NEDERLANDS SCHEEPSSTUDIECENTRUM TNO
NETHERLANDS SHIP RESEARCH CENTRE TNO
SHIPBUILDING DEPARTMENT
LEEGHWATERSTRAAT 5, DELFT*
FULL-SCALE MEASUREMENTS OF STRESSES IN THE
BULKCARRIER M.V. 'OSSENDRECHT'
ist Progress Report: General introduction and information.
Verification of the gaussian law for stress-response to waves
(METINGEN VAN SPANNINGEN AAN BOORD VAN
DE BULKCARRIER M.S. ,OSSENDRECHT'
iste Voortgangsrapport: Algemene inleiding en gegevens.
Verificatie van de wet van Gauss voor spanningsresponsie in golven)
by
IR. F. X. P. SOEJADI
(Ship Structures Laboratory, Deift Uníversity of Technology)
Voor een beter begrip aangaande het constructieve gedrag van schepen onder dienstornstandigheden, met het doe! orn betrouw-bare prognosemethoden te verkrijgen, zijn metingen aan boord onmisbaar.
Het voornaarnste doe! van de spanningsmetingen die in 1966 aan boord van het ms. , ,Ossendrecht" werden uitgevoerd was dan ook het uitbreiden van de hoeveelheid beschikbare
praktijk-gegevens. Nauwe!ijks van minder belang evenwel was de
gelegen-held orn ervaring op te doen met de instrumentatie en de registra-tietechnieken voor derge!ijke rnetingen. En ten derde was er het
probleern betreffende dc beste manier orn de resu!taten te
analyseren, dat onderzoek vereiste.
Het is dit laatste probleern, uitlopende in een evaluatie van de grondsiagen voor het verwerken en analyseren van dit soort ge-gevens, dat een van de voornaamste onderwerpen van het onder-zock is geworden. Dit vond zijn oorzaak in het felt dat een aanta! resultaten van de analyse niet overeenkwamen met de uitgangs-hypothesen.
Deze verificatie is een omvangrijk en tijdrovend werk geweest, dat onder andere vele uren cornputertijd in bes!ag narn. De resu!-taten hiervan en van de ana!yse zelf, zullen in dit en de volgende rapporten worden gepubliccerd.
De gelegenheid, geboden door de rederij Phs. van Ommeren N.y.,
om aan boord van het schip metingen uit te voeren wordt hier met dank vermeld. De waardevolle medewerking daarbij ver-leend door ve!e medewerkers van de walorganisatie van deze
Maatschappij en door gezagvoerder, officieren en overige be-manning, zij hier eveneens met dank gememoreerd.
Ook zijn wij dank verschuldigd aan het Laboratorium voor Scheepsconstructies, dat, geassisteerd door het Laboratorium
voor Scheepsbouwkunde (beide van de Technische 1-logeschool De!ft), de metingen voorbereidde, uitvoerde en analyseerde.
HET NEDERLANDS SCHEEPSSTUDIECENTRUM TNO
For a better understanding of the structural behaviour of ships in service, in order to obtain reliable preduction methods, full scale
data are indispensable.
The main purpose of the stress measurements carried out on
board of the m.v. "Ossendrecht" in 1966, therefore, was to
increase the number of available f ut! scale data. However, hardly of less importance was the opportunity to gain experience with
the instrumentation and the registration techniques for such
measurements. And thirdly there was the question as to the best method for analysing the results that required investigation.
lt is this latter problem, leading to an evaluation of the basic principles for the reduction and analysis of this type of data, that has become a main theme in the investigations. This was caused by the fact that some results of the analysis did not correspond to the basic hypotheses.
This verification has been an extensive and time consuming work, requiring among others numerous hours of computer time. The results of it and of the analysis itself will be published in this and the following reports.
We gratefully acknowledge the opportunity offered by the
shipowner Plis, van Ommcren N.y. to execute the measurements on board the vessel. Also the valuable assistance rendered by the Company's staff and the captain, officers and crew is gratefully
acknowledged.
Thanks are also due to the Ship Structures Laboratory, that, assisted by the Shipbuilding Laboratory (both of the Delft
Uni-versity of Technology), prepared, executed and analysed the
measurements.
Summary
page 7 iIntroduction
7 2Measurements
9 2.1General information
9 2.2Instrumentation
9 3Data reduction
113.1
Basic theoretical considerations
113.2
The punch-tape and the oscillofil recordings
113.3
Computer processing
123.4
General remark
124. Analysis
124.1
Introduction
124.2
The Gaussian character
124.2.1
Theory
124.2.2
Analysis of the oscillograms
144.2.3
Analysis of the punch-tape data
154.2.4
Extreme conditions
174.2.5
General conclusion
17Acknowledgements 17
References 18
Appendix 19
FULL-SCALE MEASUREMENTS OF STRESSES IN THE BULKCARRIER
M.V. 'OSSENDRECHT'
ist Progress Report: General ntroduction and information. Verification
of the gaussian law for stress-response to waves
by
h. F. X. P. SOEJADI
Summary
Measurements were made of stresses in mv. 'Ossendrecht' while crossing the North Atlantic.
Several strain gauges on the midship double bottom structure and a few on deck-level furnished digital as well as analogue
re-cordings.
The conclusion was drawn that, prior to the further analysis of the data, a verification of the basic assumptions of the statistical analysis was advisable in view of the value of the short term parameters derived for application in long term predictions.
In this report the results of the verification of the gaussian character of stress-response to waves are presented.
i
Introduction
In the course of time many measurements of stresses
in ships have been performed, starting with the taking
of snapshots of stress-conditions due to static loads
(e.g. Biles' experiments of the 'Wolf') and developing
into the technique of making measurements of stresses
due to wave-loads along statistical ways.
The character of the loading of a ship is one which is
mostly of a fluctuating sort so that we are forced to
study it along statistical ways. This so-called
'prob-ability approach' of the problem is no substitute for an
exact method (this is also stressed in the report of the
i.S.S.C.-Committee on 'Wave Bending, Shear and
Torsion - Full Scale Statistics' - 1964), but statistics
(and probability theory) are the means to analyse this
kind of problems.
give us much information about the smaller stresses
(i.e. stress variations), little about the much larger ones
and no certainty about 'the' possible extreme value.
Nowadays many research workers aim at predictions
of the stress-life of ships at very long terms along
statistical ways, expecting (hoping) to include the
extreme mentioned. Already in 1963 Yuille pointed
out that this is not the most efficient way to obtain
information about extremes [I].
In principle the extreme determines the design
crite-rion, but, on the other hand, there is the chance of
expe-riencing the extreme value and it
is up to the
re-sponsible bodies (not to the research worker) whether
or not to 'take the chance'.
The cyclic loading of a ship points to the necessity
of studying the fatigue properties of the ship's
struc-ture.
The variations in loading due to wave action,
how-ever, should be corrected for the influences of slamming,
temperature
variations,
variations in load-
(e.g.ballast-) conditions and corrosion, in order not to
have an underestimated picture of the cumulative
loading of a ship; in this respect the effect of local
loads (e.g. changes in water pressure) is also very
important.
This matter of enlarged loading conditions has been
thoroughly treated in Nibbering's 'Fatigue of Ship
Structures' [2]. As a matter of fact one objective of
the measurements on the 'Ossendrecht' was to verify
and quantify ideas put forward in Nibbering's paper.
As concerns slamming the effect of a real slam,
superimposed on the amount of loading already
present at that very instant, might be disastrous when
circumstances are favourable' (the presence of cracks,
low temperature), but what peak loadings by slams
may be expected? It is well known that the forward
bottom of a ship may experience serious damage by a
slam, but what is the influence of a slam on the stress
behaviour of parts situated at or near the position of
the largest bending moment (around L roughly)?
lt was hoped to obtain information concerning these
matters from the analysis of the measuring data
gathered on the bulkcarrier mv. 'Ossendrecht' while
crossing the North Atlantic. During the voyage a few
slams occurred, unfortunately the heavy ones
mani-festated themselves while measuring was not being
performed.
