Wake and thrust deduction from quasisteady ship model propulsion tests alone

Technische Hogeschoal

Delft

VERSUCHSANSTALT

FUR WASSERBAU UN

_SCHIFFBAU

kRCHIEF

Mani

k,

1111111UIVAI "Wv/A1111=110

vII111M.1.114

BERLIN

Wake and Thrust

_Deduction

from Quasisteady

_{Ship Model}

Propulsion Tests

_Alone

BERLIN MODEL BASIN

Wake and Thrust Deduction from Quasisteady Ship Mbdel

Propulsion Tests Alone

Michael Schmiechen

'shed on occasion of a visit

'apanese ship research institutes

'TC at Kobe in October 1987

Propulsion Tests Alone

Michael Schmiechen, VWS Berlin Model Basin

Abstract

After continued theoretical and experimental studies extending over the last eight years a procedure has been developed permitting the determination of the interaction between ship hull, propeller, and duct, if any, from rela-tively short measurements taken during quasisteady propulsion tests, i. e.

at small deviations from the service conditions. This systems identification procedure based on a few necessary and carefully selected axioms, i. e. conventions, may be the only meaningful, as e. g. for partially integrated ducts, and/or may be the only practical, as e. g. for full scale ships in operation.

The feasibility of this procedure has been proven in model tests using the standard measuring techniques available and has been finally developed for routine applications in towing tanks and circulating tunnels. After the previous fundamental work only the problems of reliable measurements of the acceleration and extrapolations to the equivalent states of vanishing thrust and vanishing advance ratio had remained to be solved. Where possible paral-lel evaluation of the measurements according to the traditional procedure is performed, as shown in the results of the model tests reported.

As expected the procedure provides much broader, more reliable, and more relevant information, even if the traditional procedure fails, and it can be performed faster and more cheaply as compared to the traditional technique based on propulsion tests at steady conditions and requiring extra hull towing and propeller open water tests, although these may provide rather meaningless results as e. g. open water tests with wake-adapted propellers.

As long as only few results are available judging the model results and predicting full scale performance remain of course major problems. One pos-sible and in some cases, e. g. of ducted propellers, necessary step towards better simulation of the flow around the ship, boundary layer suction at the model, has been successfully tested in a preceding project. The necessity of turbulence stimulation at the propeller is being investigated.

Not only for research into the scale effects, the present knowledge of which is based on very scarce data, it is imperative that the new technique be tested and utilized on board of full scale ships as soon as possible. It may then be used for research into and monitoring of the daily operation, e. g.

determination of effects of loading, water way, weather conditions, and fouling on all relevant efficiencies and factors of merit.

In view of its far-reaching impact on all aspects of performance analysis and prediction it is hoped that the community concerned will consider and

test the procedure proposed and explore its potential, maybe under the auspicies of the ITTC Powering Performance Committee as has been the case 50 years ago with Horn's proposal, an early forerunner of the present work.

1 Introduction 4

Test technique and data acquisition 6

Data reduction and extrapolation 9

Wake and propeller performance 12

Resistance and interaction 17

Conclusions 20 Appendices 22 References 24 Notation 25 Figures 27 -7. 10,

1. Introduction

Traditionally propulsion tests with ship models are performed at steady conditions. After the phase of model acceleration by the towing carriage the

model is released and its speed is adjusted to the constant carriage speed.

After steady conditions have been established the model speed, frequency of shaft revolution, propeller thrust, and propeller torque are being measured.

For a detailed analysis of the propulsive performance additional towing tests with the hull alone and open water tests with the propeller alone have

to be performed.

For many hull-propeller configurations this traditional procedure is quite

inadequate due to the different flow conditions in propulsion, towing, and

open water tests. The traditional procedure may be even impossible, as e. g.

for full scale ships. Consequently a procedure is in urgent need permitting

adequate propulsion analysis in any case under service conditions at model

as well as full scale.

A procedure taylored to suit exactly the problem outlined has been developed

on the basis of sets of axioms, principles, or conventions, i. e. three coherent and adequate mathematical models of hull-propeller interaction, namely the equivalent conditions of vanishing displacement wake, vanishing

total wake, and vanishing thrust (Schmiechen 1984, 1985). The data neces-sary are propeller thrust and torque as well as the necesneces-sary towing force

at a given constant speed for various frequencies of shaft revolution, I. e.

overload tests according to the British method.

Applying and measuring towing forces and adjusting steady conditions at model as well as full scale may be difficult if not practically impossible.

In towing tanks the application of towing forces introduces unnecessary

disturbances into the systems under investigation, while at full scale ships under service conditions towing forces cannot be realized.

Consequently it has been proposed to replace steady testing by quasisteady

testing at small quasisteady, but else arbitrary variations of the frequen-cy of shaft revolution around its service condition. In this case the

iner-tial forces replace the external towing forces. In principle this technique has been tested successfully some time ago with a set-up developed for different purpose (Schmiechen, 1984).

At this state of affairs the goal of the present project was to develop a technique for routine application in towing tanks and in circulating

tun-nels, where the problems are somewhat different as will be discussed in due

course. In order to save testing time and money and stick to steady testing at the same time the original idea was to use the control phase after re-lease of the model for data acquisition only. In view of the range and

qua-lity of data this idea was given up in favour of quasisteady oscillatory changes of the frequency of propeller revolutions.

After the preceding fundamental experimental and theoretical developments which have been carefully documented and discussed (s. 8. References) only

two problems remained to be solved, which had not been addressed thoroughly

before. The first problem was the reliable measurement of model accelera-tions in the range of less than ± 1/1000 g with a simple technique. The second problem was the meaningful, practical extrapolation to the states of

vanishing thrust and vanishing advance ratio, respectively.

The plan of this report is to describe the test technique, the model tests,

and, last but not least, the test results evaluated according to the ra-tional procedure proposed and according to the tradira-tional procedure for comparison. Theories will be presented only as far as necessary to link up

with the basic reference in English (Schmiechen, 1984). The paper will

con-clude with an outlook on future projects and prospects.

It is of historical interest that as early as 1937 at the 4th ITTC in Berlin

member organisations reported experience with an early forerunner of the

present method proposed by Horn and Dickmann (Weitbrecht, 1937). The tests had been carried out following a recommendation of the 3rd ITTC in Paris 1935. The present work is the result of a new attempt to solve the old

prob-lem in the spirit of Horn using more powerful philosophical, experimental,

2. Test technique and data acquisition

The analysis of the propulsion performance of a ship model in a towing tank

is based on

-

1...n

sampled sets of measured values of the carriage speed Vi, the frequency of

propeller revolutions Ni, the propeller thrust Ti, the propeller torque Qpi,

maybe towing forces Fi, and the model displacement Si relative to the

car-riage.

