Trial trip analysis for six sister ships using a new method of analysis

ARCHEF

11-IYA.0-

OG

AERODYNAJSK

LABORATORIUM

HYDRO- AND AERODYNAMICS LABORATORY

Lyngby Denmark

Hydrodynamics

Section

Report No. Hy-2

. August 1963

Trial Trip Analysis for

Six Sister Ships

A New Method of Analysis

BY

C. W. PRO HASKA

Reprint from

Transactions of the North East Coast Institution of

Engineers and Shipbuilders, Vol. 78

Lab.

v. Scheepsbouwkunde

Technische Hogeschal

Delft

IN CO ON:

IS

'VESTER FARIMAGSGADE 31 COPENHAGEN DENMARK

TECHNICAL PRESS

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Hy-1 PROHASKA, C. W. Analysis of Ship Model Experiments

and Prediction of Ship Performance 5,00

Hy-2 PROHASKA, C. W. Trial Trip Analysis for Six Sister Ships 6,00

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No.: Author: Title: Price: D. Kr.

A-1 TEJLGARD JENSEN, A. An Experimental Analysis of a Pebble Bed Heat

Trial Trip Analysis for Six Sister Ships

using

a New Method of Analysis

by

Professor C W. Prohaska, D. Sc.

HYDRO- OG AERODYNAMISK LABORATORI

ILYNGBY

UM

Introduction.

Acareful

for two reasons: first, the results of analysesanalysis of trial

trip data

is essentialare

to be used in checking that the stipulations of _contracts as regards speed and horse-power have been fulfilled, and secondly because the correlation of these results

with those found by model experiments is

_{of the}

greatest value to the experimenters in serving as a

basis for future ship-trial predictions.

For both reasons, but especially for the latter, high accuracy in every step of the analysis is of importance.

Accuracy in the actual measured data is equally

im-portant, but unfortunately not always obtainable. Horse-power, for instance, is often determined as

in-dicated horse-power (with a maximum accuracy of

say -± 2 per cent), which is then reduced to brake

horse-power by means of the mechanical efficiency,

derived from test-bed data (also containing possible

errors of ± 2 per cent). The accuracy of torsiometers may or may not be higher, depending on the

calibra-tion.

To get an idea of the degree of accuracy obtainable

it

_{is therefore of value to compare the results}

ob-tained from sister ships. This was one

reason for

writing the present paper, another was that it

pro-vided a good opportunity to check in practice the

method of analysis of ship model experiments adopted at the "Hydro- and Aerodynamics Laboratory" (HyA). This method was described1 to the Institution during "The Symposium on Ship Trials and Service

Perform-ance Analysis" two years ago, and in a report from

the laboratory:2

Ship-Model Correlation.

Until a few years ago most towing tanks analysed

their model experiments in accordance with the

well-known Fronde method, and the greater part of them also used Froude's original frictional coefficients or

re-analysed versions of them. Experience has shown

that ship predictions derived in this way have to be

corrected empirically. The so-called tank horse-powers are given an addition of 10-15 per cent, according to

Paper read before the North-East Coast Institution of Engineers and Shipbuilders on April 16, 1962.

Numerals refer to list of References at the end of the paper.

the practice of the model basin. This

_{addition is}

tacitly assumed or openly stated to be a roughness

allowance. Some tanks also correct the revolutions

found in the self-propulsion experiment by taking into

account differences in loading and in wake coefficients for ship and model

For more than thirty years it has been clear to the profession that this method of analysis, although it

was believed to give acceptable results, was in no way

ideal, and was based on assumptions which in the light of more recent data were even erroneous. The flat-plate frictional coefficients derived by Fronde and others were not consistent with the Reynolds number

conception; the residuary resistance obtained in de-ducting the flat-plate frictional resistance from the

total included a certain form effect, of which no proper

account was taken, and finally the non-dimensional propeller coefficients derived from trial

trip data

plotted very differently from those found in the self-propulsion experiment.

These discrepancies were discussed at length at the

International Towing Tank Conferences and

else-where,3 but up to now no agreement has been reached

as to the substitution of any new method of analysis

for the classical method. Nobody is to blame for this:

a tank having its own set of empirical correction

factors is very reluctant to throw overboard the

ex-perience of years and change to a system, the merits of which are as yet unproven.

Unfortunately, the empirical corrections in use at the various establishments are not identical, as

im-portant differences existed, and still exist, in the

ex-periments themselves and in their analysis. As will be known, self-propulsion tests were carried out in

some tanks at the self-propulsion point of the model,

in _{others at the ship self-propulsion point. These}

circumstances combined with the use of different

friction lines, differences in the estimation of

ap-pendage resistance and with numerous smaller items,

account for the fact that no agreement was ever

reached on the empirical corrections.

When tankers started to increase in size the real

difficulties began. Overestimation of horse-power had been encountered before, but now became serious, as

the percentage error was most disturbing and could

Trial Trip Analysis for Six Sister Ships

using a New Method of Analysis*)

by C W. Prohasko, D. Sc.

Ship model correlation analyses were carried out for six sister ships according to a method, which differs in _{many respects from methods} in general use. The results appear in the form of _{differences between} model and ship wake, and as allowances _{on ship resistance derived} by "three-dimensional extrapolation" from model results. The wake differences agree well with values predicted on theoretical grounds, and the aCT- values are more reasonable than those derived for the

629.12.07

same vessels by other ,methods of analysis.

I

have very costly consequences for the parties involved.

20 per cent error on 20,000 h.p. is obviously worse

than 10 per cent on 5,000 h.p. From a purely scientific

point of view it was unsettling that the "roughness

allowance" now became negative. This took place not

only in cases where Froude's frictional coefficients

had been used, but was also apparent when the

Schoenherr-line or the I.T.T.C. 1957 line were

used.", 4, 5 All tanks are giving much thought to this

question to-day. Some have already introduced new

correlation methods,5, 6 others have not yet made their

choice. As this paper throws some light on most as-pects of the correlation problem it

is to be hoped

that it

will be of some interest, not only to tank

personnel, but also to shipbuilders and shipowners. As an illustration of the author's correlation method the speed trials of a series of six 10,000 ton tankers

were analysed.

Ship and Propeller Data.

The six vessels under consideration were built as

sister ships, delivered to the same owner. Their lines

were identical, and so were the specifications, both

as regards hull and machinery. All ships were Danish built, four by one shipyard (ships A, B, C and D), the two remaining vessels (E and F) by two other yards.

The trials for all six ships were carried out on the

same measured mile and at practically identical

dis-placements.

