Experiments with bulbous bows

MEDDELANDE

FRAN

STATENS SKEPPSPROVNINGSANSTALT

"(PUBLICATIONS OF THE SWEDISH STATE SHIPBUILDING EXPERIMENTAL TANK)

Nr 3 GOTEBORG 1944

EXPERIMENTS WITH BULBOUS

BOWS

BY ANDERS LINDBLAD

es'S

))AT 4,01, IINA1611 ;

44oaa

GOTEBORG N. 3. GUMPERTS BOKHANDEL AB

GOTEBORG 1944

Synopsis.

The first part of the paper contains a review over some of the results that have been obtained by Tevnon, BRAGG and other investigators who have done research work with models fitted with bulbous bows. An attempt has also been made to present the results in some diagrams suited for design work.

The second part of the paper gives an account of some experiments which have

recently been cirried out with some models representing an intermediate liner intended for fairly high speed. One model-of an ordinary-form has been tested and compared with some models with bulbous bows of different sizes and constructions.

PART I.

Notes on The Design of Bulbous Bows.

The introduction of the bulbous bow is as is well known not a

new development but one of rather old standing. AlreadyWILLIAM

FROUDE experimented with it some 80 years ago, and in the British

Navy it was very early used in the form of the ram bow. Ih the more

modern form it was developed experimentally largely by TAYLOR,

and by him introduced into the American Navy on many vessels. The most extensive tests done were carried out at the Washington

tank, and these have been described by TAYLOR in an article in

Marine Engineering and Shipping Age, September 1923.

In "Sped

and Powers of Ships", 1910, TAYLOR has also used a form with a

very small bulbous bow for the standard lines of his series. Later on a series of experiments with bulbous bows was carried out by

BRAGG at the University of Michigan. The results of these tests are

given in a paper in the Transactions of the Society of Marine

MEDDELANDE FRAN STATENS SKEPPSPROVNINGSANSTALT NR 3 For the theoretical explanations of the wave phenomena connected with the bulb we are indebted largely to the works of 'HAVELOCK, WIGLEY and WEINBLITM. WIGLEY has in a number of papers given the results of his experiments and explained the mathematical

treat-ment of the problems. The most important of these papers seems to be "The Theory of the Bulbous Bow and its Practical Application" published in the Transactions of North East Coast Institution of

Engineers and Shipbuilders, Vol. L II, 1935-36. WEDIBLITM has on several occasions discussed the bulbous bow and has also done some

extensive series of model experiments. These are described in a

series of articles in Sclaiffbau 1935-36 and in a publication from the Berlin tank under the title "Theorie der Wulstschiffe".

The models used by these two research workers have had

mathe-matical lines, and the wave resistance could under certain assump-tions be calculated. But the lines of their models are not well suited for direct application to practical ship construction.

Some of the general conclusions from the investigations are,

however, of ,large value to the designer.

When it comes to application to actual design work it is necessary for us to go back to the research work of TAYLOR and BRAGG. In their series the models were of ordinary ship-shaped forms of a fullness appropriate to present day high speed ships.

The fullness and the useful speed.

From TAYLOR'S experiments one would expect that even at lower

speeds .say down at speed length ratios of 0.70 it might

some-times be profitable to use a bulb construction.

HOGNER also expresses the opinion that with a bulb large enough

there might be reduced resistance even at speeds as low as V/YL

of 0.67 to 0.70. His opinion was based on some experiments made by himself, which have not yet been published. WErNBLum has also expressed the same opinion.

For the higher speeds say at V/YL higher than 0.8t L there

are abundant proofs that a correctly constructed bulb can materially

reduce the resistance, so that at these speeds the adoption of a

bul-bous bow is a commercially sound proposition. The best results

AN DERS LINDBLAD, EXPERIMENTS WITH BULBOUS BOWS 5

Ships for these speeds have naturally rather small block- and

prismatic coefficients. BRAGG'S series has a prismatic coefficient (T) of 0.55. TAYLOR'S series A has a g, of 0.60 and series B a fp of 0.65. Some of WIGLEY'S as well as WEINBucrm's experiments have been made with models of very low block coefficient. One of WIG-LEY'S series has a block coefficient as low as 0.436.