Differentiation of the displacement results in values of the relative model

speed Vi and further differentiation in values of the relative model

accele-ration Ai. If the small oscillations of the carriage speed at the tests are

of higher frequencies than the changes of the relative model speed caused by

the quasisteady changes of the frequency of revolutions the total model

speed is

r

Vi Vi + Vi

and the total towing force is

Fi - Fi - m Ai .

This simple filter technique can be applied e. g. in the deep water tank of

VWS, while in the shallow water tank low frequency oscillations of the

car-riage had to be accounted for in later tests according to the complete

equa-tions of the total speed

f r

Vi Vi + Vi

and the total force

Fl - m Ai Fi

with the total acceleration

-1

-f r Al - Ai Ai .

In the circulating tunnels the equations to be applied are simply

Vi =V

and

Fi = Fi .

The differentiations necessary are simply performed via Fourier analysis with subsequent synthesis, the noise being suppressed by ignoring orders beyond the range of interest. At the tests reported 200 sets of samples have

been taken in about 2 minutes covering about 4 periods. Consequently

harmo-nic components up to the 15 order have been considered to be relevant. Small drifts have been accounted for separately. The first set of figures shows

the basic data of a randomly chosen test run without any correction.

In the range of interest of less than ± 1/1000 g measurement of the accele-ration cannot be performed by an accelerometer on the model. Although an attempt to keep the accelerometer free of the small pitch motions of the model was successful the noise introduced by the model drive did upset the

measurement. Finally a simple potentiometer was used to measure the relative displacement of the model in the range of about ± 0.3 m relative to the carriage and two consecutive differentiations were performed without problem

as described.

The inertia or mass m of the model may be derived from its desplacement volume V and the density p of the water and the inertial effects of the

sur-rounding water, i. e.

m = pV + mx .

In the present study a constant ratio

mx/pV = 0.05

has been used for the model ratios =

L/B

6.589

and

B/T = 3.917

based on the idea of an equivalent ellipsoid.

To directly measure towing forces acting on a model rigidly connected to the carriage by a balance is impossible due to carriage control. As already mentioned the situation is different in circulating tunnels. In full scale

tests the technique described for tests in towing tanks can be applied

with-out change. The solution of the various measuring problem will be subject of a research and development project funded by the German Federal Ministry

3. Data reduction and extrapolation

The basic data obtained in quasi-steady propulsion tests as described before have to be reduced before a performance analysis can be undertaken.

Follow-ing the arguments of the theory of similarity any quasisteady state may be uniquely described by

the thrust ratio

KT ; T/(pD"N2) = kT (JH, Fn, Rn)

the torque ratio

Ku

E Qp/(pD5N2) = ku (JH, Fn, Rn) and the force ratio

KF a F /(pD"N2)

=k

(JH, Fn, Rn)

as function of the hull advance ratio

JHa V/(DN)

the Froude and the Reynolds numbers Fn and Rn, respectively.

The thrust, torque, and force functions k are a complete description of the quasisteady dynamics of the hull-propeller system in the range investigated

at the average Froude number

Fn E Ti/(g

L)112

under consideration. As indicated the dynamic functions k are further de-pending on the normalized viscosity, i. e. the Reynolds number

Rn E VL/v

or the ratio of Reynolds and Froude numbers

r E R0/F0 g1/2

L3/2/v

s E (IVF,)2/s L g'13/v213

the latter two being constant for a given model at a given water condition.

Extensive investigations have shown that in the present tests the small deviations of the Froude number from the average had no detectable explicite influence on the dynamic functions. In view of the omnipresent noise it can

be safely assumed that this situation will be the same in general. Conse-quently the axiom or convention

K = k(s,Fn)(J1-1)

may be stipulated.

In view of the excellent test conditions in the deep water tank of VWS the

noise in the measurements was felt to be somewhat large. As the cross corre-lation of the torque and force ratios with the thrust ratio indicate this noise was due to the resolution of the frequency of revolution being too poor for the purpose at hand. Further the torque data of the run selected show that there has been some systematic problem at higher propeller

load-ings which was not observed at other runs.

In view of the noise, which will be larger in most cases, e. g. in

circulat-ing tunnels and at full scale, and the extreme range of extrapolation it was found after much deliberation and experimentation that the only way to

ob-tain a meaningful set of faired propulsion data, were linear fits to the

functions

1)

KT = kTH(JH) KTO

4H

41 and

(1)

Ku = ku(KT)

Kuo + KuT KT

.

Again these linear laws have to be agreed upon as axioms, I. e. as adequate

principles under the conditions given, and the way of fairing may have to be

described in the basic reference, for numerical reasons after normalisation

of the range of investigation to

-1 5 x 5 + 1

where

x E (JH JHC)/JHR

Jfic denoting the centre and JHR the radius of the range. The two linear functions so obtained may of course be combined to derive the linear

rela-tion

Ku =

Kuo

NpH oH

between the torque and the hull advance ratio.

The purpose of the extrapolations will be explained in detail in the next

chapter. They are certainly not intended to predict the performance of the

propeller outside the range of observation. Quite to the contrary the

pur-pose is to continue the tendencies observed in the vicinity of the service

condition. As can be seen from the data presented and as can be concluded by theoretical arguments a linear fit to the force data is not adequate. This

problem will be addressed after the elaboration on the determination of the

total wake and the various performance parameters of the propeller which can

be evaluated as soon as the wake is known.

4. Wake and propeller performance

The theoretical background has been comprehensively documented in the basic

reference in English

(1984)

and in the final report on model tests with boundary layer suction in German

(1985),

the latter containing in addition a complete theory of wake interpretation. This wake theory has been published

in English as an appendix in a paper on the model tests with boundary layer

suction with very limited distribution so far (Schmiechen,

1986).

Conse-quently this theory is repeated here for ready reference.

The theory of wake as presented in Section 3.5 of the ONE paper suffers from

a serious drawback: it is limited to the determination of the nominal wake

and it is based on a more or less acceptable hypothesis; it does not permit to account for the non-uniformity of the propeller inflow behind the hull and is hence not sufficient for application to cases of practical interest.

A consequence of the non-uniformity of the propeller inflow in the behind condition is the dependence of the wake fraction on propeller loading,

con-teary to

the open-water conditions, which have been extensively used to test various hypotheses.

According to the earlier considerations the problem can only be solved by the introduction of axioms or conventions coherently defining the propeller

losses as compared to an ideal propeller over the total range of advance ratios. While the concept of the equivalent state of vanishing thrust proved

to be insufficient, the concept of the equivalent open-water conditions offers a solution of this interpretation problem. As required the solution

is as close as possible to the traditional procedure which refers to the actual open-water performance of the (model) propeller.

