ri!
«European Shipbuilding» No. 2 - 1972
a clear responsibility for setting up the ground rules to cover the search and exploitation of the petroleum resources. When it comes to the
ac-tual implementation and execution of safety objectives through quality control it appears
WAVE-INDUCED MOTIONS AND LOADS - COMPARISONS BETWEEN
THEORETICAL RESULTS, MODEL TESTS AND FULL SCALE
MEASUREMENTS
By BjØrn Pedersen*)Abstract.
Theoretical calculations of wave-induced mo-tions and loads for both conventional ships and
catamarans are compared with model tests in
regular waves. Theoretical results are given
ba-sed on the strip theory developed by
Korvin-Kroukovsky and Jacobs as well as according to
the new method presented by Salvesen, Tuck
and Faltinsen for motions in six degrees of
free-dom. The correlation with model tests is
gene-rally good.
DET NORSKE VERITAS WAV LOAD PREDICT ON PROGRAMS.
SS T AIlS T IC
OF-WAVEE
NV ¿1A'
ADDED MASS AND DAMPING
L E W I S - FRAN K FORM CLOSE FITS A DMA 8=
NV ¿03A
TRANSFER FUNCTI ONS
V
I,
SIX DEGREES OF FREEDOM
rSINGLE ATAÑ fi1LiNç»r
jjIiFI
NV ¿Ii NV CAT IU 1ORILI
COMBINATR)NS UF
TRANSFER FUNCTIONS jJCL.MOflON
iBETW TWO -GENERAL SKIPS
NV RMSY SNV I3
9
V
SHORT ANO LONG TERM STATISTICAL DISTRIBUTIONS
NV ¿03C
logical and timely to employ the full capabi-lity and momentum of institutions aready
en-gaged in striving for safety at sea in the general
sense. The classification societies would fall into
this category.
Calculated response parameters in irregular waves are to some extent compared with
mo-del test and full scale measurements. Also here the agreement is reasonably good.
1. Introduction.
The necessary tools for calculating the
moti-ons and loads a ship will experience in a
sea-way were developed only some 20 years ago. By
tools are here meant mathematical methods and computer facilities. The development has been
STRUCTURAL RELIABILITYi / PO0ABILITY, CUMULATIVE OF FAILURE f DAMAGE /
//
2//
/
''Ill ¿03D II SIN SC lU RAI. ANALYSIS 'S PR J N N'G './///
Fig. 1. Det norske Ventas wave load prediction
pro-grams.
*) Det Norske Ventas - Research & Development Section. Head of Wave Loads Section.
RESiSTANCE IW' WAVES, SLAM M N C. ANO WHIPPING, MARCH 1971 Á'NNED il PER AT I V E 18 AV6. 1g72
SHIP MOTIONS AND LOA OS w
= .1 0 U I KORVIN IN TANKS KROUKOW5
"f
Fig. 2. Transfer function for heave. Series 60 form in
head sea.
very rapid during recent years and compari-ons with model tests in regular waves have generally shown that the existing methods are
adequate for most ship forms.
Different methods exist for predicting the motions and loads in irregular waves and re-sults from such calculations have proved their
importance. These new methods have provided
a sounder basis for the development of large and new types of ship.
There is, however, a lack of data with which
the calculations can be compared and this is particularly true for full scale measurements.
Det norske Ventas developed its first com-puter program for the calculation of
wave-in-duced motions and loads in the early sixties. A
large effort has since then been put into
deve-loping methods and computer programs in this
field and Det norske Ventas now have at their
disposal a family of computer programs as
shown in Fig. 1.
This paper will not be concerned with
des-criptions of the different methods on which the
computer programs are based; reference is gi-ven here to existing literature.
The purpose of this paper is to give examples of results from calculations, and by comparison
with model tests and full scale measurements,
show the good agreement that generally exists.
The paper will be restricted to results from calculations by Det norske Veritas' computer
programs only.
