The Bulbous BowA Glimpse
of Its
Past. and Present Status
(Part 11)
(Continued from p. 12. vol. 1, No. 1, March '66)
The Classic Theory of The Bulbous Bow
From relatively long ago. it has been presumd ex-perimentally that the primary cause of resistance reduc-tion with bulbous boss ssould he based upon the ssave-making interference theory. For the example, we can find the descriptiim as follows, in li). Detils of Skipe Forward and Aft', p. 56. by D. W. Taylor.
"Further study since (E. F. Eggert's extensive series
tests) would indicate that the virtue of bulbous how results from the combination of three wave systemsthe how wave, the stern wave and the bulb wave. The sum-mation, of these systems fixed the actual ',save profile, which, in turn, determines the residuary resistance.
Hence, the type of interference provided by the bulb wave is the characteristic that determines the loss or the gain in speed occasioned by the bulb."
The parenthesis and the italic, in the above
des-cription, are added by the author. And, it should be
noted carefully that Taylor considered simultaneously
the interferences by the three wave systems. consisting with the bow wave, the stern wave and the bulb wave, in the italic sentence.
At the view point to recognize the phenomena, we can not find any incorrectnesses in the Taylor's
descrip-tion. Preferably. the opinion still merits admire even now as the opinion considered by the tank expert. just like Taylor. who distantly related to the wave-making
theory.
On the contrary, in this article, author attempt to look over the postures of several experts with wave-making theory who faced the problems on the bulbous
bow.
In the investigations approaching to the problems on the bulbous bow before World War ¡I, we can find the papers reported by W. C. S. Wigley (193536r'12 and
G. Weinhlum (l935)''.
In these papers, however, Wigley's is the most famous, and quoted from his paper in the Saunder's book inu'oduced previously as follows."The dsign rules laid down by W. C. S. Wigley in the 'summary' of his classic paper can hardly be im-proved upon today, twenty years later."
by .Takao Inui
Dr. Eng.. Professor, Department of
Naval Architecture, Faculty of Engineering, University of Tokyo
In the above description, 'Summary' are as follows. (I The useful speed rapge of' a'. bulb is generally
from V' s/I-O.8 to V
'TL-l.9.The worsethe wave-making of the hull itself is, the more gain may be expected with the bulb and vice versa.
Unless the lines are extremely hollow the best
position
of the bulb is
with its centre at thehow, that is, with its nose projecting forward of the hull.
(4 The bulb should extend as low as possible con-sonant with fairness in the lined of the hull. The bulb should be as short longitudinally and as wide laterally as possible, again having regard to the fairness of the lines.
The top of the bulb should not approach too nearly to the water surface; as a working rule it is suggested that the immersion of the highest part of the bulb should not be less than its own
total thickness. -,
Reading through the above 'Summary' with the most
careful, several unsatisfied parts would stand out con-spcuousIy. Furthermore, in the experimental results introduced by Wigley himself to judge the proprieties
of the theoretical results, the L=l6 ft model which gain-ed the most effective rgain-eduction ratio for the total resistance indicates 4.0, and means only 7% under conversion to the L 400 ft actual ship.
Even though they had attempted to approach the bulb form, the Wigley's paper is better than the Wein-Mum's paper'3' without fail, from the view point of introducing the results and the practices from the most important papers in the history of the wave-making resistance theory. That is., although the classical Michell's theory (1X98) "' had been all in all to Weinbium, Wig-ley had introduced the results and the practices without a moment's delay. from the Hevelock's paper (l928)''
lh' which had described the wave by the submerged doublet and had been considered as the newest theory at that time, and from the very same Havelock's paper
(l934)(1617J which had described theasymptotic
na-ture on the free wave pattern of the ship's wave and the interrelations between the wave-making resistance and the above. Especially, his meritorious, denying the convention-al doctrine in which the reduction of the wave-making
re-sistance with bulbous bow would cause from the increase of effective wave-makinglength as the opinion without the foundation, should be highly evaluated. That is, Wigley had indicated that although the advantageous and the disad vantageous of speed resulted from the bulb in the opinion of the resistance should be appeared repeatedly in the some frequency as same as the phenomena of the hump-hollow on the assumption of changing the wave-making length with the bulb, but both experimental and theoretical results had not indicate the same phenomena, and had
indicated that the wave-making resistance decreased similarly along the wide range of Froude number.