The other objective was the study of the behaviour
of local parts in way of L, due to wave action, and
the correlation of the local loading with the total
loading; this has become of great interest in recent
years, due to the growth of ship' sizes and the
re-duction in the number of bulkheads especially in
tankers.
The reduction of our data into values which could
be used for above mentioned objectives met with
interrogatives concerning the validity of commonly
applied statistical laws (Gauss, Rayleigh). It may be
known that this is not a new problem; from the
prac-tical point of view, this matter perhaps need not be
considered to weigh so heavily were it not that the
values of the derived parameters concerned constilute
the basic material for long-term predictions.
The gaussian law for ship's response to waves is
something which almost everybody assumes to be
valid, but maybe nobody is completely sure of. A
con-tribution to the attempts of settling this matter is given
in the present (first progress) report; the relativity of
statistical tests of significance has been taken into
con-sideration in the investigation.
What follows below will be reported in next progress
reports.
The rayleiglian
law for
crest-to-following
(pre-ceding)-trough heights is a subject about which the
uncertain feeling can be repeatedly read and heard;
since our results in general failed to furnish the
po-sitive proof of validity a rather extensive investigation
regarding this matter was made.
The distribution of maxima as analyzed by
Cart-wright and Longuet-Higgins [3] seems to be a more
stable foundation, hence our data have also been
subjected to the analysis concerned.
Much useful
information
canbe drawn from
spectral density analysis, whereas the results of such an
analysis also enables one to make comparisons of the
results with those of other methods of analysis
(par-ticularly the ones concerning gaussian and rayleighan
character), e.g. in figure 8 of the present paper mention
is made of almost equal root mean square values
derived from spectral analysis and by direct
compu-tation.
In [2] and [7] it is indicated that, in view of fatigue
aspects, the knowledge of the distribution of
crest-to-immediately preceding (following) trough heights is
not all-informative; greater variations may be found
which concerns the values of 'crest-to-some one of the
not necessarily immediatelypreceding
(following)trough'; the results of the analysis of this matter will
also be reported.
The study of the behaviour of local parts, and the
correlation of local loading with the total loading
have been mentioned above; conclusions will duly be
accounted for.
An attempt will be made to contribute to the matter
of the probabilities of the enlargements of loading
conditions as meant above.
2
Measurements
2.1
General information
Table
Igives the principal particulars of the m.v.
'Ossendrecht'. in August 1966 the ship was dry-docked
with the principal objective of being lengthened. One
hold (nr. 4 - figure 1) was added amidships.
Table 1. Principal particulars
The ship made the crossing of the North Atlantic in
September 1966, outward bound to Port Churchill
(Canada) in ballast, the home voyage to Rotterdam
loaded with grain.
The weather encountered had a most varying
char-acter, ranging from completely smooth seas to a
hurricane (Beaufort
li
to
12).Unfortunately no
devices were available for recording the characteristics
of the sea, the data about the weather and the
sea-conditions were furnished by the ship's officers. As the
'Ossendrecht' was a so-called selected ship' (ship with
special orders for gathering data about weather arid
sed) this belonged to the daily routine.
Moreover data were furnished by the ocean
weather-ships 'Juliett' (outward bound) and 'India' (eastward
bound). It was kindly granted by the ship-owners and
ship's master to sail close to these weatherships while,
in the meantime, strain measurements were made
beforehand the masters of the weatherships were
requested to make measurements regarding the weather
and sea conditions.
Unfortunately the ships, stationed at the positions
'Juliett' and 'India' at the time of our passing by,
could not meet our special request to make continuous
registrations (tape, diagrams or the like), only visually
obtained data could be given.
These data were sent to the Royal Dutch
Meteoro-logical institute (K.N.M.I.) for further reduction.
It must be noted that the 'Ossendrecht' did not make
the voyage for the sake of the measurements, but the
measuring data can be considered as by-products of
an ordinary trade voyage.
2.2
Instrumentation
Since the study of the longitudinal response of local
parts of the bottomstructure round about -L (hold
no. 4) was the main objective of the measurements
most strain gauges were fixed in longitudinal direction
on structural parts having a specific longitudinal
stif-fening function, such as centre and side keelsons and
bottom longitudinals. See figures 1 and 2.
For information about the longitudinal response
on deck level a starboard and a port deck-gauge had
been attached; additionally these gauges could furnish
information about horizontal bending.
One gauge on a transverse tanktop-stiffener gave
data about the response in transverse direction.
By means of longitudinal and transverse gauges
in-formation was also acquired about the behaviour of
a bottom-panel bordered by two
bottom-longitud-maIs and two floors. Hold no. 4 being a brand new
part had the advantage that attaching the gauges was
not too difficult; nevertheless it remained quite a job
to make perfect bonds in a damp, dark, and low
double bottom tank, so that 9 of the 38 gauges proofed
to be in disorder.
The strains were recorded principally by means of
a special strain indicator able to give punch-tape
con-secutive recordings of 200 points at most, at a maximum
speed of 24 points per second. In connection with the
expected general period of the strain variations and to
obtain a sufficient number of data per point per cycle,
the speed of 10 points per second was chosen; this
meant that (four) groups of 10 points per group were
formed, while the time interval between 2 successive
scans of one point amounted to 1.2 seconds.
During each measuring period of 20 minutes (this
being the appropriate time for sufficient scans and
during which a reasonable stationarity of the
sea-conditions may be expected) one certain group of 10
20 20 cl 50 26
FRA6E 50.0201RO II H.b2
gauge Location.
Fig. 1. Ship's profile and gauge location. Lbp1) after lengthening 175.65 n moulded breadth 20.60 m moulded depth 13.25 n summer draught 9.25m displacement 26,665tons100 deadweight 19,806tons1000
numbers 31, 33, 34, 35, 36:
the other gauges: placing of the gauges:
defective numbers 'extra' gauges: Centre girder side girder longitudinal frame 1 longitudinal frame 2 bottom panel transverse tanktopframe deck (gunwale)
points was scanned. Of the iO points of each group, 2
points were the same for al! groups (reference points).
Two groups could alternatively be connected to the
'200 points recorder' mentioned or to
a Siemens
Oscillofil, the latter giving analogue recordings. The
recording of one of the 4 groups on the 200-points
recorder was always accompanied by a simultaneous
recording of another group on the oscillofil
(simul-taneous recording of one group on both devices was
not possible). The main measuring programme
con-sisted of the recording of the variational loading by
the wave action, the recording of the condition while
sailing in smooth water (pseudo-zero conditon), the
recording of the rea! zero condition while lying still
(beginning and end of both crossings), and the
proce-Fig. 2. Location of strain gauges
I, 2, 3, 4, 5, ( extra: *1*, *2*, *5*
7, 8, 9, 10, Ii, 12
13, 14, 15, 16, 17, 18, 19, 20 21, 22, 23, 24, 25, 26, 27, 28 29, 30, 31, 32, 33 extra: *29* 34, 35, 36 37, 38 extra: *37* in transverse direction in longitudinal directionon or very close to longitudinal or transverse stiffening members, so that as much as possible only either longitudinal or transverse response be reproduced (this is not relevant to the gauges of the
bottom-panel group)
2, 5, 6, 9, 10, 20, 30, 35, 36
these gauges have, during the outward-bound voyage, been used for experiments other than the measurements under discussion; during the home voyage they have been connected so as to furnish
strain-information as is done by the 'ordinary' gauges
dure for calibration (ship stationary in still water) to
obtain strain-moment conversions.
