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Report 1353

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| HYDROMECHANICS , THE TAYLOR MODEL BASIN SEAKEEPING

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DATA ANALYSIS CENTER
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AERODYNAMICS
by

Wilbur Marks and Paul E. Strausser

STRUCTURAL
MECHANICS

HYDROMECHANICS LABORATORY

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RESEARCH AND DEVELOPMENT REPORT

Bt APPLIED
G3 =MATICS JULY 1960 Report 1353
|

SEADAC
THE TAYLOR MODEL BASIN SEAKEEPING

DATA ANALYSIS CENTER

by

Wilbur Marks and Paul E. Strausser

JULY 1960 Report 1353

TABLE OF CONTENTS

Page

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3. DATA ANALYSIS .......... vie ve 8

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COMPARISON OF SEADAC ANALYSIS WITH DIGITAL METHODS............ 15
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1. LABELING OF COORDINATE AXES...............-..-.00.- 18

2. COMPUTATION OF MEAN TOTAL ENERGY...............---- 23

Se CONEUDENCEBBAND Siieperereleteielerensleneioielriicneasn anemone terion iene 24
PROPOSED EXTENSION OF THE SEADAC............. ce eecceesecceees 25
APPENDIX - AMPLITUDE MODULATION APPLIED TO THE SEADAC........... 30

ital

LIST OF FIGURES

Page
Figure l - Block Diagram of the SEADAC...............ccec cece oo 3S
Figure 2 - Page of a "Book" Showing Record of Seakeeping
Events Recorded on Magnetic Tape..............222000- 34
Figure 3 - The Integrated Spectrum of a Pitch Record Super-

posed on the Energy Spectrum of the Same Record...... 35

Figure 4 - SEADAC Analysis of a Pitch Record Using 2-, 5-, and
NOG WALES 5 oo 0p Ob DDD DDD OOD OOOO bOUDUOUONN co000n00 HO)
Figure 5 - Spectral Density Functions Computed from the Same
Seakeeping Record for Slow Scan and Fast Scan........ 37
Figure 6 = Energy Spectra of Several Seakeeping Events

Analyzed by the SEADAC with the Numerically Com-
puted Energy Spectra Superposed.........eccceccseces 30-40

Figure 7 - Calibration Curves for 2-, 5-, 10-, and 20-CPS
MLIECISS ood o0dca0DD00K0 00 DDO0S 50000000 90.000000000000 ore 41
Figure 8 - Analog Spectral Density of a Seakeeping Event

with Appropriate Calibration Curve..........cccccees 42

Figure 9 - Analog Spectral Density of a Seakeeping Event with
Cumulative Energy Distribution Function Superimposed 42

Figure 10 - Reliability of Spectral Density Estimates........... 43
Figure 11 - 90-Percent Confidence Bands (Dashed Lines} Applied to

a Spectrum with 31.64 Degrees of Freedom............ 44
Figure 12 - Block Diagram of Proposed Extensions to the SEADAC.. 45
Figure 13 - Computation of Spectral Density and Total Energy by:

1) Successive Steps in one Analyzer, and 2) Simul-
taneous Calculation in the Same Analyzer with the
Addition of Another Power Integrator and X - Y

INVCORGIEE 5 60 G0000000000000 o0000000000000000000000000 46
Figure 14 - An Example of a Modulated Carrier Wave.........eee. 47
Figure 15 - The Spectrum of the Relative Amplitudes of the

Components of a Modulated Wave as a Function of

the Frequency of Those Components............ececece 47

iii

NOTATION
Area under SEADAC calibration curve
Amplitude of carrier signal
Amplitude of modulating signal
Instantaneous value of modulated signal
Instantaneous value of carrier signal
Instantaneous value of modulating signal
Transducer calibration
Number of degrees of freedom (=2TAf .)
Analysis frequency
True frequency

Ratio of any analysis frequency band to its length
on the abscissa scale of the X-Y plot

Proportionality factor
Height of calibration curve
Maximum height of cumulative energy distribution

Maximum height of cumulative energy distribution
calibration

Modulation index

Frequency multiplication factor
Recording speed

Playback speed

Length of time required for tape loop to make one complete
passage in the loop recorder

Period of encounter

Time

rms

Mean square voltage
Root-mean-square voltage

Peak voltage

Bandwidth of filter, cycles/sec
Effective bandwidth of filter
Mean total energy in spectrum
Spectral density

Frequency of carrier signal
Frequency of modulating signal

Frequency of encounter, radians/sec

OVAVHS

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ABSTRACT

The Taylor Model Basin Seakeeping Data Analysis Center
(SEADAC) is described. The methods for preparation, analysis,
and storage of data are outlined. Confidence in the system is
demonstrated by comparison of SEADAC computation of the spectral
density of certain seakeeping events with numerical calculation
of the same data. The limitations of the SEADAC are listed and
changes that will improve the system's efficiency and extend

its capabilities are suggested.

INTRODUCTION

In recent years there has been a trend toward the collection of large
amounts of seakeeping data on full-scale trials. Two more sources of
exceptionally large data supplies will soon appear at the Taylor Model
Basin. The first is a system of automatic seakeeping instrumentation for
TMB which will permit unattended quasi-continuous recording of full-
scale seakeeping events for months at a time; the second is the new sea-
keeping facility (nearing completion) wherein much testing in irregular
waves is anticipated.

Until recently, all detailed analyses of seakeeping data have been
carried out by the Applied Mathematics Laboratory, on the UNIVAC I and II,
and on the IBM M4. On the whole, these services have been satisfactory.

Certain deficiencies in our earlier methods of data handling became
apparent, as the volume of data increased. The most obvious of these
was (and still is) the expensive and time-consuming job of data preparation
for input to the general purpose digital computer. The original dataare

displayed on chart paper from which semi-automatic readings are taken at

equally spaced record intervals and transcribed onto punch cards. This
information is then sent to the Applied Mathematics Laboratory where it

is transferred to a digital tape for input to the general purpose digital
computer. In addition to being time consuming, errors occur in reading,

card punching, and computation which are often not discovered until the
results are returned to the project manager. Furthermore, there is often

a delay of several days in gaining access to the computer. Data preparation
may be streamlined by analog to digital converters (if the original data

is on analog tape), but this is an expensive undertaking and does not solve

all the problems mentioned.

A more serious deficiency of the general purpose computer is that
it is physically remote from the project manager. This eliminates all
subjectivity in analysis. The project manager must decide, a priori,
how the analysis will be made, i.e., resolution and confidence. There is
no opportunity to "play' with the analyzer, to learn whether certain
information (such as the occurrence of slamming), which can only be
extracted from the data by changing the analysis constants during the
analysis, really exists. A more direct example of the disadvantage of
physical apartness of the computer and the project manager can be seen
in the seakeeping facility. Model test programs often require alter-
ation; that is, results may indicate that data are over-abundant in
SOme areas and sparse in others. Test programs can be altered profitably,
only if the results are available while the experiment is being conducted,

not the next week or even the next day.

In certain operational problems, a knowledge of past history of ship

motions is used to predict future behavior. This prediction is based
on statistical evaluation of the time history of the event and must be

made "on the spot''. A special purpose computer is valuable in this regard.

It may be said that a special purpose computer has the following
advantages:

1. Permits monitoring of all analysis results by the project
manager.

2. Permits change of computational program, even during an analysis.

3. Assists in modifying test programs.

4. May be used aboard ship.

The special purpose computer, in this case the analog energy spectrum
analyzer, is the heart of the SEADAC; the other components (tape recorder

and plotter) are auxiliary equipment necessary to its performance.

This paper describes the SEADAC and is intended to be an operational
guide to project managers who can only derive the maximum benefit from the
SEADAC through an understanding of its philosophy and mechanics. The
SEADAC is only. a data handling and computational tool, and is not respon-
sible for the quality of the results. Problems such as sampling variability,
confidence bands, and stationarity of data must be resolved by the project
engineer. The design of the data analysis procedure is also the responsi-
bility of the project engineer; the material in this report will assist

in formulating certain subjective decisions in this regard.

A photograph ot the SEADAC appears as the frontispiece.

