The rolling of ships under way the decrement of roll due to hull and bilge keels

THE ROLLING OF SHIPS UNDER

WAY THE DECREMENT OF ROLL

DUE TO HULL AND BILGE KEELS

B

G. S. BAKER, O.B.E., D.Sc., Hoi.

Fellow;

of the William Froude Laboratory

A Paper read before the NOrth East Coast institution

of

Engineers

and Shipbuilders

in

Newcastle upon Tyne

on the 27th October,

1939.

(Excerpt from the Institution

Transactions, Vol. LVI)

MWCASTL UPON TVNr

PUBLISHED BY THE NORTH EAST COAST INSTITUTION

OF ENGINEERS AND SHIPBUILDERS, BOLBEC HALL

LONDON

E. & F.

N. SPON. LIMITED, 57, HAYMARKET, S.W.I

E 1SFITUTION IS NOT RESPONSIBLE FOR THE STATEMENTS MADE,.NOR FOR THE OPINIONS EXPRESSED,

IN THIS\ PAPER, DISCUSSION, AND AUTIOR'S REPLY

MADE AND PRINTED IN GREAT BRITAIN

ROLLING OF SHIPS UNDER WAY

The Decrement of Roll Due to Hull and Bilge Keels

B G. S. BAKER, O.B.E., D.Sq., Hon. Fellow,

of The William Froude Laboratory

SYNQPSIS.Most of the published data on this subject have been

obtained from experiments with models and ships at rest.

In recent years,

all rolling experiments at the William Froude Laboratory have been made

with the models under way at their service

speed, as well as at rest, for

it hasbeen found that tests at rest might show some feature of hull or keels

as having an advantage which is very much modfied when the modl is

under way, and in general the decremental value, of such features when

under way, is not directly related to their decremental value when the ship

is at rest, and the latter, therefore, are no

real criterion of anti-roll values.

The experiments here detailed, with the exception of

the last model and

its modifications, have been made for various

firms, to obtain the effect of

speed; bilge keels and metacentric height upon rolling under way.

With

the last model several hull changes were tried to determine their effect upon

roll extinction.

The paper deals only with extinction arising from the hull

and its keels and is not concerned with the çffects

of any anti-rolling

mechanism.

An attempt has been made by normal statistical methods to formulate

a rough approximation for determining the extinctive value of any hull,

and afairly close approximation for any bilge keels on any normal ship at its

service speed in load conditiOn.

The criterion for this assessment is also

the criterion for maximum roll in synchronous waves and has a double

importance.

The effect of splitting the bilge keels into two discontinuous

parts is also shown.

Mode of Experiment

'THE models used for the test had the

usual smooth paraffin-wax

I

surface, and varied in length from 16 to 185 feet.

Their

dimen-sions expressed as for 400 ft.

ships are given in Table

1.

Each

model was ballasted to the normal load waterline.

An inclining

experi-ment was then made 'and the ballast moved vertically until the desired

metacentric height was achieved.

The ballast weights were then

"winged" horizontally until a rolling test at rest gave a period of roll

corresponding with the deired radius of gyration in the formula

Jgm

26 ROLLING OF SHIPS UNDER WAY

where 2 T is theperiod Port to Starboard to Port in seconds,

k is the radius of gyration in feet,

m is the metacentric height in feet.

The value of k for the two fine forms Ri and R2 was determined by The

William Froude Laboratory from the analysis Of the rolling of two

passenger ships of this type in the North Sea.

For the last form R7,

k was kept the same fraction of the beam, but for the others the value

used was that in the instructions received from the firms concerned.

The first six models were towed down the Tank by a wire attached to

the fOre-end a little above the water surface, the other end of the wire

being fixed to a stiff sprig. The model was guided by two vertical rollers

attached to the travelling carriage of th Tank, working between

hori-zontal rollers fixed in the model approximately at the level of the centre of

gravity.

This level was found from preliminary tests on two models R2

and R5 at rest as producing practically no intetferenco from the guide

rollers.

Later tests showed that this was not satisfactory if the difference

between the decrements of two models was small. The last model and its

variants R8 a, b, c, d, were therefore towed by the same tow wire forward,

and a rear wire aft, with a fair tension in both of them, and no guide rollers.

Each model when ready was tested at rest with and without these end

wires to ensure that they had no effect on the roll.

Each model when it had acquired its steady speed was heeled to about

10 degrees and then suddenly released.

The subsequent rolling was

recorded on a moving paper by two pens worked by very light vertical

rods, placed in a transverse plane at about amidships.

One of these rods

was attached to the model at the middle line, and the other eleven inches

from it transversely, both at the level of the centre of gravity. A record

of time in half Se onds was also taken on the same paper

The tests were

made usually at two or three speeds of advance, and with some models at

rest, and all runs were repeated.

At the lower speeds of advance there

was a possibility of a little interference, due to any long wave set up by the

model reflecting from the tank wall and catching the stern of the model.

Some such disturbance could be seen on the records, but was always

-slight. A set of typical curves of roll angle to base of number of rolls,

is given in Fig. 2.

Resistance to Rolling

When an upright vessel proceeding on a straight course is rolled to

one side and released, several things about the hull resist and modify the

subsequent motion.

These can be enumerated as follows :the skin

friction, the energy required for the streamline motion on each side,

the downward and lateral movement of the midship body, the lateral

movement of the ends of the ship and the diagonal movement of the bilge

keels.

These of course do not act independently of each other, but for

estimating purposes and in the following notes they are treated as separate

actions.

Taking the simplest actions first, both the deadwoods at the ends

28 ROLLING OF SHIPS UNDER WAY

lever 1 of the areas was seven-eighths the draught.

The other and more

difficult hull action to assess is the effect of middle body.

Referring to

Fig. 1, if the section were circular àf radius d, rolling would produce

no change, ar4 any action resulting from roll with a normal midship

section cai be regarded as de to the pottioii CAKflL rolling around

the cente core CA..

This has been regarded as a keel AB, whose

efficiency varies inversely as the angle AKB and a the radius r of the

bilge, and whosç leverage is the distance Q to centre of AB.

This

surface obviously becomes nil at those sections of the ship at which the

immersed part is approximately a semi-circle.

The distance between

these sections being x feet the value of

Area, (lever)2(efficiency) is defined by

x (1 r)

(l242)2

all dimensions in feet, and 1 being measured at amidships. Only one side

has been taken into account, as only one side of this "keel" is working

at any given moment.

For the frictional effect the same treatment can b adopted. The

frictional force will be exerted along the line of relative motion, which

1 _dO

will be at a small angle defined by

.1 being the lever from centre. of

roll.

The angular resisting moment due to this will be

:-fs.l2V()

where s is the wetted surface, 1 its mean lever about the rolling centre.