(7 = 1.025) 13430 t3 -=- 13650 t

Engine: Burmeister & Wain 2-stroke diesel engine:

Type 750 VTBF 110

Horse-power: 3160 b.h.p. at 132 revs./min.

TABLE 2Propeller Data

Diameter . 14ft. 8in. = 4.480 m

Pitch at 0.7 R 9ft. 10in. -= 2-995 m

Pitch ratio P/D = 0.669

Developed area 71.2sq.ft. = 6-62 m2

Disc area . 169.5sq.ft. =15.76 m2

Disc area ratio ... = 0.42

-3 4.0.10-, 51O-301O TANK CORRECTION CT TEST

v L

CT = p12 v2 °g RN = v '

R being the model resistance the density

the wetted surface (length times mean girth)

the model speed

model length on the water line, and the kinematic viscosity, all in consistent

units.

Number of blades ...

= 4

The diagram shows both the I.T.T.C.-line, defined by:

0,075 Model Experiments. _{Cv = p/2 v2 S -(log RN}

_-

₂₎₂

Model experiments were carried out with a

paraffin-wax model of scale 1:22, corresponding to a model and the Hughes lines:

length of 5.68m. or 18.63ft. and a propeller diameter 0,067 (1 K)

of 203.64mm. or 8in. Towing tests, open-water tests

_{- (log RN- 2)2}

and self-propulsion experiments were carried out for

the fully loaded condition as well as for a ballast con- The I.T.T.C.-line is seen to correspond to a Hughes dition, but only the first mentioned series of experi- factor

ments will be used in the following analysis. The

0,075

self-propulsion experiments were made at a number

1 + K -

_{0 067} = 1 12._'

,

of different propeller loadings to enable interpolation

for any desired leading of the ship propeller. In the towing experiment a speed range corresponding

The results of the towing tank test are given in

to 4 to 14 knots for the ship was adopted, the lower

TABLE 1Ship Data RN 30.108 4.0 5.0 6.0 7.0 8.0

Length b.p. ... 410ft. Oin. = 124.97 m 65 6:5

6.6 LOG RN 6'7 6.8 6.9

Breadth moulded . 62ft. Oin. = 18-90 m

Fig. I. The Model Resistance Coefficient iilidted to a Base of Log

Depth moulded ... 30ft.

9in. =

9.37 m RN.

Maximum draught moulded Thickness of keel plate .

Displacement in salt water

23ft.

llin. =

0.91in. =

7.29 m _{Fig. 1 as the non-dimensional resistance coefficient,} 0.023 m _{CT, plotted to a base of log Fix, with:}

4 TRIAL TRIP ANALYSIS FOR SIX SISTER SHIPS USING A NEW METHOD OF ANALYSIS

.

-.

-. .. ....

-+

TRIAL TRIP ANALYSIS FOR SiX sIsrFR SHIPS USiNG A NEW METHOD OF ANALYSIS

IIflIIHIflhIHHhIHIIkiHIHHIP1HflhUEIIIIIIIIHIflhIIlliHIIWt&1

- ....____

_UUW

o -_i__

t__i

-VP'4I3 i,uiwuiwu

'

UUUuuUU,IuuuuII,/IRrA

-..._.

IiiuuuuiuiiuuuuuuIuuuuurjtI

-

_{IUIUUIIT1UIII}

IIUII

L F!V/4 i -

I

U 1uuuUur/4 iiiuiiuu...uu

_

-.

'

UUUW

miu

V4U &iuu

...'...'.

uuuu , -o

_{.1lIIiuPriiiuuuuuIuuriuuR}

IIUUU /1111

,

_{IIrnuuuuuIuIIrauuIuIuuuMriaiI}

uiUiUuiiiiuuuiIiuiuuUUiUiNii

UUlIlIUIUIiIUiU!

uuuuuiiuuir u.u.u.Iø1uiI.r,u.uiu...i,L

-IIIIUUIIP!iuIhUIIIIIIIIUhuUIIIIIIIlUIIIflhuuIIuIllhiIIIuIIIII

IuhUJiIIIIUIIIuhIIIuIfluIIUIuuuIRuIuIIIIIuhIurnflhIIIIflIuI

IIIlIRlIIIIHllhIIIIllHIIhiu.uuiuiflIIIIIIIIIIlIIIIffOrJpuIiIII

p

o 0 0

0 D 0 m N0 a C iD

-,

--(0 0 -0 0 0 N Q q q - 0 0 0

--

.0

Fig. 2. Logarithioic Propeller Diagram.

I-

F-Ifl.LYM I1YS Q3iV1flD1Y

A.

II

I-A-0 -C Al .. - F--C

0zz

II II II U 2. 0, -E z I) U 2, Al 0 0 0 I-0

_I

I-0 I

F-I

II

I

F -Al 0 -C 0 F-3 z 0 0 0 A-I, I--C

Z)

II a-3

I

0 0 1 II N iii _l'(<

0-0

SI a II 0 F--C

I

U F--C II 0

F-I..

0 0 0 -C -C 3

I

.-Q F-0-C F - I--C 0 0

I I I

I.

I

a Id p-i

I

0 0. I-, 0 0 a-0 3 0 I-0 0 F, --C z 0-00 0 WI-00 00 --C 0_J 0 0

a--I

Al Ui U-z z 0 F-IA Z - I-z

I

z I, SiNIDI0

I

> I.-1YDfl2W0N z Al > 0 Al II > z 0 2 0 2 0 z II 0 I- a C? a 0 a. a I--o II cy .0a

0-0 U

I-I

_I- 00 I-0 -C 0 I-D

I

I.-U -C Al U -C Al 0 z U 1 U D I-0 0 F--C 0 I, -C -C -C a 0 > 0 LiJ F- a--J U.)

Expressed in Metric Units

** Centigrade

speed showing slight laminar influence. Stimulation

was obtained by studs corresponding to the N.P.L.

specification. A Hughes factor of 1.30 is apparent from

Fig. 1, and this factor will be used in part of the

subsequent analysis.

The results of the open-water and self-propulsion tests are given in Fig. 2, where the "open" and "be-hind" propeller coefficients are plotted on logarith-mic scales according to the usual HyA practice. In this way calculation work is considerably reduced, and errors resulting from independent fairing of the

different curves are reduced to a minimum. The method

of analysis explained below is independent of the

choice of propeller diagram and the enlarged sections of the diagram used in the wake analyses for this case were drawn to linear scales.

The Trials.

All the trials took place on the measured mile off

Hveen, a Swedish island in the Sound about 15 miles North of Copenhagen. A chart of the mile is given in

Fig. 3. The measured distance is 1,196.06 metres or

6,548.82 feet. The depth of water is 37m. or 20 fathoms.

