On collecting ship service performance data, and their analysis

For every ship, steaming at constant draught and trim, there is an exact relation between

her fuel consumption,

engine and propeller revolutions, horsepower delivered by the propeller, speed through the water.

These four factors are interdependent. The only factor which we have under control is the amount of fuel or steam inlet to the main engines. After that the propeller fixes automatically the number of revolutions, also the propeller slip and hence the

ship's speed - which will balance thrust and

resistance.

Fuel consumption and horsepower are both governed only by fuel (or steam) inlet and revo-lutions.

For diesel engines, the exact relation between con-sumption, revolutions and horsepower can be ascertained on the test bed. If the same data are

taken simultaneously, at regular intervals, on

board the ship in which the motor is installed, we are able to check these service performance data by comparing them with the test bed results.

Often it is difficult or impossible to ascertain the engine's output, with any degree of accuracy, on board a ship in service. The computation of the fuel consumption during short periods is not at all an insoluble problem. Simultaneous readings of revolutions and fuel consumption will enable us to find the corresponding horsepower from the test bed trial results.

Hence, the exact computation of the fuel consump-tion, during short periods, can have a twofold purpose:

1. if the horsepower developed by the ship's engine is also recorded, the fuel consumption per hp per hr can be computed, which is a yardstick for judging the working of the main engine;

I. AIMS AND PURPOSES

2. if the horsepower can not be recorded directly, either by taking cards or from torsionmeter readings, then the horsepower corresponding to simultaneous readings of revolution counter and consumption meter is found from the test bed trial results.

Turning from the engineering to the shipbuilding side of our subject, i.e. the exact relation between revolutions, horsepower and speed, it should be emphasized that this relation can not be deduced à priori. It must be derived from carefully collected and selected service performance data. The know-ledge of this relation is of practical value for three reasons:

It is the only means of checking accurately simultaneous records of fuel consumption, revo-lutions, horsepower and speed as to their relia-bility, and of judging the fuel consumption (lbs/HP/hr). This should be of primary impor-tance for an economic exploitation of the vessel; undue speed losses and excessive fuel consump-tions will become apparent without delay. If these technical factors: consumption,

horse-power and speed, are compared with the

external conditions prevailing at the time, we

can judge fairly the ship's speed. This will

enlighten us on how to handle the ship to the greatest advantage under service conditions; it will enable us to make impartial and clear comparisons between the seakindly qualities of different ships; and it will pave our way to the design of scakindly ships.

We are in a position to make close comparisons between service performance data and model tests, in order to ascertain power allowances on tank HP for specific external conditions and for the proper investigation of the factors governing scale effect.

A. TECHNICAL DATA

As has been stated in the preceding paragraph, there exists for each individual ship - an exact relation between the four variables

fuel consumption,

engine and propeller revolutions, horsepower delivered by the propeller, ship's speed through the water.

Items 1. and 3. and engine revolutions constitute the engineer's part of the subject. The shipbuilder's

part consists of items 3. and 4., and propeller

revolutions.

The exact relation between these factors can not be deduced à priori, but is to be found empirically. Hence the necessity to collect service performance data which should be

accurate, re]iable,

taken simultaneously.

These requirements are of fundamental impor-tance. An exact relation can only be found

empiri-cally provided that the basic observations are

exact.

The time required for taking simultaneous records may vary from a few minutes (measured mile trials) to several weeks (a voyage). In the latter case neither the fuel consumption, nor the r.p.m., horsepower or speed will be constant, on account of varying external conditions. We may compute voyage averages, as is often done, but there is no guarantee whatever that these, averages will fit

into the exact relation

existi1llg between these factors. Nobody can say whether they do or not, als long as this exact relation is not known. So it is an absolute necessity to collect individual records

simultaneously.

To put it the other way round: records should be taken during a period which is:

long enough to collect an adequate number of

accurate and reliable data, eliminating

in-accuracies inhaerent to the recording

instru-ments and the human element in taking

readings;

short enough to be sure that the external and internal conditions remain constant; a straight

II HOW TO COLLECT DATA

course should be steered, and nothing should be altered to the settings of fuel, air injecting and exhaust valves, or to the steam pressure, inlet, exhaust and vacuum.