The equivalent open-water (performance of the) propeller may be defined axiomatically or coherently by the quadratic loss function

(1) (2) 2

KPL ° kPLP(JP) KPLO KPLPO JP KPLP JP/2

or the corresponding function for the torque ratio

The fact that the loss curves of propellers in the open-water condition are practically quadratic parabolas is a plausible argument in favour of the axiom but evidently no proof. It is particularly appropriate here to note

(again): axioms cannot be proven to be true but only to be more or less

ade-quate and acceptable conventions with a very strong normative aspect.

The three parameters of the function, namely the 0th, 1st, and 2nd

deriva-tives with reference to the propeller advance ratio at the point of

vanish-ing advance ratio, may be determined as follows.

In extension of the basic propositions it is postulated that the functions

KT ' kTH(JH)

and

observed

in a limited range of the hull advance ratio can not only be

extra-polated to the state T of vanishing thrust defined by the equation

KTT kTH (HT) = 0

but also to the state 0 of vanishing advance ratio. Contrary to the state T

the state 0 cannot be reached physically at constant speed V, but only by extrapolation .

From the values of the thrust and power ratios at the state 0, KTo and KpPO,

respectively, and the values of their first derivatives at that same state,

(1) (1)

KTH0 and KppHo, respectively, the loss ratio

KPLO = KPPO (2/10112 KT0312

and its first derivative

(1) (1) (1)

KPLPO = KPPHO KTO/2 (2/w)112 3/2 KTO''' KTHO

at the state of vanishing advance ratio may be determined. The latter

WO 0

at infinite propeller loading.

At the state of vanishing thrust, i. e. at the advance ratios JHT or JpT the loss ratio equals the power ratio

KPLT KPPT

as stated earlier. Consequently the second derivative of the loss function

kpLp in question is

(2) (1)

KpLp - 2 (KpLT KPLO KPLPO JPT)/JPe

with the nominal advance ratio JPT of the propeller so far unknown.

This may now be determined from the relation

, (1) v(1) ,,,,(1)

JPT OCPPHT ,PLHT,,NTHT

and the relations

(1) (1)

KPLHT KPLPT JPT/JHT

and

(1) (1) (2)

KPLPT KPLPO KPLP JPT

The explicit result

(1) (1)

JPT (KPPHT 2 (KPLT KPLO)/JHT)/(KTHT

(1)

KPLPO/JHT)

finally and completely defines the equivalent open-water conditions, namely

expressed solely in terms of extrapolated values from propulsion tests.

The rule for the determination of the nominal propeller advance ratio stated

in the paper is equivalent to the rule

, (1) JPT -2 KpLo/KpLpo

-and is evidently a special case of the above much more general rule. Both are good approximations for a wide range of open-water conditions but the latter is insufficient for practical applications and, as shown, an

unneces-sary simplification.

At each hull advance ratio the effective propeller advance ratio may now be

determined iteratively from the relation for the jet efficiency, if this is

written as follows:

Jp

Kpj/KT - (2/7)'/' KT2/Kpj

with the power ratio

Kpj = Kpp - KPL = KPP

KPL (4) .

Consequently the values of the wake fraction

w 1 - Jp/JH

and all other quantities may be determined.

It may be mentioned here that before the final formulation of these

conven-tions, which after all appear pretty selfevident, a great number of other axioms have been proposed and tested with considerable theoretical and

nume-rical effort. All the insights and results arrived at in these attempts are incorporated in the present theory and results. Intermediate negative

re-sults, sometimes leading to the conclusion that the problem might have no acceptable solution at all, turned out to be only incomplete solutions and necessary building blocks for the total, final solution outlined here and formalized in Appendix

7.2

For ducted propellers a corresponding theory has been developed exactly along the same lines. In view of partially integrated ducts and the problems

of measuring duct thrust in general, full scale in particular, the theory is based solely on measured propeller thrust.

According to the fact that only linear functions KT and

Ku

or Kpp are prac-tical the foregoing argument assuming quadratic functions can be simplified

if the conditions

-and (1) _.(1) KIND Y,TH (2) i.e. KTH 0 (1) (1) (2) KQpHo = KQF,H , i.e. KQpH u are introduced.

Extensive numerical tests have been carried out showing only a slight

de-pendence of the wake values on the type of extrapolation. The reason may be seen in the fact that the extrapolation is used for the construction of the

loss parabola, of which only the very small portion in the range of

observa-tion is of interest. The advantage of the linear extrapolaobserva-tion advocated is

its "stability" as the results of the tests show.

After the wake has been determined the various performance parameters of the propeller can be determined. Presented are the jet efficiency as a measure

of propeller loading, the propeller efficiency in the behind condition and

the propeller factor of merit, as a measure of quality; s. below. In all plots the symbol (index) r denotes results according to the present rational method, while the symbol t refers to results of the traditional evaluation,

either according to thrust (T) or torque identity (Q) based on the open-water performance.

It is important to note here that the values of the wake fraction determined according to the method proposed from propulsion tests alone are much larger

than those of any of the wake fractions determined in the traditional way.

Accordingly the values of the rational jet and propeller efficiencies are lower. More interesting are the low values of the rational propeller factor

of merit, i. e. in the behind condition, which appear to be more reasonable than the open water values. The rational factor of merit is an appropriate

measure of quality, e. g. of adaptation to the wake, while the traditional

ones are not particularly meaningful. Who is interested in open-water performance of a wake adapted propeller and who is basing his analysis on this performance?

-5. Resistance and interaction

In order to continue the performance analysis the resistance in the range of

operation (observation) has to be determined. Traditionally this is done by

physically towing the bare hull or the ship with the propeller producing no

net thrust at the speed of interest. This procedure may result in irrele-vant values due to differences in the flows at the service and at the towing

condition, respectively.

Corresponding to the determination of the wake from the equivalent open-water conditions the concept of the equivalent state of vanishing thrust might be introduced and rendered operational as follows. With the extrapo-lation of the observed values of the force ratio

KF ' kFH(JH)

defining the service condition or "point" JHs

kFH(JHS) ° 0

and the value of the force ratio

KFT kFH(JHT) KR

at the towing "point" JHT

kTH(JHT) - 0

the resistance is obtained according to the relation

R p1)21/2CR

with

The very first tests already showed that this straightforward procedure is impractical due to the noise and the range of extrapolation. The idea to solve the problem by introducing special two-parameter functions fitting the

values of the force ratio proved to be very effective, but unsatisfactory,

not meeting the standards set in the work before. It was felt that addition-al conventions or conditions of a more generaddition-al nature should and might be constructed.

After a large number of numerical tests the axiom or convention

wE/w = const = w

was found to be the most appropriate. It reduces the problem to a two-pa-rameter problem (CR, to) requiring no artificial functions to be introduced and no extrapolation to be performed, but rather interpolation of admittedly

very noisy data.

