Experiments on vibrating propeller models

REPORT No. 70 M

MARCH 1965

STUDIECENTRUM T.N.O. VOOR SCHEEPSBOUW EN NAVIGATIE

AFDELING MACHINEBOUW - DROOGBAK lA - AMSTERDAM

(NETHERLANDS' RESEARCH CENTRE T.N.O. FOR SHIPBUILDING AND NAVIGATION)

ENGINEERING DEPARTMENT - DROOGBAK I - AMSTERDAM

*

EXPERIMENTS ON VIBRATING PROPELLER MODELS

(PROEVEN AAN TRILLENDE SCHEEPSSCHROEF MODELLEN)

by

Ir. R. WERELDSMA

(Netherlands Ship Model Basin)

LJLT10

Issued by the Council

This report is not to be published unless verbatim and unabridged

Ir. C. DRAYER Ir. N. DJJKsH00RN

Prof. Dr. Ir.J. D. VAN MANEN

Ir. W. H. C. E. RÖSINGH

Ir. H. SCHULTHEISZ Ir. R. WERELDSMA

CONTENTS

page

Summary

5

Introduction

5

i

Definitions and symbols

5

2

Brief description of the propeller exciter

5

3

The investigated propeller models

6

4

Results of measurements and comparison

with approximate calculations

12

5

Suggestions

12

EXPERIMENTS ON VIBRATING PROPELLER MODELS

by

Ir. R. WERELDSMA

Summary

Eight propeller coefficients, essential for a description of the dynamic behaviour of a ship's propulsion system, are mentioned. The instrument for the experimental determination of these coefficients, a propeller exciter, is dealt with briefly.

Finally the results of the experiments, i.e. eight propeller coefficients, are given as a function of the blade area ratio and the pitch and are compared with theoretical results and as far as possible compared with results obtained by other investi-gators. It appears that the experimentally obtained coefficients are smaller than the theoreticallyapproximated coefficients.

Introduction

For the design of a ship the knowledge of the

vibratory behaviour of the propulsion system

be-comes more and more essential.

Theoretical and experimental investigations into

the excitation forces, generated by the propeller,

are carried out by several research institutes [1, 2,

3, 4]. Due to the flexibilities of the shafting and

its supports these excitation forces are converted

into other fluctuating forces in the shafting and

into vibratory motions.

This conversion can be described by two

coupled equations of motion [5]. In these

equa-tions the hydrodynamic characteristics of the

vi-brating propeller play an important role. We can

distinguish added mass, added moment of inertia,

damping of the torsional and axial motions and

mutual coupling effects.

All these effects are indicated by hydrodynamic

propeller coefficients [6, 7, 8, 9, 10].

A rough practical estimation of the added

moment of inertia, expressed as a percentage of

the mechanical moment of inertia, had already

been made in order to determine the torsional

natural frequency of the propulsion system.

Tx

Ty

V

Fig. I. Frame of co-ordinates

4Dz _z

Tz

For the determination of the forced vibrations,

however, additional

coefficients, as

mentioned

above, have to be taken into account and these

are discussed in the next paragraphs.

i

Definitions and symbols

The six force components acting on a propeller

and the six corresponding motions of the propeller

are given in Fig.

1

with the applied frame of

co-ordinates.

The eight coefficients valid for the z-axis are

given in Table 1. The determination of these

coefficients, the aim of this research, was carried

out experimentally by means of a specially designed

propeller exciter described in the next paragraph.

Table 1

Hydrodynamic coefficients describing the characteristics of a vibrating screw propeller

2

Brief description of the propeller exciter

The propeller exciter is an instrument for

meas-uring the characteristics of a vibrating propeller.

In principle the instrument consists of an air

lubricated propeller shaft, elastically coupled to a

flywheel and provided

with

electro-magnetic

excitation

systems and with

suitable

thrust-,

torque-, acceleration- and displacement pick-ups

(see Fig. 2).

Excitation, to be applied either in torque or in

thrust direction, takes place synchroneously with

blade frequency and multiples, utilizing a photo

electric device, coupled to the propeller shaft.

Simultaneously with the

torsional or

axial

Name Symbol

Added mass Axial damping

Added moment of inertia Torsional damping

Inertia torque coupling Inertia thrust coupling Velocity torque coupling Velocity thrust coupling

F/Ê T/çi3

T/e

F/r5

F/q.