A strict periodical measuring routine (for example
every 4 hours) was not considered practicable for our
objectives, nor was it really feasible because of the
limited amount of punch-tape and sensitive paper and
of the rather great sensitivity for wear of the punching
device when constantly used at the rather high speed
chosen.
One of the considerations leading to the decision to
record the strains digitally was that the punch-tape
data could be directly processed by the computer of
the Delft University of Technology; in the case of
analogue recordings readings must first be done, be
it by eye, by an electronic digital data reader or by a
special analogue computer like e.g. the AD4-IBM 1800.
lt will be clear that our punch-tape data represent
ordinate values of the strain-response at equal time
intervals.
3 Data reduction
3.1
Basic theoretical considerations
As will be outlined in the following the basic
hypo-theses of the statistical analysis of waves and response to waves determined a certain sequence in the process
of the reduction of the data. Firstly, the character of
the distribution of ordinate-values of waves and
re-sponse to waves ought to be gaussian (normal); this is the basic hypothesis for non-extreme, stationary con-ditions.
The first thing having been examined therefore was the character of the distribution of ordinate-values. The
verification of the validity of this hypothesis may be
done by comparing the data observed or the
distri-bution of the data observed with the theoretically
expected ones by means of so-called statistical tests of significance, such as for example the x2-test. Another statistical test applied by us is the cumulative distribu-tional test.The reader who is not acquainted with, yet interested in statistical tests of significance is requested to consult
such handbooks as e.g. Cramér's Mathematical Methods of Statistics', since it is not really feasible to
give a short yet sufficiently informative account of
these tests in this report.
In cases of obvious deviation from the gaussian
hypothesis the reason could be of technical origin i.e.
disorder of the concerning part of the measuring device,
or it had to be sought in the fact that, under the
cir-cumstances concerned, the response had been confused
by the frequent occurrence of disturbing factors (such as unsteady seaconditions, vibrations, slamming).
The data which satisfied the first condition of being
normally distributed could reliably be reduced to
response spectra. The direct computation of the
re-sponse spectra, following the autocovariance method, was possible since the data were available as discrete values at equal time intervals.
As was done by St. Denis and Pierson [4] the
spectrum-definition for which the spectrum-area R isequal to 2 times the variance
2 of the distribution of
ordinates, was used: in another definition the
spectrum-area is designated as m0, so that rn0 a2.
The property R = 2a2 was one of the means to
verify the correctness of our computations.Another important characteristic value of spectra
is the spectrum-width a as defined in [3]; this
para-meter furnishes information about the character of the
distribution of maxima and minima. With due caution a can also be taken as a measure for the character of the distribution of peak-to-trough heights.
Before having reduced our measuring data into
distributions
of maxima and minima (respectively
heights) we therefore had our indications regarding
the character to be expected.
As is noted in the introduction a rather extensive
investigation concerning the subject of the distribution
of heights was considered necessary.
The above-mentioned processes of data reduction have the character of an evaluation of basic statistical principles as applied to strain-response to waves. The further reduction of the data were aimed at obtaining information about more specific subjects such as the study of the behaviour of local parts (see the
specifica-tion in the introducspecifica-tion).
3.2
The punch-tape and the oscillofil recordings
The digital punch tape recordings enabled the direct
reduction of the data into distributions of ordinates
and into spectral densities of amplitudes.
The direct punch-tape recording, however, has also its drawbacks in that only the recorded, discrete data about the phenomenon concerned are exactly known values; the values between two successive scans, in fact, are unknown, although the time interval (1.2 sec.) was small enough to expect no (excessive)
disconti-nuities between 2 successive values. Compared with the
period of the wave-induced response (8 to 10 seconds) the time interval mentioned was so small that 'aliasing'
(as e.g. in fig. 3) could not occur. Additionnally, a
check was possible of the data of a measuring point
connected to the 200-points recorder by comparison
with the oscillofil-data of another point which was
measured at the same time and of which an identical behaviour could reasonably be expected.
The analysis of the oscillograms proved to be a
delicate matter in that the entangling of the (eight)
lines representing the time records of the measuring
points in question made it very difficult, generally,
to sift out the particular record belonging to a chosen point, (the application of e.g. a tape-recorder enabling
Fig. 3. Example of 'aliasing' of a high frequency signal into a
separate hind-recordings of the behaviour of any
measuring point would have been much more effective).
Nevertheless it proved to be worth while to take
pains to analyse several of the oscillograms, in cases
when the discrete punch tape data could not be of
direct help to clear things up.
lt must be noted that, in the meantime,
measure-ments aboard other ships have been done applying
an Ampex tape-recorder.
3.3
Computer processing
The reduction of the digital measuring-data would
have been an impossible task without the help of a
computer; use was made of the computer of the Delft
University of Technology TR4 which at the moment
has been replaced by the more up-to-date IBM 360/65.
It goes without saying that several programs had to
be composed, tested, rewritten etc. before the desired
information was available.
The replacement of the TR4 by the IBM 360/65
proved to retard the progress of the data reduction
considerably in that e.g. several programs had to be
rewritten, tested and so forth.
The programs to compute the normal distributions
and the response-spectra have been indirectly
men-tioned above; other ones were made to furnish the
distributions of crest-to-trough variations (Rayleigh)
and
of amplitude
variations
(Cartwright/Longuet
Higgins) etc., while minor programs were needed as
integrating parts of the principal programs to furnish
more information (e.g.
the program for the
x2-confidence test).
.3.4
General remark
The possession of a great many measuring data
regarding so many measuring points as in our case,
obtained under several weather conditions, certainly
is of much value, but on the other side it was our
experience that in several cases comparisons of the
results led to uncommon findings which necessitated
to further analysis; an important disadvantage of
measurements with only one or two measuring points
is that uncommon findings are likely to be rejected as
not usable.
4 Analysis
4.1
Introduction
One of the important problems of ship structural
design is to predict the extreme loading conditions and
their associate probabilities; this is once again stated
explicitly by the ISSC-1970-Committee on Design
Procedure.
In view of the paucity of data regarding extreme
conditions, so the Committee continues, it seems
pru-dent (for the time being) to base the assessment of
extreme loads on ship structures by extrapolation
from the plentiful, available statistics of moderate
conditions. For this, the Committee considers the
method as outlined by ISSC 1964-Committee on
Environ mental Conditions still useful.
This method assumes as fundaments both the
gaussian property for ordinate distributions as well as
the rayleighan property for crest-to-trough height
distributions for short-term conditions.
From the study of several papers it has, however,
become quite clear to us, that particularly regarding
the validity of the rayleighan law for crest-to-trough
height distributions unanimous appreciation is
stilllacking.
The reliability of the short-term parameter values of
the distributions concerned therefore is still
question-able, and so are long term predictions which are
extrapolated from such short term parameter values.
Therefore, although it has not originally been the
objective of our measurements it was considered
meaningful to examine the fundaments of the usually
applied analysis of bending moment response to waves;
in other words an answer is sought to the question:
"What is the value of s/icrt-term recordings of response
to waves in view of the analysis following existing
statictical concepts?"
Secondly this can lead to an evaluation of the above
method of the prediction of extreme load values by an
extrapolation from moderate conditions.
In the third place it is hoped that the analysis of our
measurements, especially those made during the rather
extreme conditions (Beaufort Il-12) which we also
encountered, may contribute
to
a more
straight-forward assessment of extreme load prediction.
Firstly, therefore, the strain records were checked
con-cerning their gaussian character.
4.2
The Gaussian character
4.2.1 Theory
St. Denis and Pierson [4] state that "a description of
the wave state realistic and readily handled in the
problems to which it is applied no matter how great
the complexity of the sea is found in the form of the
energy integral for the gaussian case:
r(t) =
cos[wt+e(w)]J[r(w)]2dw
where {r(w)]2 represents the power spectral density
(spectrum)". Thus a very important property of this
integral is that ordinates of the function r(t) are
dis-tributed according to the gaussian law.
