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CALCULATION OF RESISTANCE INCREASE OF LARGE FULL SHIPS IN SHORT WAVES
Y. Wada Nagasaki Experimental Tank, Japan
E. Baba Mitsubishi Heavy Industries, Ltd.
ABSTRACT
To calculate resistance increase of large full ships in arbitrary wave
directions, the term representing the bow wave reflection in the Fujii-Takahashi's semi-empirical method was replaced with the Sakamoto-Baba's theoretical formula,
which takes account of curved flow effects around a ship and is applicable to any
wave directions.
To verify this method, resistance tests in regular and irregular waves of
various directions were performed for three full ship models with different
prin-cipal dimensions and bow bluntness. It was shown that the present method predicts
well the effect of change of hull form on resistance increase in oblique and beam waves as well as in head waves.
NOMENCLATURE
B Ship breadth Tv Average wave period
b(x) Ship breadth at x-section U Ship speed
BFT Beaufort scales GA Amplitude of regular waves
d Ship draft A Wave length
AEHP Increase of effective horse- p Density of water
power in irregular waves
°AW Coefficient of resistance
Fn Froude number
(= U//EL)
increase in regular wavesg Gravitational acceleration
(= R/pgç2B2/L)
Hw Wave height of regular waves
°AW Coefficient of resistance
H113 Significant wave height increase in irregular waves
L Ship length
(= R/Pg1/3/2)B/L)
RAW Resistance increase in regular waves X Wave direction
RAW Resistance increase in irregular waves
Bluntness coefficient sin2
V
JIn case of large ships, waves which they encounter frequently in a seaway
are regarded as short waves when compared with ship length, and contribution of
the short waves to the so called sea margin is considerable because of high
probability of appearance. Fig.1 shows
the most effective range of sea state which gives leading influence on speed loss in long-term prediction [1].
Therefore, in evaluating propulsive
per-formarice of large full ships in a seaway,
estimation of resistance increase in short waves is of primary importance.
At present, a semi-empirical method proposed by Fujii and Takahashi [2] is
known as one of the practical methods. In
this method, resistance increase RAW is
expressed as the sum of two components as
follows.
RAW = RAW(o) + RAW(l)
where RAW(o) is a component due to ship motions, and RAW(1) is that due to wave
reflection at the bow. In deriving RAw(l) Havelock's formula for drifting force
on a fixed vertical cylinder [3] is used with two empirical coefficients
repre-senting the effects of advance speed and finite draft. These empirical
coeffi-cients are determined by use of experimental data for head waves. Attempts have
also been made to extend this prediction method to oblique waves. In beam waves,
however, the predicted values are much smaller than the measured ones [4]. Thus,
this method needs to be improved when applied to long-term prediction in which the
effects of wave directions must be taken into account.
Faltinsen et al. presented a similar formula by a purely theoretical approach
and made it possible to estimate resistance increase of slow ships in short waves
from arbitrary wave directions [5]. Sakamoto and Baba made an improvement of this
theory by taking account of the effect of curved flow around a ship's waterplane
on diffraction waves in more rational way [6].
In the present study, Sakamoto-Baba's formula was used for the calculation of
resistance increase due to wave reflection in the Fujii-Takahashi's method so that
this method can be applied to the prediction of resistance increase of large full
ships in short waves from arbitrary directions. To verify this method, resistance
tests in regular and irregular head, oblique and beam waves were performed for
three models of full ships, varying principal dimensions and bow bluntness. The
experimental results were then compared with the calculated results by the
proposed method.
N.
r Hin 3 m o 4 5 Wave Period 4 6 8 IO 12 sec for a Tanker.Japan-Arabian Gulf Route
Fig. i Range of wave height and wave period which
gives leading influence on speed loss in long-term prediction (1)
NISISTANCE TEST IN WAVES
Resistance tests were carried out in the Seakeeping and Manoeuvring Basin of the Nagasaki Experimental Tank, Mitsubishi Heavy Industries, Ltd., which has a set of X-Y towing carriage and two groups of flap-type wave maker on two adjacent
sides [7]. Its plan is shown in Fig.2.