The non-linear estimation problem defined by the final axiom has been solved by the following simple minded procedure avoiding any involved non-linear search algorithms or similar, prone to instability etc. For three selected,

for simplicity equidistant values of the wake ratioco the optimum values of

the resistance coefficient CR have been estimated together with the corres-ponding values of the standard deviation. Using a quadratic fit to the

val-ues of the standard deviation its minimum value has been determined as well

as the corresponding values of CR and w.

The subsequent evaluation of all measures of interaction, namely the thrust

deduction fractions, the propulsive efficiencies, the hull efficiencies, the

configuration factors of merit, the displacement influence ratios, and the

energy wake fractions poses no problems at all, at least from the numerical

point of view.

But there are of course conceptual problems with some of the results denoted

by t, implying that they are determined according to traditional method, via the thrust or torque identity, respectively. Very clearly some of the

Consequently the above implication is misleading and the comparison between

the results of the rational procedure and the "traditional" procedure is not

possible.

The traditional procedure does not provide implausible results, but no

re-sults at all. The concepts in question are the displacement influence and the energy wake fraction. The results of the present method are, at least in

the present example, plausible and consistent. This is very remarkable in view of the well-known sensitivity of the performance analysis.

The final evaluation for the test runs at various Froude numbers depends on

the purpose at hand. In the present context cross-plots are shown for the

constant hull advance ratio

JH = 0.7.

In order to ensure consistency of the results the values of the ratios KT,

KQ, wr and (wg/w)r for the four successful runs have been used to define cubic interpolation functions (i. e. no fairing has been applied!), from which all the other functions have been derived in the whole range of Froude numbers covered. The traditional evaluation has been based on fourth order polynomial fits of the KT0, KQ0 and CRt values.

Noteworthy, maybe even surprising is the agreement between the rational and the traditional resistance values, which has already been observed at an-other model (Schmiechen,

1985,

1986).

As a consequence the values of the thrust deduction fractions and the propulsive efficiencies are in good agreement as well. The essential differences between the rational and tradi-tional procedure, respectively, appear to exist in the evaluation of the wake fractions with all the implications.

6. Conclusions

The present study has shown by way of example that based on the ideas

pro-moted now for eight years an adequate and effective system identification procedure for testing and analysing the propulsive performance of ship

mo-dels in towing tanks and circulating tunnels can be derived. As expected the

procedure provides much broader, more reliable, and more relevant

informa-tion, even if the traditional procedure fails, and it can be performed

faster and more cheaply as compared to the traditional technique based on propulsion tests at steady conditions and requiring extra hull towing and propeller open water tests, although these may provide results of rather doubtful value as e. g. open water tests with wake-adapted propellers.

The technique of quasisteady testing can be performed with the standard measuring techniques available in every towing tank. And the technique of analysis is based on the conceptual frame work familiar to every naval

ar-chitect with the addition of only a few carefully selected axioms permitting

an analysis on the basis of only one coherent set of data obtained under service conditions.

It is important to note here that the axioms are conventions to be agreed upon by the parties interested. The rational method advocated is therefor a

conventional method as is the traditional method. The difference is that the axioms of the rational method are explicitely stated and more or less

plau-sible, constituting coherent mathematical models, while the traditional

conventions and their implications are hard to grasp.

As long as only few results are available judging the model results and predicting full scale performance remain of course major problems. One

pos-sible and in some cases, e. g. of ducted propellers, necessary step towards better simulation of the flow around the ship, boundary layer suction at the

model, has been successfully tested in a preceding project. The necessity of

turbulence stimulation at the propeller is being investigated.

Not only for research into the scale effects, the present knowledge of which

is based on very scarce data, it is imperative that the new technique be tested and utilized on board of full scale ships as soon as possible. It may

then eventually be used for research into and monitoring of the daily ope-ration, e. g. determination of effects of loading, water way, weather condi-tions, and fouling on all relevant efficiencies and factors of merit. As has been mentioned a project to this effect funded by the German Ministry of Research and Technology is well under way.

In view of its far-reaching impact on all aspects of performance analysis and prediction it is hoped that the community concerned will consider and test the procedure proposed and explore its potential, maybe under the auspicies of the ITTC Powering Performance Committee as has been the case 50

years ago with Horn's proposal, an early forerunner of the present work.

It is important that the normative aspect of the whole procedure proposed be

fully understood and appreciated. Further, standardisation of procedures for measurement and analysis will have to be agreed upon. This is absolutely mandatory in view of the measurement noise and the sensitivity of the

ana-lysis.

The present report is a preliminary version of the final report on a project

administered by the Forschungszentrum des Deutschen Schiffbaus in Hamburg.

Funding derived from the European Recovery Program and made available by the Senator fur Wirtschaft und Arbeit in Berlin is gratefully acknowledged.

The impact of the present work and its underlying philosophy on the design

of propellers has not been mentioned in this report. Work has been done in this field (Schmiechen and Zhou, 1987) along the lines indicated in a

7. Appendices

7.1 Program system

For the development and testing of the whole procedure of performance analy-sis a system of integrated computer programs has been designed and

continu-ally adapted to the actual problems on the towing carriages and in the

cir-culating tunnels of VWS. The implementation was realized in terms of the BASIC-dialect HPL on the desk-top computer systems HP9825 presently still in

service in the various test fields at VWS.

The system of programs is constructed in a modular fashion and can be

inte-grated easily into larger systems. It will be further improved according to

the experience gained when implemented in FORTRAN on the new HP A600 and 400

systems to be installed in the near future and to be used in the full scale

tests to be performed within the next two years.

The structure of the system of programs reflects the basic TASKS to be per-formed. A small ROOT permanently recident in core, permits branching to the

various TASKS, the corresponding programs, segments of programs, and rou-tines being loaded as necessary, in many cases automatically.

7.2 Axiomatic theory

Basic concepts, additional

VH hull speed

N frequency of revolution

D : propeller diameter

PL : propeller lost power Qz : propeller torque

Derived concepts, selected

Jx

E Vx/(DN) : advance ratios : X e (H, P)

Ky E Y/(pD"N2) : force ratios : Y E (T, F) KQz Qz/(pDsN') : torque ratios : Z E (P, L)

Kp E Pzi(pD5N2) :

power ratios

Z E

_{(P, L)} KUV = kUX(JXV) U E (T, F, QP, QL, PP, PL) V E (0 : Jx - 0, T KT - 0) X E (H, P) (i)

Kuxv2 (3i

KuiaJxj)v

:

derivatives

:

j

1, n

Basic propositions, additional

. (4A/7)1/2 QZ Pz/(27r N) VH

-v

k(s, ',0(JH) (1) KT

_-KTO

_{KTH JH} (1) KQP - Kopp + KuH JH KPL Kpp - Kpj (1) (2) KPL kpLP(JP) KPLO KPLPO JP KPLP 42/2 w0

-o

KpLT KpPT WE = w Derived propositions KPLO KPPO (2/w)'2 KT03/' (1) (1) KPLP0- KPPHO KT0/2 - (2/7)./2 _{-T0'/2 KTHO}

k1)

KpLp 2(KpLT KPLO)/JpT2 aPLPO/JPT (1) (1) (1) JPT (KPPHT - 2(KpLT KPLO)/4T)/(KTHT KPLPO/JHT) Jp Kpj/KT - (2/w)1/2 KT2/Kpj KpJ - KpP KPL

=1

=

-8. References

Schmiechen, M. (1968): Performance Criteria for Pulse-Jet Propellers. Proc.

