Operation and utilization of data base for design and analysis of cavitating screw propellers

A P,.CHIEF

Ars.

yi1 D ROD).

,BULGARIA 9003 VARNA

CREATION AND UTILIZATION OF

DATA BASE FOR

DESIGN AND

_ANALYSIS OF CAVITATING

SCREW PROPELLERS

P. G. Kozhukharov

prepared'

for

EUROMECH Collodu im 222

Wageningen June 1987

TedInische

Hugeschnol

Delli

P

NOTATION'

AE/A0 expanded blade /area ratio propeller diameter, mT

J . - advance coefficient (general);

- propeller advanced coefficient in Oblique' flow :, ' IN

virtual advance coefficient;

KN , normal force coefficient K,., - coefficient of determination

KT propeller thrust Coefficient

KQ-

propeller torque coefficient

1

propeller rate of rotation, r.p.m.;

.- power delivered at the propeller, H.p.; P/D propeller pitch ratio_

Fh non - dimensional hub radiuS7

R - ship resistance, kgf f RSS ,- residual sum of squares;

. _{thrust deduction factor 7.} VS - ship speed ,

knots-WT

_ _{wake fraction; .}

r?

o

propeller. efficiency; 1? D propulsive efficiency l,

12r rotative efficiency:

itii , ,-- angle of flow indication, deg.:

zr

-

cavitation number

2 , 4

I)

. _ mass density of water, kg,sec /m

I. 1 4", -- ; -

-requirements reflecting some specific conditions at which the propeller is going to operate. Traditional hydrodynamics requirements for obtaining highest pro-peller efficiency are often combined with several structural limitations,

ac-oustic and / or vibrational considerations, etc. The final design is obviously compromize between these requirements . The whole variety of limitations

and

predictions cannot be treated purely theoretically at initial design stages, because some related phenomena are rather complicated. Among them the most impor -tant role plays cavitation on propeller blades, which cannot be practically avoided at ship speeds of 35 40 knots. However, the initial design should be per -formed as precisely as possible in order to minimize the difficulties arising

fur-ther in more detailed adopting of the real operating conditions . Therefore, the BSHC research programme on cavitating propellers for high - speed craft includes different aspects : erosion, acoustics, hydrodynamics, ship performance as shown on the scheme below

Low - Noise

Propeller

Design-Correlation with Full-Scale Measurements Model Experiments in Cavitation Tunnel

ACOUSTICS

HYDRODYNAMICS

Propeller Operation in Oblique Flow Tests of Systematic Propeller Series Statistical Analysis of Force and Geometry Data

Algorithms for Optimum

Propeller Desion

ISSIIIC

RESEARCH ON

CAVITAT I N G PROPELLERS

Erosion - Free Propeller Design Theoretical Evaluation of Cavitation Patterns

Full - Scale Observa-tions and InspecObserva-tions

Erosion Tests in

Cavitation Tunnel

EROSION

SHIP PERFORMANCE

Practical Procedure for Performance Prediction

Model Experiments

Full - Scale Trials

Correlation Factors

-This paper deals only with propeller performance problems, _{indicated on the}

sche-me generally as " HYDRODYNAIIICS Main attention is paid on problems arising at initial propeller design stages. Here requirements for maximum efficiency are

usually prevailing, in order to evaluate the maximum attainable ship speed. For non - cavitating propellers different type of design charts are constructed on the basis of the test data, obtained with systematic series of propeller models.

These charts are successfully applied for selection of optimum conventional

propellers. At the same time cavitation should be considered as an additional fac-tor, i.e. if similar design charts are going to be used for cavitating propeller they should be constructed at certain discrete values of the cavitation number. Such charts can be found in B - oy form in (1) or KT - J folui in (2) . The

prac-tical use of the charts for optimum design of cavitating propeller is, however rather difficult and time - consuming with a risk for lower accuracy, inherent , to all graphical procedures performed by hand. At present the computer - aided design procedures are widely applied in propeller _{design and especially for} high - speed propellers the application of computers at initial stages proves to be the most attractive alternative. Practical solution of this task could be

principally similar to that for conventional non - cavitating propellers, i.e.

using data from systematic model tests of propeller series. Such approach ne

-cessitates the following

forming of reliable and extensive base for cavitating propeller performance: conversion of available data in a form , suitable for effective computer application;

development of algorithns and related software for design and optimization

of cavitating propellers, taking into account the main features of their

operation .