2. Response in regular waves. 2.1 Ordinary ships.
Our first computer program for calculating
transfer functions, i. e. response in regular
wa-ves, was NV41O, which is based on the strip theory developed by Korvin-Kroukovsky and
«European Shipbuílding» No. 2 - 1972
Jacobs /1/ and with coefficients for added mass
and damping according to Grim /2/. Later the
program was extended to include oblique hea-dings in accordance with a method given by
Fu-kuda /3/. The possibility of calculating added mass and damping coefficients by the Frank
Close Fit technique /4/ has also been included.
Results calculated with NV41O for among
others the Series 60 and the Mariner form have
been compared with model tests in /5/. A few
examples will be given here.
Figs. 2 and 3 show transfer functions for heave
in head and following seas. The calculations were performed for a Series 60 form with CB
= 0.7. The form is described in /6/. Particulars of the ship are given in the figures.
These calculations have been compared with
model tests presented by Vossers, Swaan and
Rij ken /7/.
The agreement is considered to be good and
it can be seen that the effect of ship speed is
well described.
Similarly, figs. 4 and 5 give comparisons of
A : L' o
-':
o, O-"
C.O7?ULL o-/
/ -O\
o O, ¡ s' s' O °.. .5..
II¡ .5' '.5.5 o -s- // O. l.2- H-: / 00 06I,
04 o 02 0' '.5Fig. 3. Transfer function for heave. Series
following sea.
os 's OIL 2.0
Fig. 4. Transfer function for relative motion at the
forward perpendicular. Series 60 form in head sea.
05 0 5 OIL 2.0 05 1G 4 42 lo 06 06 04 02 OIL 20 60 form in 50 4.0 30 2.0 10
European Shipbuilding» No. 2 - 1972 50 40 30 20 10 0 Fig. 24 30 IO 12 01 04 0 05 IO
6. Transfer function for
omidships. Series 60
05
Fig. 7. Transfer function
amidships. Series
IS OIL 20 vertical bending moment
form in head sea.
calculated and measured vertical relative bow motion in head and following seas. The same
conclusions apply as above although the calcu-lations seem to under-estimate the relative mo-tion a little in head sea. However, the effects of
bow sinkage and the bow wave have not been
taken into consideration in the calculation..
Also the vertical bending moment midships has been compared with model tests, Figs. 6
and 7. /12/. Here the agreement must be
charac-terized as excellent, particularly in head sea.
The effect of varying the block coefficient is
illustrated in Fig. 8. The change in midship
bending moment with changing block coeffici-ent is very well taken care of in the theoretical
calculations.
In /5/ it is shown that also the effect of
chan-ging the length/beam ratio or the beam/draft ratio is very well described by the computer
program NV41O.
A few comparisons with the Mariner model have also been performed and the results for
heave and pitch are shown in Figs. 9 and 10. The
model tests were performed by M. K. Ochi /8/ with the Mariner model at light draft and with
a speed of 10 knots in head sea. Particulars of the prototype and the model are given in
Tab-le 1. Table I
Particulars of the Mariner form prototype and
the corresponding model /8/. I/mo
i
Model Mariner LOA (ft) 13.55 563.6 L (f t) 12.69 528.0 B (f t) 1.83 76.0 D (ft) 0.85 35.5 d (max) (ft) 0.715 29.75 CB 0.624 0.624 0.635 0.635 CM 0.983 0.983 C\V 0.745 0.745 Scale ratio 1 41.6Test condition (full scale) Light draft
Cargo loading (°/o) 40
Displacement (tons) 12818 Draft: Fore (ft) 16.4 Midship (ft) 20.0 Aft (ft) 23.6 Trim/L 0.0 136 Metacentric height (f t) 3.74
Longitudinal radius of gyration IL 0.247
Natural pitch period (sec) 7.6
Natural roil period (sec) 15.0
Fig. 5. Transfer function for relative motion at the
forward perpendicular. Series 60 form in
fol-lowing sea.
05 Is OIL
Fig. 8. Transfer function for vertical bending moment
amidships. Series 60 form with different block
coefficients.
IO 15 OIL 20
for vertical bending moment
60 form in following sea.
05 lo IS OIL 20 24 M, 0' 20 14 12 08 04
R
o
05
Fig. 9. Transfer function for heave. Mariner model at light draught with 10 knots in head sea.