DESCRIPTION OF THE SEADAC

1. GENERAL

The SEADAC is associated with one specific aspect of seakeeping data
reduction, that of converting time histories of random variables into
some form of spectral density presentation. The basic functions of the

system are summarized as follows:

1. Preparation.
2. Analysis.

3. Storage.

To get a clear general picture of the operation of the system, see
Figure 1. The raw data are transmitted from the transducers (T) to the
tape recorder in the field and are brought to the laboratory on reels of
magnetic tape. Each reel may contain the data from many runs (experiments)
and each run may comprise as many as 14 channels of information on the
tape. These data are usually recorded at 1-7/8 ips (inches per second).
The first operation involves playing the data back, on a reel recorder,
at a speed 32 times greater than the original recorded speed (that is,

60 ips)and re-recording the sped-up signal on the loop recorder at 1-7/8
ips. At the same time, the signals on eight of the channels are recorded
on 8-channel chart paper at 5 mm/sec. A second chart paper recording
will be required if more than eight channels of information were recorded
originally. The original data are coded so that rums are easily
separated. The paper records are divided into separate runs, labeled
properly for indentification, and put into a binder in the form of a

book. Figure 2 shows a typical page from such a book.

4

After the original tape is speeded-up and re-recorded, it is divided
into individual runs and each run is spliced into a loop. One loop may
be inserted into the loop recorder (Figure 1) and played into the analyzer
at 30 ips, a speed-up of 16 times that of the original recording of the
loop. Two of the possible 14 signals are sent to the "A" and "B" analyzers,
and then to their respective analog computers and X-Y plotters. The
resulting graphs (amplitude density, energy density, total energy) refer to
a frequency scale 512 (32 x 16) times the true frequencies in the
signals. Calibration signals are put on each plot, and the graphs are
given to the project engineer for statistical evaluation. The process may

be repeated for each of the signals on each of the loops.

After all the data have been analyzed, the loops are placed in
plastic capsules, labeled, and filed. The "book" is filed when the

project engineer no longer requires visual cheeks.

Figure 1 illustrates some of the shortcomings of the SEADAC as it
was originally assembled. When the data are being re-recorded anto
the loop recorder, the analyzer is inactive; when the analyzer is active,
data cannot be re-recorded. This seriously affects the time economics
involved in volume data analysis. More important is the inability of
the SEADAC to treat cross-spectrum analysis. A great deal of potential
information is available in the simultaneous recording of seakeeping
events which can only be extracted through cross-spectrum analysis. These
and other improvements will be discussed in the. section on the proposed

extension of the SEADAC.

All SEADAC components are commercially available but the analyzer
system* comprising 1) local oscillator, 2) filter networks, and 3) analog

computers is relatively new and may not be well known.

2. DATA PREPARATION .

The raw data are received from the transducer as an analog voltage,
preamplified and frequency modulated (FM) onto l-inch, 14-channel, 1.5-mil
Mylar magnetic tape. Since the raw data will be subjected to a frequency
decomposition in the filter network of the analyzer system (to be
discussed) , consideration must be given to the relationship between the
range of frequencies in seakeeping events and electronically feasible
filter networks. Seakeeping events seldom contain energy at frequencies
outside the range 0.03 to 3.0 cps. Unfortunately, commercially available
filters that are fairly sharply tuned are too wide to accommodate this
frequency range. It is only since the recent advent of iow-speed magnetic
tape Ba anes that the conventional "wave analyzer'' has lent itself to
use as a low-frequency analyzer. The principle is simply to bring the
signal frequencies to the filter rather than the filter to the signal
frequencies. This is accomplished by causing the filter to look at the
time-history of the seakeeping event, not in true time, but in a highly
condensed time scale. If a 20-minute record is speeded-up ten times, the
record will pass through the filter system in one-tenth the recording
time and the frequencies will appear to be ten times greater than they

really are. Under such conditions, the "apparent" frequency range becomes

*Instruction Booklet for TP-625 Wave Analyzer System, Technical
Products Corp., Los Angeles, Calif.

6

0.3 to 30 cps. In practice, the speed-up is much greater. Records are
made in the field at 1-7/8 ips. Through a process’ of playback (at 60 ips)
and re-record (at 1-7/8 ips), a speed-up of 32 times is achieved. When
this new signal is played through the analyzer at 30 ips, an additional
speed-up of 16 times is realized. The total speed-up is 512 times true
time and the apparent frequency scale of possible interest becomes 15.4

to 1540 cps. Lower recording speeds (less than 1-7/8 ips) are becoming
commercially available, and it may soon be possible to do away with the

re-record process in the SEADAC.

While the tape is being re-recorded on the loop recorder, it is
simultaneously recorded (at 5 mm/sec) on an 8-channel Sanborn strip
chart recorder (see Figure 1). This paper display (Figure 2) is not
suitable for analysis but certainly illustrates what is on the tape.
The information on the paper is completely described by writing in
the experimental constant information, including calibrations, for each
channel. In this form, the visual data may be used in deciding the
proper analysis constants and will also serve as a check on analysis

results, at least for orders of magnitude.

Each run constitutes a page in the "book" which is the recorded
history of the experiment. A summary sheet describing the trial is
attached to each book at the termination of the project, before it

is filed..

The magnetic tape is likewise separated into rums and each run is
spliced into a loop. A typical run which is 20 minutes in duration

7

and 187.5 feet long (recorded at 1-7/8 ips) becomes a loop 5.86 feet
long which takes 2.34 seconds (at 30 ips) to make one complete trip

through the loop recorder.

It will be recalled that the probable frequency range for seakeeping
data is 15.4 to 1540 cps at a speed-up of 512. Commercial filters from
2 to 20 cps are well suited for this range in terms of giving adequate
resolution of the spectral density and have,as well, a fairly rectangular

shape, which is desirable.

Tests in irregular waves in model tanks will often contain frequencies
which are sufficiently high (depending on speed and relative heading of
ship model) to obviate the necessity for re-recording. In such cases, the
recorded signal is bound into a loop directly and played into the analyzer

at 60 ips, providing a direct speed-up of 32.

3. DATA ANALYSIS

The data reduction portion of the SEADAC consists of two conventional
linear-frequency, constant bandwidth wave analyzers specially modified
to be driven by one stabilized local oscillator. One analyzer has four
filters (2, 5, 10, and 20 cps) and the other analyzer has two filters

(2 and 5 cps).

The oscillator is capable of sweeping three ranges:
1. 0-250 eps
2. 0-2500 cps

3. 0-25,000 cps

For most seakeeping events, the O- to 250-cps range is adequate. It
may be necessary to go to the O- to 2500-cps range for slamming and vibra-
tion data.

The technique of separating the frequency components in the signal
to be analyzed is based on amplitude modulation. The mathematics involved
will not contribute to the continuity of the discussion and is given in
the Appendix. However, a brief discussion of what amplitude modulation
does will be helpful in understanding the analysis process.

The local oscillator generates a continuously changing "carrier"
frequency which is 97,000 cps plus some frequency, let us say, in the
O- to 250-cps range. This frequency is modulated by (mixed with) all the
frequency components in the random signal being analyzed. The result of
this mixing is a new signal, which comprises all the signals which would
result from separately amplitude-modulating the carrier by each frequency
component of the random signal. Single component modulation produces a
signal that contains the carrier frequency, the sum of the carrier
frequency and the particular modulating frequency as well as the difference
of these two frequencies. The sum frequency is called the "upper sideband"
and the difference frequency is called the "lower sideband." The amplitudes
of these two waves are proportional to the amplitude of the modulating

wave and is the quantity that must be measured.

The result of modulating a multifrequency signal then is a new
signal which comprises the carrier frequency and all the upper (sum fre-
quencies) and lower (difference frequencies) sidebands associated with the

components of the signal to be analyzed.

The modulated signal is sent through a stationary band-pass filter
centered at 97,000 cps. The carrier frequency component is rejected by
the filter because it always generates signals with frequency greater
than 97,000 cps. All upper sidebands are rejected because they contain
sum frequencies which are always greater than 97,000 cps. The lower
sidebands are also rejected, with the exception of that one lower side-
band whose difference frequency is exactly 97,000 cps. The net result
of the filter's activity is the passage of a pure sinusoid whose ampli-
tude is proportional to the amplitude of that component of the modulating

(random) signal which is at that moment specified by the local oscillator.

This discussion is idealized as well as somewhat over-simplified.
The filter, in fact, is of finite width, let us say 5 cps. Consequently,
it will pass all lower sideband components with frequencies between
96,997.5 and 97,002.5 cps. Under such circumstances, it is seen that
the analyzer will sort out not individual frequencies in the spectrum
but bands of frequencies, depending on the bandwidth of the filter
employed.

Care must be exercised in the initial generation of carrier signals;
they must always be of frequency greater than that of the upper side of

the band-pass filter (in this case, greater than 97,002.5 cps).

