Prof., D. E., Department of Naval Architecture, Faculty of Engineering, Kyushu University. Naval Architect, B. E.. Hakodate Dock Co., Ltd. Naval Architect, B. E. , Mitsubishi Heavy Industries, Ltd.
Naval Architect, M. E. , Hitachi Shipbuilding and Engineering Co. , Ltd. Naval Architect, M. E. . Kawasaki Dockyard Co. , Ltd.
Assistant. Department of Naval Architecture, Faculty of Engineering, Kyushu University.
Some Experiments of Pitching Effect on Ahead
Resistance of Ships
By
Keizo UENO*, Isao ONO**, Hiroshi TAKESHITA***, Kiyoshi INOUE****, Hiroyuki MATSUMURA*****,
Sadao UCHINO******, Ko-kichi ODA.
Abstract
In order to investigate the effect of pitching on ahead resistance of ships, the authors carried out the resistance measurement experiments on the two kinds of cargo ship models, artificially forced pitching, at the Ship Model Experimental Tank of Kyushu University during the period between April 1965 and March 1968. The ahead resisi stances of the models were measured by the towing experiments of the models in still water, artificially forced pitching under the conditions of the models whose surging motions were free, but rolling, heaving, yawing and swaying motions were restrained. By the analysis of the experimental results we introduced an empirical formula calculating quantitatively the rate of increase of ahead resistance due to pitching for two types of actual cargo ships whose length, speed, pitching angle and pitching period are given. As examples, we calculated the amount of C, namely, the values of rate of increase of ahead resistance due to pitching of two types of cargo ships for two kinds of pitching angles and for three kinds of pitching periods, and those calculated values of C were indicated by the contour curves in base of the speeds of the ships.
1. Introduction
It was cleared by Prof. Hajime MaruoD that the added resistances of ships in waves are made up of the resistances due to the water pressures of ocean waves reflected by the ships' surfaces, the resistances due to the oscillations of ships, the drifting forces due to the phase lag of the oscillations of ships to waves and the resistances due to the destructions of the wave structures by the ships' surfaces. Among the four causes of the added resistances of the ships in waves as above, since a few years ago we were studying the added resistances due to the oscillations of ships in calm wather at the Ship Model Experimental Tank of Kyushu University. In the preceding papers2'. 3),4) one of the present authors and his cooperators reported the experimental results of yawing effect and also rolling effect on shead resistance of ships. Now, in order to investigate the effect of pitching on ahead resistance of ships as one of the above series tests, the present authors carried out the resistance measurement experiments ", e'," in still water on the two kinds of cargo ship models, artificially
forced pitching, at the Ship Model Experimental Tank of Kyushu University within the period from April 1965 to March 1968. The added resistances of the models were measured by the towing experi-ments of the models, artificially forced pitching under the conditions of the models whose surging motions were free, but yawing, heaving, rolling and swaying motions were restrained. Bythe analysis of the experimental results we introduced an empirical formula calculating quantitatively the rate of increase of ahead resistance of ships due to pitching. In the present paper the above experimentalresults are stated in detail.
2. Symbols and Formulae of Calculation
Symbols
L length between perpendiculars in m. B = breadth in m.
H = draught in m. CR = block coefficient
LCB = distance of longitudinal centre of buoyancy forward of midship expressed in of L = weight of displacement in kg.
S = area of wetted surface in m.2 g = gravitational acceleration in m. sec.2
V = velocity in m. sec1 V velocity in knot
F, = Froude number=V(gLY112 T period of pitching in sec.
= corresponding pesiod of pitching = T(g/L)1/2 = amplitude of pitching angle in degree or in radian
RT = total resistance of model in kg. CJ.M = frictional coefficient of model
= frictional coefficient of ship
Cy. -= total resistance coefficient of model with pitching CSM = total resistance coefficient of model without pitching Css total resistance coefficient of ship without pitching
CRM= increase of total resistance coefficient of model due to pitching ÌCRS= increase of total resistance coefficient of ship due to pitching C0 = rate of increase of ahead resistance of model due to pitching in %
C = rate of increase of ahead resistance of ship due to pitching in % b' = parameter
7 = factor of synchronism = i - T,/8rF,,
= 1gTJ8rV
C, C, C3 and n
= constants to be determined by the resistance tests with pitching K = coefficient of scale effect
Formulae of Calculation
By using the same method of analysis as those of the experimental results of yawing effect and
also rolling effect on ahead ressitance of ships 2), we shall be able to deduce the following
where
i
C C
1(E7)
+ sign for 7>0
- sign for
'y<OC=_22? X 100%
_Cb'+C2P2 1000' _ xl00%=C0 CF+ C2P x Kx 100%, ÇJMCFs_I» C,4MCFJCFS
Cs1f 42o çb0L T0F,, TVThe deduction of the equations (1), (2) and (3) will he minutely explained in the Section 5.