In Figs. 9 and 10 the response is plotted ver-sus frequency of encounter. The agreement
bet-ween model tests and calculations is excellent
except at high frequencies (small wave lengths) where the response is small. A discrepancy here is thus not very important.
It should be mentioned that comparisons of
results from NV41O with other theoretical re-sults showed only minor differences /5/.
NV41O is only capable of calculating vertical
motions and the associated loads. It soon became
apparent that there was a great need for cal-culating the motions in all six degrees of
free-dem as well as the corresponding loads; our
com-puter program NV417 became the answer. This program is based on a sink-source technique as described by Salvesen, Tuck and Faltinsen /9/. In /10/Faltinsen has given extensive compari-Sons with model tests for a Series 60 form with block coefficient 0.8. The model tests are
accor-ding to Wahab /11/ and Vossers et al /12/. A few
examples have been chosen for this paper.
In some cases comparisons have been made
with calculations with NV41O. These results are
denoted K-K & J theory, while results from
NV417 are denoted STF theory.
In Figs. li-13 comparisons for vertical
ben-ding moment amidships are shown for three
dif-ferent heading angles; 170°, 90° and 10°. It is
seen that the STF theory in most cases gives a better correlation with the model tests than the K-K & J theory. However, generally, the diffe-rence between the two methods is not large for the vertical loads.
Apart from the fact that NV417 is capable of
handling a larger variety of ship forms than
NV4IO, its largest merit lies in the possibility of
Fig: 10. Transfer function for pitch. Mariner model at light draught with 10 knots in head sea.
also calculating the lateral loads. As shown in Figs. 14 and 15 the agreement between
calcu-lated and measured horizontal bending moment amidships is reasonably good. The same may be said for the horizontal shear force, see Figs. 16
and 17. The most marked difference between
the model tests and the calculations is represen-ted by the peculiar oscillations in the measured transfer functions for wave lengths larger than AIL = 0.6. A satisfactory explanation of the dif-ference has not yet been found. It may possibly be due to deficiencies of the measuring equip-ment.
0020-00$
0010
000$
«European Shipbuilding» No. 2 - 1972
VELO SEA. ISO')
Efl Q.1S
S li IV 080105 OS 0« 0
0,1
Fig. il. Transfer function for vertical bending moment
amidships. Series 60, wave direction 170°.
AS YSSPT O TE
\'
M000I. TEST ANYAPTOTE -RODEL TEST cALCUl. *1100\
00 0.5 10 1.5 00 05 10 ISWAVE DIRECTION IT0
0(05.1000 POINTS 00900TT4001S. *40*8 0-- ST F. 10000V «.0(4 114000V (TOI dg'.. ? i 10 cl 2T1a/?V 05
«European Shipbuilding No. 2 - 1972 0 000 COI' a 000 0003 O 01 000 II 1.1IO 000v 00 0S 0.0 00 Fig. 12. Transfer function for yertical bending moment
amidships. Series 60, in beam sea.
Calculated and measured torsional moments show fair agreements as seen from Figs. 18 and 19. The axis of the torsional moment measured in the model tests was not given by Wahab. The
calculations according to the STF theory are, with respect to the axis, given by the
intersec-tion between the water plane and the ship's
centre plane: It is felt though that a possible
difference in position of moment axes will not
significantly influence the conclusion given
above.
4-Fig. 13. Transfer function for vertical bending moment
amidships. Series 60, wave direction 10°.
2.2 Catamaran.s.
Our latest development in the field of
wave-induced motions and loads is concerned with
catamarans The computer program, NVCAT, is based on the same principle for calculating ad-ded mass and damping as that used in NV417. However, the hydrodynamical interaction
bet-ween the two hulls has also been taken into
consideration and the significance of this effect
is illustrated in Fig. 20. Here, the added mass for heave is given non-dimensionally versus
wave frequency. IO i I O - --- 00000IM(W0$, SANAS IS IO IO OSLO OS 03 Os 03 SO . O IS 0 L 'su0 D O PO,",' 05000000 00 0
Fig. 14. Transfer function for lateral bending moment Fig. 15. Transfer function for lateral bending moment
amidships. Series 60, wave direction 150°. amidships. Series 60, wave direction 50°.
