REPORT 245
JULY 1969
LABORATORIUM VOOR
SCH EEFS
BOUWKUNDE
TECHNISCHE HOGESCHOOL DELFT
THE COUPLED ROLL-SWAY-YAW PERFORMANCE IN
OBLIQUE WAVES
BY
IR. J. H. VUGÎS
PREPARED FOR THE 12th INTERNATIONAL
TOWING TANK CONFERENCE (ROME 1969)
D
July 1969.
Report 215.
LABORATORIUM VOOR
SCHEEPS BOUWKUNDE
TECHNISCHE HOGESCHOOL DELFT
E
-1
TITE COUPLED ROLL-SWAY-YAW PERFORMANCE IN
OBLIQUE WAVES.
by
Ir. J.H. Vugts.
Prepared for the 12th International Towing Tank Conference (Rome
1969).
SEAKEEPING.
Abstract.
To find a practical solution for the computation of coupled roll-sway-yaw in oblique waves a procedure is sought similar to the strip theory applied in heave and pitch. A programme of investigation is carried out in three phases. At first the hydrodynamic coefficients and wave exciting forces for infinitely long cylinders have been calculated by potential theory and have been compared with experimental values. Next the results for the various cross sections were integrated along the ship length and compared with measured hydrodynamic coefficients and wave exciting forces at zero forward speed. Finally the influence of speed wiLl be included separately. The last phase of the programme is now in progress.
The results up to the second phase of the programme are very promising and suggest that a similar procedure will be possible indeed.
SEAKEEPING.
The couled rollswayraw performance in obliie waves. by
Ir.J.H. Vugts
Deift Shipbuilding Laboratory
Prepared for the 12th International Towing Tank Conference
(Rome
1969).
i . Introductj'on.
At present it is commonly excepted that the influence of surface tension and viscosity may be neglected in the consideration of ship motions due to waves and that the restriction to linearity is not a serious limitation, at least for an engineering solution of the majority of practical problems. Doing so the problem belongs to the classical field of potential theory. As long as an actual three-dimensional solution, analytical or numerical, is not available an engineering approximation may be sought, similar to the strip theory which is so successfully applied to the vertical motions heave and pitch. To investigate this approach the ultimate problem has been
divided into three parts, which are studied separately. Firstly, the two-dimensional case of infinitely long cylinders has been elaborated. Secondly three dimensional bodies in waves of different directions have been in-vestigated for zero forward speed. Finally the effects of forward speed are studied and included separately, in the expectation that it is especially this influence which will cause most difficulties in the approach suggested abOve.
2.The hydrod,ynamic forces on infinitei1long eylinders.
For the two-dimension&l case an analytic solution of the potential
piob1em exists Ursell (19119) has found a solution in the form of series
expansions which are very well usable in the generally required range of frequencies. So in principle the way was free to obtain theoretical values for all. of the hyd.rodynaniic coefficients invQlved and for the wave exciting
forces. However, it was not established a priori that the assumption of an ideal fluid and the neglect of non-linearities was just as permissible for the asymmetric sway and roll as it appeared for the symmetric heave motion. When the two dimensional values are to be used as elementary information for a three-dimensional approach, which is to be constructed, it is necessary to check their correctness at some length. To this end a series of experiments was performed with cylinders of five different cross sections. The results were published in
1968 [1].
For the definition of the hydrodynamic coefficients rolling is
considered as a rotation about a fixed axis in the waterline; see figure i. The experiments showed that the theoretical computations can serve as a sound base for further work. For practical applications viscosity may be neglected
fully, except for a distinct contribution in the roll damping. Non-linearities of any importance are restricted to the damping terms as well. Some results are presented in figure 2. The full lines represent calculations for an actual section fit of the conformal representation, the dotted lines for an approximate Lewis-form. In some cases the agreement in the very low frequency range and also with regard to the added mass moment of inertia in rolling
was less satisfactory. This is most probably due to experimental errors. However, it does hardly affect the general confirmation of the theoretical
computations, nor the quantitative application to engineering solutions for practical problems.
As to the exciting forces the Froude-Krilov hypothesis largely under-estimates the sway force and the roll moment. Two ways are open for
-2-2
prediction. In the first place Newmants method
L21 based on the
Ilaskind-relations. Within the accepted frame-work of the theory it is exact. It
is very simple in use and agrees quite well with the experiments. Unfortunately it does not present phase angles and it is hardly possible to extend it to other bodies than cylinders, either with an actual three-dimensional or a strip theory. In the second place a method which makes use of the relative
motion of body and wave particles, as for instance given by Motora [3] for the sway force. It appears to agree somewhat less with the experiments than the former, but again it is certainly usable in practice. The extension to
other bodies does not offer difficulties in combination with a strip theory. Examples of the exciting forces are presented in the figures 3 and .