7th Symp. on Naval Hydrodynamics, pp. 1085-1104.

Schmiechen, M. (1970): Ober die Bewertung hydromechanischer Propulsionssy-steme. Schiffstechnik Vol. 17, No. 89, pp. 91-94.

Schmiechen, M. (1980a): Eine axiomatische Theorie der Wechselwirkungen zwi-schen Schiffsrumpf und -propeller. Schiffstechnik, Vol. 27, No. 2,

pp. 67-99.

Schmiechen, M. (1980b): Nachstrom und Sog aus Propulsionsversuchen allein. Eine rationale Theorie der Wechselwirkungen zwischen Schiffsrumpf und -propeller. Jb. STG, Vol. 74, PP. 333-351.

Schmiechen, M. (1982): Ober Weiterentwicklung des Vorschlages "Nachstrom und Sog aus Propulsionsversuchen allein". Schiff & Hafen, Vol. 34, No. 1,

pp. 91-92.

Schmiechen, M. (1984): Wake and Thrust Deduction from Propulsion Tests Alone. A rational theory of ship hull-propeller interaction. Proc. 15th Symp. on Naval Hydrodynamics, pp. 481-500.

Schmiechen, M. (1985): Schiffsmodellversuche mit Grenzschichtbeeinflussung durch Absaugung. VWS-Bericht Nr. 1021/85; EDS-Bericht Mr. 163/85.

Schmiechen M. (1986): Ship Model Tests with Boundary Layer Suction. VWS Report No. 1071/86.

Schmiechen, M. (1983): On Optimal Ducted Propellers for Bodies of Revolu-tion. Proc. Int. Symp. on Ship Hydrodynamics and Energy Saving (El Pardo), No. VI, 2, pp. 1-7.

Schmiechen M. and Zhou, Lian-di (1987): An Advanced Method for the Design of Optimal Ducted Propellers Behind Bodies of Revolution. VWS Report No. 1083/87; Final report on a Partnership in Engineering Sciences spon-sored by Stiftung Volkswagenwerk.

Weitbrecht, H.M. (Ed) (1937): Proc. 4th ITTC: Internationale Tagung der Leiter der Schleppversuchsanstalten. Berichte, Beitrage und Ent-schliessungen. Berlin: Preussische Versuchsanstalt fur Wasserbau und

9. Notation

The symbols of concepts introduced in the sections indicated correspond as

far as possible to the ITTC Standard Symbols 1976, but have a slightly

dif-ferent meaning, which may not be inferred from the names of the concepts, but only from the formal contexts and the operational interpretations

deve-loped in preceding publications, the basic reference in particular, and the

present report. S. also Appendix 7.2

9.1 Quantities

Symbol Section Name

A 2 acceleration

2 breadth of model

CF 5 force coefficient

CR 10 resistance coefficient

3 diameter of propeller

10 efficiencies, factors of merit explanations s. 10

definitions s. Schmiechen, 1984

2 force

Fn 3 Froude number

Jli

3 hull advance ratio

JP 4 propeller advance ratio

k 3 dynamic functions

Kp 3 force ratio

KPL 4 lost power ratio

Kpp 4 propeller power ratio

KQL 4 lost torque ratio

Ku

3 torque ratio KR 5 resistance ratio KT 3 thrust ratio L 2 length of model Lpp 10 length of model m 2 mass, inertia n 2 number of samples 'B F

frequency, alias number, of revolutions resistance Reynolds number scale factor relative shift draught of model draught aft draught forward

total wake fraction

energy, alias frictional, wake fraction

kinematic viscosity density wake ratio displacement volume 9.2 Indices f 2 basic, carriage F 3 force i 2 current sample 4 loss P 3 power,

propeller

torque

2 relative 4,10 rational t 4,10 traditional tQ 4,10 torque identity tT 4,10 thrust identity T 2 towing T 3 thrust N 2 R 5 Rn 3 $ 3 S 2 T 2 TA 10 TF 10 w 4 wE 5 v 3 P 2 w 5 '7 2 L

10. Figures

Data of Model No. 2491.0 and Propeller No. 1340

Body plan

Contours of stem and stern

Towing resistance

Propeller open water performance

Basic data of test No. 8

Functions of time t

Speed of towing carriage

Shaft frequency of revolution

Thrust of the propeller

Torque of the propeller

Relative displacement of the model

Relative speed of the model

Acceleration of the model

Reduced data of test No. 8

Functions of hull advance ratio JH

Froude number

Thrust number or ratio

Torque number or ratio

Force number or ratio

V = f(t) N f(t) T f(t) Q f(t) S f(t) VR = f(t) A = f(t) FN = f(JH) KT = f(JH) KQ = f(JH) KF = f(JH)

Functions of hull advance ratio JH

Propulsion data KT, KQ, KF = f(JH)

Results of test No. 8

Functions of the force ratio KT

Torque number or ratio KQ f(KT)

Force number or ratio KF = f(KT)

Faired data of test No. 8

Functions of hull advance ratio JH

Wake fractions w = f(JH)

Jet efficiencies ETJ f(JH)

Propeller efficiencies ET? f(JH)

Propeller factors of merit EJP f(JH)

Thrust deduction fractions t f(JH)

Propulsive efficiencies ERP - f(JH)

Hull efficiencies ERT f(JH)

Configuration factors of merit ERJ = f(JR)

Displacement influence ratios CHI - f(JH)

Energy wake fractions WE - f(JH)

=

Results of tests No's

ii,

4, 5, 8 for hull advance ratio JH - 0.7

Functions of Froude number Fn

Propulsion data

Wake fractions

Jet efficiencies

Propeller efficiencies

Propeller factors of merit

Resistance data

Thrust decuction

Propulsive efficiencies

Hull efficiencies

Configuration factors of merit

Displacement influence ratios

Energy wake fractions

KT, KQ, KF f(FN)

w

f(FN) ETJ f(FN) ETP f(FN) EJP f(FN) CR, wE/w = f(FN) t f(FN) ERP f(FN) ERT f(FN) ERJ = f(FN) CHI f(FN) WE - f(FN) = =

Scale

1 :

1 60

Mod. No.