1f sea waves may be represented by the above
mathematical model then the same may be assumed
regarding the ship's responses to waves.
The mathematical model incorporates a part for
the spectral density and postulates the gaussian
prop-erty. As is evidenced by the results of the
data-reduc-tion, the link between the two is that a correct (i.e.
gaussian) distribution of ordinates goes with a regular
form of the spectral density curve; this property will
be made use of later.
In chapter 3 it was already mentioned that the
verification of the gaussian hypothesis can be done by
statistical tests of significance. It is well known that
the outcome of such tests also has the nature of
probability; the outcome is much less sharply defined
than
e.g.time-measurements
with
astopwatch.
Approving of or rejecting a hypothesis on this basis
therefore remains a delicate matter.
Any test works with so-called level(s) of significance
and so does the chi-square test. The question is what
can be called a reasonable level? Bennet [5] e.g. works
on a 0.1 % level for the peak-to-trough histograms as
tested concerning the Rayleighan character. This is a
very low level indeed.
A very low level of significance will be chosen when
some hypothesis 'most likely is true', meaning that a
very small risk is taken of falsely rejecting the
hypo-thesis concerned.
If
the truth of the hypothesis is still questionable it
will be risky to take a very low level of significance.
Of course, the case of a result which distinguishes
significantly from the level of significance of say 0.l%
is no problem in that a percentage of e.g. 65% lies far
from the 0.l%, on the safe side, but what about an
outcome of 2% for instance?
Compared to a 0.1% level the experiment concerned
will be judged as consistent with the hypothesis, but
weighed against a 5% level (which is a commonly used
value) a rejection should be made.
To avoid misinterpretation by the reader who is not
familiar with the X2-test, of the percentages used in
this context, it is explained that x% means that there
is a probability of x% of obtaining a deviation from
expected results at least as great as that actually
observed. In this respect the f-value leading to 2%
may be called relatively more certain than the one
resulting in 65%.
In addition to the f-test we also applied the
cumula-tive distributional test, but, in more cases than one, this
only contributed to confusion, because consistency
could be concluded by one test and less- or
non-consistency by the other (see table 3).
We might of course act as conforms to Jasper's
statement in [6]:
"A distribution may be of practical significance
even though the statistical tests indicate a
signifi-cant deviation between it and the data measured.
In many cases a visual inspection
of
the scatter is
sufficient to indicate that the distribution assumed
is an acceptable representation of the actual
distribution".
Decisions on this basis however, are very much subject
to individual interpretations of what is acceptable or
not, and it certainly will not appeal to theoreticians.
Non-linearity of the sea surface in the high frequency
components may cause departures
of
actual wave
records from the gaussian law. However, a ship may be
expected to function as a smoothening filter regarding
its responses to the waves encountered in that possible
capricious features of those waves may just pass by
without the ship responding to them. Consequently
the responses are less irregular than the waves and the
determination of their gaussian character may be
expected to give fewer problems; a condition like the
one represented in figure 4 answers this expectation.
ÀA
t* ,
'* 41t - t1j
'ï'\
Fig. 4. Oscillogram showing quite regular response lines.
A
ri
YJflaP j5.N
Fig. 5. Oscillogram showing irregular response patterns.
However, many of our oscillograms are of the irregular
type, figures 5 and 6, containing a high-frequency
vibration.
lt will be observed that the high frequency vibration
really disturbs the pattern of the main phenomenon;
in many cases hf. vibration coincides with (may be
is the cause of) the flattenings of crests and troughs
(figures 5 and 6). Probably there is a relation between
the two; the main response seems to be counteracted
under certain vibrational conditions.
It is obvious that the superposition of a h.f. vibration
like the one discussed here will only be detected on
analogue registrations (oscillograms, magnetic tape);
discrete recordings (on punch tape or by means of
counters) indicate
momentaryvalues only of principal
response plus additional responses
(h.f.vibration,
slamming etc.) with no possibility to separate the two.
In order to study the influence on the values of
statis-tical parameters of the additional responses meant
above and of the flattenings we therefore were forced
to the laborious analysis of the oscillograms concerned.
4.2.2
Analysis of the oscillograms
Discrete hand-readings at equal time-intervals have
been made of the ordinates of the oscillogram curves
as they are' and of the curves smoothened as regards
the h.f. vibrations' (Fig. 7). These readings were put on
punch tape and the further reduction was performed
through the computer like for those measuring-points
for which only punch tape recordings had been made.
This also enabled the evaluation of the results of the
reduction of the
latter mentioned recordings by
comparing them with the results of the analysis of
oscillograms recorded simultaneously.
The time-interval for the hand-readings was
delib-erately chosen quite small (approx. 0.48 sec. against
1.2 sec. for the direct punch-tape recordings) in order
to examine the effect of very small intervals. The choice
of every second reading, of course, meant a time
interval of 0.96 sec., and by taking every third reading
a still coarser reduction was obtained.
A random reading of ordinates should, under valid
conditions, also result in a normal distribution of the
readings; this was also examined for two cases.
Fig. 7. Example of 'smoothening'.
Table 2 (Appendix) gives the results of meant
anal-ysis of oscillograms; only oscillograms of
measure-ments during the home voyage were chosen, because
no extreme conditions were then encountered like
those when outward bound.
A sequential number of measuring runs (43/1
through 43/5, see table 2) of 15 minutes each was
chosen to examine whether any alteration of
sea-conditions would be reflected in substantial changes in
statistical properties of the strain response.
The choice of every second (respectively third)
reading furnishes two (resp. three) groups of readings
which, for the ideal cases, must be statistically
equiva-lent.Nevertheless
remarkable differences
can be
noticed between the outcome of the x2-tests applied
to such groups. For example (see table 2) No. 39/1:
65% is found against 0.9% for the other group. No.
43/2: 0.3% against 29%.
These differences may be ascribed to, what may be
called accidental group formation of a limited (short
term!) number of ordinate values which in the one
case gives occasion to a better gaussian distribution
than in the other.
In principle this fact emphasizes the relativity of
conclusions concerning short-term records. However,
it can be considered fortunate that, in view of the
conclusion stated below, viz. 'general validity of the
gaussian property for thort term records', the
niagni-tudes of the parameters (root mean square deviation
and mean) are quite unsensitive to 'accidental grouping'
as meant above, nor are they very much dependent on
the question whether the records are smoothened or
not (see the figures in table 2).
Another conclusion that can be drawn from table 2
is that the nature of strain response seems to be such
that smoothening of a record need not necessarily
mean an improvement of the character of the
distribu-tion of ordinates regarding the gaussian property. lt
was verified that this was not a matter of having
inter-changed the figures concerning smoothened and
not-smoothened records.
Another facet of the oscillograms, viz, the flattened
parts, have already been mentioned.
lt will be obvious that any long flattened part may
add to an excessive amount of ordinates of
(approxi-mately) equal magnitude, especially when the time
in-terval chosen is small. This contributes to too big
classes in the histograms impairing the gaussian
char-acter.
The influence of the flattenings on the character of
the distribution or ordinates will most likely be smaller
in the case of longer records (under stationary
con-ditions, if possible) and when the readings are done
at random time intervals.
As a general conclusion, based on the analysis of the
oscillograms mentioned in table 2, it can be stated
that validity of the gaussian property can be trustfully
assumed for non-extreme conditions with a good
reliability of the parameter-values concerned.
For analysis of records an interval reading of I to
14 seconds is recommended.
4.2.3
Analysis of the punch-tape data
The analysis of the punch tape (digital) records
regard-ing the gaussian character of the distribution of
ordi-nate values for non-extreme conditions furnishes what
follows below.
