A proposal for conducting and analysing measured mile trials

llODflRSK1 IIISTJTUT

SHIPBIIILIIIflG fiE$[AR(ll IIISTITUT[

ZAREB

A Proposal for Conducting and Analysing Measured

Mile Trials

by

-M:Fancev

Shlpbñlldlng Research Institute, Zagrb

Techrilsche Hogeschool

r4 2O

Paper to be presented at the Symposium on the

Towing Tank Facilities, Instrumentation and

Measuring Technique

by

Ing. M.Pancev

1. Introduction

There is every reason to approach the _{problem of measured} mile ship trials with great earnestness and conscientiousness. The efforts invested and the time spent in conducting measured mile trials and in analysing their results are certain to be well rewarded by the.usefulness of the data obtained from such well-organized trials.

First of all, a shipyard will use the results of ship trials to show the future shipowner the extent to which the ship's propulsive properties stipulated in the _{contract have} been actually achieved. This is mainly a matter of accomplishing a certain ship speed with a predeterm1red engine _{output and fuel} consumption. But since it is practically impossible at a trial to determine precisely the number of revolutions at which this engine output envisaged by the contract will be absorbed, the speed corresponding to the stipulated propulsion power will be determined after an Rnalysis of the trial _{results by taki'ig} readings from the diagram in which the power is plotted on the base of speed.

The possession of ample trial data simplifies to a great extent the designing of a ship as concerns its propulsive pro-perties, and. reduces to a minimum the anxiety with which the

trial results are awaited..

Trial results provide reliable information on the ship's propulsive properties, which, with a reasonable exploitation of

beacons on the shore. This method of measuring ship speed on ti3e measured mile creates certain requirements and problems as

re-gards the way the trials and the analysis of their results should be conducted.

First of all the regular phenomenon of tide causes a dis-crepancy between the ship speed over ground and. the speed through the water, only the latter being of interest as one of the essen-tial data, The time fluctuation.s of the tide further increase the complexity of the problem.

Further discrepancies in speeds measured on individual runs are caused by the difference in the relative wind, because there always exists an absolute wind, during the trial, and. owing to the difference in the ship's direction in two consecutive runs and because of the ship's own speed, the sane absolute wind, becomes a different relative wind in two runs.

The turning of the ship after each run considerably reduces its speed, so that a long approach is required for the ship's

acceleration necessary to give it adequate speed. For the deterini-nation of the acceleration length the author of this paper recom-mends the paper by Lackenby [i] which deals exiensively with this problem and also gives practical results for the solution of the problem. But at a recent trial conducted on a 19,500-ton tanker it was found out that Lackenby's acceleration approach was not

sufficient to permit the ship to develop full speed at a determi-ned number of revolutions. We wish hereby to warn all those res-ponsible for conducting ship trials to make sure if their accele-ration lengths before entering the measured mile are adequate for achieving full speed. This can be easily checked on measured miles provided with several mile marks, by measuring partial times.

The following objections could be raised to the prevailing way - considered as standard method - of conducting and analysing measured mile trials:

a! The necessity of making a great number of runs for

a relatively ama].]. number of definite data. For

-3-example, if the trial is conducted with groups of four runs at substantially constant rpm, from a].-together sixteen runs only four definite data can be obtained.

b/ Brard and. Jourdin [2] have demonstrated that it

is incorrect to apply the mean of mean method on all measured propulsion values, as Taylor [3] suggested

without offering any particular proof thereof and. as

it is also stated in the proposed standards for

con-ducting measured mile ship trials [k] and _[5].

c/ Definite data obtained through the mean of mean method have no definite pbzysical significance since they are the results of mathematical operations seeking the mean value.

dl The necessity of entering the measured mile at a given number of revolutions at equal time intervals, which constitutes the basis of the mean of. mean method.

Some proposed methods of analysing trial results, as for

insi;ance [6] , introduce data obtained from model tests. We

are, however, of opinion that it is more appropriate to analyse the results of ship trials independently, and then correlate them with model test results.

This paper endeavours to offer a proposal for conducting and analysing measured mile ship trials, which has the following advantages over the practice hitherto prevailing:

CX, The number of definite data corresponds to the number of runs, so that at substantially constant rpm it will not be necessary to make more than one run.

;

The possibility of an easy deduction of the results for calm air condition,

'/ The elimination of the necessity of entering the

measured mile at equal time intervals.

The paper first sets forth the fundamental principles of the proposal for conducting and analysing measured mile trials. This is followed by a detailed analysis, made in accordance I

with the principle suggested in this paper, of the trial resi4ts of the motor cargo-vessel "Lubuinbashi" _[7] . According to t1Le

author's opinion this represented so far the most seriously &nd conscientiously conducted trial, the results of which have ben published. Furthermore the paper gives the results of this m-thod. applied in several more ship trials conducted both abrdad and. at home, the latter having been carried out by the auth4r himself.

At the end, the paper lists the conclusions the author( has arrived at through the application of this proposal.

The author has conducted two trials in compliance with the new proposal. The results obtained are given in this paper.

2. Basic Princiiles and worked examples

The fundamental problem involved in the analysis of trik]. results is the question of eliminating the influence of the 3ea current and the wind from the results obtained, i.e _{the chief} aim underlying ship trials is to obtain, at the end of the

analysis, data based on the ship speed through the water in calm air condition. So far, it has been the method of

Rn1ySing

ship _{trial results which has dictated the way of conducting}

the trials. In the same way the analysis proposed in this paper also offers a corresponding method of conducting ship trials.

a/ Elimination of Tide

By analysing the results of numerous trials, both those conducted by the author himself /about 90 trials of almçst all types of ships/, as well as those that have been d.escrioed

-5-elsewhere, the author has become convinced that there exist a linear relation between the values

M/N2 and V/N

within the range V/N which practically occurs in ship trials.

This relation is expressed with

M/N2

a

V/N # b,

(1)

So far the author has no experience of his own as regards thrust measurements, but analogously with the relation expressed

in (i) - and. this is also shown by the analyses of the results

of some trials described elsewhere - there also exists the line-ar relation

TIN2: a2 V/N #b2

(2)

It should be at once emphasized that in these expressions it is physically essential that

a and ₂ O; b,

and b2

0

Relation (1), somewhat differing in form, is also used by Prof. Bonebakker [8]ana[9] in the development of his method of propulsion analysis of ships in service. The results of numerous self-propulsion model tests carried out in the N.S.P. at Wage-ningen, have furnished Prof. Bonebakker with ample proof as to the existence of this relation.

Numerous diagrams of open-water model tests show a slight curvature of the curves of the torque constant KM and the thrust constant L plotted on the base of the speed coefficient

A, so

that for the small range

A

a linear approi1nntion of the rela-tions

KM and is allowed with regard to

A.

Prom these

and TIN2 ama the value V/N by introducting the wake coeffi-cient In his work on wake [io] Harvald ascertains that in the case of merchant ships the change of the wake with speed is negligible and in ₆₅ per cent of cases of analysed model experiments the wake decreased with speed Ian average 0.004 per knot/, 25 per cent remaining constant, while

in

10 per cent of cases the wake coefficient increased Ian average 0.003 per knot!.

But at the transition with the propeller behind the ship model the quality pattern of the velocity field of the in-flowing medium also varies. This can lead to essential changes in the relations of the KM and KT and. the

A,

apparently acting as if a change in the pitch of the propeller had taken place. This is also evidenced by the existence of two wake coefficients obtained on the base of the torques and thrusts respectively, measured in self-propulsion ship model tests. Furthermore, going over from the model to the ship there is a difference in thrust and torque between a model and. a full-scale propeller, which is 10 - 20 thousand and 50 to 150 thousand times greater res-pectively /model scale 20 to 30/. In spite of the fact that in practical towing tank work on result prediction, the problem _of the scale effect is successfully solved by means of empirical coefficients, which provide very good predictions - we are far from being able to offer an exact explanation of all these transitions. Finally it will be enough to recall that no full-scale size propeller has been tested in open water so far.

The author was interested in finding out what data regar-ding the relations M/N2 and V/N were offered by the results .of Series 60 [11]. For that reason he chose at random four models. Their self-propulsion results plotted in the form M/N2 (or rather DEE/N3, which is the same) on the base of V/N are shown in Diagram 1. The course of the plotted points is irregular, erratic, and inconsistent, so that it is impossible to draw definite conclusions without a deeper analysis.

