NASA Contractor Report 3 366 

.~ 

.,-_ 

Statistical Analysis of 

Atmospheric Turbulence About 

a Simulated Block Building 

Sidney L. Steely, Jr., and Walter Frost 

CONTRACT NASS-32692 

JANUARY i9Sl 
>- 

NASA Contractor Report 3366 

Statistical Analysis of 

Atmospheric Turbulence About 

a Simulated Block Building 

Sidney L. Steely, Jr., and Walter Frost 

The University of Tennessee Space Institute 

Tdahoma, Tennessee 

Prepared for 

Marshall Space Flight Center 

under Contract NAS8-32692 

National Aeronautics 

and Space Administration 

Scientific 8nd Twhnicd 

Information Branch 

TECH LIBRARY KAFR. NM 
ACKNOWLEDGMENTS 

This research was supported under NASA Contract 

No. NAS8-32692. The authors are grateful for the support 

of A. Richard Tobiason of the Office of Aeronautical and 

Space Technology, NASA Headquarters,. Washington, D.C. 

Special thanks go to Dennis W. Camp of the Space Sciences 

Laboratory, Atmospheric Sciences Division, NASA/George C. 

Marshall Space Flight Center, Alabama, who monitored the 

research program. 

ii 
ABSTRACT 

An array of towers instrumented to measure the 

three components of wind speed was' used to study atmospheric 

flow about a simulated block building. Two-point spacetime .correlations of the longitudinal velocity component 

were computed along.with two-point spatial correlations. 

These correlations are in good agreement with fundamental 

concepts of fluid mechanics. 

The two-point spatial correlations computed directly 

were compared with correlations predicted by Taylor's 

hypothesis, and excellent agreement was obtained at the 

higher levels which were out of the building influence. 

The correlations fall off significantly in the building 

wake but recover beyond the wake to essentially the same 

values in the undisturbed, higher regions. 

iii 
TABLE OF CONTENTS. 

SECTION PAGE 

I. 

II. 

III. 

IV. 

V. 

INTRODUCTION. ................... 

EXPERIMENTAL DESCRIPTION. ............. 

A. Tower Facility. ................ 

B. Description of Available Data ......... 

C. Field Site Contour. .............. 

D. Instrumentation ................ 

DATA REDUCTION AND ANALYSIS GENERAL 

CONSIDERATIONS. ................. 

A. Data Acquisition and Processing ........ 

B. Digital Data Analysis Procedures. ....... 

DATA ORIENTATION, FORMATTING AND TAPE ACCESSING . . 

A. Data Recording and Initial Processing ..... 

B. Digital Data Processing ............ 

C. Fluctuating Velocity Components .. ; ..... 

D. Tape Format and Computer Programs .. ; .... 

E. General Statistical Results .......... 

PRELIMINARY RESULTS AND CONCLUSIONS ........ 

A. Computational Results ............. 

B. Conclusions .................. 

1 

9 

9 

12 

12 

15 

27 

29 

44 

59 

59 

77 

81 

84 

94 

105 

106 

172 

LIST OF REFERENCES. . . . . . . . . . . . . . . . . . . . 173 

iv 

- _-. 
LIST OF TABLES 

TABLE PAGE 

2-l 

2-2 

2-3 

2-4 

4-1 

4-2 

4-3 

4-4 

4-5 

5-1 

Tower location and elevation. . . . . . . . . . . . 14 

Specifications of Climet 011-l wind speed 

transmitter . . . . . . . . . . . . . . . . . . . 16 

Manufacturer's calibration of Climet wind speed 

transmitter . . . . . . . . . . . . . . . . . . . 17 

Specifications of Climet 021-4 wind direction 

transmitter . . . . . . . . . . . . . . . . . . . 19 

Method of recording horizontal wind speed . . . . . 61 

Method of recording wind direction. . . . . . . . . 62 

Method of recording vertical wind speed . . . . . . 63 

Towers and levels associated with the given 

channel number. . . . . . . . . . . . . . . . . . 73 

Short towers recorded as tall . . . . . . . . . . . . 76 

Computer execution time (minutes) . . . . . . . . . 164 

V 
LIST OF FIGURES 

FIGURE 

l-l The flow zones of a boundary layer disturbed by 

PAGE 

a solid wedge. . . . . . . . . . . . . . . . . . . 5 

2-l Aerial'perspective of the tower array at NASA/ 

George C. Marshall Space Flight Center, 

Boundary Layer Facility, in its present 

configuration. . . . . . . . . . . . . . . . . . . 10 

2-2 Schematic of the current configuration of the 

NASA/George C. Marshall Space Flight 

Center, Boundary Layer Facility. . . . . . . . . . 11 

2-3 Cross-sectional contour of eight-tower array . . . . 13 

2-4 Propeller calibration (wind speed versus 

propeller rpm) . . . . . . . . . . . . . . . . . . 22 

2-5 Response of four-blade propeller to wind speeds 

from threshold to 5 ft/sec . . . . . . . . . . . . 23 

2-6 Propeller response versus wind angle (fourblade polystyrene propeller) . . . . . . . . . . . 24 

2-7 Propeller response versus wind angle between 60 

and 120 degrees (four-blade polystyrene 

propeller) . . . . . . . . . . . . . . . . . . . . 25 

3-1 Key steps in data acquisition and processing . . . . 31 

3-2 Sampling a continuous record . . . . . . . . . . . . 33 

3-3 General procedures for-analyzing individual 

sample records . . . . . . . . . . . . . . . . . . 41 

vi 

._ _ . ._. _.. _.. ----- -- _ . . . . ..--__ . . . . . 
i 

FIGURE PAGE 

3-4 General procedure for analyzing a collection of 

sample records. . . . . . . ,. . . . . . . . . . . 43 

3-5 52 

4-l 

4-2 

4-3 

4-4 

4-5 

4-6 

4-7 

4-8 

4-9 

4-10 

4-11 

4-12 

4-13 

FFT subroutine. . . . . . . . . . . . . . . . . . 

Flow chart showing data processing of magnetic 

tape for an individual run. . . . . . . . . . . 

Digitization of data for simple continuous random 

record..................... 

Definition of average wind speed and respective 

wind direction. . . . . . . . . . . . . . . . . 

Definition of wind fluctuations u' and v' . . . . 

Illustration of trend removal . . . . . . . . . . 

Initialization program. . . . . . . . . . . . . . 

PL/l computer program.and JCL needed to convert 

the UNIVAC tapes into an IBM bit structure. . . 

Data format for each block of data on the 

magnetic tapes. . . . . . . . . . . . . . . . . 

Subroutine used to extract data from magnetic 

tapes...............;..... 

A typical plot of u"'versus time. . . . . . . . . 

A typical plot of probability density compared 

with a Gaussian density . . . . . . . . . . . . 

An example of leptokurtic and platykurtic curves 

as compared to a normal distribution. . . . . . 

A typical plot of the accumulative percent of 

data...................... 

vii 

. 

. 

. 78 

. 87 

. 

. 

. 

. 

69 

80 

82 

82 

85 

88 

93 

96 

97 

99 

101 
FIGURE 

4-14 A typical plot of an autocorrelation function . . 

4-15 

4-16 

5-l 

5-2 

5-3 

5-4 

5-5 

5-6 

5-7 

5-8 

5-9 

5-10 

5-11 

A typical power spectral density plot . . . . . . 

A typical printout of mean values for a 

particular test run . . . . . . . . . . . . . . 

Mean non-dimensional velocities with the block 

building in the tower array, Run #8624. . . . . 

Mean non-dimensional velocities without the block 

building in the tower array, Run #8704. . . . . 

Time hisotry signals of the different towers and 

levels..................... 

Correlation of signals obtained by shifting, in 

time, measurements made at level 4. . . . . . . 

Spatial correlation relative to each tower and 

level..................... 

Vertical correlations relative to TlL4. . . . . . 

Vertical correlations relative to T5L4. . . . . . 

Horizontal correlations relative to TlLl. . . . . 

Horizontal correlations relative to TlL2. . . . . 

Horizontal correlations relative to TlL3. . . . . 

Horizontal correlations relative to TlL4. . . . . 

PAGE 

. 102 

. 103 

. 104 

. 107 

. 108 

. 110 

. 115 

. 119 

. 153' 

. 154 

. 155 

. 156 

. 157 

. 158 

5-12 Comparison of direct and FFT methods for 

computing an autocorrelation function . . . . . . 161 

5-13 Comparison of autocorrelations computed by FFT 

procedures to autocorrelations computed by 

assuming Taylor's hypothesis. . . . . . . . . . . 166 

viii 
- 

LIST OF SYMBOLS 

f Frequency 

fC 

Nyquist frequency 

fk Discrete frequency component 

'a Lowest recognizable frequency component 

h Record sampling interval 

m meter 

t time (seconds) 

% 

u (t) 

U n 

v(t) 

V n 

w(t) 

wn 

x(t) 

ii XY 

Gk 

Sf) 

H 

L 

Discrete time corresponding to un 

Horizontal wind velocity (continuous record) 

Discrete horizontal wind velocity 

Lateral wind velocity (continuous record) 

Discrete lateral wind velocity 

Vertical wind velocity (continuous record) 

Discrete vertical wind velocity 

Transformed record such that x = 0 

Cross-correlation coefficient 

Discrete power spectral estimate 

Power spectral estimate 

Height of building (3.2 meters) 

Distance constant 

N 

% 

Number of datum points 

Autocorrelation function estimate 

sxc(rh) "Circular" correlation function 

fi XY 

S 

Cross-correlation function estimate 

Sample standard deviation (unbiased) 

ix 
S2 

X(f) 

X (f,T) 

'k 

'k* 

6 

8 

Sample variance (unbiased) 

Infinite range Fourier transform 

Finite range Fourier transform 

Discrete Fourier transform 

Complex conjugate of Xk 

Elevation of the ground relative to the base of 

Tower 3 

Angular direction of mean wind speed relative to 

tower array 

Standard deviation of total population 

Variance of total population 

Lag time of correlation functions 

Data sampling interval 
SECTIUN I 

INTRODUCTION 

Studies of atmospheric flow have been conducted for 

many years, and much knowledge has been gained from research 

in this area. Statistical analysis has helped provide a 

better understanding of many phenomena and the knowledge 

necessary to predict certain yearly, seasonal and diurnal 

variations experienced in atmospheric flow about the earth. 

These studies, being of large-scale flow, provide 

the knowledge to predict geostrophic and synoptic flow 

patterns for various locations on the surface of the earth 

and throughout the 

I comparison, little 

flow about surface 

/ 

upper layers of the atmosphere. In 

research has been devoted to atmospheric 

protuberances or man-made structures 

I which alter the local flow characteristics. 

Understanding the flow of air past a surface obstacle has become very important in developing and enhancing 

new technologies needed in the present-day physical sciences 

and in future endeavors. Any protuberance or man-made 

obstruction existing on the surface of the earth will alter 

the flow pattern and change the path any fluid particles 

. might have taken. Studying the flow phenomena about surface 

obstacles will help to better understand the predominant 

characteristics and provide valuable information relative 

to many design problems encountered by practicing engineers. 

1 

L, 
Many disciplines require specific knowledge of 

atmospheric flows and the changes which will be encountered 

by introducing into them surface changes or man-made 

obstructions. Architects and design engineers need 

pertinent knowledge of atmospheric flow when constructing 

high-rise buildings and tall towers which will be subjected 

to adverse wind conditions. The effects of large buildings 

(airport hangars, terminals, etc.) on the flow of air is 

very critical. If aircraft are landing and taking off 

in the vicinity of wakes, vortices, and/or regions of 

intense turbulence generated by surface obstructions 

upstream, then some knowledge of their effects on the 

control of aircraft in flight or when taxying must be 

gained. Some particular flow characteristics (wakes, 

vortices, severe wind shear, separated flow, intense 

turbulence, gust gradients, relative maximum wind speed, 

etc.) are of great concern when locating and operating 

conventional wind energy conversion systems. There is no 

end to the list of disciplines needing knowledge of 

atmospheric flows to advance the state of the art in their 

various technologies. 

In general, the flow of air (atmospheric) is a very 

chaotic and unpredictable phenomenon. The motion of a 

particle or a "fluid point" in the atmosphere is sometimes 

described as a random process, but not in the strictest 

sense. Even if one of the velocity components (assuming 

2 
the wind velocity can be divided into three non-coplanar 

or orthogonal components) is random, the others are 

restricted in their range simply due to the conservations 

laws of fluid mechanics. Regardless, the motion is not 

deterministic and must be analyzed from a statistical 

point of view. For a more complete understanding of 

atmospheric turbulent flow about a three-dimensional 

surface obstruction, it is necessary to carry out an 

extensive experimental data collection and reduction 

routine in order to properly analyze the flow phenomena. 

This study describes an experiment designed to 

investigate the structure and magnitude of the wind fields 

about a simulated building. A more thorough fundamental 

understanding of the mean wind and turbulence structure 

about a bluff obstacle is the final expected outgrowth of 

this study. This study addresses the following segments 

of the total research effort: nature and documentation 

of the data source; data reduction procedures; statistical 

analysis, which includes correlations: comparison of different computational procedures: and evaluation of Taylor's 

hypothesis. 

Experimental studies [1,2',3]* have been attempted, 

with much success, to define regions of flow having 

characteristic differences such as recirculation, 

*Numbers in brackets refer to similarly numbered 

references in the List of References. 

3 
vorticity, etc. A similar study, sponsored by the National 

Aeronautics and Space Administration (NASA), was conducted 

and carried out in the Colorado State University (CSU) 

boundary layer wind tunnel. The CSU study [4] concentrated 

on measuring mean velocities, velocity defects, turbulence 

intensities, and wake geometries measured at the same scaled 

locations as the wind towers located at the Marshall Space 

Flight Center (MSFC) Atmospheric Boundary Layer Facility 

(ABLF). The present tower arrangement was not modeled by 

CSU, however, several other tower arrangements in the past 

have been modeled and the.wind tunnel results compared with 

the full-scale measurements at MSFC. 

These studies have shown that the flow geometry 

behind and around a three-dimensional obstruction is a 

complex phenomenum to model, and most results have come 

from experiments similar to the CSU study. Even though 

the flow field is random, there is a definite pattern 

which can be determined statistically. In a similar 

manner, Plate [5] has attempted to describe the flow field 

about a wedge-shaped obstacle. In Figure l-l no less than 

seven flow zones of different aerodynamic behavior have 

been distinguished, evidencing the complexity of the flow. 

It should be remembered that each zone blends into the 

other in a continuous manner and that in this respect it 

is rather difficult to draw-discrete regions where each is 

defined independently of the other. Rather, the attempt 

4 
1. Undisturbed boundary layer Couter layer) 

2. Region of hill influence (middle layer) 

3. Region of reestablished boundary layer (inner layer) 

4. Blending region between middle and outer layer 

5. Blending region between inner and middle layer 

6. Standing eddy zone 

7. Potential outer flow I, u, (xl Ll A 

Figure l-l The flow zones of a boundary layer disturbed by a solid wedge [4]. 
is made to define a buffer zone where the separate regions 

blend together. 

Since many questions regarding atmospheric flows 

about three-dimensional objects remain unanswered, this 

particular study has been extended, and this study 

describes the experiment designed to investigate the 

structure and magnitude of wind fields about a simulated 

block building. The present study describes the experimental arrangement, the type and expected accuracy of the 

data, the data reduction and documentation methods, and 

the extent to which data has been collected at the time 

of this writing. The results of an initial analysis of 

selected data is given along with the methods of analysis. 

Most wind tunnel experiments, although very 

important, leave some doubt as to the validity of their 

results since the turbulence length scales, gustiness, etc. 

of the natural wind are difficult to simulate. To provide 

results comparable to wind tunnel studies, a field study 

(full-scale) of the wind over a simulated block building 

has been undertaken. Some of the results obtained from the 

full-scale experimental study are presented. (Comparison 

with wind tunnel studies [4,6,7] is planned at a future 

time.) The results presented consist of: autocorrelations 

computed by the direct method and by the Fast Fourier 

Transform (FFT) method: two-point spatial correlations 

6 
(with and without lag times); and autocorrelations of the 

horizontal velocity components computed by direct and FFT 

methods for comparison purposes only. Taylor's hypothesis 

is tested against directly measured and computed autocorrelations and is found to give good results at upper 

.levels. At lower levels, however, the hypothesis is found 

to be invalid due to the disturbance of the building. 

These results are presented along with a discussion of the 

influence of the simulated block building. 

The following sections have been arranged to 

facilitate an understanding of the experiment: data 

formatting, reduction and analysis techniques; and analysis 

of selected data sets. Section II provides an explanation 

of the experiment, including location, terrain, tower 

facilities, instrumentation and associated operating 

characteristics. Section III introduces some general 

considerations relative to data reduction and analysis 

techniques and describes the specific techniques used 

herein. Section IV describes the specific data formatting 

procedures used, along with necessary subroutines to extract 

data from magnetic tapes in a logical manner. Also given 

is a brief description of the computer systems used to 

generate the users' data tapes. Examples of plotted data 

available to researchers are included and briefly explained. 

Section V is devoted to presenting a few of the results 

obtained and to illustrating the validity of Taylor's 

7 
hypothesis for computing autocorrelations. Conclusions 

are given at the end of Section V. 

The experiment described in Section II is one part 

of a three-phase study. Validation of analytical and 

numerical models of turbulent flow field and justification 

for using scale models in wind tunnels is needed. The 

experimental study described herein has been undertaken to 

satisfy this needed verification. Full-scale empirical data 

are needed to analyze the turbulent structure of the 

atmosphere. This study will supply the information needed 

to justify the use of and'the improvement of numerical 

models, as well as justifying the usefulness of scale models 

tested in wind tunnels. Also, some of the information 

gained from this study will simply be applied to improve 

the state-of-the-art technology and for the sake of research 

in general. 

Hopefully, the explanations and results presented 

herein will be helpful to individuals continuing this 

particular study and will inspire others to pursue a more 

thorough investigation of turbulent flow fields and 

related phenomena. 