Table 3 (Appendix) shows results of the analysis of
measurements (home voyage only, because of the
reasons already mentioned above).
The punch tape recording of ordinate values made
possible the direct reduction into the distribution of
values in appropriate classes (histograms), which
after-wards were tested concerning their gaussian character.
A disadvantage of punch tape is that it is not possible
to see, on the spot, whether the tape contains
informa-tion which can be assumed correct or, by any reason
or other, is questionable this will be visible no sooner
than when the tape information is translated into
figures or diagrams.
The agreement between observed and expected
distributions of our record ordinates ranges from
correct via satisfactory and questionable to not correct.
The tests for these judgements were the x2-test,
already mentioned, the cumulative distributional test,
2m 160 120 80 RON 135-PCASIPLNG P13311 3 3 Class 360 5 ¿RS lV31l NS 23-st13s ¿807 23 7m R. ¿858 rLihON S5)J-t
while also visual inspection as recommended by Jasper
was performed.
The X2-test is well known; for the cumulative
distri-butional test the percentages of data which exceed the
99% and the 95% confidence limits was taken as a
measure for the judgements meant above.
It is clear that these two statistical tests will only
give unanimous approval for the outstanding correct
or the outstanding not-correct cases. Cases which by
one test were correct and by the other questionable
(or not-correct) have also been found; such a
circum-stance is a rather confusing one and therefore the
visual examination of the character of the histograms
of the distribution of ordinates was also performed as
an additional test.
An attempt to a further reinforcement of the basis
of our judgements was made by the reasoning and
examination following below.
It
is well known that the spectrum of a process
reflects its statistical properties in a quantitative as well
as in a qualitative way. The already mentioned
prop-erty that the spectrum area is equal to twice the variance
of the ordinates (in the notation of St. Denis and
Pierson) is an example. A qualitative feature is that a
correct spectrum-form goes with a correct gaussian
form of the distribution of ordinates and vica versa;
if the form of the distribution mentioned deviates
significantly from the gaussian form then the spectrum
which can be calculated from the same ordinate-data
will not be of a correct form either.
The (visual) examination of the form of the spectral
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Fig. 8. Examples of distribution of ordinates and corresponding spectra of amplitudes.
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density curve therefore was taken as an additional
'test of significance'.
Of course the results of the two visual tests can only
be expressed
inthe verbal qualifications such as
'correct' etc., while for the two statistical
tests the
percentages concerned are also given.
It will be noticed that table 3 does not contain cases
which, by all four tests, may indicate that the gaussian
property does not hold for those cases. As a matter of
fact there are several of such cases, but they are not
relevant to the analysis; they woúld be, when the
non-gaussian character were shown for all measuring runs,
and when this were not caused by instrumental errors
or extraordinary circumstances such as slamming (e.g.
run 138, table 3). lt is also obvious that all the data of
a measuring run under extraordinary conditions are
irrelevant to the analysis.
Table 3 contains relevant cases no matter what the
location of the measuring points in question; the
greater part of the cases concerns the response in
longitudinal direction, while measuring points 31 and
34 were gauges fixed transversely.
Figure 8 is given as an example of histograms and
of corresponding theoretical gaussian curves and
spectra.
The case of measuring point 3, run 135 (Fig. 8 and
table 3) is an example of the f-test rejecting this case
while, cumulatively, not one of the data exceeds the
95% - or even the 99% confidence limits.
The measure for the visual test of the form of the
histograms was the resemblance to the gaussian
bell-form, while a spectrum was considered correct when
it had or approached the well-known skew
energy-distribution form.
It will further be observed that in a few cases a
correct spectrum did not go with a correct gaussian
distribution of ordinates or vice versa; for example,
small direct-current drift (d.c.
drift) in some cases
appeared not to affect the gaussian character, but it
did show up in the spectral density curves. The great
majority of the cases, however, answers the expectation
that, generally, a correct spectrum and a correct
gaussian distribution go together.
Protruding from table 3 are the cases which are
qualified 'correct' by all four tests; if we denote these
cases as 'outstanding cases' and the cases which
obtained a qualification 'correct' by 3 tests as 'good
cases', the following comes out:
outstanding
112 casesgood
57 cases
rejected
34 cases
total number 203 cases
In combination with the results of the analysis of
oscillograms mentioned earlier it seems justified to draw
the conclusion that, under non-extreme conditions, the
gaussian law is valid for strain-response to waves, in
longitudinal direction. An indication exists (see table 3,
measuring point 31) that this validity may also regard
the athwartship direction.
lt was already mentioned under the heading 'General
Information' that 4 groups had to be formed of 10
measuring points each, of which 2 points (numbers
3 and 4) were the same for all four groups (reference
points); each measuring run could only be performed
while measuring one of the four groups.
From table 3 it will be seen that several runs were
performed consecutively, most of them in the sequence
group 4-3-2-1-l-2-3-4.
The underlying considerations were
group I could eventually be considered as having
been measured for two times the measuring period
of one run;
- small or large changes in
characteristics (e.g. the
r.m.s. values) could be detected from suitable
com-parisons: run no. i (first series) to run no. i (second
series) etc.
lt can be taken as certain that the ship's speed and
course were kept constant during the measuring runs,
except regarding the runs 151-152-153-154; these runs
were consecutive runs of 15 minutes each, concerning
measuring group 1, constant ship's speed, but
delibera-tely varied ship's course (see Fig. 9).
COURSE 74° RUN No 150 COURSE 55° RUN No 151 COURSE 100° RUN No 152 COURSE 145° RUN No 153 SS COURSO 92° RUN No 15h
Fig. 9. Course marloevres with measuring-runs of 15 minutes
each. Sii Lt) 30 20 10 O 10 groorhond L11 V ,, w$juLi&
Lr
jrLofld,°br)fl -_454.2.4
Extreme conditions
lt might also interest the reader to be informed about
the results of the reduction of the data concerning the
measurements under hurricane-conditions.
These conditions were encountered on September 4
to 5, 1966, westward bound, at the position 200 West,
53° North (close to the location of weathership
Juliett'); ship's speed 0 knots; mean wave
direc-tion 20 to port: mean wave height 15 to 20 metres;
Beaufort lito 12; ship in ballast.
The results of the reduction of the punch-tape data
concerning the strain response under extreme
condi-tions are gathered in table 4.
The table contains the results of two series of
con-secutive measurements of 5 minutes each.
A measuring period of 5 minutes was chosen
be-cause, under extreme conditions, stationarity of
con-ditions was assumed during 5 minutes.
Two series of 5 minutes measurements are mentioned
in table 4 (Appendix). In this table, like in table 3,
only the relevant cases are given; for this reason the
data of reference point 3 are missing in the table for
series no. 2.
Generally speaking the variation in r.m.s. values of,
for example, the reference points is smaller for series
no. 2 than for series no. 1; this might indicate that the
conditions for series no.
Iwere less stable than for
series no. 2. But it is quite remarkable that, in any case
during the 5 minutes concerned, the response under
the extreme conditions of both series no. 1 and series
no. 2 turned out to be gaussian.
From table 4 follows:
outstanding
73 cases
good
23 cases
rejected
14 casestotal
110 casesIn addition it can be stated that the oscillograms of
these measurements, by their regular character, also
point to the validity of the gaussian law. As mentioned
earlier one heavy slam occurred while no measuring
was being performed. The few light slams occurring
during the measuring periods did not prove to really
distort the gaussian character.
The combination of the data concerning measuring
point 4 from the runs numbers 57, 58, 59, 60 was made,
furnishing:
a r.m.s. value of 41.7 micro-strains,
a correct qualification of the gaussian character by the
cumulative distributional test and by the visual
exam-inations, but a questionable one by the x2-test (P2
=
0.2%).This may be considered as an indication that even
under the extrem.e conditions concerned the strain
response might be gaussian for a longer period than
5 minutes.