Fx Ex

6 I4

fAJJ

O N2 3670 =0.483 PQ7R/D=OE592 z =4 N2 3671 AD/Ao= 0.L.83 PO7R/D= 0.931 Z ' =4

displacement, the torque and thrust fluctuations

of the propeller are recorded. The mentioned

coefficients can be evaluated by the determination

of the amplitude ratio and the phase shift of the

two records.

A more detailed description is given in [11].

3

Investigated propeller models

A series of seven propeller models (scale 1

: 27.5)

was investigated. The experiments have been

car-ried out with blade frequency excitation and an

advance ratio Ve/nD equal to 0.50.

The rotational speed of the propellers was

be-tween 2.8 and 4.2 r.p.s., dependent on the

res-onance conditions of the exciter. Fig. 3 gives a

review of the propeller models and the most

im-portant parameters.

From this Figure can be seen that the blade

arca ratio and the pitch were varied systematically

in order to study the effect of these parameters.

On the other hand 3 propeller models with

different blade numbers, representing optimum

design for a given ship's hull, were investigated

and the results compared.

Fig. 4 gives details of the propeller models.

Fig. ). Review of the investigated propeller models

9 or. 111

=o

I) N° 3673 AD/4O= 0.726 0.790 Z =4 ft N° 3672 40/A0= 0.602 0790 ft

I

ft N2 2829 =0.483 PQ7R/D 0790

Z=1.

It

N9 2825 AD/AO =0531 802 Z =5

'1í

N2 2828 AD/AO =0.538 P O.7R/DO.834 Z ' =6 Number of blades

i Watertight protecting cover 6 Flywheel

2 Sliprings 7 Torque and thrust exciting units

3 Interchangeable measuring springs 8 Air lubricated bearings

4 Axial and torsional undamped accelerometer 9 Torque and thrust pick-up

5 Axial and torsional displacement pick-up 10 Propeller

Fig. 4a. General plan of propeller I, II, III and IV Screw I D 6500mm P076/. 0.790 z 4 AD / 0.483 'Ao 04 Screw II D =6500mm P07/= 0.790 Z = 4 40/4 0.604 0.552 Screw D =6500mm PD7R/D= 0.7 90 z i. A0/A 0.726 0.652 Screw i: D =6500mm 0.592 z 4 0.483 0.450 0.90 R 197.64 .- = -0.9 R 196.18 / 0.9 R I 07 R :. 05 R 0.5 R

LL.IIIIIII

172.00 ._..uuIIIIIIIII..-O ./. R 9 30 167.09 ____________________ I 0.3 R

Rh

163.09 02 P

R1I

16018 -

.=:

-flU

0.9 R 9 . eI.1I: 0 8 R 0 7 R W:I*jIUIIIIIIII _______ I 0.6 R

__________

I O S R 172.00 I 0 4 R 30 _167.09 0.3 R

h

163.09 0.2 R

1L

160,18 -- -_ 0.95R 197.64 -- = 0.9 R 196 18 0.8 R

L

192.73 0.7 R WFI.1i 0.6 R I 05 R 172.00

-0 /. R 30 167.09 0.3 R

h

_163.09

0.2 R

1I

160 18 V-L -0.9 R 14709 0.89 07 R 0.6 R . 0.59 0.4 R 93Q I

\_

0.3 R 0.2 R

1I

120.09

'r

- - =

-i.

1.0 R 199.09 1.0 R 199.09 1.0 R 149.27 Pitch distribution n per cent 1.0 9 _199.09

Pitch distribution

in per cent - 234.56

208.36

Fig. 4b. General plan of propeller V, VI and VII

Screw V D 5500mrn PO.7R/ 0.9 31 ID z 4 =0.483 jA0 Ap/ Q.il5 jA0 Screw VI D =6500mm PO7R/D= 0.802 Z 5 AD/A 0.531 0.479 Screw D =6250mm 0.8 34 Z = 6 A0/ 0.538 0.472 0.95 R 232.85 -0.9 R 1.1 0.8 R 227.07 0.7 R 220.00 ________ 0.6 R 210.79 0 5 R

RIt

202.85 04 R 8 30 WiI1L1 ____________I 0.3 R

R1

1I

(j"

. R - - _____ O 9 R h. 0.8 R 01 R

___

36 R 0.5R

RIt

I

0 4 R 8 30 168.00 ________ 0.3 R 0 .iiiiuui uuI 0.2 R W44J81

-ir

tAÈ

.pI.I_1, -. __. -z 1!w o 8 R L-5Vb

_....