MEO WOOLS 00(000 fr, EOP(*10000T51 DI'0flIA0fl.0OS'.1D0 P01,0 SUDO O TO 0 /;!/
'ç'\
--O--011J
Sn .O IO MfLOUD E LXPEDI000TIIS, WAHOO S-
0030505 Dl 10. ¡ -O- SI Ç ToraCi O (Oil 001000 W.V. 011(0100 30' 110(10 30* 110fl o,;
p',
SI. O IS - - 000101003I, -0-3 1F. WAVE 01000000 ODIAD 534.IS0'I O 00000 13O - ,4/(J -0 \. -----
3 0 00 O OIS ODIO 0001 *0,0 OPH001ION --,O. . 0055(05 (TAL.//
IV t' I i s O t .5 101O 03 Al 30 0 3131210 000100 030.0020 0.0005 o o I I i 20 b I. 3 2 000 007
«European Shipbuilding» No. 2 - 1972
0 0 0 1 1 I I. I 2.5 2,2 1,0 0.0 0.7 0 6 0.5 0,0 03 ?O/L 77. OIS -O- SOD 00*01 010001,00 t "(LO OIS .010.1 00000V ISO. SO *50000
-
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77. OIS -I;b:0*0000 . .. ..I'
. j-- j-- j-- EXPERIMENTS, MEASURED POINt WAHAB O - O- S TP. THEORY WAVE DIRECTION 150° HEAD SEA 200°)/
_,Ir_s' O__%S.O-
00/
" o1/
Fig. 16. Transfer function for lateral shear force amid- Fig. 17. Tranfer function for lateral shear force
amid-ships. Series 60, wave direction 1500. ships. Series 60, wave direction 50°.
For further information on the method see «Theory with given roll moment of inertia»
/13/. have been calculated with the experimentally
The body plan of the catamaran used in the determined roll moment of inertia. This
mo-calculations is given in Fig. 21 while particulars ment was determined with respect to a long-of the parent form are given in Table 2. itudinal axis through the centre of gravity. The
results marked «Theory. with corrected roll
Results of calculations and model tests are moment of inertia» were calculated with the
given only for zero speed. same value for the roll moment of inertia, but Some of the results given are dependent on it was taken to be valid for the axis in the inter-the roll moment of inertia. The results marked section between centreplane and waterplane.
Fn r G. i S
Fig. 18. Transfer function for torsional moment
amid-ships. Series 60, wave direction 150°.
J:
000
O0
IS IO IO 000700 0'. 0 00 IS IO IO 0807 00 00 0 01
The roll moment of
inertia about the
axisthrough the centre of gravity would in thiscase
be some 20 per cent lower than that
experi-mentally determined.
As is seen in Fig. 22 the theoretical results
with corrected roll moment of inertia agree ex-cellently with model tests. Also the agreement
between experimentally and theoretically
de-0.0015 u U) 0.0010 0.000 5 o 10 S 4 2 I t I I I 3 2 1.5 1.2 LO
Fig. 19. Transfer function for torsional moment amid-ships. Series 60, wave direction 50°.
termined roll resonance frequency is very good
in this case.
The difference observed for calculations with given roll moment of inertia may be due to non-linear effects.
Fig. 23 shows comparisons between theory and experiment for pitch. This variable is not dependent on the roll moment of inertia and
Fr 0.15 0.6 0.7 0.6 0.5
-4
- - -
EXPERIMENT, M EASURED POINT WAHAB A THEORY 500 WAVE HEAD- DS T
F. DiRECTION SEA 18001 o/
I,
/
"'AI,
/ AI,
«Europcan Shipbuildingo No. 2
- 1972
Table 2
Designation Symbol Unit Value
Length between perpendiculars L m 119.0
Beam at waterline amidships B m 30.0
Draft - even keel d ra 6.0
Displacement
y
ra3 6137.0Block coefficient CB 0.573
Waterplane coefficient CW 0.725
Midship section coefficient. CM 0.926
Breadth of one hull and
water-l)ianC amidships b ra 7.5
Distance between centrcplancs
of the two hulls 2p ra 22.5
Metacentric height GM m 19.0
Centre of gravity above keel rn 11.6
Ceni re of gravity aft of
amid-ships III 3.11)
Pitch radius of gyiatmn with respect to axis through centre of
gravity 0.245L
Roll radius of gyration with respect to axis through centre
of gravity 0.403B
Distance from the centreplane of the catamaran to the centre of
Fig. 20. Two-dimensional added mass coefficient,
heave for a catamaran section.
the agreement is seen to be good. The resonance
observed for pitch at AIL = 0.35 is most
pro-bably due to the hydrodynamical interaction.