3. Cylinder motions.
The two-dimensional case of coupled sway-roll of a cylinder in beam waves is formulated mathematically by:
(m+p)+
Py +. (i)
+ q4 +
+ py + qy
where the coefficients rnare expressed by:
+ 0G2.a
pç a
+ +q= bcq + 20G.b
yy=a
+0G.a
Py Py
4y
y?!=b +.b
.4,y (ly y yyFor the coordinate system see figure 1. a.., b. , c. . are the
hydrody-namic coefficients with respect to
pi., q.,
wi respect to Gxyz.Y , K , N represent the wave exciting force3and fiomens in Gxyz. The vertical
psitYon
f the centre of gravity below the water surface is denoted by 0G andthe mass moment of inertia about the x-axis by
To check this mathematical description expeiments in waves with the cylinder of rectangular cross section and B/T = 2 and lt were performed in a small tank for various ositions of the centre of gravity. The results have
been published in
1968
LltJ.
The calculations have been carried out in three ways:
according to the equations (i) and (2) with all of the hydrodynainic quantities obtained by potential theory.
as a), but with an additional term in the roll damping to allow for viscous contributions, so that q at roll
resonance
was equal to the valuedetermined by separate extinction experiments.
e) as b), but with the hydrodynamic cross coupling coefficients a a
and b put arbitrarily equal to zero; cross coupling efeets va the
distade
remain present; see the equations (2).An example of the results is presented in figure
5.
They clearly show that the hydrodynamic cross coupling coefficients ath and b4, are indispensable.The fact that the mathematical model () is a good description is clearly demonstrated by the dip in the sway-curve and by the phase relation
. The
increase in roll damping only influences the prediction in a narrow ange about roll resonance.
The experiments were performed in a small tank with a very restricted waterdepth for the longer waves. This influences especially swaying by the
deformation of the orbital motion. As a rough approximation of this effect the best theoretical prediction (method b) has been multiplied with the ratio
(long axis ellipse)/(diameter circle at infinite waterdepth). It appears to
w w
(2)
-3-3
acccount quite reasonably for the depth effect.
From these cylinder investigations some general conclusions may be drawn, which will probably hold for three-dimensional bodies as well.
The mutual coupling effects of sway and, roll are strongly dependent on the position of the centre of gravity;
Swaying is largely determined by the absolute wave frequency. The influence of roll into sway is small and still decreases for diminishing M.
Rolling is a typical resonance phenomenon. Relative to the natural frequency the non-dimensional response for a certain condition is
practically the same, despite large differences in GM. The influence of
sway into roll is determined by the sign and value of the coefficient p of the mass coupling term. It will often lower and narrow the roll response.
1.The hydrodynamic forces
on ashï
form.The second phase in the programme consisted of an investigation of the hydrodynamic coefficients of the Todd Sixty Series model, CB
0.70,
at zeroforward speed. The model was force-oscillated in sway, roll and yaw to check the coefficients obtained by integrating the respective two-dimensional values along the length.
It was shown that strip theory is a very usable approximation for the
hydrodynamic coefficients of the lateral motions at zero forward speed. A discrepancy at the lower frequencies as with heaving and pitching is not noticed, any-way not to an important degree.
Just as with the infinitely long cylinders the roll damping is the only coefficient which distinctly shows viscous contributions which cannot be neglected for practical applications.
Wave forces and moments on the restrained ship in oblique seas were measured as well and compared with computations by strip theory using the relative motion hypothesis. The agreement is considered quite satisfactory. Unfortunately a reliable way for the calculation of the roll exciting moment according to this method has not y-et been found.
A progress report for internal use is ready and the results will be published fully in the future.
5.The influence of forward speed.
The third and final phase is an investigation of the forward speed effect. To this end experiments have been performed in april
1969
with the same standard model divided into nine sections of equal length at Fn 0;0.10; 0.20 and 0.30. The tests consisted of forced harmonic swaying, rolling and yawing and produced the distribution of the various hydrodynamic
quantities along the length and their variation with forward speed. Results are not y-et present but will be published in the future.
6.Motion experiments.