At the end. of this paper several instances are given of ship trials the results of which are plotted in the form M/N2

-7-on the base of V/N, and which show the linearity of this rela-tion. It should be particularly stressed here that with twin-screw ships linearity (1) was shown with a negligible point dispresion, separately for the port and the starboard propeller.

We shall base our further exposition on relation (i) and. we shall apply the results of the derivation direct on the

re-lation expressed by (2)

In order to introduce the speed over ground into epresaion (i) we shall use a more appropriate form

A,m+B,N= V

(3)

where

A1: -fr-

;

B = - -

In

un accordance with

the

aforesaid, it follows: A1'(O and B1>O/. The ship speed through the water V, the ship speed. over ground Vg and. the tidal velocity C are mutually correlated, with the following equalities:

The change of tidal velocity within a shorter period of time during which four runs on the measured mile are to be con-ducted, will be approximated with a square polnom, i.e. we shall write for C:

C = c(t2f $ I (5)

where t is the time of the day to the middle of the run in individual runs.

If we add. indices 1, 2,

_3,

and 4 to the values m, N, V8

and. t belonging to the four consecutive rims alternating in direction over the measured course, we shall obtain, through

V:V

g V Vg - C C

/withtide/

/against tide!

J

(4)

a combination of expressions _(3), (ii.)

and. (5), the following

system of

four

equations

A,. m + B, N, V97 - (cL1#

(,j)

A, m2 #8, N2 =

_{Vg2 +(c(t#3 (2()}

A,

m3 #

B, N3 = V - ( f

t)

A, m4

# _B,N4

Vg4 +(ct#,3 t4a)

It will be noted that besides the values _{in, N, and. Vg} be-longing to individual runs, there appear identical coefficients which we shall call time factors and for brevity sake write:

F, =(13 _{- 2}

)(t4 - t

)(t

- t,)

F2 =(t4 -t3)(t3 -f,)( (4

_-t7)

F :((2

_-

_{1)(42 )(t4}

-t, )

F4 =( 2

)(t3 -t3)(t3 -t, )

It is very simple to remember the way in which these factors are built for an individual run: it is necessary to form all possible positive

differences, excluding the

diffe-

-9-(8)

By gradually eliminating

and Q

from this system

equations, after the sorting out, we obtain the following: A,[m,(f3 ₂₎₍₄

_{-t3)(t4 -t2)+m2(t4 -t3)( t3 -t,)(t}

_-(,)

_# +

m3(

₂

-f,)( (.

_{2)( (4 -(, )}

₊

m4(t2 _l,)

₍₍₃

2)(t3

B,[N,(t3 -2)(4

-13)('t4

2) + N2(t4

_{-(3)( (3}

-f,)(t4 -(,)

+

+N3(t2 -t1)(14

-t2)( (4 -t,) +

N4(t2

-t,)( t3 _t2)(t3

-t,7=

= V, ((3

2)( (4 -t)( (4

2) # "g2 ((4 -

3 )( t3 t7

₍

(4 - ( ) + #Vg3((2 7 )( (

)H4 -f,) + Vg4

_{((21, )(} t3 _{2)( (3} ( ) of

(7)

rences in which the t of the run in question appears /f or

example: all possible positive time differencies are:

(t2 -f1). (t., -t,L(f4-t,1(t, -t2(t4 -t) arid (t4 -t3 ).

In the forming of the time factor for run 3 all d.ifferencies containing t3 should be excluded from these d.ifferencies, so that it remains:

P3 :(t2-t1)(t4 - f,)(t4 -t2)

i.e. as above (8)

It can be furthermore easily noticed that if the time intervals of neighbour runs are identical there appear the known factors 1, 3, 3, 1 from the mean of mean method.

If we divide expression (7) with

A,(N,F,

+N2F2#N,F3 +N4F4)

after the sorting out we finally obtain:

m,F,+m2&,#m,F,+m4F4

Vg:F:+Vg2F?Vg3F34V94F4 b

N,F,+N2F+N3F3+N4F

N,F,+N2F2+N,F,+N4F4'

(9)

This expression is 8imilarly built as (1), from which we started, so that the point defined by the

ordinate

(M

- m,

F, # m. F,. m, F, # m4 F4

I N'/

N, F, + N, P3 # N, F, + N4 F4

...(10)

over the abscissa

( V)_ V9, F,# g2'2 V93F, Vg4 F4

(11)

I N /

N, F,

N, F, + N, F, + N4

.F

belongs to straight line (i)

MIN':a, V/N + b,

(1)

-At the beginning we gave relation (i) _{a general validity,} i.e. for the, whole range V/N which appears during the trial, so that at no stage of the derivation did there _{appear any} particular limitations concerning the conducting of the trial, i.e. as regards the approximate equality of revolutions in all four runs, etc. Consequently these four successive runs can be carried out with the number of revolutions differing essentially from run to run. Moreover, we can change the number of revolutions from run to run as in this way we shall obtain the maximum number of trial data.

In order to define completely relation (i) we need theo-retical].y only one more point determined by other four runs, of which the first three can be runs of ordinal numbers 2,

_3,

and Li. used. in the forming of the first _{group of runs, while}

we take as the fourth run in turn in this second group the run of ordinal number

_5.

_{But practically this relation will be the} more reliable the more points determined by the pair of values

(10) and (ii) for individual groups we possess.

When all available group points have been computed, they should be plotted in the diagram and we should check if the points lie approximately on the straight line, if there are no greater discrepancies, the level of point dispersion, _{etc. It} should be emphasized that a wrong datum in. one run will to a great extent &raw with it two group points _{of those groups in} which this run appears as the second, _{or the third run in turn,} because then the data of this run are multiplied with the time factors which are approximately three times greater than the factors belonging to the values of the first or fourth run in turn in an individual group. Besides well-marked wrong points, if there are any, there will appear an allowed dispersion of points on account of norma]. errors in measurements. As soon as there appear more than two measuring points to which linearity is generally ascribed, but which do not lie in the straight line just because of the normal dispersion of measuring data, it will be most suitable to use the least square method to determine the characteristics of the straight line. Thus we

recommend this method also for the determination of straight line (i).

In the working out of the programme it will be pEactically most convenient to make the differences in revolutions from run to run equal, because in this way the velocity range too will be equally distributed. But it is not essential to achieve exactly such revolutions, because even greater discrepancies will remain without any consequences.

Below we show the forming of groups for a case of altogether 12 runs on the measured mile with the relevant range of revolu-tions In this case we can form the following nine groups which will serve to determine straight line (1):

Group: Runs: 1

l,2,3,

2

2,3,k,

3 etc. to 9 9,10,11,12

The time factors belonging to individual runs are determi-ned according to (8) , i.e. according to the ordinal number of

this run in the group, so that for instance the fourth run time factor, when the run. is the fourth in turn in the first group, will essentially differ from the time factor belonging to this same run when the latter is, say, the second run in turn in the third group of runs.

Once we possess the characteristics a1 and b1 of straight

line (i) , we shall be able by means of (3) to figure out the

ship speed through the water for individual rune:

V =A,m+ B,N

(3)

whereby the first task of the analysis of ship trials is

ter-

-12-minated. Furthermore, it will be _{practical here to compute the} tidal velocity as the differences

and plot it on the base of the time of the day. In this case

the tide is in the course of the run when

_{- V> O}

_{or in} the opposite direction of the run when Vg - V < 0.

The derivation based. on the thrust is analogous to that based on the torque, and if we introduce the auxiliary value

-i

SN

we shall obtain individual group points in the _{similar way as} in (io) and (11) i.e. for the determinption of straight line

(2)

TIN2:

_{02 V/N}

(2)

we shall have at our disposal group points defined by the ordinate

f_i= s,F,. S2F2#S3F3#S4F4

IN2) N,F,.N2F2,NF3+N4Ic,

over the sane abscissa, as before (11) i.e.