The vertical shear force between
the twohulls is, however, dependent on the roll
mo-ment of inertia, and as seen in Fig. 24, different
results are obtained according to which value is chosen.
Although some difficulties have been expe-rienced, the comparisons are generally quite good and the results encouraging.
3. Response in irregular waves.
Our method for calculating the response in irregular waves is based on the principle of
li-near superposition. The response in a given sea
state is thus found from the transfer function and the wave spectrum. For further
informa-tion on our method see 114/.
We use a modified Pierson-Moskowitz spec-trum with the two parameters significant wave height, H1/3, and average apparent wave peri-od, T.
F OR RIA RO
W"
w
ri
*
H
B 33.0Fig 21. Body plan of the catamaran model.
a 5.0-Fig. 22. 100 OR pgBLa 0.2-oT
«European SîLipbuildinçjn No. 2 - 1972
025 05
ois os A
P[GULAR WAVEÇ WAVE OIRLCTIOT4 ITO
(HEAD SEA IRS.) ER000C NUMBI:R .0 0
"o--. o_._____
O:
10 IS ._0_ 20
Transfer function for roll of the catamaran.
REGULAR WAVES
WAVE DIR ECTION T 10° (HEAD SEA° 80°
FROUDE NUMBER O O O THEORY A EXPERIMENTS A _.__O__O----0 A o "o
O O
A o IS +I
t)I
k o REGULAR WAVES WAVE DIRECTION ITO°HEAD SEA 1601 FROUDE NUMBER O O
- -
-20
Fig. 24. Transfer function for vertical shear force of the catamaran.
35 o THEORY wITH CORRECTED ROL).
MOMENT 0F INERTIA
20 0 -'J
le °
o
THEORY WITH GIVEN ROLL MOMENT OF INERTIA. EXPERIMENTS.
O
025 05 to 20
Fig. 23. Transfer function for pitch of the catamaran.
O THEORY WITH CORRECTED ROLL MOMENT OF INERTIA. e THEORY WITH GIVEN ROLL
MOMENT OF INERTIA O EXPERIMENTS. I. L' 150 Tao Se
European Shipbuilding» No. 2 - 1972 36 o 1800 HEAD SEA HEAVE
MODERATE SEA STATE MODEL TEÍ
C.)
p 900 BEAM SEA
For given values of H 1/3 and T the irregular
wave pattern is stationary, i.e. the statistical properties are constant. They will remain so only for a limited time and therefore the
res-ponse is denoted short term resres-ponse.
The statistical distribution of individual am-plitudes of ship response is assumed to follow
the Rayleigh distribution given by
P (X) = l-exp (_(X/V2)
(1)where VE is the only parameter. P (X) is the
probability that the response amplitude is smal-ler than or equal to X.
VE is easily determined from analog recor-dings of a ship response and theoretically it is determined from the area under the response spectrum. The response spectrum is the
pro-duct of the transfer function and the wave
spec-trum.
As the response in irregular waves, as well
as the waves themselves, can be described only
by statistical methods, comparisons between
measurements and calculations will have to be performed for the same probability of occurren-ce. The \/E--value is suitable in this respect and represents the response amplitude which has a
probability of exceedance equal to
Q = 1P (VE) = exp (-1)
368°/oM. K. Ochi /8/ has performed a number of
model tests in irregular waves with the Mariner
model. Results for heave and pitch are shown
in Figs. 25 and 26 for the same draft and speed
as used in regular waves.
The agreement is quite good, particularly for pitch. The difference in results may be
explai-ned at least partly by the difference in wave
spectra used in the model tests and the calcula-tions, see Fig. 27.