The duration of a recording period depends upon the size and type of the main engine, the recording instruments and the available personnel.

Fuel consumption

The accurate measurement of coal consumption during short periods is impossible. Fortunately, about 80% of the world's mercantile tonnage uses liquid fuels.

The design and construction of a flow meter,

suitable for use on board, should not present un-surmountable difficulties. The instrument should enable us to

record accurately, using a stop

watch, the time required by the level of the oil to fall from one mark on a sight glass to another, the volume between these marks being accurately known. Fuel temperature, specific weight and ca-lorific value are to be recorded too. And there are in existence flow meters of the rotative type.

Horsepower delivered by the propeller

On a ship we can only record either shafthorse-power or indicated horseshafthorse-power. The correspon-ding propeller horsepower is found by making allowances for friction losses and engine efficiency. This is necessary if comparisons are to be made

betweçi service performance data and model

experiments; otherwise we can just as well ascertain' the exact relation between SHP or IHP as recor-ded and the other variables.

SHP can be measured by means of a torsionmeter, and instruments exist for recording thrust. So far none of these is suitable for permanent use on board; they require favourable conditions and expert handling. Their improvement has been taken in hand seriously, and it is expected that a robust and simple type of torsionmeter will be available in the near future.

The taking of indicator cards and the calculating of IHP from the recorded diagrams requires more

elaborate care than can be expected from the

ship's personnel under average service conditions. Moreover, in the case of diesel engines, the num-ber of cylinders may be so large that the proper taking of cards would require too much time. It is always advisable to check the engine output computed from torsionmeter readings or indicator cards. In the case of diesel engines this can be done by recording simultaneously fuel consumption, mean indicated pressure, and exhaust gas tempe-ratures, and comparing them with the test bed trial results. Mention has already been made of the possibility to ascertain diesel engine output from fuel consumption records only. A specimen of the diagram in which test bed trial results are repre-sented is shown in figure 1.

Fig. I

As for turbine machinery, it has been stated on good authority that there exists a linear relation between SHP and steam pressure in the second expansion of the high pressure turbine. This rela-tion can be computed from reliable and accurate data collected during trials, provided that a tor-sionmeter and trained personnel are available.

Engine and/or propeller revolutions

Rpm are not to be taken from the tachometer, but from the revolution counter, preferably of the type which has a separate dial for recording tens. With the aid of a stop watch the time is noted which corresponds to a certain number of tens of revolu-tions. In this way accurate readings can be taken.

Ship's speed through the water

Log readings should be taken in the same way as described for the revolution counter, using a stop watch.

The Walker's log is not a reliable instrument. Its readings may have errors of .25 knot or more, whereas an accuracy in tenths is required. On the

other hand careful handling and upkeep might prove that this instrument is better than its repu-tation.

Logs based on the principle of the Pitot tube,

provided that they are properly adjusted and

readjusted at regular intervals, should give readings of adequate reliability and accuracy.

The preceding survey shows that we can always obtain accurate records of rpm with the type of instrument which is usually installed on every seagoing vessel,

provided that a stopwatch is

available.

Up to the present there is no conventional device for recording accurately the oil fuel consumption. The design of such devices is quite simple in prin-ciple, and their construction and installation need not be difficult or expensive. Accurate information on fuel consumption during short periods is of particular interest, as stated before, in the case of diesel machinery for which test bed trial results are available.')

Engine output can be recorded and checked in several ways, particularly in the case o. diesel machinery: torsionmeter, fuel rate, mean l*essure, and exhaust gas temperatures.

So out of the four factors with which we are

con-cerned, three can be accurately ascertained in

the majority of cases. The recording of the ship's speed through the water remains uncertain, be-cause we have only the log, and no other means of checking accurately its records.

B. NAUTICAL DATA

One of our objects is to compare the ship's per-formance power and speed for given draught and trim - with the external conditions prevail-ing at the time.