8 
SECTZON II 

EXPERIMENTAL DESCRIPTION 

A. TOWER FACILITY, 

The experiments were conducted at the MSFC'; 

Atmospheric Sciences Division, Atmospheric Boundary Layer 

Facility (ABLF), located near kuntsville, Alabama. 

Figure 2-l illustrates an aerial perspective of the block 

building and tower arrangement. The tower facility was 

originally arranged with eight in-line 20 meter towers 

instrumented at four levels. For the present experimental 

setup, schematically illustrated in Figure 2-2, the tower 

arrangement consists of five in-line 20 meter (65 ft) 

towers (indicated by Tl through T5) and four short towers 

(indicated by Sl through S4). 

The tall towers are instrumented at the 3 m, 6 m, 

12 m, and 20 m levels, with the exception of T3 on which 

the instruments from the 20 m level were lowered to the 

9 m level and recorded as level 4. (This point is important 

in the data reduction format.) The short towers are 

instrumented at the 2 m, 3 m, and 6 m levels, with Sl and 

S2 stationed behind the block building laterally from T3, 

while S3 and S4 are stationed in line with the tall towers 

between T3 and T4. 

9 
.'j 

h 

,- M.% 

:, 

I’ 

7 

8 

SMALL BUSH 

.?: 2METERS' 

IN.HEIGHT 

TREES 5-q 

METERS Y 

IN 9 

HEIGHT 8 

INSTRUMENTATION 

AND RECORDING' 

I STATION 

- 

% 

t 

l-l 

3 lx 

PASTURELAND 

TOP VIEW OF THE TOWER FACILITY SITE. 

(ALL DIMENSIONS IN METERS)‘ 

2 FENCE 

Figure 2-l Aerial perspective of the tower array at NASA/George C. Marshall Space 

Flight Center, Boundary Layer Facility, in its present configuration. 

(All dimensions are given in meters.) 
T3 

I 0.75H t T. T5-f 6.5 

Figure 2-2 Schematic of the current configuration of the NASA/George C. Marshall 

Space Flight Center, 

H= 3.2 meters.) 

Boundary Layer Facility. (Not to scale, 
B. DESCRIPTION OF AVAILABLE DATA 

Several tower arrangements have been constructed 

and much data collected at the MSFC tower facility since its 

inception (1971). A description of the tower arrangements 

and data measurements prior to the present arrangement is 

given by Frost and Shahabi [2]. 

There are approximately 100 runs (40-minute 

recording periods) which have been carried out with the 

present tower arrangement. Half of the runs were conducted 

with a simulated block building included and half without. 

Run numbers 8600-8650 represent tower data which includes 

the building and run numbers 8700-8750 are no building 

cases. Only one building size was used for testing. The 

building dimensions are given in Tables 2-l and 2-2. 

C. FIELD SITE CONTOUR 

The tower facility is located in an open field which 

is not exactly level and which has slight undulations along 

the line of towers. The elevation of the ground with 

respect to the profile of the tower array is shown in 

Figure 2-3. Measurements of elevation are relative to the 

base of T3. T3 serves as the zero elevation datum plane: 

the other tower elevations are given in Table 2-l. From 

this table it can be determined that the building is located 

on an approximate 6.3 : 1 grade. The study of wind data 

reported herein neglects these small variations in terrain 

elevation. 

12 
. . Note: 6 Q height of ground relative to zero 

at the base of Tower 3; H 2, height of 

building.(H = 3.2 m) 

-80 -60 -40 

Figure 2-3 Cross-sectional contour of eight-tower array. (a indicates the base 

of each tower, x indicates ground level.) 

‘-20 0 20 40 60 

Horizontal Distance (meters) 

80 
TABLE 2~1 

TOWER LOCATION AND ELEVATION 

Ground 

Horizontal Elevation 

Building Building 

Heights Meters Heights Meters 

-24.12 -77.18 -0.045 -0.144 

Tower #l -9.04 -28.93 -0.039 -0.125 

Tower #2 -2.22 -7.10 -0.008 -0.026 

Building* -0.19 -0.61 -0.002 -0.006 

Tower #3 0 0 0 0 

Tower #S3 1.56 4.99 0.012 0.038 

Tower #S4 3.13 10.02 0.031 0.099 

Tower #4 4.69 15.01 0.043 0.138 

Tower #5 16.25 52.00 0.103 0.330 

*Building Dimensions: 

Height (H) = 3.2 m. 

Width = 2.4 m. 

Length = 26.8 m. 
D. INSTRUMENTATION 

The instrumentation at each level on each tower 

consists of a Climet Model 011-l three-cup anemometer 

(horizontal wind speed sensor), a Climet Model 012-l vane 

(horizontal wind direction sensor), and a Gill Model 27100 

propeller anemometer (vertical wind speed sensor). The 

four levels on Tl also contain Climet Model 016-5 

thermistors. 

Horizontal Wind Speed Sensor 

Horizontal wind speed is measured with a Climet 

011-l three-cup anemometer assembly and a precision light 

beam. The beam is chopped to produce an amplified.pulsed 

electrical output with a frequency proportional to wind 

speed. Table 2-2 lists the operational characteristics 

of the Model 011-l sensor [2]. 

Table 2-3 gives the calibration of the Climet wind 

speed transmitter. A 12 volt supply to the anemometer 

results in the creation of a O-12 volt square wave which 

is proportioned to the frequency of rotation [81. The sensor output can be filtered through a translator and recorded 

as a O-l volt continuous output, or it can be processed 

through a capacitor and recorded as a spike without regard 

for the amplitude of the signal. 

In the present study, the manufacturer's calibration 

is accepted, and only the tape recorder is calibrated 

15 
TABLE 2-2 

SPECIFICATIONS OF CLIMET 011-l WIND SPEED TRANSMITTER[8] 

Model 4 Description 

Power requirements 

Climet Model 011-l 

10.6 to 12.6 V at 15 ma - 

Operating range 0 to 110 mph 

Calibrated range 0.6 to 90 mph 

Signal output Approximately 10 V p-p* square wave 

output Less than 50 ohms 

Accuracy ?l% or 0.15.mph, whichever is greater 

Threshold 

Distance constant+ 

0.6 mph 

< 5 ft 

Operating temperature -50 OF to 155 OF 

Weight 14 oz 

Height 18.5 in 

Housing dimensions 3.5 x 2.25 in (height x width) 

Connector Climet 49-2004 

*p-p is peak-to-peak. 

+The distance constant is the length of a column of 

air which passes an anemometer after it has been distributed 

by a sharp gust until it reaches 63 percent (1 - l/e> of 

the new equilibrium value [8]. 

16 
TABLE 2-3 

MANUFACTURER'S CALIBRATION OF,CLIMET WIND SPEED TRhNSMITTER [8] 

Velocity Frequency Velocity Frequency Velocity Frequency 

(m/s 1 (Hz) (mph) (Hz) (Knots) (Hz) 

~0.000 

.,O. 232 

0.250 

l..OOO 

21000 

3.000 

4.000 

5.000 

7.000 

10.000 

15.000 

20.000 

25.000 

30.000 

35.000 

40.000 

60.000 

-16.57 0.000 -16.57 0.000 -16.57 

0.00 0.519 0.00 0.561. 0.00 

1.25 5.000 142.80 5.000 166.70 

54.73 10.000 302.10 10.000 350.40 

126.00 15.000 461.50 15.000 533.90 

197.30 20.000 620.80 20.doo 717.40 

268.60 22.500 700.50 25.000 900.90 

339.90 25.000 780.20 30.000 1084.40 

482.50 30.000 939.50 35.000 1267.90 

696.40 35.000 1098.90 40.000 1451.40 

1052.90 40.000 1258.20 45.000 1634.90 

1409.40 45.000 1417.60 50.000 1818..40 

1765.90 50.000 1576.90 60.000 2185.40 

2120.40 62.000 1895.60 70.000 2552.40 

2478.90 70.000 2214.30 80.000 2919.40 

2835.40 80.000 2533.00 90.000 3286.40 

4261.00 90.000 2851.70 100.000 3653.40 

17 

L- 
before each run. This calibration consists of first shorting out the oscillator plug to give zero voltage and then 

employing a Hewlett Packard oscillator to give a 1409 cps 

record on each channel. In Table 2-3 this corresponds.to 

a 44.74 mph (20 m/set) reading which is taken as full-scale 

in the data reduction. Each calibration is run one minute, 

and a microphone is employed to inform the computer laboratory of the beginning of each calibration input. This 

microphone is also used to communicate with the computer 

laboratory as to the point on each tape where simultaneous 

reduction of test data is to begin. There is additionally 

an IRIG "B" timing unit for synchronizing events occurring 

on different tapes. 

Wind Direction Transmitter 

The Climet Model 021-l vane type wind direction 

transmitter which delivers a O-4.8 volt DC signal proportional to horizontal wind direction is employed to measure 

wind direction. The sensing potentiometer which proportions 

the voltage signal is sealed within the transmitter housing, 

thereby receiving maximum protection from contamination. 

Table 2-4 depicts the characteristics of this sensor. 

The voltage amplitude output of the direction 

transmitter is proportional to the wind direction. The 

Climet wind direction sensor is a 10 kilohms continuous 

turn-potentiometer. A 4 volt input is porportioned according to the wind vane position. The instrument is calibrated [9]: 

18 
TABLE 2-4 

SPECIFICATIONS OF CLIMET 021&4 WIND DIRECTION TRANSMITTER [9] 

.___-~~.- - .~ 

Model 4 Description Climet Model 012-l' 

Power requirements 4.8 volts DC 

Mechanical range 0 to 360' continuous 

Horizontal range 3540 f 20 

Signal output 

Output impedance 

0 to 4.0'~ corresponding to 0-360° 

Potentiometric output, impedance 

varies from approximately zero 

to maximum of 10 kilohms 

Linearity *l/2% 

Threshold 0.75 mph 

Damping ratio 0.4 with Climet 014-6 vane 

Distant constant Less than 3.3 ft 

Operating temperature -50' to 155 OF 

Weight 14 oz 

Height 18.5 in 

Housing dimensions 3.5 x 2.25 in (height x diameter) 

Connector Climet 49-2001 

19 

- 
a. i volt -- 90 degrees 

b. 2 volts -- 180 degrees 

C. 3 volts -- 270 degrees 

d. 4 volts -- 360 degrees 

The 180 degree position has been aligned straight down the 

tower array in the present installation, i.e., from Tl to 

T6. A rifle scope is used to align the alignment collar 

on each tower. The towers were initially aligned with a 

surveyor's transit. The alignment procedure was conducted 

prior to each major measurement program (i.e., prior to 

the 8600 and 8700 runs). -Calibrations of the recording 

tapes are performed with a precision power supply. 

Vertical Wind Speed Anemometer 

Vertical wind speed was measured with a Gill Model 

27100 vertical axis propeller anemometer. This instrument 

is a sensitive precision air speed measuring instrument 

employing a framed polystyrene propeller molded in the form 

of a true generated helicoid. The horizontally positioned 

propeller (vertical axis) is designed to provide a given 

arc of revolution for each foot of vertically passing air. 

Extensive wind tunnel tests have shown that the propeller 

actually rotates 0.96 revolutions per foot of air for all 

wind speeds above 2.7 mph (4 ft/sec) [lo]. Increasing slippage 

occurs down to the threshold speed of 0.5 mph (0.8 ft/sec). 

In the standard instrument the propeller drives a miniature 

20 
DC tachometer generator providing an analog voltage output 

which is directly proportional to wind speed. 

The propeller anemometer will measure both forward 

and reverse air flow. When the propeller rotation reverses, 

the generator signal polarity reverses. Thus the meter or 

recorder can be calibrated to read both positively and 

negatively from a central zero position. 

Calibration of the instrument is as follows: The 

positive or negative DC voltage amplitude is directly 

proportional to the vertical velocity. At 1800 rpm 

(0.96 actual propeller revolutions per foot of air) the 

velocity equals 69.9 mph (31.25 ft/sec). Figures 2-4 and 

2-5 are used to find the vertical velocity, w(t), when the 

revolutions per minute are known [lo]. The output voltage 

signal for an updraft is recorded as a positive voltage, 

and a negative voltage corresponds to a downdraft. Also, 

the output signal is calibrated to 26.6 mph at 1800 rpm. 

Propeller response follows the cosine law within +3 percent 

in the range of 60 to 120 degrees (k60 degrees each side 

of stall). The propeller responds when the component of 

the wind is parallel to its axis of rotation. Four-blade 

polystyrene propellers provide slightly better symmetry of 

response to various wind angles, especially near the stall 

region. Figures 2-6 and 2-7 show the variation of wind 

angle with propeller and percentage of.response. The Model 

27100 was designed for optimum dynamic response in wind 

ranging from threshold to 50 mph. 

21 
3000 

2500 

E 

2 

; 2000 

9-l 

& 

E 

04 1500 

1000 

500 

0.0 

meters/second 

Calibration Points 

-1800 rpm 

-1500 rpm 

-300 rpm 

-250 rpm 

I I I I I I I I I I 

0 5 10 15 20 25 30 35 40 45 50 

Figure 2-4 Propeller calibration (wind speed versus propeller rpm) [lo]. 
. 

I 

Figure 2-5 Response of four-blade propeller to wind speeds from threshold to 

5 ft/sec [lo]. 

1.2 

1.0 

0.8 

0.6 

0.4 

0.2 

0 

0.96 r&olutions/fcmt of air 

Threshold-Generator 

Threshold-Photo-Chopper 

0 0.5 1.0 1.5 2;O 2.5 3.0 3.5 4.0 4.5 5.0 

Wind ,Speed ft/sec 
80 

60 

-60 

-80 

-100 

200 220 240 260 280 300 320 340 0 20 40 60 80 100 120 140 160 180 

Wind Angle 8. Degrees 

Figure 2-6 Propeller response versus wind angle (four-blade polystyrene propeller) 

cm. 

. 

. _-i 
100 

80 

60 

40 

3 

g 

20 

% 

d 0 

2 

$ k 

d -20 

-40 

-60 

-80 

-100 

Wind Angle,e 

I I I I I I 

60 70 80 90 100 110 120 

Wind Angle 8 Degrees 

to 40) 

Figure 2-7 Propeller response versus wind angle between 60 

and 120 degrees (four-blade polystyrene 

propeller) [LO]. 

25 
As angle of attack approaches 90 degrees, the 

distance constant, L, equals Tu',where T is the time constant and u' is the wind tunnel calibration equilibrium 

speed. The percentage of response is given by ui/u', 

where ui is the indicated speed. Also, the ratio is the 

cosine of the angle of attack cos c1 = ui/u'. 

The tape recorders are calibrated prior to each 

run by recording on each tape -0.2 volts for one minute 

and +0.2 volts for one minute supplied by a precision 

power source. The computer laboratory, when reducing the 

data, then assigns 0.0 to the -0.2 volt reading and 1000 

to the +0.2 volt reading, thus dividing a range of -10.64 

to 10.64 mph into l/1000 increments. 

26 
lr 

SECTION III 

DATA REDUCTION AND ANALYSIS 

GENERAL CONSIDERATIONS 

Data reduction and analysis is a process in which 

mathematical and statistical operations are performed with 

the assistance of probability theory to infer a logical 

conclusion from data which may otherwise seem practically 

impossible. In being called a process, these two steps 

(reduction and analysis) are necessary and inseparable when 

meaningful results are to be obtained. In general, all 

data analysis is preceded by data reduction, and each step 

can be further divided into additional steps, depending on 

the ultimate goal to be achieved from the analysis performed. 

To better understand the phenomenon of turbulent 

flow about a simulated block building, the experiment 

described herein has been designed to gather data from 

which conclusions about the flow field can be inferred. 

Much research, both analytical and experimental, has been 

conducted relative to turbulent fluid motion. Turbulence, 

in its own respect, is proving to be one of the most 

complicated problems to solve in present-day scientific 

research. 

To classify fluid motion as random or "turbulent" 

might be debated in many cases from a philosophical point 

27 
of view. It could be argued that no physical process is 

truly deterministic since at any time an unforeseen event 

could occur which would alter supposedly predictable results. 

On the other.hand, it might be argued that turbulent fluid 

motion, or any physical process, is deterministic since no 

process is random in the sense that mathematical models 

might be possible if a sufficient knowledge of the underlying mechanisms of the phenomenon producing the data were 

known. 

Even if exact mathematical models did exist, it 

would be physically impossible to verify them. To accurately 

measure the motions of the turbulent flow field with an insitu instrument, it is necessary to extract kinetic energy from 

the medium and, in so doing, alter the flow. Any such instrument 

used to measure the flow will "always" disturb the flow; thus 

the measured quantity is always modified by the simple act of 

measurement, and in principle no exact measurement can be made. 

Faced with this dilemma, it might be asked exactly how any 

empirical results should be used to verify theoretical models. 

Measurement of turbulent motion is a process, 

however, including the sampling of a quantity from which the 

error obtained is the difference between the measurement and 

the corresponding "true value." When using an instrument, 

however, there is concern for the characteristics of the 

measurement process associated with that particular instrument. That is to say, a simple reading may be taken to 

28 
measure turbulence, but this is only a sample from a statistical population generated by the process of measuring the 

turbulence itself. If the characteristics of the process 

are known, it is possible to put bounds on the error of a 

single measurement, although it is not possible to know the 

error exactly, for to do so would mean the true or exact 

value being measured is known. At least some estimate can 

be made of this particular problem. 

The process of measurement is not the theme of this 

paper, but the results obtained from measurements are of 

particular concern. This chapter is concerned with the' 

process of reducing data and performing specific analyses. 

There are general procedures followed when evaluating 

random data, and these are explained in Section A. 

A. DATA ACQUISITION AND PROCESSING 

Appropriate techniques for the acquisition and 

processing of random data (turbulent fluctuations) are 

heavily dependent upon the physical phenomenon represented 

by the data and the desired engineering goals of the 

processing. In general terms, however, processing performed 

in both the past and present has been divided into five 

primary categories: (1) collection, (2) recording and 

transmission, (3) preparation, (4) qualification, and 

(5) analysis. 