The ships were all very nearly down to their marks.

Four were on level keel, one was slightly trimmed and

one had about 4ft. trim by the stern. All relevant

particulars are set forth in Table 3.

During each run indicator diagrams were taken on all cylinders, and total number of revolutions counted. The indicated horse-powers calculated have been

con-verted to brake horse-power by means of the

me-chanical efficiencies derived from shop tests. These

range from 0.88 at full loading to about 0.73 at 114-load.

One per cent was deducted for shaft losses to obtain propeller horse-power, p.h.p.

On the first trial it had not been possible to fit in

the necessary installation for measurement of apparent

wind velocity and direction. This is to be regretted, as the wind turned out to be rather strong (Beaufort

5-7) on that particular day. Absolute wind force was estimated and checked against the observations from

nearby light-ships. Relative wind direction was

ob-served during the runs and thus it was possible to

construct an approximate wind diagram, Fig. 4 b. For

the remaining five trials continuous readings of

re-lative wind direction and velocity were taken. The wind vane and the anemometer were mounted lm.

above the samson posts amidships, Fig. 10. From these measurements fairly accurate wind diagrams could be

drawn, Figs. 5b-9b. As the wind direction usually

varied -± 5° during a run and the velocity 10 per

cent, average figures were used.

The course was plotted continuously. During most

runs automatic steering was used, giving very small course deviations. When hand steering was used the maximum deviations were slightly

greater, on an

average 2-3 degrees, in a single instance as much as

5 degrees. The water depth, which is fairly constant,

was checked by the echo-sounder. Speed was calculated

from time observations in the usual manner, except

for Ship E. For this vessel the Decca dials were

photographed every 20 seconds. Thus the position of

HVEEN

HELSINGOR

COPCNHAGE

HALSINGBORO

THE SOUND

THE MEASURED MILE

ANDSKRONA

MALMO

Fig. 3. Chart of the Sound. Ship _{Trial Trip}Date of Hour Specific_Gravity Density

Sea Temper-ature Days out of Dock Moakled Volume of Displace-merit in3 External Displace-ment in Met ric Twig Mean Draught mid. in Trim by Stern Wetted Surface m2 Number of Runs A June 28, 1350 1130-1845 1,013 103,2 15° 14 13302 13561 7,292

0,05

3425 12 B Aug. 5, 1960 1030-1535 1,008 102,7 18° 22 13429 13623 7,355

0,025

3449 8 C Sept. 23, 1960 1330-1600 1,012 103,1 14° 23 13327 13573 7,305 +0,025 3433 4 D Dec. 30, 1960 0955-1145 1,012 103,1 4° 16 13335 13581 7,305 +1,294 3440 4 E March 15, 1961 1045-1300 1,013 103,2 4° 20 13251 13509 7,267 0 3422 4 F April 4, 1961 0900-1115 1,008 102,7 5° 1 13240 13431 7,261 +0,261 3417 4 M«Iel experiment 13245 1 7,264 0 1 3421

6 'TRIAL TRIP ANALYSIS FOR SIX SISTER SHIPS USING A NEW METHOD OF ANALYSIS

TABLE 3List of Trials and Corresponding Ship Data.

I

1.ILKNOT Ss=Ye+ 11 12 15 04 15 16 17 18 19 HOURS D: WEND-DIAGRAM 311° PHP METRIC 3500 000 9 25 DO 80 2000' 1500 H,y0,11M IT 0

r

to

z

2 12 14 IA( NO IS 0.018 0.01 0.01 0.0151 001 0.0

d:

WAKE =DIAGRAM Ka OPEN W TER a. 0.5 0.6 0.7 SHIP MODEL, 0.8 16 12'5 LI.:KNOTT 8.5 6.0 0.5 6 !I KNOTS' a: CURRE Wir-tiTAGIUM 5 10KNOTS 112sNi 1.11KNOT los p5 '16 HOURS

4/10

-111111111.01%,, 1PHP METRI 3000 i 2500 /2 1500, I 0000 H 90 1 11 12 11 KNOTS 0.018 0.0 0.0161 0.0T Kq OPEN WATER 0. la 11 ODEL 06 6 1.4 CURRE NT- DIAGRAM KNOTS Ar-Ve" 10 12 03 14 WEND-DIAGRAM 0 10 KNOTS

'TRIAL TRIP ANALYSTS FOR SIX SISTER SHIPS USING A NEW. METHOD! OF ANALYSIS

e=g-C: HORSEPOWER-DIAGRAM RE IN 1140 130 140 130 120 110' SHIP A MEASURED POINTS CORRECTED -"-TRIAL TRIP FEB. 1962 ANALYSIS

Fig. 4. Ship A: Tria Trip Analysis.

C :HORSEPOWER-DIAGRAM REVS/IN SHIP IB MEASURED POINTS CORRECTED -"-L. TRIAL TRIP FEB. 1962 C'ANALYSIS

gig. 5. Ship B: Trial Trip Analysis.

14040 3.0.10 CT- DIAGRAM 0 : WAKE-DIAGRAM e. CT- DIAGRAM C CT SHIP CFR( 1 +10.- 1.3 Cp ,7 C CTH C040+140.3' a, 46 12 KNOTS 6 670 .8.75 8.80 8.85 RAO 120 6 1000 3.0.1 100 001 0.01 2000 2 9 8.5

b:

9 0!7 0.8 LOG

a:, CURRENT-DIAGRAM IKNOTS TI >I b: WIND- DIAGRAM 3, %KNOT L,1 2 / K NOT

a: CURRENT- DIAGRAM C: HORSEPOWER-DIAGRAM

REVSAN 160 150 Of 30 KNOTS, N' :WIND, DIAGRAM, HOURS 12 HOURS 'HP MET RI 3500. 000, 2500 2000 HORSEPOWER-DIAGRAM R E V N 40 H P ₀ MET,RC 0 SHIP C MEASURED POINTS CORRECTED -"-13 IL KNOTS TRIAL TRIP FEB. 1962 I ANALYSIS

Fig. 6. Ship C Trial Trip Analysis.

SHP Dr1

MEASURED POINTS

CORRECTED

-)i-ORO Anal>, AA.