It has been found that the bulb is of the greatest advantage in ships that are "over-driven", and some of the best results have been

obtained in such cases where a previous model with high resistance has been changed and provided with a bulb.

If, however, we start with a very good model of ordinary design and wish to improve this by constructing -a bulb, the chances are that the gain will be rather small, especially at low speed length

ratios.

The construction of the bulb.

The sectional area curve.

When a bulbous bow is used, the sectional area curve of the

fore-body differs materially from that of an ordinary bow construction. As a rule a fairly large part of the displacement is transferred from

near midships to the forward end of the area curve.

It is usual to describe the. characteristics of the sectional area curve by the size of the bulb, f, and by the slope of the curve at the

bow, t.

We define f as the ratio between the area at the forward

perpendi-cular and the area at the midship section. If f = 0.04, this means

then that the area of the bulb is 4 % of the area of the midship

section.

Fig. 1 shows how by TAYLOR'S method we define t, the slope at the

bow of the sectional area curve. Draw the tangent to the area curve

at the perpendicular.

This tangent cuts off a distance = lt

at

midships. Call the midship ordinate of the sectional area curve ix.

it

The slope is now expressed by t

If as usual we have an area at the bow with corresponding

it

ordinate = l, then the slope will be t

6 MEDDELANDE FRA.N STATENS SKEPPSPROVNINGSANSTALT NR 3

Thylors' Sec//ono/ Area Curves

= C:65 r 1g Fig. IA. o=0.60 3.0 Fig. 1 B.

The form and location of the bulb.

In TAYLOR'S experiments the bulbs were very narrow at the load

waterline gradually widening down at the keel so as to give almost

triangular sections, as shown by A on Fig. 2. From a practical point

of view such sections are hardly suitable because the flat surface

down at the bottom will in pitching probably cause serious slamming.

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ANDERS LINDBLAD, EXPERIMENTS WITH BrLsors BOWS

In most of other experiments the bulb has been formed like an elongated pear as B on Fig. 2. Some other forms have also been

tried. HOGNER, for example, has tested a bulb of cylindrical form with an eleptical section as shown by C on the figure.

Another type of bulb, marked D on Fig. 2, has also been tried.

This would, perhaps, more correctly be called a "soft nose construc-tion". This type of bulbous -bow has been investigated by WEIN-BLtrra. In his researches some of the sectional area curves are of a

similar character as those which in early days were tried by WILLIAM

FROUDE and described as S w an -ne ck forms. It is known

that some recently built ships have been constructed with this kind of bow with very blunt round endings at the upper waterlines. This is in direct contrast to the very sharp fine ended upper waterlines

used in the models of TAYLOR and BRAGG.

The majority of experiments seem to Show that the best results

have been obtained with the maximum thickness of the bulb placed as low as possible. In spite of the good results obtained by WEIN-Bum& with bulbs of type D on Fig. 2, he himself states') that they are objectionable because they throw a large mass of water spray over the whole forward part of the ship. The fact that some types

of bulb by water spray cause a wet deck has by some designers been

considered as such a serious drawback that on that groUnd alone

they have objected to the adoption of any kind of a bulb.

1) Discussion p. D15 of Wigley's paper, Trans. N. E. Coast Inst. of Engineers & Shipbuilders 1935-36.

8 MEDDELANDE FEIN STATENS SKEPPSPROVNINGSANSTALT NR 3

With all the various types of bulbs the lower waterlines have, in

general, been rounded off either by circles or by parabolic endings,

and the terminations of all the waterlines have been on a vertical

line through the forward perpendicular. In some experiments,

however, both WIGLEY and HONER have tried bulbs protuding under

water forward of the perpendiculars, and these bulbs have in some

cases shown very good results. WIGLEY states in a paper') "Unless

the lines are extremely hollow, the best position of the bulb is with its centre at the bow, that is, with its nose projecting forward of the

hull". In the early work of R. E. FROUDE with warship models it was also found that a bow with the ram protuding down under the

waterline gave very small resistance. From the viewpoint of con-struction there are, of course, serious objections against the re-introduction of the long ram bow, but the more moderate use of it,

as proposed by WIGLEY, can probably be accepted to advantage.