4 VE'[degree sJ
3
2
PITCH
The S/S «Hoosier State» is similar.
Measurements of midship longitudinal stres-ses were reported in /15/. Theoretical results for
a Series 60 form have been used for
compari-sons with the measurements. The measurements were related to sea state by Beaufort numbers. The comparison shown in Fig. 28 was perform-ed utilizing the average wave height and period as a function of Beaufort given by Roll /16/ and reproduced in Table 4.
The agreement is very good and even if the
Series 60 form is not entirely representative for the two ships, it is obvious that the correct
or-der of magnitude and the correct trend is
ob-tamed.
Det norske Ventas took some measurements in the fore ship of a tanker of 95,000 t.dw. /17/;
TEST kIOEL
CALCULATION
MODERATE SEA STATE 7"
(f t) B (f t) 496.0 71.5 Design Typical operating d (ft) 30 18 Displacement (tons) 20000 11130 CB 0.654 0.6 10 Cp 0.664 0.628 Cw 0.752 0.685
Normal operating speed 16 to 17 knots
Midship section
modulus (in 2 ft) 45631
1800 p 90
Fig. 25. Short term response parameter for heave. The HEAD SEA BEAM SEA
Mariner model in irregular waves.
Fig. 26. Short term response parameter for pitch. The mariner model in irregular waves.
S/S «Hoosier State>' and S/S «Wolverine Sta-te» have been used for quite extensive full scale measurements. Table 3 gives particulars of S/S
«Wolverine State».
Table 3.
Particulars of the S/S «Wolverine State».
-TabLe 4.
Wave height and period as a function of
Beaufort.
According to Roll /161
celeration approximately O.04L aft of the
for-vard_perpendicular. Comparisons with
theore-ica1 results are shown in Fig. 29. Again the agreement is good except for the ballast con-dition where, however, the number of
recor-dings are small. Observations onboard of wave
height, wave period and Beaufort have been
used here.
(ici icra i ly, it is a problem with fu Il scale
mea-surements to get reliable information on the sea state. The comparisons may be influenced by this, but at least the order of magnitude is
seen to be correct.
Finally I would like to give a few results
from full scale measurements of longitudinal deck stresses amidships taken by Det norske
Ventas on a 200,000 t.dw. tanker. 200 E 100 o Tv (sec) 6.7 5.8 58 5.9 6.1 6.5 7.2 7.8 8.3 9.0 9.5 10.0 10.4 vertical
ac-Fig. 27. Wave spectrum used in tests with Mariner
model compared with theoretical wave spectrum.
As simultaneous measurements were taken at both sides of the ship it was possible to observe the effect of the horizontal bending moment to the longitud i nul stresses. This is illustrated in
Fig. 1() where the ratio between stresses in the
windward and the leeward deck corner is
plot-ted versus the relative direction between ship and wave. It is seen that the phase difference
between the vertical and the horizontal bending moment is such that the stresses in the leeward deck corner are higher than those in the wind-ward deck corner.
Although no exact comparisons have been
«European Shipbuilding» No. 2 - 1972
MODERATE MODEL TEST SEA STATE 7 J J T =002 CALCUtATN 951 Sec I D S.S. HOOSIER O S.S. WOLVERINE CALCULATED FROM STATE STATE SERIES I SEE J GIVEN -60 I ¡15/. PARTICULARS N TABLE FORM 3 I
OF THE SHIPS ARE
:
Dvv
OQD
o NH 37 6 Ti6 102 83 332 360 366 NUMBER OF MEASUREMENTS 287 66 ¿2 30 316 166 119 72 I I I ' 37 6 4 II 7 3 0.0 05 10WAVE FREQUENCY (seca)
2 3 /. 5 6 7 8 9 10 11 12
BEAUFORT
Fig. 28. Average VÊalues for peak-to-peak stresses amidships. Beaufort Hv (m) o 1.1 1 1.1 2 1.2 o 1.4 4 1.7 5 2.2 6 2.9 7 3.8 8 4.9 9 6.2 10 7.4 11 8.4 12 8.5
these measurements also included
40 2( =,) Im2. sec) 30 20 10
«1 roj)an Sh.ipl uildinçj» No. 2 - 1972 005 0 04 0.03 0.02 0- OT 0 NUMBER 0F VALUES
Fig. 29. Average \ÏEfor acceleration versus Beaufort.
made, the same trend has been found by
theo-retical calculations. Transfer functions for ver-tical and horizontal bending moments calculat-ed by NV417 were combincalculat-ed to give stresses in the deck corner.