FORMATION OF DATA BASE FOR CAVITATING PROPELLER PERFORMANCE

The most important task is the proper selection of systematic model series suitable for high - speed application. In this respect some principles of selection of

propeller series for inclusion in the data base can be formulated as follows availability of reliable experimental information about main hydrodynamic characteristics ( KT K _Lo ) ;

as wide as possible range of variation of main geometry parameters P/D

AE/A0;

wide range of variation of main experimental condition ( J, G") with special

emphasis on the lower cavitation number values ( i.e. c.".c1 ) ;

availability of full information regarding detailed propeller geometry ( sufficient for exact reproduction of the propeller ) .

There are several systematic propeller series tested in wide range of variation of cavitation number and usually applied in high - speed propeller design. The most popular are Gawn - Burrill (3) and Newton - Rader (4) series, developed in the United Kingdom, as well as SK - series (2) and Five - Bladed series (2), developed

and tested in the USSR. All these series are tested in cavitation tunnel in

uni-form axial flow. Several years ago a new propeller series was developed and

tested in the BSHC cavitation tunnel, (5) in axial and oblique flow , in latter case the normal force was measured as well . So, these five series are selected for inclusion in the data base and their main characteristics are presented in the following table .

4 , -: -, -- -- -. .

Main Characteristics of Cavitating Propeller Model Series

Generally for all series the experimental data are presented in graphical form ( only for Newton - Rader series numerical results are provided as well ).There-fore the direct application of these results is rather difficult and time -

con-suming, especially for design of optimum propeller by hand. The computer - aided design and analysis of propellers for high - speed craft necessitates the mathe-matical description of propeller performance characteristics. It proves to be

a tradition to use linear polynomial regression equations for proper evaluation of propeller thrust and torque (6), (7) . However, the influence of cavitation on propeller characteristics proves to be clearly non- linear and the treatment of direct experimental data with linear regression analysis fails to give satis-factory accuracy. For this reason the first problem in adopting existing propel-ler performance data for computer use is to find proper mathematical representa-tion of propeller in cavitating environment. During the implementarepresenta-tion of BSHC programme a special procedure was created for statistical analysis of cavitating propeller performance. In this way regression polynomials were obtained for a number of systematic propeller series in cavitating conditions. This procedure is illustrated on the next scheme .

Series Gawn-Burrill Newton Rader SK BSHC Three Bladed Series Five Bladed Series Number of Propeller Models 30 12 28 4 22 Minimum Pitch Ratio 0.6 1.04 1.0 1.11 1.10 Maximum Pitch Ratio 2.0 2.08 2.2 1.81 1.55 Minimum Expanded Area Ratio 0.51 0.48 0.65 0.80 Maximum Expanded Area Ratio 1.18 0.95 1.10 0.95 1.40 Number of Blades 3 5 Minimum Cavitation_ Number 0.50 0.25 0.30 0.40 0.40 Type of Blade Sections Flat

Segment CAMBERED SEGMENT

Radial Face Pitch

Distribution Constant Variable

-.

-OBTAINING OF REGRESSION POLYNOMIALS

DIGITAIZER TEKTRONIX AND GRAPHIC STATION

pdp11/45

Editing of Data Files

Regression Analysis for Three Independent Variables

4

Print-out

Obtaining of Initial Data

from Diagrams

Plotting of Obtained Points for Error Checking

Corrections of Initial Data

Record on Disc

Sectional Plots for each

Independent Variable

Modification of the Form of

Independent Variables and

Choosing of Powers

Regression Analysis for 4 Independent Variables

FINAL OUTPUT

Comparison

Input Data

nomial s

Formation of Polynomial Model for 4 Independent Variables

Between

and

Poly-The first obstacle to be overcome is to convert the original graphical information

in numerical form . Digitizer, connected with the graphic station TEKTRONIX

ter-minal was used to obtain discrete points from original graphics for Gawn - Burrill

series , SK and Five Bladed series . The data collected were plotted in order to

check for accidental errors introduced and data files obtained were finally

edi-ted for further processing .