2491.0

VW'S Berlin

Body

Plan

u,

:i

1 ransom

\

0. 5

1. 5

3

Scale

1 :

160

1 8 I

2

ig

Contours of Stem and Stern

20

VW'S Berift

2

H

Mod. No

2491.0

Towing Resistance.

"V [m/s]

V WS Bailin

1

0.6 -

0.5 -

0.4

0.3 -

0.2 -

0.1 -

0.0

00

0.1

0.2

0.3

0.4

Prop. No.

_1338-1345

no

0.5

0.6

0.7

0.8

CP-Propeller No. 1340

Dm = 0,195 m

P/D = 0,813

AE/A0 = 0,65

0.9

z = 4

right-handed

J

VWS Berlin

Propeller Open Water Test

QUASI STEADY PROPULSION

GESCHWI ND I GrE I!T

BASIC SPEED

DATUM

= 8609090000

MOO. NO . =

2491 . 00

P FOP .NO =

1340.00

TEST .NO .=

8.00

TF /LPP

=

3.93E-02

TAAPP

=

3. 93E-02

5.19E 07

FN =

1.68E-01

CF

1.83E-01

JHS

=

6.97E-01

1.40 0.00 1.20 1.40

t/(100see)

QUASISTATIONAERE PROPULSION

QUASISTEADY PROPULSION

DREHFREQUENZ

FREQUENCY OF REVOLUTION

J.03 1.10 N/(10Hz) k

*

k k k * * * * * * *

.

*

*

*

* Mc * Nt

*

*

*

* * * MO *

*

*

1* k * * * * * * *

*

k

*

* Oria

.

*

.

k *

* *

*

*

I*

k

*

*

*

k k

*

Mc

.

*

0* It Mk

*

3.30 ft

DATUM

= 8609090000

MOD. NO.=

2491.00

PROP.N0.=

1340.00

TEST.N0.=

8.00

TF/LPP

= 3.93E-02

TA/LPP

= 3.93E-02

PN/FM

=

5.19E 07

FM = 1.68E-01 CF =

1.83r-01

JpS = 6.97E-01 1.40 t/( 100sec)

QUASISTEADY PROPULSION

SCRUB

THRUST

r/(100N),, * *

*0

*k:

DATUM

= 8609090000

M01. NO.=

2491.00

PROP.N0.=

1340.00

TEST.N0.=

8.00

TF/LPP

=

3.93E-02

TA/LPP

=

3.93E-02

RA/FN

=

5.19E 07

FN

=

1.68E-01

CF =

1.83E-01

JHS =

6.97E-01

1.40

t/(100sec)

QUASISTATIONAERE PROPULSION

QUASISTENDY PROPULSION

DREHMOMENT

TORQUE

0.1)0 0.90 OP/(Nm)'

***

1***; # **

* *

**ft *

.

k 1*

*

*

:

*

_*#

**,, 19, * * * * k N * ** * ft ft Jr

*

* k

*

irk 0.'53 11,4* **t. * * ft

DATUM

= 8609090000

MOD. MO.=

2491.00

PROP.NO.=

1340.00

TEST.N0.=

8.00

TF/LPP

= 3.93E-02

TN/LPP

3.939-02

RN/FN

5.19E 07

FN

1.68E-01

CF

1.83E-01

711S

6.97E-01

*ft

:*

* k * * _* * ** *1,

*

*

* _* * * * *

*

*

41, * * * * Or

*

I

*

_*

* * **

:

ft * 4* P, I I 4 I 4 .444

I*

4

4I

ft 1.40

t/(100sec)

=

QUA FI FTFAD Y PrOPULFION

DATUM

= 86090 90 00 0

MOD. NO =

24 91. 00

PPOP .NO .=

1340.00

TEST

.NO .=

8.00

TF/LPP

=

2. 93E-02

TA/LPP

=

3. 93E-02

PN/FN

=

5.19E 07

PE LATIVF VF PSCNT FBU VC FY =

1. 68E-01

PELATIVE SHIFT

Cr

1. 8 3F-01

JFF

6. 97F-01

,QUASISTATIONAERE PROPULSION

QUASI STEADY PROPULSION

RELATIVE GESCHWI,NDIGKE'Ir

RELATIVE SPEED

0. 301

VR/(0.1m/s1

et,*

*

t.

*4

**

it

*

.

* .

*.

*.

i

,

...

*

*

.

* ,..

*

6

*

.

*

it ir * -* * *. ' ti, 444'' *. * * * * _* * * _*

* :

* * * .00 *. *

"'1.40

t/(100sed)

' * 8* * *

* *

*' * * * *lit* _* *

* *

* *fte,

0. 40

DATUM

= 860909,0000

MOD. NO.=

2491.00

PROP .NO = 1340. 00 TEST .NO .= 8.00

TF/LPP

3. 93E-02 TA/L PP =

3.93E-02

RN/FN

5.19E 07

FN

1.68E-01

CF

1.83E-01

JHS

6.97E-01

= *

QUAS1STEADY PROPULSION

DATUM

= 8609090000

4)0. NO.=

2491.00

PROP.N0.=

1340.00

TESP.N0.=

8.00 TF/LPP = 3.93E-02

TA/LPP

= 3.93E-02 R1/F1 =

5.19E 07

FN =

1.68E-01

CF =

1.83E-01

ills

=

6.97C-01

BESCHLEUNIGUNG

QUASISTATIONAERE PROPULSION

QUASI STEAD

PROPULSION

FROUDE-ZAHL

FROUDE NUMBER

DATUM

= 8609090000

MOD. = 2491.00 PROP .NO. = 1340.00 TESP.NO .= 8.00 TF/L PP = 3.93E-02

TA/LPP

3. 93E-02 RN /FN 5. 19E 07

FN

1. 68E-01 CF

1.83E-01

J HS

6.97E-01

=

WASItiTEADY

pROPuLSION

SCHUBZAHL

THRUST

NUMBER DATUM = 86.0909000J

43B. NO.=

2491.00

PROP.N3.=

1340.00

TESP.N0.='

8.00

rF/LPP = 3.930-02

'TA/PP

= 3.93E-02 RI/FN

5.19E 07

FN =

1.68E-01

CF

1.83E-01

JHS

6.97E-01

=

QUASISTATIONAERE

PROPULSION

QUASISTEADY PROPULSION'

MOMENTZ

TORQUE NUMBER

0. 30

10*KQ

j* ** t*

0

na

*** ** * *

:*

** * * *# *

0

0.10

DATUM

= 8609090000

MOD. ND.