The methods of measuring the value of each of these features is open

to some variation in detail, but

they are thought to be reasonably

correct.

So far, all these resisting couples have varied with (). If a ship of

displacement W tons rolls from 0 on one side to 02 on the other in time

T the work done by a

resisting couple b () =

x b(012+022)

and this must equal the loss of energy in the ship='m(0i2_022)

0_022_

b

Hence

_{012+022 WmTr}

_{Wk/m -.}

/- approximately.

Hene the dcremet of roll due to any of the

foregoing actions of the

ROLLING OF SHIPS UNDER WAY 27

which ae advancing at the ship speed V, and at any moment moving

idO\

laterally with a speed 1

where 1 is the mean radius of each featUre

about the centre of roll, and 0 is the instantaneous angle of roll.

With a maximum roll of 10 degrees and a 10-second period, the mean

lateral speed comes to2 fs. when 1 is 30 feet, and is quite small compared

with the service Speed of advance.

These surfaces, therefore, can be

regarded as areas moving at small angles to the dfrection of motion,

i/dO

these angles being defined by p

where J' is the relative ahead

velocity at the locality of the surface concerned. For the deadwood forward

V0 is the speed of the ship, and at the lower end of the deadwood aft, it will

not differ seriously from this speed.

At amidships on a 400-ft. ship, the

velocity of the wake belt will vary from 0-5 Vat the hull surface to 0 1 V

at about one foot from the surface.

In general, therefore, the outer edge

of the bilge keel will be in water having a relative fore-and-aft velocity

not much different from the ship's speed.

The pressure on such a surface

Al

dO

of area A, will therefore be proportional toT (V)2

and the moment

resisting tolling will vary as A 12V ().

In the following estimates the centre of roll has been taken as in the

'water plane, and 1 has been measured from this to the middle of the keels

for bilge keel&

Fig.!

For the deadwoods, the area A has been taken as that from the keel to

075 the draught, from the end of the vessel to a section at which the

radius of this Section was One-third the draught, or at which the mean

slope of the section at the keel over this depth was 45 degrees.

The

ROLLING OF ShIPS UNDER WAY 29

Al2V1

_kVmjn5t

For skin friction, it can be given its precise value by taking f as having

s.12V

-a v-alue of OO28 for lb. fOot sec. tmits -and -

14Wrn T

W and V

being in lbs. and ft. per S.

With the eAception of one

action of the hul1=--the. energy absorbed. in

the disturbance of the stream

lineswe are able to. connect any

decrement

Al2V.

-obtained oll the model with its

value

_{yr "vm}

This connection brëáks

down when the initial assumption, that the lateral velocity is small

relative

tO the ahead velocity, becomes untënäble, and the effect

of such featuies

can then be dealt

with by assuming speed zero.

The effect of the disturbance of the streamline flow when rolling,

is a more diffiëtilt problem for which no solution has yet

been found.

The following comments, howevef, give a general idea of its

characte'.

In 1918f the atithor and

Miss Kea.ry read a paper describing

the changes

in transverse stability ofvarious ship models due to their speed

of advance.

The paper-showed that at moderate speeds Some gained and others

lost

stability, and suggested that the increase was obtained with

vessels having

either high ratios of beam to

draught, or high centres of gravity, the

data being indecisive on this point.

Payne's: work in 1924 showed a

gain in stability with some battleship models of the wide beam to

draught

type ófhull.

In all these tests the stability was measured by measuring the

inclination produced by a fliedmOthentin smooth water at various speeds,

and it included not only the effect of any ahead motion on the stream

flow,

but also the effect of transverse inclination, and it will be noted that the

fOrmer is a pure speed effect,

but that the latter depends upon and

varies

with the roll angle.

This variation Of stability with speed arises from several causes.

The

siftkage of the hull, and the fall in the level of the water against the

hull

affect the heights of the centre of buoyancy and hence the metacentric

height.

The inbrëäse of virtual gravity in wave hollows and diminution

at wave crests has an

effect which, although rery small with cargo

:aftd

passenger ships, becomes

important' at really high speeds, and leads to

- * It trill be noted that for the isochtonous rolling of a vessel in waves resisted by a

cOiileb (), the general

sol'ution of the equation of motion is

- If-

X'

Tmax

p-,, being the niaximum slope of the wave. When n is large theultimate steady roll

becomes o.?" B

or B in terms of the above. This expression

thCrefóre controls not only the decrement of roll, but the ultih:iate roll in synchronous

waves.

Trans. I.N.A. "Effect of longituciiml motion on transverse stability."

30 ROLLING OF SHIPS UNDER WAY

loss of stability before "skimming" is achieved

Transverse inclination

produces a transfer of pressure (and of wave-making) from

one side

to another, particularly towards the ends, and this transfer varies with

inclination, for all moderate speeds. When held at a fixedangle it shows

itself as an apparent variation in stability* (and was included as such in

the results given in the two papers quOted)

In reality -it is a resistance

(or assistance) to rolling, and in a rolling experiment would show itself as

such.

_{That these changes in pressure can be serious is shown by the}

fact that a high bow wave will destroy the longitudinal stability of

some

old-class submarines, when this has been reduced by partial submergence,

so that they are bound to nose-dive ; -also that som&seaplane floats at a

transverse angle, even at a small positive fore-and-aft angle, nose-dive

violently, and that planing vessels have capsized transversely

_{due to}

want of stability as they stop planingustially on a turn when somewhat

inclined.

More research is required to determine this, or even to show

on what features it essentially depends.

_{Probably something could be}

Jearned by taking Serat'sf midship bOdy models,

develOping ship forms

on them and testing these at speed, as he did at rest, with centre of gravity

at various heights, but this has not been attempted.

Results

To see whether the data available were sufficient to afford

a means of

estimating the decrement of roilfor any normal hull,

_{or its bilge keels, the}

decrement factors 9 found with the models have been plotted in Fig. 3

to a base of total value of A J2 V

_{estimated in the manner already}

Wk./m

given.

_{The data on which the figure is based are given in Tables 2a,}

b, c, d, e, f, g.

These show the estimated relative values of amidships,

deadwoods and keels, so far as eddy-making is concerned. The lines

joining various spots indicate the nature of the difference between

con-nected spots.

_{It will be noted that at the large abscissa values the speed}

effect is small. The models at this end were of fairly fine foms and

at the

top speeds there was, considerable wave-making, and this' probably

affected the "streamline" loss.

At the lower end the scattering of the

spots is not unreasonable apart from model Rh

The base of this curve does not take into account the effect of

any

wave-making due to lateral movement of the middle body or loss in

stream-line pressures, and the positive value of the ordinite for 'any form at zero

abscissa would depend upon this.