3. Ship Models Tested
Particulars of two models tested are indicated in Table 1, in which the model ships having same types as those used in the yawing effect and also rolling effect experiments have the same Model No. as the preceding experiments.2), , The body plans and fore and after forms of the model ships
are omitted in the present paper because they are indicated in the preceding paper." All models are made of wood with their surfaces varnished, and they are provided with no rudder and no bilge keel. As the turbulence stimulation devices, piano wires of 1 mm. diameter were fitted on model surfaces at the stations of 1/20. L abaft the leading edges of the models.
Table 1. Particulars of Ship Models Tested Model No. Types of Ships Items 4. Mothods of Tests 3 4 cargo ship (normal form) cargo ship (semi-Maier form)
There are two methods in giving forced pitching to the model ships towed in still water. One is
L in m. 1.800 1.800 B in m. 0. 242 0. 246 H in m.
°' °
0. 0898 LCB in %0.53
+0.66 CB 0.641 0. 702 in kg. 24. 50 27. 89Sin m
0. 5400 0. 5788(3)
(5)
the case of the forced pitching apparatus loaded in the towing carriage, and the other is the case of the forced pitching apparatus loaded in the model ships. We adopted the former case. As for the forced pitching devices, initially we designed the methods 6) of adding vertically and periodically two opposite forces on the two, fore and after, points in the centre vertical plane of the model ships, but in such methods as above the exact measurements of the resistances of the model ships were very difficult because of the model motions accompanying by the very large surging motions of the models. In the present experiments, therefore, we used the method " of adding pitching moments directly about the transverse axis through the centre of gravity of the model ship.
The rough plan of the mechanism of the forced pitching apparatus is shown in FIG. 1. As shown in FIG. 1, the vertical linear oscillations of contrary moving two vertical rods C, members of the crank systems which are composed of two eccentric discs E, two levers L and contrary moving two vertical rods C, may be given through the bevel gear F, driven by a motor. The lower ends of two vertical rods C are connected by the ball bearings respectively to the both edges, left and right sided, of a horizontal transverse blade B, through which longitudinal centre line axis is fixed a longitudinal horizontal shaft S in the centre vertical plane of the model ship as indicated in FIG. 1 and also in FIG. 2. The horizontal blade B and accordingly the longitudinal horizontal shaft S may be oscillated about its longitudinal hotizontal axis by the vertical oscillations of contrary moving two vertical rods C. The oscillations of the shaft S about its longitudinal horizontal axis can be transmitted to the oscillations of a bevel gear D' about its transverse horizotal axis through a bevel gear D. The axis of the bevel gear D' is coincided with the transverse horizontal axis through the centre of gravity of the model ship and also fixed to the frame work having the longitudinal horizontal channel G, at which fore and after two points two ball bearings H and H' are fitted. The frame work touches to the model ships' bottom floor through the two ball bearings H and H'. Thus, by the oscillations of the bevel gear D' about its transverse horizontal axis can be given the pitching motion of the model ship about its transverse axis through the centre of gravity of the model ship. Through the two ball bearings H and H' the surging motion of the model ship can be freely permissible in the resistance measurement experiments.
Since the gear ratio between the bevel gears D and D' is 1/4, and the eccentricity of the eccentric disc E is e and the transverse distance between two ball bearings of the horizontal transverse blade B is 2h as indicated in FIG. 2, the amplitude of forced pitching angle can be expressed as
'1 1/4. sin(e/b)
The pitching amplitude , therefore, can be varied by controlling the values of the eccentricity e, and also the pitching period T can be varied by controlling the revolution of the motor. In the case of the towing experiments of the model ships. such a specially manufactured towing apparatus as indicated in FIG. 3 was used.