2491.00

PROP .NO =

1340.00

rEsT .N3 . =

8.00

PF/LPP

=

3.93E-02

TA/GPP

=

3.93E-02

RN /FN =

5.19E 07

FN

1.68E-01

CF

1.83E-01

JHS

6:97E-01

* * *4*** -*

_{* *}

4

_{* -*}*it

0.80

TIT

QUASISTEADY PROPULSION

KRAFTZAHL

FORCE NUMBER

DATUM

= 8609090000

MOO. NO.=

2491.00

PROP.N0.=

1340.00

TEST.N0.=

8.00

TF/LPP

=

3.93E-02

TA/LPP

=

3.93E-02

RN/FN =

5.19E 07

FN

1.68E-01

CF

1.83E-01

JHS

=

6.97E-01

QUASISTATIONAEPE PPOPULSION

QUASISTEADY PPOPULSION

MOMENTZAEL

TORQUE NUMBER

DATUM

= 8609090000

MOD. NO.=

2491.00

PROP.40.=

1340.00

TESP.NO.=

8.00 rF/LPP = 3.93E-02 TA/L,PF = 3.93E-02 RN/FN 5.19E 07 FN

1.68E-01

CF 1.83E-01

J8S

=

6.97E-01

0.10

QUASISTEADY

PROPULSION

KRAFTGAHL

FORCE NUMBER

DATUM

= 8609090000

MD). 'fl.=

2491.00

PROP . NO . =

1340.00

TES r .NO =

8.00

TF/LPP

=

3.93E-02

TA/LP 2

=

3.93E-02

/FN = 5.19E

07

FN

=

1.68E-01

CF =

1.83E-01

J HS =

(3. 97E-01

.

QUASISTATIONAERE PROPULSION'

QUASISTEADY PROPULSION

PROPULSIONSDATEN

PROPULSION DATA

0.40 -DATUM

= 8609090000

MOD. NO.=

2491.00

PROP.N0.=

1340.00

-rssr.No.=

8.00

TF/LPP

= 3.93E-02

TA/LP?

= 3.93E-02

RN/FN

5.19E 07

FN

1.68E-01

CF

1.83E-01

3E11

6.97E-01

WNSISTEADY

PROPULSION

NACHSTROMZAHLEN

WNKE EMMONS

0

0

0.60

kkh""

+++

++

++++

tT

oo

tO

oo

o

000

DATUM

= 8609090000

MOD. NO.=

2491.00

PROP.N0.=

1340.00

rESr.N0.=

8.00

rF/LPP

= 3.93E-02

TN/LPP

= 3.93E-02

RN/FN

=

5.19E 07

FN =

1.68E-01

CF

=

1.83E-01

JHS =

6.97E-01

0.40 0.90

OH

0.10

QUASISTATIONAEPE PROPULSION

QUASISTEADY PROPULSION

II. 90 ETJ

DATUM

= 8609090000

MOD. NO.=

2491.00

PPOP.N0.=

1340.00

TEST.N0.=

8.00

TF/LPP

= 3.93E-02

TA/LPP

=

3.93E-02

RN/FN

=

5.19E 07

STPABLWIRKUNGSGRADE

FN =

1.68E-01

JET EFFICIENCIES

CF =

1.83E-01

OUST STFACY P repur. slop

DrTUM

= P6090900001

MOD. NO.=

24 91 . 00

PFOP .NO . =

1340 . 00

TEST .NO .=

8. CO

TF/LPP

=

2. 93F-02

/LPP

=

2. 93E-02

AN/Fr

"=

5.19E 07

PFOFFILFFV1 FRITTSCRPCF

Fr

1. 68E -V)

PFOPELLFF ,FFF ICIFNCIFF

CF

1.82F-01

JPF

6. 97C-C1

WASISTATIONAEFE PPOPULSION

OUASISTFADY PPOPULSION

PPOPFLLFPGUETECPADF

PPOPELLEF FACTORS OF MEPIT

DATUM

= 8609090000

MOD. Nn.=

2491.00

PFOP.N0.=

1340.00

TEST.N0.=

8.00

TF/LPP

=

3.93E-02

TA/LPP

=

3.93E-02

PN/FN

=

5.10E 07

FN =

1.68E-01

CF =

1.83E-01

JHS = 6.97E-01

WASISTEADY PROPULSION

SOGZAHLEN

THRUST DEDUCTION FRACTIONS

DATUM

= 8609090000

MOD. NO.=

2491.00

PROP.N0.=

1340.00

TEST.N0.=

8.00

TF/LPP

= 3.93E-02

TA/LPP

= 3.93E-02

RN/FN

= 5.19E 07 FN

1.68E-01

CF

1.83E-01

JFS =

6.97E-01

QUASISrATIONAERE PROPULSION

OUASISTEADY PROPULSION

0.40

*: +++++

t + ++ 0.30

JH

0.90

DATUM

=

MOD. NO.=

PROP.N0.=

TEST.N0.=

8609090000

2491.00

1340.00

8.00

TF/LPP

= 3.93E-02

TN/LPP

= 3.93E-02

RN/FN

5.19E 07

GESAMPGUETEGRADE

FM

1.68E-01

PROPULSIVE EFFICIENCIES

CF

1.83E-01

JRS f 0.80

6.97E-01

ER? * *

r

=

QUASI ST EADY PROPULSION

RUMP? EINFLUSSGRADE

HULL EFE' LCIENCI ES

DATUM

= 86 0 90 90000

MOO. NO.=

24 91 . 00

PROP .NO =

1340.00

TEST .NO . =

8.00

TF /LPP

=

3. 93 E- 02

TA /!.PP

=

3. 93 F.- 02

RN /FN L-4

5. 19E 0 7'

FN

1.68E-01

CF "="

1.83I-01

fr;

6 . 97E-01

=

QUASISTATIONAERE PROPULSION

QUASISTEADY PROPULSION

AONFIGURATIONSGUETECRNDE

CONFIGURATION FACTORS OF MERIT

TEST .NO . = 8.00 TF /LPP = 3. 93 TA/t, PP = 3. 93E-02

RN/FN

= 5. 19E 07 FM =

1.68E-01

CF 1. 8 3E-01 J PS

6.97E-01

DATUM

=

MOD. NO . =

P POP .NO . = 86 090 900 24co1 . 1 340. 00 00 0 0

QUASI STEADX PROPULSION

t[

VEPDPAENGUNGSEINFLUSSGRAD F

DISPLACEMENT INFLUENCE PATIOS

DATUM

= 86109090000

MOD. NO.

2491 . 00 P POP . NO . =

1340.00

TF ST .140 .

8.00

TF /LPP 3; 93E -02 TA /L PP 3. 938 -02

PN/FN

=

5.198 07

FN =

1.68r-03

CF 3 . 82E -01 IFS s

6.97E-01

= =

QUASISTATIONAERE PR1PULSr01

WASISTEADY PROPULSION

ENERGIENACHSTROMZAHLEN

ENERGY 4AKE1 FRACTIONS'

nbaum

= 860909000)

MOO. NO.=

2491.00

PROP.N0.=

1340.00

TESP.N0.=

8.,00

TF/LPP

=_

3.93E-02

TA/LPP

=

3.93E-02

RN/FN

=

5.19E 07

FN

1.68E-01

CF

1.83E-01

JH3

6.97E-01

= = =

0.5

-KT

0.4

0.3

0.2

0.1

-QUASISTEADY PROPULSIONSDATEN PROPULSION

10.