(V).Vg,

_{Fg+V22F2+Vg3F3+V94F4}

IN/

N, F,

N2F2N3F3 N4F4

After the points thus obtained have been plotted in the diagram with the view of checking the sequence of points, and. of discovering possible errors, we shall obtain the characte-ristics a2 and b2 of straight line (2) through the application of the least square method, _{which also allows for the} ca].cu].a-tion of the ship speed through

_the

_{water for individual runs:}

(13)

13

where

is:

B---The speeds obtained. by help. of'

(3)

and.- ('1LI,)will géneräily

slightly differ, and. the

average values of these two 'can be

accepted

_a

dUinite.speeds..-.- '. S

In order to illustrate the application of these

deriva-'tions we

are,

presently

giving the

example

Of' the trial conducted

on the motor vessel

"Lubumbashi"

_{[71 ...}

The calculation of straight

lines' (1) and (2) and

the compitation of

the ship

speed.through the *ater are set forth in Tables 1 to ₅ contained in the appen-dix.

Tfireeit

of Table 1.. contains the ship

trial

results, while the second

part

gives the computation of the ship speed

'and

the tidal velocity, made by the

thrust

and torque method.

Tables-2

'and

₃

give

the computation of the time factors

ki

where the first

index jk/

refers to the

group and

the last

indeç

lu

to the run.

In Table'11 a calculation is made of values WN2,

T/N2 and

V/N for individual groups. The same table gives the cOmputations of some auxiliary values for the application of

the least square method,

while

the clôlaiO of straiht

lines (i) and. (2) ave given in

Table

5. -

The values

M/N2

TIN2 f or individual

groups are ,.plot

ted, in Diagram '2. on the ase

of V/N, and the obtained straight lines are d±awn in. The

devi-ations from the straight lines to

within per cent

are marked

in

tbediagram

in the -form Of-a cross,

and it' can

be o.ted that'

point

dispersion is considerably below 1 per-cent. The ship speeds

through

the water obtained

through

the

method

of the torque VM

and

_{the'thrust VT}

agree

very well, which indicates a high degree of measurement accuracy.

The, results obtained are listed once again in 'the

fol-iowing.table:

' _- '

-14--The last column in. the table shows the greatest deviation

of + 0,17 per cent between the speeds VM

and

VT, while the average difference is about ± 0,1 per cent, which is negligible indeed. This further indicates that the relative accuracy of thrust and. torque measurements is considerably greater than is usually considered.

Diagram 3 shows tidal velocity on the base of the time of the day. The tide curve is for an average 0,1 knot

higher

than the curve given in Prof. Aertssen's paper [7] , which was

computed by the

Ship

Division of the N.P.L.

It will be ndw

possible to plot the revolutions, the

de-livered horse power, and the propeller thrust on the base of

the ship speed. through the water for individual runs

This is

done in Diagram 4, where sets of two separate curves appear

for

runs against and

with the wind respectively.

Runs

_{knots knots}VT Vmean_knots Vj_VT_knots Vmean VM

± knots + per cent

1 ])-i.,79 14,83 14,81 - 0,04 0,o2 0,11

2 15,12 15,17 15,14 - 0,o5 0,o25 0,17

3

14,72

14,73 14,73 - 0,ol 0,005 0,o3

4 16,22 16,23 16,22 - 0,01 0,005 0,o3

5

15,88 15,86 15.87 + 0,o2 O,ol 0,o6

6 16,12 16,11 16,11 + 0,ol 0,005 0,o3

7

16,33

16,34

16,34

- 0,ol O,005 0,03

8 16,71 16,72 16,72 - 0,01 0,005 0,03

9

16,35 16,3o 16,32 + 0,o5 0,o25 0,15

10 _12,51

_12,52

_12,52 - 0,ol 0,005 0,014.

11 12,14 12,11 12,12 + 0,o3 0,o15 0,12

It has to be pointed out here that' the trial on the

motor-vessel 'I,ubumbashi" was conducted in the classical way with

three -runs in each'.of:the four groups. On the strength of the

above expounded principles altogether' nine groups with Li.

con-sécutive runs were formed regardless of ilid:ividual runs

belon-ging to classicai roups. It seems obvious that this trial

would have been made better use, of if it had- been conducted in -'

accordance with the author's proposal, i.e. if the revolutions

had been changed from run to. run.

'

- At the begiiming of -his work on measured mile ship trials

about four years ago, the author often sought patterns in

vari-ous valuable :wor]

from this field by 'French authors. Prom the

numeious ship trials that they have carried out and whose

re-sults ha.ire been pub1ished,

the author chose the trial

conduc-ted on board the twinscrew passenger and cargo-vessel tijean

Laborde" [12] and made an analysis of' the findins' on the basis

of the foregoing principles This paper gives only the final

results of the analysii. Diagram 5 lists -the group points N/N2

on the base of V/N separately for the port and. starboard screw,

and also the group points TIN2 for the port propeller, because,

as the authors themselves point out, in the measurements of

the' thizst of the: starboard propeller there ôocuréd a major

systematic error, which rendered any calculation with the

mea-sured data of the starboard propeller thrust impossible. The

diagram shows a very good sequence of points round. all the three

straiht lineS with the exception of groups 3 'and 4 fo

N/N2

the port propeller. The ship speeds through the water obtained

by, these three methods' agree to a great extent'. They are

tabu-lated be-low as follows:'.

'

Runs

-from port

propeller

torque

, TP

from port

propeller

thrust.

- - ' MS

-from starboard

propeller

-

torque

Remark on

' agreement

of speeds

,

ots

'

knOts

knots

1

_18,86

_18,88

_l8,90

_excellent

2

_19,22

'

19,21.

l9,23

- '

-excellent

At the trial of a twin-screw passenger ship built by the shipyard "3.Maj", Rijeka, measurements were taken by a team of the Shipbuilding Research Institute, Zagreb, headed by the author. The results of the application of the analysis separately for the port and starboard propeller torques are listed in Diagram 6.

As can be seen from the diagram, _{the sequence of points round} the straight lines is excellent and the differences in speeds obtained with the torques of the port and the starboard propeller are practically non-existant.

In addition, Diagrams 7, 8, and 9 give more survey of the results of measured mile ship trials in the form of M/N2 on the base of V/N. Diagram 7 shows the trial of a 10,500 tDW in ballast

condition, and. Diagram 8 _{demonstrates the trials of three}

smaller cargo sisterships in ballast condition , which were built in the "3.May" shipyard. Diagram 9 gives an analysis as described above of the results of the trial _{conducted with the passenger} motor-vessel "Maribor", built in the "Uljanjk" shipyard in Pula. The measurements are described in detail in the bibliograp}y [13] ,

while this paper gives only the differences in speeds obtained through the port and starboard propeller torques respectively.

4 _{17,41 17,31 17,25 not so bad}

5 16,21.5 16,37 _{16,33 not so bad}

6 _{17,37 17,33}

17,1t-o good

7 l8,o8 18,o8,1 _{l8,o5 excellent}

8 18,61 18,61 _{18,69 very good}

9 18,18 _{18,25 18,o5 not so bad}

10 _{19,85 19,81} 19,81 excellent 11 _{19,57 19,57} 19,64 very good 12 _{19,90 19,91 l9,81} good

All the above surveys of ship trial results in the form

of M/N2 on the base of V/N and. computed in compliance with the aforesaid principles, show a dispersion of points considerably lower than 1 per cent. All these examples as well as xna.y others

that the author has had. at his disposal, have firmly convinced

him of the linearity of the relation M/N2 and. TIN2 with regard to V/N. On the strength of this conviction the author offers his proposal for conducting measured mile ship trials with one run for individual substantially constant rpm instead of hitherto practiced three, four, and. even more runs, as recommended by the existing standards. The author would be very pleased if other people having ship trial data at their disposal would. also try

to apply the suggested method of trial result analysis and. would make their relevant experiences known.

from port propeller torque from starboard propeller torque Remark on agreement of speed.s knots knots 1 15,96 16,0k good

2 16,].o 16,o7 excellent

3 15,97 16,00 excellent

LI. _l6,o6 16,0k excellent

16,13 16,1k excellent 6 16,27 16,31 very good 7 16,17 16,17 excellent 8 16,32 16,25 good.

9

16,27 16,25 excellent 10 16,42 16,4.8 very good. 11 16,30 16,31 excellent 12 16,50 16,46 very good.

It is obvious that besides good. instruments this proposal requires a high degree of accuracy in thhip trial measurements,

and. also a well-trained staff.