07 R 192.00 . 184.36

-0.5 R 176.55 0.4 R 8 30 0.3 R

III

WI1III! 02 R

i

II

151.55

--Th

10 R 20309 8 1.0 R

Fz Fz Ez Fz Fz LZ PropeUer number I U ifi x10° [kgsec2I 21) _L m Dernedde[8] 1.6 _. 1.0 Fz

/

o as 0.5p 1.2 0.1. o 10 B x1°-1 2.0 1.5 10 0.5 o 21-011 02 0.3 04

0.5 06 07

-AD/A [kgsecl L m J Dernedde[8] O 01 02 03 04 1)5 0.6 o-Dernedde [s] -- [kgsec] -

2c

-ion

n3.15 xlO1 2 i. -0.1 0.2 1)3 0.4 0.5 0.6

0.7

-n-ADI IA0 Dernedde [s]

4

[gsec2

_\p

/ -2 3L pR4

07

-n-100 3 Fz/. /Ez pnR3 2 Fzi. 1 /Pz pnR4 01 0.2 03 0.4 (15 0.6 07

Fig. 5. Effect of B.A.R. on propeller coefficients

theoretical results Investigated propellers I, II and III with Z = 4 and = 0.79

experimental results Tz [kgmsec] r DerneddeL8j x10 Visser[9] _{"\ ___08} 6--- -0.4 Tz/. 2 -

_-'

n = 3,15 Lz 0 02 pnR5 07 01 0.2 0.3 04 0,5 0.6

-n-AI

IA0 x103 [kg5ec2] Dernedde[8] 5

\

_'..p/ Yzl 1. _{// 2} Ez . -0 .0' o 2 ¡Ez p R4 0.1 0.2 03 04 05 06 OE7-n-AD/A x1°-1 x100 20 Dernedde [s] Tz - [kgsec] 4., ..® -3 Ez 1.5 -2 1.0 _{_-- reduced} ,..- Tz/. 0.5 o - _,-- 3.15 -1 fEz pnR4 01 0.2 0.3 0.4 05 0.6 0.7 AD/Ao 1.4 Dernedde [B] 1.2- l [9] i' -5 Tz 1.0- _-4

lo

Fz Ez Fz k 21

[

m 10- gsec Propeller 8- -"-_-

i

iv 0.5 O x10 6 a) -o 2-O 5 L. 3 2 O a) -o o

____d--

-0.3 0.6 0.9 reduced on fl 3.1.0 r.p.s. 0.8 0.6 0.1. -o--° -1 0.8 -

_{Lc-educed or}

n=3.1.Or.p.s-0.25 Fi/ PR3 Po 7 R/ D '.10 Fz / 02

/Ei

3 PnR O.7RI 'D

-3

2 O a)

'

-0.6 -o

/

.

Z,

-0.2

/

/

¿3 ¿6 ¿9 0.3 06

0.9

-.-Tz Lz xlO 5 I. 3 2 O -3 -reduced on na3.L.0

4/

-g ç,ç?/' cv --05 -03 0.1. Tz/. 0.2 _/t.p 0.1 ₅ PnR xlQ 0.3 0,6 [kgs ec 0.9 Ti Li 2 - _-b Fz/. 1

-/

1.

Ti..

/Lz

h PR ° 0.2 _PR1. O.7 R/D x11 [kgseci alO Tz

r

Lk g m s ec21 1. cPz B-3. 6

4w

_-o o 2 Tz/

_/z

2 -O t I PR5 0.3 06 0.9

-O.7 R -3 D x 10 [kg m se cl xlO Fz/ Iz Ei 2 1.5 O --

c°reduced on

0rp s -2 3 Tz /

¡Li

L, PoR PoR1. 0.3 0.5 09 O.7 R/D P07R/D

Fig. 6. Effect of pitch on propeller coefficients

- theoretical results Investigated propellers I, IV and V with Z = 4 and AD/AO = 0.483

- experimental results [kgs ec x10 0.3 0.6 0.9 rk g sec.

Lm

-3 alO -2 Fz 1-s 0.5 O 2 Fi 1.5 0.5 O xlO - _{[kg s ec}

Fz Ez

Fz

Fz

rio_2 PropelLer number rk9sec2] I Y111 10 I m 8 6 o L. X 2 x1O

-5_ [igsec

Lm

L.-

-3- -

-w o

2-o [kgsec2l o

123456

12

rduced on -n3.1L. rp.s.