Since the SEADAC has two analyzer systems (Figure 1), the carrier
wave is modulated simultaneously (and separately) by two of the signals
on the magnetic tape and everything that has just been discussed occurs

independently and simultaneously, with respect to these two signals. For

10

the sake of simplicity, the discussion will continue on the basis of one

signal to be analyzed and one analysis system.

While the filter network, which is the wave analyzer, operates on
the modulated carrier-input signal, through the entire frequency range
generated by the oscillator, the passed components proceed to the analog
computer portion of the SEADAC for further treatment. In the analog
computer, one of the following operational modes may be programmed:

1. Average linear amplitude.

2. ‘Mean square energy,

3. Integral of energy.

The average linear amplitude may be thought of as an estimate of the
Fourier coefficients in a Fourier series analysis, where the amplitude assigned
to a particular harmonic is the average amplitude of it and the neighboring
harmonics within the bandwidth of the filter. As the width of the filter
approaches zero, the Fourier representation of the seakeeping event is
approached. This type of computer calculation is not desired at this

time, and has consequently not been applied to any data.

The "mean square energy" operation is equivalent to computing energy
spectral density. The amplitudes of the frequency components in the pass-
band are continuously squared and averaged. This mode of operation is

used most frequently.

Since the total energy in the spectrum is a measure of the "peak-

to-peak" distribution of the record of the seakeeping event being

11

Studied, the “integral of energy" mode of operation is often used. Here
the average square energy of the frequency components are added to pro-
vide a monotonic nondecreasing function (curve which never goes down)
whose maximum (asymptotic) value is a measure of the total energy in

the seakeeping record.

The output of the analog computer is applied to an X-Y plotter.
The net result of analysis is a graphical display on 8%-in. X 10-in.
paper of the output of one of the operational modes as ordinate, and

frequency (magnified by speed-up ratio) as abscissa.

Figure 3 illustrates the most frequently used operational modes.
Both the density function (spectrum) and the distribution function (inte-
grated spectrum) relate to the same input data. It will be noted that the
rate of change of the distribution function corresponds well with the ups
and downs of the density function, as expected from the integration pro-
cess involved. The maximum value of the cumulative distribution function
is, as stated, a measure of the total energy and is therefore equivalent
to the integral of the density function, or to the area it represents

on the X-Y plotter.

Several analysis constants require discussion before the subject
is closed. The width of the filter determines the resolution of the
energy spectrum. A narrow filter provides fine detail but is a relatively
poor estimate because fewer frequency components are averaged. Conversely,
a wide filter provides good estimates but poor resolution. A priori
knowledge of the shape of the spectrum is helpful in filter selection.

12

It is sometimes necessary to repeat analyses using different
filters before the optimum one is found. Figure 4 shows the

effect of different filters operating on the same input data.

The oscillator motor determines the time it takes the oscillator
to scan the entire frequency range, which consequently determines the
maximum analysis time. There are two choices: 11 minutes (fast scan)
or 22 minutes (slow scan). Slow scan allows the filter to remain
longer in its local frequency environment and ‘permits better resolution.
Fast scan may have a relative "smearing" effect because new frequencies
are being scanned by the filter at a faster rate and corresponding
new amplitudes are being squared and averaged at the same faster rate.
The error or ''smearing'" thus introduced depends on the steepness of the
spectrum. A flat spectrum is unaffected by fast scan. Figure 5 shows
the same data subjected to slow and fast scan. In either case, it is
important for the filter to scan the entire loop, before the frequency
band it is examining moves very much, to get the benefit of all the
available data. For this purpose the time (T) it takes the data to
make one passage through the analyzer is important. A rule of thumb
that suggests TAf>> 1 may be used as one guide in the selection of
an appropriate filter bandwidth (Qf). A 20-minute record, for example,
which is sped-up 512 times takes 2.34 seconds to pass through the
analyzer once (loop time). A 5-cps filter would appear to be adequate
in this case. Choice of both filter and scanning speed depends mostly
on the shape of the spectrum. A flat spectrum can tolerate a wide filter

and fast scan; a steep, rapidly changing spectrum requires a narrow

13

filter and slow scan. Experience with the system has shown that
most seakeeping analyses may be made a slow scan with a 5-cps filter.
An exception to this is the usually narrow roll spectrum which suggests

using a 2-cps filter with slow scan.

One further analysis constant to be considered is the averaging
time constant. This is a memory medium that controls the length of
time, in the past history of the excursion of the filter through the
frequency range, that the analog computer will consider amplitudes in
its averaging duties. The time constant is adjustable in the range of
0.1to 100 seconds and should be at least as long as the loop time, to
utilize all the data in the loop. The longer the time constant,
however, the greater the range of amplitudes that will be averaged.
A time constant of 3.5 seconds has been used successfully with seakeeping

data.

The effect of creating a discontinuity in the record, where it is
spliced into a loop, is to introduce spurious information in the signal
that manifests itself as spikes in the energy spectrum. These spikes
will appear at the fundamental of the new frequency created by the splice
and at its harmonics. If the record is long and/or the filter wide
and/or the time constant long, the splice effect will be reduced. There
is no appreciable evidence of the splice effect im any of our analyses

to date.

Since only about half the 0 to0250-cps oscillator frequency range
contains energy, analyses usually take 5 or 10 minutes, depending on
whether slow or fast scan is applied.

14

It should be obvious by now that the experimental setup for a
particular analysis is highly subjective. The results depend on:
1. Loop time (length of record).
2. Filter bandwidth.
3. Scan rate.

4. Time constant.

Project engineers are encouraged to familiarize themselves with
the operation of the equipment so that, with the cooperation of the

SEADAC engineer, the most useful analysis can be made.

4. DATA STORAGE

After all the analyses are completed for a particular magnetic
tape loop, the loop is stored in a small plastic cylinder and the
cylinder is labeled with identification that relates its contents to
a particular page in the "book" (Figure 2) wherein is contained all

pertinent information on the trial.

Both the tapes and the book are filed for future reference.

COMPARISON OF SEADAC ANALYSIS WITH DIGITAL METHODS

The SEADAC is concerned primarily with the electronic determination
of the spectral density function of a seakeeping event as represented
by the observed time-history of that event. In a very general way,
the spectral density function may be considered to be a display of the
harmonic components contained in a signal such that the amplitude of
each component is squared (ordinate) and assigned to its respective
frequency (abscissa).

15

The particular process generated by the analyzer system of the
SEADAC for realization of the spectral density function has been
described. It should be noted, however, that certain errors, which
arise in computation, may cast some doubt.onm the validity of results.
These errors are not large but one is still obligated to establish
confidence in such a new computing machine even if its principles
are well-known and accepted. Some of the questionable features of this
electronic analog computer are: (1) the creation of a discontinuity in
the time history of the event being analyzed when it is joined to itself
in a loop (splice effect), (2) the use of a nonideal filter (i.e., one
which is not a perfect rectangle), and (3) the method of calculating
running averages over the effective bandwidth of the filter as if the

energy were constant over that bandwidth.

These deviations from an ideal method of analysis may be treated
independently (as in the last section), to assess their individual
effects on the outcome. It is, however, more profitable to examine
the effect of the aggregate of all these errors; if the total error
is sufficiently small, there is no reason to pursue the matter further.,
The best method for verification of SEADAC operation is a comparison
of the output of the SEADAC with the known and understood results of
a general purpose digital computer, wherein.the numerical analysis is
governed by an entirely different computational procedure than is the
analog method. Instead of filtering, squaring, and averaging, the
numerical method deals with a convolution of the original time history
with itself, and then a Fourier transformation generates the spectral
density function. The point is that the numerical technique is so

16

different that a successful comparison of the two methods cannot

be ascribed to like errors being propagated in the same way. The
digital spectral densities computed for this comparison are considered
to be representative of the data; it remains to be established that

the analog analyzer of the SEADAC produces similar results.

For the sake of comparison, a set of data obtained on a Liberty
ship full-scale trial was analyzed by both methods. The ship speed was
approximately 15 knots in a head sea where the highest waves were about

8 - 10 feet.

The seakeeping events which were recorded and analyzed are listed
below and appear as Figure 6:
1. Roll
2. Pitch
3. Heave Acceleration
4. Starboard Strain
5. Port Strain

6. Wave Height

Examination of the graphs in Figure 6 shows that the agreement is
quite good so far as shape is concerned, and this is essentially all
that may be required of the SEADAC. Where the curves do not superpose
indentically, it is believed that instrumentation calibration is at
fault. This is discussed in the next section. An unexplainable
discrepancy occurs in Figure 6c, where the SEADAC shows a third peak
in the spectrum that does not exist in the numerical calculations.