The latter come under three headings:

roughness of the ship's bottom, depending on the condition of her coating and the degree of fouling (days out of drydock);

meteorological

conditions: wind force and

direction in connection with the vessel's true course;

state of the sea: direction, height and period of waves and swell, also in connection with the vessel's true course.

For many years, quite a number of ,,selected" Dutch merchant ships have been collecting

me-1) _{The latter should cover the widest possible range in SHP and revolutions, in order to get clearly positioned lines of}

constant revolutions, see fig. 1.

5

teorological information for the benefit of the Koninklijk Nederlandsch Meteorologisch Insti-tuut (Royal Netherlands Institute of Meteorology). It covers the data mentioned under 2 and 3. The K.N.M.I.'s forms ask for observations to be taken at zero, 6, 12 and 18 hr. G.M.T. It might be con-venient to collect the technical information at least once a day during short recording periods round about one of these hours.

For ships which have not been ,,selected" the only thing that matters is that technical records and information regarding external conditions are collected simultaneously at regular intervals, once a day during the same watch.

Telfer (1) and Kan (2) have put forward pro-posals for summarizing the conditions of wind and

sea in one figure, a ,,weather factor", ranging

from zero to 300:

O = fine, 100 = moderate,

Model experiments constitute a simplification of the actual vessel's performance. They are a repro-duction to scale of the ship steaming under ideal conditions; no wind, no currents, no waves; no changes in draught or trim; no rudder angles; and

a wetted surface of uniform smoothness.

The procedure which will be put forward for the analysis of service performance data can be applied as well to the analysis of model experiments. Ofthe two cases, the latter should be the simpler. More-over, model records should be reliable and accu-rate; experiments can be repeated, and their scope can be as extensive as would seem to be necessary.

A. MODEL DATA

Using the symbols put forward in Van Lammeren's ,,Resistance, Propulsion and Steering of Ships", the fundamental assumption is made that a linear connection exists between the torque constant Km of the screw and the velocity coefficient A.

III. THE ANALYSIS OF TECHNICAL DATA

Telfer, E. V. ,,The practical analysis of merchant ship trials and service performance". N.E.C. Inst. Vol. 43, 1926/27.

Kan, A.

The design and Cost estimating of merchant and passenger ships.

200 = heavy, 300 = very heavy.

It is not known whether these proposals have ever been put in effect extensively; it certainly seems to be worth trying. Comparisons between loss of speed and weather factor would show the influence

of nautical conditions on ship's performance. It would be of interest to record the vessel's be-haviour as well: amplitudes and periods of her three rotative movements: rolling, pitching and yawing, and their angular accelerations.

In this way we might get a complete picture of

external forces, the vessel's reactions, and the

resulting losses in speed.This picture will disclose

the ship's seakindly qualities and the factors

governing them. Ultimately we may be able to design ships of which we can be sure that they will

be seakindly - always provided that they are

expertly handled.

nD

The connection can be represented

by the

equation

Kmao+aiA

(I)

Whether this

assumption holds good can be

verified by considering the Km -- A diagrams of model screws, for instance those published by the N.S.P. Wageningen. It will be seen that the slip interval with which we are concerned in the case of ships in service is small in comparison with the total range of the diagrams.

From equation (I), the following equation can be deduced, as shown in appendix A.

DHP (0.lN)3 (C1Sa + c) (II) Substituting 1852 V Sa = 100 100 60 NH = 100 in (II), we get 18520 V

6HN

18520 V

DHP=

(0.lN)3(l00ci_

6H

ciÑ+c)

M Km = eD5n2

= c"N3 - c"1N°V (III) Equation (III) represents the exact relation be-tween revolutions, power and speed, which is our first aim. If we plot DHP over N or N3 for constant speed V, we will get a fair curve, but not a straight line. In fig. 2 this has been done for a model tested

Fig. 2

at speeds corresponding to 14-19 knots for the

actual ship and with overload factors ranging

from 0.8 to 1.8 at 16.25 knots. From the same experiments the procentual changes in DHP and N have been computed, for overloads ranging from 1.0 to 1.8, and plotted in fig. 3. Here again

Fig. 3

the result is a fair curve, which should be a most refined check upon the accuracy and consistency of the model data.