PROPULSION DATA 4 5

KO, KF

1 PROP.NO.

=

TF/LPP

=

3.926E-02

TA/LPP

=

3.926E-02

RN/FN

=

5.190E

JH

=

7.000E-01

TEST NO'S

=

8

1340.00

07

4,5,1,8

10.KQ KT KF

0.0

1 1 i 1

0.10

0.12

0.14

0.16

FN

--0.2

0.1

r

tT

tQ

QUASISTATIONAERE PROPULSION MOD. NO.

=

2451.00

QUASISTEADY PROPULSION PROP.NO.

=

1340.00

TF/LPP

=

3.926E-02

TA/LPP

=

3.926E-02

RN/FN

=

5.190E 07

NACHSTROMZAH LEN JH

=

7.000E-01

WAKE FRACTIONS

TEST NO'S=

4,5,1,8

0.10

0.12

0.14

0.1 6

FN

-0.6

4 5 8 W

0.5

0.4

0.3

0.9,

ETJ

0.8

-0.7

-0.4

0.1 0

44.

0.112

0.1 4,

0.16

FN

tQ,

tT

QUASISTEADY PROPULSION PROP.N01.

=

1340.00

TF/LPP

3.926E-02

TA/LPP

=

3.926E-02

RN/FN

=

5.190E 07

STRAHLWIRKUNGSGRADE JH .

=

7.000E-01

JET EFFICIENCIES' -

TEST NO'S =

4,5,1 At

-5 8

0.6

-0.5

=

QUASISTATIONAERE PROPULSION QUASISTEADY PROPULSION PROPELLERW1RKUNGSGRADE PROPELLER EFFICIENCIES

ET

0.7

0.6

0.5

0.4

0.3

TEST NO'S =

4,5,1,8

to

tT r MOD. NO.

=

2451.00

PROP.NO.

=

1340.00

TF/LPP

=

3.926E-O2

TA/LPP

=

3.926E-02

RN/FN

=

5.190E 07

JH

=

7.000E-01

0.8

4 5 1 8

0.10

0.12

0.14

0.16

FN

-1;0

1 1

FN

tQ kW ir

QUASISTEADY PROPULSION PROP.IN O.

1340.00

TF/LPP

=

3.926E-02

RP

TA/LPP

=

1926E-02

RN/FN.

=

5A 90E 07

PROPELLERGUETEGRADE JH

=

7:000E-01

PROPELLER FACTORS OF MERIT

TEST NO'S =,

.4,5,1,8

-4 5 8

EJP

0.9

0.8

0.7

0.6

-0.5

=

0.10

0.12

0.14

0.16

QUASISTATIONAERE PROPULSION QUASISTEADY PROPULSION WIDERSTANDSDATEN RESISTANCE DATA

0.6

-I ,

TEST NO'S .=

MOD. NO.

=

2451.00

PROP.NO. .=

1340.00

TF/LPP

=

3.926E-02

TA/LPP

=

3.926E-02

RN/FN

5.190E 07

°al

5

Ii 8

CR.

0.5

0.4

0.3

0.2

-0.1

0.10

4 r

t

=

=

4,5,1,8

0.12

0.14

0.16

FN

0.3

0.4

-_

0.2

0.1

-_ i

0.12

0.14

TEST NO'S=

4,5,1,8

4 5 1 8 1

0.16

EN

-,

QUASISTEADY PROPULSION

PROP.NO. =

1340.00

TF/LPP

=

3.926E-02

TA/LPP

=

3.926E-02

RN/FN

=

5.190E 07

SOGZAH LEN JH

=

7.000E-01

THRUST DEDUCTION FRACTIONS

0.5

-t

-0.0

0.8

ERP

0.7

0.6

0.5

0.4

0.3

0.10

4

0.12

QUASISTATIONAERE PROPULSION MOD. NO.

=

2451.00

QUASISTEADY PROPULSION PROP.NO.

=

1340.00

TF/LPP

=

3.926E-02

TA/LPP

=

3.926E-02

RN/FN

=

5.190E 07

GESAMTGUETEGRADE JH

=

7.000E-01

PROPULSIVE EFFICIENCIES

TEST NO'S=

4,5,1,8

1 5

0.14

0.16

FN

1.5

ERT

5

1.4

1.3

1.2

1.1

tT tQ

1.0

1 I 1

QUASISTEADY PROPULSION PROP.NO.

=

1340.00

TF/LPP

=

3.926E-02

TA/LPP

=

3.926E-02

RN/FN

=

5.190E 07

RUM P FEIN FLU SSGRAD E JH

=

7.000E-01

HULL EFFICIENCIES

TEST NO'S

=

4,5,1,8

0.10

0.12

0.14

0.16

---QUASISTATIONAERE PROPULSION QUASISTEADY PROPULSION

KONFIGURATIONSGUETEGRADE

CONFIGURATION FACTORS OF MERIT

ER

0.9

0.8

0.7

0.6

0.5

TEST NO'S =

4,5,1,8

tT

to

MOD. NO.

=

2451.00

PROP.NO.

=

1340.00

TF/LPP

=

3.926E-02

TA/LPP

=

3.926E-02

RN/FN

=

5.190E 07

JH

=

7.000E-01

1.0

4 5 1 8

0.10

0.12

0.14

0.16

FN

0.9

-CHI

0.8

0.7

0.6

0.5

-0.4

4 5 1 1

TEST NO'S=

4,5,1,8

1 8 1 1

0.16

FN

-tT tQ

QUASISTEADY PROPULSION PROP.NO.

=

1340.00

TF/LPP

=

3.926E-02

TA/LPP

=

3.926E-02

RN/FN

=

5.190E 07

VERDRAENGUNGSEINFLUSSGRADE JH

=

7.000E-01

DISPLACEMENT INFLUENCE RATIOS

0.12

0.14

WE

0.1

0.1

0.2

0.3

TEST NO'S =

4,5,1,8

0.2

4 5 1 8

.10

I

0.12

I

0.14

I I

0.16

FN

QUASISTATIONAERE PROPULSION MOD. NO.

=

2451.00

QUASISTEADY PROPULSION PROP.NO.

=

1340.00

TF/LPP

=

3.926E-02

TA/LPP

=

3.926E-02

RN/FN

=

5.190E 07

EN ERGIENACHSTROM ZAH LEN JH

=

7.000E-01

ENERGY WAKE FRACTIONS

0.0

o

r

tT