TRIAL TRIP FEB. 1962' ANALYSIS

Fig. 7. Ship, D: Trial Trip Analysis..

d:

WAKE -DIAGRAM 0.0171 001 0015 0.014 0.0 Kg 0.019 0.0191 0.0171 10.016 0.0151 0.013 .540 25.10' 1.540'1 865 ,8.70

CTH-d:

WAKE-DIAGRAM 11.4 SHIP! MODEL. 0.6 HI CrDIA GR AM: MODEL CFH1414K)1.3 125 13 135 KNOTS 8.70 8.75 8.80 625 LOGR. C1T to 6 1.4 1,2 10 0.8 0.6 at 0.2

8 TRIAL TRIP ANALYSIS FOR SIX SISTER SHIPS USING A NEW METHOD OF ANALYSIS

3000 250 200 I 12, 13 KNOTS 10 KNOTS 0,5

C:

- ISO 140 -130 20 20 3500_ 11 I2 114 0 018 0.014_ OPEN WATER 1.4 05 OPEN WATER -DIAGRAM 04 01.8 13 15 04 C p CT 11 -875 8,80 885 8.90

a: CURRENT-DIAGRAM b: WI ND- DIAGRAM 110 KNOTS Pup NETRI 3500 3000 C: HORSEPOWER-DIAGRAM REVS//M rN 150 140 130 120 3 4 250 200 1500 SHIP E MEASURED POINTS CORRECTED

d:

WAKE -DIAGRAM OPEN WATER MODEL e: CT DIAGRAM Cp CT CTH CFH . 10 .1.3 115 12 125 13 135 KNOTS 855 8.70 675 80 8 LOG

S. Ship Trip Analysis.

a: CURRENT-DIAGRAM KNOTS b: WIND-DIAGRAM 31 10KNOTS 131° C: HORSEPOWER-DIAGRAM 10 11 12 13 14 KNOTS SHIP F 0 MEASURED POINTS CORRECTED ... "°"*""""" FEB. 1962 TRIAL TRIP ANALYSIS WAKE- DIAGRAM Kg OPEN WATER OT CT-DIAGRAM

Fig. 9. Shin F: 1i iI trip Analysis.

TRIAL TRIP ANALYSIS FOR SIX SISTER SHIPS USING A NEW METHOD OF ANALYSIS 9

P H P METRI 20 300 14 12 KNOTS TRIAL TRIP FEB. 1962 ANALYSIS 74 016 RE VS4 /50 140 130 350 00 2500 2000 1500 055 8.70 8.75 _as _04 42 Kg. 0018 0.017 0416 0015 0414 0013 Fig. 0.017 0.016 051 10.01 1101

JO _{TRIAL TRIP ANALYSIS FOR SIX SISTER SHIPS USING A NEV METHOD OF ANALYSIS}

TABLE 4-Speed, Revolutions and Wind Data during the Six Trial Trips

' For \vs..). A, see text.

the ship could be plotted thirty-six times (luring a

twelve minute run. In this way not only can the

average speed be determined, but also speed and

course variations. Both were moderate, although the

wind was 5 to 6 Beaufort.

As the courses steered on the mile (311° and 131°)

PITOT LOG/

Fig. 10. Profile, showing Position of Anemometer and Pitot Log.

are not parallel to the axis of the Sound, which is

very nearly South, the currents along the

North-East coast of the island of Hveen, where the mile is situated, will necessarily have the character of a po-tential flow around an obstacle. It is therefore to be expected that a positive "wake" is present near the northern rape of the island from where the currents wilt increase in intensity in South-Eastern direction. The influence along the mile itself is probably very small, but this phenomenon might play a part on the

longer Deceit runs of ship E, which carried the vessel

very close to the stagnation line. .

The currents in the Sound are not regular tidal

cur-rents, but mainly dependent on wind conditions and temperature differences between the North Sea and

the Baltic.

For Ships C and F the velocity curve of the

fric-tional belt was measured by means of pitot-logs. The

results are shown in

Fig. 11. The observed speed,

revolutions and wind data are given in Table 4.

Trial Trip Analysis.

The analysis is illustrated in Figs. 4 to 9. Each of these contains five diagrams marked a to e. These diagrams correspond to five steps in the analysis

out-lined in the following.

As an introduction to the analysis some general

remarks on propeller diagrams will probably be of

value. The curves of KT = 2_ 4 , Kg = 2 5 and p D J K J

TD T-ve

= 2a = 27r Q

2tQn

plotted in Fig. 12 to a base of

ve v

= Thn = Thri

-w) = J0(1 -w),

are well known and need no explanation, nor do the symbols .used, except perhaps J., which means

ad-vance coefficient

for zero wake. A scale of

slip,

S = 1 - /fix has been added above the .1-scale. The figure also contains curves of the thrust

load-coef-ficient 8 KT ar = P/9 . v2_e

-D2

₄ TD Ka and of p = 3 .

of the thrust-torque ratio

_ _{7:111111211ELECIIIIM}

WIND VANE AND ANEMOMETER

Ship Nun)- DourRun

Lln-corrected Speed i.h.p. Revs. per Ap_ parent Wind Ap-parent Wind Di cc-Sea Dis-

turb-ber _{Knots (metric) Mi"'}

Knots* _from61)11 ancel

Scale Bow A 1 1136 8,21 1540 101,4 34 12 2 2 1213 10,51 1545 102,5 10 83 2 3 1251 9,49 1925 112,0 27 41 2 4 1325 11,35 1875 110.5 35 73 2 5 1358 10,49 2435 122,2 36 73 2 6 1428 12,05 2450 120,8 37 67 2 7 1519 12,81 4000 145,0 27 73 2 8 1546 14,37 3980 144,2 23 56 2 9 1651 12,44 3500 138,4 20 49 2 10 1722 13,64 3490 138,0 19 42 2 11 1807 12,79 3465 139,0 15 40 2 12 1842 13,52 3470 138,0 14 28 2 B 1 1035 7,67 805 81,3 12 92 1 2 1124 6,42 766 77,2 17 36 1 3 1223 12,09 2440 125,2 12 73 1 4 1256 11,41 2462 123,2 21 32 1 5 1348 13,33 3460 140,0 12 40 1 6 1418 13,02 3550 139,5 19 10 1 7 1503 13,40 3500 140,0 11 30 1 8 1532 13,14 3450 139,0 15 5 1 C 1 1335 12,20 2490 125,3 _{2,5 59 0} 2 1428 11,76 2540 125,2 21 15 0 3 1537 13,47 3540 141,2 6,5 40 0 4 1557 13,06 3510 139,5 21 10 0 D 1 1001 12,48 2630 127,3 3,1 5 0 2 1033 11,87 2560 125,0 14 2,5 0 3 1108 13,81 3770 144,6 6,4 6 0 4 1142 13,52 3755 143,2 14 2 0 E 1 1049 10,51 2620 125,2 31 15 2 2 1133 13,83 2680 127,5 11 165 2 3 1216 11,43 3510 137,8 33 10 2 4 1255 15,05 3560 140,4 7,8 155 2 F 1 909 13,38 2820 128,8 5,8 22 0 2 942 12,09 2745 126,5 22 21 0 3 1027 14,23 3730 143,2 5,8 14 0 4 1104 13,52 3650 141,0 23 20 0 -T' _Q -e I i I I

SHIP -V max

3

K,x10 K. Rx .3,7 108 Vm a x = 14,0 KNOTS t =14' 03% 900 mm _700 00 00 .00 300 200 100

These curves are rarely shown on propeller diagrams

although they are of the greatest importance for the understanding of the mechanism of the propeller as

a torque-thrust converter. Any vertical line in the dia-gram defines corresponding values of the coefficients:

T D KR

s, J,

K.