The measurements therefore show that, under extreme
conditions,
a ship can be in the circumstances (i.e. the
combina-tion of encountered condicombina-tions and the skill and
feeling of the captain) that the probability of
exceeding short term response values is governed
by the gaussian law;
higher loading (such as by a heavy slam) has a much
lower probability level.
If further evidence can be gained concerning this
matter then this will be of help to find the magnitudes
and probabilities of longer term extremes: the
determ-ination of both the magnitude as well as the probability
of long term extremes is indispensable in view of the,
for ship structural design, modern concept of
permis-sible stresses (see Nibbering [7]).
4.2.5
General conclusion
As the general conclusion it may be stated that the
gaussian character of strain-response to waves can
generally be assumed.
In the foregoing analysis the fact that sagging
mo-ments may be larger than hogging momo-ments is not
taken into consideration. It is known that, for this
reason, a skew distribution is proposed by
Norden-strøm [8].
The difficulty concerning this matter is that it is not
possible to indicate exactly the zero line of an arbitrary
recording; the fact, however, remains that the
fore-going investigation show that most of our recordings,
as they are, prove to be of a gaussian character.
Acknowledgements
The measurements were prepared and performed by
personnel of the Ship Structures Laboratory of the
Delft University of Technology, under the sponsorship
of the Netherlands Ship Research Centre TNO.
The author sincerely acknowledges the help of all
involved. Mr. J. Verschoor and Mr. D. Buitenhek (of
the Shipbuilding Laboratory of the University of
Technology) may be mentioned for the able
prepara-tion and execuprepara-tion of the measurements; Mr. W. B.
Tinbergen and Mr. B. P. Maat for the valuable
assis-tance concerning the data reduction.
We are indebted to the owners of the ship, Messrs.
Ph. van Ommeren N.Y., not only for allowing to make
the measurements, but also for the full cooperation
concerning all that rendered the enterprise successful;
this includes of course, the master and the crew of
the ship, in function on the 'Ossendrecht' at the time of
the measurements.
Thanks is also due to the masters of the ocean
weather-ships Juliett and India and to the Royal
Dutch Meteorological Institute (K.N.M.1.) for the
wave observation data and their data reduction
res-pectively.References
1. YUILLE, J. M., Longitudinal strength of ships. Trans. R.I.N.
A., Vol. 105, 1963.
NIBBERING, J. J. W., Fatigue of ship structures. Neth. Ship
Res. Centre TNO, Report36S, also in mt. Shipb. Progress,
Oct. 1963.
CARTWRIGHT, D.
E. and M. S.
LONGUET-IIIGGINS, Thestatistical distribution of the maxima of a random function. Proc. Roy. Soc., London, A237, 1956.
ST. DENtS,M. and W. J. PIERSON,On the motions of ships in confused seas. Trans. S.N.A.M.E. 1953.
BENNET,R., Stress and motion measurements on ships at sea.
The Swedish Shipbuilding Research Foundation. Report
no. 13, 1958.
JASPER,N., Statistical distribution patterns of ocean waves
and of wave-induced ship stresses and motions, with engi-neering applications. Trans. S.N.A.M.E. 1956.
NIBBERING, J. J. W.,Permissible stresses and their limitations. Ship Structure Committee SSC-206, 1970.
NORDENSTRÖM, N.,Contribution to the Report of Committee
Appendix
General
The tables mention r.m.s.
strain response ordinate
values in microstrains the u nit strain values a, of course,
are
loo times smaller, and multiplication with
the
modulus of elasticity of steel E gives the Ea-values
which, at the locations for which uniaxial stress can be
assumed, also represent the stress-values concerned.
Most of the measuring during the home voyage, as
reported in the tables, was performed in the evenings
and in the nights, since by coincidence these proved
to be the periods of rather wavy seas while by day
mostly smooth seas were encountered. This had the
unfortunate consequence that no reliable wave
obser-vations could be done.
Table 2
This table concerns the oscillograms.
The number of readings is stated in the third column,
beginning with the total number of readings e.g. 2892
for run no. 24/1; then follow two groups of 1446
readings each, that is, by taking every other reading
two groups of 1446 readings were obtained.
For run no. 37/1 even 3 groups were formed by
taking every third reading.
The digital (punch tape) recording number
corres-ponding to the oscillogram mentioned is also stated,
e.g. oscillogram no. 24/1 corresponds to digital
ing no. 122 (see table 3). In this case the digital
record-ing no. 122 proved not to be correct, while the
corres-ponding oscillogram did not show irregularities. From
this the conclusion could be drawn that the digital data
were not reliable on account of the fact that the
re-cording apparatus concerned did not function as it
should, and not because of the occurrence of very
irregular response conditions during that particular
measuring run.
TABLES 2,
3 AND 4 WITH ACCOMPANYING NOTES
Table3and4
These tables concern the punch-tape recordings.
The extra gauges are indicated by the additions of
the word 'extra' and the asterisks.
Under sub-chapter 4.2.3 it was already stated why
severalruns were performed in a certain
group-sequence viz, numbers 4-3-2-l-l-2-3-4; this concerns
the runs numbers 118 through 124 and numbers 138
through 145. lt is recalled that measuring points
num-ber 3 and numnum-ber 4 formed part of every measuring
group so that the variation in r.m.s. values concerned
may be regarded as indications of the variation in the
conditions encountered.
It is repeated here that runs numbers 151 through
154 were consecutively made with group I, each run
under another ship's course, but equal ship's speed
(see fig. 9), while during the measuring-time of the
above-mentioned sequence 118-124 and 138-145 the
ship's speed and heading were kept as constant as
possible.Under sub-chapter 4.2.3 it was already noted that
only the relevant cases are mentioned in table 3 (and
table 4); this is the reason why not all the measuring
points belonging to one measuring group are always
mentioned.
Groups of strain gauges for the punch-tape recording
(home voyage)
group no. gauge no.
2 3 4 3, 3, 3, 3, 4, 4, 4, 4, 1, 13, 7, 21, 29, *29*, extre 14, 15, 8, *37* extra 22, 23, 31, 34, 32, 33, *5* Cxra 16, 17, 18, 19, *1* extra dummy, 11, 12, 37, 24, 25, 26, 27, 28 38
Table 2. Gaussian character (oscillograms) run no. duration measuring point no. number of readings (equal time intervals) 24/1 20 min.
corresponds to digital record
37/1 28
20 min.
corresponds to digital record
39/1 37/extra 20 min. corresponds to digital 40/1 28 20 min. corresponds to digital 43/1 28 15 min. corresponds to digital 43/2 28 15 min. corresponds to digital 43/3 28 15 min. see fig. 6
no. 139 (see table 3)
2524 32.5 1262 32.7 1262 32.4 841 32.6 841 32.4 841 32.6 842 (random) 32.8
no. 140 (see table 3)
2516 37.6
Ç 1258 37.6
1 1258 37.8
record no. 143 (see table 3)
2570 31.7
1 1285 31.7
1285 31.8
record no. 144 (see table 3)
1937 28.0
f
968 28.0968 28.1
record no. 146 (see table 3)
1937 25.7
1 968 25.8
968 25.8
record no. 147 (see table 3)
1926 29.2 963 28.8 963 28.9 642 28.8 642 28.9 642 28.8 642 (random) 29.0
I
{I
{
corresponds to digital record no. 148 (see table 3)
43/4 37/extra 1954 35.1
15 min
f
977 34.8977 34.7
corresponds to digital record no. 149 (see table 3)
43/5 38 1944 48.6
15 min. 972 48.5
972 48.7
corresponds to digital record no. 150 (see table 3)
44/1 28 1912 29.3
15 min. 956 29.3
\
956 29.2corresponds to digital record no. 152 (see table 3)
not-smoothened R.M.S. mean
(IL-strain) (v-strain)
*) The readings were made from an arbitrarily chosen base; this resulted in a certain value im The mean value of the case 'all readings - not smoothened' is expressed as m.