17

The analog analysis was repeated several times without any change. The
original data will be re-submitted for numerical analysis. At this
time, there is no explanation for the anomaly. Since the other five

comparisons are good, there is probably little cause for concern.

It is reasonable to conclude that a SEADAC analysis is equivalent
to a numerical analysis, made in an analogous way. It has been shown
that different filter bandwidths, time constants, and scanning times
affect the resultant spectrum. Consequently, the original data could
have produced spectra that might look somewhat different from those in
Figure 6, if the analysis constants were changed. The same, however,
applies to the numerical analysis constants and equivalent results
will only be obtained under analogous conditions. The SEADAC analyzer
is therefore considered to produce good estimates of the spectral

density function of a random signal.

PRESENTATION OF RESULTS

1. LABELING OF COORDINATE AXES
To derive meaning from the spectral density representation, it
is necessary to label the coordinate axes; this assigns quantitative
value to the graph. Certain basic information is required:
1. Frequency multiplication factor.
2. SEADAC calibration.
3. Effective filter bandwidth.
4. Instrument calibration.
The first step is to convert the frequency scale, which is given

18

by the local oscillator, into true frequencies appropriate to the true
recording time. Analyses will, in general, be made for the O- to 250-cps
scale or O- to 2500-cps scale. If the O- to 2500-cps scale is used,
the oscillator frequencies are multiplied by 10 to give analysis
frequencies.

The frequency multiplication factor (S) is that number by which
the true frequencies (f£,) in the record have been multiplied, during
data preparation and analysis, to yield the analysis frequencies (£,),

f= —8 py)

The frequency multiplication factor (S) is determined by the
recording tape speed (s,), and the playback tape speed (sp) by
the equation

5 = sp), 8 (2) a

suc |) ane)
where (1) and (2) in Equation [2] refer to first or second record and/or
playback. From Equations [1] and [2] , the true frequencies are found

to be
s_(1) s_(2)
putes x x

t ~ “as (1) s,(2) [3]

If, for example, a signal is recorded at 1-7/8 ips, played back at 30 ips,
re-recorded at 3-3/4 ips, and played into the analyzer at 15 ips, then
Equation [3] states that the analyzer frequencies must be divided by

64 to get the true frequencies.

It is sometimes desirable to display the abscissa scale in terms
of the circular frequency of encounter (we). This is given by

19

a = 2nf [4]

or directly by multiplying Equation US ] by 2x

The ordinate scale of the spectrum representation requires
attention next. Where the local oscillator scale was used to represent
the analysis frequency scale, the peak voltage output of a pure
sinusoid is used to represent one point on the analysis ordinate scale.
This calibration factor is obtained by analyzing a pure sinusoid
in the same way (same constants) as the particular seakeeping event
being analyzed. Since the bandwidth of the filter is much greater
than the frequency band of the calibration signal (zero), the result
is a curve which represents the characteristics of the filter rather
than the pure sinusoid. This is all right because only the peak value
of this curve is important, at the moment. Figure 7 shows typical
calibration curves for different filters. According to our analysis
technique, the peak value of the calibration curve is the square of
the amplitude of the pure sinusoid being analyzed. If this amplitude

);

is characterized by its rms (root-mean-square) voltage input (Views

then the peak value of the resulting calibration curve (v,") is
Bo DENG: 2
ve = (V2v_.) V_,volts®) [5]

Figure 8 shows a spectral density analysis of a seakeeping
variable made with a 5-cps filter. The calibration curve appears
at the right. Since the rms input voltage is V,_. =0.04, the output
peak value is by Equation [5] , Ws = 0.0031 volts=. This is the

20

height of the ordinate scale appropriate to the peak of the
calibration. Since also, the base of the ordinate scale is zero,
the ordinate scale will be completely defined, in terms of the

analysis parameters, once the filter bandwidth is taken into account.

It should be noted that the application of different filters to
the same random signal results in spectra of different apparent sizes
(Figure 4), yet the peak values of the calibration will be the same
(Figure 7). This results in the same scale for all the spectra in
Figure 4, but is not paradoxical so long as it is remembered that
the ordinates represent averaging over the filter bandwidth. That
is, a 10-cps filter analysis should result in a spectrum which has

twice the area of that resulting from a 5-cps filter analysis.

It has become the practice in the SEADAC to eliminate the
confusion resulting from the averaging process by relating the
spectral density to a unit frequency band. This is accomplished by
dividing the ordinate scale by the "effective bandwidth" ( a iy)

defined as
A
WE ore ye [6]

where A is the area under the calibration curve (Figure 8) measured

in square units of the graph paper, L is the height of the calibration
curve measured in units of graph paper, and k is the ratio of any
convenient frequency band on the analysis frequency scale to its

length in units of graph paper. As an example, consider the area

21

under a particular calibration curve, purporting to represent a

5-cps filter, to be 137 units?. The height of the calibration

curve is measured as 15.2 units and a frequency band of 10 cps is
equivalent to 16 scale divisions on the analysis frequency scale.
Equation [6] shows that the effective filter bandwidth is 5.63 cps

and states that the effective filter bandwidth is equivalent to the
width of a rectangle whose height is the height of the calibration

curve and whose area is the area under the calibration curve. In
principle, the effective bandwidth of each filter should be constant

but variations of several percent indicate instability of the crystalline

structure of the filter which, it is hoped, will be corrected with air

conditioning of the space in which the system is installed.

To complete the universalized ordinate scale, in terms of the
seakeeping event being studied, it is necessary to introduce the
instrument calibration. The signal being analyzed is a fluctuating
voltage which may represent heave, pitch, etc. Before each run,
a calibration should be applied to the tape which relates particular voltage
settings to particular transducer signals. The value of the calibration
squared (GL) is all that is required to complete the ordinate scale.

If the squared calibration is taken together with Equations [5]
and [6] , the resultant spectral density ordinate 9) associated with

the peak of the calibration curve is

ce v2 2c Vel
es ET cn URTV i (7)

which has the dimensions of seakeeping units (degrees, feet, etc.)

22

squared, times time.

A mode of operation called "bandwidth divisor," which has not
been discussed, essentially divides the ordinate scale by a frequency
bandwidth related to the effective bandwidth. This mode is being
investigated with a view toward eliminating the necessity for manual

division.

2. COMPUTATION OF MEAN TOTAL ENERGY

The total energy in the spectrum @ , which yields important
statistical information on the amplitude distribution of the event
being studied, is defined by the area under the spectral density

curve as

co

@ = \ @ ( @,) da, [8]

One obvious method of calculating © is by measuring the area bounded
by 6 (o,) and the abscissa scale. Another less troublesome,

more accurate method was mentioned in the section DATA ANALYSIS (page
8) as"integral of energy" where the operation described in Equation [8 ]
is performed in the analog computer of the SEADAC. Such an integration
appears in Figure 9 where the integrated spectrum is superimposed

on the spectral density curve derived from the same data, Examination
of this cumulative representation of the spectrum shows that it is
steep when the spectral density curve is steep (upward), has inflection
poiuts where the spectral density curve has peaks, and becomes

asymptotic to a constant as the spectral density function goes to zero.

23

The value o is the highest value assumed by the integrated
curve. To find this value, a calibration is made of a pure sinusoid
for the "integral of energy'' mode of operation. This appears in
the lower right-hand corner of Figure 9. The maximum value of the
calibration curve is given by Equation [5] . The maximum value of

the cumulative curve is given by

in Ge Ae 9

gs oe VG [9]
where L,/Ls is the ratio of the height of the seakeeping cumulative
curve to the height of the calibration curve. ®is given in sea-

keeping units squared.

3. CONFIDENCE BANDS

The presentation of the energy spectrum of a seakeeping
event would not be complete without some measure of confidence.
This confidence is usually expressed by a pair of curves which
flank the spectral density curve in such a way that it may be said:
"The true spectrum is expected to lie between the two curves with

a probability of x."