5. Test Results and their Analysis
The range of pitching amplitude , pitching period T, towing velocity V anti its corresponding Froude number F,, tested for each model are expressed in Table 2, in which the cases of =0 correspond to the cases of the model advancing without pitching. The towing experiments were carried out for each model artificially forced pitching by the method explained in Section 4, and the amounts of total resistances were measured. All measured values of total resistances of the models were converted into those for the standard temperature 15°C, say RT, using the I. T. T. C. 1957 friction formula, while the values of Rr were not corrected for the tank boundary effect. The values of R/.
It was cleared up from the theoretical investigations of Prof. Hajime Maruo 1) and also Hiroyuki Matsumura that the amounts of Rr have the maximum values at the factor of synchronism
that is, there arises a synchronism at the speed F,
T58r.
This phenomenon was experimentally proved by the facts that the amounts of R/ have distinctly the humps at the speeds F, = T5 / 87r as shown in FIG. 4 to FIG. 11. Using the same method of analysis as those of the experimental results of yawing effect and also rolling effect on ahead resistance of ships 2), and considering such the synchronizing phenomenon as above, we introduced the equation (1) as the approximate expressions of the results of the present experiments. Putting the experimental values of C.,/Cs into the equation (1), we can get the values of ¿CRM/CsM and consequently the values of CO3 that is, the rate of increase of ahead resistance of the model ship due to pitching by the equation (2).In order to determine the numerical values of two constants C1 and C! in the equation (1), we considered the case of synchronism. nemely, the case of 7=0. First, the values of F,,=T5/8r for the T,, values tested can be calculated and next, putting those two values of T,, and F,, and also the values of f,, tested into the equation (5), the values of F can be obtained. On the other hand, using the RT/Í - V curves indicated in FIG. 4 to FIG. 11, we can calculate the values corres-ponding to those F- values. Then we can plot the values of CMM/CSM thus obtained for the Model No. 3 and also the Model No. 4 in base the values of F as represented in FIG. 12 and FIG. 13 respectively, where the mean lines through the spots are drawn. Those mean lines can be clearly expressed by a quadratic equation of F as seen in FIG. 12 and FIG. 13. The values of two constants C1 and C2 calculated from those mean lines are as follows
For Model No. 3 : C1=0.09, C2=rO. 005, For Model No. 4 C = 0. 078, C2 = 0.0058.
The values of C1 and C7 as above are given for the values of in degree.
In order to determine the numerical values of two constants C3 and n in the equation (1), we took Table 2. Test Conditions of Model Ships
Model No. 3 4 Pitching Amplitude 0 0.78 1.85 0 0.56 0.78 1.88 '1'o in 2.85 3.94 2.71 3.69 Degree Pitching Period T 0.9 1.3 1.7 2.1 0.9 1.3 1.7 2.1 in sec. Velocity
V in
0.30 ..- 1.180.30 -
1.18 m.seC. -Froude number 0.07-
0.24 0.07 - 0.24mean lines through the experimental spots are drawn. The ratios of the values of RT/ of the models with pitching to those of the models without pitching represent identically the values of
the following method. The equation (2) can be transformed into the following shape.
C3(+7)=
CLF+CFi X1OO 1co
Now we express the right hand term of the above equation (6) by a symbol J. Namely
J=
ÇÇ-xioo
-1
If we take the logarithms of each term of the equation (6), we get
log C3+n log(±1)=logJ
(8)
It is evident from (8) that log J is a linear equation of log(±7). Therefore, if we plot logarithmically the experimental values of J in base the values of (+7), we may determine the numerical values of two constants C3 and n from the mean straight line through the above experimental spots. Now, if we assume sorne numerical values, for instance, 0. 1, 0. 2, 0. 3, 0. 4, etc. as the values of 7, the values of F,, for the T, values tested can be calculated. Putting those two values of T,, and F, and also the values of ,, tested into the equation (5), the values of F can be obtained. On the other hand, using
the R/
- V curves indicated in FIG. 4 to FIG. 11, we can calculate the C/CSM values,conse-quently C,, values corresponding to those F values. Putting the above two values of F and C,, into the equation (7), the values of J can be obtained. If we plot logarithmically the values of J obtained as above in base the assumed values of 7 as represented in FIG. 14 aud FIG. 15, where the mean
straight lines through the spots are drawn, the values of two constants C3 and n can be determined from those mean straight lines as follows
For Model No. 3 : C3=15.21. n=1.5. For Model No. 4 : C3=11.07, n=1.5.