From statistical point of view the blade area ratio AE/A0, the pitch ratio P/D

the advance coefficient J and the cavitation numberVare considered to be

in-dependent variables in the functions, describing the independent varia

-bles, i. e. thrust coefficient K and torque coefficient K . In or

-der to check the possibility for application of polynomials as a mathematical TI10

del it is necessary to analyze sectional plots, i.e. relations between the depen dent variable and one independent variable, keeping fixed values of all other in-dependent variables. In this way was established, that the relation _{KT =} f (0-) at

J, AE/A0 , P/D = fix cannot be approximated by polynomials with satisfactory ac

-curacy Therefore, some modifications should be introduced in the form of inde -pendent variables as they are included in the mathematical model. Typical example

for modification process is illustrated on next page .

.

.

-0 3

KT

0.2

0.1

MODIFICATION

Newton-Racier Series J=I.35 P/D=I.66 Ae/A6--0.71

Original

Experimental Data

0,3 KT 0,2 -0,1 0

G=exp(-0.3

In 6" la ) 2.5 I

It can be seen that modified data can be easily approximated by polynomials. The other task is to prescribe the maximum powers of independent variables in the po-lynomials and it is desirable to keep the values of these powers as low as pos-sible in order to prevent the well - known oscillations of computed results.

The next step is to check the quality of the mathematical model, constructed as described above.EVen with relatively limited computer resources ( for instance

with minicomputer ) this check can be performed by treating three independent

variables ( i.e. J, t5, and P/D ), obtaining different mathematical descriptions

for groups of data with given value of _{AE/A0 .} The algorithm for regression ana -lysis used (8) is based on stepwise reversive numerical procedure. At each stage a new term is added to the polynomial and this teim is selected among possible combinations to cause maximum reduction

in

the residual sum

in

squares (RSS).

1.0 2.0 3 0G"

Modified Data

G 1 0 0,1 -.

termine certain mathematical model, applying to the terms found in three - para-metric models a full combination of powers for the fourth independent variable.

So, the basic mathematical model for _{final treating with regression analysis} with respect to 4 independent variables is not a full polynomial, but comprises only certain terms found at lower level of treatment (i.e. with 3 independent

variables ). In this. way considerable saving of computer _{resources can be}

rea-lized to obtain the final polynomials, although in our case was necessary to use larger computer, such as IBM 370/145 .

The accuracy of the statistical model can be generally estimated at each step by the coefficient of determination

kR as shown for Gawn - Burrill series .

STATISTICS FOR GAWN - BURRILL SERIES

REGRESSION

POLYNOM IALS

Data for three indepen-dent variables

(52 terms in each polynomial)

Data .for four independent variables

(1685 data points)

Where the coefficient of determination is

Residual sum of squares (standard deviation)2 in percent. AE /A0 Number of Data Points KT 10 K_Q 0.51 260 99.37 99.58 0.665 400 99.51 99.76 0.82 390 99.34 99.65 1.00 362 99.52 99.74 1.18 273 99.58 99.77 Polynomial Number of KR for terms KT 121 99.47 10 KQ 116 99.71

Limiting Parameters of Cavitating Propeller Series

Prescribed

limiting values:

A_ )

t4Au min ( AE/A0) max

( P/D

) min

( P/D )max

(3.

min

a

max

Additionally found relations for:

Jmin = a + b D

Jmax = ( a1 + b1

where

a, b,

a/, b/

f _{, AE/AO} )

In this way for all systematic series regression polynomials were obtained. Poly-nomials for Newton - Rader series are presented in (9), for Gawn - Burrill series in (10 ) and for remaining three series - in (11) .