-The result of such a calculation for a Series
60 form is shown in Fig. 31. The ratio between WH and WV was assumed to be 1.2. WV is the section modulus with respect to a transverse axis, while W H is the section modulus with respect to a vertical axis.
:: : 5&tt TO 0.5 W I Ç II.EEWANDI
Fig. 30. Ratio between stresses in windward and lee-ward deck corner amidships versus heading.
WAVE DIRECTION I I O TOTAL FULL LOAD DALLADO TRE000IICAL T ¡ TICS RESULTS . J
j
.1
OO - O
A A
TO STATIS- -
ACCORDINO 003ERVOD BEAUFORT O T 2 3 4 S 6 SULl BALLAST 3 6 5 5 8-
-
27 FULL LOAD 3 6 22 38 26 13 4 112 SUM 6 22 27 13 31. 3 6 139S ALL BALLAST TRIPS ALL LOB000 TRIPS
IS IL I) IT II 3 9 IS IL Il 11 II O N I 2 3 L 5 6 02 -o * 5 ALL TRIPS 02 o IN IL I) I L IT L 11 R IO A WAVE DIRECTION 6 C WINDWARD
ALL JAPAN TRIPS ALL EUROPE TRIPS
02-IS IL II 2 II IO T IS IL 3 IO II Io 2 2 L I WAVE DIRECTION 0.2. 0 L-I 80 I 35 90 TICUO DEA FOLLOWING SEA
Fig. 31. Calculated stresses in deck corner amidships. Series 60 form, CB = 0.8.
4. Conclusion-s
As a result of the different investigations we have made concerning the realibility of our the-oretical methods, we have concluded that these methods give answers which are very good for practical purposes.
The use of these methods at Det norske
Ve-ritas has greatly increased during recent years. However, great care must always be taken when
applying the methods to unconventional ship designs. The theory must not be extended
be-yond its limitations and the results must be care
fully examined when obtained for ship types
G 10 F5 O IS 355
o 2 5 6
in five volumes
by Dr.-lng. Lebrecht Tetzlaff and Dipl-Ing. Edwin Stoebe
Grundlagen des Werftbetrebes VIII, 107 pages with 20 illustrations
Format 21 X 27,5 cm. Price, bound, DM 39,50 ISBN 3 528 0 8301 8
This handbook will aid those persons, from managers to trainees, who work daily in the ship-yards. Trainees will find that the book offers them comprehensive information in
all questions concerning yard operation.
Furthermore, special consideration has
been given to the desire, expressed by students of ship technology at the higher
technical colleges, for a practical study
plan. There is a short, clear description under each subject heading, as well as
detailed explanations. In addition, examples
are quoted which should be of particular
interest to the specialist. Ask us for further
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To be published In the spring 1972 Grundlagen des Werftbetriebes
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Indispensable for: Shipbuilding yards, technical col-eges, ship-building sub-contractors, classification
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where experiments and experience have not yet
proved the applicability of the methods. It is very important that the theoretical
re-suits are checked against measurements. In this
way the practical limits of the theories may be established and one will also be able to direct effort to the right problems.
Notations
L length between perpendiculars.
B beam at waterline.
d draught.
r = longitudinal radius of gyration.
F = Froude number (= VIVgL)
2p distance between centreplanes of the two
catamaran hulls. acceleration of gravity.
= mass density of water.
'y = specific gravity of water (= 8g)
À = wave length. a = wave amplitude.
e = frequency of wave encounter.
Hv = visually observed wave height (vertical
distance between crest and trough).
Tv = visually observed wave period.
H113 significant wave height.
T average apparent wave period.
o = pitch amplitude.
0 = roll amplitude.
H = heave amplitude.
RM amplitude of vertical relative motion
be-tween ship and wave.