29 
Even though the.operations are divided into these 

categories, each of the categories involves a number of 

sequential steps, as schematically illustrated in Figure l-l. 

Data Collection 

The primary element in data collection is.the 

instrumentation transducer (the particular instruments 

and their specifications were given in Section II-D). 

For some applications it is possible to perform all desired data processing directly on the transducer signals 

in real time. However, this was not the case for this 

particular experiment. 

Data Recording and Transmission 

During the experiment magnetic tape recorders were 

used to record all data. A detailed explanation of the 

procedures used is given inSection III. Magnetic tape 

recorders are more convenient than other types of recorders 

because they can both store the large quantity of data and 

reproduce them in electrical form for easy transmission and 

processing by computer systems. 

Data Preparation 

The next key step in data acquisition and processing 

is preparation of the raw analog data for detailed analysis. 

The raw data is supplied from an analog tape in the form 

of voltage time histories. A number of operations are 

30 
RECORDING 

COLLECTIONWAND TWS- e PREP-- e QUALIF1- e TION CATION ANALYSIS 

MISSION 

. 

(1) COLLECTION 

----e--------c--------- 

l INTERMEbIATE INTERM!ZDIATE 1 

I ' MECHANICAL ELECTRICAL . 9 I 

MECHANICAL QUANTITY 

!-CONVERSION 

PICK-- QUANTITY , ELECTRICALA 

OFF 1 CONVERSION 1 

I- I I -, I 

I -----------------3---e A 

(2) RECORDING AND TRANSMISSION 

I 

-------------------------~ 

(3) PREPARATION 

l- 

------------------------1 

EDITING CONVERSION PRE- I 

PROCESSING -I 

& 1 I 

i-a,-,------- e---v -----w-J 

(4) QUALIFICATION 

r ---e----w--------------- 1 

i I 

I I 

I STATIONARITY PERIODICITIES * NORMALITY - I 

! i ____ ---------------m-----J 

(5) ANALYSIS 

r ----------------------- 1 

I INDIVIDUAL MULTIPLE LINEAR 

RELATION- I 

RECORDS RECORDS SHIPS 

Figure 3-l Key steps in data acquisition and 

processing. 

31 
needed at this point to transform the voltage time histories 

suitably for further processing and analysis. 

Data editinq. The data editing performed on the 

analog tapes is a pre-analysis procedure designed to 

detect and eliminate spurious and/or degraded data signals 

which might have resulted from acquisition and recording 

problems such as excessive noise, signal dropout, loss of 

signal due to instrumentation malfunction, etc. 

Once the bad data has been eliminated, the voltage 

signals are converted into engineering units (calibration). 

This step includes the necessary scaling factor for 

conversion and the actual process of calculating the new 

values by means of multiplying the appropriate scaling 

factor. The scaling factor will depend on the particular 

units used to express the data (MKS units in this experiment). 

Diqitization. The next step, digitization, 

requires special attention. This process consists of two 

separate and distinct operations: (a) sampling and 

(b) quantization. These two operations must remain 

separate and distinct even though occurring practically 

simultaneously. Many problems and limitations exist when 

data has been digitized. An explanation of these problems 

will provide an understanding of the usefulness and 

limitations placed on any digitized data. 

32 
r 

The sampling of analog data is ideally performed 

at equally spaced intervals, as illustrated in Figure 3-2. 

t0 % t2 +;h j_ 

Figure 3-2 Sampling a continuous record. 

Generally there is a problem in determining the appropriate 

interval, h, for sampling. On the one hand, sampling at 

points which are too close (small h) will yield correlated 

and highly redundant data, thus unnecessarily increasing 

the labor and cost of calculations. On the other hand, 

sampling at points which are too far apart (large h) will 

lead to confusion between the high and low frequency 

components of the original data. This latter problem, 

generally referred to as aliasing, is inherent in all 

digital processing which is preceded by an analog to 

33 
digital conversion , ,as in the case of this experimental 

operation. 

If the sampling is at every interval, h, as 

illustrated in Figure 3-2, then the sampling rate is l/h 

samples per second. However, at least two samples per cycle 

are required to define a frequency component in the original 

data. Hence, the highest frequency which can be defined 

by sampling at a rate of l/h samples per second is 1/2h Hz. 

Any frequencies in the original data above 1/2h Hz will be 

folded back into the frequency range 0 to 1/2h Hz and 

will be confused with data in this lower range. Because 

of this phenomenon, the cutoff frequency, 

is defined as the Nyquist frequency or folding frequency. 

There are two practical methods by which this aliasing 

problem can be reduced or possibly avoided. The first 

method is to choose h sufficiently small so that-it is 

physically unreasonable for data to exist above the 

associated cutoff frequency, fc. The second method is to 

filter the data prior to sampling so that information 

above a maximum prescribed frequency is no longer contained 

in the filtered data. Then choosing fc equal to the 

maximum frequency of interest will produce accurate results 

for frequencies below fc. The first of the two methods was 

used 'in this study because it saves computing time and costs. 

34 
A similar problem associated with frequency, but 

not necessarily with digital data, is the maximum length 

of the recorded signal (tN in the case of digital data). 

With this limitation (finite record length) there exists 

an equivalent lower.recognizable frequency, which is 

1 =- fQ tN 

However, trends may still exist in the data due to frequencies whose wavelength is longer than fE. Trend removal, 

a process which improves the stationarity of the data, 

will be discussed later in this chapter and more specifically in Section IV. 

Since the magnitude of each data sample must be 

expressed by some fixed number of digits, only a finite 

set of levels are available for approximating the infinite 

number of levels in the original continuous data. No 

matter how fine the scale, a choice between two consecutive 

levels or values will be required. By performing the 

quantization properly, the true level will be approximated 

by the quantizing level closest to it. The accuracy of 

the approximating process is a function of the number of 

available levels. The present digitizer produces binary 

outputs compatible with the computer system used and 

described in Section IV. The analog to digital conversion 

system produces 6 to 16 bits, which corresponds to a range 

of 64 to 65,536 levels. Other errors which occur during 

35 
the digitization process include aperture error, jitter 

and nonlinearities. These common errors encountered with 

any digitization.process will not be discussed: however, 

very descriptive explanations of these problems and 

their associated error analyses are given by Sebestyan [ll] 

and Oppenheim [12]. 

After the data are digitized, further operations 

must be performed on the data prior to any actual analysis. 

The first operation, reformatting, is theoretically trivial 

but requires considerable effort to get the data in optimum 

form for computer usage. Present-day computer operating 

systems accept system-generated formats; but the types of 

formats generated by the analog to digital conversion 

system are nonstandard and require special machine language 

formats. (These are described briefly insection IV.) 

A detailed explanation is not given here; Section IV 

describes the final data format on the digital tapes so 

that future researchers have the information needed to 

reduce complications. 

The next operation performed is conversion of the 

digitized data to physical units. The digitizing procedure 

produces information in units that are related to the true 

physical units (speed, direction, etc. in meters per 

second, degrees, etc.). A reference or calibration signal 

is recorded at the beginning of each tape when the data are 

recorded. To provide an indication of operating status, 

36 
r 

a zero calibration is also included on each tape prior to 

the actual recording periods. 

The final step , pre-qualifying the data, involves 

the detection and removal of isolated outliers,-level 

shifts and trends. The actual process used is schematically 

illustrated in Section IV. 

Data Qualification 

The correct procedures for reducing random data, 

as well as interpreting or analyzing the results, are 

strongly influenced by certain basic characteristics which 

may or may not be exhibited by the data. The three most 

important of these basic characteristics are the stationarity of the data, the presence of periodicities in the 

data, and the normality of the data. 

Standard analysis procedures apply to only the 

stationary data, whereas nonstationary data require special 

analysis for each situation. Procedures to determine 

whether the data are stationary and to remove nonstationary 

trends are discussed later. Periodicities in the data are 

identified to avoid erroneous interpretation of the results. 

Autocorrelations and spectral analysis are used to evaluate 

predominant periodicities in the data and are discussed in 

general later in this chapter. The procedures for computations are given in Section D. The validity of the assumption that the data have a Gaussian probability density 

function is investigated since the normality assumption is 

vital to some analytical applications of random data. 

37 
Stationarity. There are several means.of defining 

stationarity of random data: generally, in the strictest 

sense, the definition incorporates ensemble averages and 

ensemble probability distributions. For the purposes of 

this experiment, where only a single sample record is 

available, the assumption of ergodicity is evoked. It can 

be shown *that ergodic data (by definition) satisfy stationarity. The stationarity of data can be estimated crudely 

by visual observation of the data or can be tested by 

investigating a single record as follows: 

1. Divide the sample record into N equal time 

intervals where the data in each interval 

may be considered independently, 

2. Compute a mean square value (or mean value 

and variance) separately for each interval 

and align the sample values in the same 

time sequence as they occur in the original 

data. 

3. Test the sequence of mean square values for 

the presence of underlying trends or variations other than those due to expected 

sampling variations (sometimes performed 

using the run test). 

The mathematical calculations which require the assumption 

of stationarity are given at the end of Section III. 

38 
Periodicity. Intense periodic components in the 

data can usually be detected by visual inspection: however, 

less .intense periodic components in random data are 

not normally detected by visual inspection. This less 

intense periodicity can often be detected by inspection 

of either the power spectral density function, the probability density function, or the autocorrelation function 

of the respective sample record. Each method used to 

detect periodicity expresses it in a different manner, 

and further details can be obtained from [12). 

Normality. The most direct way to test samples 

of stationary random data for normality is to measure 

the probability density function of the data and compare 

it to the theoretical normal distributions. (This is 

done by calculating the skewness and kurtosis and plotting 

the curve using the theoretical equation and the calculated 

variance.) This was performed for each record and plotted 

(Section IV presents examples of such plots) along with 

the computed skewness and kurtosis, which are presented 

in tabular form above each plot. 

Data Analysis 

The procedures for analyzing the properties of 

sample records and/or random data may be divided logically 

into two categories: analysis of individual sample 

records and analysis of a collection of sample records, 

39 
given the properties of the individual records. Applicable 

data analysis procedures for these two categories are 

outlined below. 

Individual records. A sample procedure for 

analyzing the statistical properties of individual time 

history records is presented in Figure 3-3. It should 

be noted that many of the suggested steps in the procedure 

might be omitted for some applications, while additional 

steps might be required for other applications. Further, 

the data qualification step discussed previously is 

incorporated into the procedures to help clarify how 

these two parts of the overall data processing problem 

interact. 

All of the analysis techniques discussed in this 

report apply to sample records of only stationary data. 

However, if data are determined to be nonstationary 

during the qualification phase of the processing, special 

analysis techniques will be required, as indicated by 

Block E of Figure 3-3 (included for completeness). Since 

only stationary data are considered herein, no discussion 

of the techniques for nonstationary and transient data 

analysis is given, but they are discussed in [12]. Various 

other analyses of individual time history records are often 

required, depending upon the specific goals of the data 

processing. For example, studies of fatigue damage in 

40 
STATIONARY AND RANDOM NONSTATIONARY WITH PERIODIC COMPONENTS 

f QUALIFICATION 

A. I 

- MEAN AND MEAN SQUARE TEST FOR 

STATIONARITY 

VALUE ANALYSIS 

I 

I r 

I 

I STATIONARY 

B. I 

- AUTOCORRELATION 

ANALYSIS -I v 

I TEST FOR 

PERIODICITIES 

C. 

POWER SPECTRAL 

mwsrw ANALYSIS 

I 

I 

STATIONARY AND 

RANDOM (WITH 

I PERIODICITIES 

I E. 

NONSTATIONARY NONSTATIONARY AND 

I TRANSIENT DATA 

ANALYSIS 

IDENTIFIED OR 

I 

D. I TEST FOR G. 

- PROBABILITY r NORMALITY SPECIALIZED DATA 

DENSITY ANALYSIS 

I 

I ANALYSIS 

I - i 

NON-GAUSSIAN L---'-w-- ------ J 

Figure 3-3 General procedures for analyzing individual sample recoyds. 
mechanical systems and gust gradient analysis involve the 

peak probability density functions of strain data, as 

discussed by Frost et al.[13] relative to wind turbine 

generator development. An investigation of zero crossings 

or arbitrary level'crossings might be warranted for 

certain fatigue analysis of wind turbines experiencing 

velocity gusts whose magnitude will induce structural 

damage with repeated occurrence. 

A collection of records. In the preceding, a 

discussion for analyzing each individual sample record 

from an experiment was given. A procedure for further 

statistical analyses of a collection. of sample records 

is presented in Figure 3-4. The first step in the procedure 

is to analyze the pertinent statistical properties of the 

individual sample records, as outlined in Figure 3-3. 

Hence, the applicable portions of Figure 3-3 constitute 

Block A in Figure 3-4. 

The next step in analyzing the records is to test 

for correlation among them. As in the case of autocorrelation and power spectral density functions, the crosscorrelation and cross-spectral density functions are 

Fourier transform pairs. The measurements of a crosscorrelogram will technically not yield any new information 

from that given by a cross-spectrum. However, since it 

may present desired information in a more convenient format 

it will be addressed insection V, where Taylor's hypothesis 

42 
1 

A. B. UNCOR- C. 

ANALYSIS OF TEST FOR CORRELATION RELATED 

k m TEST FOR EQUIVALENCE 

INDIVIDUAL RECORDS OF UNCORRE&ATEDATA 

I I 

, 

I AMONG RECORDS I 

CORRJZATED 

CROSS-CORRELATION 

ANALYSIS 

D. 

POOLING OF EQUIVALENT 

UNCORRELATED DATA 

I CROSS-SPECTRAL 

t-l 

COHERENCE 

DENSITY 'ANALYSIS ANALYSIS 

H. 

FREQUENCY RESPONSE 

Figure 3-4 -General procedure for analyzing a collection of sample records. 
is described and tested using the data sets of this report. 

The cross-spectral density and coherence function analyses 

will aid in the test for correlation among the collection 

of sample records. The coherence function tells not only 

whether the records are correlated, but to what degree 

they are correlated as a function of frequency, as well as 

how much lag time exists between the two records as a 

function of frequency. The cross-spectral and coherence 

analyses were not performed during the research reported. 

B. DIGITAL DATA ANALYSIS PROCEDURES 

This section discusses the digital techniques 

(distinct from analog data analysis procedures) developed 

for analyzing the data tapes obtained from MSFC. Most 

formulae assume the data to be processed as discrete 

time series values representing sample records from 

stationary (ergodic) random processes. This discussion 

includes only methods used to compute the mean, the standard 

deviation, the removal of trends, the Fourier Transform, 

the Fast Fourier Transform, the correlation functions, and 

the spectral density function. Many procedures commonly 

used in digital data processing are not discussed in this 

section but can be found in [12]. 

Let a single continuous random record u(t) be 

sampled at points At = h apart. These points determine a 

Nyquist folding frequency, fc, given by 

44 
fc = & 

as discussed in the previous section. Let 

{tin> ; n = 1,2,3,...,N (3.2) 

be the data values found at the N points 

'n = to + nh i n = 1,2,3,...,N (3.3) 

(3.1) 

where the initial point to is arbitrary and does not enter 

into the later formulae unless the sequence is assumed to 

start at n = 0 and end at n = N - 1 as a matter of 

convenience. In equation form, the original data values 

(illustrated in Figure 3-2, page 33) are 

U n = u(to + nh) in = 1,2,3 I-*-, N (3.4) 

Arithmetic Quantities 

The sample mean value is given by 

USN l F un 

n=l 

(3.5) 

where N is the number of data samples and un represents the 

data values. The quantity u calculated here is an unbiased 

estimate of the mean value 1-1 of the total population being 

sampled. In order that subsequent formulae and calculations 

may be simplified, the data is now transformed to have a 

zero mean value. A new time history record x(t) = u(t) - u 

is therefore defined where x(t) has data values {x,1 given by 

X n = x(to + nh) = un - c i n = 1,2,3,...,N (3.6) 

Note that z = 0. The original data values are represented 

45 
by {u,) instead of by {xn) so that the.{xn) notation 

indicates a zero sample mean value. As appropriate, 

subsequent formulae will be stated in terms of the transformed data values'{xn). 

The sample standard deviation is given by 

s = [njl ;?y2 = [N t 1 ,l, txny2 (3.7) 

where N is the number of data samples. The quantities 

S and S2 are unbiased estimates of the standard deviation 

2 and variance ox and ox , respectively, of the total population being sampled. 

A further transformation of the data is convenient 

at this time if the computer calculations are to be performed 

with fixed point, as opposed to floating point arithmetic. 

Multiplying the transformed values xn by l/S yields 

'n = x,/s ; n = 1,2,3,...,N (3.8) 

This results in final data with a sample mean of zero and 

a sample standard deviation of unity. This is generally 

performed to reduce overflow and underflow errors when 

using fixed point computer calculations. 

Trend Removal 

A special correction is needed to remove any trends 

which might be in the data, defined as any frequency 

components whose periods are longer than the record length 

(f < l/tN) l In particular, this type of component cannot 

46 
be removed by highpass digital filtering [123. Hence, 

special trend removal techniques must be applied. Least 

squares procedures can be employed for the linear as well 

as the higher order polynomial trends. To remove linear 

trends only an alternative method, which is not as accurate 

as least squares procedures, is the average slope method. 

In this experiment the trend was removed by taking a least 

squares fit of a polynomial throughout the data. This 

procedure is defined in detail in Section IV. 

Autocorrelation Estimates Via Direct Computations 

For N data values'{xn), n = 1,2,...,N, from a 

transformed record x(t) which is stationary with % = 0, 

the estimated autocorrelation function at the displacement 

rh is defined by the formula 

N-r 

'r = fix(rh) = & 1 xnxn+r ; r = 0,1,2 ,...,m 

n=l 

(3.9) 

where r is the lag number, m is the maximum lag number, and 

fix(rh) is the estimate of the true value Rx(~) at lag T, 

corresponding to the displacement rh. Note that the 

maximum lag number m is related to the maximum time displacement of the estimate by 

T = T = mh max m (3.10) 

Equation (3.9) was selected since it represents an unbiased 

estimated as compared to the following biased estimate. 