_{To obtain some idea of the decrement}

due to the flow past the hull, etc., the later experiments with model R8a,

b, c, d were made.

Model R8a was a normal form, similar to R7, but

c _{is also shown by the yawing moment which develops with transverse inclination.}

This moment is constant ncharacterfor lOw speeds, the model yawing to the immersed

side; but when material wave-making starts, the yaw momentreverses and is much

increased in the other diiection. t Soc. N.A. & M. E., 1933.

38 _{ROLLING OF SHIPS UNDER WAY}

TABLE 2(F)

Model Keels m

(feet) k Speed in knots

8'7

l26

165

RS None _{C amidships}

₁₀₀

_l45

₁₈₉

C from deadwood

₃₀

_{4 3}

_{5 7}

680

325

TofalC

130

188

246

from model 046 056 063 Carnidships

il7

170

223

C from deadwood

₃₅

₅₁

_{6 6} 276

TotalC

l52

221

289

from model 054 065

074

0728 ft.

Additional C fromkeels (from

43

6 2

8 1

325 model)

TotalC(froni

model)

173

250

327

l3lftlong

68O _ao - from model _{.067 .077 093} A = 191 sq. ft. _{Additional Ckeels}

_5l

_7.3

_9.5

276

TotalC

203

294

384

frommodel 085 093 108

ROLLING OF SHIPS UNDER WAY

TABLE 2(D)

TABLE 2(E)

Model Keels m (feet) k

--

_B Speed in knots

₁₅₃

₁₉₄

R4

1O4ft.

114 ft. long

156

36 C amidships C' from deadivoods Cfromkeels

127

135

171

161

171

216

A = 237 sq. ft.

TotaiC

433

548

from-mode1

172

188 Camidships

9.9

l26

CfromdeadWOOdS

105

13-3 V

26O 36 Cfromkeels

132

167

336

426.

TotaiC

frornthode1 146 175 Model Keels m (feet) k

-Speed in knot

85

l24

-162

R.5 None - -.328 Cajnidships CfromdeadWpOd -100 3.5

146

51

l91

69

51

TotalC

135

197

260

from model 055 065 075 CamidshiPS

114

166

217

V C-from deadwood

42

61

80

P288 Total C

156

227

297

from model 054

063

076 0.728 ft. 328 Additional C from keels

40

59

77

TOtal C

178

256

337

131 ft long

-51

from model

088

098

j()

A 191 sq. ft. V Additioral C from keels 4 3 6 2 8' 1

288

Total C

l99

289

378

from model 08l

090

110

36

iottno

OF SHE UNDER WAY

TABLE 2(c)

Model Keels m

(feet) k

-

Speed in knots

153

194

B R3 1 O4ft. C ainidships

260

330

114 ft. long

l56

36 Cfromdeãdwood

l23

l57

Cfrom keels

l96

249.

A=233sq.ft.

TotaIC

579

736

from model 205 214

208ft.

Camidships

260

330

156

36 C from deadwood

123

157

114 ft. lông C from keels

392

498

A.=466sq.ft.

TotalC

77.5

985

from model 270 . 3)() 1 04 ft. C amidships -

202

256

114 ft. long

c

from deadwôbd

95

12 1

260

36 Cfromkeels

l52

192

A=233sq.ft.

TotaiC

44.9

569

from model 160 160

208ft.

Camidships

202

256

114ft.long Cfrbmdeádwood

95

12I

260

36

Cfromkeels

304

384

A 466 sq. ft.

Tdta1C

601

76l

ROLLING OF SHIPS UNDER WAY 35

TABLE 2(B)

Model Keels m (feet) k Speed in knots

153

204

R2 None C amidships

214

285

161

36 Cfrom deadwood

167

222

TotalC

381

5O7 from model 180 194 C amidships

153

()i4

312 36 Cfromdeadwoo4

120

16O

TotalC

273

364

frommodel

llO

095

Additional C from keels

590

788

3.12ft.

161

36

TotálC

971

1295

114 ft. long from model 300 3lO

A=700sq.ft.

-

Additionaicfromkeels

425

565

312

36

TotalC

698

929

34 ROLLING OP SHIPS UNDER WAY

TABLE 2(A)

Swnmary of c

Al 2J7

and

Values

WkVm

0

Dime,ssions and Speeds for 400-foot Ship

Model Keels m (feet) k Speed in knots 15-3

204

RI

None Carmdships

43

57

C from deadwood 17-8 23-8 1-61 36

TotaiC

22-1 29-5 from model -16 -184 C amidships

31

4-1 C from deadwood 12-8 17-2 3-12 -36 -15-9 21-3

TotalC

fromthodel 092 -104

Each 3 12 ft. Additional C from keels 53-0 70'4

1-61 -36

TotalC

75-1 99-9

114 ft. long ₈₀

from model - 25 27)

A = 700 sq. ft. Additional C from keels 38-2 50-6

3-12 -36

TotalC

54-1 71-9

frommodel -154 168

312 ft. in two

Additional C from keels 51-4 68-2

lengthseachside 1-61 -36

TotaiC

73.5 97.7

from model - 261 -294

A==680sq.ft.

AdditionalCfromkeels 37-0 49-0

3-12 -36

TotalC

52-9

703

ROLLING OF SHIPS UNDER WAY 33

TABLE 1

Hull forms as 400-foot Ships

(For conditions of experiments, see separate tables)

x is the distance between those two stations at which the immersed section is

approximately a semicircle of radius d.

Bread

Draught Dis-

Coefficient Bilge Length Wetted

Dia-Model B

d

place- - radius x surface gonal

Block Mid sec

No. (fCet) (feet) ment,

- W

r

(feet). (feet) s (sq. ft.) (feet)I (tons)

Ri

572

218

7,110 495 86

166

214 25,800

282

R2 57.3

202

7,110

532

92

885

233 25,800

305

R3

S73

1975

7,220

56

96

78

243 25,800

306

R4

S61

202

7,220 55

885

109- 254 26,320

285

R5 55-3

217

9,250

667

983

5-10 240 31,600

328

R6 59.5

226

10,300 667 985 5-65 250 32,550 34-9 R7 60-6 23-2 10,150 -629 .973

7-i

240 30,550

352

R8(a) 60-6 23-2 10,150 629 973 7-1 240 30,550

352

R8(b) 60-6 23-2 9,318

580

83 24-0 240 29,900 28-5 R8(ó) 6O-6

232

9,084 -565

83

240

240 28,850

285

R8(d) 60-6 23.2 9,900 -615 .973 7-1 240 29,500 35-2

32 _{ROLLING OF SHIPS UNDER WAY}

abOut O2 on full to O3 on fine vessels for streamline and

wave effect,

and a similar, small decrement (see Table 3) for skin-friction

_effect.