, J,

and ?I. A change imposed on one of these coefficients will therefore automatical-ly cause a corresponding change in the others.

The load-coefficient can be transformed as follows:

S/F = pI2 v2. F PI2 V2 * S ( 1 t )(1 ) 2 CT S/F

(1- t) (1-w)

6.0%

40%20010

5

'ói'

2 ₃ 6

Fig. 12. Propeller Diagram.

SHIP F Rx =4,0 Vrnax =12,6 KNOTS t =5' Timax 0.3 0,4 0,5 0,6 0,7 Q8 Q9 1,0 0.3 04 0,5 0,6 0,7

Fig it. .Velocity Gradients in Frictional Belt of Ships C and F

1,0 800 mm 700 600 500 400 _Under

where F is disc area

S wetted surface

t thrust deduction coef-ficient

w Taylor wake coefficient,

and

CT is the total specific

resi-stance of the ship or

model.

the assumption that t and

w remain fairly constant (luring

300 a trial trip the load coefficient is

seen to be directly proportional

200 to I he specific resistance.

If due to head wind the

resi-100 stance at constant speed increases

by a certain percentage, the load coefficient aT varies in the same

0

proportion. From this variation the new advance coefficient J =

rip is found, and this determines the new revolutions.

The horse-power is finally calculated by means of the

new KR-coefficient.

Let 1 be a point on the Kg-curve (Fig. 12). J

in-dicates the corresponding advance coefficient, and a, can be read off at point 3. If aT increases to the value-indicated at 4, point 5 is the corresponding Kg-value. When wake is present, the observed Kg-values when

plotted on J. will define a "Kg-behind" curve also

shown in the figure. As 1-wg = JTJØ the distances 1-2

and 5-6 in the figure represent the wake influence.

Remembering now that the speed measured on a trial

trip is generally the speed over the ground, which

due to currents present c, is different from the speed

through the water, i. C. vobserved = v c, it will be

understood, that J.-coefficients (points 7 and 9 of Fig.

v c 12), calculated by means of observed speeds _nD , can

differ considerably from the correct

J.-values: (points 2 and 6). A

T171 _{'doffing of K4 Oil} v c

nD will give a 9 _ 6 0 _{confused picture (see for instance}

Fig. 4(1, open circles) and the points

8 do not define a single continuous

50./0 curve. To bring them in line, the

c-influence must be corrected for.

Remembering now that wind

in-s 400Io fluence will make a point, such as

2, move to 6 or vice versa,

it is

obvious that points such as 7 and 9

can move along lines (7-8, 9-10)

more or less parallel to the

"Kg-behind" curve, and to the Kg-open

curve as well, if the wake can be

200/0 _{regarded as constant for the region}

of load variations considered. The influence of c is therefore defined

100/0 by the distances between the curve 2-6 and curves such as 7-8 and 9-10.

The curve

2-6 being unknown,

00/0 curve 1-5 may be substituted. In the

analysis used at HyA v0h.-Jnd =

v c - v. = w c is plottet to

TRIAL TRIP ANALYSIS FOR SIX SISTER SHIPS USING A NEW METHOD OF ANALYSIS

ii

0,8 0,9

KT,

R

+

Metric

TABLE 6-Ship C: Wind Horse-power Calculation

TABLE 7 Ship C: Cp and C't Analysis and N Corrected for Wind

Metric

a base of time. The vertical distances 2 e between the

curves wv + c and wv - c is dependent on time only

and therefore should define a fair curve. The two

curves on the other hand are dependent on the re-suiting speeds which do not necessarily vary

con-tinuously with time and might therefore be irregular.

The HyAanalysis is now performed as follows:

-Determination of currents. Calculation of wind resistance.

Plotting of horse-power curve. Determination of wake.

The wind resistance thus derived, minus the

corresponding still-air resistance, was con-verted to e.h.p. and subsequently to p.h.p.,

see Table 6.

Fig. 13. Corrected CT-Curves for Ships A-I' and for Model (for corrections applied, see text).

Lob i.h.p. * N blip. p.h.p.

'

K, J from Fig. 6 d vot.=1 v±c knots v-±c j j J. e v - v,:-±e knots c knots v knots J. 1 - vv c, e nD 1 2490 125,3 2118 2095 0,01474 0,495 12,20 0,671 0,176 3.20 0,32 11,88 0,653 0,758 2 2510 125,2 2155 2132 0,01504 0,488 11.76 0,647 0,159 2,89 0,23 11,99 0,660 0,740 3 3540 141,2 3092 3060 0,01505 0,486 13,47 0,657 0,171 3,51 0,15 13,32 0,650 0,747 4 3510 139,5 3069 3035 0,01547 0,476 13,06 0,645 0,169 3,42 0,10 13,16 0,650 0,733 0.01509 0,745

Wind Resistance Air Resistance Differences

Ha n 8° Apsine Aicose A. c WR 1 - A W 2 e' 2 " 5 Rcosa o° A. Cw 1 _ ,v2A. 2 II., licosa-R,, p.h.p. m2 m2 m2 w misce kg kg r,12 _kg kg kg ,, 1 59 730 155 885 0,13 1,3 90 12 0 300 0,81 700 567 -555

-45 -73

2 15 220 290 510 0,38 11 3850 1470 0 300 0,81 711 576 894 74 114 3 40 545 230 775 0,22 3,3 510 110 0 300 0,81 880 713 -603

-57 -92

4 10 150 295 445 0,43 11 3400 1750 0 300 0,81 857 694 1056 93 146 p.h.. p _p.h.p. knots _v8 P 2 N _{nB '7/1} nt 103C, 10-3R log Br,

From faired curve

11,94 2090 1.227 3,822 0.1268 0,491 124,8 0.614 1,056 0,648 2,475 6,580 8,8182 12,50 2480 1,270 3,951 0,1299 0,488 131,5 0,614 1,056 0,648 2,562 6,891 8,8382 13,24 3030 1,306 4,061 0,1336 0,485 140.1 0,614 1,056 0,648 2,632 7,297 8,8631

( e) Conversion of h.p. to CT and determination

of 5 CT. _2.5x10

These five steps of the analysis are illustrated in dia-grams a to e respectively of Figs. 4 to 9, and Tables 5 to 7, give the corresponding calculations for ship C.