In the above derivation, through the introduction of ex-pression (5) the change of tidal velocity with _{the time is} ap-proximated in the form of a square polynom. We considered it more justified than. linear approximation. However, the square polynom has a disadvantage inasmuch _{as nowhere in. the course of} the curve does there appear a point of inflection which would change the character of the curvature, and. the course of the ti-de curve regularly has several such inflections. Consequently, an approximation with a cube polynom would be _{more justified.} This would require the forming of groups of five runs with slightly changed time factors. The principle of forming time

factors for the values in, s, Vg

and N

of individual runs

remains the same as before, i.e. the time differences in which appears the time of the respective run Xor which the time factor is sought, are omitted.

The table below demonstrates an example of determining time factors f or five runs making the first _group:

Time differences

/f or the first group of runs!

Time of day to the middle

ofrun

First differences Second differences Third differences Fourth differences t1

t5-t2

t5-t1

2 t2

t2-t1

3 5

III.

t3 t5

t3-t2

tLt3

t5-t

t3-t1

t4t2

t5-t3

Time factors,

/f or the first group of runs!

F,

(t3 -t2)( t-t3)(t5 -t4)(t4 -t2)(ts

-t3) (t5 -t2)

F2: (

f4-t3)(t5 -t4)(t3t )(t5 -t3)(t4 -t, )( t5-t,)

Forming of the groups

/twelve -run case!

The author abandoned the groups with five runs mostly on account of the greater complexity of time factors, as computa-tions made with a hand-operated calculating machine would incre-ase the probability of errors, and. would prolong the actual time of computing. However if calculations were made by an electronic computer, the author would recommend this method of forming five-run groups. In this case, besides definite results, the computer should also give the values M,'N2, TIN2 and. V/N belonging to in-dividual groups as the plotting of these points in the diagram would make it possible to check up the sequence of points and. also to discover possible errors in measurement data.

Croup: Runs: 1 1, 2, 3, 4,

5

2

2,

3,

L,

5,

6

3 3, 1i,

5,

etc. to 6, 7 8 8, 9, 10, 11, 12

(2 -t,)( (5

-t4)((4

(4 -t,)( (5

2)( (5

F4 :(

t21

)( t

-2)( t-t,)( (5

tj)( (5 -t2)( t5 -t,)

Consequently at the end. of the first stage of the nalysis of the ship trial result we shall be in possession of the data covering the torques br power!, thrusts, revolutions, and the ship speed through the water, as well as two expressions for correlating these values:

M/N2:

a,.V/N + ₍₁₎

TIN2:

₂ V/N .# b2 (2)

We shall consider these expressions _{as valid only for the} V/N range which appears at trials and which is relatively narrow, so that a further extrapolation of these straight lines could lead to serious errors which we need not fear in these narrower range.

On the strength of these data we can tackle the next task in the result analysis, viz, the el(mination of the wind

in.flu-ence from measured data.

b/ Elimination of wind influence

Every ship trial is almost regularly accompanied by wind. The date of a ship trial is usually fixed well in advance, and only really bad weather conditions will postpone _{a trial as the} reduced visibility makes the conducting of trials practically impossible. From the point of view of the shipyard this reluctanoe to put off a trial is understandable, as every ship unduly kept in the shipyard without an urgent need causes considerable mate-rial losses to the shipyard as well as to the shipowner. Thus it often happens that trials are conducted with much abronger wind than allowed by the standards. This leads to speed losses at a given engine power in runs agafnt the wind that _{are greater} than the speed gains in runs with the wind. It is normal there-f ore that it is there-felt necessary to reduce ship trial _{results to}

a standard condition in ord.sr to make them equivalent and suitable for comparison and correlation. We shall consider as standard conditions to which the result will be reduced the calm air con-dition, i.e. there will remain only the relative wind of the speed equal to the ship speed.

The following principle was applied in the elimination of wind, effects from trial results: from the results of the tests of the above-water portion model of the ship undergoing trials, or of a similar ship, we accept the relative change in the wind.

resistance coefficient with the angle of the relative wind. Prom the thrust data obtained. at the trial we determine, by means of

this relative change of coefficient, the absolute value of the wind resistance coefficient, with which we then deduct the wind

lorce from the thrust. By accepting only the relative change of the wind resistance coefficient from the above-water portion model tests we intended to reduce the scale effect to a minimum. As we are already in possession of expressions (i) and. (2)

/which are given above! we can, from the thrust changed for calm air condition, compute the revolutions and. the torques,

br

rather power! corresponding to this condition. By neglecting the minimum changes of the thrust deduction coefficient for the range of propeller load at the trial, no error that could exer-cise a greater influence on the final results introduced. in

the calculation.

ae absolute value of the head wind, resistance coefficient

R0

_{/tons per square knots! (16)}

rw

will be determined for the common ship speed V' of two neighbour runs on the measured mile made in opposite direction. For this common speed we must first find. out the corresponding corrected

thrusis T and. T and also the speeds and the directions of the

relative wind for these two fictitious runs. The correction of the thrust can be made by plotting f o? individual runs the values V,'N on the base of the ship speed and by extending the points of

sequence of all the points. By taking readings of the values

V and V'/N at this coinn(on speed, we shall be able to

cal-culate tzie revolutions and and. by means of these and.

expression (2) , obtained before, we can determine the thrusts

and corrected for the common speed V'. We shall ma1e

the correction of the relative wind by means of a diagram in which are vectorially plotted the ship speeds over ground and the speeds of the relative and. absolute wind for individual runs on the measured mile. If in this diagram we increase or reduce the ship speed. over ground for the difference between speeds of the tested neighbour runs and. the common speed of the fictitious runs, and. retain the same absolute wind, we can read off the corrected value as well as the direction and speed of the relative wind that would correspond to this common speed. In order to obtain the thrust T corresponding to the condition

without relative wind, we must deduct from the thrusts and.

the wind force which is proportional with the square speed of. the relative wind and is also the function of the direction of the relative wind. As the computation is made for the common, average speed of two runs, we must arrive at the same thrust T ,

starting from both and T , i.e.

- K,t, V1f, = - K,'2 _i'?W2 (17)

At the beginning we assumed to have the curve of the depen-dence of the wind resistance coefficient ratio K9/K0 with re-gard. to the direction of the relative wind. 0 , so that after the introduction of this ratio we obtain from expression (17)

T

-K, =

.2 - -

i2

K,, rip, K,, rW2

(18

Each group of two neighbour runs will give a coefficient 10,. and in the end we accept the average value of all the coefficients obtained.

For comparison sake, it is convenient to express this head wind resistance coefficient in a dimnsionless form

Ii,wo

consf

-F,

When we have the coefficient K0 , we can determine the wind resistance coefficient for each run

and by means of. them we can eliminate the influence of the wind. from the results of individual runs,

Prom the measured thrust T of individual runs we obtain the thrust _{for calm air condition, i.e. for the condition when} the speed of the relative wind. is equal to the ship speed, by means of the expression:

To

T - Ke V,y

# K0 V2 (20)

We have from before the relation between the thrust, speed, and the revolutions expressed with

TIN2

C ₂ V/N b2 ₍₂₎

from which we can calculate the revolutions N _{corresponding to}

the thrusts and speed V

(19)

For the calculation of the torque M0 corresponding to these conditions we use expression (i)

M0 a VN0 + b7

N

(22)

or for power DI0

DHP0

M0N0

(23)

It will be convenient to plot the revolutions N0 in the diagram on the base of the speed on a greater scale, to draw the curve which now must pass through the origin and. read off the revolutions for the values of speed in terms of round fi-gures. The computation of the torques and power for these speeds can be made by means of (22) and (23) and. that of thrust with the expression

o2VN + b2

(24)

By plotting the curves of power and thrusts on the base of speed besides the alrea&y plotted curve of revolutions we have completed the power, thrust, and revo1utiox diagram based on the ship speed for calm air condition. In this way the results of ship trials are given in a definite form, which was the task set at the beginning of this exposition.

We shall continue with the example of our analysis of the measured mile trial conducted on the motor-vessel 11Lubumbashi" with the elimination of wind, influence.