Putting the numerical values of four constants CI.C,C3 and n obtained as above into the equation (2), we can get the values of C,,, namely, the rate of increase of ahead resistance of model due to pitching.
6. Application to Actual Ships
If length L. service speed V (or V8) and type of any actual ship are given, the values of
coefficient of scale effect K for the ship can be calculated by the equation (4), using any appropriate friction formula, for instance, the I. T. T. C. 1957 friction line, model dimensions corresponding to the type of the ship represented in Table 1 and the R/t - V curve of the model advancing without pitching represented in FIG. 4 to FIG. 11. The values of K of two types of cargo ships calculated by the method mentioned above, assuming the length of actual ships L and the range of service speeds V8 be as in Table 3, are indicated in base the speed V. in FIG. 16. It is seen in FIG. 16 that the values of K decrease with the increase of the speed Vs.
The value of C, the rate of increase of ahead resistance of a ship who advances at any speed V,, pitching with an arbitrary amplitude j,,, and also an arbitrary period T, can be evaluated by the equation (3), using the value of K obtained above and also the values of constants C, C2,' C3 and n corresponding to the type of the ship. As examples, the values of C of the two types of actual cargo ships calculated by the method mentioned above for three values of pitching period T and two values of pitching amplitude ,, as indicated in Table 3, assuming the length of actual ships L and the range of service speeds V8 be as in Table 3, are represented in base the speeds V8 in FIG. 17 and FIG. 18. It is seen in FIG. 17 and FIG. 18 that the values of C have the maximum values
for T = 15 sec. at the synchronous speed Vs= 11. 37 imots, but the maximumvalues of C for T = lo sec, and also T = 5 sec. are not seen in FIG. 17 and FIG. 18 because the synchronous speeds of both 7.58 knots for T = 10 sec. and also 3.79 knots for T=5 sec. are smaller than the lowest speed 10 knots in the figures. It is clear from the equation (3) that the values of C are greatly affected by the values of F' and also K. In accordance with the decrease of the values of 'i,, and also with the increase of the speeds Vs. the values of F, consequently, the values of C decrease. As mentioned before, the values of K decrease with the increase of the speeds Vs. Therefore, by superposing the above two causes, the values of C are made to decrease greatly with the increase of speeds Vs. The trends of the values of C mentioned above for the greaterspeeds than the synchronous speeds are clearly shown in FIG. 17 and FIG. 18.
In order to explain the above results in a little more concrete way, the values of T and V5 are asswrìed as in Table 4, and the values of C of each type of actual cargo ships, read in FIG. 17 and FIG. 18, for two values of ç5,, = 2° and 4°, are indicated in the right hand columns of Table 4, in which the values of Froude number F,, corresponding to Vs are shown, too.
Table 4. Calculated Examples of Actual Ships
7. Conclusions
In the present paper we investigated experimentally the ahead resistances of two types of cargo ships advancing with pitching and the results are as follows
The amounts of ahead resistance of a ship with pitching is higher than that without pitching. The value of C, that is, the rate of increase of ahead resistance of a ship due to pitching depends upon an amplitude of pitching ',, a corresponding period of pitching
T,, = T(g/L)+
and Froude number F,,
It was experimentally proved that the value of C has a hump at the factor of synchronism
y=1T/8rF=0,
that is, there arises a synchronism at the speed F,,=T,,/8r.
The value of C can be expressed by a quadratic equation of a parameter F, which is 0/T,F',, = POL/TV, for any definite value of 'y.
The value of C of an arbitrary actual ship can be calculated as functions of a parameter F, a
factor y and a coefficient of scale effect K.
The value of C decreases in accordance with the decrease of the values of L and r/,, and also with the increase of V.
Table 3. Conditions of Actual Ships (Calculated)
4 140 10 2 10 Model No. 3 140 10 2 10 15 4 20
Linm.
Tinsec.
in degree V8 in knot 5 15 4 20 5Model No. T in sec. Vs in knot
F
C in %=2° 4° 3 4 7 7 16 16 0.222 0. 222 13 30 15 37
In the present paper we reported the experimental results of added resistance due to pitching on two kinds of cargo ship models. In order to obtain the ships' form effect on the added resistance clue to pitching, we are now carrying out the towing experiments with forced pitching on the various types of ship models besides the above, which will be reported in near future.
References
Hajime Maruo "On the Increase of the Resistance of a Ship in Rough Seas", Journal of the Society of Naval Architects of Japan, No. 101, 1957.