(a) The currents were determined as outlined

-above. For trials, where only four single runs

are made, the analysis is of course very

ap-proximate, each of the curves wv + c and

wv - c being determined by two points only, and a straight line through these points

hav-ing a priori no preference

fo:.' any other

curve.

(b), Wind resistance was calculated from the

for-mulae and diagrams developed at A.E.W.,

AIR RESISTANCE

CORRECTION

1+1(.13

cE T TC

Haslar7. 8.

The same projected areas were used iii I hi'

calculations for all six vessels:

_1.5.163

CEHBASIC

Ai = 300 m." and A, = 850 m2. The aspect ratio 8;80

I LOP RN t 8185

A _- 6.0 6.5 10(11,2,4 7.0

1,1 115 12 12.5 13 135KNOTS

is 0052.

(L)2

12 TRIAL TRIP ANALYSIS FOR SIX SISTER SHIPS USING A NEW METHOD OF ANALYSIS

TABLE 5-Ship C: Current Analysis

-3 _3.0.10 A

-I I I I

Results of the Analyses

TABLE 8

(c) In diagram "c" open circles indicate the

un-corrected p.h.p.-values plotted on unun-corrected

speed. The black circles, defining the

cor-rected horse-power curve, were obtained by making horizontal shifts corresponding to the

currents determined under (a) and vertical

shifts representing wind-h.p. From a propeller diagram containing a curve (Fig. 12) or scale

(Fig. 2) of:

KQ Q n3 Qn p.h.p.

p =

p n2D5 V: p D2 ' V3 V3

C -values, calculated for a number of speeds,

define the corresponding J-values and thus revolutions for the still-air, no-current

con-dition.

(d) After determination of the current for each run the correct Jo-values are calculated and

the K -points in diagram d shifted

horizontal-ly to their "correct" positions, in which

ac-cording to theory they should define a single

curve. Due to errors present, mainly in h.p.

values, the choice of a representative

KQ-be-2000_ 1500_ A B C D

Fig. 19. Hors,- powers and Revolutions for all Six Ships, corrected for

Currents and to Still-air Conditions.

hind ship-curve is somewhat

arbitrary, but the torque-wake

wQ is, nevertheless, determined

with an accuracy of about

0.01, which seems quite

satis-factory.

The p.h.p.-curves are converted

to CT in one of the following

manners:

(1) Corresponding p.h.p. and V-values define the power

coef-ficient

10.8 . p.h.p. _p15

Cp =

S*173 Pa

in which metric horse-power, wetted surface expressed in square-metres and speed in knots

have been used, and where 1915 and pa denote

the density in salt water at 15° Centigrade

and the actual density. The figure 10.8 in the nominator has been chosen so as to make:

CT = ??T_T

C =

_{p/2 v2}

To determine CT the total efficiency nT (q.p.c.)

must be evaluated. This necessitates some as-sumptions. Those made for the present ana-lysis are as follows: the thrust deduction and

the propeller efficiency from the model

ex-periment at the ship loading of the propeller

are both assumed to apply to the ship with-out scale effect. These assumptions will be

discussed later.

From corresponding p.h.p. and N-values, the propeller torque and the corresponding

ve

.1 = are calculated. The latter determines

TD/Q, see Fig. 12, from which the thrust T

and (using 1 - t from the model experiment) the resistance R are found, finally giving C. The same procedure as for 2, except that KT

is used to determine T, from which CT is

calculated.

The same as for 3, except that aT is used to

determine T.

The four methods will, of course, give the same

values of CT. As the derivation of Cp, the

non-dimen-sional power coefficient, is of interest for the eva-luation of the results, the first method was used in

the analyses.

The CT-curves found are shown in the "e" diagram

of Figs. 4 to 9. They have been further collected in Fig. 13 for cotnparison after corrections for the dif-ferences in water temperature and density. A

tem-perature of 15° Centigrade (59°F), a p-value of 104.6

kg.sec.2/in.4 or 199.05 lb.sec.2/ft.4 and a (-value of

1.191 . 10-6 m.2/sec. or 1.2817 . I0 ft.2/sec. have been

adopted, and the Hughes-line with 1 K = 1.30 used for shifting the CT-curves to the new Reynolds' num-bers. Fig. 13 also contains a curve marked CT., which is the CT-curve derived from the model experiment by

means of the F30 Hughes-line. To this is added an

allowance of 0.00008 for still-air resistance. The dif-ferences in the ordinates of the CT-curves and the

lat-ter curve represent the resistance allowances SCT,

which will be discussed in the following.

Ship

corresponding lo 12,5 kiwis

103CT 103SCT vv0 owc, Trimin. BeaufortWind Sea Days out_{or Dock '1""ki}bath A 2,675 0,22 0,280 0,120 2

3-7

2 14 June B 2,610 0,16 0,253 0,147 1

1-4

1 22 Aug. C 2,565 0,12 0,255 0,145 + 1 3 0 23 S,pt. D 2,495 (0,04) 0,266 0,134 +51

1-3

0 16 Dec. E 2,485 0,03? 0,281 0,119 0

5-6

1 20 Feb. F 2,419 (-0,03) 0,300 0,100 ± 8 i- 3 0 1 Apr.

TRIAL TRIP ANALYSIS FOR SIX SISTER SHIPS USING A NEW METHOD OF ANALYSIS 13

REV9/MIN PH P METRIC 140 3500 120 3000 100 2500 11 12 13 14 KNOTS

-(-3) (4) . ,.

Ship A Method 018 016 014 Hughes 1,3 0,22 0,16 0,12 Author's

TRIAL TRIP ANALYSIS FOR SIX SISTER SHIPS USING A NEW METHOD OF ANALYSIS

Ship wake Friction line Froude

0,49

0,55

0,59

TABLE 9 I.T.T.C. Froude

0,04

0,10

0,14

Ship wake

Frict ion line

I.T.T.C. Froude

0,54 0,05 0,26

0,60 0,13 0,26

0,63 0,15 0,30

Discu3sion of the Results of the Analyses.