However, the Wigley's laborious work inclusive the following disadvantageous and then it can be considered regrettable that he did not grasp the correct meaning with true effectiveness of the bulbous bow and that he did not attain to support his opinion by the actual ex-periments. Hence, some investigators had pointed out that his work could not be used practically. For the examples. E. V. Telfer said in the discussion
of the
above Wigley's paper as follows. "These lessons appear still very remote to me. a humble practioner," and "The theory is still catching up to knowledge established by experience and experiment". Eventually, his theory was 'also' the one in which only the qualitative substantia-tion was held laterly to support the experientically fact with ihe bulbous bow introduced by the tank tests justlike the conventional wave-making theory.
And then, his work lacked the active nature facing front the new
stage, and, using his theory, it could not achieve the
new stage to which conventionally pure experimental approaching, based on the trial and error, could not reach.
Then, what and how were the imperfections in the Wigley's paper? These may he devided into the two categories described as follows. Accordingly, in the first, it is imperfect fundamentally that he did attempt
to approach the problems of interferences between three wave systemsthe how wave, the stern wave and the bulb wave, under the considerations as same as D. W. Taylor's concept. The secondary imperfection was that he did not observe the waves made by the models, as pointed out by Taylor. Especially, he did not deal the problems in which compared the difference between the experimental results and the theoretical concepts of the phase of free waves made by the main hull itself, and did not weigh the theory with the experimental result dealing with the newly addition of wave forms by the bulb. Above two points should be devided into two categories
"Half-Body Concept"
and "Wave Analysis",andauthor will describe them in details in following.
"Half-Body Concept"
The waves made by the ship principally are devided into "the bow wave" and "the stern wave". However. it should be supposed that the ships do not receive the effect of viscosity of the water and have not the parallel
6
middle body, consequently that the ships have not so-called shoulder wave caused by the fore shoulder the aft shoulder. Furthermore, the value of Fn shot not exceed 0.35 generally under the common. speed
the merchant ships.
Assume the newly fixing of the bulb at the F. position for the above hull form. It should not
'
allowed to consider the coexistence
of the three wai
systems consisting with the bow wave, the stern wav and the bulb wave at the starting stage, because such concept would result in the ambiguity complicating the problems. Then, attempt to simplify the problem before considering the total wave. Assume the condition having the two bodies consisted with the fore body and the aft body, respectively, separated at the midship. Thus, when the changes of the form between F. P. and midship are continuously smooth under existing fore body only, the elementary free waves originatedat the each point of
the fore body overlap each other at the rear point of the midship, and when the above elementary free waves are observed at the rear point far off the ship, the total of only two visual free wave systems consisted with the sin-free wave originated atF. P. with (+) sin phase
and the cos-free wave originated
at F. P. with (:+)
or() cos phase, by the integrally total
effects ofover-laped elementary free waves, allow to approach the total effects of the wave-making collectively. The larger en-trance angle of the waterlines the larger sin wave, and the more changes of curvature of waterlines the more large cos wave. Furthermore, in the case with
L/B10
it results in () cos phase
on the hollow water line and(+) cos phase on the full water line. Among them, of course, the ship form with non cos wave may be
con-sidered. That is the form with so-called equivalent source explained by the sinusoridal curves originated from mid-ship.
Of course, these sin-wave and cos-wave, described above, are not the simple wave as explained as the two-dimensional problems, and the orbital motion of these waves, that is the movement of the water as a token of the 'wave-motion', can be described as the three dimen-sional problems. Observing the surface of water, so-called the wave elevation equation on the sin-wave results in as follows. To simplify the problem in this following discussion, author considers with the sin-wave only,
however, the same concept can inclusive the case with coexistence of the cos-wave.
r
Cw (xy)=J
r A(0) sin (Kop sec26) dO, (1)
2
where p=.r cosO+y sin 0, (2)
Ko=g/V2, (3)
In the above equations (I) and (2), the origin of co-ordinate
is at the F.