3/.56

123/.56

o -[kgmsec2] 4 Tz cpz 0.5 lU_S 0.4 Fz/./ Ez ₆ -a) -w 3 Tz/ pR3 pR5 0.3 L. o .0'. o...

-I

o 2 0.2 0.1 2 o

23456

-alOi alDo 1.0 io [kgm sec] 06 0.8 Tz 1. 0.5 0.6 0.4 0.2 Fz/. /Ez pz 3 2 a) -o o reduced on n=314 rp.s. 0.1. 03 0.2 01 Tz. /tPz pnR3 pnR5

1234 56

-. z

alO1 io [kgsec2] rio-1 1.0 Tz -1.0 0.8 0.6 Q) -o -z 0.8 0.6 0.4 Fz/ 0.4 T2/É 0.2 O -0.2 pR4 p R4

123456

z

- z

1.5 10-1 xlO° 2 1.5 10_1

"'°

-2 alO0 1.0 0.5 - [kgsec] a) 0J o

-z

reduced on -n=311. rps

F/

lfl 0.5 - [kgsec] a) o

-X

rduced on n=3.1L. rps. Tz/. Fz LPZ Tz Ez / Ez o n I _I t _J. I p n R4 o t t I t I p n R4

123456

z

123456

-Fig. 7. Effect of blade-number on propeller coefficients

- - - - theoretical results Investigated propellers I, VI and VII with slightly different parameters

12

4 Results of measurements and comparison

with approximate calculations

The results of the measurements are given in

Figs. 5, 6 and 7.

Due to the basic operation of the propeller

exciter the number of revolutions of the propeller

model can not be chosen in advance, but it

depends on the natural frequency of the excited

system. This r.p.m. differs therefore for each

in-dividual case. In order to show only the effects of

blade area ratio and pitch the effects of the

dif-ferent numbers of revolutions are eliminated by

assuming a proportional r.p.m. dependency of the

damping and an r.p.m. independency of the

in-ertia effects, as follows from the two-dimensional

approximate theory [Il].

The results of the measurements of the velocity

effects are for each individual case corrected for a

constant r.p.m., slightly deviating from the

num-ber of revolutions during the measurements.

The coefficients are given in absolute model

quantities and are also expressed as dimensionless

quantities, as can be introduced from theoretical

considerations [5, 8].

From these coefficients full size values can be

obtained easily.

In the same Figures theoretical curves are given

by dotted lines.

In order to obtain the character of the curves

near the origin, fictive propellers with an extended

variation of the studied parameter had been

an-alysed.

As far as possible the measurements are

com-pared with results obtained by other

investiga-tors [8, 9].

In general it can be concluded that the

exper-imentally obtained coefficients are smaller than

those theoretically obtained, and that the

agree-ment between theory and experiagree-ment is better as

far as the considered effects result from torsional

motions.

No systematic effects can be observed from a

change in the number of blades (see Fig. 7).

This is in accordance with theoretical

considera-tions, from which it follows that the number of

blades does not essentially affect the dynamic

characteristics of a propeller.

It must be remarked that in contradistinction

to the theoretically obtained values the

exper-imentally obtained values of the coupling terms

do not satisfy the rules of Maxwell.

The two-dimensional

analysis can only be

applied for rough estimations as can be seen from

the deviations between theory and experiments.

5

Suggestions

From theoretical considerations it follows, that the

damping ratio is proportional to the r.p.m. of the

propeller. It would be interesting to verify this

effect experimentally.

For very small reduced frequencies the added

mass and moment of inertia appear to be negative.

An experimental justification of this effect will

be instructive.

For normal propeller shaft vibration analyses

the measured coefficients are suitable for

appli-cation.

References

KROHN, J., Numerische und experimentelle

Unter-suchungen über die Abhängigkeit der Schub- und

Drehmomentschwankungen vom Flächenverhältnis bei vierflügeligen Schiffspropellern. Schiffstechnik, Vol. 9, 1962.

SCHUSTER, S., Beitrag zur Frage des füniflügeligen

Pro-pellers. Jahrbuch d. Schiffbautechn. Gesellschaft, Vol. 49 (1955), P. 87/109.