Turning to equation (II) and writing DHP

(0.IN)3 c1S,, + c

it will be seen that DHP/(0.lN) is constant for

constant slip, and that the plotting of DHP/

(0.1N)3 over Sa will show a straight line. This has

been done for the above mentioned model in

fig. 4. Obviously, diagrams like those represented in figures 2 and 4 can only be prepared, provided that overloaded model test results are available.

I

3 17 16 -z o 14

5

o-

MODEL EXPERIMENTS OVERLOADTEST AT 16'f KN

PROGRESSIVE SPEED TEST DHP _0.175,+1511 R = 0.995

10 15

Fig. 4

The importance of such tests for the analysis of service performance data will be shown presently. From fig. 4, the values of the coefficient c1 and the constant c of equation (II) can be read off.

From experiments, carried out with the model of

a single screw cargo steamer 400' x 54' x 30'

moulded draught, the following equations have been computed:

DHP(tank) = (0.1N)3 (0.0881Sa

₊

5.024)

DHP(tank) = 0.01383 N - 0.0423 VN2 N being propeller revolutions per minute and V the ship's speed in knots.

Variations in draught

It is common practice to test models on an even keel, at one draught only. We will now consider the question whether the equations (II) and (III)

remain the same when the draught is altered.

Variations in draught will cause variations in

wake; the shape of the K,,, curve will change when the submersion of the screw becomes too small. The single screw 400' model has been tested at three draughts (even keel), see table 1.

TABLE i 7

46,l.K

KN 60 65 N- 0 75 80 05 200. 150 loo SQ

I

D 'l 50. . -MODEL EXPERIMENTS 0 5 10 N°/o 15 - 20 - 25 30

Model tests Draught _Speed

knots

Nr. Type feet metrcs

I progressive 30-1 9-18

9 12-5

overloaded 30-1 9-18 11.0 II progressive 246 7-50 9-5 - 13 overloaded 24-6 750 11.25 III progressive 197 6-00 10. 13 overloaded 19-7 600 11-5 Propeller data: diameter 5-639 m. virtual pitch 6-428 m.

TABLE 2

Values of c1 and c, computed from model ex-periments.

It appears that for draugths ranging from 08 to full loaded draught, the influence of draught on c1 and c is negligeable; for all practical purposes

we can write

DHP(tank) = (0.1N)3 (0.09 Sa + 5.0)

Nevertheless, the draught can be introduced into the regression equation, as will be discussed in a later paragraph. For the model under conside-ration, the equation becomes

DHP(tank) = (01N)3 (0.085 S0 + 374T-1 + + 4.66).

This equation is based on the data of tables i and 2, viz. 56 runs at 3 different draughts; R = 0992

and F = 072%.

Progressive and overload tests at one draught, similar to those of table 2, test I, have been carried out with a number of other models. The resulting c1 and c values vary widely from ship to ship. By introducing the actual propeller dimensions

(dia-meter and virtual pitch) into equation (II),

it becomes

DHP(tank) = l0

H,,D4 (c'iSa ± c') (0.1N)3 Consequently, the dispersion of the coefficient c'1

preceding Sa and of the constant c'

is greatly reduced, especially for the first three ships, as will be gathered from table 3.

TABLE 3

R = correlation coefficient F = mean deviation percentage

Full particulars of the hulls and screw propellers of these 10 ships are given in tables 4 and 5. The

causes of the dispersion in c'1 and c' are a subject for further investigations.

TABLE 4

Principal dimensions of the hulls.

L length between perpendiculars (length on load waterline)

B breadth T draught A displacement 5 blockcoefficient , wakefraction (Continental) TABLE 5

Principal dimensions of the screws.