The confidence bands are determined from the chi-squared distri-

bution with f degrees of freedom where

Eis oT AE [11]
T is the time it takes the magnetic tape loop to make one traverse

through the analyzer.
The number of degrees of freedom is entered into Figure 10

24

to obtain the numbers by which the spectral ordinates must be multiplied

to gain any desired percentage of confidence.* For example, consider the
energy spectrum in Figure 11. This graph resulted from an analysis with

a filter whose effective bandwidth was 5.63 cps; the record length was T = 2.81
seconds. From Equation [10] it is seen that f = 31.64. The 90-percent
confidence bands are found by entering 31.64 om the abscissa scale of

Figure 10 and reading off the multiplying factor from the projections on

the ordinate scale of the intersections of f = 31.64 with the 5-percent and
95-percent curves. Figure 11 shows the energy spectrum of that seakeeping

event with its associated 90-percent confidence bands.

PROPOSED EXTENSION OF THE SEADAC
Even while the SEADAC is relatively new, some additional components
are being considered which will: (1) increase its efficiency through
saving of computational time, (2) extend its usefulness through new

operations, and (3) prepare magnetic tape for re-use in the field.

Figure 12 is a block diagram showing the SEADAC, with the proposed
additions (dotted lines). The magnetic-tape recording brought from the
field to the laboratory will be reproduced at 60 ips on a reel recorder,
as before. Instead of re-recording, at 1-7/8 ips, on the loop recorder,
this operation is now performed on another reel recorder. The benefits
derived from the addition of a reel recorder are two-fold: (1) all the
information on the reel may be transcribed on one re-recording and (2) the

loop recorder is always free to play data into the analyzer. No time will

*Figure 10 was constructed from tables of the chi-square distribution found
in most textbooks on statistics.

25

be lost in the re-record process. A magnetic-tape signal eraser will be
incorporated to remove the signals from the original tape after it is
transcribed onto the other reel. The original tape will then be sent back
into the field for re-use. The transcribed tape is then 1/32 of its
original length and after being converted to loop form (appropriate to
each run), it is ready for analysis. During the re-record period, the
information will be simultaneously transcribed onto graphic chart paper,
as at present, and a book of the experiment will be prepared and filed.
After the loops are played through the analyzer, they will also be stored,

as at present.

Two changes are planned for the analyzer; one is simple and direct, and
the other requires some careful electronic engineering. As mentioned in
the preceding section, the two most popular modes of SEADAC operation are
computation of the spectral density function and computation of the total
energy in the signal. In the present system, each calculation can be
made either successively on one analyzer or simultaneously on both analyzers.
If each analyzer can be made to perform both operations simultaneously,
analysis time will be cut in half. The way to accomplish this is to
incorporate an additional power integrator and recorder into each analyzer.
This was done experimentally with the existing equipment and the result
appears in Figure 13. The spectral density curve and integrated curve
marked "A'' represent successive analyses on a single analyzer, whereas
the curves marked "A + B"' represent simultaneous analyses of the same data
on the same analyzer with the addition of the power integrator and recorder
of the other analyzer. The small differences are attributed to the different
gains of the two systems and are corrected by the calibrations. The good

26

agreement of the curves seems to justify the extension of the analyzer

system in this direction.

Computation of cross spectra is not yet available as commercial
analog electronic equipment, so this matter must be pursued at the
users' level. Some cross-spectrum analyzers have been built in the

laboratory, and at least one is known to be successful.

There are two known methods of performing cross-spectrum analysis that
are amenable to incorporation in the SEADAC:
1. Single-filter, and

2. Matched filters.

The first method requires the combination of two simultaneous records
by addition and by differentiation and addition. The record which
results from these operations is treated like an ordinary record and its
spectrum is analyzed accordingly. The result played out on the X-Y
recorder is operated upon, in certain ways, to extract the co=and quadrature-

spectra (the desired components of the cross spectrum).

The second method involves the simultaneous modulation and filtering
of the two records. The outputs of the matched filters are multiplied

together, once directly, and once after one signal is phase-shifted 90 degrees

The results, after integrating and averaging, are played out on the

X-Y recorders as the co-and quadrature-spectra.

To accommodate both types of cross-spectrum analysis in the SEADAC
(which is our intent), the following operations must be incorporated

27

into the analog computer:
1. Addition of signals,
2. Differentiation,
3. Multiplication, and

4. Phase shifting.

After completion of the SEADAC, as described, there will be two
alternative methods of treating data (Figure 12):
1. Auto-Spectra
a. The energy spectrum of each of two signals.
b. The total energy in each of two signals.
2. Cross- Spectra
a. The energy spectrum of each of two signals.
b. The co-spectrum (in-phase) of the two signals.
c. The quad-spectrum (90° out-of-phase) of the two signals.
In the prospective form discussed in this section, the data-processing
method employed by the SEADAC may be considered to be comprised of three
separate operations, as shown in Figure 12:
1. Data collection.
2. Data preparation.

3. Data analysis.

The sole interdependence of these operations is in the necessity
for each operation to provide work for the succeeding operation. As long
as each operation has data on which to operate, it is completely independent

of the others.

It is possible that the system as outlined here will sometimes suffer

28

from an imbalance because of the piling-up of data in one operation and

a dearth of data in another. The frequency and magnitude of such occurrences
are difficult to predict in such a dynamic environment, and problems of

this sort will have to be treated aS they arise. It is believed that the
system design is capable of handling the present and near future workloads

of the Model Basin, insofar as they can now be determined.

29

APPENDIX

AMPLITUDE MODULATION APPLIED TO THE SEADAC

The analyzer system of the SEADAC is essentially a beat frequency
analyzer commonly encountered in the field of acoustics; that is, a pure
carrier frequency is mixed in a certain way with the random signal (sea-
keeping event) being studied. The process of mixing the carrier with
the random signal, to assign amplitudes to the frequency components in the
random signal, is called amplitude modulation. The carrier frequency is
called the modulated frequency, and the frequencies in the random signal

are called the modulating frequencies.

In the SEADAC, the oscillator produces a range of frequencies between
97,000 cps and 122,000 cps. This generation of frequencies by the oscillator
occurs in a continuous fashion so that the resulting modulated signal is

always changing.

For the sake of simplicity, we shall deal with the modulation process
which occurs at any particular instant of time and a modulating signal
which is a single frequency; we will then generalize for the random signdl

containing many frequencies.

Consider the unmodulated carrier signal to be
a =A coswmt [A-1]
c c c

where c means carrier and uw is the frequency. The modulating signal

combining with the carrier is

an = AL cos ant [A-2]
™ m

30

where m refers to the modulating signal and wD. >> w for reasons not of
interest here. The process of modulation results in a combination of

Equations [A-1] and [A-2] into the form

a=A cosmt+k A coswmt cosmt [A-3 ]
c Cc am ™m Cc

[A +k A cos wt] cosmt
c am ™m Cc

where Kk. is a proportionality factor which determines the maximum variation
in amplitude for a given modulating signal an The term [A. + kAL cos wt]

is the envelope of the modulated carrier frequency in Eyuation [A-3].

A trigonometric expansion of Equation [A-3] results in the component

separation of the modulated carrier frequency

mA m
ac ac
a= A, cos wt + —5— cos [w, + wit 1 =o cos [w, - wt [A-4]

where m,= kA A, is called the modulation index and determines the
degree or nature of the modulation as dictated by AL and A.- A sample

of a modulated carrier wave given by Equation [A-3] appears in Figure 14.
The graph of Equation [A-4] is shown in Figure 15 as a frequency spectrum
of the relative amplitudes of the component waves in the modulated signal.
Equation [A-4] and Figure 15 show that the frequencies of the resultant
modulation are the carrier frequency and the sum and difference of the

carrier and modulating signal.

Consider now an example where a carrier signal of 97,100 cps is
mixed with a modulating signal of 10@ cps. The resulting frequencies in
Figure 15 will be, from left to right; 97,000 cps, 97,100 cps, and
97,200 cps. If then a filter designed to pass only 97,000 cps receives

the modulated signal, only that component which is the lower sideband

31

(difference frequency) may pass through the filter.

Examination of the term representing the difference frequency in
Equation [A-4] shows that the amplitude of the lower sideband is pro-
portional to the amplitude of the modulating signal (AD because
moA. = kA . To generalize to the random signal, consider that a
given carrier frequency will mix with all the components in the random
signal, but only that component which produces a lower sideband (difference
frequency) of 97,000 cps will pass through the filter.

It should be noted that filters are not as narrow as suggested here
so that a 5-cps filter, for example, will be centered at 97,000 cps but
will permit all difference frequencies between 96,997.5 cps and 97,002.5
cps to pass. The analog computer squares and averages all these frequencies
and assigns this estimate of the spectral density to the appropriate oo

designated by the oscillator which generates the carrier frequency. As

long as the spectrum is relatively flat in this area, the estimate is good.