MANEN, J. D. VAN and R. WERELDSMA, Propeller

excited vibratory forces in the shaft of a single screw

tanker. Netherlands' Research Centre T.N.O. for

Shipbuilding and Navigation, Report no. 37 M, 1960. STUNTZ, G. R., P. C. PIEN, W. B. HINTERTHAN and N. L. FICKEN, serie 60. The effect of variations in

afterbody shape upon resistance, power, wake

dis-tribution and propeller excited vibratory

forces. S.N.A.M.E. 1960.

SCHUSTER, S., Ueber den Einflusz des Propellers auf die Längs- und Drehschwingungen in der Wellenleitung. Schiff und Hafen, Vol. 13 (1961), p. 498!505. LERBS, H. and H. BAUMANN, Trägheitsmoment und

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(1940), p. 32.

ARCHER, S., Torsional vibration damping coefficients for marine propellers. Engineering (1955).

DERNEDDE, R., Ein Verfahren zur näherungsweisen

Berechnung der mitschwingenden Wassermassen, Dämpfungen, Koppelkräfte und Koppelmomente an schwingenden Schiffspropellern. Schiffstechnik, Vol. 7 (1960), p. 199/205.

VISSER, N. J., Model tests concerning the damping

coefficient and the increase in the moment of inertia

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Lxwss, F. M. and J. AUSLAENDER, Virtual inertia of propellers. Journal of Ship Research, Vol. 3 (1960), No. 4, p. 37/46.

Il. WERELDSMA, R., Dynamic behaviour of ship propellers (to be published).

Reports

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No. 3 S Practical possibilities of constructional applications of aluminium alloys to ship construction. By prof. ir H. E. Jaeger. March 1951.

No. 4 S

Corrugation of bottom shell plating in ships with all-welded or partially welded bottoms (Dutch). By prof. ir H. E. Jaeger and ir H. A. Verbeek. November 1951.

No. 5 S Standard-recommendations for measured mile and endurance trials ofsea-going ships (Dutch. By prof. ir J. W. Bonebakker, dr ir W. J. iVIuller and ir E. J. Diehi. February 1952.

No. 6 S Some tests on stayed and unstayed masts and a comparison ofexperimental results and calculated stresses (Dutch. By ir A. Verduin and ir B. Burghgraef. June 1952.

No. 7 M Cylinder wear in marine diesel engines (Dutch). By ir H. Visser. December 1952.

No. 8 M

Analysis and testing of lubricating oils (Dutch).

By ir R. N. M. A. Malotaux and irj. G. SmiLJuly 1953.

No. 9 S

Stability experiments on models of Dutch and French standardized lifeboats.

By prof ir H. E. Jaeger, prof. ir J. W. Bonebakker and j. Pereboom, in collaboration with A. Audigé. October 1952. No. 10 S On collecting ship service performance data and their analysis.

By prof ir J. W. Bonebakker. January 1953.

No. 1 1 M The use of three-phase current for auxiliary purposes (Dutch).

By ir J. C. G. van WUk. May 1953.

No. 12 M Noise and noise abatement in niarine engine rooms (Dutch). By " Technisch-Physische Dienst T.N.O.- T.H." April 1953.

No. 1 3 M Investigation of cylinder wear in diesel engines by means of laboratory machines (Du tch. By ir H. Visser. December 1954.

No. 14 M The purification ofheavy fuel oil for diesel engines (Dutch). By A. Bremer. August 1953.

No. I 5 S Investigation of the stress distribution in corrugated bulkheads with vertical troughs. Bv prof. ir H. E. Jaeger, ir B. Burghgraefand I. van der Ham. September 1954. No. 16 M Analysis and testing of lubricating oils II (Dutch).

By ir R. N. M. A. Malotaux and drs J. B. Zabel. March 1956.

No. I 7 M The application ofnew physical methods in the examination of lubricating oils. By ir R. N. M. A. Malotaux and dr F. van Zeggeren. March 1957.

No. 18 M Considerations on the application of three phase current on board ships for auxiliary purposes especially with

regard to fault protection, with a survey of winch drives recently applied on board of these ships and their

in-fluence on the generating capacity (Dutch). By ir J. C. G. van Wjk. February 1957. No. 19 M Crankcase explosions (Dutch).

By ir 7. H. Minklwrst. April 1957.

No. 20 S An analysis of the application of aluminium alloys in ships' structures.

Suggestions about the riveting between steel and aluminium alloy ships' structures. By prof. ir H. E. Jaeger. January 1955.