Finally it 'should be emphasized that the regression polynomials are valid in

the domain, restricted by the limiting values of main parameters . It is expedient to establish relations especially for minimum and maximum values of advance coef-ficient as shown below :

UTILIZATION OF DATA BASE

The main purpose of data base created is to contribute propeller design and

analysis procedures. Special emphasis is given to propeller operation in oblique flow, which is the most typical case for high - speed craft. The comparison

be-tween the experimental data obtained and calculations based on quasi - steady ap-proach showed, that propeller thrust and torque in oblique flow can be predicted

with satisfactory accuracy when using respective quantities in axial flow (11),(12).

The major relations for this type of calculations are illustrated below

Propeller Operation in Oblique

_Flow

Calculation of Propeller Characteristics

( Quasi-Steady Approach )

21r 1

( J6-i (

J1' 2 ) 69-KT Q `34) ' ) T ,C A' 4" 2W o o 2 J.., 2 N 4' K

( J) -

1

f

KQo 1/413* , ) ( ) d

where e is found for each as a solution of the equation

( 1 - '117 Jx.arctg x2 2 + Tr .rh = J arctg Y Jx o o h J ( l+tg2y .sin243.) + (1r-r v + .r h

vtg

Y. sin ( J = -- fh)

At the same time quasi - steady predictions for normal force may lead to serious inaccuracies (5). Therefore systematic experimental investigations were carried out with BSHC three - bladed series. The results obtained were treated with regression analysis as illustrated below :

PROPELLER NORMAL FORCE IN OBLIQUE

FLOW

BSHC Three-Bladed Series

P/D=1.11±1.80

=00

-.

120

6=0.4

10.0

Experiments

Regression Polynomial

101 10 KM i=1 Ai ( 0.15-0.10 0.05-a. b. J-0.4 i P ) .G --- 1 ) 1.4 c. d.

6.1

05 1.5 Jo ( where : G = 0.4 + 1n arc t96) Coefficient of determination KR = 99.91 % -P/D-1.56 4J-12°

5-0.4

G-0.8 G-2.5 1.(N 0

optimum propeller, i.e. propeller providing maximum attainable propulsive ef -ficiency at certain prescribed main operational conditions. In this way it is pos-sible to formulate the

Main Design Problem:

FOR GIVEN SYSTEMATIC PROPELLER SERIES TO FIND A PROPELLER ENSURING

MAXIMUM PROPULSIVE EFFICIENCY WHEN CONSUMING PRESCRIBED POWER

(P/D)min 5 P/D 5 (P/D)ma. (AE/A)min 5 AE/Ao 5 (AE/A)°min 5 cr 6 °max jmin 5j sjniax - t no . ,Ina). . max 1 - W P - IL Vs fix

-Taking into account some conditions for computer time saving, the main design problem can be modified, leading to three relatively independent problems as illustrated by the following scheme

MODIFIED DESIGN PROBLEM:

To find an optimum cavitating

propeller at prescribed A

/Aoys

Problem

DETERMINE THE DOMAIN ( J, P/D ) OF

POSSIBLE SOLUTIONS OF THE DESIrN PROBLEM

Problem E3

IN DOMAIN ( J,P/D) TO FIND PROPELLERS WITH CERTAIN THRUSTING CAPABILITY

-Problem C

/WONG ALL PROPELLERS FOUND IN PROBLEM B TO DETERMINE THOSE PRO-VIDING MAXIMUM 7 , -max -t ; A

Solution of Problem A is described in (14). Problem B and problem C are treated in

(13) . Therefore here all details are omitted and only some final results ob

-tamed are discussed

Three computer programs have been developed .

Program CPDSYS performs various types design procedures as illustrated in the

Table . Designs are prepared for certain selected systematic propeller series.

Various Types of Propeller Design Calculations Performed by Program CPDSYS

Program PRG performs calculation of ship performance when propellers designed with programme CPDSYS are applied . Here the BSHC procedure (15) for high-speed ship performance prediction is used, treating the case when cavitating propellers

are used . Special attention is paid on multi screw ship configurations .