_It

Will also be seen from the figure that the most effective way of increasing

the decrement, apart from fitting keels, is to increase the abscissa by

diminishing m, and this should be done as far as stability considerations

Will allow.

_{Before leaving this, it may be pointed out that the diagräth}

dñ1' holds

for loaded ship,

for ships under way at a reasonable speed, and

for ships in which the metacentric height is

at least 05 foot

for 400-ft. ship.

For ships with smaller m values the restoring couple

_{in the equation of}

roll is W (mO++ BM tan2 8) and this last terth becomes a controlling term

as m vanishes, and affects the whole performance.

Attention is drawn to the spots marked "split

".

Details of these are

given in Tables 2a and 2g. For several

years now, when the streamline flow

around the bilge of any hull has shown

any marked diagonal movement,

it has been suggested to firms that the bilge-keel trace should be broken

into two parts, stepping the after part above or below the forward as the

streamline indicates is necessary.

_{The opportunity was taken with these}

two models to test the efi'ect of any such break upon

the anti-rolling

qualities of the keels.

_{In general the split keel shows a small advantagb,}

except at low speeds 'where there was 'a small loss on One model.

It

would appear, therefore, that when a bilge keel trace cuts across a plate

edge and riveting becomes difficult, it can be shifted bodily to one side,

where the angle could be properly secured to the hull instead of leaving

the keel plate only partially supported, and if anything a small increase

in effect would be obtained.

ROLLING OF SHIPS UNDER WAY 31

fitted with a rudder and with

the propeller gap filled solid.

It had a

cruiser stern and-a moderate cut-up bow contour.

Its service speed was

about 17 knots for a 400-ft. ship.

This was rolled at a series of

speeds

in the condition specified in

Tables 1 and 3.

The midship body was

then cut away to a very rounded

midship section, leaving the load

water-line and the ends of the

model unaltered. This became model R8b,

which was also rolled at the same speeds as before. Th metacentric

height and radius of gyration were modified slightly to keep the product

(Wm) constant, and to hold the period unaltered, with the

changing

displacement. The "decremental" value of any part of the hull

then

remained unaffected by the change

in displacement. The ends of

this

model were then cut away, the new contours orcut-ups reaching the load

waterline at the fore-end, and the bottom of the cruiser stern at the

after-end, all sections being well

rounded at the bottom.

This became model

R8c, and was rolled at the same speeds as before, with m and k

adjusted

in the same way. Lastly, the midship body was

restored to a normal

form, but the ends were still left cut away,

giving model R8d, which was

again rolled at the same speeds.

The results with these four models are given in Table 3,

together

with the estimated decrements based on

Fig. 3 with regard to hull and

deadwood effects, with the addition of the decrements due to skin

friction.

The difference between the estimated and actual decrement

varies from

nil to

04.

The largest discrepancy occurs in estimating the effect of

cutting away the midship section to a

rounded form.

It may be that

some adjustment of the term assessing its value is requiredfor

example,

putting Va=about .9 V would improve

mattersbut the data are too

incomplete to make any suggestion

worth while.

This process of cutting

away portions of the hull inevitably affects the flow over what

remains

and this to some extent clouds the

results.

Thus, the removal of the

deadwood not only removed its resistance

to roll, but eased away the

bow

wave, and increased the slope of the area curve in the

fore-body.

Also

the vertical distribution of pressure was altered as well as the horizontal.

Again it would not be unreasonable to suppose

that in models R8b and

c the wave-making due to the rolling of the midship body

will be

neglig-ible.

Yet the effect of rounding the

midship section is almost negligible

(comparison a and b) and the decrement

of model R8c with little end

effect and round midship body, is

still appreciable.

The unaccounted

decrement in this case varies from

02 to 03 and this would appear to

be about the value of the decrement arising from streamline disturbance

during roll.

Actually this loss should vary inversely as the product (Wm),

so that apart from the effect of position of centre of

oscillation, the finer

the vessel the larger wifi be this

decrement.

It is considered that, in the main, the

general consistency of the plotting

in Fig.: 3 shows that the method can be used for comparison of hulls or

for

estimating bilge-keel effects. For vessels without

keels, a slant Such

as A B would be used, and with keels a steeper line such as

Cl). To the

decrements estimated from these slopes is to

be made a small addition of

10

06 04

DECREMENT OF ROLL IROM ONE SIDE TO THEOTHER

VALUES OF

FROM SPOTS BELOW.

MEAN ANGLE OF ROLL

0J

O1Q

cj On 0 -, 1O Oc

ANGLE OF ROLL FROM VERTICAL AT THE END OF SUCCESSIVE ROLLS.

4 6 7 q 10 II 2 iS 4. IS 16 7 IS

NUMBER OF COMPLETE ROLLS - PORT TO STARBOARD TO PORT

Fig. 2.Rolling in Still Water of Model R8a, Naked Hull in Load Condition at Various Speeds

Ii3

20

21

24

R8(c) mostly cut away

no

large _radius bilge

9,085

.

.

49

38

C from, deadwood not cut away 80 -- from Fig. 3

.

Skin friction decrement Estimated

l0

003 012 015 1 25 004 015 ' 019

140

004 017 021

155

005 022 027 Actual 8 023 O35 053 053 062 R8(d)

mostly cut away

no normal 9,900

445

'363 C

from deadwood not cut away

C from amidships Total C

.0 .

135

1 25 17'5 .

140

196

F55

216

. 145

l875

,

2l0

231

from Fig. 3

Skin friction decrement Estimated .04 012 052 052 fl5 067 059 017 076 064 022 086 Actual -022 -055 070 -083 ,, -096

TABLE 3

Variation of Hull ShapeEffect on Decrement of Roll

(Dimensions, etc.,. are for 400ioot ship.

Geizejal oari1cula'rs of 1w!! a Table 1.

Model Dead- wood Rudder Midship body W tons m feet

k_

B A!2v 80 Speed in knots

wkVflland

--0

l2'06

15'68 1749

193

Cfrom amidships 13'S 17'S . 19'6

216

Cfrom deadwood and rudder

-79

.

l0'3

11'S 12'8 R8(a) nomial yes normal 10,150

4'4

36

Total C

214

27'8

31'l

344

from 'Fig. 3 '05! 066 074

082

Skin friction decrement

012 '015 '017 '022

Estimated°

063 '081 091

104

Actual '022 '070 '083 '089 096

C from deadwood and rudder

..

79

. 103 11'S 12' 8 large from Fig. 3 '018. '025 .

028.

'031 R8(b) normal yes radius bilge 9,320 .