The obtained relative wind velocity and. direction data are shown in Diagram 11 a! in vector form together with the ship speed over ground and the absolute wind speed. These three velo-cities are mutually linked with the vector equation

- -.

The absolute wind, in Diagram 11 a! shows a regular change of direction from run to run, so that odd runs give absolute wind more from a western direction, and even runs more from a northern direction. It is hardly probable that the actual

abso-lute wind really behaved in this way, so that it must have evi-dently been caused by some error in measuring the relative wind. An assumption was made that the relative wind direction was wrongly measured and the data recorded by the anemometer, i.e.

the relative wind speed, were accepted as correct. Under this presumption a correction was made of the original wind data in Diagram 1]. b/ where absolute wind shows a more realistic change of direction from run to run /for example, the corrected abso-lute wind for run 3 was obtained in the following way: let us suppose for a moment that durin runs 2 and 3 there had been one and. the same absolute wind which we can easily determine in the vector diagram by plotting the relative wind speeds for runs 2

and 3 from the vector vertices of the ship speeds over ground of runs 2 and 3. If we make the same assumption for runs 3 and Li'

we shall obtain an absolute wind slightly differing from that in runs 2 and 3, so that for run 3 we accept the mean value of these two absolute wind values as the most realistic solution!.

To determine wind resistance coefficient (16) of the

"Lubumbashi", nine pairs of fictitious runs with common speeds were formed.. Individual values of these fictitious runs were

obtained in the above described way by using Diagram 10 /VIN on the base of V/ and Diagram 11 c /wind datal. For the change of the ratios of the coefficients Xe/Kc, with the angle of relative wind Diagram 12 was used. This diagram was made after Figure 11, p. lo2 of the apanese paper on measurements of the ship "Nissei

Maru'1 [l2] , so that mean line was drawn. The calculus is given

in Table 6. The last column in the table gives the coefficient K0 for individual pairs of runs, and in spite of a slightly greater disperison, the mean value of the wind resistance coef-ficient obtained, in dimensionless form (19) :

= 0.785

which Prof. Aertssen placed at the author's disposal, the trans-verse projected area of the above-water portion of the ltLubum_ bashi" totals 3o4 sq.m./. This coefficient value was plotted in Diagram 13, which shows wind resistance coefficients for various ships. The diagram was photo-copied from the aforesaid Japanese paper [14] , Fig. 12, page 103. It is noted that the wind resi-stance coefficient of the "Lubumbashi" is identical with that of the "Nissei Maru" loaded.

By means of the obtained, head wind resistance coefficient a correction was made of the results for calm air condition in Table 7. For round ship speed values definite revolutions, power and thrust are given in Table 8, and. also shown in Diagram 4. In Table ₉ a comparison was made between the results for calm air condition given by Prof. Aertasen

[7]

_,

which were computed by the N.P .L., and the results arrived at by the author. While at speeds of 16.05 and 16.51 knots the differences are not great, they are greater at speeds of 14.88 and 12.35 knots, and. amount to as much as ₅ per cent in the thrust.

c/ Elimination of wind effect by means of measured toraue The characteristics of wind in nature differ from those of the wind reprodud in a wind, tunnel. The main features of the former are sudden changes both in direction and speed. For one thing, they make wind measurements difficult, and secondly, they

create a reasonable limit to accuracy in the computation with wind data. This limit allows for certain approximation in the

setting of the relation of the and torque, which makes

it practically possible to eliminate the wind influence from the trial results when we are in possession only of data covering the measured torque without thrust data.

Thus for the narrower range of the speed coefficient and within the set limits of accuracy, we can write

i.e. that the thrust is directly proportional to the torque.

The approximation of this expression for a given propeller is connected with the approximate constancy of the relation

const.

because from

KM 2?T

it follows

T=const.,

MconSt.2M

un

its naive initial stage the theory of propeller influence put the expression for the propeller efficiency in the form

V. VP

1Dr7H

nO

which at once gives for a given propeller

_'?.

_:COf)St.

But in genera]. this leads to completely wrong results [15]

1.

In our exposition under b/we described how we could obtain the head wind resistance cofi-ient from the measured thrust,

and so if we introduce in (18) approximation (26) , we have

k (M', -M'2)

iaL v2-

_{twi K0}

- v'2W2

1

-

_a

1_

Rather than trying to determine more precisely the factor we shall introduce an auxiliary coefficient

k

-V'2

K9.2 v;2

K0 1w? I(o

By means c'f this coefficient we can eliminate the wind effect from the measured torque and we can determine the former without knowing the thrust and. without model tests results. Physically this coefficient has not much sense, but it practi-cally enables us to solve the set problem. For the relative

change of the coefficient with the angle of the relative wind

0 we can use the change of the coefficient K0, because with the accepted approximation we can write:

1(9

.c0

Consequently for the change of the ratio ..Z/X0 with the angle of relative wind Owe can use Diagram 12 from this paper, or one similar to it, according to the type of the ship.

lVhen we have determined the coefficient

K0, in

a way ana-logous to that under b/, for the determination of the coefficient K0 reckoning with torques instead of with thrusts, we are able to

determine the coefficient for each run

7,-1(01 J1,O

and. by means of this eliminate the wind effect from the measured torque. Or rather, for calm air condition, i.e. for conditions when the speed of the relative wind is equal to the ship's

of the expression:

M0

2M-3C9-VJ+JC,.V2.

.(27)

When we have the, relation of the torque, speed and revolu-tions, i.e.

MIN2 = a1 V/N + b, (1)

we compute the revolutions which correspond to the torque M0 and the speed V

N0=

-21,

V +

/_fv2

+

+

M0 (28)

Besides the already given example of the analysis of the trial conducted with the m.v. nLubulnbashiu, in Table 10 the

coef-ficient

74

and the torque for calm air condition were

corn-puted..A comparison between the torques thus obtained and the

earlier computed torques on the base of the measured thrust is made

below:

Run

-from measured torques H.P./rpm.

,, M /T!

from measured thrusts

H.P./rpm. . Difference 1

37,93

37,62 + 0,8 2 40,85 4o.57 + _0,7 3 37,87 37,711. + 0,3 11. 51,18 51,10 +

0,2

5

46,86 46,88 -

0,0

6

5o,92

5o,88 + 0,1

7

51,26

51,o8 + 0,11.

As can be seen from the last column of the above table, the greatest difference in the torques M0 obtained in two different ways amounts to 0,8 per cent, while the mean differbnce totals 0 ,L1 per cent, which is within the limits of accuracy generally

observed when reckoning with measured wind data.

. Some General Remarks

All the examples listed with the expositions of the funda-mental principles refer to trials with several runs in individual groups at substantially constant rpm. The trial of the rn/v "Ma-ribor" was conducted with four runs in a group, that of the ve8sels

"Lubumbashi" and. "Jean Labord.e" with three runs, while the trials of the ships "Mascot", "Boka", "Pirot" "Zemum" and "Varadin", were conducted with two runs in a group. In all the above examples, in order to determine relations (i) an (2) , groups of four runs

were formed, regardlessly of the runs belonging to "classical" groups. When relations (i) and (2) are known, individual runs get their full importance with complete data, not as it has hitherto been the case three or four runs serving for the determination of one mean datum of the group. Consequently, in conducting ship trials, too, we can treat each single run individually, which makes it possible to change the rpm from run. to run, so that the whole trial can be conducted with a smaller number of runs.

Perhaps on some other occasion the author will say more about his experience in ship trial measurements. Here, however, he would like to point out only two things on which the success

8 55,95 - _55,811. + 0,2

9 52,81 53,2o - 0,7

10 25,99 25,99 0

11 _211,54 211.,7o - 0,7

of trials mostly depends, viz, sufficient acceleration approach and the zero point of the torsionmeter. In this respect the author has met with full understanding at our shipyards, so that the progranme of a ship trial includes obligatory the zero point of the torsionmeter before and. immediately after the trial, which, with a careful stopping of the ship, takes altogether about Z.5 minutes.