'r 

N-r 

= ii, = i 1 xnxn+r : r? 0,1,2,...,m (3.11) 

n=l 

47 
This estimate will provide very accurate results when N 

is much larger than m. When N is large and m is small,with 

respect to N, then Equations (3.9) and (3.11) provide 

comparable results. 

A normalized value for the autocorrelation function 

is obtained by dividing Br by go where 

GO 

= ii,(o) = ; 1 (x,)2 = 7 

n=l 

(3.12) 

Note that the quantity go is a sample estimate of the true 

mean square value of the data. The quantity fro is related 

to the sample variance S2 by the relation 

so= Nil [ I S2 

Thus for large N, there is negligible difference between fro 

and S 2 . When fir is normalized, one obtains gr/fio which is 

theoretically between plus and minus one; that is, 

-1 f firBo 5 1 

The autocorrelation can also be computed by Fast Fourier 

Transform (FFT) techniques as discussed at the end of this 

section. 

Cross-Correlation Functions 

There are two basic approaches used for estimating 

cross-correlation functions, namely, the direct approach 

(discussed in this section) and.the FFT approach (discussed 

later in this section). 

48 
Unbiased estimates of the sample cross-correlation 

functions 

gxy(rh) = 

at lag numbers r = 0,1,2,...,m are defined by 

1 N-r 

N - r n-l XnYn+r c (3.14) 

Eyx(rh) = 

1 N-r 

N - r n-l 'nxn+r c (3.15) 

Note that the two cross-correlation functions s xy (rh) and 

ii,, differ by th e interchange of the xn and y, data 

values. 

The sample cross-correlation function 6 xy(rh) may 

be normalized to have values between plus and minus one 

by dividing by m v. This defines a sample 

cross-correlation coefficient 

Gxy(rh) = 

ffx (rh) 

= 0,1,2,...,m (3.16) 

which theoretically should satisfy -1 5 6 xy(rh) 2 1. 

Fast Fourier Transform 

The FFT is an algorithm for fast 

the Fourier transformations on a digital 

computation of 

computer. A short 

history of the FFT, as well as its many applications, 

is provided in [12] and [14]. 

The FFT is a powerful tool for calculating spectral 

density functions, cross-spectra, autocorrelations and 

cross-correlations and is discussed here for later 

reference. 

. 

49 
An infiniteArange Fourier Transform of a real-valued 

or a complex-valued record x(t) is defined by the complexvalue quantity 

03 

X(f) = 

I x(t) exp[-j2rft] dt (3.17) 

co 

Theoretically this transform, X(f), will not exist, [14], 

for an x(t) which is a representative member of a stationary 

random process when the "infinite" limits are used. 

However, by restricting the limits to a finite time interval 

of x(t), say in the range (o,T), the finite range Fourier 

Transform will exist, [S], as defined by 

T 

X(f,T) = 

I 

x(t) exp[-j2nft] dt (3.18) 

0 

For arbitrary f, the discrete version of Equation (3.18) [14] is 

X(f,T) = h Ii; xn exp[-j2rfnh] 

= 

(3.19) 

The selection of discrete frequency values for the computation of X(f,T) is 

fk = kfo = $ = & ;k= 0,1,2 ,*-*I N-l (3.20) 

At these frequencies, the transformed values of the Fourier 

components are defined by 

X(fk,T) N-l 

'k = h = n=O c xn exp[-j ~1 ; k = 0,1,2,...,~-1 

(3.21) 

where h has been included with X(f,T) to have a scale factor 

50 
of unity before the summation. Note that results are unique 

only out to k = N/2 since the Nyquist cutoff frequency 

occurs at this point. A Fast Fourier Transform method has 

been developed [14] and a modified version of the subroutine 

is.given in Figure 3-5. This subroutine computes the FFT 

of N data values. It requires N to be an integral power 

of 2. For example, N = 2a where "a" is a positive integer. 

A complete explanation of the original subroutine is given 

in [14]. The present FFT subroutine was modified to also 

calculate the inverse FFT by changing the signs of the 

imaginary parts of x(t) (noted as XI in the subroutine). 

If the value of NGG is equal to 1, the subroutine computes 

the FFT; otherwise it computes the inverse FFT. This subroutine was used extensively in the computation of the 

autocorrelations, cross-correlations and spectral density 

functions present in this thesis. The following sections 

describe briefly the indirect FFT technique for computation 

of the autocorrelation and cross-correlation functions. 

Autocorrelation Via FFT Computations 

An indirect method for computing autocorrelation 

function estimates is to first compute the power spectral 

density function directly by FFT and to then compute the 

autocorrelation by the inverse FFT of the result. The 

double use of the FFT procedure is in most cases more 

efficient than the direct procedure: of course, this 

depends upon the maximum lag values desired. 

51 
320 

321 

102 

101 

100 

103 

124 

121 

200 

SUBROUTINE FFT(N,NUvNGG) 

COMMON/ST3/XR(2048),XI(2048) 

IF(NGGeER.1) GO TO 321 

DO 320 I=lrN 

X1(1)=-X1(1) 

N2=N/2 

NUl=NU-1 

K=O 

DO 100 L=lrNU 

DO 101 I=l,N2 

P=IBITR(K/2ttNUlvNU) 

ARG=6.283155*P/FLOAT(N) 

C=COS(ARG) 

S=SIN(ARG) 

Kl=K+l KlN2::zKl+N2 

TR=XR(KlN2)WtXI(KIN2)IS 

TI=XI(KlN2)*C-XR(KlN2)tS 

XR(KlN2)=XR(Kl)-TR 

XI(KlN2)=XI(Kl)-TI 

XR(Kl)=XR(Kl)tTR 

XI(Kl~=XI(Kl)tTI 

K=K.fl 

K=K+N2 

IF(K.LT.N) GO TO 102 

K=O 

NUl=NUl-1 N2=N2/2 

DO 103 K=lrN 

I=IBITR(K-1rNU)tl 

IF(1.LE.K) GO TO 103 

TR=XR(K) TI=XI(K) 

XR(K)=XR(I) 

XI(K)=XI(I) 

XR(I)=TR 

XI(I)=TI 

CONTINUE 

IF(NGG.ER.1) GO TO 121 

DO 124 I=lvN 

XR(I)=XR(I)/N 

X1(1)=X1(1)/N 

CONTINUE 

RETURN 

ENI, 

FUNCTION IRITR(J,N!J) 

Jl=J 

IHITR=O 

DO 200 I=l,NU 

J2=Jl/2 

IEITR=IBITR*2t(Ji-2$J2) 

Jl=J2 

RETURN 

END 

Figure 37.5 FFT subroutine. 

52 
Care must be exercised in using this indirect 

method since the usual correlation function is not computed. 

Rather, this method computes a "circular" correlation 

function which is defined by the relationship 

ixc'(rh) = (N i r, fi,(rh) + 6 6,[(N - r)h] (3.22) 

where R,(rh) has been defined by Equation (3.9) and 

gxc(rh) = Gxc[(N - r)h] i r '= 0,1,2 , l - l I m (3.23) 

The "circular" correlation function can be avoided by 

adding zeros to the end of the original data. The effect 

on the correlation function by adding zeros to the data is 

to spread apart the two portions of the "circular" correlation function. In particular, if N zeros are added to 

the original N data values, the two portions will separate 

completely. 

Power spectral estimates via FFT. Computation of 

the autocorrelation function estimate requires calculation 

of the power spectra, and the procedures used are discussed 

below. 

For sampled data from a transformed record x(t) 

which is stationary with z = 0, 8 raw estimate Cx (f) ‘Of a 

true power spectral density function Gx(f) [14] is defined 

for an arbitrary f in the range 0 5 f 5 fc by 

Exe) +km' cos - lTmf [ fC II (3.24) 

53 
where h is the time interval between samples, Rr is the 

estimate of the autocorrelation function at lag r, m is the 

maximum lag number, and f, = 1/2h is the cutoff or Nyquist 

frequency as described earlier. However, the spectral 

estimate at discrete frequencies can also be obtained as 

follows: 

Gk = Z;x(fk) = & IX(fk,T)12 = $ IXkj2 (3.25) 

where X k was defined in Equation (3.21) and will be calculated using the FFT. 

The following steps are recommended [12] to compute 

the power spectrum estimates via FFT procedures. (Steps 

2 and 5 were not used since N is relatively large.) 

Assume that the sample size for the data sequence xn is 

initially of arbitrary size N. (For this experiment the 

value of N is selected to be an integral power of 2 as 

described earlier.) 

1. 

2. 

3. 

4. 

Truncate the data sequence or add zeros so 

that N = 2a, where a is an integer. 

Taper the resulting sequence using the cosine 

taper window. 

Compute the Xk using the FFT subroutine for 

. 

k = 0,l ***-I N-l. 

Compute the ek of Equation (3.25) for 

k = 0,l , l l l I N-l. 

54 
5. Adjust these estimates for the scale factor 

due to tapering [by replacing Ek with (1/0.875)Gk 

if the cosine tapering is used]. r 

Using the above procedure to calculate the power spectra 

estimate, the autocorrelation function is computed as 

.I follows. 

1. 

2. 

3. 

4. 

5. 

Augment the N data values of xnt where 

n = O,l,..., N-l, with N zeros to obtain a new 

X n sequence of 2N terms. Remember to initialize 

the imaginary values to zero if only real 

valued functions are being computed. 

Compute the 2N-point FFT giving Xk for 

k = 011 ,...,2N-1, using the FFT subroutine 

with 2N replacing N. 

Compute the raw spectral estimates Gk for 

k = O,l,..., 2N-1, using Equation (3.25). 

Compute the inverse FFT (NGG = 1) of Gk = Gk/2 

to obtain fixc(rh) for r = 0,1,2,...,2N-1. 

Discard the last half of fir to obtain results 

for r = 0,l ,...,N-1, and multiply by the scale 

factor N/(N - r). 

This procedure provides a very accurate estimate of the 

autocorrelation, as illustrated relative to the direct 

procedures in Section V , where both techniques are compared 

by plotting 

tional time 

the results and determining the total computafor different values of N. 

55 
Cross-Correlation Functions Via FFT 

The procedure used to compute the cross-correlation 

function via FFT is similar to that of the autocorrelation, 

but some differences exist. The initial size of the sample 

for both x(t) and y(t) is assumed to be N = 2a, where a is 

an integer.' For these computations, the cross-correlation 

function is obtained from the cross-spectral density 

function and involves two separate FFT's, one for x(t) and 

one for y(t). These two FFT's can be computed simultaneously 

by using the following equations and procedures. 

The FFT's of the two real-valued records are 

computed simultaneously by inserting one record x(n) as the 

real part and one record y(n) as the imaginary part of a 

complex record z(n). In equation form, let 

z (n) = x(n) + jy(n) : n = 0,1,2,...,N-1 (3.26) 

The Fourier transform of z(n) by Equation (3.19) is 

Z(k) = .Z1 [x(n) + jy(n)l exp -j 

n=O 

[ F] ; k = O,,,...,,;: 27) 

. 

This is computed by using the modified FFT subroutine 

described in the last section. It is assumed in Equations 

(3.26) and (3.27) that N data points in x(n) and y(n) are 

transformed into N frequency points which are spaced l/T 

apart. For these situations, the Nyquist cutoff frequency 

occurs when k = N/2 so that for N even, unique results 

occur only for k = 0,1,2,...,(N/2)-1. To obtain X(k) and 

Y(k) , observe that 

56 
. 

exp j ll 2.rrn.(N - k) N ] = exp[-j y] 

since expCj2mnl = 1 for any n. Hence, if Z*(k) is the 

complex conjugate of Z(k), then 

Z*(N - k) = 'jl [x(n) - jyb)] exp -3 

n=O c ' 

(3.28) 

(3.29) 

From Equations (3.27) and (3.29) it follows that 

N-l 

.Z(k) +Z*(N-k) =2 1 

n=O 

x(n) exp[-j y]= 2X(k) 

Z(k) - Z*(N - k) = 2j 'il y(n) expkj ?I= 2jy(k) 

n=O 

From this the real valued records x(n) and y(n) have Fourier 

Transforms X(k) and Y(k) given by 

X(k) = 

Z(k) + Z*(N - k) 

2 

; k = O,l,...,N-1 (3.30) 

Y(k) = z(k) - ;; 0 - k) 

Using this final result the following procedure is used to 

compute the cross-correlation Using the supplied FFT subroutine. 

1. 

2. 

3. 

4. 

Store xn in the real part and y, in the 

imaginary part of z 

n =x n + jy,, n = O,l,...,N-1. 

Augment both the real and imaginary parts with 

N zeros to obtain a new zn sequence of 2N terms. 

Compute the 2N-point FFT giving Z(k) for 

k = 0,l ,...,2N-1, using the supplied FFT 

subroutine. 

Compute Xk and Yk for k = 0,1,...,2N-1, using 

Equation (3.30). 

57 
,'5 . 

6. 

Compute the raw cross-spectral density estimate 

zxy(fk) for k = 0,1,...,2N-1, where axy(fk) = 

:I XiYkl and Xg is the complex conjugate of Xk. 

Compute the inverse FFT of e xy(k) and multiply 

by the'scale factor N/(N - r) to obtain fi xy (rh) 

for r = -N,-N+l,...,O,l,...,N-1. This scale 

factor is required because of a similar 

"circular" correlation effect as the autocorrelation function described earlier. 

These procedures have been programmed using Fortran 

language to analyze the wind data stored on the MSFC 

magnetic computer tapes. A short discussion of these data 

tapes and the associated programs needed to obtain data 

from the tapes is given in Chapter IV, and some preliminary 

analyses and results of this experiment are given in 

Section V. 

58 
- -- 

SECTION IV 

DATA ORIENTATION, FORMATTING, AND 

TAPE ACCRSSING 

Prior to using any experimental data a particular 

frame of reference is needed. The orientation of the tower 

system with respect to the ground is given in Chapter II; 

however, it is necessary to explain the frame of reference 

by which data is recorded and the relatively simple procedures used to record and retrieve data. It is also appropriate at this time to explain the procedures and the 

associated computer programs developed for extracting data 

from the available magnetic data tapes. Finally, a few of 

the example plots and computer printouts of past data 

reduction and analyses performed by MSFC are illustrated. 

These plots are in general self-explanatory, and only a 

brief explanation of each is given. With this introduction 

and explanation the following section is intended for use 

by future researchers using MSFC data tapes. 

A. DATA RFCORDING AND m.ITIAL PROCESSING 

The output from the sensors described in Section II-D 

is recorded on nine analog recorders located in the Instrumentation and Recording Station (Figure 2-1, page 10). 

59 
Recording Methods 

Horizontal wind speed. Signals produced by the 

horizontal wind speed sensors (Climet Model 011-1, three-cup 

anemometers) are recorded on analog recorders 1, 2 and 3 

(indicated in Table 4-l). The square wave with frequency 

proportional to the wind speed signal is utilized for this 

experiment. 

Wind direction. Signals produced by the wind 

direction sensors (Climet Model 012-l vanes) are recorded 

on analog,recorders 4, 5 and 6 (indicated in Table 4-2) as 

a positive DC voltage whose amplitude is directly proportional to the wind direction. 

Vertical velocity. Signals produced by the vertical velocity sensors (Gill Model 27100 propeller anemometers) are recorded on analog recorders 7, 8 and 9 

(indicated in Table 4-3) as a positive or negative DC 

voltage whose amplitude is directly proportional to the 

vertical velocity. 

Temperature. Signals produced by the temperature 

sensors (Climet Model 016-5 thermistors) are recorded on 

analog recorder 9 (indicated in Table 4-3) as a positive 

DC voltage that is directly proportional to the temperature. 

Analoq recorders. The nine analog recorders are 

Ampex Model CP-100 recorders. Each recorder has the 

60 
TABLE 4-1 

METHOD OF RECORDING HORIZONTAL WIND SPEED 

Recorder #l Recorder #2 Recorder #3 

Channel # Tower Level Channel # Tower Level Channel # Tower Level 

m 6 P 

7 

8 

9 

10 

11 

12 

13 Time 13 Time 

14 Voice 14 Voice 

1 

1 

1 

1 

2 

2 

2 

2 

3 

3 

3 

3 

1 

2 

3 

4 

1 

2 

3 

4 

1 

2 

3 

4 

4 1 

4 2 

4 3 

4 4 

5 1 

5 2 

5 3 

5 4 

6 1 

6 2 

6 3 

6 4 

4 

5 

6 

7 

8 

9 Blank 

10 Blank 

11 Blank 

12 Blank 

13 Time 

14.Voice 
TABLE 4-2 

METHOD OF RECORDING WIND DIRECTION 

Recorder #4 Recorder #5 Recorder #6 

Channel # Tower Level Channel # Tower Level Channel # Tower Level 

1 

2 

3 

4 

5 

m 6 

h, 

7 

8 

9 

10 

11 

12 

13 Time 

14 Voice 

1 

1 

1 

1 

2 

2 

2 

2 

3 

3 

3 

3 

1 

2 

3 

4 

1 

2 

3 

4 

1 

2 

3 

4 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 Time 

14 Voice 

4 

4 

4 

4 

5 

5 

5 

5 

6 

6 

6 

6 

1 1 7 

2 2 7 

3 3 7 

4 4 7 

1 5 8 

2 6 8 

3 7 8 

4 8 8 

1 9 Blank 

2 10 Blank 

3 11 Blank 

4 12 Blank 

13 Time 

14 Voice 

1 

2 

3‘ 

4 

1 

2 

3 

4 
TABLE 4-3 

METHOD OF RECORDING VERTICAL WIND SPEED 

Recorder #7 Recorder #8 Recorder #9 

Channel # Tower Level Channel # Tower Level Channel # Tower Level 

- 

1 1 1 1 4 1 1 7 1 

2 1 2 2 4 2 2 7 2 

3 

4 

u-t 5 

W 

6 

7 

8 

9 

10 

11 

12 

13 Time 

14 Voice 

1 

1 

2 

2 

2 

2 

3 

3 

3 

3 

3 

4 

1 

2 

3 

4 

1 

2 

3 

4 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 Time 

14 Voice 

4 3 

4 4 

5 1 

5 2 

5 3 

5 4 

6 1 

6 2 

6 3 

6 4 

3 

4 

5 

6 

7 

8 

9 (Temp) 

10 (Temp) 

11 (Temp) 

12 (Temp) 

13 Time 

14 Voice 

7 3 

7 4 

8 1 

8 2 

8 3 

8 4 

1 1 

1 2 

1 3 

1 4 
capability of recording 12 channels of data plus voice 

and time. The allocation of the data to the respective 

channels is indicated in Tables 4-1, 4-2, and 4-3. 