48

'376 Skin' friction decremeñt

. 80 '012 0l5 '017 022 Estimated -. '030 '040 .'045 '053 Actual '024

070

'082 '083 09C

ROLLING OF SHIPS UNDER wAY 39

TABLE 2(G)

Model Keels m (feet) k Speed in knots

1206

1568

1749

l93

R7 same as None

44

36

C from amidships Cfromdeadwood . : .

216

1OO R8(a) but

TotaiC

.

316

-towed

guidérs frOm model I I

-with

2O8 Additional Cfromkeels

246

274

3O3

ft

keels

4.4

36

TotalC

502

560

619

from model . 178 18l

With Additional C from

239

26 6 29 4

208

ft.

44

36 keels (frommodel)

keels

TotalCfrom

495

552

610

split model)

80

25 20 '10 _.05

Rolling of Ships under Way

DIFFERENCE IN ROLLING CONDITION OF THE SAME MODEL IS INDICATED BY THE TYPE OF LINE JOINING SPOTS.

ADDITION OF BILGE KEELS. VARIATION OF SPEED OF ADVANCE

-VARYING HEIGHT OF CENTRE OF GRAVITY.

AGAINST A SPOT INDICATES MODEL HAS BILGE KEELS. AGMNST A LINE INDICATES RADIUS OF GYRATION CHANGE:

DECREMENT OF ROLL, FROM ONE SIDE TO THE OTHER.

- MEAN ANGLE OF ROLL MEASURED FROM THE UPRIGHT.

SPOT MODEL TABLES

o o

R.I. IANO2a

XX

R2.

i'28

O c

R..

I

-1.1

R.4.

.I2S

A A

R.5.

I2

? V

R.6.

++

R.7. 5PLIT. 35 50 .0 70 80 qo 100 110 120 130

5CAL OF

DISCUSSION-ON "ROLLING OF SHIPS UNDER

WAY"*

MR. W. MUCKLE, Associate Member:

I am not quite clear how Dr. Baker

arrived at the expression for taking into

account the bilge-keel effect of the midship body. I should appreciate some explanation

of the derivation of the formula.

I presume that the model in Fig. 2

marked "naked" is without bilge keels.

The curves show the vast difference between

the effect when a vessel is under way and when it is at rest. The effect of bilge keels

seems to be due to the fact that lift is

obtained on the keel by the water approach-lag the keel with a small angle of incidence.

Further, it would appear that the value of

the lift increases with aspect ratio of keel, and it therefore seems that a great

improve-ment could be made in the present-day

bilge keel. Experiments on a Dutch naval

vessel have shown this to be so. The vessel

was fitted with a series of fins projecting

from the ship side which could be regarded

as a long keel split up into a number of

small keels of large aspect ratio. The aspect ratio was actually 4. From data published,

the great superiority of this -type of keel over the ordinary type is showa.

Since the bilge-keel action under way is

due to the angle of incidence of the keel relative to the water producing a lift, this

MR. JAMES F. ALLAN (Dumbarton):

This Paper contains useful information

on a subject which is still very imperfectly

known. The empirical method developed

by the Author to assess values of

appears to be applicable with accuracy

only to vessels of very -sumlar form.

In connection with the development of

this method, it

would be appreciated

if the Author would justify in more detail the arguments leading to the formula on

p. 27 for areax lever2x efficiency. Table 3

contains the test case for the method and an examination of this shows large

differ-ences between estimated and actual valtie of

especially in assessing the "amidship" effect.

The experimental results show some odd effects as, e.g. the marked influence of large bilge radius on the model without deadwood

compared to the model with deadwood. Also, the different influence of removing

the deadwood on the normal midship model md on the large -radius bilge-model is noted. If, as Dr. &ker suggests, these -differences

arise from mutual flow interference- and

'Paper by Dr. G. S. Baker, O.B.E., i-ion. FeUow See p.25 ante.

must also be accompanied by drag. Has this any appreciable effect on the

horse-power of a vessel under way and compared with the power necessary to overcome the

resistance of the keel when the vessel is upright?

Finally, I should like to ask Dr. Baker

if the ratio is independent of angle of

heel. I ask this because Froude in his work

on rolling gives the decrement as 80=

aO+b02.

MR. D. M. BAKER, Student:

With reference to

the values of given in Table 3 from Fig. 3, on plotting these in Fig. 3, it is not quite clear- how

the lines and their slopes were determined

80 when the values of

- were lifted.

It appears from the paper that models

R.l to R.7 were tested without rudders.

It would be interesting to know why this

was done, and whether they have any

material effect on the rolling properties

of a ship.

if that is as extensive as these results show, it infers that a successful analysis of rolling

characteristics must take it into account.

The method developed in the paper fails in this respect.

It is worthy of note that none of the

changes made on model R8 had any

appreciable influence on the stationary

tests. It is assumed that these tests were

made with the model's length across the

tank ; otherwise the results are -hopelessly

confused by interference from the model

wave reflected from the side walls.

-It is somewhat difileult to follow the

argument regarding streanline disturbance

at the foot of p. 31.

If one considers a long tapered solid of- revolution with its

axis on the waterline, advancing in line

with and rolling about that

axis, the

resistance to rolling will be purely frictional,

although the streamline would be to some

extent influenced by the frictional

dis-turbance. For all other forms the rolling

will cause a disturbance of the streamlines varying in degree with the departure of the

sections from circular form, -and

this disturbance of the streamlines -i,ifl in turn

produce pressure differences on -the hull

having moments about the axis- of rolling.

From this point of view the influence of CORRESP ONDENCE

2

DISCUSSIONROLLING OF SHIPS UNDER WAY

bilge keels is also obtained by disturbing

the streamline.

The unaccounted decrement of O2 to 03

of modeic R8 c mentioned towards the

foot of p. 31 is attributed by the author

to streamline disturbance. The removal

of the deadwood and the bilge clearly

greatly reduced the streamline disturbance caused by rolling, and any decrement then

left in excess of the frictional suggests

that the sections of the model R8 c were

not all semi-circular about the rolling axis.

(The sniill value of read from Fig. 3

in this case is obviously a very arbitrary figure, but it is unimportant.) This in its turn is bound up with the choice of line where the deadwood was cut off, so that,

in the absence of sufficient detail to

investi-gate the matter, it may be suggested that

the use of this residuary value as proposed

in the paper on page 32 will require care

and experience.

Referring to p. 29, the middle paragraph et seq., in our opinion the effect ofadvance

on initial stability is a rather different one

from its effect on rolling. Our experience

with finer and faster forms in

forced rolling tests shows that, generally speaking, the energy required to roll a ship to a given

angle increases rapidly with speed of

advance. This is in agreement with

published data available. Any slight

shoulder" in the fore-body waterline

form has a marked effect on the increase

of energy required to

roll the ship at

speed.