Program GEOMCP identifies detailed propeller geometry for all systematic series included in the data base.

Program PRCVCP evaluates pressure distribution on propeller blades. The main in-terest is to check the occurence of face cavitation, usually met for root

sec-tions during propeller operation in oblique flow . This type of cavitation should

be in any case eliminated, because it leads to severe cavitation erosion. The

latter is done introducing corrections in original propeller geometry (section

curvature, local pitch ) .

Combined application of these programs, as illustrated on the flow chart,

provi-des possibilities for reliable design of model propellers during initial stages

of high - speed craft investigation. Finally the program NPPSDA prepares data

for model manufacturing with numerically controlled milling machine .

Type of Problem Input Parameters Output Parameters

Selection of Optimum Gear Ratio D, N1 < N2 P70' AE/A0' NI Nopt -,c N2 D Not. P/DA 'A ' E' 0 Selection of Optimum Propeller Diameter N D P P/D AE / A0 N, D

max Dopt D max

N, IC, < 1 D = K . D

opt

N, K < I, 0x . K .

Dopt ,C Dmax

Looking for Propeller Consuming Prescribed Power ( used usually with data base with individual propel-ler ) N, D P/D, AE/ A N, P/D, AF/A, D D, P/D, AE/AO N . . -. -max I

P R OT OT Y P E

DATA

for

propefler

re-design,

corrections

in

basic

propeller

geometry

DATA

for hull resistance and propulsive factors

INPUT DATA(formu

lation of the probleMi

SELECTION OF 'FINAL

PROPE LLER AMONG

ALL DESIGNS

PROPELLER DESIGN

WITH

VARIOUS

SYSTEMATIC SERIES

SHIP

PE R FOR MANCE

PREDICTION

.14.,,resmasec=

CALCULATION

OF BLADE CAVITATION

PATTERNS

DETERMINATION

I

OF DETA IL ED

PROPELLER GEOMETRY PREPARATION OF DATA FOR PROPELLER MODEL

MANUFACTURING

PROGRAM

CPDSYS

PROGRAM

ritOVCP

t,

'PROGRAM

NPPSDA.

DATA BASE *

,

PROGRAM

IP

G

P ROG .14 A M

GE0101CP

In order to check the quality of described computerized .design procedure, it is

expedient to perform some comparative calculations for examples take'1 from the

literature. There is a number of publications, treating in different extent the

high speed propeller problems . However, the significant part of them does not

provide a full set of Input data, permitting to reproduce the design procedure . This set includes main engine characteristics, resistance curve, propulsion factors, hull and shaft line particulars, data for selected propellers, details on design Procedure, ship performance calculations, etc .

First of all it seems necessary to carry out comparative design of optimum propel-ler for axial flow conditions. Design example .1 is provided with the information,

published in (16). The problem is to select stock propeller to attain maximum speed in calm water of twin - screw hard - chine planing vessel . Two alternative gear

ratios are treated providing required value of propeller rate of rotation 1150 r.p.m. and 920 r.p.m. respectively. A three - bladed propeller with expanded blade - area ratio ratio

APrJA0

= 0.7

is considered and basic calculations in (16) are carried out with

computer program PHPRLM, developed in DTNSRDC (17),It is believed that the calcula-tions in (16) are performed for segmental section propellers, which geometry is closely similar to Gawn Burrill series . Accordingly, the comparative calcula -tions with program CPDSYS are carried out for Gawn - Burrill series propellers and the main data are presented in table

DESIGN EXAMPLE

1

(Data from D.Blount, E.N.Hubble - Propellers'81 Symposium Virginia Beach, 1981, paper No.7)

Planning Vessel, N = 1150 r.p.m., Delivered horsepower = 1176 h.p.

n 1150 r.p.m. _{AE/A0 = 0'700} Diameter Pitch Ratio Maximum Speed ,kn Remarks DTNSRDC computer program PHPRLM 0.864 0.88 23.8 Design for optimum Diameter AE/A0=0.70 BSHC Computer Programme 0.810 1.062 24.2 Design for Optimum Diam-eter A_/A =0 70 E. 0 ' 0.864 0.92 23.8 Comparitive