No. 2 1 S On stress calculations in helicoidal shells and propeller blades. By dr irj. W. Cohen.July 1955.

No. 22 S Some notes on the calculation ofpitching and heaving in longitudinal waves. By ir J. Cerritsma. December 1955.

No. 23 5 Second series of stability experiments on models of lifeboats. By ir B. Burghgraef. September 1956.

No. 24 M Outside corrosion of and slagformation on tubes in oil-fired boilers (Dutch). Bydr W.J. Taat. April 1957.

No. 25 S Experimental determination of damping, added mass and added mass moment of inertia of a shipmodel.

By ir J. Gerritsma. October 1957.

No. 26 M Noise measurements and noise reduction in ships. By ir G. J. van Os and B. van Steenbrugge. May 1957.

No. 27 5 Initial metacentric height of small seagoing ships and the inaccuracy and unreliability of calculated curves of

righting levers.

By /rof. ir J. W. Bonebakker. December 1957.

No. 28 M Influence of piston temperature on piston fouling and piston-ring wear in diesel engines using residual fuels. By ir H. Visser. June 1959.

No. 29 M The influence of hysteresis on the value of the modulus of rigidity of steel. By ir A. Hoppe and ir A. M. Hens. December 1959.

No. 30 S An experimental analysis of shipmotions in longitudinal regular waves. By ir J. Gerritsma. December 1958.

No. 31 M Model tests concerning damping coefficients and the increase in the moments of inertia due to entrained water of ship's propellers.

By N. J. Visser. October 1959.

No. 32 S The effect of a keel on the rolling characteristics of a ship. By ir J. Gerritsma. July 1959.

No. 33 M The application oí new physical methods in the examination of lubricating oils. (Continuation of report No. 17 M.)

By ir R. N. M. A. Mal otaux and dr F. van Zeggeren. November 1959. No. 34 S Acoustical principles in ship design.

By ir J. H. Janssen. October 1959.

No. 35 S Shipmotions in longitudinal waves.

By ir J. Gerritsma. February 1960.

No. 36 S Experimental determination of bending moments for three models of different fullness in regular waves. By ir J. Ch. De Does. April 1960.

No. 37 M Propeller excited vibratory forces in the shaft of a single screw tanker. By dr ir J. D. van Manen and ir R. Wereldsma. June 1960.

No. 38 S Beamknees and other bracketed connections.

By prof. ir H. E. Jaeger and irJ. J. W. Nibbering. January 1961.

No. 39 M Crankshaft coupled free torsional-axial vibrations of a ship's propulsion system. By ir D. van Dort and N. J. Visser. September 1963.

No. 40 S On the longitudinal reduction factor for the added mass of vibrating ships with rectangular cross-section.

By ir W. P. A. Joosen and dr J. A. Sparenberg. April 1961.

No. 41 5 Stresses in flat propeller blade models determined by the moiré-method.

No. 42 S Application of modern digital computers in naval-architecture. By ir H. J. Zunderdorp. June 1962.

No. 43 C Raft trials and ships' trials with some underwater paint systems. By drs P. de Wolfand A. M. van Londen. July 1962.

No. 44 S Some acoustical properties ofships with respect to noise-control. Part I. By ir J. H. Janssen. August 1962.

No. 45 S Sorne acoustical properties of ships with respect to noise-control. Part Il. By ir J. H. Janssen. August 1962.

No. 46 C An investigation into the influence ofthe method ofapplication on the behaviour ofanti-corrosive paint systems in seawater.

By A. i\Ï. van Landen. August 1962.

No. 47 C Results ofan inquiry into the condition ofships' hulls in relation to fouling and corrosion. By ir H. C. Ekama, A. M. van Lünden and drs P. de Wolf. December 1962.

No. 48 C Investigations into the use of the wheel-abrator fbr removing rust and miliscale rom shipbuilding steel (Dutch) Interim report.

By ir j. Reminelis and L. D. B. van dn Burg. December 1962.

No. 49 S Distribution of damping and added mass along the length of a shipmodel. By prof. ir J. Gerritsma and W. Beukelman. March 1963.

No. 50 S The influence of a bulbous bow on the motions and the propusion in longitudinal waves. By prof. i' J. Gerriisma and W. Beuke(rnan. April 1963.

No. 51 M Stress measurements on a propeller blade of a 42,000 ton tanker on full scale. By ir R. Wereldsma. January 1964.

No. 52 C Comparativc investigations on the surface preparation of shipbuilding steel by using wheel-abrators and the

application of shop-coats.