Referring to the top of p. 32, it is agreed

that the experiments show that if G.M.

is diminished the decrement is increased,

but the case is not so simple for, apart from the change of natural period brought about,

the ship with the smaller G.M. will roll

to a larger angle under equal sea impulses and this may completely offset the gain in decrement thus obtained.

Our experience endorses what Dr. Baker

has found regarding

split bilge, keels.

This splitting up, carried to its limit, gives the grid bilge keels of Mr. Rosingh which

on an area basis are immensely more

efficient than ordimry keels.

It is interesting to note from an examina-tion of Table 2, etc., that the effect of G.M. on the decrement is always less than directly

'reciprocal. A similar

effect has been

observed in forced rolling tests at

Dumbarton.

One feature of importance of which no mention is made is the very marked effect

on decrement-of boss webbing where fitted,

especially in fine vessels.

No figures for periods are given in the

paper. These would have been of nterest

o compare with the available evidence

that natural period shortens with increase

of speed.

One may be permitted in conclusion to

make one or two practical remarks

regard-ing the experiments. It is our experience

using paraffin models of similar size to

those in the paper, that great difficulty is

found in reducing the K value to the correct amount owing to the concentration of mass in the paraffin shell.

The remarks on page 26 on the method of towing are very interesting as, using a method similar to the first one described, great difficulty has been experienced in locating the height of the guide point to

avoid interference with the rolling.

The method adopted for model R8 is

open to the objection that the considerable

tension required in the wires to prevent

yawing, interferes with the sinkage

and trim of the model at speed, and this

in turn affects the rolling.

For tests statiOnary, the model may be

left entirely free of control if the roll is

measured by recorder on the model. For

tests advancing, some constraint is essential,

and a suggested arrangement is to fit a

towing frame such as

is in use at the

sea-plane tank at Farnborough,* attaching

the one end to a transverse bar swtably

mounted inside the model and the other end through a swivel to the towing point

on the carriage, as near the water surface as possible.

MR. H. BOCLER, Member:

Consideration of ship qualities and bilge

keels in relation to the rolling of ships

has, perhaps, been somewhat overshadowed

of late years by proposals for other

anti-rolling devices of various kinds. In general, these other devices involve control factors

needing expert handling on board, while

the ship's own qualities and the bilge keels are design features which more or less avoid

such complications. It is, therefore, very

desirable

that knowledge of the

anti-rolling effects of the ship's own qualities and bilge keels should. be explored to the full in order that, the greatest advantage may be taken of these features. This, I

take it, is the object of Dr Baker's valuable paper and it is very opportune that he again

draws attention to what may be termed

primary aspects of the subject.

An interesting feature in Dr. Baker's

results is the confirmation given of earlier experience as to the important effect of ship

speed in damping out rolling, and hence

the unsuitability of experience with a ship not under way for gauging relativeeffects.

As regards Dr. Baker's methods of

assessing the effects of the various factors dealt with by him, a practical point of view

is that, accepting these methods as the

DlSCUSSIONROLLl1'G OF. SHIPS UNDER WAY 3

One hesitates to criticize Dr. Baker on his suggested method of determining the retarding influence of the displacement

amidships.

I note, however, that I am

treading on safe ground, as Dr. Baker

acknowledges that the suggested method

re-quires further consideration. This is

clearly shown by the discrepancy between

the estimated

value and the

apparent

actual value in the case of models R.8a and R.8b.

Dr. Baker has probably not had Sufficient

time to proceed with further experiments

to determine this influence and it

has

probably already occurred to him, as it

has undoubtedly occurred to some of us,

that it would be useful to test a model of a

vessel of semi-cylindrical section having

the weights so placed to give approximately the same displacement, radius of gyration, and metacentric height as in model R.8b.

In comparing the midship sections of

R.Sa and R.8b models, it will be seen

that there is quite an appreciable amount

of displacement outside

of the

semi-cylindrical section in R.8b ; in fact, it

appears to be about half of that in model

R.8a. Therefore, it does not appear

reasonable to allocate a value of C=l35 in model R.8a and nothing in the case of

model R.8b.

Dr. Baker's approximate method of

determining the retarding value of the

midship displacement is ingenious, but I

have no doubt that he will now be studying some other approximate method of

assess-ing this value.

For instance, I think it

should provide some value for the

displace-ment outside of the semi-circular section

in the case where the bilge diagonal distance

L is equal to the draught, but where the half-breadth of the load waterline

amid-ships is greater.

Everyone appreciates that the data given

in the paper represent a great amount of

work by Dr. Baker and his staff. Many

experiments and much time are required for the presentation of such information

'which, in

turn,

is so clearly given in

condensed form for Our use.

That it is

useful to have this information I think we all agree and are thankful to have it; but

at the same time, I cannot help feeling

that the result of wave energy on a

practically inert mass such as a ship at sea, differs so much from the result obtained by applying a momentary force to a model in

a tank, or a ship floating in an inert mass of water, that despite all our knowledge of rolling, the design of a ship as regards

rolling will be mainly decided by practical experience in choosing a suitable metacen-tric height, sUitable area of bilge keels, and range of stability.

MR. R. W. L. GAWN, R.C.N.C. (Haslar):

It would be appreciated and facilitate

I(i

result of Dr. Baker's expert investigation,

his formulae may be generally used for

comparisons. In this connection, I think

it would be an advantage if Dr. Baker

would give for one of the models the detail

calculations as to how the results in the

tables have been arrived at, making clear the units employed.

I am surprised that in case of models

R.8 (b) and (c) the actual rolling

experi-1

ments should have shown so little effectfor rounding the bilge of the midship body.

I can give no quantitative figures, but

general report had led me to the opinion that a round bilge, unless the effect were masked by deeper bilge keels, was

un-favourable from the rolling point of view.

Dr. Baker's formula for form effect also

leads to the same inference. Taking for

example model R.8 (b) at l206 knots the

e.

estimated value of -- is given m Table 3 ()3, against 063 for the round section.

The.actual value for the round section from

the model rolling experiments is 07. Here

is a discrepancy of more than 100 per cent. Some further investigation seems necessary

before the inference can be accepted that

the rounding of the section does not affect

the results. I notice all the models tested

by Dr. Baker are of fairly

fine block

coefficient, and would thus not have much actual parallel middle body, if any. Perhaps this has a bearing on the matter.

I notice in the technical press that the

new large passenger motorship Oranje just completed in Holland, has been fitted with

a novel arrangement of bilge keels consisting of a series of projecting blades of

stream-lined form in section, connected by a

longitudinal strip

at their outer edges.

This arrangement is also stated to have been previously adopted with success in a Dutch

torpedo boat. It would be interesting to

have Dr. Baker's opinion of this arrange-,

ment.

MR. N. H. BURGESS, Member:

Dr. Baker's paper on rolling experiments

is of great interest and is another example

of his practical methods of helping the

average naval architect.