Test description. A test consists of the simultaneous recording of the output of each of the 100 sensors 

for approximately 1.5 hours. Each of the analog tapes 

are calibrated prior to the start of each test with 

approximately 30 seconds minimum and maximum calibration. 

These calibrations represent 0.0 and 100.0 percent levels 

for each sensor output. When each test is completed, the 

data tape is internally processed by the computer center 

and prepared for distribution to the user. 

Hardware Systems 

The hardware systems necessary to process and reduce 

the analog data are a cycle counter, an SDS station, a 

DDP-224 computer, and a DDP-116 computer. The following 

paragraphs describe the processing performed by each of 

the systems. 

Cycle counter. The cycle counter is used to 

digitize the wind speed data contained on analog recorders 

1, 2 and 3. This system counts the frequency of the square 

wave signal on the analog tapes for a fixed time increment 

(0.1 second) and outputs the count on a magnetic tape as a 

function of time. 

64 
SDS station. The SDS station is used to digitize 

the wind direction data on analog tapes 4, 5 and 6: the 

vertical velocity data on analog tapes 7, 8 and 9; and the 

temperature data on analog tape 9. This system converts 

the DC voltages .recorded.on these analog tapes to digital 

counts at a specified sample rate (10 per second).. These 

digital data are then written on a magnetic tape as a 

function of time. 

The calibrations on each analog tape are digitized 

using the above procedures. These calibration data are 

then written as the first two files on the digital data 

tapes to insure all units are working properly. (Malfunction is easily detected by analyzing the first two records 

containing the calibration results.) 

To digitize all 68 channels of data on analog tapes 

4-9, six runs on the SDS station are required (one for each 

data tape). 

DDP-224. The DDP-224 is used to convert the data 

from the above stations from raw counts to engineering 

units and to prepare the data for analysis using the DDP-116 

system. The data is later edited. 

DDP-116. The DDP-116 is used to compute the 

several statistidal properties of turbulence described in 

Section III. 

65 
Software Used in Preparing Master Digital Tapes 

In response to a request from.MSFC; the Computer 

Applications Section, Data Reduction Department of Computer 

Sciences Corporation has developed the software required to 

support the internal data reduction. This software is comprised of three DDP-224 programs and one DDP-116 program. 

DDP-224 programs. The DDP-224 programs are used 

to do all preliminary processing required to prepare the 

data for analysis. There are three main programs used in 

the DDP-224; namely, 

1. Merge program. 

2. Lon-Lat program. 

3. Filter-Edit program. 

The merge program uses as input the 14 tapes 

created at the Analog to Digital (A/D) Stations. The 

program converts the data from raw counts to engineering 

units and merges the data into a time history stored on 

the disk for output to tape. This program also does a 

preliminary edit of each data channel for data out of range 

and compiles a parity history for each input tape. The 

program may be restarted with any number of the input tapes 

if there are problems encountered while merging. 

The Lon-Lat program uses the output tape generated 

by the merge program to compute an overall mean for each 

data channel and the components of turbulence contained in 

the data. The components of turbulence are output on tape 

as a function of time. 

66 
The Filter-Edit program uses as input the tape 

generated by the Lon-Lat program. These components of 

turbulence are filtered and edited for missing data and 

data flagged as out of range during the merge process. 

The Filter-Edit program will linearly interpolate for up to 

2.0 seconds of bad or missing data on each channel. Data 

channels that contain more than 2.0 seconds of erroneous 

data are flagged as being permanently missing. These data 

channels receive no further processing, however, they are 

retained for future inspection. This Filter-Edit program 

outputs the filtered data on tape as a function of time for 

processing on the DDP-116 system. 

DDP-116 program. The DDP-116 program uses as 

input the tape generated by the Filter-Edit program. This 

system (DDP-116) is used to analyze the components of turbulence and to display the analysis in a form that is easily 

interpreted by a researcher having an adequate background in 

statistical techniques and representations. The program 

used in the DDP-116 computes statistics, autocorrelation 

functions, and power spectral densities of the turbulence. 

These results are plotted using an SC-4020 plotter. The 

program also outputs the analysis on magnetic tape for 

future reference. 

Magnetic Tape Reduction Summary 

The data reduction process for the MSFC eight tower 

array can best be described as a sequence of events in which 

67 
the status of each event determines the action required 

for initiation of the next event. The initial magnetic 

tape reduction and analysis process can be divided into 

eight events as follows: 

1. Receive nine data tapes for each run and 

enter in permanent log all pertinent infor2. 

3. 

4. 

mation necessary for internal 

operations. 

Run request submitted by MSFC 

Application Section, Computer 

Corporation. 

Digitize the analog tapes. 

computer 

to Computer 

Sciences 

5. 

6. 

7. 

8. 

The 

Indicate reel's start and stop time for 

submission to the merge program. 

Merge the digitized data and convert from raw 

counts to engineering units. 

Convert digital data from speed and direction 

to longitudinal and lateral (Lon-Lat) components. (The details of this conversion 

are given in Section B of this chapter.) 

Filter and edit the components of turbulence. 

Analyze the components of turbulence. 

complete process of producing the digital 

magnetic tapes and preliminary data reduction and statistical analysis is presented in Figure 4-1. It must be 

remembered that this process is necessary for each 

68 
I 

Recorder 1, 2 & 3 

3 Analog Tapes with 

32 Channels of 

Horizontal Wind Speeds 

Cycle Counter 

3 

Cycle Counter 

2 Runs 

Recorder 4, 5 & 6 1 

SDS -I . ..- laf 'I .I. Kun 

ata =2l I I J I - 

I I -# 

3 Analog Tapes with 

32 Channels of 

Horizontal Wind Direc 

3 

SDS 

1 Run 

Recorder 7, 8 & 9 

3 Analog Tapes with 

32 Channels of 

Vertical Wind Velocity 

and 4 Channels of 

Temperature 

0 1 

” SDS 

1Run 

0 3 

Figure 4-l Flow chart showing data processing of 

magnetic tape for an individual run. 

69 
experimental run and that certain plots are produced and 

a digital magnetic tape for future reference and analysis 

of the data is generated. 

Data Channels and Tower Representation 

The reported data for the various instrumentation 

locations are listed according to channel numbers. There 

are 96 channels, which are arranged as follows: Channels 

l-32 record horizontal wind speed, channels 33-64 record 

wind direction, and channels 65-96 record vertical wind 

speed. Table 4-4 indicates the corresponding channels, 

towers and levels recorded on tape and used in determining 

the various plots produced by the MSFC data systems 

laboratory. 

It should be noted that the instrumentation on 

T3, level 4, (T3L4) has been moved to the 9 meter level and 

recorded on channels 12, 44 and 76, which correspond to 

the longitudinal, lateral and vertical velocity components, 

respectively. Also, short towers (SILJ, where I and J 

represent tower and level numbers respectively) Sl, 52, S3 

and S4 are recorded as T6Ll - T8L4 in ascending order 

and listed in Table 4-5. This method of recording was 

accomplished by simply moving the appropriate sensors to 

their perspective towers and levels and noting the change 

in the log for future reference. 

72 
TABLE 4-4 

TOWERS AND LEVELS ASSOCIATED WITH THE GIVEN CHANNEL NUMBER 

Data 

Recorder 

#-Channel 

Data Systems' 

Lab Output 

Data Type 

Channel Data 

Tower 

and 

Level 

Wind 

Speed 

-4 

l-l 1. 

l-2 2 

l-3 3 

l-4 4 

l-5 5 

l-6 6 

l-7 7 

l-8 8 

l-9 9 

l-10 10 

l-11 11 

1-12 12 

2-l 13 

2-2 14 

2-3 15 

2-4 16 

2-5 17 

2-6 18 

2-7 19 

2-8 20 

2-9 21 

2-10 22 

2-11 23 

2-12 24 

3-l 25 

3-2 26 

3-3 27 

3-4 28 

3-5 29 

3-6 30 

3-7 31 

3-8 32 

Wind 4-l 33 

Direction 4-2 34 

+ 4-3 35 

4-4 36 

4-5 37 

4-6 38 

Longitudinal 

Component 

Spectra 

+ 

Lateral 

Component 

Spectra 

JTlLl 

T1L2 

TlL3 

T1L4 

T2Ll 

T2L2 

T2L3 

T2L4 

T3Ll 

T3L2 

T3L3 

T3L4 

T4Ll 

T4L2 

T4L3 

T4L4 

T5Ll 

T5L2 

T5L3 

T5L4 

T6Ll 

T6L2 

T6L3 

T6L4 

T7L1 

T7L2 

T7L3 

T7L4 

T8Ll 

T8L2 

T8L3 

T8L4 

TlLl 

TlL2 

TlL3 

TlL4 

T2Ll 

T2L2 

73 
TABLE 4-4 (Continued) 

Data Systems 

Lab Output 

Data Type 

Data Channel Data 

Recorder 

X-Channel 

Tower 

and 

Level 

Wind 4-7 

Direction 4-8 

+ J 4-9 

4-10 

4-11 

4-12 

5-l 

5-2 

5-3 

5-4 

5-5 

5-6 

5-7 

5-8 

5-9 

5-10 

5-11 

5-12 

6-l 

6-2 

6-3 

6-4 

6-5 

6-6 

6-7 

6-8 

Vertical 

Wind 

Speed 

-4 

7-l 65 

7-2 66 

7-3 67 

7-4 68 

7-5 69 

7-6 70 

7-7 71 

7-8 @' 7 2 

7-9 73 

7-10 74 

7-11 75 

7-12 76 

8-l 77 

8-2 78 

39 

40 

41 

42 

43 

44 

45 

46 

47 

48 

49 

50 

51 

52 

53 

54 

55 

56 

57 

58 

59 

ZY 

62 

63 

64 

Lateral 

Component 

Spectra 

+ 

Vertical 

Component 

Spectra 

4 

T2L3 

T2L4 

T3Ll 

T3L2 

T3L3 

T3L4 

T4Ll 

T4L2 

T4L3 

T4L4 

T5Ll 

T5L2 

T5L3 

T5L4 

T6Ll 

T6L2 

T6L3 

T6L4 

T7Ll 

T7L2 

T7L3 

T7L4 

T8Ll 

T8L2 

T8L3 

T8L4 

TlLl 

TlL2 

TlL3 

TlL4 

T2Ll 

T2L2 

T2L3 

T2L4 

T3Ll 

T3L2 

T3L3 

T3L4 

T4Ll 

T4L2 

74 
TABLE 4-4 (Continued) 

Data 

Recorder 

#-Channel 

Data Systems 

Lab Output 

Data Type 

Channel Data 

Tower 

and 

Level 

Vertical 8-3 79 

Wind 8-4 80 

Speed 8-5 81 

+ 8-6 82 

8-7 83 

8-8 84 

8-9 85 

8-10 86 

8-11 87 

8-12 88 

9-l 89 

9-2 90 

9-3 91 

9-4 92 

9-5 93 

9-6 94 

9-7 95 

9-8 96 

Vertical 

Component 

Spectra 

+ 

T4L3 

T4L4 

T5Ll 

T5L2 

T5L3 

T5L4 

T6Ll 

T6L2 

T6L3 

T6L4 

T7Ll 

T7L2 

T7L3 

T7L4 

T8Ll 

T8L2 

T8L3 

T8L4 

75 
TABLE 4-5 

SHORT TOWERS RECORDED AS TALL* 

Short Tower Tall Tower 

Tower Level Tower Level 

Sl 

Sl 

Ll 

L2 

L3 

T6 

T6 

Ll 

L2 

L3 

s2 Ll T6 L4 

s2 L2 T7 Ll 

s2 L3 T7 L2 

s3 Ll T7 L3 

s3 L2 

s3 L3 T8 Ll 

s4 Ll T8 L2 

L3 

s4 L3 T8 L4 

*The method of recording was accomplished by simply 

moving the appropriate sensors from the tall towers (were 

disassembled) to the newer short towers and recording on 

magnetic tape as indicated above. 

76 
; B. DIGITAL DATA PROCESSING 

The analog to digital convertor, described generally 

in Chapter II along with the digitization procedure explained in Chapter III is used to produce a digital signal 

having 0.1 second averages. Tapes containing these data 

are produced by the NASA/MSFC computer laboratory. The 

data include horizontal, lateral and vertical components 

of wind speed (and temperature as described in Section II). 

The original digital data, prior to processing, was in 

the form of 0.1 second averages of the horizontal wind 

speed, V, horizontal wind direction, 8, and vertical wind 

speed, w. The principle used for digitization is illustrated 

in Figure 4-2. Let Vn be the average value of V(t) over the 

time increment At between tn.and tnWl. The frequency of 

sampling, n, now essentially becomes n = l/At. The mean 

velocity is then given by 

Q-z; Y vn 

n=l 

(4.1) 

where N is the total number of time increments'(tN - to)/At. 

The time t P = (tN - to) is the total time period of the 

data record recorded. The same computation is performed 

for the vertical velocity obtaining 

(4.2) 

All digitized data is first bulk-averaged with the 

following relationships 

77 
True North 

Building 

S 

x; 

W 

E 

N 

Note: Wind from 0 degree is from the north, and wind from 

180 degrees is from the south. 

Figure 4-3 Definition of average wind speed and respective 

wind direction. 

80 
array (from Tl to T5) as shown also in Figure 4-3. Then 

v is a positive wind component from the west or a 'positive 

wind component toward the east. In a similar mariner,,,, is 

a positive wind component toward the north or equally a 

positive wind component from the south. 

c. FLUCTUATING VELOCITY COMPONENTS 

A new frame of reference is now used from which 

the'fluctuating components are measured. Letting the mean 

horizontal wind velocity, VH, be the longitudinal area 

of the new frame of reference, the fluctuating velocity 

components can be defined. The lateral and longitudinal 

velocity components are illustrated in Figure 4-4 relative 

to the horizontal mean velocity. The fluctuating components of the wind in the lateral direction, v', and in 

the horizontal direction, u', are perpendicular and parallel 

to the mean wind direction, respectively. The following 

relationships may be employed to compute vk and uk for 

the kth time increment, tk = to + (2k - 1) At/2; 

= v(tk) sin[e(tk) - e] 

= Wk) cos[e(tk) - 5'3 - VH 

(4.6) 

The resulting fluctuating components will appear as 

shown in Figure 4-5 having in many cases a trend with time 

(.usually non-linear). The,trend results from diurnal 

variations. The procedure for removing the trend is to 

81 
V’ 

Array Line 

Figure 4-4 Definition of wind fluctuations u' and v'. 

l/10 Set Increments 

u" is u' .- vpttJJ 

Figure 4-5 Illustration of trend removal. 

v (t 1 P k 

82 
take a least squares fit of a polynomial throughout the 

data, i.e., v P = C + Bt + At2. Where the values of A, B 

and C are obtained by solving the following system of 

equations; 

NC + BCtk + ACt; = Cu,: 

1 

CCtk + BEt: + ACt; = Ctku; 

t 

CEt; + BCt: + AR; = +; 

1 

where A, B, and C are unknown constant coefficients, 

tk = to + (2K - 1) At/2 and uk is the kth value of u' or 

u’ (t,) l The mean of the fluctuating velocity u' is then 

calculated from 

1 lN U =- 

c 

N k=l "lk 

(4.7) 

(4.8) 

where N is the total number of data samples. The computed 

parabolic curve fit estimates the variations of the 

averaged data over the sampling interval. A similar procedure is carried out for 7 and w' also. Thus, new 

random variables are defined as: 

% k = u' - C + Btk + At; 

"IT k =: v' - 

2 Cl + Bltk + Altk 

"ir k = w' - C2 2 + B2tk + A2tk 

I 1 

(4.9) 

Averaging the three components u", v", and w" we get 

83 

I 
(4.10) 

In general, the mean value of these double prime quantities 

will not be zero, hence in order to obtain a mean value of 

zero the following triple prime quantities are defined: 

ull' = u" = u" 

vw' = v" = v" 

will = wll = w" 

These final triple prime quantities are digitally 

recorded on a magnetic tape in a format to be discussed in 

the following section. 

D. TAPE FORMAT AND COMPUTER PROGRWS 

The data tapes received from the MSFC computer 

center were generated on a UNIVAC computer having a bit 

structure different from that of the IBM/360 used for 

retrieving data from the tapes and performing the data 

analysis reported herein. The data tapes from MSFC are 

nine track unlabeled tapes having unformatted records 

with a block size of 2300. These tapes have been retained 

as masters from which a working copy is produced on the 

IBM tape drives. 

84 
The working copy of all master data tapes is 

produced on a scratch data tape which has been initialized 

and labeled using the program listed in Figure 4-6. Scratch 

tapes are assigned to the programmer by the computer 

facilities but must be initialized and labeled prior to 

their use. In this example, tape number 8886 is a scratch 

tape previously assigned to a particular project code 

(TTTTTT is where the project code is indicated) and the 

programmer's code is indicated also in Figure 4-6 as PPPPPP. 

Any serial number could be logically written on the tape 

at the programmer's preference; however, serial numbers 

equal to the label number are convenient. 

IIQIXII II 1 

//,JUtiNAME JOB ('~TT~TT,YPEPPP,GIB),NAME 

//*TAPL OObS86,W 

//*KLMAKIG PLEASL ~YICIJEJT 8886 INSTEAD UC' SCHA'lCtr 

// EXLC PGM=IEHINlW 

//SYSYkldT DD SYSUU'l'=A 

//TAPE uD DCB=~OW=3,U~~lT=3400-4 

usrsuv i)u * 

TAPE INTT'I' SEH=008b86 

Figure 4-6 Initialization program. 