To summarize then, the random signal modulates a particular carrier
signal in such a way that only the resulting difference frequencies pass
through a narrow band fixed filter. The amplitudes of the passed components
are proportional to the amplitudes of the modulating components and the
frequencies are related to the carrier wave. If the carrier wave frequency
is constantly increased, all the frequencies in the random signal may be
identified. After a component is passed through the filter, it is sent to
an analog computer where it is squared, and then to an X-Y plotter where
the squared amplitude-voltage is displayed against frequency. Adjust-

ment of the ordinate and abscissa scale to account for transducer and

analyzer calibrations results in a plot of spectral density versus frequency.
32

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55.2

46.0
Spectral Density

36.8

27.6
Cumulative Spectral Energy

#(w,) in deg?-sec

18.4

9.2

I
0.246, 0.368 0.491 0.614 0.736 0.858 0.981 1.100 1.245
@,22n/T. in seconds”!

Figure 3 — The Integrated Spectrum of a Pitch Record Superposed on the Energy
Spectrum of the Same Record

35

Relative Spectral Density

SS —

0.246 0.368 0.491 0.614 0.736 0.858 0.98! 1.100
@e=2n/T. in seconds

Figure 4 — SEADAC Analysis of a Pitch Record Using 2-, 5-, and 10-CPS Filters

36

1.250

aa tI AN RT AES STE PE VO neem) ee PEE

102 5! 2.2

f, in cycles per seconds

Figure 5a — Slow Scan

(i, EN ae ES rl Se ae ES See

10.2 SI 122

fy in cycles per seconds

Figure 5b — Fast Scan

Figure 5 — Spectral Density Functions Computed from Same Seakeeping Record
for Slow Scan and Fast Scan

37

Figure 6 — Energy Spectra of Several Seakeeping Events Analyzed by the SEADAC with the
Numerically Computed Energy Spectra Superposed

32.0

24.0

i)

9

fo}
T

@&,) in deg? -sec
a
°
T

nN
iS)
T

-8.0

4.0

0 =
0.184 0.367 0.429 0.55! 0.675 0.797
@e%2n/T, in seconds"!

Figure 6a — Roll

17.5

15.0

N
a

7.5

Ww.) in deg?-sec

5.0

o&
0.429 0.55! 0.675 0.797 0.919 1.042 1.710
@,*2"/T. in seconds ~

Figure 6b — Pitch

38

40 5

32

24

: .2
S,() in kpsi*- second

al.) in g* second

0.030

0.025

0.020

9.015

0.010

0.005

0245 0368

0491

a6l4 0.736 0.858 098i

w=277/Te in seconds |

Figure 6c — Heave Acceleration

O64 0736 O858 O98!

w,=27/ Te in seconds|

Figure 6d — Starboard Strain

39

1100

1.100

1245,

O
~
ORD

1.245

1360

1485

Sp (we) in Kpsi® -sec

H(we) in ft? -sec

Ny
to)

1.36

0.246 0.368 0.491 0.614 0.736 0.858 0.981 1.100 1.245
439=2n/Te» in seconds”!

Figure 6e — Port Strain

46.0

36.8

27.6

9.2

nt

° ee eee EE EE EES)
0.246 0.368 0491 0614 0736 0858 0.981 LIO0O 1245
Ww, =2m/T, in seconds”!

Figure 6f — Wave Height

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0.0093

0.0062

(w,)

0.003! volts2
OvoXoR] |= SS Ss

fo 5-cps

Figure 8 — Analog Spectral Density of a Seakeeping Event with Appropriate Calibration Curve

00093

0.0062
=,
3
2

0.003! L,

he
O

5-cps
fa

Figure 9 — Analog Spectral Density of a Seakeeping Event with Cumulative Energy
Distribution Function Superimposed

42

Percent
9

cates

IN a
Ce

NE aa PA
Ne ES ee

AN|OA BNE 0} P2AsaSGO 40 O1NDY

10

20

30
Degrees of Freedom

70 50

Si

2 X Bandwidth X Sample Length

Figure 10 — Reliability of Spectral Density Estimates

43

$(w,)

726

55.2 | \

aie! | |
27.6 | | ' V La
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Figure 11 — 90-Percent Confidence Bands (Dashed Lines) Applied to a Spectrum
with 31.64 Degrees of Freedom

44

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Wwe) in deg -sec

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C38)

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Figure 13 — Computation of Spectral Density and Total Energy by: 1) Successive Steps
in One Analyzer, and 2) Simultaneous Calculation in the Same Analyzer
with the Addition of Another Power Integrator and X-Y Recorder

46

Figure 14 — An Example of a Modulated Carrier Wave

Modulating
Signal

Carrier

Lower Upper
Side Band Side Band
io)
e Hi th f

o|cu

els

Relative
Amplitude

We + Wm

Ym WYo-Wm We

Figure 15 — The Spectrum of the Relative Amplitudes of the Components of a Modulated
Wave as a Function of the Frequency of Those Components

47

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SUPSHIP, New York Shipbldg Comp, Camden

1 Mr. J.W. Thompson, Nav Arch (Design) 1
Newport News Shipbldg & Dry Dock Co,

Newport News 1

1 Asst Nav Arch

2 Dir, Hydrau Lab P

James: Forrestal Res Ctr, Princeton Univ, Princeton
Attn: Mr. M.H. Smith, Asst to Dir

Tech Dir, Ship Struc Com, NRC

Technical Products Co, Los Angeles
1 Mr. R.C. Moody, Chief Engr

Dr. M.L. Albertson, Head, Fluid Mech Res, Dept of 1
Civil Engin, Colorado St Univ, Fort Collins

Prof. B.V. Korvin-Kroukovsky, E. Randolph, Vt.

Prof. M.A. Abkowitz, Dept of NAME, MIT, Cambridge
Dr. George C. Manning, Prof, Nav Arch, MIT, Cambridge
Prof. F.M. Lewis, Dept NAME, MIT, Cambridge

Dr. V.G. Szebehely, Aero Sci Lab, General Electric
Co, Philadelphia

ALUSNA, London

49

Dir, Hydro Lab, NRC, Ottawa 2, Canada

Dr. Georg Weinblum, Universitaet Hamburg,
Berliner Tor 21, Germany

RADM R. Brard, Dir, Bassin d’Essais des Carenes,
6 Blvd Victor, Paris (15e), France

Dr. L. Malavard, Office Natl d'Etudes et de Recherches
Aeronautiques, 25 Ave de la Division, LeClerc,
Chatillon, Paris, France

Gen Ing. U. Pugliese, Pres, Istituto Nazionale per Studi
ed Esperienze di Arch Nav via della Vasca Navale 89,
Rome, Italy

Senor Manuel Lopez-Acevedo, Dir, Canal fe Experiencias
Hidrodinamicas, El Pardo, Madrid, Spain

Dir, Nederlandsch Scheepsbouwkundig-Proefstation,
Haagsteeg 2, Wageningen, The Netherlands
1 Dr. G. Vossers

Mr. Otto Bussemaker, Hoofd. V.H. Bureau Scheepsbouw
Ministerie, Van Defensie (Marine), Torenstraat 172,
The Hague, Netherlands

Prof. J.K. Lunde, Dir, Statens Skipsmodelltanken,
Trondheim, Norway

Dr. Hans Edstrand, Dir, Statens Skeppsprovningsanstalt,
Goteborg C, Sweden

Dir of Res, BSRA, Curzon St, London, W-:1, England
Supt, Ship Div, NPL, Teddington, Middlesex, England

Dr. J. Okabe, Res Inst for App! Mech, Kyushu Univ,
Hakozaki-Machi, Fukuoka-shi, Japan

Chief Supt, Nav Res Estab, Halifax, Nova Scotia, Canada

Prof. L. Howarth, Dept of Math, Univ of Bristol,
Bristol, England

Ir. J. Gerritsma, Delft Shipbldg Lab, Prof. Mekelweg 2,
Delft, The Netherlands

Dr. Siegried Schuster, Head, Berlin Model Basin,
Berlin 87, Germany

Dr. H.W. Lerbs, Dir, Hamburg Model Basin,
Hamburg 33, Germany

Dir, AEW, Gosport, Hants, England
1 Mr. E.C. Tupper

Prof.C.W. Prohaska, Hydro-Og Aerodynamisk Laboratorium,
Hjortekaersveg 99, Lyngby, Denmark