Recent patent applications have shown that also a system with

two bulbs combined have been under consideration. _{One of the}

bulbs should be located at or near the load waterline and the other

low down. This would give some frame sections near the stem of

a form resembling the figure 8. Nothing is known, however, about

the results obtained from any constructions of the kind.

The selection of suitable values of bulbsize (f) and tangent (t) for drawing the sectional area curve.

In his works TAYLOR gives some very useful diagrams showing which and t values should be chosen at the different speed length

ratios, and it is mainly from his and BRAGG'S data that Figs. 3 to 8

have been prepared.

TAYLOR has used two different series of models. One has a

pris-matic coefficient of 0.65 and the other of 0.60. The sectional area

curves of these series are shown in Fig. 1. A gives the prismatic

coefficient of 0.65 and B gives 0.60. _{In each series several bulb}

siZes have been used, and the results are given in form of cross curves from which the various 1 and t values call be read off. BRAGG'S series

covers the lower prismatic coefficient of 0.55. In his series only

three values of bulbsizes were uied, and no cross curves are available for this series.

ANDERS LINDBLAD, EXPERIMENTS WITH BULBOUS BOWS r =a 65 If the models the dimensions Length B. P. Breadth Draught A V/brf .0850 Ro/4 Z Rrld v/vr .0etos R,A =17 Ifir =0.7/5 Rrid -1.10 (111 150 00)3

05

0 0.5 10 1.5 2.0 Tangen4

The con/our lines "give 7the region of /7.

residUary. resis;lance in /be per io.1 Fig. 3.

The prismatic coefficient of 0.65. (TAYLOR'S series B).

of this series are expanded to a length of 400 feet

would be

= 400 feet .Block coefficient = 0.6435

= 64.64 feet Mid. section coefficient = 0.99

= 29.2 feet Prismatic coefficient = 0.65.

= 32

The breadth is in excess of ordinary merchant practice and the

B

ratio is also rather large.

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On Fig. 3 is drawn a composite diagram, which is composed from -TAYLOR'S diagrams in "Speed & Power of Ships". For the given speed length ratios it shows the regions within which the residuary

resistance is a minimum and gives suitable values of f and 1. From

this diagram Table I and Fig. 4 have been obtained. They give the

f and t values that should be chosen at the different speed length ra-tios. The middle f curve, gives the optimum values, but other values

within the shaded area can also be used. The corresponding best

values of t are shown with the dotted curve marked optimum tcurve. It should be noted that this curve for the lower speeds gives negative values of the slope I. This means that the sectional area curve some small distance aft of the perpendicular would have a smaller area than f. It is not easy to accomplish this in practical construction, andwe should use the values given by the proposed t curve instead.

If / = 0, this indicates that the sectional area curveruns parallel

with the base for some distance. That would lead to a cylindrical

bulb. Such bulbs with a parallel part have also to advantage

been used in some cases. HOGNER has tested some bulbs of this type which gave very good results.

Our diagramS show that at lower speeds only a very small bulb

should be used. At Via lower than 0.70 f should be only 3 % to

4 %, and as has been mentioned previously it is often doubtful

if it pays at all to use a bulb at these speeds. At higher speeds again

there is an advantage in using large bulbs. At Virf = 0.80 / should

ANDERS LINDBLAD, EXPERIMENTS WITH BULBOUS BOWS 101

should increase to about 18 %. The corresponding t values should

be as shown by the t curve. That is, t should be between 0.1 to

0.2 for speed length ratios up to about 0.85 and 0.3 to 0.6 for the

higher speeds. If smaller bulbareas are chosen - as on curve B

- the values at the

higher speeds should be taken somewhat greater

as given by the curve marked t for curve B. All these t values will

lead to sectional area curves with very marked hollowness forward.