For the other cases the deviation with respect to m is stated in percentages of m. Ordinate = reading minus m..
smoothened R.M.S. mean (v-strain) (ri-strain) P72 m*) 45% 46.8 +0.05% 39% O.0l° 59% 46.8 +0.05% 33% 0.0I0 27% 46.8 +0.05% 28% m 0.9% 38.3 +0.2% 31% -0.01% 31% 38.3 +0.1% 72% +0.0l% 23% 38.2 +0.1% 63% m 1% 34.2 +0.01% <0.1% +0% 15% 34.3 +0.01% 5% +0% 44% 34.3 +0.01% <0.1% m 0.2% 31.8
-0.1%
<0.1% +0% 8% 31.8-0.1%
0.9% +0% 17% 31.8-0.1%
3% -0.03% 44% 32.6-0.1%
8% +0% 14% 31,9-0.1%
8% +0.02% 37% 31.7-0.1%
21%-0.1%
38% m 29% 37.3 +0.2% 0.5%-0.1%
17% 37.4 +0.3% 65%-0.4%
46% 37.2 +0.2% 0.9% m 0.1% 31.3 +0.1% 1%-0.1%
40% 31.4 +0.1% 0.6%-0.1%
9% 31.3 +0.1% 9.3% m 2% 27.8 +0.1% 2% +0.04% 20% 27.8 +0.1% 11% + 0.04% 5% 27.8 +0.2% 9% m 0.4% 25.5 +0.1% 0.2% -0.04% 6% 25.4 +0.1% 0.3% -0.04% 38% 25.4 +0.1% 29% m 10% 28.4 +0.05% 9%-0.1%
63% 28.4 +0.1% 5%-0.2%
27% 28.4 +0.04% 12%-0.2%
26% 28.3 +0.03% 10%-0.1%
20% 28.5 +0.06% 32%-0.1%
27% 28.4 +0.1% 44%-0.2%
83% m 8% 34.7 +0.03% 5% ±0.03% 21% 35.3 --0.02% 27% +0.1% 7% 35.0 -! 0.02% 21% m 0.8% 48.4 --0.2% 20% +0% 44% 48.4 +0.2% 5% +0% 36% 48.5 -0.1% 64% m 0.2% 29.2 +0.2% +0% 12% 29.3 +0.2% 2.4% +0.01% 0.1% 29.2 +0.1% 0.3% 36/2 20 min. 28 1 2534 1267 1267 34.9 34.8 34.9 38 1 2892 1446 1446 47.1 47.2 47.0corresponds to digital record no. 122 (see table 3)
31/1 38 2550 38.5
20 min.
f
1275 38.61275 38.5
Table 3. Punch-tape (digital) records
Gaussian distribution spectrum cumulative
distributional test
run no. (c.d.-test) Z2-test
number of ordinates measuring R. M .S. visual visual
time point (p-strain) (*) °Á
P()°
examination examinationgroup 3 118 3 12.6 0/0 C 77 C C S 250 4 16.3 0/0 C 64 C S C 30-9-1966 7 10.2 0/0 C 24 C S C GMT 21.28-21.33 8 17.5 0/0 C 43 C S Q 12 13.0 0/0 C 33 C C Q 37 27.1 12/O S 42 C S C *37* 29.0 11/11 Q 15 C S S 38 37.1 0/0 C 43 C C S group 2 119 3 10.4 7/0 C 66 C C C 250 4 14.1 0/0 C 18 C C C 30-9-1966 13 27.1 6/6 S 42 C C C GMT2I.42-21.47 14 16.2 0/0 C 26 C C C 15 17.9 9/0 C 35 C C C 17 18.4 O/O C <0.1
notC
C C 18 14.8 9/9 5 3 S C C 19 30.6 6/0 C 9 C Q not C group 1 120 3 14.0 0/0 C 65 C C C 250 4 18.0 0/0 C 34 C C C 30-9-1 966 1 12.4 OJO C 65 C C C GMT 22.28-22.33 29 35.6 0/0 C 92 C C C 31 22.8 8/0 C 78 C C C 32 16.5 9/9 Q 17 C S C 33 20.1 17/8 Q 7 C C C group 1 121 3 13.5 0/0 C 77 C C C 1000 4 17.4 14/0 5 II C C C 30-9-1966 29 34.3 5/0 C 51 C C C GMT 22.53-23.13 31 22.5 0/0 C 25 C C C 32 17.0 29/29notC
14 C C C 33 21.6 20/13notC
0.5 Q C C122 digital recording: not correct
1000
30-9-1966 oscillogram of measuring point 38 (see table 2 no. 24/1):
GMT23.20-23.40 C C C C group 3 123 3 18.3 15/8 Q 53 C C C 1000 4 22.3 0/0 C 66 C C C 30-9-1966 7 16.0 0/0 C 28 C C S GMT 23.50-24.10 8 27.2 0/0 C 92 C C S 12 20.5 0/0 C 9 C C S 37 35.0 48/59 not C 11 C S C *37* 33.9 4/4 C 82 C C C group 4 124 3 18.3 0/0 C 22 C C C 1000 4 22.5 0/0 C 65 C C C 30-9-1966 22 36.0 O/O C 36 C C C GMT24.36-24.56 23 51.2 010 C 2 Q C C 24 38.3 0/0 C 5 5 C C 26 32.4 0/0 C 12 C C C 27 48.1 0/0 C 25 C C C group 4 125 3 14.0 0/0 C I Q Q C 250 4 17.4 0/0 C 18 C S C l-10-1966 21 53.3 36/28 not C 22 C S not C GMT 11.42-11.47 22 28.4 0/0 C 54 C C C 23 38.3 0/0 C 28 C C C 24 30.6 5/0 C 22 C S C 25 32.7 0/0 C 25 C S C 26 25.9 0/0 C 22 C C C 27 40.2 14/0 C 14 C C C
notes C = correct measuring points indicated by asterisks** are the extra' gauges
S = satisfactory
Table 3 (continued)
cumulative distributional test
run no. (c.d.test) X2-test
number of ordinates measuring R.M.S. visual visual
time point
(-strain)
(*) % P(y2) examination examinationgroup 4 126 21 45.2 7/0 C 18 C C C 960 22 26.8 0/0 C 22 C C C l-10-1966 23 36.6 33/22
notC
12 C C C GMT 12.23-1 2.43 26 24.8 6/0 C 0.9 Q C C 27 34.7 9/5 S 14 C C C 28 29.3 11/0 C 9 C C C group 3 127 7 11.2 0/0 C 34 C C C 990 11 21.2 6/0 C 24 C C C l-10-1966 12 14.1 8/0 C 5 S C C GMT 13.11-13.31 37 22.0 0/0 C 0.1 Q C C *37* 23.6 0/0 C 2 S C C 38 41.0 7/7 S 2 S C C group 2 128 4 15.4 8/0 C 26 C C C 1000 13 30.2 4/4 C 28 C C C 1-10-1966 14 18.3 7/7 S 69 C C C GMT 13.37-13.57 15 20.7 0/0 C 70 C C C 17 22.0 12/0 S 33 C C C 18 16.8 0/0 C 69 C C C *1* 10.8 0/0 C 43 C C C group 1 129 3 13.7 27/27 not C 56 C C C 1000 4 17.1 0/0 C 22 C C C l-lU-1966 1 12.5 8/8 Q 36 C C C GMT 14.05- *5* 18.5 0/0 C 5 C C C 14.25 29 31.6 23/23 not C 54 C C C 31 21.8 0/0 C 6 C C C 32 13.0 20/20notC