Once the scratch tape has been initialized and a 

serial number has been logically written on the tape by 

the operating system, a working copy of the master tape can 

be produced. In order to convert from UNIVAC to IBM bit 

structure, a special PL/l program was developed. This 

85 
66. 

67, 

&8+ 

6'1, 

70, 

71. 

72. 

73, 

74, 

75 * 

76, 

77, 

7a l 

7P* 

$30 + 

81, 

I32 + 

83 + 

I34 + 

I35 + 

86, 

t37+ 

80 + 

I3Y + 

40 + 

4 I. * 

P2 + 

93, 

94 , 

95. 

96. 

c17 + 

VERTICAL 

VERTICAL 

UERTICAL 

U!?:RTICAL. 

UERTI:CAL 

VERTICAL 

VERTICAL 

VERTICAL 

VERTICAL 

UERT1:CAL 

VERTICAL 

UELRT Xwll... 

UEtiTlXN.. 

UERTICAL 

UERTICAL 

UERTICAI... 

ukwwxd, 

UERT I CAL. 

uixT I: m... 

uEF2.r i:cAL 

UERT ICAL 

VERTICAL. 

UERT I CAL.. 

UERTICAL.. 

urxr:mi... 

utxr n-m.. 

UERT:I:CAL.. 

UERT ICAL. 

VERTICAL 

ummccd.. 

UEXT ICRL.. 

umTmd. 

COMPONENT 

COMPONENT 

CC)MF:‘(3NENT 

COMF:‘ONEN’l 

COMPCINENT 

COMF’ONENT 

COMF'ONENT 

COMF'ONENT 

COMPONEN'I 

COMPONEWT 

COMPONENT 

COMPONEN’I 

C:OMF”ONENT 

COMPONENT 

COMPCINENl 

COMPONENT 

COMPONEN’T 

COMPONENl 

COMPONENT 

COMPONENl 

COMF’ONEN’I 

COMF:‘ONE:Nl 

COMF’~:lNE,NT 

COMF:‘ONENT 

COMF:‘ClNENl 

COMF:‘ONENl 

COMPC)NE..NT 

cmwONENi 

COMF:‘ONE:NT 

COMF’CINENT 

COt~F:‘QNE:NT 

COMF’ONENl 

TOWER 1 

TCIWER 1 

TOWEFt 1 

TOWER 1 

TOWEX 2 

TOWER 2 

TOWER 2 

Towm 2 

TOWER 3 

TOWER 3 

TOWEX 3 

Towm 3 

TOWEX 4 

TOWER ,,4 

TOWE:R 4 

Towm 4 

TgWE:R 5 

TowEFt 5 

TOWER 5 

TOWER 5 

TOWEFI’ 6 

TC)WE,R 6 

TOWER 6 

TOWER 6 

TcIWER 7 

Towm 7 

TOWER 7 

TOWER 7 

TCIWEX 8 

TOWE:R a 

TCIWEZR a 

TT)WER a 

LEUEX 

LEUEX 

LEUEX 

LEUE:L 

LE:UE:L 

LEUEL 

LEUEL 

LEX’EL 

LEUEX 

LEZUEL 

LEVEL 

LEZUEIL 

L.E:UEL 

LE::UE,L 

LE:UEL 

LEIUEL 

LE:UEL 

LEZiJE:L 

LEUE:L.. 

LEUEL 

LEXJEL 

LE:UE:L 

LE:UE::L~ 

LE:UEL 

LE:UEL 

L..E:UE:L 

LE,UE~L 

l.,EUEL 

LEVEL 

LEUEL 

LEUE:L 

LEZUEL 

1 

2 

3 

4 

1 

2 

3 

4 

1 

I;! 

3 

4 

1 

L. 3 

3 

4 

1. 

2 

3 

4 

1 

2 

3 

4 

1 

2 

3 

4 

1 

2 

3 

4 

Figure 4-8 (continued) 

90 
9a. TEMF'ERATURE TCIWEFI' 1 LEUEX 1 

99, TE:MF:'ERATIJRE TOWER 1 LESUEX 2 

IOQ+ TEZMPELRRTURE: TOWER 1 L,E~UE:L, 3 

1.01. TE:MPEi:h'ATURE TUWER 1 L,ENE:L, 3 

l 

401.: 

4 () ‘7 a.. E 

+ 

SECONII ELOCK OF BATA RE:F:'E:ATEi THE F~E:I:ORD F-OFirMRT CIF 

m...~:hwxm WI:I~~DS 2 Tl+mJCiti 101 , TIME FOR THIS BLTKK 

OF IIATA 1s EQUAL. TO WORrI 1 PLIJS 0. 1 ,SE:C:DNDB. 

THIIW BL,(JCK + 

F 0 1.1 ~:r: Tki E I... (3 (2 K . 

Tl::sT NIJMBEI:;: 

yE;:?‘ltJ 

MCINTH 

1:' c?r Y 

TIME OF I:lAY TEST EE:GAN 

sTml:m NIJI~~~ . . . 

Figure 4-8 (continued) 

91 
data from the tape in a logical manner. An algorithm 

has been developed to extract data from the tapes in a 

sequential manner. It is possible to extract data from a 

single point by dimensioning an array by 507 and specifying 

the exact location of the data being sought. This in 

essence has been performed: however, instead of sampling 

only one of the velocity components, a subroutine program 

has been developed to sample four components with only 

one pass of the tape. Also, the option of selecting 

every time increment or to' select only equally spaced 

time increments (every point, every other point, every 

third point, etc.) has been included. This program is 

illustrated in Figure 4-9. The argument contains all the 

information needed to read and control the magnetic tape. 

The data arrays W, X, Y, and 2 are used to store the 

total number of data values, NDV, being read from each 

channel of the tape. NTW, NLW, and NCW, respectively, 

are the tower number (l-81, level number (l-41, and 

component number (1, 2 or 3 corresponding to the longitudinal, lateral and vertical components, respectively). 

NSTEP indicates the number of data time intervals to be 

skipped: for example 1 would cause every point to be 

extracted, 2 would cause every other point to be extracted, 

3 would extract every third point, etc. NRUN is data passed 

back to the calling program and represents the run number 

of the tape. NT is a switch to indicate whether an end 

92 

._______ --. .- __--..- 
Figure 4-9 Subroutine used to extract data from magnetic 

tapes. 

93 
of file has been reached (NT = 1 means no end of file had 

been reached and the subroutine finished normally, whereas 

when NT is returned as a-l, then it indicates an end of file 

has been reached while reading the tape). This automatically 

rewinds the tape in the last branch of the subroutine. 

NTX, NTY, and NTZ are tower numbers: NLX, NLY, and NLZ are 

the corresponding levels; and NCX, NCY, and NCZ are the 

respective components for the other data arrays X, Y, and Z. 

It should be noted that this subroutine only rewinds the 

magnetic tape upon encountering an end of file, and if it 

is necessary to use data at the beginning of the tape 

repeatedly, a rewind statement must be used after the call 

statement. This is very important and should be remembered 

when any correlation or spectral functions are being computed. 

This subroutine can easily be modified to read any number 

of elements by simply reducing or increasing the number of 

arrays within the subroutine and associated statements. 

E. GENERAL STATISTICAL RESULTS 

Several statistics of the triple prime random 

variables developed in Section III are computed and plotted 

by the MSFC computer laboratory. A set of plots for 

each data channel for each run is provided by the MSFC 

computer facilities. A sample set of the plots for one 

channel is presented and described in this section. 

Similar data and plots are available for other channels 

94 
and runs and provide a good means of assessing the data 

prior to further analysis. 

A typical plot of u"' versus time is given in 

Figure 4-10. This plot provides a visual indication of 

the fluctuating digital signal as a function of time. 

Information of significance is tabulated above the 

figure and includes test number, 8624: channel number, 1; 

sample rate, 2/set; and the variance (erroneously labeled 

as RMS value), 0.938. Approximately 8.33 minutes are 

plotted of the full 40 minute time history available on 

magnetic tape. 

The probability density distribution function is 

compared with a Gaussian distribution having the same 

variance, in Figure 4-11. The probability density function 

is computed by dividing the range of u"' into increments 

Au"'. By scanning u"', summing the number of data points 

which lie in each Au"' increment, and dividing by the 

total number of data points, the probability density 

function is obtained. The density is then plotted versus 

c"'/S as shown in Figure 4-10. ii"' is the midpoint value of 

the increment Au"'. In addition to the standard information 

listed on all the computer plots; the mean, standard 

deviation, skewness and kurtosis, along with other statistical results, are tabulated above the plot in Figure 4-11. 

The skewness is a tendency of a distribution to 

depart from a symmetrical form or to have a larger tail on 

95 
ELI 

b.aw+w m 6.22lf44 

WI 

2.fOofIO4f 

I 

: 

LWOYIO~ 

s 

0.0001104 

: 

x MfO210* 

4 .0001104’ 

4.fWflO~ 

4.eYO110* 

t 

I I I, I 

I, I I I, I 'I I I I, I 

II I I I' I I I I II I 

I, I -I I 

I, I I I II I 

0.0 100.0 202.0 200.0 400.0 4Qo.o MO.0 100.0 W.0 400.0 

Figure 4-10 A typical plot of u"' versus time: TAU = 0:s 

sec.; units of m s-'(not a complete record). 
6 

L 

lfsl Fll.IER B.Y. 

LIII(Slw &%I 

b.bbbf4f 

2.(QI 2 

LlCf 11M b.19f49 m L*If* !iTi$s 442-2712 

IELI. 110. m*l cllw.ms 0.424 

rrmrnlnm f4E4ufmclfs 

FNEO. ms *+. FREO. ms w. MS w. ms w. 

4.bbbE-42 O.IIb 9.333E42 O.lb9 4.2E52 O.lbO 2.2Ei2 0.151 

2.bbJOOO4lbE42 0.142 0.109 0.129 0.194 4.124 0.1'9 0. 

0.193 0.103 O.Ib9 0.101 0.129 4.b44M2 0.2% 9.b42f42 

0.299 9.4blE-02 0.219 4.26OE-02 0.143 4.992E42 0.21) I.YIE-O? 

0.9Ob 7.21bE-02 0.293 b.991E42 4.2b3 b.OlE42 0.39b b.bnE-02 

QI-f4LlIRI 90.134 2.4 YERCENh 15.012 4 FERxNk 19.Obb ’ 

LzE, 

CM. WCE o.wo lo o.ow Wlb IubEs wGwEs -2.w IfmfT 3.149 

S.0.Z 0.924 OIEUZ 0.941 NnOSlS 2.194 

Y.OZh 2.Ibb rn.9l4h 1.949 MMMk 2.w2 

2.4W110+41 

2.0001'04' 

: 

'.T401'0~' 

I 

c 1.4wa10+4' 

c ii 

1 

'.2401'0*' 

0 

C 

0 '.4401'0*' 

1" 

0 1.4001'0@4 

4.404:10@4 

2.4WllO* 

-2.00012 -1.00009 O.OWOb l.OOWb 2.WOOb 2.WOOJOOOW9 

. s rnsf4wED IWSITV 111 S.D. . s GNSSlnu CEUSIIY I* S.D. 

Figure 4-11 A typical plot of probability density compared 

with a Gaussian density. 
one side or the other. gnterest in this parameter lies 

in its measure of the amount of departure or skewnbss from 

a symmetrical probability distribution, 

N 

Skewness = i 1 (L$')~/S~ 

k=l 

It can be seen in Figure 4-11 that the skewness is calculated to be 0.458, as compared to 0.0 for a Gaussian curve. 

The probability density distribution may conceivably 

be perfectly symmetrical, yet differ from a normal curve as 

shown in Figure 4-12. The curve illustrated in case 1 is 

higher and narrower than the normal distribution and is 

labeled as being leptokurtic. This differs from case 2 

where the curve is lower and wider than a normal distribution and is labeled as platykurtic. 

Kurtosis = i 

N 

1 (ug 4/s4 

k=l 

The calculated value of the kurtosis is 3.145, Figure 4-11, 

and since it is slightly higher than the value of three 

for a true Gaussian curve, this particular data is 

leptokurtic. 

The range of the u"' data is also listed "In Figure 

4-11. The maximum value of u"' (3.789) and the minimum 

value (-2.489) provide the extremes in the data over the 

range plotted. These values are tabulated above the plot 

in Figure 4-11. 

98 
r Kurtosis (leptokurtic) 

r Kytosis (platykurtic) 

Case 1 

Curve 

Case 2 

Curve 

Figure 4-12 An example of leptokurtic and platykurtic curves 

as compared to a normal distribution. 
A cumulative probability distribution of the data 

is plotted in Figure 4-13. 

. Plots of the autocorrelation function and power 

spectral density function are illustrated in Figure 4-14 

and 4-15, respectively. Computation of these functions 

is described in Chapter III along with a brief explanation 

of their applications. 

Mean values for each run are available in computer 

printouts. A typical printout of mean values for test run 

8624 is illustrated in Figure 4-16. Data similar to those 

tabulated have been used in the past [l] to plot velocity 

profiles and velocity deficits behind the block building 

using a slightly different tower arrangement from that 

described in Figure 2-2, page 11. 

The plots and printouts described in this section 

are valuable for quick reference prior to performing 

additional analyses. For more detailed analysis and for 

application of the data, however, the plots are not useful, 

and recomputation of the results is necessary. 

100 
Y 

b r 

I TEST 4b29 

LINKfCHN )(UEbl 

4LlCE 1lllE b.049bM 1'0 b.fOlhM 

IFns. No. twuyl 

ml44 4.u. b.bbbf43 IIf 

9Nl.E Wlf 2.000 #SEC. 

9E-cR?4nP 992-2132 

cm~. ms 0.932 I 

L 

: b.OWXIO1ol 

I 

" 

-1.oow9 O.OOOOb 1.00001 2.WOOb ..OWG9 

. s mPME0 DFNlllP IN I.D. 

Figure 4-13 A typical plot of the accumulative percent of data. 
Wlf 01101ffb IO w * 1022 2 

lE5T 

LIUtCtW ElkI 

PILIEn 0-u. IA&E41 I@2 

SnFLfIIlf 2.w Isa. 

IICf we b.aw49 TO b.24lE~ 2”fmP”wP *2-2n2 

(Fns. no. cum1 cm. ms 0.930 

4.0401’0~’ 

2.4W4104’ 

n 

: 

: 

0 

: 

O.WOXlO~ 

f 

I. 

: 

’ -L.4WIIO4’ 

: 

4.WO2104’ 

I 1-t 

o.ow w.ow IW.00’ 14O.WJ 2W.W1 z4o.w3 #.Wl 

lln! flaul 

Figure 4-14 A typical plot of an autocorrelation function: 

TAU = 0.5 sec.: units of m2sm2 . 
I.IOOIl0-Q' 

? 

: 

I 

F 

: 

1.0001104~ 

a 

Figure 4-15 A typical power spectral density plot: units 

t i 1 ii I I 
--- 

TEST NO, 8624 

-_._-_~-- -_. -._ ..-_. _..-_._- .-. . ..- _ 

2/?6/?6 TINE 165000 STATION NO, llfiO1 

--m-m --.- 

..- __.-. 

MEAN 

.- -__._-- 

MEAN VfRT~CiL”---~-~O~--~~-~~SERVATIO~~~-.. 

SCAL?R --.--DIRECTION _____ Y!LDC~TY_-SW ..__ CR DIRECJ~dW?II.~~L 

___--- --- .i;9605 --.. - ---. .-.A -___ 2si45---- .- 

-Li 2.0487.5700 2,??3i 4.4719 -4,2263.--- 3.6241 214.4623 ;.$$‘J;;. . m-m.:.-. 498229 !02?2 __.__-____ 24245 37..-. 24275 _- _ 3.4Cb8 24975 

4 .3.92?1 _4.??$4 

,12/Z 

-;. 1.9303 2,lbJO 5,13a 682179 2,8?92 ,_______ 219.9246 221.3415 .-_______ :;~;;..----.e 241457 ..--...;~;;;- 

-L---- . ; .2,673? 3.C376 -4,1743 223.5492 -----.’ ,509o ‘-- 74245 ?477!i - 

2 3 3.2904 3.63>9 Pi9760 221.9519 !415%4 24745 24275 

t: --.- 4 1- 3.*6?2? .Otb9 --- -. 4.9111 .2014 ---. 6,235? ,2',19 _-- 216.OP23 3.3279 _ ,2592 -.- -- y;...--. y-- 

--. 3 --- 1; 2.0917 4.0726 .-- 4,574n _.__- 207.1117 ,__ .--ml:E:: ‘---‘. 34345 -, 24775 

3 2.5370 4 .!ibZi 5,2301 2g9.1173 - ,I225 24355 24375 

3 4 l 34,2?04 I on09 w -. ..--.- 2,,?92? +.ljii49 4,942? ..-_-_. ,0255-- .?4?45 --.2!??5- 

-.-i ______ -i- _-___ 

.922S ,34i3’ ,9W’----.249,?402 - ?4ib5 24375 

2.3?9j--- 3.2753 _ 4.0’177 .-..-- --.. 215.2295 .____ -. .1?b4 ________. ?4765 _ 

3.2h12 4,35/9 5,oe:r\ . 216.61Yb !lb76 ?53b5 

;W; 

-;--- ? --- 2e4”91em-. 3.2951 5., 24210 2211 ---5,7~‘~l---.. 4.0”09 205,,5:73 233.0546 .-.-.-.,0~70 ,I119 --.-- 34365 274----.24775- 24275 

-. 5 ---;. 

