl  O  01  •  Q2 03 Q5 Rl  * A <&  O  THE NORMALIZED DOWNWIND SPECTRA.  + R2 VR3 • R4  esi  <>S2  FIGURE 42b. Kl Ql  O ©  Q2 X Q3 A  THE NORMALIZED DOWNWIND SPECTRA^ PLOTTED VS logic- k. Q5 R l R2  <t>  O +  V R3 R4 © SI O S2 0  FIGURE 4 3 . Kl Ql  O  Q2  X  •  Q3'A  T h e NORMALIZED V E R T I C A L V E L O C I T Y SPECTRA.  Q 5  Rl  R 2  X +  O  ^7  •  e  O  R  R3 4  SI S2  9  «13  I—.00  Kl  0  Q5  Ql Q2 Q3  X  R2 R3  <i> -4-  • Rl  •  --.20 6  o o  I  A  * o ® -,€0  o A  O  O  X  A  6  \7  4  O A  1  o O  6  *  6  +  di  a  o  log, 10  f  0  •  0  2  _L_  —r  FIGURE  44. T  _J_  _L THE NORMALIZED COSPECTRA R T —i 1 r T  =  1 3  Co  0i (0ii033)~ r  s  3  1  r  THRUST ANEMOMETER « RUNS WITH ACCURATE L E V E L L I N G . C ' AFTER V E R T I C A L ROTATION D  K.002  0.2  Q»5 B«2  F.I  E«1  Q®2  R©3  E.2 J.4  -.001  0.5 F*2 F »3  J.S 0.lj. |* 6*1 J2*°._ J 0 J  3  K«l  Q®3  si  R®2  s-2  R4'  G.O G'3 6 .2  200  400  600  800  1000  u  5  (  c m  I I L JL I FIGURE 45 DRAG COEFFICIENT OF THE SEA SURFACE FROM 33 RUNS o f 32 MINUTES DURATION.  sec  "') I  RUN Q l  1830-1902  12/5/66  FIGURE 46 CONT'D TIME VARIATION OF SPECTRAL ESTIMATES RUN Ql  1830-1902  12/5/66  r:::-.:»:~n !•::!• il::' .li.  j—|  f =0.062  m :|:.TI  b-:|-::.: -:r::|:-:.:::  i....  •1  ::":  p •.: :i:  r .11 •  *F  II  :":::V:  lifi.;  I  i :::.!  mm  f  =0.088  f  =0.125  f  =0-.177  11111  .-I  cycles Sec  FIGURE 46 CONT'D  0»  TIME VARIATION. OF SPECTRAL ESTIMATES RUN Q l  1830-1902  12/5/66  .:!:. i...  I«i iiii  THT Trrr .iii!.  ;;IT  :::( Y'x.  i i" .! 1...  iiii -ii^i  i  ::::  d  ft:  i...  f =0.25  .. ; i  i.iiii. ;;|. ii TT|;;;;  :! vi  :  '»• •  1  iiii  iiii Hi!II! lit; i ill! til w ;| iff !!]! iiii  1  if lih  iii ti.!i • 1 ' • • :} .' -| t •J!  i.j |;i]i:  If tiif  ii!: li-li  :;:'.)•  i'ii jifi " i ;•!!}  1 W1  til: •J.  •it;  1!T hi.:  :••:! 'A 1  :  f =0.35  ii.^  m  :§  1  ::!:  ! •  l  I  iii.i  1  1  }  C-.i:l;:r:l:  Ti!  ;  •i iii-i •if  1  iliH  i-ii  f =0.50  s ft-T1  0,3  FIGURE 46 CONT'D TIME VARIATION OF SPECTRAL ESTIMATES RUN Ql  1830-1902  12/5/66  ^0' -rrr •:;i .i:;:; Li.:.:_  ~r:~\ :  (u.  U j  (cm  100  )  «  sec"^)  "80  % O  6 0 -60  40  I 20  0  5  5 K1  Q3  i  i  R3 R2  Rl  U ( c m sec') 5  200 I  FIGURE 4 7 .  O #  T^T) * 5  400  600 L_  I  800 L  I000  _ J  I200  MEAN V E L O C I T Y PRODUCTS AS A FUNCTION OF WIND SPEED FOR THE RUNS K l , Q l , Q2, Q 3 , Q5, R l , R 2 , a n d R 3 . SUMMATION OF SPECTRUM JZTT)^ WIDE-BAND ANALYSIS • |  (u,  )X  u 3  SUMMATION OF SPECTRUM A, WIDE-BAND A N A L Y S I S A  SUMMATION OF SPECTRUM WIDE-BAND ANALYSIS  1_  I  I  TIME 1 1  U1M/SEC)  RUN  RELATIVE  E,&E  2  26/6/66  DIRECTION  hSO°  h-50° FIGURE 4 8 . WIND SPEED ( 1 MINUTE AVERAGES) AND DIRECTION.  -50°  I  I  RELATIVE  DIRECTION  RELATIVE  DIRECTION  l  T  I  --50° FIGURE 49. WIND SPEED (1 MINUTE AVERAGES) AND D I R E C T I O N CONTINUED.  TIME 2352 k30  0002  RELATIVE  0012  0022 I  0042 I  0032 i  DIRECTION  -30  . k  RUN  Si &;S  2  13/5/66  n \  4 !in< Vl I  1-9 U(M/SEC) TIME  h50  0134 0144 ' V 0154 I f I RELATIVE DIRECTION  1—30 FIGURE 5 0 . WIND SPEED ( 1 MINUTE AVERAGES) AND DIRECTION CONTINUED.  1  FIGURE  51  TIME V A R I A T I O N OF V E L O C I T Y PRODUCTS RUN K l  1528-1600  8/5/66  FREQUENCY .0039 t o 4.0 H z .  m x x m  m  rr.1.;-:!tT4.  •m ffiil  ffttfi u„  u  tit  tJilitt.: iii I  . ...i:  - ,p 1H tflrii tl jjll ..J :: rl  ::•:!:  •i  IT  u  'iH  ii f l  " r* '' r  f.:. ~!7J:  *Mi>. ""iffi T  fff  iU lt;l i  V" it  li 4a  ITT ' 1  itU  i ; !'i I .;;!:;!:(  Hit -i (• ff: *  4-  !! ' i I  ! f!  : :  :  |  lilt Ti -fl::::' [J::  )U  H i If  1  s1|  f  #  ^ifl^ ! •::•!( i  :$  lilt  w  trt-r  iff  : i  •Hi jit:  fi;  w v  111  Vs  ft-y. .: VV IT.. .  <•... .  :T::t  Si FIGURE 52 RUN Ql 1830-1902 12/5/66 TIME VARIATION OF VELOCITY PRODUCTS  FIGURE 53 RUN Q2 1902-1934 12/5/66 0039 to 4.0 Hz  TIME V A R I A T I O N OF V E L O C I T Y PRODUCTS  0 0 3 9 t o 4.0 H z .  FIGURE 56 RUN R l 2238-2310 12/5/66  TIME V A R I A T I O N OF V E L O C I T Y PRODUCTS  FIGURE 57 RUN R2 2310-2342 12/5/66  .0039 t o 4.0  Hz  TIME V A R I A T I O N OF V E L O C I T Y PRODUCTS  0039 t o 4.0 Hz.  FIGURE 60 RUN SI 0124-0156 13/5/66 TIME VARIATION OF VELOCITY PRODUCTS  FIGURE 61 RUN S2 0156-0228 13/5/66 -  .0039 to 4.0 Hz  A A  A,  P.j  A  4  cm sec  &  i  x  §  f0 Cf) x 2 9  fG)3g(f)  o FIGURE 62.  f0n(f)O  A  A  F013(OB |-f | l o g l Q f  i  NOISE SPECTRA OF THRUST ANEMOMETER IN WIND TUNNEL, U=292.  T (f)  T  T  T  f0 (f) O f022(f) X f0 (f) A  cm' sec -2  0 A  1 1  6  3 3  f013(f)  •  x A  A A  A  *k  X  x  0  8 — •  -L=J_ FIGURE 63.  NOISE SPECTRA OF THRUST ANEMOMETER IN WIND TUNNEL, U=412.  T f cm  0  a—e—B-  T  T  T A  sec -2  f0 (f) n  0  O  f022(f)* f0 (f) & f013(f)Q 3 3  JO  X  A  X A  A  x A  A  A A A.  A  X  x  x  X  0  O B  FIGURE 64.  O  n  0 B  0 B  *  0  _Q—a  Q  X  0  Q—a.  NOISE SPECTRA OF THRUST ANEMOMETER IN WIND TUNNEL, U = 583 cm s e c 1  1  1  1  1  1  f f (f) -2 cm sec  —  r~ A  —  _30 A f f f  0U 022  f 013  (f) © (f) X (f) A ( )  •  f  _20  A A A  —  X  X A  A  X  A  X  X  A X  JO  A  X A X X  A  O  X  * t oft {1  O UJ  y—Rl  ID  O  X  © © —n  m-  UJ  © n  Id  0  O  ©  X  ©  Pi  0 Q  ©  ui  X  O  0 R  X  O  n  r-i  U  U  •  •  o  ©  •  u log  -1 1 FIGURE 65.  1  0 1  1  1 0  f  tl 1  NOISE SPECTRA OF THRUST ANEMOMETER IN WIND TUNNEL., U = 825 cm s e c " . 1  FIGURE 6 6 .  INDIRECT DETERMINATIONS OF u * OF -IVjUg.  2  VS DIRECT DETERMINATIONS  I  F 3 C  D  .004  -  O O O  DIRECT DETERMINATIONS FROM MEAN V E L O C I T Y PROFILES FROM DOWNWIND SPECTRUM f 0 ( f ) 1 X  .003  O  F2  9D2  O -  0 I  .002 D2  o  •°  d 2  Q5  PI*  OD3  9  0 5 0  R  _  r '  ;i2o r .  