27 C C C 33 15.3 17/8 Q 2 Q C C group 1 130 3 14.6 0/0 C 92 C C C 1000 4 18.2 0/0 C 54 C C C I-10-1966 29 32.1 5/0 C 16 C C C GMTI6.20-16.40 31 22.! 0/0 C 66 C C C 32 12.6 22/0 Q 35 C C C 33 15.0 0/0 C 4 C C C *5* 19.9 8/0 C 0.8 Q C C group 2 131 3 13.0 4/0 C 8 C C C 1000 4 16.3 0/0 C 44 C C C l-10-1966 13 30.2 0/0 C 5! C C C GMT17.09-l7.29 14 18.7 0/0 C 17 C C C 15 22.0 13/0 C 6 C C C 17 21.8 0/0 C 32 C C C 18 17.6 17/8 S 2 S C C 19 29.0 29/13 not C 9 C C d.c. drift *1* 11.6 0/0 C 81 C C C group 3 132 3 13.1 0/0 C 12 C C C 1000 4 16.3 0/0 C 96 C C C 1-10-1966 7 10.8 5/0 C 34 C C C GMT 17.50-18.10 11 21.1 6/0 C 14 C C C 12 13.8 0/0 C 11 C C C 37 23.9 0/0 C 43 C C C *37* 25.2 0/0 C 19 C C C 38 39.3 20/13notC
34 C C Cflotes: C = correct measuring points indicated by asterisks** are the 'extra' gauges S = satisfactory
Q = questionable (*) number of exceedings of 95%/99% confidence limits in percentage of cumulative data
Table 3 (continued)
16.24 corresponds to oscillogram 36/2 (see table 2)
Gaussian distribution spectrum
cumulative
distributional test
run no. (c.d.test)
f-test
number of ordinates measuring R.M.S. visual visual
time point (v-strain) (*)% P(72)% examination examination
group4 133 3 11.8 6/0 C <0.1
notC
S C 1000 4 14.9 17/6 Q <0.1notC
S C i-10-1966 21 35.4 0/0 C 36 C C C GMT 18.40-19.00 22 21.3 4/0 C 4 C C C 23 28.4 6/6 S 52 C C C 24 22.5 8/8 S 24 C C C 25 25.2 7/7 S 29 C C C 26 20.0 12/0 C <0.1 not C S C 27 27.6 0/0 C 75 C C C 28 23.3 7/0 C 25 C C C group 1 134 3 17.8 4/0 C <0.1 not C C C 1000 29 36.3 9/5 S 14 C S C I-10-1966 31 27.2 6/0 C 0.9 Q C C GMT 19.12-19.32 32 13.1 0/0 C 3 S S C *5* 26.8 31/15notC
17 C C Q group 2 135 3 15.6 0/0 C <0.1notC
C C 1000 4 19.7 4/4 C <0.1notC
S C l-10-1966 13 35.5 0/0 C 44 C C C GMT 19.35-19.55 14 22.5 8/8 5 31 C C C 17 25.7 0/0 C 15 C C C 18 21.1 9/4 S <0.1notC
S C *1* 15.0 5/5 C 0.6 Q C d.c. drift group 3 136 3 16.6 4/0 C 37 C C C 1000 4 20.8 0/0 C 31 C C C l-10-1966 7 12.2 0/0 C 43 C C C GMT2O.l0-20.30 12 16.3 4/0 C 9 C C C 37 30.7 5/0 C 89 C C C *37* 32.1 0/0 C 52 C C C 38 45.5 7/7 C 4 C C C group 4 137 3 16.5 9/0 C 72 C C C 1000 4 20.7 0/0 C 54 C C C l-10-1966 21 44.7 0/0 C 9 C C C GMT 20.35-20.55 22 27.5 0/0 C 52 C C C 24 28.9 0/0 C 43 C C C 25 32.1 0/0 C 72 C C C 26 27.4 67/67 not C 8 C C C 27 34.4 0/0 C 61 C C C 28 29.7 0/0 C 62 C C C 1381000 disturbance by slamming (clearly visible on oscillogram) 2-10-1966 GMT 15.39-15.59 group 3 139 3 23.8 16/5 S 53 C C C 1000 11 34.4 0/0 C 8 C C C 2-10-1966 37 43.3 0/0 C 12 C C C GMT 16.04- *37* 46.2 0/0 C 6 C C C
flotes: C = correct measuring points indicated by asterisks** are the extra gauges
S = satisfactory
Table 3 (continued)
Gaussian distribution spectrum
run no. number of ordinates time group 2 140 1000 2-10-1966 GMT 16.34-16.54 group 1 141 1000 2-10-1966 GMT 17.05-17.25 group 1 142 1000 2-10-1966 GMT 17.28-17.48
group 2 143 digital recording: not correct
1000 oscillogram of measuring point 37-extra (see table 2 no. 39/1):
2-10-1966 C C C C
GMT 17.51-18.11
group 3 144 37 34.5 0/0 C 36 C C C
1000 oscillogram of measuring point 28 (see table 2 no. 40/1):
2-10-1966 C C C Q GMT 18.28-18.48 group 4 145 22 33.6 5/0 C 44 C C C 1000 27 43.3 7/0 C 96 C C C 2-10-1966 28 38.3 0/0 C 78 C C C GMT 18.52-19.12 group 1 146 3 19.2 17/8 s 2 Q C C 750 4 23.9 17/13 Q 33 C C C 4-10-1966 29 40.1 7/7 C 31 C C C GMTOO.42-00.57 33 16.3 9/0 C 6 C C C *5* 28.1 10/0 C 3 S C C
corresponds to oscillogram 43/1 (see table 2)
group 2 147 3 17.9 8/0 C 4 S C C
750 14 24.2 6/0 C 0.8 Q C C
4-10-1966 19 30.8 0/0 C 5 C C C
GMTOI.03- *1* 16.1 8/0 C 9 C C C
01.18 corresponds to oscillogram 43/2 (see table 2)
group 3 148 37 38.9 8/4 s 0.3 Q S C
750 oscillogram of measuring point 28 (see table 2 no. 43/3):
4-10-1966 C C C C GMT 01.19-01.34 group 4 149 3 18.6 0/0 C 54 C C Q 750 22 26.2 0/0 C 63 C C C 4-10-1966 26 26.6 38/31
notC
21 C Q Q GMTOI.36-01.51 27 32.6 0/0 C 73 C C C corresponds to oscillogram 43/4group 2 150 3 24.9 43/24
not C <0.1
not C Q Q750 14 27.4 0/0 C 15 C C C 4-10-1966 19 34.4 4/0 C 22 C C C GMT 02.00-02.15 cumulative distributional test (c.d.test) X2-test measuring R.M.S. visual
point (s-strain) (*) 0/ p(72) % examination
3 22.4 0/0 C 33 C C
14 30.3 0/0 C 43 C C
17 36.0 15/8 Q 16 C C
19 51.7 24/12 not C 0.4 not C C
corresponds to oscillogram 37/1 (see table 2)
3 22.0 19/6 Q 5 s
c
4 27.4 10/lO Q 0.7 Q C 29 47.1 3/7 Q 25 C C 33 19.4 7/0 C 16 C C 3 20.5 8/4 s<o.i
not C S 4 25.1 0/0 C 77 C C 29 45.0 0/0 C 53 C C 32 16.0 5/0 C <0.1notC
C 33 18.8 0/0 C 69 C Cnotes: C = correct measuring points indicated by asterisks** are the extra' gauges S = satisfactory
Q = questionable (*) number of exceedings of 95%/99% confidence limits in percentage of cumulative data
visual examination C C C d.c. drift C C C C C C C C C