The value of bilge keels is clearly shown

in the diagram and tables.

It would,

however, be interesting to know whether

Dr. Baker could supply us with some

useful methcd of determining the pressure on the keels from the information obtained

in these experiments. This would appear

to be possible now that Dr. Baker has

approximately determined the proportion

of the resistance to rolling due to the

fitting of bilge keels. Such information

would be of help to us in deciding what could be the greatest depth and thickness

for a single-plate bilge keel without having to. resort to the more costly V-type of keel.

4

_{DISCUSSIONROLLG OE SHIPS JNER WAY}

further analysis

if

the information given

in the paper could be supplemented by the

addition of

extinction curves with and

without bilge keels. _{These would permit}

ofa comparison with warships, which it is

inferred from Figs. 2 and 3 have a greater standard of damping than the vessels dealt

with in the paper. This is probably due

partly to thó bilge keels being of greater

extent and area than in merchant ships

and partly to the quicker periodofwarships.

In this latter connection it would be of

interest, if particulars of the rolling period

of the various models could be added _to

the tables. The rolling period is not only of great importance as far as extinction is

concerned, but it is also of use to the naval architect in estimating strength and stiffness

of masts and other high erectiOns and for

considering reaction on sensitivity of

instruments.

Would the Author please state whether the units of the various quantities in the

abscissa function Care knots, feet and tons.

It is noted with interest that the most

satisfactory method of tow was by

a

tensioned line without guide rollers. This confirms experience at Haslar as described

in the paper by Mr. M. P. Payne, read

before the Institution of Naval Architects

in 1924, which procedure is still found the

most satisfactory.

-The Author prefers 80/0 for the

decre-ment and it would be appreciated if he

would state the value of 0 to which this applies. At very small angles ofroll it is

reasonably constant, but in warship models it shows considerable variation even within

the moderate inclination of 10, degrees

dealt with in the paper, and more so up

to 20 degrees. Considerable variation of

86/0 with angle is apparent from Fig. 2. The results afford striking confirmation

'd :of the great increase of extinction when a

ship is under way as compared with rolling

1 at rest. Experiments with warship models

do not, however, support the Author's

statement that rolling, experiments at rest are "no real criterion of anti-roll values." We have not as yet made a test in which the arrangement of bilge keels which was

found most satisfactory at rest was not

also the most satisfactory when under way.

This result indicates that experiments at

rest afford a suflicient criterion for satisfying the primary object of most rolling

investiga-tions with models, nairiely, to obtain the

best damping with

the least possible

prejudice to propulsive performance. As

usual, the resistance of the naked hull

increases at a much greater rate with

:speed than that of the bilge keelsa fact

clearly brought out in the papersince

the

_{extinction of models R.8 (c) and}

R.8 (d), which is due almost entirely to

hull, increases rapidly with speed. Thus,

the smaller the bilge keel, the greater the

proportional effect of motion ahead on

damping. In vessels of high speed such

as destroyers, the extinction due to the hull

is only a small proportion of the total at

rest, whereas at full speed it is about half,

the increased damping due to the hull

_at

speed being greater

than the increase

due to the bilge keels. _{These effects of}

bilge keels may arise from the flow being

non-uniform, and the reaction is governed

not only by velocity of roll and the speed

of ship, but also by the hydrodynamjc

reverse current at the bilge when rolling..

The effect of the acceleration and

decelera-tion of water square to the plane

_{of the}

roll may well be much greater than_that

due to the velocity of flow past it, parti-cularly having regard to the exceedingly small aspect ratio of the bilge keels and

the effect of wake.

This action and other effects of inter-action between the hull and the various

appendages which are, in the present state of knowledge, necessarily neglected in the

Author's analytical treatment, must limit

the application of the method proposed.

The problem is an extremely complicated one and the Author's attempt to estimate

the extinction characteristics is ingenious,. but in view of the formidable complexities,

it is not surprising that considerable

differences are found, as witnessed by the width of the band of spots in Fig. 3.

It is, however, greatly to be hoped

that

Dr. Baker will be able to extend histests

and analytical treatment to throw further

light on this complicated and important

subject.

PROFESSOR T. H. HAVELOCK, F.R.S (King's College, Newcastle upon Tyne): The results in this paper, and Dr. Baker's

analysis of them, confirm his view that

the hull of a ship may have features whose

decremental value when the ship is under

way is not directly related to the value

when the ship is at rest. _{Nevertheless, I}

hope that experimental work on suitable

models at rest will be continued. It should

be possible to devise experiments _{to give}

information which is not yet available

for instance,

_{if we had more reliable}

estimates of the resisting moments due

_to

friction and eddies, we should know how

much had to be accounted for by

wave-making or other causes.

Moreover, a

complete theory would include the _shii>

at rest as well as under way ; we could

then distinguish more clearly the effet

of speed upon the action of any feature,

whether by increasing the magnitude

_of

the action, or by altering its character.

Dr. Baker's analysis shows that

the

general problem is simplified in -some

respects when the ship has sufliciënt speed

ahead.

For instance, he takes 80/0 t

DISCUSSSIONROLLING OF SHIPS UNDER WAY. 5

approximation, both in theory and as

deduced from the experimental results

shown in Fig. 2.

It is not quite clear whether any of the

resisting moments when the ship is at rest,

remainin operation when it is under way,,

in addition to those more obviOusly affected

by the speed. On p. 30 with. reference to

Fig. 3, Dr. Baker refers to the positive

value of the ordinate for any form at

zero abscissa.. This curve,, if completed,

would give the variation of 80/U with,

the speed Vfor a given form;

the'inter-section of this curve with the zero abscissa

line would give the value, say P, of e /0

for the. ship at rest.

Dr. &ker shows

that for sufficiently high values of V, the

curve approximates to a straight line, say,

L+MV. Is L or P the value referred to

by Dr. Baker, or is it some other quantity,

and what is its relation to the actual

value for the form at rest.?

The same point occursin..the estimates

for the forms R.8in Table 3by the method

explained on pp.

3 1-32. The various items which are estimated, appear 'to be those proportional to the speed ; but, on

the preceding argument, it would seem

that some constant term should be added,

presumably some portion of the

decre-mental value at zero speed.

The action of bilge keels when the ship is

rolling and under way

is specially interesting. Dr. Baker's description of the keel as effectively a plane area at a small

(variable) angle to the direction of motion,

suggests the analogy of an aerofoil,

the-force normal to the bilge keel corresponding

to the lift on the aerofoil. It is hardly

likely that one could evaluate this force by results from normal aerofoils; among

other reasons, the bilge keel is of very cmiIl

ratio of span to chord, it is attached to

the bull along one edge, and the angle of

attack varies periodically. Nevertheless,

the analogy gives a useful picture of the

action;

further, the increased effect

obtained by splitting the keel is readily

understood from this point of view.