Table I.

' The prismatic coefficient of 0.60. (Taylor's series A)

The dimensions for this series are

Length B. P. = 400 feet Block coefficient --= 0.552

Breadth = 45.66 feet Mid. section coefficient = 0.92 Draught = 13.62 feet Prismatic coefficient = 0.60

A

\ 3 - 60

3.35 100)

This series has proportions and coefficients corresponding to some cruisers and high speed liners. Such a small breadth as has been

used can, however, very seldom be accepted in merchant ships. The

small draught makes it hard for the hulb to be fully effective.

Speed length V/171 0.65 0.70 0.75 0.8 0.85 0.90 0.95

Bulb area f % 3.6 4.0 5.0 7.0 10.0 14.0 18.0

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ANDERS LINDBLAD, EXPERIMENTS WITH BULBOUS BOWS 13 The results from this series are given in Figs. 5 and 6.

The optimum f increases gradually with the speed. Starting with

% at a speed length ratio of 0.7 it reaches a maximum of about

13 % at V/YL of 1.2. The usual speed for this fullness (5 = 0.552,

is a speed length ratio of 1.0 to 1.1. In order to take full advantage of a bulb construction here, we should use a large bulb with 11 %

area and a tangent slope t of about 0.95. It is interesting to note

that for the whole useful speed range t is around 1.0. Only at the

higher speeds does ,t increase. If smaller / values as on curve B

are used the t values should be increased correspondingly as given

by the upper t curve. The results for this series are summarized in

Table II.

Table II.

The prismatic coefficient of 0.55. (BRAGG's series)

In this series two displacement length ratios were used. The

dimensions corresponding to the 400 foot ship were

Displacement length ratio =60 100

Length B. P. 400 feet 400 feet

Breadth 42_8 feet 55.27 feet

Draught 14.56 feet 18.8 feet

Block .coefficient 0.539 0.539

Midship section coefficient = 0.98 0.98 Displacement .... . ... = 3840 tons 6400 tons

2.94 2.94

Speed length ... 0.7 0.8 0.9 1.0 1.1 1.2 1.3

Bulb area 1 % 7 8.3 9.5 11 12 13 14

14 MEDDELANDE FRAN STATENS SKEPPSPROVNINGSANSTALT NR 3

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Fig. 7.

At the smaller displacement length ratio of 60 the breadth is

un-usually small, but at the higher displacement length ratio the breadth

is more normal. Fig. 7 shows the sectional area curves used in

BRAGG'S series.

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ANDERS LINDBLAD, EXPERIMENTS WITH BULBOUS BOWS 15

The usual speed for this fullness is a speed length ratio of 1.05

to 1.15. Only two bulbareas (f) 4 % and 8 % have been used, and

the interpolation for other values is therefore rather uncertain.

I

have, however, in Fig. 8 tried to draw curves also for other f values.

At speed length ratios below 0.8 there was nothing gained by the

bulb. The best slope t of the tangent varies with the displacement A

length ratio. F of 60 it is about 0.45 and for 100 it is

about 1.12.

The results are given in Table III.

Table III.

(100)

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PART II.

Experiments with Models of a Liner.

For this series of experiments a model No. 55 was donated

by A. - B. Götaverke n,

which Company also paid for the

tests of this model. All the model experiments described in this

section were carried out at The Swedish State Shi

p-building Experimental Tank in collaboration with

the Department of Naval Architecture of the Chalmers Un

versity of Technology in Gothenburg.

Description of original model No. 55.

This model represents an intermediate twin screw liner with a length between perpendiculars of 465 feet (141.729 meters).

The service speed was to be between 19 and 20 knots.

The particulars are as follows:

Fig. 9 shows the body plan and Fig. 10 the profiles of the ends.

A full naidship section has been used. The rise of floors is 9 inches and the bilge radius is about 7 feet (2.1 meters). There.4.is no parallel midship body. For reasons of stability a large beam has been used and in the forebody the frame sections are V formed. A cruiser stern of moderate size to suit a twin screw arrangement has been

adopted.