K  D3  F2  9  F  ^  °3  F3  •  • J2 J2  *  ' »  ®  02 9 Q2  00  2  (».RI  °i  #  °  Q3  Q3  °  R  »  2  R  Z  63  o 63  Ug  200  <•  __]  FIGURE 6 7 a .  400  |  600  I  800  I  1000  I  INDIRECT AND DIRECT DETERMINATIONS OF THE DRAG C O E F F I C I E N T OF THE SURFACE OF THE SEA.  (cm  sec  - 1  )  FIGURE 6 7 b .  DETERMINATIONS OF THE DRAG C O E F F I C I E N T OF THE SURFACE OF THE SEA BY VARIOUS WORKERS  a  R  5R -5(e  R e  (  +e ) 2  2°—VvV  Jw R C,  fo e  e,  R  (jwR, C, + l ) ( j w R C + l ) 0  ~RCJ  o—'VvV  FIGURE  0  =  6 8 . OPERATIONAL A M P L I F I E R  t '  CIRCUITS:  a. F e e d b a c k n e t w o r k b . D u a l - i m p u t DC a m p l i f i e r ^ c. Band-pass a m p l i f i e r d. I n t e g r a t o r  g a i n -5  6  d  t  0  c  READ L I S T OF FREOUENCIES Awn r.RAPH SYMROLS  (  READ RUN NAME AND 0 i j fOR ONE RUN  DO LOOP  CALCULATE  *\  J  T H £ T A  1  DO LOOP  CALCULATE 033' and 0 i ' 3  1 DO LOOP  CALCULATE U1U3  c  PRINT OUT HEADINGS  J  BLANK L I N E AND INSERT HEADINGS  <45O<0 <2O5tK^_ML 11  YES CALCULATE POSITION OF 0 ON GRAPH 1 : I  NO  CALC. POSITION OF 033 on GRAPH NO  CALC. POSITION OF 013 on GRAPH  (^ww^r  graph  )  FIGURE 6 9 . FLOW DIAGRAM OF D I G I T A L PROGRAM FOR VERTICAL ROTATION OF COORDINATES.  DIMENSION  A ( 2 5 ) , B ( 2 5 ) , C ( 2 5 ) , A P ( 2 5 ) , C P ( 2 5 ) , B P  DIMENSION  LINE(50),NAME  REAL  C  FORMAT READ READ  8  ( F R ( I ),1 =  1,25)  (10F8.4)  SYMBOLS DATA  C  FOR  PLOT  BLANK,DOT,DOWN,CROSS,VERT/IH-,1H+,1H0,1H*,IHA/  RUN  NAME  READ(5,30)NAME  30  FORMAT  (12A6)  10  READ ( 5,  1 M A I I ) , B ( I ) , C ( I ) , I = 1, 25 )  1  FORMAT  (  THETA= DO 7  9F8.1) 0.0  7  1=1,5  THETA  =  THETA  1(0.4948  4  *  =  (COS(THETA))**2  =  (SIN(THETA))**2  G  =  SIN12.0*  THETA)  H  =  G0S(2.0*  THETA)  4  +  0.25*B(I)*F+  0 . 5 * C ( I ) * G  +  4 . 0 * A ( I ) * F  2 . 0 * C ( I ) * G  25  I  =  1HI, 12A6/1X.9H  ,'F9.3,  =  ,F8.5 ,8H a  R A D I A N S , 8X , 8 H  F011  FREQ.  200  F033  F013  , 6 X , 4 H - 5 0 0 , 8 X , 1 H 0 , 1 5 X , 6 H  F O i l '  1=1,25  103  J = l , 5 0  IN  MARKERS  L I N E ( l ) DO  =  110  K  LINE(K)  COMPUTE  AND  SET  ZERO  DOT =10,50,10  =  DOT  SUBSCRIPTS  I F ( ( A P ( I ) . G E . 2 0 4 9 . 9 ) . O R . ( A P ( I ) . L E . - 4 4 9 . 9 ) ) L  =(  API I ) /  LINE IF M  (L)  ((BP( =  =  =  ( C P ( I ) / 5 0 . 0 ) (N)  85  +  GO  TO  95  10.0  =  +  TO  105  10.0  CROSS  CONTINUE FORMAT  A l I ) , B ( I ) , C ( I ) , A P ( I ) , B P ( 1 ) , C P ( I ) , F R ( 1 ) , L I N E  ( 1 H 0 , 6 F 9 . 1 , F 9 . 4 , 7 X , 5 0 A I )  CONTINUE GO  9  TO  VERT  WRITE(6,5) 200  GO  10.0  DOWN  IBPII 1/50.0)  LINE  5  +  I F ( ( C P ( I ) . G E . 2 0 4 9 . 9 ) . O R . ( C P ( I ) . L E . - 4 4 9 . 9 ) ) G 0 N  105  50.0)  I ) . G E . 204k9. 9 ) . O R . ( BP ( I ) . L E . - 4 4 9 . 9 ) )  LINE(M)= 95  F033«  1,000,12X,5H2,000)  LINE(J)=BLANK  PUT  85  Ull  )  LINE  DO  110  THETA  '8HCM2/SE<;2  (6,3)  F013•  BLANK  103  C  0.3466*CP(I)  FORMAT(63H0 DO  C  +  (6,35)NAME,THETA,UIU3  WRITE 1  C ( I ) * H  1,23  UIU3  FORMAT(  3  *•  0.0  =  WRITE =  -  0 . 2 5 * ( B ( I ) - 4 . 0 * A ( I ) ) * G  =  UIU3  13  +  1=1,25  BP(I)=B(I)*E  DO  (1.0  ) ) )/C( I ) )  AP(I)=A(I)*E  U1U3  35  ( ( 0 . 4 * C ( I > ) / ( 4 . 0 * A < I ) - B ( I ) ) ) *  F  CP(I)=  25  +  SQRT(A( I )*B(I  E  DO  C  ),FR(25  LINE  READ(5,2) 2  I 25  (12)  TO  8  STOP END  FIGURE  70. D I G I T A L PROGRAM FOR VERTICAL ROTATION OF COORDINATES.  FIGURE 7 1 .  a. f 0  W  THE WAVE SPECTRUM (FROM GILCHRIST, 1 9 6 5 ) U = 600 cm s e c - 1 , WIND DIRECTION 102°  (f) vs. log f? 1 0  b. l o g  1 0  0 (f) vs. l o g w  1 Q  f  FIGURE RUN AR THETA  72. 1 0 3 5 - 1 1 0 3 1 5 / 2 / 6 4 U= = 0 . 0 6 2 2 0 RADIANS  F011  F033  F013  840  CM/SEC U1U3  Z =  = 7 6 0 CM -1602.915GM2/SEC2  (-lift F O l l '  F033«  J%*..otof  U i Sx)  F013'  FREQ.  -500  1,000  5320.0  30.0  250.0  5315.0  , 50. I  -411,1  0.0039  *  3720.0  54.0  140.0  3714.4  76.5  -321.0  0.0055  •  3400.0  200.0  -130.0  3379.0  284.0  -544.7  0.0078  1960.0  174.0  140.0  1961.3  168.9  -98.9  0.0109  3000.0  170.0  41.0  2991.1  205.5  -326.3  0.0156  2420.0  173.0  6.4  2411.2  208.1  -288,6  0.0220  1890.0  157.0  17.0  188 3 . 9  181.4  -212.8  0.0310  +  *  +—A  1550.0  166.0  -26.0  1542.6  195,8  -213.0  0.0440  +  *  +—A  1210.0  171.0  -119.0  1198.1  218.6  -262.9  0.0620  +—*  1270.0  222.0  -108.0  1258.6  267.6  -257.9  0.0880  1030.0  2 70.0  -126.0  1018.5  316.1  -244.5  0.1250  1024.0  348.0  -111.0  1013.5  390.0  -226.4  0.1770  956.0  353.0  -132.0  944.5  399.2  -238.7  0.2500  924.0  344.0  -151.0  911.4  394.4  -253.8  0.3500  <•—*  673.0  387.0  -108.0  664. 1  422.7  -178.7  0.5000  +  678.0  429.0  -79.0  670.9  457.4  •149.2  0.7000  +  « —  532.0  426.0  ^69.0  526.1  449.7  -121.3  1.0000  F  *—+  438.0  382.0  -50.0  433.6  399.7  -92.1  1.4000  +  394.0  372.0  -23.0  391.4  382.4  -60.2  2.0000  -*-+  A-  362.0  2 54.0  -23.0  359.4  264.3  -59.9  2.8000  •*-+  A-0-  213.0  234.0  -16.0  211.4  240.4  -35.0  4.0000  --* + - — A — —  173.0  203.0  16.0  173.5  200.9  0.7  5.6000  +  145.0  170.0  -16.0  143.6  175.6  -28.6  •8.0000  •  — - O A  116.0  134.0  -10.0  115.1  137.8  -20.2  11.3000  >  »+-A  76.0  143.0  0.0  75.8  143.6  -5.0  16.0000  2,000  --+A +A—  -0«-  -+  *  -3—•  +-  A  +  A--+  +  A-  +—0  A* —  3  A-O —  -  +  +  A0-+  *—OA  -*+0A-  • — — + — •  —  FIGURE 73 RUN 60 THETA  1 8 4 4 - 1 9 3 2 2 4 / 7 / 6 4 U= = 0.03070 RADIANS  F011  F033  F013  492  CM/SEC UIU3  F011-»  U5= 5 6 0 C M / S E C Z = 1 5 0 = -268.914CM2/SEC2  F033"  F013*  CM  FREQ.  -500  0  1,000  135.0  1.9  2.1  134.9  2.1  -6.2  0.0039  171.0  1.9  2.9  170.9  2.2  -7.6  0.0055  345.0  2.7  2.9  344.8  3.6  -18.2  0.0078  510.0  4.2  4.6  509.7  5.6  -26.6  0.0109  769.0  6.9  7.6  768.5  8.9  -39.5  0.0156  657.0  7.6  15.0  656.8  8.2  -25.2  0.0220  446.0  10.7  2.0  445.6  12.1  -25.2  0.0310  682.0  14.5  -0.6  681.3  17.1  -42.2  0.0440  584.0  16.8  -2.4  583.4  19.3  -38.0  0.0620  554.0  22.4  -7.3  553.3  25.4  -40.9  0.0880  536.0  28.7  -24.3  534.8  33.7  -56.7  0.1250  +  * - A  0  547.0  42.4  -34.3  545.4  48.6  -67.2  0.1770  t  * - A  508.0  62.2  -31.7  506.6  67.9  -61.9  0.2500  402.0  75.3  -31.3  400.7  80.6  -54.8  0.3500  340.0  81.8  -32.5  338.7  87.0  -52.0  0.5000  298.0  81.6  -33.0  296.7  86.7  -50.0  0.7000  285.0  92.8  -29.7  283.8  97.4  -45.7  1.0000  232.0  103.7  -26.6  231.0  107.7  -39.2  1.4000  182.0  140.4  -23.6  181.1  143.9  -32.6  2.0000  140.0  89.0  -15.7  139.4  91.4  -22.9  91.0  67.5  -8.2  90.7  68.8  63.0  40.4  -3.6  62.8  43.0  51.7  -1.9  0.0  0.0 0.0  0.0  +  * A —  0—-+  -  •  +  +  •  +  0  +  *  •  +  •  *•  ;  *  •  *+A  2.8000  •  «+A0  +  +  +  +  -12.7  4.0000  *•  *+A  +  +  •  +  41.0  -6.8  5.6000  +  *A0—  +  +  •  +  42.9  52.0  -3.7  8.0000  +  *  +  +  0.0  0.0  -0.0  0.0  11.3000  +  *  +  +  +  •  0.0  0.0  -0.0  0.0  16.0000  •  *  +  +  +  +  0  A  0  +  2,000  •  +  riT"B l 2CC0-20 32 24/7/64 U = 576 CM/SEC U5= 670 CM/SEC Z=l33 CM THETA = C. 01295 RACIAfiS U1U3 = -232.626CN2/SEC2 74  FC11  F033  F013  FOll*  H033'  F013'  FREC.  -500  1,000  48.C  3 .8  --3.3  47.9  4. L  -6.5  0.0C39  -*A-  51 .C  3.7  -5. 1  50.9  4.0  -6.4  0.CC55  — *A0  219.C  5.3  -11.3  218.8  6.0  -16.9  0.0078  — *A  176. C  5.1  •- 10 . 5  175.8  5.8  -15.0  0.0109  — «A—0  19 7.. C  7.5  -15.9  196.8  8.5.  -20.9  0.0156  — *A—0  215.C  10.9  -24.2  214.7  12. 3  -29.7  0.0220  — *A  0—  249. C  17.9  -30. 1  24 8.6  19.6  -36.4  0.0310  — *A  0—  254. C  21.7  -33.4  253.5  23.6  •39.8  0.0440  *A  241.C  28.2  -43. P  240.3  30.9  •54.(5  0.0620  *-A  0  245.C  3 3 . ti  -5 1.1  244.3  36.6  •57.2  0.0880  *-A  0  193.C  46.8  -51.1  192.3  49. 6  -55.8  0. 1250  -*-A—0-  156.C  52.2  -38.9  155.5  54.3  -42.6  0.1770  —*+A-0-  160.C  68.3  -44.2  1 59.4  70. 7  -47.9  0.2500  —*+A-0-  146.C  76.3  -39 . t  145.5  78. 4  -42.4  0.3500  -*+A0-  1 37. C  81 .8  -35.6  136. 5  83.7  -38.6  0.5C00  -*+A0-  104.C  86. 1  -35.5  103.5  88.0  -37.6  0.7CQ0  -*+A0-  102.C  99 . 1  -31.3  101.6  ICO. 8  -33.3  I.OOOO  — *+-A-  8 3.1  LO 1 .3  -23.7  82.7  102.8  -30. 2  1.4CC0  —*+0A-  63.4  t! 6 . 6  -23.1  63. 1  87.6  -24.2  2.0C00  — * + A—  44.3  7 1.2  -14.7  44. L  72.0  -15.4  2.8000  — *0A  30. 4  57.7  -8 . 2  30. 3  58. I  -8.7  4.0CC0  —*0A  2 2.9  38. 7  -5.5  22.8  3 9.0  -5.8  5.6000  — *A—  54.2  -4.7  21.2  54.4  -4.9  3.0000  — *0A-  0.0  0.0  0.0  -0.0  0.0  11.3000  CO  CO  0.0  -0.0  0.0  16.0000  21.  i  0. C 0.0  * —  0  0—  2,000  FIGURE 75.  RUN H2 2C32-2104 24/7/64 U= 484 CM/SEC U5= 560 CM/SEC Z= 143 CM TrETA = 0.0940b rfACIANS U1U3 » -435.037CM2/SEC2 FCll  F033  230. C  ,  (-013  LiLii  F0L1'  <L*h  22S.4  FC33*  F013'  74.0  FREC.  -37.7  0-0039  -500 «A  254.C  17.0  12. 5  253.0  21.1  -34.4  0.0055  L86.C  25.0  17.1  186.C  24.9  -16.8  0.0078  340.0  1 7-r  -<<2.2  0.Q1Q9  531.C  16.0  -69.7  0.0156  275.C  19.0  1.3. C  2 73. b  23.7  -37.fi  0.0220  23P.C.  3C.n  in. 5  J36.1  37.7  -51.5  Q.P31Q  572.C  35.0  30.0  569.e  43.6  -75.8  0.0440  440.C  35.0  -23.0  434.0  58.8  -i03.2  0.0620  492.C  4 P . c  no.a  -131.5  o.oaao  443.C  62.C  -29.2  436.5  88.0  -108.6  0.1250  -*—+ A-  354.C  71.0  -25.0  34P.3  93.7  -91.4  0.1770  — * - + A-  3QF.C  K4.0  --jl.i  302.5  126.0 -84.4  0.2500  287.C  123.0 -31.1  263.0  14?.0 -34.2  2CC.C-  136.0 -29.7  195.8  193.0  145.0 -23.0  150.0  147. C  lie.C  135.0 -13.C  ?n.«8  339. C  20.4  529.1  7 1 -l) 23.6  - 4 ? . 5483.8  - * A — 0 -  «*-«A-  -*-A-  - »  -*-+-A—0-  -75.9  0.5000  -*-•—A-0-  153.0  -60.2  0.7000  -»-•—A  189.5  159.1  -51.9  l.OCCO  147.0  159.2  -42.7  1.4C00  -28.5  7.0000  1 16.Q  149.6 167.8  142.8  ua.c  -5.2  85.0  121.9  -15.7  2.80C0  -*+0A-  54.C  88.0  -1.6  53.6  89.7  -7.6  4.0000  -* + A —  3P.C  53.C  37.7  54.2  -5.5  5.6C00  -»0A-  -*0A-  81.0  -1. I  35.8  82.0  -4.0  8.0000  C.C  C.C  o.c  0.0  -0.0  0.0  11.3000  C C  CO  Q-Q  -0.0  O.Q  16.0C00  CATA CARCS EXHAUSTED. EXECUTION CCMPILE T1ME CHJECT PRCG  87C0 615  —  -*.-0 A-  86.c  36. C  - + 0-  -0 + -  0.3500  257.8  -21.  0-  -78.2  281.8  2,000  1.000  — *—  TERMINATED.  TOTAL TIME DATA STORAGE  18166 255  AVAILABLE CORE  10547  SYMBOL TABLE  320  FIGURE 76. RUN 01 THETA FOll  F033  F013  "  :  425  :  '  CM/SEC UIU3  FOll*  '  —  ^  F033«  *  :  U5= 4 9 5 C M / S E C Z = 1 4 7 » -220.674CM2/SEC2 F013'  :  :  CM  FREQ.  -500  0  1,000  122.0  15.0  11.9  122.1  14.5  -9.0  0.0039  +  *A-0  +  108.0  . 6.3  -0.6  107.1  9.8  -19.2  0.0055  «•  *A-0  181.0  4.6  9.0  180.4  7.0  -22.6  0.0078  •  *A—0  193.0  4.3  16.0  192.9  4.6  ^TTTS  0.0109  +  *A—0  15.1.0  6.2  14.3  151.1  5.8  -12.1  0.0156  + — — — *A—0  +  151.0  7.0  12.6  151.0  7.2  -13.7  0.0220  +--  • —  872  679  172.3  11.1  -23.1  0.0310  +  *A—0  +  177.0  9.8  -0.6  175.6  15.4  -31.1  0.0440  •—-->  * A - - 0  +  181.0  13.3  -1.8  179.5  19.4  -32.9  0.0620  +  *A—0  +  193.0  19.0  23.8  -30.2  0.0880  •  * A ~ 0  205.0  17.8  -40.2  199.9  38. 