E 

a..2224 --..3,4lJ2 4,bC41 2%3.5969, ,I422 34364 --?4?7j .- 

5 m ,031s 3.52C5 3,5365 j,ii(i,5093 ,2154 24;bS 24275 

P 5 213*?9C5 e 24265 24??5 -em .--- ;..__-__2*9w f.4481 5,35si, .-_- .-._ ..__ ! 2771 _-- .-..---- -.-- 

-; 

.939b l.lJ891 1,015’) 23C.~lCO m a1513 3STb5 94375 

-;-.-,?jll 2.32bl 2.2599 3 ..llb!i a,eoo5 2,659n -- 217*a:14 216,7596 ‘.----- m ,30?5274O --- -- - 242t565 - 243754;173- 

b . -..4768 ,4784 355.1710 24975 

--- .d ..D'@?j -.__ -_- .,--'I . . m:--.--.-.J;;;: 2ir;75 ..- 

1. f .4594 . .23Y3 ,515n 297.5690 - 

--. 7’ .--. ---3.. 1 ?S? --_. 3.6307 _ -.-. -. 4.7990 .._. ____. 220.7332 ____...___ ,m3 .-____ 2k75 _, 2477-j -.- - - 

7’ 3 .:*2’1 . .bT’Lb , bC20 34b,4559 10126 23375 24??5 

-. ? --- 4 .?$S? ____ ._.. -_ !0462 -___ 2jT75 _____ 

.U9J7 .2q4i 250.7672 l .-._ 

_5-: 4 2.1279 .KPO5 . -$.35d2’----- J?bQ 3,9714 a !I3 212,4383 296.7516 - ,,OQ91263 ;:;;:..~. 14275249752 . . -- 

3 .4531 .5ia2 ,cierj4 221.2112 - !oibb 24375 24275 

4 -3 2,?91(17 3-;?_Cy@ 6~-rw,l?.a? - Kod?l) -!4!?5 C4.?2_5____ 

. 

._- _. -._-_. _ ..--. --_ -_,_ - _._. 

Figure 4-16 A typical printout of mean values for a particular test run. 
SECTION V 

PRELIMINARY RESULTS AND CONCLUSIONS 

Statistical results have been'computed from the data 

described in the preceding chapters. Selected results are 

presented and explained. The results described in this 

chapter have been selected to emphasize the statistical 

characteristics of the turbulent flow field about a simulated 

block building. 

The results presented consist of mean velocity 

profiles, velocity time histories, two-point spatial correlations (with and without lag times), and autocorrelations 

computed by the direct method and by the FFT method. It is 

possible to compute the autocorrelations by using the mean 

velocitiesti spatial correlations, and assuming Taylor's 

hypothesis when knowing the spatial distances separating 

each point in space. These results are presented with a 

brief explanation of the accuracy relative to the height of 

the measurement and the related building or surface protuberances. 

The results presented are for the longitudinal 

velocity components only. For definition, the velocity components, after trend removal, are denoted by u ij (t), vij (t), 

and w ij(t) for the longitudinal, lateral, and vertical wind 

speeds, respectively, where i and j represent the tower 

105 
position and level of the.velocity measurement being 'discussed. The nomenclature (t) indicates the velocity is a 

function of time. For example, ul4(t) represents the longitudinal wind speed at.TlL4 for a particular time, t, relative 

to the beginning of the record. .Each plot in Section V 

which utilizes u53 (t) produces erroneous results as a result 

of spiking in the data and can be ignored (it has been 

included to illustrate its effect and methods of detection). 

The spiking in the data at T5L3 is possibly due to a malfunctioning transducer; however, the computational results 

clearly indicate this error. 

A. COMPUTATIONAL RESULTS 

Mean Velocities 

Figures 5-1 and 5-2 are plots of the mean longitudinal velocities at each of the five towers nondimensionalized with respect to the level 4 value. For 

tower number 3 it was necessary to interpolate between the 

- - 

mean velocities u24 and u44 to determine the upper level nondimensionalizing velocity. 

Near the building (run 8624) the velocity profile 

shows a pronounced deficit compared to the profiles farther 

from the building. The profile has practically recovered by 

the time it reaches T5. This phenomenon is not apparent in 

the no-building case (run 8704, Figure 5-2) where the profiles are similar at each tower. Other statistical work 

106 
1.0 

0.8 

z(k) 0.6 

z(4) '. 

0.4 

0.2 

0 I I I I I I 

0.2 0.4 0.6 0.8 1.0 

V(k) 

V(4) 

0.8 

0.6 

0.4 

0.2 

0 

1.0 

0.8 

0.6 

0.4 

0.2 

0 I I I I I I 

0.2 0.4 0.6 0.8 1.0 

0.8 - 

0.6 - 

0- 0.2 0.4 0.6 0.8 1.0 

//( 

0.2 0.4 0.6 0.8 1.0 

0.8 

0.6 

0.4 

0.2 

0 

LO? 

Br I 

I I I I I 

0.2 0.4 0.6 0.8 1.0 

Figure 5-1 Mean non-dimensional velocities with the block 

building in the tower array, Run #8624. 

107 
0.2 0.4 0.6 0.8 1.0 

V(k) 

V(4) 

0- 0.2 0.4 0.6 0.8 1.0 

0.8 - 

0.6 - 

0.4 - 

0.2 - 

0 I I 

0.2 0.4 0.6 0.8 1.0 

0.8 

0.6 

0.4 

Figure 5-2 

1.0 TS 

0.8 

0.6 

0.4 

0.2 

i 

I I I 1 I 01 I I I I I 

0.2 0.4 0.6 0.8 1.0 0.2 0.4 0.6 0.8 1.0 

Mean non-dimensional velocities without the block 

building in the tower array, Run #8704. 

108 
related to mean velocities and velocity defects of the flow 

about surface obstructions is given by Frost, et al. [1,2]. 

In these studies good correlation with wind tunnel studies 

[3] was accomplished using a slightly different tower arrangement than the one used and described in Section II. Other 

velocity profiles were computed and plotted; however, they 

are not included for the sake of brevity and provide sufficient room for other results to be presented. 

Time History Plots 

To get some indication of the relative time histories 

for each level and tower, they have been plotted at their 

respective altitude in Figure 5-3. Visually inspecting 

these time history plots, some indication of the vertical 

correlations can be seen. A signal or turbulent fluctuation 

generally appears at the upper levels and is felt at the 

lower levels in descending order. Although not overly 

apparent from the time history plots, this becomes much more 

apparent when cross-correlations of the data are computed. 

Figure 5-3 clearly indicates spiking of the data for the 

u53(t) signal as mentioned earlier. 

If the signals measured at the upper level (4) are 

plotted relative to each other or rather the time history 

plots of the upper levels are "stacked," one on top of the 

other, the signals' propagation downstream can be seen. This 

can be observed in Figure 5-4, where each time history plot 

109 
92 (t) 

Figure 5-3 Time history signals of the different towers and'levels. 

‘(Only 100 seconds for each level have been plotted.) 
! 

92 (t) 

91 (t) 

I 

Figure 5-3 (continued) 1 I 
I 

I 

w 

P 

w 

, 

Figure 5-3 (continued 
u43 (t) 

u42It) 

u4p 

Figure 5-3 (continued) 
U54W 

h 

u53 t-k) 

c 

Figure 5-3 (continued) 
=: WI 

u4* (t) 

I 

Figure 5-4 Correlation of signals obtained by shifting, in time, 

measurements made at level 4. 
has been shifted, relative to u14(t), in time corresponding 

to the time it takes a signal to travel from one point to 

the next at the mean wind speed velocity (this time is proportional to the ratio of the distance to the mean wind 

speed). 

A turbulence fluctuation existing at one point in 

space thus propagates in the mean wind direction and can be 

experienced downstream. The intensity and reproducibility 

of the signal will depend on several factors; for example, 

mean velocity, boundary conditions, spatial separation, etc. 

These will be discussed in detail when Taylor's hypothesis 

is examined near the end of this section. 

Spatial Correlations 

To get some indication of the effect surface obstructions have on the flow of air, it is necessary to measure 

the flow at selected points in space (Eulerian measurements) 

or to trace the position of air parcels in the flow as a 

function of time (Lagrangian measurements). The latter of 

these two measurements is rather difficult to make but is 

sometimes accomplished (not very successfully) by time-lapse 

photography of colored particles or radioactive tracer 

elements inserted at selected points in the flow field 191. 

Usually, Eulerian velocities are measured by inserting a 

probe in the flow field and measuring its velocity relative 

to some position and time. 

116 
Two-point space-time correlations can be used to 

measure the general dependence of the flow field at one 

point in space relative to another point. This dependence 

can be a function of boundary conditions (flow direction and 

surface obstruction), of position in the flow field in which 

the measurements are being made, and of time (instantaneous 

effects or possibly effects after some lapse of time). 

Two-point space-time correlations of the atmospheric 

flow about a simulated block building have been computed 

from the wind data described herein, some of which are 

presented in this section. In general, given two sets of 

- - 

data x(t) and y(t) with mean equal to zero [x(t) = y(t) = 01, 

then a correlation function Rxy(-r) is defined as 

T 

Rxy(r) = ;tE I 

x(t)y(t + 'c) dt 

0 

A correlation coefficient is then defined as 

B 

Rxy (‘~1 

xytT) = CT u XY 

(5.1) 

(5.2) 

where ux and c y are the standard deviations of x(t) and y(t), 

respectively. As defined, B ,,(T) is--n ormalized and theoretically bound within the range -1 < R ,,w 2 1. For the data 

described herein, digital techniques were used to compute 

the correlation coefficient and the method is explained in 

Section III. The digital estimate of B Xy(~) is given as 

Gxy(rh) and is defined in Equation (3.16). 

117 

I 
In this study, the symbol for the correlation 

coefficient, B uijukll(-c), will be used where uij and ukR are 

longitudinal velocity components with u.. being measured at 13 

tower "i" and level "j" and with ukR being measured at tower 

"k" and level "2." When i # k and j # R, & ijukR tT) is 

called a two-point space-time correlation. The term coefficient is dropped throughout the remainder of this report 

for simplicity of presentation. If T = 0, then B Ui jUkJ, (‘I 

is called a two-point spatial correlation. If i = k and 

j = R, then it is called a one-point correlation and will be 

written as B uij(r) to indicate only the tower and level at 

which the measurements were made. The terminology "auto-" 

and "cross--" correlations, used frequently in the literature, 

are used to denote velocity components. Since only the 

longitudinal velocity components are used for discussion in 

this paper, R, ij(~) will b e called an autocorrelation, 

whereas R xijYij' where x and y are components (u,v,w) in 

different directions, will be called a cross-correlation. 

It should be noted that a cross-correlation can be measured 

at the same point spatially or, as often thought of, at 

different points in space. 

In Figure 5-5 two-point spatial correlations have 

been plotted schematically, relative to their tower position 

and level. The correlations are computed relative to the 

position designated in the figure. For example, in the plot 

in Figure 5-5(a) the correlations have been computed 

118 
,776 

t.@@@ 

T3 

&lllLli j (0) 

(a) 

T5 

,119 

! 

484 

I ,429 

. ,376 

Figure 5-5 Spatial correlation relative to each tower and level. 
T’.547 

TTm T3 

I I A51 

.617 

6 Ul2Uij(O) 

.449 

(b) 

Figure 5-5 (continued) 

.436 

.321 

b K!t 

,449 

.38@ 
Tl T2 T3 

SU 13"ij (0) 

l.Qoo .-.6Q1 

,723 

t 

,594 

(cl 

Figure 5-5 (continued) 

T4 T5 

354 

.613 
T3 

6 U14Ui j ‘O’ 

,547 

,471 

T4 

T ,642 

.563 

T5 

354 

,110 

,468 

(d) 

Figure 5-5 (continued) 
T1.415 

T2 T3 

I I 

,452 

,434 

,493 

,498 

T4 T5 ,490 

(e) 

Figure 5-5 (continued) 

.4u6 

,369 
,617 

t 

I ,601 

,594 

%J u 22 ij !O) 

,713 

.a36 

:“, 

.569 ,525 

.15@ l Og4 :!z 

I I 

s3 s4 

.661 

,481 

,277 

T5 

+Ul 

A 14 

1476 

‘435 

.r. 

..1 

d 

(f) 

Figure'S-5 (continued) 
Tl 

I 

.637 TT71J’ T3 

T 

,691 

,651 

,589 

(9) 

Figure 5-5 (continued) 

T5 

I 

.59

L 132 

.479 

,410 
T573 T$ 88(1 T3 

I 1 

l 

%I 24Ui j ‘O’ 

(h) 

Figure 5-5 (continued) 

,659 

.476 

,235 

,132 

,465 

,441 
Tl T2 T3 

I 

.@13 I 

(iI 

Figure 5-5 (continued) 
Tl T2 T3 

.578 

1 I 

.595 

. ..5Ql 

. ..6@6 

-.a@ 

i3 U32Ui j ‘O 1 

Cj> 

Figure 5-5 (continued) 

,593 

,253 

T5 ,a632 

all8 

39 

,456 
T1.612 

I 

If644 T3 

,629 . ..767 

,632 . ..0@6 

h 

‘h 33"ij (0) 

i 

,555 

,087 

,136 

s3 s4 

. 

(k) 

Figure 5-5 (continued) 

,716 

,496 

,196 

T5 

,.622 . 

.m : 

.4B5 

,428 
Tl 

m.631 

,64@ 

T2 

! 

,710 

6 U34Uij ‘Oi 

Figure 5-5 (continued) 

T4 T5 

I 

.730 T .627 

.744 

,523 

.232 

,136 

a6 

.4X 
TS T2 T3 

,193 

I I 

,235 

.210 

,321 

,318 

(ml 

Figure 5-5 (continued) 

T4 T5 

,261 

I I 

.26@‘ 

,262 

,368 

1.899 

.205 

,264 
Tl T2 T3 

.476 

,436 

B 445 

(n) 

Figure 5-5 (continued) 

T4 

d518 

w.618 

T5 

,.519 

-.. 1’15 

La@@@ ,467 

.3M) 

t. 

.4w 
T1 T2 T3 

.563 

I I 

.659 

.613 

I 

38 

h 

Bu 43"i j (0) 

s3 s4 

(0) 

Figure 5-5 (continued) 

T4 75 ,739 

I l.OW I 

,618 

..7@2 

I. 141 

,.551 

,.472 
..a739 

. ..518 

-. ,261 

s3 s4 

(P) 

Figure 5-5 (continued) 

T5 

,.73@ 

,139 

,512 

-.a 1470 
. ..422 

. ..30@ 

-..376 

%l 51"ij (0) 

T4 T5 

T 

.478 ’ T .5Z@ 

. ..QZ 

. ..4@6 

t 

.264 

Figure 5-5 (continued) 
T3 

I 

,461 

,440 

,429 

; u52"ij (0) 

-. 426 

-.I 156 

. . . 158 

s3 s4 

W 

Figure 5-5 (continued) 

Tt51* 

I 

T5585 T 

,551 

.467 

l 285 

,158 

1,809 

.773 
. 137 

I 

b 122 

,119 

132 

,114 

6 u53"ij (0) 

I 

381 

:E! 

(s) 

Figure 5-5 (continued) 

141 

,115 

.095’ 

‘900 

.I58 

,141 
Tl 

-.554 

,554 

. 

.522 

e 484 

.595 

.601 

is U54Ui j (O 1 

.7@2 

.519 

,260 

.151 

.585 

.520 

(t) 

Figure 5-5 (continued) 
-356 

-.m 

-.136 

is U61Uij ‘0’ 

---. 113 2,941 

-.-. 113 -.-. 188 

(u) 

Figure 5-5 (continued) 

-,a8 

-,lW 

-a226 

F 
T2 T3 

T -032 I 

(VI 

Figure.%5 (continued) 

-.1@9 

-.lee 

-.244 

-347 

I 

-.a74 

-35 

I - 
Tl T2 T3 .467 

.483 

.4@ 

h 

Bu 63ui j (0) 

i 

.431 

,114 

,127 

(w) 

Figure 5-5 (continued) 

T4 

,,.498 

,518 

,395 

.159 

T5 

.@81 

,385 

,344 
. 

Tl T2 T3 ,.@35 ,.a30 

.-.E!9 --,826 

.016 

(xl 

Figure 5-5 (continued) 

T4 T5 

-.w4 

I 1 

-.@16 

.W5 

t 

-,@19 

,021 

I 

-.066 

,825 -,I353 
Tl T2 T3 

-.m9 

i, i 

-.m * 

6 u71"ij (0) 

-.wo 

I 

-.m 

da48 

-a063 

-. 

@i 

L ,056 -a83 

,l .Oll -J352 

.075 ,041 

s3 s4 

(Y) 

Figure 5-5 (continued) 

T535 -. 121 

T5 

i i -373 -.u61 I 

-386 

423 

-. 148 

-. 157 
P 

P 

P 

,581 

i 

.657 

.567 

354 

.632 

ci U7z”i j lo) 

Figure 5-5 (continued) 

.666 

.484 

.107 

,125 

.477 

.444 
TTosP T3 T4 T5 

T I T .@M 

.-a 127 I 

354 

d865 .A28 

u-.087 w-.163 ---.@@6 

--l.ow A88 

s3 s4 

,997 

.@45 

352 

(aa) 

Figure 5-5 (continued) 
Tl 

,.102 

.115 

.13lI 

.m 

,142 

T2 T3 

Tf14Q 

T5 

T 

6 U74Ui j ‘O’ 

.rs 182 336 I 

,152 

,135 

(bb) 

Figure 5-5 (continued) 
.-.474 

--.457 

.-.449 

- 

.@8@ 

.433 

,397 

(cc) 

Figure 5-5 (continued) 
T5 

. . 149 

A61 

.158 

.138 

Tl T2 T3 

6 (0) u82"ij 

,139 t 126 

180 

1157 

,211 

,238 

b 145 

,302 

I I I 

s3 s4 

(da) 

Figure 5-5 (continued) 
ii u83ui j (0) 

. . . 136 

,266 . ..288 

..-‘:E l 3 

s3 s4 

(eel 

Figure 5-5 (continued) 
l-1 

d445 

. ..454 

t 

.449 

,451 L 

,551 

,525 

,471 

T3 

h 

Bu 84Ui j (O) 

T4 ,339 

.rl ,617 

(ff) 

Figure 5-5 (continued) 

T5 

,316 

301 

,426 

,389 
relative to TlLl, which is clearly evident from the fact 

that the correlation coefficient is unity at that position. 