Test

Nr Draughtfeet Numberof runs C correlation_{coeff. R} mean

de-viatjon F I 30-1 17 0-088 5-02 0-992 0.47% II 24-6 19 0-092 5-00 0-994 0-66% III 19-7 20 0-080 5-37 0-998 0-46% Ship Nr. L m B m T m m'A Number ofscrews 1 72,86 10,67 3,81 1985 1 0,678 0,289 2 90,17 13,15 5,56 4870 1 0,739 0,320 3 151,75 22,80 9,00 20939 1 0,672 0,286 4 121,92 16,46 9,18 14101 1 0,765 0,333 5 144,78 21,03 8,84 17945 1 0,656 0,278 6 141,73 19,96 8,99 16943 1 0,666 0,283 7 150,63 19,05 8,54 16240 2 0,670 0,169 8 150,14 19,51 9,14 17613 2 0,658 0,162 9 111,10 14,33 3,96 3274 2 0,519 0,085 10 152,40 19,05 8,37 15695 2 0,646 0,155 Ship Nr z _F D H0 7R H H0,7R H D Si D D 1 4 0.419 2.300 1.527 1.680 0.664 0.730 0.050 2 4 0.400 3.600 2.880 3.197 0.800 0.888 -3 4 0.383 5.000 3.721 4.188 0.743 0.838 0.046 4 4 0.402 5.639 5.639 6.428 1.000 1.140 0.040 5 4 0.463 6.604 6.605 7.304 1.000 1.106 0.044 6 4 0.514 5.800 5.375 6.079 0.927 1.048 0.057 7 3 0.397 4.588 4.761 5.374 1.040 1.17 1 0.052 8 3 0.373 4.925 5.100 5.655 1.036 1.148 9 3 0.451 3.200 3.624 3.792 1.133 1.185 0.049 10 3 0.388 4.920 5.690 6.150 1.157 1.250 0.045 Model Nr screwsNr of Nr ofruns c1 e R F / c c 1 1 13 0.00043 0.0412 0-991 0-39 0-90 88 2 1 12 0-0047 0-480 0-981 0-69 0-87 89 3 1 14 0-023 2.27 0-997 0-30 0-89 87 4 1 17 0-088 5-02 0-992 0-47 1-23 70 5 1 22 0.19 13.10 0-993 0-93 1-40 94 6 1 20 0-12 5-79 0-996 0-70 1-67 84 7 2 23 0-072 291 0-994 0-59 3-04 122 8 2 19 0-11 4-51 0-992 0-97 3-30 136 9 2 16 0-015 0-468 0-996 1-65 3-87 118 10 2 32 0-14 4-82 0-994 1-22 3-93 134 z number of blades FA

F expanded blade-area ratio

screw diameter in m D

face pitch at 0,7R in m

H0,7R

mean virtual pitch in m Hv

Si

blade-thickness ratio D

Estimating a model's regression equation

When no overload test results are available, a

model's regression equation can be estimated from the data of the usual experiments carried out at progressive speeds. This amounts to estimating c1 in equation (II): DHP = (0.1N)3 (cS0 + c) As shown in appendix A

- 20

D4H C1

=

60.75

a1 (1-

) (metric units)

Fig. 5 en 6 g 0.09 0.08 0.07 0.06

irn

0 03 N.S.P. WAGENINGEN B3 SERIES 0.02

r'

05 06 07 08 09 1.0 11 12 13 14 15 1.6 0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 «

fN.S.P. WAGENINGEN

B 4 SERIES 05 0.6 07 08 0.9 1.0 1.1 12 13 14 15 16

Consequently, estimating e1 means estimating the term a1 (1

a1 represents the slope of the K, curve over a

certain range, say from A (optimal) to 0.75 A (optimal). Using the N.S.P. Wageningen diagrams already referred to, the A (optimal) is taken from the B,-9- 6 charts.

a1 depends upon Hv/D and Fa/F; see figures 5 and 6. can be estimated by using Taylor's well known formulae:

=

0.05 + 0.506 for single screw ships,

=

0.20 + 0.556 for twin screw ships. For ship nr. 5 of tables 3-4-5, the exact equation based on progressive and overloaded model ex-periments is

DHP

=

(0.IN)3 (0.190 S,, + 13.10)

Using

=

0.278 from Taylor's formula and

a1

= -

0.490 from fig. 6, the estimated equation based only on progressive model experiments would be

DHP

=

(0.lN) (0.199 Sa + 13.08)

Similar calculations have been made for the other models of tables 3-4-5; generally speaking there is close agreement between the exact and the esti-mated equation. Nevertheless, the former proce-dure is to be preferred; overloaded model experi-ments should become common practice.