1  -74.7  0.1250  +  186.0  36.5  -15.2  183.3  47.3  -45.9  0.1770  +—  184.0  43.1  -17.8  181.1  54.7  -47.8  0.2500  *  167.0  62.4  -23.4  163.8  75.3  -49.5  0.3500  +—  130.0  72.1  -21.6  127.2  83.1  -40.9  0.5000  129.9  95.7  -24.5  126.9  107.5  -42.7  113.0  110.0  -20.5  110.5  119.8  104.0  129.0  -23.6  101.4  79.0  111.5  -21.0  60.4  102.0  48. 3  105.0  69. I  127.0  0.0  173.0  -  "  1 8 2 4 - 1 3 5 6 2 3 / 7 / 6 4 U= = 0 . 0 8 7 9 3 RADIANS  :  278"  :  191.8  '•  — * A — 0  —  2,000  •  «••- —  •  — •  *  *  •  •  •  «•  +  • —  *•  — •  •  *  •  +  <•  — +  ;—  —  — + -+— =  —  -  +  +  —+  +-  • — •  *•  +  •  — +  * - A — 0  +  -+  - * A — 0  +  -+  *+A-0  +  -*+A-0  +  +  * + A0  •»•  0.7000  +  * +- A  •  ;+  -35.1  1.0000  +  *+-A  +  +  +  +  139.5  -35.8  1.4000  +  * +- A  +  •  «•  +  76.8  120.4  -29.6  2.0000  +  *+0A  +  «•  +  -13.3  59.0  107.7  -19.2  2.8000  +  *+0A  •  +  -3.2  47.9  106.8  -7.0  4.0000  +  *0-A  +  +  979  69.7  124.7  3.2  5.6000  +  *0A  +-  0.0  0.0  0.0  -0.0  0.0  8.0000  +  *  0.0  0.0  0.0  0.0  -0.0  0.0  11.3000  +  * -  +  oTp  o.o  o76  oTo  -o.o  o.o  16.0000  +-  *  +  r  +  ••  +  +  «•  +  v  +  + +  —+  •  - - + •  :  *  :  — - +  +  +—  :  + +—  +  •  •  +  -••  +  ••  •  +  f*TJW D-2 r8 5 6 - l 9 2 8 2 3 / 7 / 6 * U= 337 CM/SEC U5= 395 CM/SEC Z=144 CH THETA = 0 . 0 6 9 9 1 RADIANS U1U3 = -251.800CM2/SEC2 R  77  FOU  F033  F013  F011'  F033'  F013*  FREQ.  -500  0  1,000  132.0  16.5  379  131.6  17.9  -14.0  0.0039  *A-0  •  288.0  7.1  8.0  287.2  10.5  -32.0  0.0055  *A  316.0  7.5  8. 1  315.0  11.4  -35.8  0.0078  +  *A  218.0  979  iT5  217.3  12.6  -24.6  0.0109  +  *A  151.0  6.1  7.0  150.8  7.1  -13.9  0.0156  *•  *A—0--  190.0  6.9  2.9  189.3  9.8  -23.4  0.0220  +-  *A—0  188.0  10.8  -4.1  186.8  15.6  -29.9  0.0310  •  *A—0  219.0  13.5  -2.4  217.8  18.4  -32.4  0.0440  •  *A  0  235.0  16.8  -4.8  233.5  22.6  -36.9  0.0620  *  *A  242.0  22.8  771  241.4  25.2  -25.2  0.0880  +  241.0  12.9  -33. 1  237.5  26.8  -65.9  0.1250  233.0  4.9  -12.1  231.0  12.8  -44.3  259.0  80. 7  -19.0  256.5  90.7  233.0  98.6  -19.2  230.6  183.0  106.0  -28.7  167. 1  122.0  151.0  2,000  •  •  •  -•  *  •  •  *  •  •  •  •  •  +  •  *•  •  •—•  •  •  *  +  *•  •  +  •  *•  •  0-  •  •  — « -  •  *A  0  +  +  •  •  *-A  0  +  •  •  •  0.1770  •  *A  0  +  •  *•'  «•  -52. I  0.2500  •  »-+A  +  •  *•  •  108.0  -48.1  0.3500  •  +  •  180.2  117. 1  -50.2  0.5000  +  «•  +  -35.9  163.9  134.7  -54.6  0.7000  • —  •  •  135.0  -33.7  148.1  146.7  -49.7  1.0000  +  *+-A  +  •  +  •  135.0  162.0  -28.5  132.6  171.8  -41.4  1.4000  +  *+-0A  +  +  f  •  88.2  142.5  -25.9  86. 1  150.7  -33.0  2.0000  +  * + 0-A—r  +  +  69.4  132.0  -16. 3  68. 1  137.3  -21.2  2.8000  +  +  +  56.8  139.0  -3.2  56.5  140.3  -6.2  4.0000  •  84.8  163.0  14.5  85.6  159.8  871  5.6000  +  *0-A———>  0.0  0.0  0.0  0.0  -0.0  0.0  8.0000  +-  *  0.0  0.0  0.0  0.0  -0.0  0.0  11.3000  •—:  *  0.0  oTo  oTo  oTo  -o.o  6T6  16.0000  —  *  0  «• 0  •  0  :  0  »+-A-0 •  AO— *-+-A0  •  -*+0A * + 0A  •  -  +  —'•—+ +— : —  —  •  •  :  — *  • «-  • •  ««•--  +  •  ••  +  +  •  •  +  +  + + +  •  *• •  + — +  ^5ft% U  THETA  7  |q28-2000 *  23/7/64  0.12263 F033  FOll  335.0  U=  F013  13.1  375 CM/SEC  RADIANS F O l l '  54.2  U5=  U1U3 =  ill  F013«  F033'  336.6  CM/SEC  Z=141 CH  -177.047CM2/SEC2  6.6  FREQ.  -28.0  -500  0  1,000  0.0039  •  *A  0  o-— + o—+  53.6  322.7  1.7  -25.4  0.0055  +  #ft  61.7  351.3  3.2  -24.1  0.0078  +  *A  9.0  47.6  288.5  2.9  -23.0  0.0109  +  »A  0  347.0  7.1  39.7  346.7  8.5  -45.3  0.0156  211.6  5.8  22.7  210.6  7.3  -28.9  0.0220  +  *A  3—  213.0  10.8  38.7  214.6  4.6  -13.5  0.0310  145.0  11.0  26.4  146.1  6.7  -8.9  0.0440  145.0  11.8  8.7  143.9  16.1  -26.1  0.0620  167.0  16.3  6.7  165.4  22.8  -33.1  0.0880  142.0  11.5  •10.6  138.6  25.0  -44.1  0.1250  123.0  26.0  3.6  121.7  31.2  -24.8  0.1770  123.0  37.5  -8.4  120.3  48.4  -35.7  0.2500  96.2  54.4  -7.8  94.0  63.1  -27.6  0.3500  81.9  59.6  -14.2  79.2  70.5  -30.0  0.5000  +  70.6  60.7  -23.3  66.9  75.3  -36.1  0.7000  +  0.0  0.0  0.0  0.0  -0.0  0.0  1.0000  +  67.6  93.8  -14.1  65.2  103.3  -24.4  1.4000  73.1  -16.4  2.0000  -11.1 2.8000  321.0  8.6  349.0  12.5  287.0  •  •  2,000  *  *•  • +  •  - «•  :  *  :-+  •  +  +.  +  +  •  *+A  +  +  •  +  # +A  1  •  +  •—+  +  +  1-  +  +  *0  A  4.  +  +  +  *  *0A  +  •  f  +  4.0000  +  *0A  +  +  *•  •  0.4  5.6000  +  *A  +  +  •  +  -0.0  0.0  8.0000  +  *  +  «.  +.  0.0  -0.0  0.0  11.3000  +  *  f  +  0.0  -0.0  0.0  16.0000  +  *  •  •  34.3  66.0  -12.4  32.5  34.5  66.8  -7.0  33.4  71.3  24.5  71.8  -3.3  24.0  73.8  -4.8  16.0  83.4  -0.8  16.0  83.5  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  0.0  +  + +  +  :  +  o o o  +  •  +  +  +  o o o  I  I I I I I I I <  <  o o  fl  -* fM IN II  u tu  O UJ  oe  +  m in o o  co r» o o  + I I I I I I I I I  +  <  +  +  o o o  I I I I I •» I I  fN O  o •* •Jo  o  IN  o  o o in  O  in  (M  o  O  in  ' + I  I O I I I <t I + I I I I I I I  I  o  I I I I  <r l + I I I  I  o I I I I I I  I  I + I I I I » I I I  + I I I I I I  +  +  o o o o  o o o  o o o  o o o o  rsl IS! U <M  ui s: i/> o co x in o ui • >o f l o -i-  •v  n I  in  3  II  O fl UJ 3 i/>  I  I  fi  in  <0  1 o. ~"  0  0">  l  o m i  fi  fN  CO  a  fM  fN CO  c o •4fi  ~>  in —'  tM  l  ->  —> CM  0-  O fN  in ~>  in  fl  IN  -o  tM  •o  0>  o  o  —-»  fN  •o  o  ro  (N  o  m z ~c < \ —. o -o o u.  