Prof. Dr. Aldo Andreoni, Instituto de Pesquisas, Techni-
colocqicas, Caixa Postal 7141, Sao Paulo, Brazil

Dr. J. Dieudonne, Dir, General Inst de Recherches de la
Construc Navale, 47 Rue de Monceau, Paris (8e) France

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SLT REIN Fl
queuldinby — ulseg
T@POW JojAvy praeq “F

spusq aoueptj
-uog — Bayoads Asiougq *¢
OVdVds
— Sieyjnduiod sojeuy °Z
UISBY [@PO]W
jojAey, plAvg — uortjonpel
B4Bq — SSeUTyOMBEG *T

*poysedsns ale sorjtjiqedvo sjt pue}xe pus

Aguetoijje s,we sks ay} OAosdut [[IM JBYy} SeSuvyo pus peqsty] oie

OVGVAS 942 jo suorqeqIwI] oy, ‘eJBp eUBS oY} Jo UOTIBINOT[BO

[BOljeunu YIM sjUeAe Sutdeeyves urezI09 Jo AyIsuep [ejoeds

ey} Jo uolenduos DYQYUS Jo uostiedwios Aq payejsuowep

SI woSAs 04} UI EOUEPIJUOD ‘peUT]}NO 218 BVP jo axBI0}s puL

‘stsXjeue ‘uoryeiedaid J0oj spoyjow oy, *peqriosep st (QyaVvdas)
1ejuaD stsk[euy ByVq BuIdeeyeeg uIseg apo; JO[ABT, oy,

GaladIssvTONN
*sjoi ‘‘sadeip ‘sydeas ‘ssnqj1 ‘dep ‘ta "Qg96T Ajng ‘aessneiyg
“d [nvq pus syxzey anqqty Aq ‘YALNAD SISAIVNV VLVG
ONIGAUNVUS NISVE TAGOW YOTAVL AHL — OVGVaS
ESE] Hoday ‘ulspg japow s0jADy plang

[neg ‘jessneyjg “Ij

INQTI A “SYP

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quowdinby — urseg

[OPOW JojARL, plavq “+

spueq aouaeptj

-uod — vaqoeds Adiougq “¢

OVdVaS

— siejnduioo dojeuy °Z

UrSe aalePoNn
lojAvy, plavg — uomonpal

BIB — SSOUTYWOMBEg

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*poysedans aie sarqtjiqedvo sqt pueyxe pus
Aouatorjje s,waqsks ay} oaoiduit [IM 4By] Sosuvyo puv poyst] ose
OVGVAS 94) Jo suoNEIIWI] ayy, ‘ep eul¥S ey] Jo UOTB[NoO]BO
[BolIOWNU YIIM SjUeAe Suldeayevas UIe}Ie0 Jo AqyIsuep [esqoeds
94} JO uoljendwods DYGYAS JO uostedwoo Aq peyeajysuowep
SI Wo}SAS OY} UL eOUEpIJUOD “pouT[}NO aiB vyep Jo advio}s puv
‘stsAjeue ‘uorjesedeid Joj spoyjew oyy, *peqiosep st (O¥aVyuas)
Jajuey stsh[euy eywq duldeeyveg uIseg Japoyy JojAey, oy,

GaIdISSV TON
sje ‘saderp ‘sydeas ‘:snij1 ‘dep ‘ta "Qg6T A[ng ‘zessneajg
“g [Neg puw sysey anqiiM Aq ‘YALNAO SISATWNV VLVG
DNIGHUHNVAS NISVE THCOW YOTAVL GHL — OVGVUS
"EGEL s4odayy ‘ulspg japow sojADy plang

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INQIIA ‘SHIVA
queudinby — utseg
Tepow J0jAvy, pravqg “F
spueq eoueplj
-uog — Biqoeds Adiougq *¢
OVdVas
— Sioejnduioo Sojeuy °Z
UISe a TeRON
jojAey, pravg — uoronpel
eyeq — SSOUTYWOMBAG aT

[neg ‘iassneyg ‘yy
INQIIM *SyseW ‘]
queudinby — uiseg
T@PpoW JoyABy prawq “F
spusq souepy
-u0) — Bijoeds Adiouq *¢
OVdVds
— sioynduioo Sojeuuy °z
uIseg [epoyW
Joj|ABy, plaeqg — uolonpea
BBQ — SSOUTyOMBeg *T

*poqseddns ole serjt[iqedeo sj pueyxe pus

Aouetotjje S,weqsks ay] eaosduit [[IM BY) SeSuvyo pus poysty] oie

OVGVAS 94} JO suOT}ezIWI] OY, “BJBp eUlBS OY} JO UOIZB[NO[BO

[BolJowNU YAIM S}UeAe SuIdeeyves uTBIIeD Jo AqISuep [esjoeds

ay} Jo uolyeyndwos OyqYaS JO uostmwdwoo Aq peyesysuowep

SI Wej}SAS OY] UI EOUEPIjUOD ‘peUl{jno e1B Bywp Jo oFB1048 pus

‘stsA]sus ‘uorjesedaid Joj spoyjew eyy, *poqiiosep st (QyqVvas)
Joqued sisk]Buy Byvq Sutdeoyveg uIseg Jopow Jo[ABy, oy,

Ga IdISSV'TONN
*sjoi ‘sadeip ‘sydvad ‘-snqyr “dep ‘ta = ‘Q96] A[ng ‘iessneng
“A [neg puw syzey angiig Aq ‘YALNAD SISAIVNV VLVG
ONIdGANVUS NISVG THCOW YOTAVL AHL — OVGVaS
“EGE soday -ulspg japow 40;ADy prang

*peysedans o1v sert[iqedeo sqt puezxe pus

Aouoloyjje s,weysks ay} erosduit []IM 4BY) Sesueyo pue poysty ose

OVGVUS 4} Jo SuoTzeqIWI] eyy, ‘eqVp oU"S oY} JO UOTYBINO]BO

[Boliewnu YIIM S}UeAe DSuIdeeyves uIBjJ00 Jo AyIsuop [Bajoeds

24} JO uoTyejndwoo OYGYUs jo uostiwdwuoo Kq poqwaysuowep

SI We}Shs 04} UI edUepIjUOD ‘peulyyno elv BIwpP jo edBIO}S pu

‘stsX]Bue ‘uorqeiedaid 10) spoyjow oy, “poquiosep st (QV¥aVas)
JojUeD sisdjeuy 8yeq dutdeoyveg uIseg Jopoy JO[ABT, oy,

GdaI4ISSV'TONN
*sjoi ‘‘sadeip ‘sydead ‘-snqyt “dep ‘tA “Qg96T A[ng ‘aossneayg
“A [nBq pues syxzey inqiim Aq ‘YALNAD SISATIVNV V.LVG
ONIdGANVAS NISVG THCOW YOTAVL HHL — OVGVaS
"EGE soday = ‘ulsog japow 4s0jAD] plang

[neg ‘dessneyg ‘]]
INQIIM ‘SYIVW “]
quewdinby — ulseg
[@pOW JOyABy, pravqg “7%
spusq oouepy
-uog — Bijoeds Ad10uUq ‘¢g
Ovdvds
— Sdoynduioo sojeuy °Z
uISsBg [@poW
dojAvy, plavg — uoonpea
BqBq — SSeUIyWOMBEG *T

[neg ‘iessneyng ‘yy

INGIIM “SHIVA *]
quowdinby — uiseg

[epow sojAvy, pravq *F
spueq oouepy

-u0D — viqoeds Adiouy *¢g
OVdVvds

— Sdojnduioo sojvuy °Z
Ure delePoW

JO|ABL, plavg — uoronpes
BIB — SSOUTYyWOMBEG “T

*poyseaans ole serji[iqedeo sqt puejxe pus

Aouotorjje s,woysks ey} eAosdut [[IM 4By3 SesuByo pus poyst] ose

OVGVGS °y} JO suorzezIWI] oY y, *ByBp eUBS 9y} Jo UOTZB[NOTBO

[BolJewnu YIIM sjUeAe DuIdeeyves u1B{Je0 Jo AqISuep [Bajoeds

8y} JO UoOIBIndWOD OYGWaAS JO Uostreduios Aq peyeyysuowep

SI weiss oY} Ul eoUepPIjuOD ‘peur]yNo ee ByBp jo es¥I0}s puB

‘stsh[eue ‘uoryesedasd 10} spoyjyou oy, “poqtiosep st (Qyqyas)
Jeyued siskjeuy Bywq dutdeeyveg uIseg Jopow; IO[ABy, oy,