P. point, the ship moves in the negative direction of the axis-x with velocity 'V' and axis-z is in the upward direction of the vertical line.As well known, the forms of the sin-wave in the two-dimensional problems can be described as,
Fig. 7 Kelvin wave group
the right hand side of the equation (1), as the integrand of the integration, are noi more than the substitution
K0 sec2 8 for K0, the replacement constant amplitude A with amplitude function A(e), and subsequently
inte-gration from r/2 to +/2 on 8.
As pointed out by Havelock (l934)''. the wave, described as theinte-grand A (e) sin (Kop sec2 8) in the r.h.s. of the
equa-tion (1), is the two-dimensional sin-wave propagating with the velocity V cos e in the direction at an angle
±8 against the axis of the moving direction, meaning the negative direction of axis-x in this case. However,
we can not distinguish these waves with the naked eye. and we can only observe the final wave pattern caused
by the mutual interference of these waves. The
inter-relatiöns of them showed as Fig. 7, where the thin lines
explain the former and the thick lines explain the latter. As shown apparently in Fig. 7 and as well known
by our familiar daily experience and the observation,
the ship's wave indicates the complex pattern which can-not bear comparison with the two dimensional sin-wave and have the isophasal line. The conclusion, introduced directly from the above, is that the perfect interferences. meaning the complete vanish of the wave, are absolutely impossible to cause by the mutual interference with the
two wave systems differing the origines of the wave.
respectively. on the ship's wave. lt is important what
would occur if the above underlined requirements
would not be satisfied. That is the question what
would cause if the two different three-dimensional
wave movements, as A and B. originated
respec-tively. at the same point. In describing the above
more definitely, what would results in if the another ( )
sin-wave having the exact reverse phase, as described in
the equation (5). in the addition to the equation (I)?
w(x.y) =-J
B(8) sin (K0psectO) dO (5) Supposing by the linearization, it is the clear evidencethat the resultant wave elevation, resulted from the
mutual interference by the equation (I) and (5),
re-sults in
w (x.y) =J
A(0)B(0))sin
(Kapsec2O)dO-/2
(6)May 1966
Supposing that the requirement for approximate equal amplitude between the both amplitude functions of A and B wave systems, A (e) and B (8). to be sought to
be satisfied in the integrand of integration of the right
h.s. of the equation (6). as
A(0)B(0),
O/8/
2 (7.)
it may be easily imagined that the resultant wave in the equation (6) will become particularly small as compared with the initial wave equation (I). In the results
in-troduced by Havelock' ' with the strict theoretical cal-culation, the following equations had been given,
respec-tively. corresponding to the equation (I)
Rw=-_pV2J
[A(0)J2costOdf (8) 2and corresponding to the equation (6),
-Rw=---PV2L EA(0) B(0)J2 cos2 fi dO 2
(9)
Both integrands of the r.h.s. in the equation (8) and
(9) take the form of (squared amplitude x cos3 8)
and cosi 8=1 when 0 =0 and tend to O rapidly when
/8/*r/2.
Consequently, the requirement for theap-proximately synchromesh amplitude described in the
equation (7) should be satisfied as exactly as possible at
the part in which/8/is closed to 0. but would be of little importance at the part in which/e/is closed to T12.
Applying the bow-wave considered with the fore-body
only as A(e) and the bulb-wave as B((i) into the con-cept just described above, when the following two
re-quirements,
inverse phase relation, and
approximately equal amplitude relation
are realized, the complete wave-making interference is
nearly realized between the both wave systems and the bow-wave almost vanishes practically. Furthermore, it
is expected that the wave-making resistanceembodied
from the wave cauused by the all fore-body having the
bulb at F.P.caused by the above decreases to the value
regarded as 0. Disregarding the aft-body with the
half-body concept, it becomes possible to obtain the simple
inference. For the remained aft-body, as same as the
fore-body. disregarding the fore-body and then paying the attention to the combination of the stern-wave and
the waves caused by the stern-bulb wave, there are little
difference. Actually, because the dimension of the
stern-wave is reduced by half compared with the one under the ideal fluid, it can be allowed to consider that about 70% of the wave-making resistance of the ship
ori-ginated in the existence of the bow-wave. Consequently.
if the good design of the main hull and the bulb would
be attained, it may be expected theoretically to obtain
a large amount of decrease in the wave-making resistance
proportionated to 60% to 70% of the original
wave-making resistance.