I  ac  o o  •4-  fl  -i  r-*  —I  I  I  —I  o CO  o u.  fl •i  —« (M  m m  o  fN  o in m  o o  o  —•  CO  fM  fl  o  4>  — I  o in  o  — I  CO  l  I  O  o  -1-  fM  I  <N O  1 •  a-  o  in I  fN  IM O l\J II  fM  o o  I  o  in -j- r~* m fl  a:  in  CO  r-  II  tM  o  fN  i  fsl  CM  fi o  U  0  CO fN I fj>  -l  <N  o  o  fM  CO  1  o in  fM  I  fl  -o  in  —* in  in  -1-  -O  —I  FIGURE 8 0 . R U N E 2 2 3 1 4 - 2 3 4 6 2 6 / 6 / 6 5 U= THETA = 0 . 0 1 0 8 1 RADIANS FOll  F033  F013  943  CM/SEC U5=1032 C H / S E C Z * 2 0 3 UIU3.« -U97.478CM2/SEC2  FOll*  F033'  F013*  CM  FREQ.  -500  0  1,000  833.0  16.8  -24.0  832.6  18.2  -41.9  0.0039  •  *A  +  1065.0  27.0  -52.0  1064.3  29.7  -74.9  0.0055  •  * - A  +  +0  *•—  1187.0  35.8  -141.0  1185.3  42.4  -166.4  0.0078  •  A  •  «•—0  *•  «•  1342.0  38.2  -106.0  1340.7  43.4  -134.8  0.0109  •  * — A  •  +  •  •  1474.0  39.9  -25.0  1473.6  41.7  -56.7  0.0156  +-  +  +  0*-  >  1485.0  47.2  15.0  1485.0  47.2  -16.9  0.0220  +  »A  •  0«-  — *  1425.0  54.3  -69.0  1424.1  57.9  -99.5  0.0310  •  *-+A  +  •  2026.0  89.7  -155.0  2024.1  97.3  -198.3  0.0440  •  *  +A  +  +  1761.C  97.0  -148.0  1759.2  104.2  -185.5  0.0620  +  *  +-A  +  •  *  2018.0  147.0  -182.0  2015.8  155.8  -224.8  0.0880  •  +—A  +  +  •  1805.0  193.0  -219.0  1802.4  203. 3  -256.9  0.1250  • — *  A  +  *  *•  1473.0  252.0  -205.0  1470.6  261.5  -235.4  0.1770  +  *  • — — A  +  +  0«-  +  1351.0  437.0  -223.0  1348.4  447.2  -249.8  0.2500  *  *  +  A-+  •  0  •  +  1304.0  488.0  -213.0  1301.6  497.8  -238.5  0.3500  +  *  A*  +  0  «•  •  1200.0  569.0  -203.0  1197.7  578.3  -225.8  0.5000  •  *  +  +A  +—0  •  •  580.0  -203.3  1070.7  589.2  -223.3  0.7000  +  *  +  *A  +0  *  *•  915.0  623.0  -205.0  912.7  632.2  -221.4  1.0000  + — *  +  +- A  •  +  976.0  694.0  -184.0  973.9  702.3  -201.3  1.4000  •  •  +  *•  •  625.0  690.0  -151.0  623.3  696.7  -160. 7  2.0000  +  •  +-0A  - — *  +  522.0  601.0  -110.0  520.8  605.9  -118.0  2.8000  + _ — - * — +  •  +  +  423.0  549.0  -69.0  422.2  552. 1  -75.2  4.0000  +  +  *•  ••  308.0  313.0  -29.0  307.7  314.4  -34.0  5.6000  +  •  •  •  236.0  404.0  -12.0  235.9  404.6  -14.9  8.0000  +  *•  »  «•  247.0  611.0  26.0  247.3  609.9  24.0  11.3000  +  +  445.0  2541.0  260.0  447.8  2529.7  264.1  16.0000  *  «•  1073.0  :  *  * - A  *  •  -+  * *  0  * - +  - A  0-+A A  *+  0  •  *  0  •  •  • A-+ +-A  *—0-+  0  2,000  +  •  0  0-*  0+ *•  • •  + 0  0-+ A  •  •  0  + 0 0  •  FIGURE 81. RUN  F l  THETA  :  2017-2049 =  FOll  29/6/65  0.03525 F033  U=  335  CM/SEC  RADIANS F013  U1U3 F O l l '  U5=  390  =  -210.254CM2/SEC2  F033*  CM/SEC  Z=  90  CM  FREO.  F013'  -500  1,000  6.4  -4.4  0.0039  -*A—0 —  221.7  10.0  -16.9  0.0055  -»A  185.9  14.0  -38.7  0.00i'8  -*A—0--  -23.4  0.0109  *A  I  0.0156  *A—0  -21.2  0.0220  14.8  -29.6  0.0310  185.9  14.5  -38.4  0.0440  - * A — 0  -31.6  163.7  19.4  -42.9  0.0620  - * A — 0  15.4  -31.4  142.7  20.5  -41.2  0.0R80  -*A-0  118.0  19.4  -28. 3  116.9  23.9  -36.2  0.1250  -*A-0  129.0  26. 1  -36. 7  127.6  31.9  -45.2  0 . 1770  +  •*A-0  145.0  35.7  -44.7  143.3  42.7  -54.2  0.2500  +  *-A-0  137.0  48.7  -41.9  135.4  55.2  -50.6  0.3500  *-+A0  122.0  52.1  -27.6  120.9  56.5  -35.2  0.5000  -*+A0  107.0  54.8  -27.6  105.9  59.2  -34.  I  0.7000  -«+A0-  100.0  58.4  -23.0  99. 1  62. 1  -29.0  I.OOOO  -»+A—  82.0  53.7  -19.0  81.2  56.7  -23.8  1.4000  -«+A —  61.3  48.7  -10.7  60.9  50.5  -14.1  2.0000  - * + A-  37.8  43. 7  -6.3  37.5  44.7  -8.2  2.8000  -*A—  27.8  42.0  -4.1  27.6  42.7  -5.3  4.0000  -*A--  22. 1  46.3  22.2  46.0  1.9  5.6000  —*_  0.2  8.0000  177.0  6.7  222.0  8.7  -1.4  187. C  9.4  -25.8  237.0  6.0  -6.8  236.5  178.0  9.4  -3.7  177.7  10.8  194.0  6.7  -7.7  193.5  8.7  156.0  11.4  -18.9  155.1  187.0  10.0  -25.5  165.0  14.1  144.0  8.0  2.6  177.1  8. 1  20.4  32.5  1. I  20.4  32.4  24.5  17.5  0.0  24.5  17.6  11.5  13.9  3.1  11.6  13.5  -16.  -1.4 2.5  11.3000 16.0000  -*A —  0-  0 —  0—  * A — 0 ~  —  *-  -*A-  2,000  FIGURE 8 2 . R U N F 2 2 0 4 9 - 2 1 2 1 2 9 / 6 / 6 5 U= THETA = 0 . 0 1 7 5 2 RA01ANS FOll  F033  F013  320  C M / S E G U 5 * 370 C M / S E C 2=110 U 1 U 3 '»• -126.078CM2/SEC2  F O l l '  FREQ.  F013*  F033'  CM  -500  1,000  120.0  1.1  -7.9  U 9 . 8  1.8  -12.1  0.0039  *A-0  170.0  2.0  -13.4  169.7  3.1  -19.3  0.0055  * A ~ 0  109.0  2.3  -5.0  108.9  2.8  -8.8  0.0078  *A-0-  129.0  3.1  0.5  129.0  3.2  -4.0  0.0109  «A-0  135.0  4.4  2.9  135.0  4.4  -1.8  0.0156  *A-0  103.0  3.9  -2.4  102.9  4.2  -6.0  0.0220  *A-0-  113.0  5.6  -5.0  112.9  6. 1  -8.9  0.0310  +  *A-0—  120.0  7.6  -3.9  119.9  8.0  - 8 . 0  0.0440  +  *A-0—  100.0  9.6  -11.5  99.8  10.5  -14.9  0.0620  +  118.0  12.9  -19.9  117.6  14.4  -23.9  0.0880  *A-0  119.0  18.7  -23.6  118.6  20.5  -27.6  0.1250  *A-0-  106.0  26.4  -27.0  105.5  28.4  -30.5  0.1770  *A-0  117.0  37.6  -30.9  116.4  39.9  -34.7  0.2500  *A-0  124.0  42.0  -32.3  123.4  44.4  -36.3  0.3500  *A-0--  105.0  43.7  -26.5  104.5  45.7  -29.8  0.5000  *A-0—  87.5  46.3  -27.0  87.0  48.3  -29.6  0.7000  -*A0-  78.0  51.1  -23.6  77.6  52.8  -25.9  1.0000  -*+A-  58.6  43.3  -17.6  58.3  44.6  -19.3  1.4000  -*A0-  42.9  34.2  -12.1  42.7  35.1  -13.3  2.0000  -*A-  29.0  38.9  -5.8  28.9  39.3  -6.5  2.8000  -*A-  21.0  37.3  -3.9  20.9  37.6  - 4 . 3  4.0000  -*A-  16.4  32.9  1.8  16.4  32.8  1.5  5.6000  19.2  26.4  0.5  19.2  26.4  0.1  8.0000  19.3  13.7  1.6  19.3  13.6  1.0  11.3000  9.8  3.7  19.1  9.6  3.1  16.0000  19.0  -•  *A0  2,000  —  .