Some interesting properties of the correlation 

coefficient are observed in Figure 5-5. Again taking the 

plot in Figure 5-5(a) as an example, it can be seen that 

directly behind the block building there is very little 

correlation with the upstream position TlLl. This indicates 

a breakdown in the flow structure between the undisturbed 

flow upstream and the wake region behind the building. As 

the reference point for the correlation is raised to higher 

levels, the correlations (at the same level as the reference 

point) increase in the downstream direction. Also, as would 

be expected, the correlations in the free stream decrease 

with an increase in the distance separating the two points 

from which measurements were made. It should be noted that 

due to the definition of the two-point spatial correlation, 

6 ui jUkR (0) = ~UkRUi j (0). (This is not true in general for 

all -c or the two-point space-time correlations.) A correlation of 1 indicates that the exact signal is felt 

instantaneously at the.two points in question, and it is * 

obvious that a point correlated with itself gives 

h 

BU i juij (O) = 1 in all cases. (It should be noted that if 

S = 0, then 2 uijuij(r) is not defined.) A negative correlation between two points suggests a structured reverse flow 

region where a longitudinal fluctuation in the positive 

direction at one point results in a negative fluctuation at 

151 
another point. If B Ui jUkfi (O) = -1, then the velocities are 

equal in magnitude but opposite in sign. 

The extent to which a signal is felt at two different 

points depends upon the time it takes the signal to travel 

from one point to the other, plus any changes which may have 

occurred during this time. A two-point space-time correlation, B, ijl.lkfi(‘)’ describes the general'dependence of the 

longitudinal velocities at one tower and level to those at 

another position. Information relative to the time required 

for a signal to pass from one point to another in the wind 

field can be determined from the two-point space-time 

correlation. As the signal at one point is displaced in 

time relative to another point, the space-time correlation 

function will peak at the value of 'c equal to the time 

required for the signal to propagate at the speed of the 

mean wind to the second point in space. 

Figures 5-6 through 5-11 are plots of two-point 

space-time correlations. Figures 5-6 and 5-7 illustrate 

vertical correlations, whereas Figures 5-8 through 5-11 

illustrate horizontal correlations. Figures 5-6 and 5-7 are 

plots of the space-time correlations of TlL4 with all other 

levels on Tl and of T5L4 with all other levels on T5, 

respectively. It can be seen from these two plots (Figures 

5-6 and 5-7) that the correlation between levels on the 

downstream tower is relatively less in magnitude and that 

the peaks in the correlations occur with an increased lag 

152 
CORRELflTION VIF) FFT 

RUN=8624 

TOW?= 1 

LEVEL=4, 

N=8192 

LflG TIME IN SECONDS t-r) 

Figure 5-6 Vertical correlations relative to TlL4. 

153 
CORRELRTION VIR FFT 

-80 

F\ b 

j=2 

RUN=8624 

TOWER=5 

LEVEL=4 

N=8192 

LRG TIME IN SECOND%) 

Figure 5-7 Vertical correlations relative to T5L4. 

154 
CORRELRTION YIR FFT = 1 

1. 

RUN=8624 

TOWER=l' 

LEVEL=1 

N=8192 

0 19 20 30 40 50 

LRG TIME IN SECONDS ('c) 

Figure 5-8 Horizontal correlations relative to TlLl. 

155 
CORRELRT I ON VI R .FFT 

1= 1 

RUN=8624 

TOWER= 1 

LEVEL = 2 

N=8192 

0.08 :::~::.~~~l~~~~““‘ll~llll~~lll,llll+,ll,lll,l,ll~ 

11,111 

0 IQ 28 30 40 58 

LflG TIME IN SECONDS (T) 

Figure 5-9 Horizontal correlations relative to TlL2. 

156 
CORRELRTION VIR FFT 

RUN=8624 

N=8192 

0.0d::~:~:::tl-t:::~ 

9 10 20 30 40 50 

LflG TIME IN SECONOS~) 

Figure 5-10 Horizontal correlations relative to TlL3. 

157 
CORRELRTION VIfl FFT 

i=l 

RU'J=8624 

TOWER,=1 

$.~-H:::::::I:::::::XS:::!~:!!!‘:!::!~::!’!CH:::CCI 

0 10 28 30 40 58 

LflG TIME IN SECONOST) 

Figure 5-11 Horizontal correlations relative to TlL4. 

158 
time (f). As mentioned earlier, it should be noted that the 

instrumentation on T5L3 was not operating correctly and is 

apparent from the erroneous plots of the correlation. The 

reduced relative magnitudes of the correlations relative to 

T5L4 are possible due to the higher levels of turbulence 

created by the shear. layer emanating from the leading edge 

of the block. The increase in lag time at which the peak in 

the correlation occurs can be explained by the fact that the 

boundary layer has not fully recovered at T5. The lower 

mean velocities in the uncovered region result in the signal 

propagating at a slower speed and thus requiring a longer 

time to traverse a given distance. 

In Figures 5-8 through 5-11 (horizontal two-point 

space-time correlations of the longitudinal velocity components) it can be seen that the correlations near the ground 

are greatly affected by the presence of the block building. 

As the reference point of the correlations is increased to 

higher levels, the effect of the building is less pronounced 

(higher correlations and shorter lag times at which the peak 

in the correlations occurs). It should again be noted that 

the instrumentation on T3L4 was moved to the 9 meter level, 

and for this reason it has not been included in Figure 5-11. 

The correlations in Figures 5-8 through 5-11 peak at a lag 

time which decreases with an increase in the reference point 

height and is due to increased mean velocities at the upper 

levels. This phenomenon also occurs with a decrease in the 

159 
distance separating'the points from,which the measurements 

were made and the correlations were computed. If a signal 

did not change as it propagated downstream, each peak would 

occur at a lag time equal to the ratio of the distance to 

the mean velocity at the time the measurements were made and 

the correlation function would have a peak value equal to 1, 

indicating the exact signal is felt downstream. However, 

this is not true, because the signal changes due to shearing, 

boundary and viscous effects and the peak in the correlations 

reduces as the distance between the two points of measurement increases. 

It should be noted that B uijuka(~) is simply the 

autocorrelation function (coefficient) when i = k and j = R. 

When this is the case, B, ij(.c) is a maximum at =c = 0. This 

can be shown theoretically and is readily seen in Figures 

5-6 through 5-11 for the different correlation coefficients 

%.l ijukR(~) when i = k, j = R, and the lag time (T) equals 

zero. 

Computational Techniques 

Computation of the correlation coefficients was 

carried out originally to compare the FFT and the direct 

method computational techniques. In Figure 5-12 the accuracy 

of the two methods is exemplified. Only a selected number 

of points which were computed by the FFT method were plotted 

to illustrate the closeness of the two methods. The agreement is obviously very good. The numbers of datum points (N) 

160 
-~ 

t 

FUTOCORRELRTION, DIRECT - 

FFT D 

RUN=8624 

TOWER= 1 

LEVEL=4’ 

60 12el 1Wb 

LflG TIME IN SECONDS(T) 

Figure 5-12 Comparison of direct and FFT methods for computing an autocorrelation function. 

161 
-fUTOCORAELfiTION, DIRECT - 

FFT IZJ 

RUN=8624 

TOWER= 1 

LEVEL=4 

N=8192 

60 128 100 

LFIG TlME IN SECONDS(T) 

Figure 5-12 (continued) 

162 
RUTOCORRELfITION, DIRECT - 

FFT c3 

RUN=8624 

TOWER= 1 

LEVEL=4 

N= 16384 

60 120 180 240 

LRG TIME IN SECONDS (~1 

Figure 5-12 (continued) 

163 
used in the computational comparisons were 4096, 8192, and 

16384. (Each is an integral power of two as required by the 

FFT procedure described in Section III.) The total cpu 

times for each computation are shown in Table 5-l. In all 

cases, the FFT method required less time, and as N increases, 

the ratio. of the time for the direct method to the time of 

the FFT method increases very rapidly. (This, ultimately, 

will depend on the maximum lag time used in.the computational 

procedure.) It should also be noted that the FFT procedure 

computes the correlation coefficient for a lag equal to the 

total length of the recor'd being computed. Hence, the best 

comparison of the two methods would be to let the maximum 

lag time be equal to the record length. 

Very little difference exists between the correlations using 8192 and 16384 datum points; therefore, all 

other plots are computed using 8192 datum points to minimize 

the total computer time. An autocorrelation function will 

generally decrease as -c increases and oscillate about zero 

Method 

TABLE 5-l 

COMPUTER EXECUTION TIME (MINUTES) 

-p--- 

Number of Data Points 

4096 8192 16384 

FFT 2.08 4.41 9.36 

Direct 3.24 6.55 27.26 

164 
after a sufficiently long period of lag. Any sharp, predominant peak in the autocorrelation function is an 

indication of the presence of a periodic signal having a 

wavelength equal to the lag time at which the peak occurs. 

Thus, this method could be used to detect any periodic 

fluctuations in the flow field such as vortex shedding or 

low frequency directional fluctuations. 

Testing Taylor's Hypothesis 

It is interesting to test Taylor's hypothesis for 

the atmospheric flow over the simulated building. Mathematically, Taylor's hypothesis can be expressed as x = Et 

where x is the distance separating the two points in 

question, ii is the mean velocity, and t is the time required 

for the signal to propagate from one point to the other. 

Sometimes this is stated as u(t) = u(x/$ or a/at = -?i(a/ax). 

The range over which Taylor's hypothesis can be 

applied is restricted. As the distance between the two 

points increases, the results become less valid; also, the 

mean velocity has to be relatively larger than the magnitudes 

of the turbulence fluctuations, r (u(t) -ii) <<ii]. A 

1 detailed explanation of the restrictions to Taylor's hypothesis is given by Hinze [163. 

Figure 5-13 shows a comparison between the spatial 

correlation computed from measurements separated in space to 

the correlation estimated by Taylor's hypothesis. In 

165 
IWTUCOFHELFITION VS SPflTIflL CORRELf3TION 

1 

. 

-WI:WI: 

.2!ei2!ei / 

x 

O.~~:!I:f!!!!!:r’FFFFFH!!I!!~!!!!C) O.~~:!I:f!!!!!:r’FFFFFH!!I!!~!!!!C) 

0 10 20 30 w 50 

LflG TIME IN SECONDS(T) 

Figure 5-13 Comparison of autocorrelations computed by FFT 

procedures to autocorrelations computed by 

assuming Taylor's hypothesis. 

166 
flUTOCORAELflTION VS SPRTIFIL CORRELflTION 

LflG TIME IN SECONDS 

Figure 5-13 (continued) 

167 
RUTOCORRELRTION VS SPRTIRL CORRELRTION 

0.86 ;:::::,111111111111111111::::y 

0 10 20 JB 40 !50 

LRG TIME IN SECONDS(T) 

Figure 5-13 (continued) 

168 
--- 

RUTOCORRELfiTION VS SPflTIRL CORRELRTION 

0 10 20 30 40 50 

LRG TIME IN SECONDS (~1 

Figure 5-13 (continued) 

169 
producing these plots, the tower spacing was 0.0, 21.8, 43.3, 

and 80.3 meters between towers Tl and Tl, T2, T4, and 

T5, respectively. The mean velocity 5 at levels Ll, L2, 

L3, and L4 is 3.6, 4.2, 5.1, and 6.2 m/s, respectively. 

The two-point spatial correlations are indicated with an x 

in Figure 5-13. It is seen from this Figure (S-13) that 

in the undisturbed stream, very close predictions of the 

spatial is achieved by using Taylor's hypothesis. Less 

accurate results are obtained, however, at the lower levels 

where the influence of the building is more pronounced. 

The more accurate results at the upper levels are 

expected, but some question exists as to the very close 

agreement obtained using Taylor's hypothesis at the lower 

levels for T5. Two explanations are proposed: (1) the 

signal felt upstream at Tl propagates over the building, 

remaining outside the wake region and therefore not being 

disrupted by the wake disturbance or (2) the direction of 

the mean wind is such that the upstream flow passes around 

the building without interacting with it. The latter of 

these two explanations is the most probable since the mean 

wind direction was 201 degrees for this particular study. 

According to Lin [171, there is no justification, in 

general, for extending Taylor's hypothesis to shear flow, 

such as is found in the atmospheric boundary layer. However, 

it is felt by Lin that Taylor's hypothesis may still be a 

good approximation for those wavenumbers K of the turbulence 

170 
such that 

Kii >> 1 

dii/dz 

holds. : The corresponding equation using frequency rather 

than wavenumber is 

2xn >> 1 

dii/dz 

where n is cyclic frequency. 

Taylor's hypothesis, as used in this study, assumes 

correlation irrespective of frequency such that 

g(T) = fi(x = UT) 

where T is the lag time of the autocorrelation and x is 

space lag with x = UT, as described earlier. 

It is desirable to ascertain in what manner this 

expression is supported by analysis of the field data taken 

in the surface boundary layer without the simulated block 

building being used (runs numbered 8700 and above). These 

data were not available due to errors encountered in tape 

conversions. 

It would be of interest to measure the coherence in 

the horizontal plane and downwind direction at several 

levels to further test Taylor's hypothesis. The coherence 

function, when computed directly instead of the FFT method, 

would yield the correlation between two points as a function 

of frequency. The coherence function also provides the 

phase shift in the signals as a function of frequency from 

which the lag time can be obtained. It is believed that 

171 

I 
--. .P . -..-.. . .._. . .-.- . .._. . . ..----.-- . . ..-.-_-.-- . ...,-.., ,, .,., . _ _--.-. _. ---- . .--_ ,... 

- -...--. --.---.---.-..-.. ,, ,-.-. . . ..,. - -- 

higher frequencies (small eddies) are attenuated more than 

lower frequencies (large eddies) propagating downstream. 

Additionally, any protuberance will disrupt the signal propagating downstream and introduce new uncorrelated eddies. 

For this reason the analysis should be performed with data 

from the 8700 series tapes and compared with results 

obtained from the 8600 series tapes. 

B. CONCLUSIONS 

The experiment described herein is designed to 

obtain relevant measurements of the turbulent atmospheric 

boundary layer. 'In particular, the influence of a simulated 

block building is under investigation along with gust 

gradient analysis relative to flight characteristics and 

structural loading of wind turbine generators. 

Hopefully, the experiment and data reduction procedures are described in sufficient detail to allow access to 

the available data. The preliminary analysis presented in 

this study has been performed to better understand the 

influence of surface obstructions on atmospheric flow. A 

much better understanding of the flow will be accomplished 

upon completion of the study which will investigate additional data sets and computation of power spectral density 

functions and coherence functions. This analysis is being 

completed and will be discussed at a later date. 

172 
1. 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

9. 

10. 

11. 

LIST OF REFERENCES 

Frost, W., G. Fichtl, J. R. Connell, and M. L. Hutto. 

"Mean Horizontal Wind Profiles Measured in the 

Atmospheric Boundary Layer About a Simulated Block 

Building,,' Proceedings of the Second U.S. National 

Conference On Wind Engineering Research. Fort 

Collins: Colorado State University, June 1975. 

Frost, W., and A. M. Shahabi. "A Field Study of Wind 

Over a Simulated Block Building," National Aeronautics and Space Administration Contract Report 

No. NAS8-29584, George C. Marshall Space Flight 

Center, Huntsville, Alabama, March 1977. 

Sacre, C. "Une Methode Numerique Pour Le Calcul Approche 

De La Surviteese du Vent Sur Une Colline," Centre 

Scientifique et Technique du Batiment, Establissement 

de Nantes, France. 

Woo, H. G. C., J. A. Peterka, and J. E. Cermack. "Winds 

Tunnel Measurements in the Wakes of Structures," 

National Aeronautics and Space Administration Contract 

No. NASA CR-3806, prepared by Colorado State University, 

Fort Collins, March 1977. 

Plate, E. J. Aerodynamic Characteristics of Atmospheric 

Boundry Layers. Oak Ridge, Tennessee: USAEC Technical 

Information Center, March 1972. 

Logan, E., and J. Chang. "Wake Characteristics of Buildings 

in Disturbed Boundary Layers," National Aeronautics and 

Space Administration Contract Report No. NAS8-32357, 

George C. Marshall Space Flight Center, Huntsville, 

Alabama, May 1980. 

Logan, E., and D. W. Camp. "Preliminary Comparison of Model 

and Prototype Wakes," AIAA Paper No. 78-254, 1978. 

Instruction Manual for Model 011-1, Wind Speed Transmitter. 

Climet Instruments, Sunnyvale, California, February 1970. 

Instruction Manual for Model 012-1, Wind Direction Transmitter. 

Climet Instruments, Sunnyvale, California, February 1970. 

Instructions Gill Propeller Anemometer Model 27100, Model 

27101. R. M. Young Company, Ann Arbor, Michigan, 

December 1969. 

Sebestyen, L. G. Digital Magnetic Tape Recordinq for 

Computer Applications. London, England: Chapman 

Hall, 1973. 

173 

. 

and 
12. Oppenheim, A. V., and R. W.- Schafer. Diqital Signal 

Processing. Englewood Cliffs, New Jersey: Prentice 

Hall, Inc., 1975 

13. Frost, W., B. H. Long, and R. E. Turner. Engineerinq 

Handbook on'the Atmospheric Environmental Guidelines 

for Use in Wind Turbine Generator Development. 

National Aeronautics and Space Administration TR-1359, 

George C. Marshall Space-Flight Center, Huntsville, 

Alabama, December 1978. 

14. Brigham, E. 0. The Fast Fourier-Transform. Englewood 

Cliffs, New Jersey: Prentice Hall, Inc., 1974. 

15. Merzkirch, Wolfgang. Flow Visualization. New York: 

Academic Press, 1974. 

16. Hinze, J. 0. Turbulence. New York: McGraw-Hill Book 

Company, Inc., 1975. 

17. Lin, C. C. Statistical Theories of Turbulence. Princeton, 

New Jersey: Princeton University Press, 1961. 

174