It will be necessary here to make a few additional remarks, to the proposed method. of conducting and analyzing ship trials. With

all

present merchant ships there will appear at trials a

sufficiently wide range of the speed coefficient V/N necessary for a reliable .etermination of straight lines (i) and (2). The

change of V/N is linked with the speed exponent with which the ship resistance is changed with the ship speed, and if the expo-nent is two , there will be no change of V/N, which is the case with submarines in underwater travel or with slow merchant

ves-sels, the like of which are not built today any more. Thus in. the analysis of the well-known trial with the ship "Clairton"

[16] there appeared a too narrow range of V/N, which was not sufficient for a reliable determination of straight lines (1) and

(2) . But according to Troost [17] the prevailing good practice in the designing of new ships allows the variation of resistance with the exponent

2,5

between 0.9 V and V5 /V8=service speed!, or with exponent 3 between V and. Vt 1Vt= trial speed/, Such a

change in resistance with speed will offer practically a wide range of the speed coefficient V/N suitable for the analysis described above.

In his practice the author has conducted a considerable nuaber of trials with twin-screw ships 30 to 80 m long, whose relative speeds amounted up to V/

V

L = 1.3 . The analysis of the results of all these trials conducted according to the sug-gested method have given a reliable straight line (1) and reli-able speeds through the water.

The stream flow round the ship at a speed approximately

v, ViT=

1.5 -i-- 1.6 has a considerable influence on the wake,

mainly on. the wake's component caused by ship wave-ma]d.ngn

the case of a greater number of smaller. f as

_{units' and one bigger}

fast

unit,

the

author noticed that from V/

VT=

l5-'l.Gon*ards

an increase in the speed coefficieni V/N vias recorded but with the, values M/N2 slightly lower

than

_{those thatoccured with a}

speed increase, up to

that

,L. The

_{.latter is very well knovin.}

in connection, with the last /the most serious one! hump in ahip

resistance.

oii

account of that in case., of

sUch units the range of

speed up to V/

Y=

_I.5l.6

_and

_{the range beyond this limit}

should be separately studied. Te same cnsiderations

are valid.

for ships sailing in shallow waters, where particular notice should be paid to the speed

range

near the

cri'ial

speed for

depth. ,

L. _{Two examples of ship trials conducted accordinR to the new}

proposal

With this experience in the application of the above

exp].ai-ned. n1ysis of the '.'resuits ôf.

ship

.trials

cond,uctad. 'in the

"classical" way, the proposal to 'conduct trials, with 'one run at

substantially constant

_rpm

_{was rnade with much confidence. The} authOr hAs conducted several triaIS'wjth

smaller

_{craft, up to}

55

m

long,

in accordance with this

proposal. The .fol'l'owing are

the results given in the form

M/N2

on the base of V/ST for a small

fishing boat about

15.m"in' length

_{/Digrml4/,:and.foz a}

twin-screw coastal passenger ship about ₅₅ m long.

/Diagram 15/. The

dispersion of points. 'froza the 'plotted sraight'line _{in both}

diagrams is considerably below 1 per cent,

_and

_{the computed tidal} velocity, which is also entered in the loweth.'part.of the diagram, shows a good. sequence of point. The trial with the fishing boat was conducted with altogether eight

_runs

_{:with change of} revolu-tions from run to run, for which the speed range from

4.,5

to

8.5.

knots V/..V.Q.65 to l..2 :wasteted.The,,t.jal

of. the

coastal passenger ship

was carried out with altogether nine runs,

with

change of retolutions from run to zuñ. The greatest

discre-pancy in computed speeds through the water, reckoning with

_the

torque of the port. or the

starboard

_{créw;[ 'amounted.to}

_±,°95

List of Symbols

a1, a2, A, A2 - coefficients

b1, b2, B1, B2 - coefficients

- dimensionless wind resistance coefficients

C - tidal velocity, knots

/

- delivered horse power, HP

F - time factor

P

- transverse projected area of above water portion of

ship,m orft

k

- coefficient

- head wind, resistance coefficient,

9 = 0,

tons per square knots

- wind resistance coefficient for direction of relative

wind.

9,

tons per square knots

- HP per rpm per square knots

- K9/k, HP per rpm per square knots

- torque constant

- thrust constant

Mm

- torque measured on the shaft, HP per rpm

- torque of friction along shaftline, HP per rpm

m

-M/N

N

- revolutions per minute, rpm

R - wind resistance, kg or lbs

s - TIN

T - tb.rust of the screw, corrected for static _{head, tons}

t - time of day

V

- ship speed through water, knots

- ship speed over ground, knots

Vaw - speed of absolute wind, knots

- speed of relative wind, knots

- coefficients

9

-

direction of relative wind, degrees

A

-

advance coefficient

In the context the numbers in [ ] brackets denote references and those in

[io]

[ii]

References:

[i] - Lackenby,. H. "On the

Acôe].eatiofl.

of hi", Trans.

I.E.S.S. 1951/52, vol. 95, p.357

Brard, R., Jourdain, M. :"Critique des .essais la mer",

Bull. A0T.M.A.

1953, vol.52, p.63.

[3] - ;Tay].or,I).W. :.'-The Spedand Power. of Ships", Washington

1943,

* *

-L4J -

*

.:

"Standardization Trials Code

1949",

Soc. N.A.M.L,

New Yourk ,

1949.

* *

: "Code of Procedure -for Measured Mile. Trials" ,:

B.S.R.A., Report No.7.,

1947.

-

Schoenherr, .E.: "On the Analysis o Ship Trial Data", Trans. Soc. N.A.M.E.,

1934., Vol.39,

p..2Sl.--

Aertssen, G.: "Sea Trials ona 95OO.ton Deatheight Motor Cargo Liner", Trans. I.N.A.

1955, Vol.97,p.Jl.

- Bónebakker, J.W.: "On Collecting Ship Service Performance

Data, and Their Analysis",

T.N.O. for Shipbuilding and Navigation, Report No.

105,

1953

i.

Alicatión of Statistical Methods

tothe Analysis of Service PerformancëData", Trans

N.E.C.I.E.S., Vol. 67,195]., p.277.

-

Harvald, S.A. : "Wake of Merchant Ships", The Danish

Technical Press, Copenhagen

1951.

-

Todd, P.H., Stuntz, G.R., and. Pien, P.C. :T1Series

60

-The Effect upon. Resistance and. Power of Variation in

Brard, R. .Jourdain, M. and. de Mas Latrie, D. : "Les essais

a la mer du paquebot mixte 'Jean Labord.e", Bull .A.T0M.A.,

1954. Vol. 55

i1ovié, S., Pancev,. MO. :"Paquebots cotiers du type

'Osijek':Essaisâ lamer et analyse des resultats en service",'Bull. A.T.M.A.

i97, Vol. 56.

*

* *: "An Investigation into Sea-going Qualities of

tb Single-Screw Cargo Ship 'Nissei Maru' by Actual and Model Ship Experiments", Edited by Experimental Tank Committee of Japan, .Transportation Technical Research Institute Mejiro, Toshimaku, Tokyo, Japan

_1954.

[ii]

-

Van Lammeren, W.P.A., Troost, L., .Koning, J.G.:

Ce, Propulsion and. Steering of Ships", The Technical publ.

comp. H.Stam,.. Harlem 1948, Holland.

[l]..

.Pitre, A.S. : "Trial Analysis Methods", Trans. Soc. N.AOM.E.,

1932.,

Vol. 4o,

p.17.

[r7]

-

Troost, L.:"ASimplifiedMethod. for Preiiminaiy Powering of Single-Screw Merchant Ships", Trans.Soc. N.A.M.2.

_1957,

APPENDIX

Diagram N I

Series 60

_{DHP/N' (or M/N}

_{on a base of V/N}

for

FOUR MODELS OF SERIES 60

.0 I-_ I f -Model -NQ 4241 Model NQ 4258 z5

65 N

I

_'

_rr

--

zo

N'

1s a V/N 0740 .150 070 .150 V/N 0160

IModel

ND 4270 MOOel N 4275 -

I

.,

-jj

kl-M "Lubumbashi'

M/N' and 1/N2 on V/N base

N'2

041 0.42 0.40 6 .4 4,xio 6 r/Nc_ao48o78 V/N.0.070836 039 040 38 M/N-Q054628 V/N.t0,077900 2 9 oj.9 S Q37 TIN1 9 0.142

a

143 V N Q 746 0.747

42-M. v "Luburnbashi" Diagram N3

TIDAL VELOCITY on a base of

TIME CF DAY

Polpeirro. January 10. 1954 0.7 0,6 + 9 0.7 06 o.5 8.