Keizo Ueno, Jun-ichiro Ueno. Takashi Hosoda and Makoto Maeda : "Some Experiments of Yawing Effect on Ahead Resistance of Ships", Memoirs of the Faculty of Engineering, Kyushu University, Vol. XXII, No. 1, July 1962 and Journal of the Society of Naval Architects of West Japan, No. 23, March 1962.
Keizo Ueno, Kazuaki Egi, Kunihisa Kondo and Masanobu Yamaguchi: "Further Experiments of Yawing Effect on Ahead Resistance of Ships", Memoirs of the Faculty of Engineering, Kyushu University, Vol. XXIII, No. 3. March 1964. and Journal of the Society of Naval Architects of West Japan, No. 27, March 1964.
Keizo Ueno, Jun-ichi Nakamura, Nobutake Sato and Masa-aki Tachiki :" Some Experiments of Ròlling Effect on Ahead Resistance of Ships", Memoirs of the Faculty of Engineering, Kyushu Universty, Vb. XXV, No. 4, June 1966 and Journal of the Society of Naval Archi-tects of West Japan, No. 31, March 1966.
Isao Ono and Hiroshi Takeshita: "Experimental Investigation.s of Pitching Effect on Ahead Resistance of Ships", Graduate Thesis, Department of Naval Architecture, Faculty of
Engineer-ing, Kyushu University (1966).
Kiyoshi moue : "Experimental Investigations of Heaving and Pitching Effect on Ahead
Resistance of Ships", Graduate Thesis, Master Cou.rse of Naval Architecture, Engineering Division, Kyusliu University (1967).
Hiroyuki Matsumura : "Added Resistances of a Ship due to Forced Pitching in Still Water", Graduate Thesis, Master Course of Naval Architecture, Engineering Division. Kyushu University (1968).
E L E VAT ION
VERTICAL ROD C
BALL BEARING
PLAN
SHAFT BALL BEARING
V!fr
I;I
II
i..
bFIG2 BLADE B
BALANCE WEIGHT BALANCE WEIGHTHeH
ELEVATION PLA N MODEL SHIP SIDEPIVOT
MODEL SHIP SID\
VERTICAL ROD C
BLADE B
SHAFT S
2L
FIG I ROUGH PLAN OF THE FORCED PITCHING APPARATUS
PI VOT
5 o 5 5
MODEL
NO 3
T0.9 SEC
0.1 0.2 0.3 0.4 0 5SPEED IN
M/SEC FIGMODEL NO 3
T1.3 SEC
0.1 0.2 0.3 0.4 0.5> SPEED
I N M/SEC FIG 5 1.0 0.9 0.6 0.8 1.1 0.75 5
lo
MODEL NO 3
1= 1.7 SEC
0.2 0.3 0,4 05 0.6 SPEEDIN
M/SEC FIG 6 0.1 0.7 0.8 0.9 10li
o 0.1 0.2 SPEED 0.
MODEL NO 3
T2.1 SEC
3 0.4 05 IN FIG 7 0.6 0.7 0.8 0.9 10 1.125
cri
o 5 o 5 5MODEL
N04
T0.9 SEC
0 0.1 0.2 0.3 0.4 0.5 0.6> SPEED IN M/SEC
FIG 8 0.7 0.8 0.9 1.0 1.1(n
05
II
AMODEL NO 4
T=1.3 SEC
0.2 03 0.4>SPEED IN
FIG 9 05 0.6 0.7 0.8 0.9 10 1.15 >(
cî
MODEL NO 4
T= 1.7 SEC
0.1 0.2 0.3 04 05) SPEED IN
M/SEC FIG 10 0.6 0.8 0.9 1.0 1.10.1 0,2 0.3 0h 0.5
> SPEED IN M/SEC
MODEL NO 4
T2.1 SEC
0.6 FIG 11 0,7 0.8 0.9 1.0 1.1THE CASE OF T=O MODEL NO 3 5 10
_L
TnFn - T V 15 T=0.9 * T=1.3 + T=1.7 o T=21 o T=0.9 * T=1.3 + T=1.7 o T=2.l 0 5 10 15>
TnFn TV FIG 13 ¿+. o 3.5 3.0 2.5 2,0 FIG 12 MOOEL N04 THE CASE 0F O2 1.5 0.7
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