EXPERIMENTAL INVESTIGATION OF INFLUENCE OF SHIP'S SPEED ON ITS TRANSVERSE STABILITY
by W. B. Obrastsov Translated by Michail Aleksandrov and Geoffrey Gardner
The Department of Naval Architecture and Marine Engineering The University of Michigan
College of Engineering March 1970
Until recently, it was considered that the stability of a ship moving with a certain speed was the same as that of a non-moving ship. Some practical observations have indicated that the problem of stability variation as a function of ship's speed is important. In Reference [3], where the capsizing of two fishing trawlers was analyzed, it is stated that the cause of these casualties might be a decrease of stability due to an
increase of speed. It was also indicated that casualties of this kind occur more frequently with small, fast ships. In References [21 and [3] , some experimental results are given which prove, independently, the aforementioned conclusion. The
results of tests on models of a cargo ship with a large block coefficient (CB = .72) and of a tug with a block coefficient of
.57 are given in Reference [2] . These tests were performed for
angles of heel which correspond to the linear portion of the stability diagram. As a result, it is pointed out that the stability of the cargo ship increases with motion, while the opposite is true for the tug boat. The influence of speed
becomes quite evident for FR > 0.22. The results of model tests for a block coefficient of .65, Reference [3] , indicated that
for a speed which is less than a certain critical value the ship's stability increases; when the speed is greater the sta-bility decreases. None of these experiments were designed to evaluate the main parameters which influence stability varia-tions, however, they are very important for the correct
statement of this problem.
The most comprehensive approach is developed in Reference [1] which gives a review of previous experiments and a theore-tical explanation of this phenomena. In this reference it is indicated that the restoring moment of a moving vessel varies due to the change of pressure distribution on the wetted
surface. Formulas based on hydrostatic pressure distributions cannot give the correct results for a ship in motion.
The pressure distribution and consequently the restoring moments is influences by the following factors:
The difference between the hydrostatic and hydro-dynamic pressure distributions.
The influence of the free surface. Here we must mention that for a moving ship in a heeled condition an unsymmetrical wave pattern accounts for additional forces and moments.
An assymmetrical boundary layer due to heel.
The influence of the forces arising on the appendages of a ship with heel.
Unfortunately the experimental study was limited to models without appendages and only a summarized result of the first
three causes was presented. It is impossible to record the change of metacentric height during the experiment. We can measure either the change of heeling angle for a constant
restoring moment or the change of restoring moment for a constant angle of heel. The first approach, when the model can have any angle of heel, is only possible for test angles corresponding to those on the rising portion of the stability diagram. Because the heeling moment for this experiment is constant, and so the displacement is constant we can use the formula
M=Dh&,
to calculate the change of metacentric height for that given
angle. This approach is adequate for modeling the dynamic actions because the model has enough degrees of freedom. The
angular variations were recorded by a special device (an inclinograph) and an oscillograph.
The main particulars of the six models which were tested are given in Table 1. Based on these results, the curves of
D1iÌ
\D
(Fr,)
were plotted, where
D - model displacement h - metacentric height y - speed
Table 1
The values of A(Dh) (y), for some fixed magnitude of h, are shown in figure 1 for models 1, 2 and 3. We can see here that the influence of speed on transverse stability might be
A(Dh) considerable,
Dh = 0.3) . It reaches its maximum for
FN 0.35.
For everodel we can establish some critical
speed when
ADh)
- 0. For speeds greater than critical, the magnitude of changes its sign.The greatest increase in stability was recorded for model 1, which has the largest block coefficient. At the same time, the greatest increase in stability occurs at Froude numbers ranging from 0.32 - 0.33. From figure 1, we can see that for models with small block coefficients, the change of stability is negative.
The experimental technique must differ when testing models with heeling angles related to the decreasing portion of the stability diagram. Here we must prevent capsizing and the model is tested with a fixed angle of heel. In this case we measure the restoring moment.