-_-_

11 Q5 0.4

/

/

/

/

0,4.. Tidal velocity in the direction 03

/

/

/

w knots 0.3 knots 22 6

/

/

// Q2 5

/

/

/

/

/

/

Tidal velocity obtained

0.1 by the tortue and thrust method

()

0

(.)

0 0 4

/

/

/

Q..L 0 0.2 Tadal velocity in the direction 02 E 2 3

/

from prof Aerts.senTidal velocity knots 03

/

/

/

paper in the knots 0.3 I.N.A.T raris

0.41/1

/{

0.4

/

hI Time of day 12' 13' 74' 15'

Mv. 'Zubumboshi" Diagram. N.Q 4

MEASURED MILE TRIAL DATA

Delivered Horse Powr Thrust and R.PM. on a bose of Ship Speed

Polperro, January 10, 7954.; Loaded Condition

120 nO 60 N rpm ifi S

I!700O

90 40 80 Thrust (tons) 30

T__________

70 20 DHP (HP) 5, 60 10 DHP (HP) 000 0 '00

-+

Against the windWith the wind

_f

Trial resultsuncorrected

Trial results corrected

for calm air condition

1000

10 11 72

V

Mv... an Laborde Diayam N5

M/N2ard T/N2on V/N base

for a twin screw hca,,,,o _nLd passenger ship of 142.9 m

O22 9 0.19

PORT SCREW ._Tio2

Ni \,r/N'=_eo53357 V/N ooO92255

.9

Q21 + 1 0.78 10/. 1% 7% Q20 8 6 o,i M N

I/.

4 STBD SCREW 7 M/N'= -Q047235 v/Ne Q0085559 0.79 PORT SCREW 2 0.16 M/W -Q046671 V/Ne0fl084598 4 T/?4F'

M/N'

SCREW STARBOARD SCREW .5 0j37 41138 N 4L 4140

34

4147 0.142

_Ls.5

My...scoS"

Diagram NQ6

M/N2

_on

_{V/N base}

for a twin screw motor yacht of 42.23 m length on WL

075 4 0)5

2-..

aM b0' 014 M i10 I SIBO. M/N2=-000066040.VATTh/xr)o4266o SCREW 0,13 PORT SCREW 0.13 M/N'-Q00067033 V/N.Q0fXk42874 6. 412 0,72 RT STARBOARD SCREW SCREW 0.41 0.42 N (444 0.45 0.46

M. v .Bolco" Dyam

'7

M/N'on V/N base

for a cargo ship of 10500 t Ow in

ballast conditions

Q274 Q214 Q213 Q273 a.212 Q212 W7 Q211. r1O' Q270

\

102

oio

I.. Q209 M/N2:Q027377 V/N + O0054650 1./I Q209 7% :2 oe

.Q7

10 Q207 0.206 09 (2206 (4722 0123 V/N 10 0.124

il.

M. v. ,, P1 rot" Diagram NS8

M. v. ..Zemun" M.b..VUithfl"

M/N2on V/N base

for three

sisterships in ballast

conditions

0.128 0728 0,127 4

5. .3

0127 0126 M.i .,VAAZD!N"(T0f=3,09m 0= 520 1) 0126 1 M Ns= -'0015564 VN +0,0X227305 0.125 0725 0,124 M 0,124 0.123

\

0,123 0.122 M.v. .,P!R0T"(Toft3,73m;D=1/8t) M/_QX16888 V/N +0,0002236 0,122 0121 0,121 0.120 6 0120 and. M.v...ZUN'YTofi=3.03m;D=732otJ 0)19 M/Nt-0.0017313.V/N .000023014 0.118 a 60

a

61 Q162 0.63 v/,v!02 Q 64 0 (166

osi

M.v.,Marib

M/N'

for a twin screw

Diagram N1

on V/N base

passenger ship of 5423m

length onWL 9 117 7.17 7.66

\9.

7.66 7.65

\.

.RT SCREW $5 - is' £185 .$/.OXLO446l 7.64 1

74

35

I

_7.14 413 1% $3 7.62 7% 7.62

+

i,o5 1% 410 6 M 7 7.60 159 STBD SCREW vki + 0XV05244 -aoXô2S . 15'

1

.

(SS 7.57 (57 1 2

\

L

M.v.,LubtgnbasW _{Diagram N1 10}

V/N on the base of V

0)9 P4 V(knotsfl 0)49 0)48 0.748

\2'

l+fth te wind 0747

\

0)46 0/45 -0)45

3\

\

\

A7Qirist the win.

\'

0744

,\

0143

\

\

6\

%

'

\'

0743 + Against the

IiththeJAnd

4742 wind

\\

4742 0)41 _'I 4741 12 13 V(knots) 14 . "I

t v Lubumbash, N 975 37 II Datgram NQII

;

1012 2 g w

A Mean Line

Diagram N272

of

Wind Direction Effect Coefficient

Q5 -to 45

7

4

Direction 110 3 13, 17 1.0 Q5 143 off bow -0,5

IL

K0 -7D

-

51

-470

- . 0)0

Jr

I'

NEPTUNE IM'CEVTEE) LONDON M4RINER G,tGHES) .-I ' 2 4 6 8 2.

46

REYNOLD'S NUMBER -0---- -. SAN GERAROO(HLJGHES) LUBUMBASHI Diagram Nt 13

HEAb

WIND RESISTANCE OEFFIC/ENT

4r 1NISSEI P4ARU. 1.040

-

-iip--j TUNA FISMMIG (KINdSHITA)

I

- ii

NISSEI MARU LIGHT ,HOQVER flEMKE- CARSON)

MAURETARL4(HUGHES?

\ W_

,.k-X--. Qj

-

-,- LIGHT CRUISER aZJJBUT/)

...

HTM! M4I (ARAKI H4N4OKA)

BA1TLE SlID' - L - - H14MBURG(FOTTIM3ER) .

-- ---- CHINESE FRItCE (WE/N GARfl

V1RK (FÔTTINGER)

TOA MARLI(ARAKI HANAOKA) AIRCRAFT C4RIER (IAIBUTI)

MODIFIED HOOVER (HEMKE -CARSON) PARTIAL STREAMLINED HOOVER (HEMKE - CARSON) STREAM LINED HOOVER (HEHKE CARSON)

-

2.

--

53

-DIQQrOmN*74

M/N2.on a base V/N

for a fishing boat

0)8 5 7.70 t.79 v/N.7O' 0,20 421 IJo L05 4 V/N + Q000020605 z05

Ms

100 T 1% _'4 too

I

Tidal pelocity

ks

LL.

of

:

V/N.e

M/Noh V/N: :base

for a twin icrew passenger ship

OAE v/N.10 7

:)

DiogiamN2- 15

£

.V/N.1O

- Tirnotomiddti Ot run V Spud ov.r ground V9 PO,iutien$ p.r nun.?. N Meqsqrd torque m Torque obsor6d 6? screw H Thrust corr.fid for utaficlunot T P4/N m -TIN s

I

TORQUE METHOD - T H RUST METHOD

i

(a) B, N 2T788 (b) At m A,.l8,3O5

(J(J

?hro h wot:: V

Current Ic) Id)

-A2m through Current Spud - v Dir.cg,onj 82N I8,.-g225f,A,.--2Oft25 Spud 0

-;

Direction 3 rn/n knots rpm HP/rpm HP/rpm tons knots knet3 knots knots

I

IV 10 28 /4,4, /01:89 */.'6 +488 s9,59 0, +oil 0,389* 22.62 -7,360 f4 ?9 -438 5 2 9*4' -, /09 /+t98 - 442 F

2 £ if

0 /5,29 1045? 4i.47 4449 393I 0,39*9 Q3832 .ea34'8 -1225 F5,12 4/7 6 23,/k? -7,980 ,5,F? 4/2 1

3 W ii 25

is,1f /0i22 41,55 +o,s5 jg4l 4+006 43894 22,054 - 33 F4 72 -41? 6 22,9+? -8,109 1*. 73 - o,#5 £

4 £ /1 f429 FI2,J8 5/56 10,50 49jta5 4*5/0 0,4.333 24',4'8/ -825 /6,22 407 5 25,355 -4/28 g'523 c06 £

5 W /225

1400 1,1:31 5.169 5490 4s,+s 4*57.3 4+445 2*252 -4 .37?'