Length B. P. 465'-0" = 141.729 m

Length W. L. ... ... 477'-0" = 145.387

Breadth

67'-0" = 20.421 m

Block coefficient 6 0.594

Midship section coefficient .... . ... # -= 0.975

ANDERS LINDBLAD, EXPERIMENTS WITH BULBOUS. 17

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ANDERS LINDBLAD, EXPERIMENTS WITH BULBOUS BOWS 19

Fig. 11 shows that the sectional area curve is rather hollow in the

forebody. If we define the hollowness (h) as a percentage of the

ordinate at midships as shown on Fig. 11, h is about 8 %. The

sectional area curve in the run is quite straight with a hollowness of about 4.5 % The load waterline, shown in Fig. 12, is nearly straight in the entrance with a hollowness of only about 3 °A. The entrance angle is about 93/40.

The resistance tests with model 55.

The model was run at two draughts. The Aoad draught on the

ship was 7.7 meters (25.26 feet) giving a beam draught ratio of 2.65.

The light draught was 6.4 meters (21 feet) aft and 5.4 meters (17.7

feet) forward. With a mean draught of 5.9 meters this gives a beam--

er

The results are given in Figs. 13 and 14 as curves of C, vueess.

draught ratio of 3.46.

The model was fitted with a rudder but had no other appendaa

and as effective horsepower (E.H.P.) for a 400 foot ship. In Figs.

15 and 16 they are also given as © values.

v2/3 x \./3 Ci E.H.P. E.H.P.

° =

427.1 A213 X V3 V = Displacement in na3 A Displacement in tons V = Speed in knots

This model No 55 showed, in comparison with several other models,

good results at the resistance tests of both draughts, and it seemed

to be satisfactory for the speeds which we wished to reach. In order

to find out if, perhaps, even better results could be obtained by

some minor changes on the model, some further experiments were

decided on.

Tests with model 55 a.

It was thought that a smaller increase of the length might, possi-bly, decrease the resistance. We wanted to make this lengthening

without making any great changes on the original model, which we

wanted to preserve for some further experiments. In order to do

this some parafin extensions were melted on to both ends of the woo-den model. In this way the model was lengthened so as to represent

Load wetter lige," for models 53 556 55c 55c/ "14 '15 55, 55b Fig. 12B. 53c 550'

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ANDERS LLNDBLAD, EXPERIMENTS WITH BULBOUS BOWS 21

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I-019 020 2;21 022a' _23 2122 0125 026 027 022 029 0.30 CL.w 032g

Fig. 13.

a 475 foot ship (144.77 meters). These extensions of 5 feet fore and 5 feet aft produced only very small changes in the character of the sectional area curve. In fact, they only gave to the sectional area curve some longer and sharper ends, while the increase in

displace-ment at full draught only amounted to 66 m3. This small change

could not be expected to carry with it any greater changes in the

resistance. Fig. 13 shows the results for the load draught condition. The wetted surface increased approximately 1.3 % with

correspond-ing increase in the frictional horsepower. At all speeds below 19.5

knots there was an appreciable increase in the wave horsepower. At

lower speeds the increase in wave horsepower amounted to about

6 % compared with model 55 and at 19 knots there was an increase of about 11.7 °/0. At higher speeds, however, the wave horsepower showed a decrease, which at 20 knots amounted to 5.5 %. The total horsepower, frictional ± wave, of model 55 a wasincreased

for all the lower speeds up to 19.5 knots. The maximum increase

of 4.5 % was reached at 19 knots.

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The results from this kind of lengthening with 10 feet _without

any radical change of the sectional area curve _{were accordingly}

rather discouraging, and some other changes had to be tried. A

comparison with some other sectional area curves suggested that a small shift of the displacement further aft might, possibly, produce

better results. The easiest way to accomplish this was to _{run the}

model at some trim by the stern.