Dv = vertical shear force amplitude. Mv = vertical bending moment amplitude.
DL = lateral shear force amplitude. ML lateral bending moment amplitude.
= torsional moment amplitude.
X Wave-induced response.
P(x) = probability distribution of X
Q = probability of exceedance.
VE parameter of the Rayleigh distribution. (21))
A two-dimensional added mass, heave.
A = cross-sectional area of cylinder.
References:
Korvin-Kroukovsky, B. V. and Jacobs, W. R.:
«Pit-ching and heaving motions of a ship in regular
waves.» SNAME Transaction, vol 65, (1957). Grim, O.: «Die Schwingungen von Schwimmenden Zweidimensionalen Körpern». Hamb.
Schiffbau-Versuchsanst. Bericht Nr. 1171, (1959).
Fukuda, J.: «Computer program results for
respon-se operators of ship motions and vertical wave
bending moments in regular waves». Kyushu Uni-versity, Faculty of Engineering. (1966).
Frank, W.: «Oscillation of Cylinders in or below
the Free Surface of Deep Fluids». Naval Ship R&D Center Report 2357, Washington, D. C., (1967).
European Shipbuilding» No. 2 - 1972
«Luropcaii Sliip/iiililhiig» No. 2 - / 972
Nordenstrom, N. and Pcdcrsen B.: «Caiculations of 12. Vossers, G., Swaan, W. A. and Rijkcn, IL: «Verti-wave induced motions and loads. Progress Report cal and lateral bending moment measurements on No. 6. Comparisons with results from model ex- «Series 60>'-models». International Shipbuilding periments and full scale measurements». Bet norske Progress, Vol. 8, no. 83, (1961).
Vertas, Research Departement, Report No. 68-12-5. 13. Nordenstrøm, N., Faltinsen, O. and Pedersen B.:
Todd, F. H.: Some further experiments on single- "Prediction of wave-induced motions and loads for
screw merchant ship forms-Series 60. Trans. SNA- catamarans". Offshore Technology Conference,
ME, vol. 61, 1953, pp. 567-569. Houston, 1971, Paper Number OTC 1418, and Bet '7. Vessers, G. Swaan, W. A. and Rijken, H.: Experi- norske Ventas, Publication No. 77, 1971.
ments with Series 60 models in waves, Trans. 14. Abrahamsen, E.: "Recent developments in
practi-SNAME, Vol. 68, 1960, pp. 364-450. cal philosophy of ship structural design". Det
nor-Ochi, M. K.: Extreme behaviour of a ship in rough ske Ventas, Publication No. 60, 1967.
seas. Slamming and shipping of green water. Trans. 15. Fnitch, D. I., Bailey, F. C. and Wise, N. S.: Results SNAME, Vol. 72, 1964, pp. 143-202. from full-scale measurements of midship bending Salvesen, N., Tuck, E. O. and Faltinsen, O.: «Ship stresses on two C4-S-135 dry cango ships operating
motions and sea loads». SNAME Transaction, Vol. in North Atlantic service, Ship Struct. Comm. Rep.
78, (1970). SSC - 164, 1964.
Faltinsen, O.: »Comparison between theory and 16. Roll, I-I. U.: Height, 1cnth and steepness of sea
experiments of wave-induced loads for Series 60 waves in the North-Atlantic and dimensions of sea hull with CB 0.80». Det norskc Ventas, Research waves as function of wind force, SNAME Tech. & Department, Report No. 70-27-5. Res. Bull. No. i - 19, 1958..
Wahab, R./' «Amidship forces and moments on a - 17. Pederscn, B.: "Wave loads on the fore-ship of a
C = 0.80 «Series 60» model in waves from vari- tanker". European Shipbuilding No. 6, 1968. ous directions». Netherlands Ship Research
Cen-ter TNO. Report No. 100S, (1967).
fl1t2\ ifl
L
.D
Buildings berths for ships up to 450 ft. Dockings of ships up to 675 ft.
Marine boilers
manu-factured on the licence from Babcock & Wilcox.
London
Vertical watertube
boilers.
Exhaust gas boilers.
Scotch boilers. Double evaporation boilers. Oil burners.