=
C.)
Steering Gear
Manneuvring-Basiri
Clump
Fig. 2 General plan of the seakeeping and manoeuvring basin (7)
2.1. PROCEDURES OF TEST
All the necessary apparatus, for example resistance dynamometer, were mounted
on the Y-carnage. Arrangement of measuring apparatus is shown in Fig.3.
A resistance dynamometer of load cell type was used in the measurement, where a
load cell was set at the bottom of a vertical towing rod. This rod is attached to
the center of gravity of a model through the load cell, and it is supported by
sub-carriages, which are capable of surging and swaying at the same time. Effect
of friction of the surging carriage is removed by setting a load cell directly to
the model. Steering gear and directional gyro were on board.
Wave height probe of servo-type was set about 3 m ahead of a model of about 7 m long.
In oblique and beam waves, drift of a model in sway direction was balanced by
soft springs which hardly disturb sway motion of a model and restrain only the mean
drift due to wave, and the mean direction of advance was kept on an intended
course by an auto-pilot device on the Y-carnage, allowing yaw motion.
O yna mo m et er
Fig. 3 Arrangement of measuring apparatus
Wave Height Probe
/
Y- Carria ge E C-) E 190m 160m X- Carria Y- Carria ge geWave Maker(Shorter Side) Seak eepïng-Basin
Wave Maker (Longer Side)
Lab. & Office
30m 30m
)
Three models of large full ship were used in the experiment. These models have
different principal dimensions and bow bluntness as shown in Table 1. Fig.4 shows
definition of bluntness coefficient sin2 [2] and wave direction. Waterlines of
the models are compared in Fig.5. Ship A has the most blunt how and Ship C is
most slender. Transverse metacentric height and natural period of roll were
adjusted to the designed values. Advance speed of models was about 0.12 in Froude
number.
Wave conditions set up in the tests are shown in Table 2 - 4. Beaufort scales
were used for the representation of sea conditions, and one-dimensional Standard
Sea Spectra S'(w) recommended by ISSC (1964) were used. Significant wave height
for Beaufort scales is based on WNO (World Meteorological Organization) Code 1100,
and the relation between significant wave height and average wave period is based
on that for fully developed irregular waves by Pierson-Moskowitz spectra.
Table i Principal geometric parameters of model
Table 3 Conditions of long crested irregular waves
8/2
B/2 HuH Surface 2ß .8'?-
. / sin1/Idy sin7/1 B .i Y Reflected Waves Incident WavesTable 2 Conditions of regular waves
Table 4 Test conditions
Incident Waves
Fig. 4 Definition of bluntness coefficient arid wave direction
U
X(deg) 180(head), 150. 90(beam)
A/L 02. 0.3, 0.4, 0.5 Hw/L 1/50 LIB B/d sin2ß Ship A 5.3 3.0 0.39 Ship B 5.0 3.2 018 Ship c 6.0 2.9 0.21
X (deg) 180(head). 150, 90(beam)
BU 6 7 8
HI/3 (m) 3.0 4.0 5.5
Tv (sec) 6,1 7.7 9.1
Regular Waves Irregular Waves
ShipA X X
ShipB X
Fig. 5 Comparison of waterlines
3. COMPARISON BETWEEN MEASURED AND CALCULATED RESULTS IN REGULAR WAVES
Measured results in regular waves are shown in Fig.6 in comparison with
calcu-lated results by Sakamoto-Baba's formula and Fujii-Takahashi's method. The
resistance increase by Sakamoto-Baba's formula consists of a component due to wave reflection only, and Fujii-Takahashi's method, on the other hand, takes account of components due to wave reflection, vertical ship motions and lateral ship motions. The outlines of calculation formulas of the wave reflection term in both methods
are shown in Appendix.