+  —  —+  —  +  +  FIGURE 83.  RUN F3 2121-2153 29/6/65 U= 313 CM/SEC U5= 385 CM/SEC Z=120 CM THETA = 0.02317 RADIANS UIU3 = -152.454CM2/SEC2, FOll  F033  FOll'  F013  f r»n> .Oio» F033'(-tlo F013'  to SFREQ. w)  380.0  5.5  -19.9  379.3  8.2  -37.4  0.0039  330.0  7.4  -20.2  329.4  10.0  -35.4  0.0055  267.0  8.7  -7.6  266. 7  10.0  -19.9  0.0078  24 7.0  9.4  0.3  246.9  9.9  -11.0  0.0109  192.0  11.4  -13.4  191.6  13.0  -22.1  0.0156  122.0  11.4  -8. 1  121.7  12.4  -13.6  0.0220  144.0  12.7  -9.2  143.7  13.9  -15.7  0.0310  147.0  12. 1  -12.1  146.6  13.5  -18.8  150.0  15.5  -16.3  149.5  17.3  123.0  18. 1  -18. 1  127.5  107.0  21.2  -22.0  10 1.0  23.5  93.0 96.0  0  -500  2,000  •  •  *  •  -*A-0  •  •  •  1  0.0440  -*A-0  *  •  .  •  -23.1  0.0620  -*A-0  •  •  „  •  20.0  -23.8  0.0880  106.4  23. 5  -26.7  0.1250  -*A-0  +  -17.6  100.5  25.3  -22.0  0.1770  -*A-0  «•  32.4  -21.2  92.5  34.5  -25.1  0.2500  -*A0  •  42.2  -24.1  95.4  44.6  -28.0  0.3500  -*A0  +  -*A0  +  -*A0  +  -*A0  +  90. 1  42.9  -21.2  89.6  45.0  -24.9  0.5000  74.3  43.2  -41.4  73.3  47.2  -44.3  0.7000  •  +.  4.  -*A  66. 1  41.6  -16.2  65.7  43.2  -18.8  I.OOOO  49. 1  38.6  -11.5  48.8  39.8  -13.3  1.4000  36.0  35.8  -8.1  35.8  36.6  -9.3  2.0000  23.7  31.8  -4. 5  23.6  32.3  -5.2  2.8000  -*A _*  17.2  32.2  -2.9  17.1  32.5  -3.3  4.0000  13.5  34.3  2.1  13.5  34.1  1.9  5.6000  18.4  21.0  0.6  18.4  21.0  -0.0  8.0000  25.5  14.5  4.7  25.6  14. 1  3.7  11.3000  21.1  10.4  3.7  21.2  10.1  2.8  16.0000  DATA CARDS EXHAUSTED. EXECUTION COMPILE TIME OBJECT PROG  1,000  8733 615  A  -*A  0  «.  •• .  +  +-  +  TERMINATED.  TOTAL TIME DATA STORAGE  26400 255  AVAILABLE CORE  10547  SYMBOL TABLE  320  FIGURE 8 4 RUN GO 1 4 5 3 - 1 5 2 5 2 2 / 7 / 6 5 U= THETA = 0 . 0 9 4 1 2 RADIANS FOll  F033  53.0  776  C M / S E C U5= U1U3 =  F O l l '  370 CM/SEC Z=24l -97.010CM2/SEC2  F033'  F013'  CM  FREO.  -500  0  1,000  2T0  52.7  5.7  -7.7  0.0039  •  *A0  103.3  8.1  -6.1  0.0055  •  *A-0  +  •  2,000  +-  +  *  +  9.4  13.0  13 3 . 0  7.8  7.0  132.5  9.8  -17.6  0.0078  •  *A-0  +  •  •  •  184.0  975  27T  182.6  14.6  -31.9  0.0109  +  *A—0  •  «•  •  *  150.0  13.0  3.7  149.1  16.8  -23.8  0.0156  +  *A-0  +  •  ^  —+  127.0  16.4  -4.2  125.5  22.3  -27.1  0.0220  +  *A-0  —*•  •  *•  +  94.8  13.1  -4.0  93.6  17.8  -21.1  0.0310  •  *A0  +  •  •  +  20.9  -5.8  118.4  27.1  -27.2  0.0440  +  *A-0  •  •  *  •  76.9  25.2  -11.0  75.2  31.8  -24.0  0.0620  +  *A0  •  •  ••  +  75.8  27.8  -13.0  74.0  35. 1  -25. 7  0.0680  +  *A0  •  +  •  •  55.8  29.2  -7.6  54.7  33.8  -16.5  0.1250  +  *A0  •  +—  »•  +  45.0  28.0  -4.2  44.3  30.9  -11.2  0.1770  •  *A  •  +  1 -  +  40. I  29.7  -3.6  39.5  32.2  -9.7  0.2500  +  *A  +  +  *  +  37.7  32.2  -6.3  36.8  35.6  -11.7  0.3500  +  *A  1  +  •  +  36.0  36.4  -5.2  35.3  39. 3  -10. 1  0.5000  +  *A  +  •  «•  +  31.2  34.4  -2.5  30.8  36. 1  -6.7  0.7000  •  *A  •  +  39.0  35.2  3.8  39.1  34.8  -1.9  1.0000  +  *A  +  +  *  +  61. 5  32.7  7.3  61.7  31.9  -2.8  1.4000  +  *A0  +  +  *•  +  22.0  25.3  FTg  22.0  25. I  - 1 . 1  2.0000  +  *A  •  ••  +  12.1  20.9  1.4  12.2  20.6  0. 1  2.8000  •  *  +  •  +  9.7  20.3  2.1  9.9  19.7  1.2  4.0000  +  *  +  +  •  6T0  25.6  ITl  671  25. 1  U 4  5.6000  +—  *  +  *  .»•  +  5.3  23.9  1.4  5.4  23.4  1.5  8.0000  *  *  +  +  *-  +  17.9  21.0  2.9  18.1  20.4  0.5  11.3000  +-  *  +—  +  •—«•  +  25.3  62.4  11.4  26. 3  58.5  574  16.0000  +  *A  +  +  •  +  -+ +•—+  :  —  •  103.0  120.0  ~~  F013  341  —  *  o o o  o o  o  I I I I I I I I  + I I I I I I I  <  o  o <  < «  <  <  o o  I < « I I I I I I I  a  o  o in  o p-  o o  o <  < +  o <  o o o in  o o o o  o o o •4-  rf  rf  +  IT I  0>  o o in  •  a UJ  PM  o  PM it a i F*J I/)  ro o  o  PM  •  ro  I  i  m  ll  O rn3 UJ  (/) rf m m  <y  >*•  oo m  in l  I  l  n  n  I  o  ry  PM  00 rf  I  I  I  PM  Mi  <T>  o o o  o o o o  o  CO  o o o  •0  o o o o  o o o  ro  pn pn o u. IM  —*  OO  pn  -0  rf CO X0  0>  PM PM <\J  in  00 CO  z  m -o < "V rf  r*a ^ < <M ac  m  rf  o  00 a  o  Cf  CO  o  1 o•  in iri in  rf ^ 2  UJ 1  3  l-  I  00  —4  rf  I  I  00 00  m ro O u.  I  rf  o  rf  I  r4-  rr-  I  co o  o  00 -o  in  <o rf  m pn  —i pn  PM  m  PM  rf  PM  rf  o rf  PM pn  in  p-  PO  •O  PM  rf  PM  •o in rO  in  o  —4 rf  o  U.  o  rf  O o  PM  ro -o  rf  pn  PM PM  in —'  %0  PM  I  O  II  O I-  rf a> I  o u.  PM  o PM r* 0 r—  o o o o  -1-  00  u.  ll  oc  I  o  o  -t  rf  ro in  -0  O  PM  rf m rf  o  o  o  PM  -i  _  II  rf  I  PM O  o  <t  3  pm  o .* -Jo  o  U-  >*• -«r-  in  o o * pn  in  • IT) PO ^ rf (_) —< £ CO <0  >0 IT,  CO  po o  u.  U PM UJ X.  u  in  ui o o  in  rf  rf  PM  O  o o  o o o  . + I I I I ! I I I  + I  I I I I I  I I  I I I  *  I  t  O < *  I  I I  o  I  o < .«  o <  <  I I I  < »  <  <  <  *  t l  I I  o  +  o in  . a: o i/< O IN CM U II UJ  o p  a  in  o o  at  o  IN  o  O  o  o  m  co  o  —< m  o  o o  ^ •*  o o  IN >o  o in  o o ui rt  o o o m  co I  ri  CO  r-  fM  rfM  rfM  rfM  <M  o  -H  o-  o  o o o o  o o o  O  fM  fM  -*  o o o 00  o o o o  o o o o  o o o o  IM  CO  co  o I  o  o  o  o  f>  -I  o o o rt  o o o o  l/l  Kl  O  <M UJ X f» O  •v rt x r-  o in •  •*• oo eo co rt t  w m 3  »  O M UJ 3 </) N» 3  o  >0  r> «\j  I  I  —i I  -< I  - H O IM  fN  t> IN  I  I  I  tM  fM  I  I  rt 03  o  u. co o  rt rt o — 1  z o  o  m  -I  fM  r-l  -4  IM  fl  -I  rt.  fN  in  fM  rt  fM co  r*-  -o rt  fN  -*  m  -* I  I  -<  o  o  m  fN  IN  IM  o  in  rt  m rt  O  o  o  -<  fM  m  *  0>  CO  o  o  CO  •«*'  tl  O  N  3 .  