In both cases we have to eliminate the influence of
moö ir B, r, 3 ' D, s'r I 2,00 0,30 0,12 0,88 0,99 0,87 63,0 2 2,00 0,30 0,12 0,88 0,5 0,44 36,0 3 2,00 0,30 0,12 0,88 0,75 0,66 48,6 4 2,00 0,30 Q,12 0,84 0,80 0,66 48,6 5 2,00 0,30 0,12 0,82 0,68 0,50 36,0 6 2,00 0,30 0,12 0,88 0,95 0,82 59,0
lateral forces caused by the inability to change the drift
angle. If a real ship is moving with some heel, then the lateral force which appears due to the unsymmetrical flow
is eliminated by rudder action, so that the ship moves straight. During the model tests, the drift angle was selected to keep the lateral force at a minimum value.
As a result of tests using the second approach the stability diagrams for angles from 0 to 400 for different speeds were obtained.
AMb
The dependence of
M (FR) on speed for constant heeling angle is given in figure b2
CONCLUS IONS 0,3 0,25 A (r4 Dh - 0,30 Q,3 04Q 0,45 1,5 ß.j, 75 0,5 Figure 1
1. For all similar conditions the sign and magnitude of
AMb
Mb depends upon the block coefficient. An example of this
ß0, gg
re;
ir M
dependence is given in figure 3. It shows that for a given FNI a critical block coefficient exists. For this critical value, speed does not influence the stability.
2. For every model there exists a critical speed when
Mb AMiD
- O and at some speed which corresponds to ()
. ItAMb MAX
was calculated that is proportional to
[F,(± (F-PjEj,
0,75 1,00 Figure 3 vCRIT where (FR)CRIT - gL andmax qr
V-
model speedE -
numerical coefficient3. is proportional to the relative metacentric
height. It can be calculated using
he
---k
rL.+ (FzmcxF,)e]i
L 2CR -where: K - coefficient of proportionality V - volume displacement i/=const 8= cansE atResults obtained using this formula sufficiently reflect the experimental data.
6
REFERENCES
Semenov-Tjan-Shanskie, W. W., "To the Problem of the Stability of a Moving Ship," Shipbuilding Scientific
Society - Proc. No. 39, 1961
Basilewskie, A. N., "The Influence of Speed on Ship Transverse Stability," Morskoi Flot No. 1, 1956 [31 Stenvaag, O., Garberg, A., "Hvalbaters Stabilitet
THE CALCULATION OF THE RIGHTING MOMENT FOR A MOVING SHIP WITH AN INITIAL
ANGLE OF HEEL by G. V. Sobolev and W. B. Obrastsov Translated by Michail Aleksandrov and Geoffrey Gardner
The Department of Naval Architecture and Marine Engineering The University of Michigan
College of Engineering March 1970
The fact that there is a stability change for a moving ship may be considered to be experimentally proven. In References [1] , [2] and [3] it is stated that for a full
ship (CB > 0.6) with a speed less than a certain critical value, the change of righting moment is positive and vice-versa (curves i and 3 of figure 1)
Figure 1
For a fine hull form (CB < 0.5) the picture is reversed.
(Curve 2, figure 1) . The magnitude of the critical speed depends upon the stability diagram and corresponds to FR,
0.35 - 0.50. In Reference [4] an empirical method for calculating the restoring moment for a moving ship was in-troduced on the basis of experimental results. The first theoretical considerations concerning this problem were presented in Reference [51. There, it was pointed out that the stability characteristics obtained without accounting for speed cannot be correct for a ship in motion. The reason for this is the change of pressure distribution on the hull, from hydrostatic to hydrodynamic in nature. The pressure distribution is given by:
P() = a1
2 ()
2 (i)where T - draft
2
in Reference [51 . For the change of restoring moment, the
following expression was also obtained.
dMx
defDh('-i
-r)
vh
+2(i-rv
29)].