The b.h.p. curves for all six vessels are compared

in Fig. 14. Five of the curves are in reasonably good

accordance, the maximum horse-power differences

from a mean of the five being three to four per cent. The curve for the sixth vessel, ship F, is on the other

hand lower than the rest by as much as 200 p.h.p.

Although the differences in displacement between the

six vessels were small, the trial conditions were not identical (see Table 3). Differences in water density and temperature play their part, and so do the

dif-ferences in trim. As relatively strong winds were

present on some of the trials (A and E), the differences in propeller loadings have been important and perhaps not correctly taken into account. To get a better

com-parison between the vessels a study of Fig. 13 is of

interest. The non-dimensional total resistance

coeffi-cients, CT, corrected to 15° Centigrade and to y=1.025,

are here plotted together with the curve of CT,

derived from the model experiment. It is interesting

to note that the curves A, B, C and E for the ships with little or no trim are nearly parallel to the CT.-curve thus defining 8CT-values, which in the speed

range shown in the figure, are practically independent of speed, but vary from ship to ship.

K0 OPEN WATER SHIPS

Model wake

10 lo 20 25 30 35

\\ W,

For the vessels D and F, which were trimmed by the stern, the CT-curves are less steep. The

trim will shift the centre of buoyancy somewhat

aft and this might be of advantage at the higher

speeds and explain the trend of these two curves.

The CT CT _{CTn values at 12.5} knots are

tabulated in Table 8, together with the values

of SwQ = w_{model 'ship'}

derived from Fig.

15,

and some other relevant data. The first

three

CT-values of Table 8 average 2-617 with a

maxi-mum difference of 2 per cent from their mean

I.T.T.C. _{value. The average SCT value is 0-000166. The}

slight differences might be attributed to the

dif-ferent sea conditions.

0,29 0,31 0,28 2c MODEL 40°,4

CT derived by means of

effic-Derivation by means of p iencies from self-propulsion and using: experiment at

and using:proper loading

.4 5 6 7

_{are on the other hand not}

re-Fig. 15. KQ-Curves derived from Observations taken on the Six Trial Trips. _{presentative of the frictional}

re-For these ships the wake figures show the

same trend as the SCT values, although perhaps

not to the same degree. The actual values are

in good agreement with the theoretical values given in Fig. 3 of Ref. 2. A suspicion that

the wake differences were due to pitch or

thick-ness differences in the six propellers, is not

sub-stantiated by a perusal of the check measurements of these,

as in fact

all

six screws, delivered by

the same manufacturer, were well within the usual

tolerances. The wQ and SwQ must necessarily be

some-what uncertain when derived from i.h.p. figures. Apart from random errors which may arise from the

deter-mination of the indicator diagram areas, systematic

errors from the use of uncorrect mechanical efficien-cies may have also been included. In the present ana-lysis the same 77,n values as a function of i.h.p. have

been used for all six vessels. For the same mean

in-dicated pressure, differences of say 0.1 kg./cm.= on the

mean effective pressure may occur from one engine

to another of the same series. This would correspond

to about 1 per cent on the mechanical efficiency at the higher loadings and 2 per cent at one third load,

which again would produce changes in the results of

the analyses amounting to about 0.01 on wake and

to nearly 0.07 . 10-3 on SCT. In view of this, further

attempts to explain small differences between the

re-sulting figures from Table 8 are of little value. The

inaccuracy of the results of the Decca runs for ship E

have already been commented on, and as no model experiments were carried out at

trim conditions corresponding to

ships D and F, the 6CT-values

have no real meanings in these

cases.

One detail, however, deserves

to be mentioned. The pitot-log

measurements of the velocity

gradient in the frictional layers

of ships C and F indicate,

in fact, as seen from Fig. 11, a

lower frictional resistance in the

case of ship F. Both these

dia-grams are inaccurate as regards

the position

of the

coordinate

axis, but the difference in

cur-vature is obvious. The areas

VMalt. V ( 1 _dy v

la

I 2a

lb

2b

le

A C D

-F

= .

sistance coefficients to

be expected, but

it must

be remembered that the thickness of the boundary layer varies along the girth of the cross section, and

that a single measurement therefore cannot give

cor-rect values. Whether the increased curvature in the

case of ship F as compared with ship C and the

seem-ingly thinner frictional layer are due to the fact that this ship was freshly painted and the other ship had been more than three weeks out of dock, or that the trimmed condition of ship F is responsible for the

difference, cannot be stated. The shell plates of all six ships had been shot-blasted, the vessels were all fully welded, and the same commercial paint was used. At

HyA supplementary "hate-plate" experiments were

carried out with this paint to get an idea of the proper

roughness allowance. The differences in resistance

between a polished and a painted plate were measured

and extrapolated to a 400ft. ship by means of

Gran-ville's method.. At the Reynolds number correspond-ing to 12-5 knots for the ships in question the

rough-ness allowance found did not exceed 0.04 10-3. As the

application of paint to the real ship surface probably

is less uniform, and the surface itself even on a new ship must have a certain degree of roughness, it is

reasonable to expect higher roughness allowances,

such as those found for ships AC. A value of 0.15 10 (:-was suggested in Ref. 5, based mainly on B.S.R.A. and Haslar data. It is also to be remembered, that the eiCT

values found include allowances for steering, bilge

keels and, as already mentioned, for the sea state. The present analysis has been based on the assump-tion that no scale effects are present in the thrust

de-duction and propeller efficiency. There is reason to

believe that both assumptions are acceptable. A change of 0.01 in thrust deduction coefficient will change the

SC, values by about 0.05, but not alter the general picture. Due to the higher Reynolds number of the

ship propeller in comparison with its model a

reduc-tion of drag might be expected. On the other hand,

as the roughness of the blade surface of the ship

pro-peller is higher than that of its model, and as the

model blades may have had some laminar flow at

the root sections, nothing points definitely towards a

scale effect correction at present. This view is also

supported by Ref. 10.

The analysis has further been based on the Hughes system. It is not without interest to see how the adop-tion of other fricadop-tion lines would have influenced the results. In Table 9 such SC,,, values for 12.5 knots are given, corresponding to analyses based on:

Froude's lines.

The I.T.T.C. 1957 line.

The SCT-values were calculated as SCT = 77., Cp- CFR

or VTCp- Ci.T.T.c. respectively. The total efficiency ?IT

was for both cases calculated in three different ways: a: By using the coefficient p and ship wake. 13: By using the efficiency found in the

self-pro-pulsion experiment at the proper loading, and using ship wake.

c: As for b, but with model wake.