Supplementing the approximately equal amplitude in
the two requirements (a) and (b) described above for the completion of the complete wave-making interference,
it means that the bow-wave A(e) forms the exact re-verse waves against the bulb-wave B(e). Originally, the bulb equivalents to the hydrodynamical sing-ularity'source' or 'doublet' in practicallyconcen-trated in lengthwise, and forms the wave with 'simple' nature in which the amplitude function B(e) does not
change the sign in the demain of /6/=Ov'/2.
Con-sequently, it is the most important requirement for the most effectiveness of the bulb that the main hullbow-wave also forms the 'simple' nature wave. In the opposition to the above, if the wave-making character-istic of the original main hull is complex, the bulb negates the some part only and the total effectiveness of the interference can not be expected so much.
In the above conception, the main hull end wave
and the simple bulb wave are corresponded on the equal condition and the wave-cancellation is obtained with the combination of them. The engineering approach, based
on such concept to realize the waveless stale, is called as the first class waveless form, and are distinguish-ed from the other process attempting to employ the more complex wave-making interference described below. In the last reports, actual ship's photo 7 corresponds to
the former and the photo 6 corresponds to the latter. In the first class waveless forms as described above, it is necessary first that the main hull wave should be 'simple' because considered the combination of the simple main hull and the bulb. And the dimension of the main hull wave is not important so much. Of course, it is more desirable that the dimension of the wave s
small under the practical requirement to reduce the
necessary size of the bulb as possible. This fact is the main cause that, anyhow; satisfy the fairly the present theory for the wave-making involving many insufficient
problems. The view point for the above will be detailed in the "Wave Analysis" written in the following
para-graph.
"Wave Analysis"
For the problems of the wave-making interference, the requirement for the approximately equal amplitude (b) may not be treated so highly nervous, however, the requirement for the reverse phase of (a) should be treat-ed as respectably sever. At the usual speed of the marchant ship as Fn=0.l5-0.35, the ratio between the basical wave length X0 and the ship's length L, Xo/L, is about 1/7 to 2/3. Especially, at the low Fn value, even supposing the phasical difference values 1/100 L between the actually measured wave form and the theoretical
wave form, the requirements for the reverse phase
con-dition would be fairly broken because the phasial dif-ference equivalents to the difference of the phasial angle of the wave by IO'. At the present status of
the wave-making resistance theory, it
may be
pos-sible to obtain the theoretical wave form on the given
ship's forms approximately, however, it should not be allowed to guipe down the whole of ihem. Con-sequently, it is indispensable to know where they
cor-respond to in detail and where they differ from by corn-paring the theoretical wave forms obtained from the calculated results with the observed records of the actual
wave forms obtained by the suitable method during the running of the models in the experimental tank. For the wave observation techniques, the conventional meth-ods employing the measure of the wave profiles from the ship's side only is indispensable, however, there are something yet to observe essentially. Because the wave profile on the ship's side corresponds the vertical section of the transverse wave,/e/0-..35°16, in the free wave patterns, the information for the diverging wave,/e/= 35°I6'9O', spread into the transverse direction at the outsides of the ship can not be obtained.
For
supple-meeting these faults, the vertical pictures or the bird's eye views are effective, and the stereo-analizing them with two camera, the contours of the wave elevations in the whole wave patterns can be obtained, and result in the complete information as the wave information made by
the models. In the conventional experimental tanks, the whole arrangements of the tank housing and the construction of the towing carriage are designed moon-veniently to observe the whole model's wave as dea-cribed above especially to take a vertical photographs. Taking a decade since 1955, the University of Tokyo have been taking away these several faults at the own experimental tank, and then the University can do at any time to optically observe the model's wave pattern and to stereo-analyze almost adequately. The outline of the improvement is described in the Reference I 8.