(2) However, without the data related to the pressure distri-bution for the moving ship, formula (2) is difficult to use.For a qualitative analysis the ship hull can be repre-sented by a foil of small aspect ratio, and chord equal to the ship length. Considering the heeling of a non-circular ship hull we can see that the waterlines become unsymmetrical. Due to this fact, a force similar to the rising force on a foil will appear. The magnitude of this force varies in the vertical direction. The total force will cause a lateral drift and consequently a hydrodynamic reaction. Therefore,
a ship moving with heel is subjected to these mentioned forces as well as those reactions on the rudder which occur as a
result of trying to keep a straight course.
The application of foil theory to this problem was developed in Reference [6] as a means of calculating the damping coefficient for rolling motions. For the problem under consideration, the solution based on this theory, can be obtained if we account for the non-symmetry in calculating
the angle of attack for each waterline. This can only be done by assuming that the flow is two dimensional and that each waterline is independent of the influence of neighboring
waterlines. The last assumption is valid only for foils with very large or infantesimal aspect ratios. The case of a ship hull belongs to the second classification (X = < 0.08)
It is known that for foils with this aspect ratio the total force can be resolved into two components:
a) The component which is linearly dependent upon the
b) The component dependent upon the angle of attack
squared.
To obtain the linear solution with respect to the angle of attack (heeling angle) we can consider only the longitu-dinal flow. The consequent procedure of calculating the
attack angle is the following
Figure 3
Approximating this contour by a circular arc we can calculate the angle of attack for zero lift using the known formula of foil theory:
z
Figure 2
Each waterline is replaced by a simplified contour
where f(z) - the maximum value of f (see fig. 3).
For ships, with main particulars given in table 1, the distribution of this angle along the ship draft, is given in figure 4. Q20 40 0,60 I8Û PO
z
a02(n
004 Table 1 Figure 4 4 008T
o 7 k M BT, u
J
¿9 - D X6 I 2 3 2,00 2,00 2,00 0,30 0,30 0,30 0,12 0,12 0,12 0,88 0,88 0,88 0,99 0,5 0,75 0,7 0,44 0,66 63,0 36,0 48,6Each curve corresponds to a certain model and a certain heeling angle which can be obtained from table 2. For the
approximation of these curves the following power series can be uSed: = (3) Ti-O modeL iV J Hilt. Qrtg. Table 2
In the following solution we can limit ourselves to the first three members. When obtaining the restoring moment
the constant component of the angle of attack is of no interest. Therefore, we are only concerned with coefficients a and a
(see table 2).
The simplified integral equation of the hydrofoil with a small aspect ratio, Reference [8] , was used to obtain a
solution. X
fo
dç(
,+,
(4) After denotingti
'p (x,ç,
I
(5) I I 15 -0,015 0,061 2 I 30 0,052 0,012 3 I 45 0,110 -0,052 4 2 15 0,031 -0,042 5 2 30 0, C7 -0,030 6 2 45 0,029-o,9
7 3 15 0,050 0,0(77 8 3 30 0,015 0,024 9 3 45 0,023 0,010 al a2and transforming equation (4) according to Reference [91 we have:
i
2 o I ii
1V-
'
-
2
f
o o After integrationcf(r,2).r2Vz_22f_1(2Z+1)+
.(2222
+The last expression can be effectively replaced by the system of algebraic equations which are suitable for computer appli-cations. The result of the computation for three models with three heeling angles are given in figure 5, where the pressure distributions on a ship's side are given. Using a power series
I
40 050 s 7 os 3)2
Pj
Figure 5approximation we can obtain the additional restoring moment using formula (2). At the same time, the additional restoring moment can be calculated directly, using
(6)
(7)
The additional restoring moment due to ship's speed can exceed the value for a steady ship by 15 - 20%.
The change of restoring moment for full ships and practical Froude numbers is always positive.
The increase of ship block coefficient causes the increase of restoring moment due to ship's speed.
For fine ships the change of restoring moment is small, and might be positive or negative.
The negative value of additional restoring moment corresponds to the heeling angle for which the stability diagram has an "S" type form.
For FR < 0.25 the main part of the additional restoring moment is a vortex component. For FN > 0.25 the primea part of this moment is a wave component of hydro-dynamic forces.