Fig. 6 Comparison of resistance increase in regular waves
Calculated Results by Sakamoto-Babas Formula
-
Calculated Results by Fujii-Takahashi's Method O Experimental Results 4.0 20 Head Waves( 180) Ship A Fujii-Takahashi's _oo.is8-'---Method 4.0-2.0 Oblique Waves (1 50rn)Ship A Fujii-Takahashi's Method
4.0-
2.0-Beam Waees(90)
Ship A Fujii-Takahashis Method
Sakamoto-Babas Formula
° o
\-
-7---Sakaniotc-Baba's Formula Sakamoto-Bahas Formula
00 0.1 0.2 0.3 0.4 0.5 0.6 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0 0.1 0.2 0.3 0.4 0.5 0.6
A/L AIL AIL
40 Ship B 4.0 Ship B 4.0- Ship B
e 2.0 - -o
o-0 -
2.0 5__-o-- 0___ 00 00 0.0 0.1 0.2 0.3 04 05 0.6 O I 0 2 0.3 04 0 5 0.6 0.1 0.2 0.3 0.4 05 0 6A/L AIL AIL
4.0 Ship C 40 Ship C 4.0 Ship C
2.0 8 2.0 o 2.0
Q-S
o00
01 02 03 0,4 05 06 00 0 1 0.2 03 0.4 0.5 06 0.0 0.1 0.2 03 0.4 0.5 06
AIL AIL AIL
F.P. Ship A
Ship B Ship C
Vin
neau waves ana oolique waves, the coetticient 01. resistance increase,
changes with the shapes of waterplane. It is biggest for Ship A, and it takes
nearly the same value for Ship B and Ship C which have similar waterplanes b(x)/B
as shown in Fig.5. lt is said that 0AW mainly depends on the shape of waterplane
at the bow part. Both methods give similar values o. °AW in short wave range
where the effect of ship motions is negligible.
In beam waves, difference in 0AW among three ships are not so large as in head
waves. Calculated results coincide well with measured results for Sakamoto-Baba's
formula, which takes into account the effect of the deformation of diffraction
waves due to curved flow around a ship. As for Fujii-Takahashi's method, the
cal-culated results which are mainly attributed to ship motions are much smaller than
measured results.
From these comparative studies, it is considered that in case of full ships in
short waves a way to improve Fujii-Takahashi's method for any wave directions is
to introduce Sakamoto-Baba's formula into the term due to the wave reflection.
4. COMPARISON BETWEEN MEASURED AND CALCULATED RESULTS IN IRREGULAR WAVES
Calculation of resistance increase in irregular waves RAW was performed by the
conventional way, namely by the principle of linear superposition. A component of
resistance increase due to ship motions in regular waves was calculated by
Fujii-Takahashi's method, and a component due to wave reflection in regular waves was
calculated by Sakamoto-Baba's formula as suggested in the previous section. In
the calculation of the component due to wave reflection, the value of
°AW at AIL
= 0.2 was used by making use of the fact that measured resistance increase in
regular waves is regarded approximately as constant up to AIL = 0.5. This
approximation is considered to be valid up to around Beaufort scale 8 for ships of about 300 m long, because contributions of waves longer than half the ship length
to the wave energy are small in these sea conditions.