Photo I O and Fig. 8 are adduced from the initial study for the waveless
bow by
Dr. Takahei"19.The top (a)
of the photo
10 shows the bow-wave of the theoretical model C-201 and the bottom (b)shows the bow-wave of the model C-201 with
the bulb F2, and the Fig. 8 shows the
stereocon-tours of the (a) and (b) in the Photo 10.
When the wave contours as shown in Fig. 8 are obtained, the de--tails of the wave patterns can be understood in the whole. For the one method, supposing the number of the radial lines passing through the starting points of the wave, and then tracing the wave profiles on the each line result in the followings. That is, Fig. 9 shows the comparison between these wave profiles, at the radial angle H=15°, showing the results for the main hull model C-201 and the model with the bulb C-201 X F2 respectively in the top, and showing the difference be-tween the both wave profiles in the bottom. The bottom means the comparison between the component wave caused by the bulb and the theoretical wave profile of the doublet.
Although the theoretical starting point of the main hull bow wave should be in accord with F.P., obviously as shown in the Fig. 9, it is proved clearly in the experiments that the starting point locates forward from F.P. by 0.06 L. (For this reason, the center of the bulb was shifted forward from F.P. by the corresponding distance). Fur-thermore, it also proved that the spreading angle of the actually measured diverging wave is larger than the one of the theoretical waves at the one side by 45°.
At all events on the applying the theory as described above, the following attitudes are essentially necessitate to take the care about necessary requirements adequately in the first, and to compare with the experimental results positively, and then to take a step forward carefully.
After all the other, the requirement for the flat bot-tom shall be mentioned. The Model C-201 used by Dr. Takahel is obtained by the streamline tracing and has so
-Photo IO Wave patterns for Model 201 and
C-201F2 (F=O.267 K0L=14) (a) Model C-201 (without bulb)
4OMajn Hull %%ave (without Bulb) C-201
imeasured) ," '\ 20 !caIculted)
/
"
1420
,(ealculated) ,(measured)Fig. 8
Stereo-analysis for the wave patterns in
Photo 10
(a) Model C-201 (without bulb)
Bulb Wave (Difference between C-201 F2 and C-201)
Hull Wave (with Bulb)
C-201 F2 (mea cured) C
2 KR
O 40 20 o --20Fig. 9
Measured and calculated wave profiles on the radial line for Model C-201 and C-201F2 (0=
19°30 for measured wave profile, 0=15° for calculated
wave profile)May 1966 9
(b) Model C-201F2
(with bulb)
(b) Model C-201F2(with bulb)
mm
lhutu II
Rudy ulan Modd 1. S8 and S3 F3 Ihut u 12IroIiks
IotkJ 1 and S3 F3 3 4 s 6 9 -4 s¡
called 'curved bottom', in which the keel line hangs deeply at the midship instead of the flat bottom. Because any practical ships have the flat bottom, it is necessary to solve this problem in the practical use of the first class waveless form. However, it is easy to obtain the flat bottom ship form hydrodynamically. In fact, attempt-ing to solve this problem was started with the study at David Taylor Model Basin reported by Dr. P. C. Pien in summer of 1964. Consequently, during 1960 to 1961 when the concept on the first class waveless form and the study on the practical use of them were started, it is impossible to deal with this problem precisely.