De-sign for Fixed

D and n,Optimum AE/A0 . 0'761 Diameter Pitch Ratio Maximum Speed,kfl Renarks

DTNSRUC 0.940 1.08 24.4 Design for Optimum

Computer Program

Diameter; Both Pro-pellers Found

Ac-PHPRLM 0.965 1.03 24.4 ceptable

0.90 1.19 25.1 Optimum Diameter Design

8SHC

Computer Comparitive Design

Programme 0.940 1.086 24.8 for Fixed D and n;

Op-timum A/A ' = 0 7E4 ___ 0 n =920 r.p.m AE/A0 = 070 -= : . =

The next examples illustrate the possibility for s,,lection of the best propeller among different systematic series.Firstly some results are presented for propeller operating in axial flow;the basic data are taken from (19).

COMPARATIVE DESIGNS

Propeller Operating in Axial Flow

Basic input data taken from the discussion to the paper

" The Design and Estimated Performance of a Series

of Supercavitating Propellers " ( Authors :

A.J.Tachmi-dji, W.B.Morgan ), presented at IV ONR Symposium on

Naval Ilydrodynamics(1962)

Hydrofoil Boat RI00

propeller selection for SES Bell - Halter 110, presented in ( 18 ). All cal culations are for Gawn - Burrill series propellers and the main purpose

is optimization of gear ratio .

It can be seen that for examples discussed the results obtained with our program are in good correspondence with the original data .

DESIGN EXAMPLE 2

Hand Calculation (Intermediate Stage) .

for SES Bell - Halter 110

(J.Allison, Marine Technology, vol.15, No.4, 1978)

Given: Expanded Blade Area Ratio 1.18

Diameter = 1.067 m

Pitch Ratio 1.40

Calculations for Opl.Mpim Rate of Rotation

Quantities Allison 115HC Program

Rate of Rotation 855 r.p.m. 840 r.p.m. Attainable Speed 35 kn 34.8 kn Propeller Diameter, m AE/A0 P/D Attainable speed, kn Original Superca-vitating Propeller 0.457 0.44 1.53 40.0 Newton-Rader Series 0.440 0.95 1.26 42.0 SK-Series 0.472 0.95 1.17 40.9 BSHC Three Bla-, _{0 ,i,1} I

4: '

-= : 47 .

Further , comparative designs are performed for propeller on inclined shaft.

This particular example is based on data presented in (20). The type of original propeller in (20) remains practically unknown, but as can be seen, certain pos -sibilities exist for selecting of propeller, providing nearly the same speed. In this particular case ( at low cavitation numbers ), the increase of disk area

leads to increase of attainable speed, as illustrated with calculations with Gawn - Burrill series .

COMPARATIVE

DESIGNS

Propeller Operating in Oblique Flow

Basic input data taken from example in Ship Theory Handbook, vol.3 , ( Ed.by Y.I. Voitkounski, Sudo

stroenie Publishing House,1985 ):

.

Planing Vessel

Delivered power Pu = 1571 kW

Propeller rate of rotation N = 1030 r.p.m. Angle of flow inclination = 12 deg

Propeller Diameter, m AE/A0 P/D Attainable ship speed, knots Original Propeller 0.95 1.10 1.60 40.5 Dawn- 1.018 1.18 1.517 39.6 Burrill 1.019 1.10 1.503 39.3 Series 1.069 0.95 1.394 38.7 Newton -Rader Series 0.918 0.95 1.716 39.6 BSHC Three Bladed Se-ries 1.018 0.95 1.446 40.7 1

I. Emerson A., and Sinclair L., Propeller Design and Model Experiments, SMM Ltd. Techn.Paper No.19, Birkenhead, England, 1979 .

Mavludov M.A., Roussetsky A.A., Sadovnikov Y.M., Fisher E.A., Propellers for

Nigh Speed Ships, Sudostroenie Publ. House,

1982, 280 p (

in Russian )

Pawn R.W.L., Burrill L.C., Effect of Cavitation on the Perfazmance of a Series of 16 - inch Model Propellers , Trans. INA,

vol.99,

March

1957 .