Model 55 a was accordingly towed at two different trims by _the

stern. At a total trim of 1.0 meter by the ship (3.28 feet) the change in the resistance was hardly noticeable, but at a trim of 1.5 meters there was a reduction at the higher speeds. Below a speed of 17 knots there was no change. At 18 knots the reduction in the total resistance was 1.3 %, at 19 knots it was 2.4 %, and at 20 knots it amounted to 3.5 %.

Another test was run with the model trimmed by the _{stem to}

correspond to a total trim of 1.0 meter on the ship. This trim did

not produce any noticeable change. Hence, a small shift of the

dis-placement more forward cannot be expected to procure a better

driving model. The experiments with the model trimmed by stern

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ANDERS LINDBLAD, EXPERIMENTS Willi BULBOUS Bows 23 seemed, however, to indicate that a change of the sectional area

curve with a shift of the displacement further aft would be of advan-tage. That would in all probability also be the case, if the same change was Made on the original model 55.

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24 MEDDELANDE FR4N STATENS SKEPPSPROVNINGSANSTALT NR 3

Experiments with Bulbous Bows.

From a study of various experiments with bulbous bows it appeared that for this type of liner sometimes a bulbous bow would be advan-tageous, and we decided to try this construction on the original model

55. This bulb was constructed purely as an addition to the old

form. The sectional area curve was changed only for the length of

the bulb, and on the load water line there was no change made from the original model. This gave model 55 b. It was, of course, realized

from the start that this was not the right way of constructing a

bulbous bow, and it was done more as a sort of preliminary test.

Further tests were therefore decided on. For these experiments

more radical changes on the models were needed. A whole new forebody was constructed in which both the sectional area curve

and the upper waterlines were entirely changed. This gave model

55 c with a bulb area (f) at the stem of 7.5 % of the midship area. Later this bulb was cut down to an area of 5 % while retaining the

main part of the forebody as before. This change gave us model

55 d.

Model 55 b.

Fig. 11 gives the sectional area curve. The bulb area at the bow was only 6.5 %, and the changes forward extended only for about

one fifth of the length of the forebody. The frame sections were

also changed only for the length of the bulb. The load line was kept

exactly as on model 55 as the body plan Fig. 17 shows. The bulb

was "pearformed" and extended clear down to the base line. All

the waterlines extended out to the forward perpendicular, and each

waterline was rounded off to a half-circle.

The slope of the sectional area curve (t) was about 0.5, and the

entrance angle of the load waterline was about 9.5 degrees. The

addition to the load displacement amounted to 98 m3, that is an

increase of about 3/4 of one per cent. The added Wetted surface

ANDERS LINDBLAD, EXPERIMENTS WITH BULBOUS BOWS 25

Fig. 18 A. Fig. 18B.

Body Pion

Model. 55 orki556 °

26 MEDDELANDE FRAN STATENS SKEPPSFROVNENGSANSTALT NR 3

The model was tried at two draughts, 7.7 and 5.9 meters. The

results from the resistance tests are given by Figs. 13 to 16.

Com-pared with model 55 the resistance at load draught is considerably greater with the bulb at all the lower speeds. At 17 and 18 knots

it is about 4.2 cy, worse. At the speed of 19.8 knots the horsepower curves cross each other and from this speed on the bulb is superior.

At 20 knots the bulb is better by 1.3 %, and at 21 knots the gain

amounts to 2 %.

Fig. 14 gives the resistance curves for the light draught. These

show that the bulb still gives a greater resistance at lower speeds.

At 17 and 18 knots there is a difference of about 1.5 %.

At the speed of 19 knots the resistances are equal, and at 20 knots there is a gain in favour of the bulb of 4.2 % and at 22 knots of 9 %. The fact that the bulb shows up relatively better at the greater beam draught ratio is a common observation. This is so, probably, because

at the smaller draught the bulb area is a greater percentage of the

midship section area.

"1k

Fig. 19 A. Model 55 C.

Model 55 c.