Then, the practice in which the bottom hang at the midship of the ship's form with the curved bottom obtained from the stream-line tracing is cut off intrepidly and is combined with the bulb is employed
unavoid-ably. The first application of this concept to the high-speed liner is the bulb as shown in the photo 7. Another example, the comparison between the models for the Seikan Railway ferry boat and the wave pattern caused by the model at design speed Fn=0.267 (Vs= 18.0 knots for L=l2Om) are shown in the photos ii, 12 and 13. In these photos, SI shows the near best conven-tional form and S3 shows the form which has the aft body as same as SI and changes the forbody only to simplify the main hull wave characteristics as much as possible and to control the wave-making levels below the necessary height stimulatenously. (But, the bottom forms flat in the foregoing method). SI xS3 has the bulb F3 determined to realize the requirements for the approxi-mately equal amplitude (7) in the foregoing designing points against the S3. Where, the volume ratio of the bulb F5 is reduced by 60% compairing with the bulb F3 on the bulb's own wave height. And the bulb F4 is the optimum bulb which is selected for the position and the size from the conventional model Si to reduce the
resistance most effectively. Fig. IO shows these
wave-making resistance coefficient curves, L=2.4 m. From these figures and the pictures showing the wave patterns, the followings are introduced;
(I)
For the simple main hull, it may be allowed to take the rough treatment in which the midship's lower part is cut off. That is, the simplicity of the main hull wave, would not be disturbed so fatal with the above treatment. (To be compared the wave pat-terns of SI with one of the S3).The conventional forms have the complex wave-ma-king characteristics generally, and consequently, the interference effectiveness would be limited even if the considerably large bulb is installed.
lt is effective to determine the fore-body with the stream-line tracing, and once comfirming the op-timum position of the bulb by the actual measure-ment of the wave form, the size of bulb may be obtained with the compromised point between the theoretical value, corresponded to about 2% for the total displacement, and the practical condition. As described above, the reality of the bulbous bow has been clarified with the combination of the wave-making resistance theory and the wave form analysis.
However, it may be permitted to. say that the earnest study on the bulbous bow has just start, because there leaves mani problems as follows;
May 1966
J
s
o
Photo 13 Wave patterns (Fn=O.267)
Model Si
Model S3
t.
Model S3xF3
C,, is obtained bi using HugtteUn. with fo,'rn factor K.0.25
Designed Speed
Fig. 10 Wave-making resistance for railway-ferry boat Models Si and 53 (L =2.4 m)
li
PI. No. Without 9. With Bulb
SI F4
53
---0.15 0.20 0.25
Theoretical development of the ship's form which reduce the size of the bulb as possible and can obtain the wave vanish condition as same as the large sized bulb.
Fabricating techniques to join the bulb with the main hull.
The strict formularized expression of the bulb
form inclusive above. And the interrelation
be-tween the hydrodynamic characteristic and the above.
The occurence mechanism of the ship's bottom separating eddy. experienced frequently on the full
W. c. S. Wigley: The Theory o/the Bulbous Bow
and Its Practical Application, Trans. NEIS. vol. 52 (1.935/36).
G. Weinbium: Die Theorie der Wülst.cchiff e,
Shiffbaü (1935).
J. H. Michell: The Wave-Resistance of a Ship.
Phil. Mag.. vol. 45 (1898).
(IS) T. H. Havelock: The Wave Pattern of a Doublet
in a Strea,,?. Proc. Roy. Soc. A.. vol. 121 (1928). (16) T. T. Havelock: The Calculation of Wave
Resis-tance. Proc. Roy. Soc. A., vol. 144 (1934).
References
form just like the oil tanker and the preventir.. effectiveness with the above.
The interrelation between the bulb and the sel! propulsion factors including wake, and thrust de duction. etc.
The optimum design for the ship as the oil tanker in which the loading conditions change considerab-ly.
Today, after all, the shipbuilding party in Japan are wrestling with these problems enthusiastically under the close cooperations of the academic fields and the
indus-trial fields.
T. H. Havelock: Wave Pattern and Wave
Resis-tance, TINA. vol. 74 (1934).
T. Inui, T. Takahei. T. Tagori: A Guide Note for
Design of Ship Model Basins with Special Ref er-ences to "Wave A nalysis" Work, Proc. mt. Semi-nar on Theoretical Wave Resistance, vol. 2
(1963). Z
T. Takahei: A Study on the Waveless Bow, Part
I and II. Jour. Soc. N. A. Japan. vols. 108, 109 (1960/61).
4'
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