I should like to ask if Dr. Baker could add one more item to the results given in the various tables, and that is the

decre-mental value for each model at zero speed;

this is already given for model R.8, and

if the values are known for the other types,

it might be possible to include them. This information would be useful because the paper is an important contribution to the

subject and is sure to be studied carefully,

not only for practical purposes, but also by anyone who attempts further work on

the general problem.

Ma. TI-IAMAS MflRTS()N

Vice-the William Froude Tank, especially in

connection with the resistance Of hulls and propeller experiments, the, latest

investiga-tions carried out at the Tank in an effort

to determine the effect of the form ofhull

and appendages, combined with weight

distribution on rolling,

axe bound to

be of general interest, especially to those who have, from time to time, to travel by

sea and- who axe more concerned with their

personal comfort than with the efficiency

of the propeller or the resistance of the

\ship to forward motion.

it is noted that some of the experiments

were made on the the model of a

vessel

which traded 'between this country an

Scandinavia, a comparatively high-speed

passenger ship, and the results of

these

experiments are noted with interest. 'One

unfortunate circumstance which vessels on

that trade have to endure, is that the

prevailing winds and seas very often follow

the ship on the after quarter: which

pro-duces uncomfortable rolling, especially

when the natural periods of the ship and the seas' synchronize. To overcome this,

the course of the ship has to be altered,

and actually this is often done during the meal hours on several ships on the same

route.

In some of these vessels

there being

spare deadweight and capacity, theG.M.

can be varied, but experimenting in this

way did not

produce any appreciable

improvement in the behaviour of the.ships.

By increasing the depth of the bilge keel,

however, to

about 36 in. and making

it of a special form; a definite improvement

was observed.

Actually, the maximum

inclination of roll due to synchronization

was not very much reduced, but

the maximum rolls occurred less frequently.

It would be of great value if a model

could be tested in waves of various lengths

and at varying angles of approach. DR. A. M. ROBB:

Dr. Baker has given values of k based

on analysis of records of rolling.

Is it

too much to ask that the analysis should

be published as an appendix to the present

paper? The consideration underlying the question is that theories of rolling motion

are crude and ill-developed,

and it

is

possible to expect improvement in the

theoretical treatment of the subject only, if all records of actual rolling motion are

made fully available.

This consideration is connected again

with

another matter which

is merely indicated by Dr. Baker in his penultimate

paragraph. The indication is

that m

akine is not an adeauate measure of the

president:

'

stability element in he determination of

While members of the shipbuilding and the period of the roll. it is possible that

shipowning industries are well infOrmed Dr. Baker does not sufficiently emphasize

6 DISCUSSiONROLLING OF ShIPS UNDER WAY

(To be continued)

not accompanied by such an effect. This

again may be justification for the inclusion of a BM term in the expression for period.

In view of numerous expressions of

opinion in technical publications as to there being no disadvantage in generous

metacentric heights, it is refreshing to

find Dr. Baker advocating minimum

metacentric heights.

He thus takes his

position alongside the master mar ners

who, from their knowledge of happenings at sea, deliberately load their shipS so that excessive stability is avoided.

MR LLOYD WOOLLARD, R.C.N.C.

Dr. Baker has made a bold attempt

to estimate the resistances to rolling

caused by the various elements of a ship's

form and appendages. The results obtained

by his theory for the R.8 models seems

to be more reasonable than those actually observed, and one wonders whether some

experimental error is possible.

The observed data, with one exception, support the established view that a sharp

bilge is more resistful to rolling than a

rounded bilge.

The "Bryan" effect is

evident, though it is found smaller than one would have expected.

If we compare the results on R.1 (bilge radius 166 feet) with those on R.2 (bilge

radius 885 feet), taking The same G.M.

the same speed, and the same bilge-keel

area, it appears that the sharper bilge leads

to a decrement about 20 to 40 per cent.

greater.

If no bilge keel is

fitted, the

advantage is very slight. The comparison obtained when comparing the results on

models R.8 (c) and R.8 (d), to which

bilge keels were not fitted, shows an

advantage of SO per cent. in favour of the

sharp bilge. However, when comparing

R.8 (a) and R.8 (b), the increase of bilge radius from 7 feet to 24 feet makes very

little difference to the decrement. The

large deadwood in these two models might

be expected to mask any difference, but

hardly to obliterate

it. This suggests

that a sharp bilge without bilge keels

cannot be relied upon to reduce rolling.

The results as a whole confirm the value

of bilge keels as roll reducers, a matter

of interest

to warship designers who habitually fit bilge keels of much greater

area and extent than those usually adopted in mercantile vessels.

I hope Dr. Bakerwill be able to continue

these valuable experiments, and throw

more light on some of the unexpected

features he has revealed.

J which are reputed to be guilty of severe

rolling although their metacentric heights

are relatively moderate, while being greater than the O 5 foot mentioned by Dr. baker;

/and it

would seem that the value of BM

is an important element.

The modern

tendency in design being generally towards

large beam-draught ratios,

it

is also

towards large values of BM in relation to m: hence, it does not seem possible any

' longer to exclude a BM term in the

expres-sion for a period of roll.

Dr. Baker does not pretend that his

assessment of the effect of hull features

can be correct in

detail, although he

considers the total result to be generally reliable. There does, however, seem to be

a need for fairly drastic modifications since

it is apparent that the effect of speed is

serously over-estimated. Tables 2(A)-2(G)

show that the increase in C value wtih

speed is invariably much greater than the

corresponding increase in p36/0. In this

con-nection it would be appreciated if Dr.

Baker would expand his treatment of the

method of assessing middle body. The

origin of the denominator in the expression near the top of page 28 is not obvious, nor

is it easy to see why an efficiency factor is introduced at that stage.

In the same connection it would seem

that the treatment of the effect of bilge

keels is open to question. The question

arises from comparison of the results of

fitting bilge keels as shown by the records

for forms R.l and R.2 in relation to those for R.5 and R.6. For the former models,

with displacement of 7,110

tons, the

increasó in due to keels of 700 sq. feet

area is just about the same as that in the latter, where the bilge keels are less than

one-third of that area, and the displacement

is, roughly, 40 per cent. greater.

The

explanation would seem to lie in the fact

that the latter forms have much sharper

bilges than the former:

and there is

I

theOretical justification fOr the belief that

bilge keels are more efficient on sharp

than on easy bilges. It would seem that

Dr. Baker's treatment does not adequately

recognize this consideration.

It may be interestin'g to note that increase

of period due to reduction of m is

accom-panied by an increase in

of greater

extent than the increase in period, whereas