For an evaluation of the computational method derived above motion experiments are necessary to compare. For the Todd Sixty- Series model, C., 0.70, such experiments have been reported in [5] and [6]. Calculations tave shown,
however, that they are rather sensitive for correct ship data as the absolute position of the metacentre and the centre of gravity and the mass moment of
inertia in air. Generally the information on these data is either absent or
rather inaccurate. Another point is that self-propelled models suffer from the influence of radio controlled rudder motions, which may be clearly
perceptible in the rolling recorded. Therefore it is suggested that some well
controlled motion tests in oblique waves be performed to compare with the computations. For equivalent reasons model experiments are preferred over full scale observations.
14
References.
[i] Vugta, J.H.,
"The hydrodynamic coefficients for swaying, heaving and. rolling cylinders in a free surface".
Report 1125 of the Netherlands Ship Research Centre TNO; May
1968.
Newman, J.N.,"The exciting forces on fixed. bodies in waves". J.S.R.
vol.6,
No.3, December1962.
Motora, s.,
"Stripwise calculation of hydrodynamic forces due to beam waves".
J.S.R.
vol.8
No.1, June 19614.[14] Vugts, J.H.,
"Cylinder motions in beam waves".
Report 115S of the Netherlands Ship Research Centre TNO; December
1968.
[5]
Tasai, F.,"Ship motions in beam seas".
Reports of Research Institute for Applied Mechanics, vol.XIII,
No.145, 1965.
16]
Yamanouchi, Y and Ando, S.,"Experiments on a series
60, CB
=O.T0
ship model in oblique regular waves".WI
G,
jo
z
Figure 1: Definition of Symbols.
X
X
V
Ship motions are defined with respect to Gxyz. Basic
two-dimensional hydrodyriamic quantities and their integrated values are defined with respect to OFnt.
o
G.
=,p.y
pA t pA Y 2 g 1.25 1.00 t :.5: 025 o o O pAB
t ::
020 025 -030 o 0.05 pABl2g 010 0.15 o 0.2Added mass and damping coefficient In swaying
0 25 - 025 0.50 050 050 0.75 075 075 1.00 100 1 25 100 125 1.50 1.75 2.00 wYi. 150 175 2.00 125 150 175 200 -wY a pA 0.125 0.100 pAB
i:::
0.025 o 0.05 pAB 12gr::
o 020 o. o 0.05t ::
0.20 -025 0.25Added mass moment of Inertia and damping coefficient in roLl Y.25 025 0.50 050 0.75 0.75 1.00 1.00 1.25 1.25 1.25
Figure 2: Comparison of cömputed and measured hyd.rodynamic coefficients for a cylinder [i].
Ir-wyi
1.50 1.75 -1.50 1.50 w 1.75 200 2.00 1.75 B 2g 2.00n
32 0.075 0.050 3025 o O D000 O 0 050 0.75 1.00 1.25 150 175 23] 200 050 o:-Tdk
o 0 025 050 0.75 1.00 5 1.50 1.75 2.3 O a 0.05 o 0.10-D 0.20 OD DODD DO . 88 8 ° 00 O 6/1 2 o ¿ s BF10
;IE
-
j,,-I 00/
/
u o/0
o\
/ / u O\_/
o o9 u o.o.
oo0
0000
k I
1.00 0.75 z0 pgB0 0.50 0.25 o 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 0.9 1.0 1.1 vo pgMo 2.00
t::
o 0.25rr
vi.
Figure 3: Comparison of computed and measured wave exciting forces for various cylinders
Ei].
.1 0.2 0.3 0.4 05 0.6 0.7 0e 0.9 1.0 1.1
Vf
Figure 14; Comparison of computed and measured wave exciting moment for various cylinders [i]
o
--U
-.- -1 A\
'
\
\
'S -S -- N Newman -- Motora b 025 I I 0.50 I 0.75 1.00 I I I 1.25 I 1.50 1.75'ir
I b. I 2.00 -S a 0.50 0 0 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.0 2.00 O - Newman 0 0 025 0.50 0 75 1.00 1.25 150 i 75 I I I Newman O manured about G 0 0.25 0,50 0.75 1.00 1.25 1.50 1.75tir
W o 0.25 0.50 075 1.00 125 1.50 1.75 2.00 )vi 100 1.25 1.50 1.75 2.00tir
b. W 2.50 2.00 YO pgAk 050 O 2.50 200 pgAk0 t ;: 0.50 o K0 pgk t12.5 10 7.5 5 2.5 o 12.5 7.5 5.( 2.5 o 2.5 50 75 100 12.5 W sect
Figure 5: Compàrison of computed and measured swaying and rolling for
a cylinder in beam waves [14] in two different conditions.
I I \..1_b_1QLfl ' water