Aìlodel experiments in artificial waves

In actual service, ships will roll and pitch. Un-doubtedly these movements will cause periodical or irregular variations in the direction of the intake velocity of the water flowing through the propeller. Probably, these phenomenae will influence the shape of the K,,. - A curve.

Model experiments might enlighten us on this subject. Towing and self propelling tests with models amongst waves might be completed by open smooth water tests with propeller models oscillating in a vertical plane.

B. SERVICE PERFORMANCE DATA

In the preceding paragraphs the analysis of model data has been treated, starting with the simplest case, and introducing step by step other factors. The same line will be followed in this chapter.

Shaft friction losses and engine efficiencies

Ships will meet more or less adverse conditions during the greater part of their time at sea.

Horse-power, speed and propeller revolutions will vary over a smaller or a larger range. These circum-stances are the counterpart of the progressive and overloaded model experiments. But there remain some differences:

During a loaded passage the draught will not remain constant. On the other hand it will be remembered that the influence of variations in draught from 0.8 to fully loaded is negligeable in the case of models.

The smoothness of the ship's bottom will dete-riorate during a long passage, especially in tropical waters. The initial smoothness, after drydocking, will depend upon the vessel's age

and the quality of the bottom paints. The

smoothness of a paraffin model is always the

same.

On board, SHP or IHP are recorded instead of pope1Ier horsepower DHP. No accurate information on friction losses and engine effi-ciency is available.

Nevertheless, common and simple cases

- such

as the diesel driven tanker - can be treated to

advantage on the lines described in chapter III, A. Equation (II) becomes in the case of ships' data:

SHP IHP

(O.1N)lOr (o.1N)3 C1Sa + c . . . . (lia)

Now, ifa sufficient number of service performance data is available, covering a wide range of SHP (or IHP), N V and Sa, we can plot SHP/(0.1N)3 or IHP/(0.lN)3 over Sa. Unlike the model data, the spots will now not come exactly on a straight line;

they are scattered over a straight course (see

fig. 7). The more accurate and reliable the basic

Fig. 7

data, the closer the approximation of the spots to a straight line.

Given a scatter diagram" like fig.

7, the next point is to fix the position of the straight line which is nearest to all the spots. A sample calculation for

8_ 0.0. an O SERVICE DATA 7 _{LOADED CONDITION} 0.0711k 6.21 R- 0. 908 10 is S°5 - 20 25 30

determining c1 and c is given in appendix B (I). It

will be understood that the regression line

represented by equation (ITa) can be derived from a limited number of service data, provided that the range of Sa and HP/(O.1N)3 is large, and that the data themselves are based on readings which are

reliable, accurate,

taken simultaneously.

The fundamental importance of these three requi-rements has been stressed in chapter II, and they should always be kept in view whenever data are collected.

In the merchant navy it is rather difficult to obtain data over a wide range of horsepower, r.p.m. and speed. Usually, seagoing cargo and passenger ships sail with the steam or fuel inlet to the main engines at one particular setting, which is only altered in an emergency, such as very heavy weather neces-sitating slowing down, or increasing speed in order to recover lost time.

Two suggestions present themselves.

During progressive measured mile trials, on a course parallel to the wind direction, a low speed run with a strong wind astern might give low values of HP/(O.1N)3 and Sa; on the other

hand a high speed run with a strong wind

ahead might give high values.

In twin screw vessels, runs for taking records might be made at progessive speeds with an appreciable difference between the rpm of the Port and SB engines.