mz  I  »»i o  v. < ru rc fM  «* o> f*-  o  I  m  ir - i •O K  o  fM  1-1 I  r. -J I  o  ~»  IM  in  •o r-CO  fM  —H  -I  I  o  o I  I  CO IM IN  fM  in  IN  in  fM  a-  •a  fM  -O  fM  ui  rt  fIN  rfM  rv fM  CO  in  tn  fM  -I  in  -t  in  o  I • r- O IM  •O QO  o  •"•  <M <  W<-9 >£ r i  z  " 3  UJ x  t-  ro  CO  fj>  rt O  •O  CO  rt  CO  o o o  o o o  I I I I t I I I I + I I I I I I I  O  <  o < *  o  I  o  in  NO  O PM  O  O  <  o <  o <  <r  <  <  <  o o o  o o o o  o o o •4-  rf  rf  < »  o o  m  I  o o  r-  CM PM <-) II UJ NJ l/> •V o PM UJ l/> u V. «*  PM x.rf •  u  ir< o  pn rn  O  a or  m  rf o  u.  PM  eg  oo  co  0  CM 1  I  in  •PI  I  I  rf  0>  co  o  CO  m  m  PM  rf rf o  o  O  PM  o o  o o  O  m  in  o  O  pn  -4  ->  PM  O PM  rf PM  pn  ro O  O -O  O  PM rf  I  I  -o l  4I  O0  CM  in PM  rM PM  in  4-  o PM  CO  rf I  PM  PM  o m  I  co rf pn  o-  ro  o  z rf < or  pcr  o  rf rf 1 « cr o in  in  o  m  O  I  rf o  o I  pn  o . oo  o  o o o  o  o  I  PM  •o  cr PM  PM PM  PM  P-  •O PM  I  GO PM  rf  PM  00 1  in in  1  o  rf r-  1  m  C  •O  .0  41  PM  rf  o  0-  m m O u.  rf cr  in  in rf PM  o  m  pn  PM  >o  PM  pUJ z  o  o  PM  r-  pn  rf II ?  o  o  u.  oo  M rf P m -r  C  o o o  o  o  o M3  o I  r4-  m  o  o  u.  i•o n < r- u \  o  -t  o  in  ll  •>»  pn o  o  •  m  o rf  U-  m  p<M  o  rf PM  CM  -  n  O  o  u.  m m  UJ 3 i/» rf 3  o  UJ  •  II  in  in in o  t  x  o LL  00 o  m  o  r-  -3-  NO  PM  03  FIGURE 8 8 . R U N J O 1 3 0 4 - 1 3 3 6 2 3 / 7 / 6 5 U= THETA * 0 . 0 2 4 5 6 RADIANS FOll  F033  F013  583  C M / S E C U5= 6 1 6 C M / S E C Z=242 U1U3 » -315.704CM2/SEC2  F O l l '  F033'  F013'  CM  FREQ.  -500  0  1,000  2,000  479  17.0  415.2  4T2  -3.3  0.0039  +  *A  --0-+  •  • - —  1-  +  326.0  3.7  3.4  325.9  4.2  -12.6  0.0055  +  *A  0  ;-  +—  •  +  390.0  4.5  -13.2  389.4  6.7  -32.3  0.0078  + — - — — * A -  • — •  +  +  586.0  7.9  -17.9  585.2  11. I  -46.6  oToi09  •  *  589.0  10.7  -15.3  588.3  13.6  -44.1  0.0156  +  *A  469.0  13.2  -15.5  468.3  15.8  -38.3  0.0220  •  *A  0+  387.0  15.4  -22.9  386.2  18.6  -41.7  0.0310  +•  *A  0—+  493.0  27.1  -39.2  491.7  32. 1  -63.0  0.0440  +  ^ * - A  389.0  39.2  -62.6  387.2  46.3  -81.1  0.0620  «•-  * - A  374.0  46.3  -56.9  372.4  52.8  -74.6  0.0880  +  *_  367.0  62.2  -64.3  365.2  69.4  -81.5  0.1250  +  * - +A  314.0  76.7  -53.9  312.5  82.7  -68.3  0.1770  +  *-+A——0  274.6  110.5  -62.0  0.2500  +  415.0  ~~  «.  *  +•  —+  +  +  •  •  +—-  +  •  0+  +  «•  •  0—+  +  •  •  ;  __  — + 0  +0—  A  0  —+  :  0—•  «-  -«•  +  *  +  +  +  •  +  +  •  •  +-'  *  •  +  *  +  105.0  -49.8  249.0  112.0  -45.8  247.7  117.0  -56.6  0.3500  •  *-+-A-0  +  214.0  128.0  -44.9  212.8  132.8  -53.8  0.5000  +  *-+-A-0  +  185.0  137.0  4 l . 7  183.9  141.5  -49. I  0.7000  y  * +- A 0  +  +-  +  +  164.0  136.0  -25.8  163.3  138.8  -32.2  1.0000  •  *+-A0  +  +•  *•  +  186.0  137.0  -24. 3  185.3  139.8  -31.7  1.4000  +  *+-A0  +  +  115.0  126.0  -18.0  114.5  128.0  -22.1  2.0000  +  *+-A  *  *  -11.3  2.8000  +  *+0A  +  -+  [  —*-+-A—0  +  +  276.0  I  .•  0—•  A  +  •  —  +  —• —  *  •  +  +  84.0  108.0  -8.5  83.8  109.0  59.0  101.0  -2.  58.9  101.3  -3.8  4.0000  +  *+0A  +  +  <•  46.0  106.0  0.0  46.0  106.0  -1.0  5.6000  +  *0-A  +  +  «•-  25.0  119.0  -0.3  25.0  119.0  -0.1  8.0000  +  *0-A—  +  •  •  52.0  203.0  3.8  52.1  202.6  3.7  11.3000  +  — *0—A  +-  +  «•  94.0  724.0  0T3  94.1  723.8  4T6  16.0000  +  1  *  0  _  fl  +  «.  •  + +  •  • +  FIGURE 8 9 . R U N J l 1 4 0 0 - 1 4 3 2 2 3 / 7 / 6 5 U= THETA = 0 . 0 3 6 7 3 RADIANS FOll  F033  F013  507  CM/SEC UIU3  F O l l '  U5= 5 3 6 C M / S E C Z = 2 0 6 = -257.195CM2/SEC2 F013«  F033'  CH  FREQ.  395.0  2.6  18.8  395.2  2.2  -10.2  0.0039  277.0  2.7  5.9  276.8  3.3  -14.4  0.0055  342.0  4.7  8.3  341.6  5.3  -16.7  0.0078  413.0  7.2  4.7  412.6  e.7  -25.5  0.0109  341.0  7.4  - 8 . 6  340.2  10.5  -33.5  0.0156  276.0  11.3  -18.1  275.0  15.4  -38.1  0.0220  342.0  18.9  -18.6  340.9  23.4  -43.3  0.0310  464.0  24.2  -23.2  462.5  30.1  -56.7  0.0440  302.0  34.0  -28.6  300.6  39.8  -50.1  0.0620  295.0  42.2  -42.5  293.1  50.0  -63.3  0.0880  284.0  51.2  -47.0  261.9  59.6  -66.8  0.1250  245.0  59.5  -34.2  243.4  65.8  -51.0  0.1770  195.0  89.0  -33.2  193.5  94.8  -45.8  0.2500  196.0  102.0  -40.6  194.3  108.9  -53.0  0.3500  182.0  125.0  -38.6  180.4  131.5  -49.6  0.5000  159.0  126.0  -37.3  157.5  132.2  -46.6  0.7000  123.0  116.0  -19.7  122.2  119.4  -26.5  1.0000  132.0  115.0  -16.3  131.3  117.9  -23.8  1.4000  83.0  106.0  -11.6  82.5  108.0  -15.7  2.0000  60.0  93.5  - 4 . 7  59.8  94.4  -7.4  2.8000  45.0  84.2  - 0 . 9  44.9  84.5  - 2 . 7  4.0000  33.0  91.2  - 0 . 3  33.0  91.3  -1.0  5.6000  33.0  107.0  0.0  33.0  107.0  - 0 . 5  8.0000  57.0  138.0  - 7 . 5  56.7  139.2  -9.1  11.3000  109.0  376.0  7.9  109.3  374.9  6.8  16.0000  -500  •  0  —  *  -  1,000  A  0  —  —  -  —  •  2,000  FIGURE 9 0 . RUN J 2 1 4 3 2 - 1 5 0 4 2 3 / 7 / 6 5 U = THETA = 0.04941 RADIANS FOll  F033  F013  5 16  CM/SEC UIU3  FOll'  U5=  565  =  -282.704CM2/SEC2  F033'  CM/SEC  F013'  Z = 2 0 0 CM  FREQ.  1,000  -500  157.0  3.5  16.0  157.'*  1.9  0.5  0.0039  195.0  4.4  4.3  194.7  5.4  -14.8  0.0055  213.0  4.9  4.6  212.7  6.0  -16.1  0.0078  254.0  4.8  1.5  2 53.5  7.0  -23.4  0.0109  *A  332.0  6.7  -7.5  330.8  11.4  -40. 1  0.0156  — *A  364.0  30.4  -20.6  362. 