4I6

4/2 W 25 119 - 1St? _/5,66 0,1* W

6 8

/2 55 /589 ff1.94 1i 51 10,59 *4/9 4*5/9 44394 2*, 385 -6,292 14'i - 423 W 26,2(1 -9151 6,/f _-422 W

7 W lb

119 4?* /15,90

_{5 *'}

55,92 5*i'f 0,4839 4*68/ 25, '87 -4854 /6,3 q*# w I is. Os, - '*8 /43* O,+o W

tF1 1/'4 ₅₅₉ 546/ 53,9* 0,496* 0,4621 25+35 -9,72/ #6,1/ 459 W 243*5 -9,623 ?2 -0,59

9 W l+Z+ 6,93 FF5+9 1451 55,59 54,14' 4*8/2 4*688 :5, /63 - 805 /6,35 58 W es, 063 - 3 _w

& £

ftQ*

916 egp

25,99 26,4'3 0,3/If 0,39*3 /4206 -5,695 12.51 -0,57 W /8,85? -6,53? '2,61 -0,65 w Fl W

_'°

/2,91 92,56 2739 26,4/ 15,85 0,3998 0.3/32 #9,993 -5,85+ /2,1+ 0,57

I'

'6,635 -5,522 14/I 419 W

M v. ..Lubumbashi Sheet N°-2

ANALYSIS of TRIAL RESULTS (continued)

Table N! 2 - Differences of times of day to the middle ol each run

Table N 3 - Time (actors kFI

56

-Run N9 (I) Time of day rnidd!e of h '0 run mm differences mm 2nd d.!ferer,ces . mm .3rd differences mm I 28 2 f2 0 _L1f2-1 32 3 t 25 4 ti-2- 25

4tj_:

57 4 t4 1, 52 41ç_3: 2? 4t42 52 4t4-i- 6 5 (5 /2 25 41 33

4f_j:

60

4f_,:

85 6

fr 12

55 4!,c.s 30

4t_

63 4lç..j 90 7 f 13 29

4t7:

3* .4t?- 6* 4t74: 9? 8 1g 13 53 Ljt6_7 29 4tae 63

4t_

93 S tq /4 24

4(_:

26 Atç_i: 55

4tç

89 10

tr 14

58 4 17fl_Q: 34 4 t:o-8 60 4 ff..7.3 89 11 _ti, 15 Jo 4 t,,-,F 32 4 t,i_g: 66 4 tn-8 92 I 2 t12 16 2 4 t12-11 32 64 4 l7

Time factors 0 3 Time factors

7 ,P:4t.., 4t.j

25275i 35/00 8#j:i3Ijo_ _11-I0I5-9 3 32-66 ri/lOS

2

1 ,F2 4t_ 414.7 27 5784 :129276

9 :4f77 32 6c 91 /76640

3 ,F3 4 -2 .. :32 52.8* 3/39776 10 4te-e

tn-g1-.

.92 f57g72

4 1F4 'I1_7 Otj_7 4tj 322557 +5100 11 6Fl,r1te_! . f10_9.t10_5: 26 3*. 60 :53040 2 2 r4t4_ 41$ _4 4tS_ 27- 33 60 53460 9SF9 :4' 12_tI 4172_tO: 32 32 64 65536 4f5 2t5-2 5185:1*1860 41 ,,_,41 l29 32 . 66 91 r20976 2 4. 5 4 .t3_241t5_31l5_2/560-81 127500 179,F,,,0_94t,2_,04t,2_9 34 6495 2132*8 Fs :43_2-4t4_J4t4_2-25-27-32 15/00 129Fj4t,0_g4t,j_,04tti_;r 34-3266: 7f606 j F3 1t 416-5 4t- 333063 623W F4 r4t6_5.4t5_34t6_3:.J06090:/62800 F5 .tj-4t5_.M6.j3 27.63./530P6 s 6 F6 :414_3 4t5_44t5_3r 2?. 3360 534O :4t5.5.4t,.4t7_5 30-34-6* 65260 4t6_44t?4:4*639?:207hf4 6 415_4 4t7_5417_4 :33 6497.204864

5iF4ti-6 7F 4t_ At. 4t ,3.3o.63:62370 6 F6 :4t_74t9_..4t,_7 291657' 41'IW .F, :419. ..6.4t_63 26;89 :f4572 F8 34.5589:166+30

.F-4

.t._ t...

43: 62f/8 7 ,F,:AIQ_a4tw,_94t,o..e. 243*60.530*6 :4t*,_gAtg_74t,O_7r 34.55.99:,a*30 .iFg 7: s.F, 3411_741,O_841W719l089 :15*860 ,r4t

4f4f_ ,,9.26.55:*/*90

Table N?4 -Detrminotion of _{k(M/N). k TIN2) and k(V/N)} --

yl_y2_x

j

*F, m

,,Fm,

S

_kF,s/

_{N; ,FiN:} .Vg ,,F,V1 I 35/00 44021 /4,13,7/ 4319*

'iP94

,',6r

J5/7

/6.4/ 505 -a /29276 43947 IIO25,2+ 4 1632 *g534,56 /O 5? /3259139

/3,29 130

3 _{liP I/I} 4*006 _{55994,27 4}380* 5+#p479 ,t'l, 22 1* 48 /2'? 1*, 55 10337+1 4 *5800 4*5/0 2056S00 4*383 ,9926*1 /14, 36 5/235/6

/9g

7*292*

r.

1*16941! £2 /37621,75 £ 35/aV)/99 _{5231986 003925 4003912 4i'4g 4$?/79*00 qs1S.saa 4,2226}

2 53+0 0,194? 31 1O46 43832 1o+8487 '02,5'? 5*83392

I29

8/7*03

j

/45160 44006 g4s,sa 4399* 16791,98 /o.I2 f*7W394'9 /*,55 2(2253 2 _{129300 4*1/0 5930250 .0, *i83 csg93,6} 1/2.36 /*815g00 'i, 20 75 995 5 35/00 44193 I(P5 23 4

*6 /56095

//1 31 90595/ 56F'00 1,. ,'650849f _{I2/+8795 £3 39+80222 Z55'?gZ*' 4003976 00J866 4/*495} 4596650S841'535 .4l6l.0/6 3 61390 4*001 24983,42 0,3894

2*,aII

'o,,22 61/3091 f*,5 907*1+ * 162000 4*1/0 73062,00 4 #393 Wo0*,60 36 19102320 /6,29 2618 9$O

7 _{5 /53090} 0,*5'73 i000S,06 4*4+5 680*3,50 I/f, 3/ 170*0*48 #6.00 2*+94'4'o

6 63*10 4*119 24E8,J? 4439* 13+93S f/fOil 591*1/2 /5,69 8*9*79 '/9/2/4,05 £' fF6S3430 Er4lS*0/T1 . 6845193 0,0040*3 4003930 0,14399 4582/5/57 O,Jf/'18D 1DF9511D/ + 653o 0,4,5/0 _99tp/j9 4+383 186&)l /l,36 733*96/ /4,39 /0634/1 1 107774' O,*5'73 OsoiS,os 44*46 .91365,1*

l'.3f

23/2732* 14,00 3,2*35* 4 10,15* 0,45/9 91579,04 4*39+ 9of9,l* sf, 9* 22932+96 /. 8 J55 219 7 L?J7'O 4*13? Jo/68,37 4468/ 29/91,40 1,5,60 7209972 /,'?# ,04*00*

1, '2*7202,76 12 2*o/1D* E3OI043J L J9?'ii 400O'079 0,003963 4/433* 0,59+6gm qs6,9ss4, 2,#635

5 62/18 - 0,1,573 _{2$4O4,5 0,44*6 IXFV,4'S 1/1,3/} 9I* 355 16,00 993898

#72601 445/9 001,56 4 '39* c'p496 94 /712/7*0 _'U9 27*294/

5 _{9 /96990 4*839 95019,45 4/}

_gjp9*

_{i5,6o ,ppjfoo/l}

16,94. 29*1390

8 65a80 0,*76* 3,p99,39 0,*621 30,5589

.'if*

jo95q I1,5 /05*272