By ir H. C. Eka,na, A. M. van Londen and ir J. Renvnelts. July 1963. No. 53 S The braking of large vessels.

By prof ir H. E. Jaeger. August 1963.

No. 54 C A study of ship bottom paints in particular pertaining to the behaviour and action of anti-fouling paints.

By A. M. van Londen. September 1963. No. 55 S Fatigue of ship structures.

By ir J J. W. Nibbering. September 1963.

No. 56 C The possibilities of exposure of anti-fouling paints in Curaçao, Dutch Lesser Antilles. By drs P. de Wolf and Mrs M. Meujer-Schriel. November 1963.

No. 57 M Determination of the dynamic properties and propeller excited vibrations of a special ship stern arrangement. By ir R. Wereldsrna. March 1964.

No. 58 S Numerical calculation of vertical hull vibrations of shipc by discretizing the vibration system. By J. de Vries. April 1964.

No. 59 M Controllable pitch propellers, their suitability and economy for large sea-going ships propelled by conventional, directly-coupled engines.

v ir C. Kapsenberg. June 1964.

No. 60 S Natural frequencies of free vertical ship vibrations. Br ir C. B. Vreugdenhil. August 1964.

No. 61 S The distribution of the hydrodynamic forces on a heaving and pitching shipmodel in still water. By prof. ir J. Gerritsma and W. Beukelman. September 1964.

No. 62 C The mode of action of anti-fouling paints : Interaction between anti-fouling paints and sea water. By A. M. van Londen. October 1964.

No. 63 M Corrosion in exhaust driven turbochargers on marine diesel engines using heavy fuels. 13)' prof R. W. Stuart Mitchell and V. A. Ogale. March 1965.

No. 64 C Barnacle fouling on aged anti-fouling paints; a survey of pertinent literature and some recent observations. By drs P. de Wolf. November 1964.

No. 65 S The lateral damping and added mass of a horizontally oscillating shipmodel. Br G. van Leeuwen. December 1 964.

No. 66 S Investigations into the strength of ships' derricks. Part I. By ir F. X. P. Soejadi. February 1965.

No. 67 S Heat-transfer in cargotanks of a 50,000 DWT tanker. By D. J. van Heeden and ir L. L. Mulder. March 1965.

No. 68 M Guide to the application of "method for calculation of cylinder liner temperatures in diesel engines". By dr ir H. W. van Tjea. February 1965.

No. 69 M Stress measurements on a propeller model for a 42,000 DWT tanker. By ir R. Wereidsina. March 1965.

No. 70 M Experiments on vibrating propeller models. By ir R. Wereldsnza. March 1965.

Communications

No. 1 M Report on the use of heavy fuel oil in the tanker "Auricula" of the Anglo-Saxon Petroleum Company (Dutch). August 1950.

No. 2 5

Ship speeds over the measured mile (Dutch). By ir W. H. C. E. Rösingh. February 1951.

No. 3 S On voyage logs of sea-going ships and their analysis (Dutch). By prof ir J. W. Bonebakker and ir J. Gerritsma. November 1952.

No. 4 S

Analysis of model experiments, trial and service performance data of a single-screw tanker. By prof ir J. W. Bonehakker. October 1954.

No. 5 S Determination of the dimensions of panels subjected to water pressure only or to a combination of water pressure and edge compression (Dutch).

By prof ir H. E. Jaeger. November 1954.

No. 6 S Approximative calculation of the effect of free surfaces on transverse stability (Dutch). By ir L. P. Herfst. April 1956.

No. 7 S On the calculation of stresses in a stayed mast. By ir B. Burghgraef August 1956.

No. 8 S Simply supported rectangular plates subjected to the combined action of a uniformly distributed lateral load and compressive forces in the middle plane.

By ir B. Burghgraef February 1958.

No. 9 C Review of the investigations into the prevention of corrosion and fouling of ships' hulls (Dutch). By ir H. C. Ekama. October 1962.

No. 10 S/M Condensed report ola design study for a 53,000 dwt-class nuclear powered tanker.

By the Dutch International Team (D.l.T.) directed by ir A. M. Fabery de Jonge. October 1963. No. 11 C Investigations into the use of some shipbottom paints, based on scarcely saponifiable vehicles (Dutch).

By A. M. van Londen and drs. P. de Wolf October 1964.

M = engineering department S = shipbuilding department