1  37.9  -55.7  0.0220  A  377.0  14.6  -26.6  374.0  23.5  -63.3  0.0310  -*-A-  509.0  22.5  -29. 7  506. 3  33.3  -79.2  0.0440  -*-A-  320.0  23.6  -33.9  317.6  3 3.4  -64.7  0.0620  -*-A-  321.0  35.1  - 3 1 . f.  3 18.7  T4T4"  -62.2  0.0880  *-A  0  +  316.0  43.7  -41.1  3 13. 2  54.8  -71.0  0.1250  * - +A  0  +  272.0  54.0  -40.C  2O9.H  64.4  -65.3  0.1770  206.0  77.4  -28.2  204.2  34.8  -46.5  0.2500  * +A—0  +-  189.0  89.5  -23.3  18 7 . 4  95.3  -40.1  0.3500  * +A-0  +-  174.0  112.0  -25.4  172.4  118.4  -39.7  0.5000  - * +-A0  +-  148.0  112.0  -25.7  146.4  118.2  -37.4  0.7000  -*+-A-  125.0  112.0  -24.6  123.5  117.8  -34.0  1.0000  -*+-A-  144.0  119.0  -19.9  142.7  124.0  -31.1  1.4000  -*+-A-  90.0  111.0  -13. 5  89.?  114. 3  -19.6  2.0000  -*+0A-  62.0  94.4  -5.2  61.6  95.8  -9.0  2.8000  -«+A —  45.0  84.9  -1.4  44. 9  85.4  -3.7  4.0000  -*0A—  33.0  92.9  0.6  33.0  92.9  -0.4  5.6000  —*0A  29.0  112.0  1.3  2  111.8  1.2  8.0000  - — * - A  +-  54.0  135.0  -4. 8  I  -6.8  11.3000  — *+0A  +-  152.0  322.0  318.4  14.4  16.0000  21.6  q  . I  53. 7 152.9  136.  2,000  -*—0-  +  0 -0  10—  * - +A  •  +-  0  -0--A-  +  —+  +  o o o  I I I I I I I I  o o o  + I I I I I I I I I  + I I I I I I  o I  <  < +  <  <  o I <  # I  < o •  < o  i  < o  o o o co  o o o o  o o o  4f  PO  o  t I I I  o o  (M O CM rg o n UJ IM i/> O PM UJ X l/l O CO s: m O 00 1/N lf>  * rm f\j  n in 3  z o o o  o  o o  c o o o m PM rf rf PM o o o  II  o rf  PO  o  o  4'4-  o  o  o  -0  3D O  <M  o  co  o  m  o r»  PM P— rf  rf  o o n  o o o m  u. po  4  PM I  o  pn  4/  I  I  I  4-  *  MP  -*  4-  I  1  •»  0>  O  rf ro  rf 4-  O  I  I  0  cr m  O  o o o O rf  cr ro  I  I  4>  I  I  M3  rf c o rf  •o •o  ro  o o o  oa —  t  I  O  o  O O  rf ao I  o u.  cn  m o  o O  in O  in  rr  O  -i  po  PM  cr rf  rf  ro  r~  PM  O  00  O  O  cr  -<  3  rf  4-  o 4-  PM PM 0* CO rn  rn  ro 4-  m  CO 00 rf 00 cr  (M 4  -4  PM  o cr  4in  o  PM PM  CO O  4" rf  4"  co  CO 4"  O ro  •o PM  -0  PM  o  in  11 3  o o  I  om  UJ CO  +  LL  PM in l  i/>  m z CO PM «orf< rf v o r- Q U-  cr rf PO PO I  I  4ro I  ro I  I  I  ro  PM I  -• I  I  I  cr o  PM  4-  00 PM nI  rf  v. <  m <V  rt  rf oo m pin in  r»  CO  rf uo . I o • 4- o o in - « II m  <i  -> r-  rfZ LUI  rf rf uo .  pn  o  o  cr •4  PM  o  CO r-  rf  m o  in 4-  O  rf 4-  PM  rf  cr o  4-  PO  as  po  PM  in  4-  p~  in  00 o  o  o in  in in o rf  o  4-  oo  r-  rr  •O  4-  PM  00  PM  O  cr  o o I  I I I + I I I I I I I I I  o o  I I I I I I I I I + I I I I  o i i i i < « l i i i I  o o in  + I  I I I I I  I I I I I I I  I I  + I I I I I  o I I I < « I I I I I I I  +  I I  I I I  o I I I l I  o  I I I I  <  « I I I I I I I  <  <  I I •*• I I  I  o I I I I  I I I I I  o I < I  I  I I I  I I  I  o <  o  I  <  I +  #  I I I I I I I  +  1  X  u  ro O IM  fM (_> II UJ K l IvO ' »s  O rv uj x  i/> •v .0 O  X  o m  •  I T <T>  o> m ro tn o • o bo o UJ  co  K.  J3  o o  o  IM  X  o  sr  o  o  N  CO  NJ-  0> -H  |  rH  _H  I  I  II  tn 3  II  O ro UJ 3 to - i  X  o  — ro  —«  I  I-I  o u.  CC O  in fM  tM <}•  I  I  D  o in  o o  IN  rH  o  to -o  rH  |  -J"  o o o in  o o  o o o  CO ro I  O rO I  o o o  o o o o  CO i  !  o o o o  o o o  a  o  o o o o  m I  l  ro in I  -o  -H  l  I  Cr0>  „  in  ro ro O u.  o  in r\l  •—»  X  o  0>  •O  r\J  o  fM  rro  o ro  bu .  in  o co  m ro  3  u  it  X  oo roi n vn 1  c  -i  fO  co  fN  ro  K.  oo CO rH  IN  o  o o  -H  si" in  o o  m  -1-  >0  .n  IN  r-tr  r\i  n ro I  l/>  in  z  <o <  K,  rv. — o < ro oc CJ  co <o o -> •o -I o 1 •  •o o  ro tn -  ro  -H  o ti-  I—  a: UJ 5z I  I  in  <»• I  o>  iI  I  fM  rH  I  I  —•  in  O  -H  I  I  O  CO  ro ro O u.  O  IM  O -1-  O  o  II  * <  -H  — IN  in  o  fM  fN  rg cc  -4  m  o  ro ro  O  rH  fM  o  o IM  CO  fM  CO  FIGURE 93.  RUN J 5 1*608-1640 23/7/65 U = 490 CM/SEC U5= 524 CM/SEC Z = 207 CM THETA = 0.07625 RADIANS U1U3 = -270.715CM2/SEC2 FOll  F033  F013  FOll'  F033'  F013  FREO.  1  -500  1,000  86.0  4.4  9.7  86.2  3.  -3.3  0.0039  -*A0-  91.0  3.7  11.1  91.3  2.  -2.7  0.0055  -*A0-  93.0  3.0  8.0  93.1  2.  -6. 1  0.0078  -«A0-  139.0  4.7  5.9  138.6  6.  -15.1  0.0109  -*A-0  206.0  6.3  0.0  204.8  11.  -31.1  0.0156  -*A  295.0  9.5  0.8  293.4  16.  -43.7  0.0220  -*A  311.0  15.7  -20.7  307.6  29.  -67.1  0.0310  •  *-A  385.0  24.3  -29.3  380.6  42.  -86.5  0.0440  ••  #-A  282.0  32.2  -37.5  277.6  50.  -78.7  0.0620  +  *-  288.0  34.2  -35.1  283.7  51.  -77.1  0.0880  >- + A  o-  263.0  41.8  -35.8  258.8  58.  -73.8  0.1250  *-+A  0-  221.0  50.4  -12.3  218.9  59.  -43.8  0.1770  -» + A — 0 —  175.0  65.6  -20.9  172.5  75.  -44. 8  0.2500  -**A-0-  158.0  84.5  -23.9  155.4  94.  -44.4  0.3500  -*+A-0-  148.0  106.0  -27.0  145.2  117.  -45. I  0.5000  -* + - A —  127.0  LC8.0  -27.2  124.4  118.  -42. 1  0.7000  -* + -A-  99.0  L02.0  -19.3  97.1  109.  -30.2  I.OOOO  -*+0A-  108.0  99.3  -13.6  106.5  105.  -26. 1  1.4000  -*+-A-  65.0  90.9  -8.7  64. I  94.  -15.0  2.0000  -* + A-  48.0  81.6  -1.9  47.7  82.  -6.1  2.8000  -*0A-  34.0  75.0  0. I  33. 9  75.  -2.2  4.0000  -*0A-  26.0  84.0  2.0  26. 1  83.  1.2  5.6000  —*A-  23.0  96.1  2.6  23.2  95.  2.7  8.0000  — *A-  27.0  92.1  -2.7  26.8  93.  -3.3  11.3000  -*0A-  59.0  162.0  11.3  59.8  159.  8.4  16.0000  + 0  A  *0-A  2 ,000  • 0  + 0  +  0—• o  •  *  DATA CARDS EXHAUSTEO. EXECUTION TERM I MATED. COMPILE TIME OBJECT PROG  8666 • 6L5  TOTAL TIME DATA STORAGE  79433 25_J_  AVAILABLE CORE  10547  SYMBOL TABLE  320  

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