The sectional area curve of this model is shown in Fig. 11. The

bulb area at the stem was 7.5 % of the midship area. The area

curve was changed entirely from those of models 55 and 55 b. A

large part of the displacement was taken from the region near mid-ships and moved to the forward part of the area curve, so that this

ANDERS LINDBLAD, EXPERIMENTS WITH BULBOUS BOWS 27

The tangent slope t = 0.85. The load waterline is much sharper

than on model 55 b, and the entrance angle is 60 as compared with

9.5° on 55 b. The frame sections are more U formed. With these

changes the wetted surface was increased by about 1.5 %.

This model was also run at the draughts of 7.7 and 5.9 meters. At the deeper draught the resistance of this model is considerably

greater at all lower speeds below 19 knots than 55 and 55 b. At 17 knots there is a difference between 55 c and 55 of 9.4 % and at 18 knots of 7.3 %. When we come to higher speeds, the

condi-tions change and the bulb shows to advantage. At 20 knots there

is a reduction in the resistance of 6.9 %, at 21 knots of 10.8 %, and

at 22 knots the reduction is 12.7 %.

Model 55 had in the light condition been tested at a trim by the stern of 1 meter (3.28 feet), but model 55 c was tried at an even

draught. Both models were, however, tested at the same

displace-ment of 9680 m3. The model with the bulb shows also here a very

poor result at low speeds, and the resistance is increased by no less

than 16.3 % at a speed of 17 knots and 15.8 % at 18 knots. At

about 19.3 knots the curves show equal resistance, and at higher speeds the bulb starts to decrease the resistance so that at 20 knots there is a reduction of 5.8 %, at 21 knots of 7.2 % and at 22 knots

of 8.75 %.

Fig. 19B. Fig. 19C.

28 MEDDELANDE FRAN STATENS SKEPPSPROVNINGSANSTALT NR 3

Model 55 d.

From TAYLOR'S systematic bulb series it is clear that a bulb area

of 7.5 cyo as on 55 c is by no means too large. In fact, even better results might be expected with a somewhat larger bulb area. No such model was, however, tried because it was thought that a

larger bulb for certain practical reasons would be objected to. Our tests with 55 b and 55 c showed that at lower speeds the bulb

caused a marked increase in the resistance. It was thought that,

if we adopted a smaller bulb, the resistance at lower speeds might, perhaps, be decreased without any corresponding greater change

at higher speeds: Accordingly a model with a smaller bulb was

Made by cutting down 55 c to give model 55 d, in which the bulb area was decreased to 5 %. The body plan of 55 d is shown in Fig.

18 B .

Figs. 13 and 15 give the results for the deep draught of 7.7 meters. At the lower speeds of 17 to 19 knots there was practically no

reduc-tion obtained by cutting down the bulb area and the resistance

was still much greater than that of the bulbless model 55. Thus at

17 knots the increase was 9.5 °/0, at 18 knots 6.3 % and at 19 knots

3.9 %. Above 19.5 knots the resistance starts to become lower, and

at 20 knots it was 4.8 %, at 21 knots 9.1 % and at 22 knots 10.7 %

lower than that of model 55. At all these speeds, however, the gain

by the smaller bulb was lower than that obtained by the larger bulb.

The results from the light draught of 5.9 meters are shown in Figs. 14 and 16. At. the lower speeds there was a marked reduction in the resistance as compared with model 55 c, but the resistance

was still much higher than without the bulb. At a speed of about

19.3 knots the resistance curves of 55 and 55 c cross, and from this

speed on there is a gain in adopting the bulb. For 21 knots the gain

Summary.

It is interesting to note that while the "pasted on" bulb of

55 b does not materially increase the resistance at the lower speeds

as compared with the bulbless on the other hand it doesn't

help much in reducing the resistance at the higher speeds.

The sectional area curve adopted in 55 c and 55 d was

appa-rently good only for high speeds above a speed length ratio of about 0.88.

The bulb series of TAYLOR seem to indicate that, perhaps, a

more suitable sectional area curve might be obtained, if more of

the displacement was placed closer to midships and the curve was

hollowed out more nearer to the bulb. This would give smaller t