Ga1adISsvV TONN
*sjoa ‘*sadeip ‘sydeid ‘snqjt “dep ‘tA "O96, A[ng ‘sossneayg
“a [neg pus syzey angi Aq ‘YALNAO SISAIWNV VLVG
ONIdAAYVAS NISVA THGOW YOTAVL SHL — OVGVaS
"EGE, soday -ulsog japow 4ojAny piAng

*paysosans oie soljijiqudvo sqt pueyxe pus

Aoueloje s,weysks ayj erosduit [JIM JBYy) SeduByo puv peysty ov

OVAVUS 94} Jo SuoByIWI] oY, ‘BIVp OUvS ay} Jo UOIZB[NoTBO

[BolIownu YIIM sjueAe Sutdoayves ulezIe0 Jo AyIsuep [eajoeds

ay} JO UoIyeIndWod DYQGWas JO Uostedwoo Aq pezesysuowep

ST Woshs 04} UI BOUEPIjUOD ‘peuT]yno oiw vywp jo advioOys puL

‘stsh|eue ‘uoryeaedesd 10) spoyjow oy, *poqiiosep st (Q¥GVas)
Jojua9 sisk]euy evywq dutdsexveg uIseg [apo 1o[Aey, oy,

GdaIdISSV'TIONN
*sjoi ‘‘sadeip ‘sydeas ‘:snyjt ‘dep ‘ta ‘ggey Ainge *laSsneljyg
“A [neq puw sxsw inqiim Aq ‘YALNAD SISATVNV VLVG
ONIGGANVaS NISVE THGOW YOTAVL AHL — OVGVaS
"EGEL Hoday ‘ulspg japow 40)ADy plang

[neg ‘iessneyg ‘TJ
ANGIIM ‘SYA *]
quewdinby — ulseg
[epoy JojAvy, pravq “F
spusq aoueptj
-uog — Bijoeds Asiouy *¢
OVdvas
— sieqinduios Sojeuy °Z%
uIseg [@POW
lojAey, plavqg — uorqonpedl
BBQ — SSeUTYWIOMBES “T

[neg ‘jessneyg ‘jj
INQIIM ‘SYIBW *]
jueudinby — uiseg
T@POW JojABL praeq “F
Spueq aoueplyy
-uog — Bijoeds Adiouq “¢g
OVdVds
— sieqjnduios sojeuy °Z
UISBa [OPOW
Jo|ABy, plavg — uorjonpel
B18q — SSeULYyWIOMBEG “T

*peqjsessns ele sertiiqedvo sqrt pueyxe pus

Aguetotjje S,weysks oy} eAosduil [[IM IBY} SesuByo pus poqst] ole

OVAVUS 94) JO SUOTIBIIWI] oY, *BJBp eUBS ay JO UOTZe[No[BO

[Bollownu YIIM SjUeAe SuIdeeyveS UIeJIe0 Jo AjISuep [eij0eds

ay} Jo uoeyndwos OYqyas Jo uostmeduioo Aq peyeajsuowep

St wesks 0Y} UI edUEpIJUOH ‘peUr]INO ai BIBp Jo edB104s pus

‘stsX[eue ‘uoryeiedeid 10j spoyjow oyy, “poqiiosep st (QyaVvas)
19jUaD SISA]BUYy BIVq DUIdeeyBeg UISeg Jopo~ JO[AB], oy L

GdaIdISSV'TONN
*sjoi ‘‘sadeip ‘sydvas ‘sny[t ‘dep ‘tA "Qg6] A[ng ‘jessneyg
“A [neq pus syzey inqiim Aq ‘YALNAO SISATVNV VLYG
DNIdAANVAS NISVG THCOW YOTAVL FHL — OVGVAS
EGE] Hoday ‘ulspg japow 4ojADy plang

*pojsedsns ele semtiiqedeo sqt pue}yxe pus

Aduetorjje s,weysks ay} eaosdul [[IM BY SeSuvyo pus post] ols

OVGVGS °4} JO SUOI}BIIWT] EY, ‘BJBp eWBS ay} Jo UOIJE[NOI[BO

[Boleunu YIM SjUeAe SuIdeeyeves ulEzI00 Jo AjISuop [eijoeds

ey} Jo uowyndwos Oyqyays Jo uostiwdwioo Aq peyeyysuowep

SI Waq}SAS OY] UL COUEPIJUOD ‘pauUT[jNo aie vyBp jo asB104s pus

‘stsAjeue ‘uoryesedaaid oj spoyjow oyy, *peqtiosap st (Qyqvas)
Joyueg sisk[euy Bjvq duldeaysveg uIseg Japoy; JO[ABy, oy,

GaldISSVTONN
*sjoi ‘‘sadeip ‘sydeas ‘«snqqt dep ‘tA “Qg6T A[ng ‘iessneayg
“a [n’g puv sxsw anqyt4 Aq ‘YaLNAO SISATIVNV VLYG
ONIdGANVUS NISVA THCOW YOTAVL FHL — OVAGVUS
"ESEL soday -ulspg japow 40)4D] pang

[neg ‘iessneiyg "]]
INGIIM ‘SHIVA *T
juoudinby — uiseg
TOPOW JOTABT, plasq “F
spueq ooueply
-uog — vajoeds Asiouq ‘¢g
Ovdavds
— Siojnduioo sojeuy °Z
uIseq [9poW
JojAey, plavg — uoronpel
B48Q — SSOUTYWOMBEgG *T

[neg ‘Jessneiyjg “jj
ANGTIM “SHIVA *
quowdinby — urseg
[@pow JOjAvT, pravq *F
spueq eoueptj
-uoy — vajyoeds Adiouq ‘¢e
OVdVds
— siojndulos Sojeuy °Z
UISBY [@PO]\
1ojAB, pilav — uoTjonpea
BIB — SSOUTYWOMBEg *T

*pojsessns ele serji[iqudvo sj pueyxo pus

Aouetoyje s,weysks ay} eAosdut [[IM JBy) SesuByo pus poyst] oie

OVGVAS 94} JO SuOT{BIWI] OY, “BIBp EMBs EY} JO UOlB[No]BO

[Bolounu YZIM SsjUeAe duIdeeyeves ulEzI00 Jo AyIsuep [esqoeds

ey} Jo uoleqjndwos OyGyaAS JO uostseduioo Aq poyeyysuowep

St weqsks oY] Ul edUePIjUOD ‘poeUr[}NO ee vyBp Jo esBI0}S PUB

‘stsh|eus ‘uorjesedesd 10} spoyjow oy, *poqtiosep st (Q¥qWas)
10qUe9 sIsk]euy Bywq dutdeoyveg uIseg Jopoyw jo[ABy, oy,

GaladIssv TONN
*sjoi ‘sadeip ‘sydvis ‘-snyjt “dep ‘tA ‘o967 Ane ‘sessneajyg
“@ [hvq puv syzey anita Aq ‘YALNAO SISATVNV VLVG
ONIdHAUVUS NISVE THCOW YOTAVL FHL — OVGVdS
"EGE Hoday -uispg japow s0jADy plang

‘peqsedans ole serji[iqudvo sj pueyxe pus

Aoueatoje S,weysks ay) edosdut [[IM yVYy SesuvYyo pu poyst] ole
OVGVUS 943 JO SuOT}BIIWI] AY, ‘BJP aulVS 9y] Jo UOTyB[NOTBO
[BolMewNu YyIIM SsjUeAe duldeeyves ulead Jo AqIsuep [eaqoeds
ay} Jo uolyeqjndwos HDyqyas Jo uostiwdwoo Aq peyesysuowep

SI Wea3SAs 984} Ul BOUAPIJUOD ‘paul{]No aiv vyVp jo asvIOS pu
‘stsA]eue ‘uorjviedeid 10} spoyjow ayy, *peqiosep st (QO¥aVas)
Joya, sisd]euy Byeq dutdeoyveg uIseg Jopoyy Jo[Aey, oy,

Gd IdISsV TIONN
*sjoi ‘*sadvip ‘sydvas ‘*snyjt ‘dep ‘tA "O96, A[ng ‘aessneajsg
“q [neg puw syzey anqyiq Aq ‘YALNAO SISAIVNV VLVG
ONIdAANVUS NISVA THCOW YOTAVL 4HL — OVGVdS
"EGE, Hodayy “ulspg japow 4sojADy plang

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