M,
rq-sm 7.3 A14X o (8)The results of these calculations are given in figures 6, 7 and 8 as functions of FR.
Figure 7
8
'Û a,2o 0,30 0, 'û 0,50
RE F ERENC ES
[lii Basilewskie, A. N., "The Influence of Speed on Ship
Transverse Stability," Morskoy Fot, No. 1, 1956
[2] Stenvaag, D., Garberg, A., "Huolbates Stabilitet under fast," Shipsmodel tankers, Moddelekse, No. 26, 1953
[31 Obrastsov, W. B., "Experimental Investigation of
Influences of Ships Speed on its Transverse Stability," Proc. of LSI, 1966
Obrastsov, W. B., "Method of Calculating the Restoring Moment of a Moving Ship," Proc. of LSI, 1967
Semenov-Tjan-Shanskie, W. W., "To the Problem of the Stability of a Moving Ship," Shipbuilding Scientific Society, Proc. No. 39, 1961
Sobolev, G. V., "Damping of Rolling for a Moving Ship,"
Proc. of LSI, 1958
Mirochin, B. V., "Calculation of V type Hydrofoils
Using Vortex Technique," Aveatseonnaja Techneka, 1964,
No. 1
Sobolev, G. V., "Hydrodynamics of Small Aspect Ratio Hydrofoil Applied to Maneuverability," KIEV, 1967
Sobolev, G. V., "Linear Components of Ship Hydrodynamic Coefficients," S.S.T.S. No. 90, 1967
METHOD OF CALCULATING THE RESTORING MOMENT OF A MOVING SHIP by W. B. Obrastsov Translated by Michail Aleksandrov and Geoffrey Gardner
The Department of Naval Architecture and Marine Engineering The University of Michigan
College of Engineering March 1970
The problem has been stated in the previous paper,
where, using experimental results, the charge of metacentric height and restoring moment, were obtained as a function of FN. In the conclusion, the following formula was given:
jMRf Íii 5
-IMR
1k Vl,(
t
5)[F±(F
f7101-F1)],
which gives the dependence of the righting moment variation upon FR, block coefficient, metacentric height and displace-ment of the model.
In figure 1, the stability diagrams for the tested models are given.
Figure 1
The first curve corresponds to a model with a block co-efficient of 0.80 and a midship coco-efficient of 0.99 along with some initial magnitude
of
metacentric height, h = const. Thesecond curve is drawn for the same model, but with a smaller metacentric height. Curve three corresponds to a model with CB = 0.66 and CM = 0.75. The last curve is given for a very fine model with CB 0.44 and CM = 0.50.
Let us now consider the relationship between for
the rising part of the stability diagram, at a given speed, and the character of the stability diagram. It can be proved that for stable ships (curve 1, figure 1) is small, due to a large value in the denominator. For less stable ships AM
is smaller, but a lower value of MB makes the ratio con-siderably bigger than in the first case. An analysis of experimental results has proven that the quantitative char-acteristics of the stability diagram can be given as
where h - initial metacentric height o
V - volume displacement
- ratio of the relative area of the stability diagram to the enclosing rectangle
This parameter, n, can be used for selecting the values of (FR)CRITICAL and (FR)x, using figures (2) and (3). These two values are needed for formula (1)
0,3I 0,32 0,30 Figure 2 'flax Figure 3
For the given range of Froude numbers, 0.22 - 0.60, (critical) is limited to the range 0.44 - 0.50. After
2
(2)
accumulating a sufficient amount experimental data it will be possible to give an accurate magnitude for 5KP as a
function of FR and heeling angle.
The calculation procedure can be described as follows: After plotting the stability diagram for a given model with
zero speed we can calculate n. Then, using figures (2) and (3) we can obtain (FN)Ix and (FN)Kp (critical) assuming
KP 0.45. Substituting FR and h into formula (1) we can MB
calculate for any angle of heel and speed. The final result can be represented as a series of stability diagrams for different speeds.
For the models tested, the comparison of analytical and experimental results, is quite satisfactory for E 4.88