4.0 0.0-NI 0.0e' 4 5 6 7 8 4 5 6 BIT BIT 4.0 2.0 Head Waves g Oblique Waves 40 2____ 2.0 Beam Waves
Fujii- Takahashi's Method
o Ô:xw = * Calcula ed results by present method Raw f)g(H,3/2 )?B)/
Fig. 7 Coefficients of resistance increase in irreguiar waves
(Fn 0.12) Exp. Cal.* ShipA O ShipC A £ BIT 8 0.0 1t 4
I 5
¿
BIT
Fig. 8 Increase of effective horsepower in irregular waves
The calculated results based on this procedure were compared with the measured
resistance increase in head, oblique and beam waves with respect to Beaufort
scales as shown in Fig.7. In case of beam waves, the calculated results by the
Fujii-Takahashi's method are also shown for reference. Due to the difficulties in
measuring small quantities, there are some scatters of measured data. As a whole,
however, a trend of hull form difference is predicted comparatively well by the
present method in head, oblique and beam waves. For reference, in Fig.8 measured
resistance increase in irregular waves are plotted in a form of effective
horse-power increase for full-scale ships of about 300 m in length and compared with the
predicted values. 5. CONCLUDING REMARKS Beam Waves Iujii-Takahashis Method BIT * Calculated results by present method (Fri 0 12)
A modified version of Fujii-Takahashi's method was introduced for the
pre-diction of resistance increase of large full ships in short waves. In principle,
this method can take account of the effect of wave reflection in arbitrary wave
directions in short waves. By the present study, a possibility was shown in
im-proving prediction accuracy of resistance increase in arbitrary wave directions. The authors hope that the present experimental data also contribute to the further improvement of prediction methods, though there is still a room for improvement in
experimental accuracy. Exp. Cal.* ShipA O Ship C A 15000 Head Waves 15000 ç; 10000 10000
/
o-/
o-5000 g 5000r-
I 0-
4 5 6 8 BI T 15000 Oblique Waves 10000 o-5000 o o' / / 4 5 6VThe authors express their
sincere gratitude to Dr. T. Takahashi, ProjectManager, Nagasaki Research and Development Center, Mitsubishi
Heavy Industries,
Ltd. for his instructive discussions.
REFERENCES
Takahashi, T., "Added Resistance, Energy-saving from the View Point
of Ship
Motion", Bulletin of the Society of Naval Architects of Japan, No.632 (1982).
Fujii, H. and Takahashi, T., "Experimental Study on Resistance Increase
of a
Large Full Ships in Regular Oblique Waves", Journal of the Society of Naval
Architects of Japan," Vol.137 (1975); also see 14th ITTC (1974).
Havelock, T.1-I., "The Pressure of Water Waves upon a Fixed Obstacle,"
Proc. of the Royal Society of London, Series A, Vol.175, No.963 (1940).
Takahashi, T., A Practical Prediction Method of Added Resistance, Doctoral
Thesis, Kyushu University (1986).
Faltinsen, 0.M., Minsaas, K.J., Liapis, N. and Skjordal, S.D., "Prediction
of
Resistance and Propulsion of a Ship in a Seaway", Proc. of 13th Symposium
ori
Naval Hydrodynamics (1980).
Sakamoto, T. and Baba, E., "Minimization of Resistance of Slowly Moving
Full
Hull Forms in Short Waves", Proc. of 16th Symposium on Naval
Hydrodynamics
(1986).
Taniguchi, K. and Fujii, H., "On the New Seakeeping and Manoeuvring
Basin of
Nagasaki Technical Institute, MHI", Trans. of the West-Japan Society of Naval
V
APPENDIX Calculation formulas of resistance increase due to wave
reflection RAW( 1)
(1) Fujii and Takahashi [4]
= + o)pgç2B sin2(3-X)/2 n2 I( I. 5k0d) n2112(1.5k0d) + K12(1.5k0d) 07 =
3.5/Fn
(c0sX) sin2 (B-x) [ flsin2(B_x)dy+f
sin2(-ß-X)dy]I, K1
: Modified Bessel functionsk0 : Wave number of incident wave
u
Wave Direction X
Zone I y
(2) Sakamoto and Baba [6]
Faltinsen et al. derived the following formula [5].
RAW(1)
=fsinBd
21 k k2 - siro(B+cy)] = - cos2(Bta) k0 k1 = {w - Vk0cos(B+co)}2/g k2 =/k12 - k02cos2(ß+a)7TX
We Circular frequency of encounter waves
V : Velocity around waterplane
In this formula, Sakamoto and Baba recommended to use the velocity V around waterplane calculated by double model flow, while Faltinsen et al. assumed approximately V = UcosB [5].
X
Zone II