Newton R.N., Rader H.P., Performance Data of Propellers for High - Speed Craft, Trans. RINA,

1961, vo1.103, p. 93 - 179

.

Kozhukharov P., Sadovnikov Y., Frolov V., investigation of Cavitating Screw Propellers Operating in Oblique Flow, Second IME Conference on Cavitation, Edinburg,

1983

.

Ooosterveld M.W.C., Oossanen P.Van, Further Computer Analysis Data of the

Wageningen B - Screw Series, int. Shipbuilding Progress, vo1.22,

_1975.

Yossifov K., Zlatev Z. and Staneva A., Optimum Characteristics Equations _for the Wageingen B mod Screw Series, BSHC, 10th Anniversary Jubilee _Scientific

Ses-sion, vol.1,

1981,

Varna .

Zlatev Z., An Algorithm and Computer _{Programme for Multiple Linear Regression} Analysis , BSHC, 10th Anniversary Scientific Session,

vol.3, 1981,

Varna .

Kozhukharov P., Zlatev Z., Cavitating Propeller Characteristics and their Use in Propeller Design., High - Speed Surface Craft Conference, London,

_1983.

10.Kozhukharov P., Regression Analysis of Gawn-Burrill Series for Application _in

Computer-Aided High-Speed Propeller Desig,High-Speed Surface Craft Conf.,Southampton,1

1 986

Kozhukharov P., _{Investigation and Design of Cavitating Screw Propellers}

Opera-ting in Oblique Flow, Ph.D. Thesis, Leningrad Shipbuild. Inst.,

_1984.

Sadovnikov Y., and Kozhukharov P., On the Evaluation of Hydrodynamic Characte-ristics of Cavitating Screw Propellers in Oblique Flow : BSHC, 10th Anniversary

Jubilee Sci.Session, vo1.1,

1981,

Varna .

Kozhukharov P., Dimitrov V., Some Features of Computerized High - Speed Pro-peller Design Based on Data from Systematic Tests of Cavitating Propeller Se

-ries., Proc. IV IMAEM Congress, vo1.1, Varna, Bay,

1987 .

Kozhukharov P

Propeller Design,

1986, pp. 27 - 36

Bogdanov A.,

Speed Ships with

Hadjimikhalev Proc. of Intern. Hadjimikhalev V., Cavitating Screw Kozhukharov P., Propellers, Proc.

Performance Predictions for

High-16 ITTC,vol.2,

Leningrad,1981.

Blount D.L., and Hubble, N. Sizing Segmental Section - Commercially _Available Propellers for Small Craft, SNAME Propellers'81

_Symp.,1981,

Virginia Beach

Hubble N., Performance Predictions for Planning Craft in a Seaway, DTNSRDC Rep.

SPD-0840-02,

Sept. 1980.

Allison J., Propellers for High - Performance Craft, Marine Technology, No.

_15,

Oct. 15, Oct:

1978, 135 - 380

.

Tachmindji A.J., Morgan W.B., The Design and Estimated Performance of a Series

of

Super Cavitating Propellers,

4th

Symp.on Naval Hydrodynamics,

1964, 489-552.

Ship Theory Handbook Ed.by Y.I.Voitkunski, vol.3, Manoeuvrability of

Conven-tional Ships, Hydrodynamics of Gliders Hydrofoils and Hovercraft, Leningrad, Sudostroenie Publ. House,

1985

( in

Russian )

V., An Approach to Computer - Aided High - Speed Symp.on Propellers and Cavitation, Wuxi, China,

-4 -4. Mooring tension influence on :sway motion 1 characteristics , -- a .1 PageSi hl 11111,10C1' .01 '2".

Fig. 15c Wind force influence on %way motion characteristics g X C22 2,5 kg/m 3,7 kg/m 5,5 kg/m 0,0 kg/m 20 0,5 2 6 10 Fig.