The differences between SC, values derived from the author's method and those listed in columns la and 2a of the table are solely due to the adoption of friction lines other than Hughes 1.30. The differences between the figures of columns la and lb are due to the

adop-tion of different n values. For la V has been derived

by means of the p-coefficient corresponding to the

actual trial trip horse-power curves, whereas for lb has been taken for a propeller loading corresponding to the CT value found from the model experiment.

The figures of the two last columns are similarly

derived, but model wake has been used, giving lower

propeller efficiencies, and higher total efficiencies,

since hull efficiency is inversely proportional to 1 - w.

It is seen that for the ships considered most of the methods give negative SG,. An exception is the last

column. These figures are in good agreement and are

consistent with the idea that SCT should not only

correspond to a roughness allowance, but also include allowances for sea state, steering and bilge keels.

For large ships method 2c is known to give negative SCr-values. As further it neglects the well established scale effect on wake, the author is convinced that his

proposed method is more promising. At HyA a number

of ship trials are at present being analyzed accord-ing to this method, and up to now the results have been encouraging. The Hughes factor 1 + K, which

was found to be 1.30 for the ships of this paper,

varies of course from ship to ship and is determined

for each case by the low speed towing test.

It would be unfair not to state that the Lap-Troost

system could probably have been applied to the same advantage. The slope of the Hughes lines, seem,

how-ever, to correspond better to the CT curves in the

model range found at HyA, but it is too early to give final judgment on this question.

Conclusions.

As said in the introduction to this paper, the

high-est possible accuracy is desirable in the observations made during speed trials. Reliable torque- and thrust-meters would certainly help in this matter. Continuous plotting of horse-power and revolutions on a scale of

time is preferable, and additional plotting of thrust values would make the observations of still greater

value and enable correlations with the model

experi-ment without guess as to scale effect on rotative

ef-ficiency and the like.

Apparent wind velocity and direction should al-ways be registered, and the sea state evaluated for

each run.

The number of single runs should be eight at least, but ten or twelve should be aimed at in adverse

wea-ther conditions. The runs should be performed at

revolutions increasing steadily with time from run to

run

(to make the determination of the current as

exact as possible). Double runs can be used, but are, in fact, less desirable. No acceleration or retardation is permissible over the measured distance, the setting of the engine must therefore be accomplished in good

time before the observations are to b3 taken and re-main unchanged (luring the run. It is important that the courses selected during the runs are chosen in

such a manner that no irregular currents are

en-countered. In confined waters differences in depth or the presence of islands very often produce appreciable variations in the strength of Ihe currents.

During runs on a measured mile the course steered

should be perpendicular to the lines defined by the

beacons, and all runs made at the same distance from

the coast. On Decca runs it is essential that

conse-cutive runs are made in opposite directions as on

TRIAL TRIP ANALYSIS FOR SIX SISTER SHIPS USING A NEW METHOD OF ANALYSIS 15

(1)1

the mile, and that measurements are taken over the same sea bed if the depth of water is limited.

Automatic sleeting is

to be preferred

to reduce

course variations to a minimum. Course and rudder

angles should he plotted during the runs. The

displace-ment and trim to be kept constant during all

runs

(apart from the slight changes due to fuel

consump-tion). The ship should have no list. When differences

in displacement and trim exist between model and ship, an analysis of the trial results is of little or no value and new model experiments should be carried out at the correct conditions.

To increase our knowledge of ship friction,

measure-ments of surface roughness should be taken before the

trials, and velocity gradients in the frictional layer

determined.

In order to increase the accuracy of the ship-model

correlation, wind tunnel measurements of air

resist-ance are desirable when strong winds have been

present during the trials or for ships with high

super-structures.

If all this could be attained, ship-model experiments would become a still more valuable tool for the naval architect. Reliable correlation of model and ship would be the rule, not the exception, and correct predictions

could he made from model experiments.

The correlation analysis can be performed in a

number of ways. The method outlined in this paper is in many respects different from those generally used. As it is based on reasonable assumption and gives results, which so far as can be ascertained to-day, are also reasonable, it is the author's hope that

it will be studied and compared with other methods.

P. HANSENS BOGTRYKKERI A/5

Acknowledgment.

The author is indebted to the three Danish

ship-yards who gave their consent to the publication of the

data contained in the paper. He also gratefully

ack-nowledges the assistance given in preparation of this

paper by the staff of the "Hydro- and Aerodynamics

Laboratory". He especially thanks Mr. Bent Pedersen,

in charge of the drawing office, and Mr. Kaj Kure, who supervised five of the trials and performed all

the analyses.

References:

I. Discussion on Professor L. C. Burrill's paper: uPropellers in Action behind a Ship., N.E.C. Inst., 76, p. SD 27 (see also p. SD 74). Prohaska, C. W.: uAnalysis of Ship Model Experiments and Predictions og Ship Performance., Report No. Hy-1 from the

Hydro- and Aerodynamics Laboratory, Lyngby, Denmark. Lindgren, II. and Johnsson, C.-A., uThe Correlation of Ship Power and Revolutions with Model Test Result.. Report No. 46

from the Swedish State Shipbuilding Experimental Tank. Clements, R. E., u An Analysis of Ship-Model Correlation Data using the 1957 I.T.T.C. Linei, R.I.N.A., 1959, p. 373.

Report of the Committee on Skin Friction (Resistance Committee), 9th International Towing Tank Conference, Paris 1960 (as yet

un-published).

Jourdain, M., uContribution a l'Etude de la Correlation Mer -

Bas-sin, Paper and Discussion, Bull. de l'Ass. Techn. Maritime el Aeronautique, 61, Paris 1961.

Contribution by H. L. Dove to the Discussion on ,Wind Tunnel Tests on Models of Merchant Ship., by K. D. A. Shearer and W. M. Lynn: N.E.C. Inst., 76, 1960.

Contribution by R. N. Newton to the Report of the 9th

Inter-national Towing Tank Conference (awaiting publication).

Granville, Paul S., The Frictional Resistance and Turbulent

1B9o5uodary Layer of Rough Surfaces., TMB Rep. No. 1024, June

',Scale Effect in Model Testing of Large Tankers, Report No. 8,

The Sweedish Shipbuilding Research Association, 1958.

Eiffel, G., ',Nouvelles Recherches sur la Resistance de l'Air et de l'Aviation, Paris 1914.

Schmidt, Wilhelm, uZusammenfassende Darstellung von Schrauben-versuchen, Berlin 1926.

Saunders, Harold E., uHyclrodynamics in Ship Design., 2, p. 589.

16 TRIAL ANALYSIS _{FOR SIX SISTER SHIPS USING A NEW METHOD OF ANALYSIS}

4.

-11.