The fast running propeller will then show an excessive apparent slip, the slow running pro-peller a reduced slip.

Neither of these two suggestions has been tried out exhaustively so far.

Reference has been made in chapter II A to shaft friction losses and engine efficiencies. The former are supposed to be of the order of 2 to 4%, but definite information is lacking.

If it is assumed that the torque required to over-come shaft friction is constant for all practical purposes, we can write:

SHP (or IHP) = (O.1N)3 (ciSa + c) + bN = (O.lN)3(ciSa + c + bN2) (IV) and

SHP/(O.lN)

or IHP/(O.lN)= c1S,+ bN-2

(V)

The calculation of c1, b and c from accumulated

service performance data (SHP or IHP, N, V

and Sq) is an extension of the problem treated in appendix B.

In the case of fig. 7 we were able to prepare a

scatter diagram, because we had to do with a

two-dimensional problem. Now, our problem has become three-dimensional; our three axes are SHP/(0.lN)3, (or IHP/(0.1N)3),

Sa and N2,

and we must try and find the position of the plane which is closest to all the spots whose positions are fixed by their respective simultaneously-recor-ded coordinates. A sample calculation for deter-mining c1, b and c is given in appendix B (II). The efficiency of dieselengines can be ascertained from test bed trial results.

In the case of steam reiprocating machinery it wculd be necessary to take simultaneously indi-cator cards and torsionmeter readings over a wide range of rpm.

Shaft friction losses and engine efficiencies have been treated here because they should be kept in view whenever service records are collected. They will turn up again when we come to comparisons between model and ship data.

Suppose that we have succeeded in ascertaining a satisfactory regression equation based on accurate and reliable records, how are we to make use of it? Take for instance the service performance equation of ship nr. 4, table 4:

SHP(ship) = (O.lN)3 (0.0694 Sa + 1103N-2 + 5.992)

If a complete set of simultaneous records (SHP, N and Sa) is reported, we can substitute them in the above equation and see whether they fit in pro-perly. If the record of one factor is doubtful for instance the speed by log, and hence Sa we

substitute SHP and N in the equation and cal-culate Sa and V; the calcal-culated value of V is a check on the doubtful log reading. If one record

is lacking - for instance SHP - it can be

com-puted by substituting N and Sa in the equation. But it is more convenient to prepare a ,,generali-zed power diagram" (fig. 8), as originally proposed by Telfer (1). By substituting every possible com-bination of slip and revolutions likely to occur in service in the equation

SHP (or IHP) = (0.1N)3 (C1Sa + bN2 + c) the corresponding horsepowers are calculated; the corresponding speeds V are a function of N, 5a and the propeller pitch.

It will be appreciated that the original data: SHP, N and Sa have been plotted first in such a manner,

4500 4000 3500 3000 2500

I

ç,, 2000 1500 7

f

w-.

8 9 10 V(KN)-1l

that we have to draw one straight line as close as possible to a number of spots that are chearly approximately in line (fig. 7). The resulting gene-ralized power diagram shows a number of curves and cross-curves for constant N and constant S, values in a diagram of SHP over V.

The introduction of S0 recommends itself because the apparent slip is a clear reflection of the external conditions under which the vessel is steaming, irrespective of her speed and engine output. It is, however, only a matter of convenience whe-ther a diagram similar to fig. 2 - or any owhe-ther way of representation - is preferred.

Variations in draught

Tankers are operated at two draughts, correspon-ding to the loaded and the ballast condition. There will be some difference between the draugth at the beginning and at the end of a loaded or a ballasted

10 Fig. 8 12 e0 13 SHP -(0.1 N)3 (0.047 5A + 1227 N-2 + 4.39) (DERIVED FROM MODEL EXPERIMENTS)

14 15

passage, and there will be different ballast condi-tions. All the same satisfactory results can be ex-pected if for this type of ship two separate regres-sion equations are computed, one based on the data of loaded passages, and the other on those of ballasted passages, without introducing draught into either of them.

Cargo liner voyage records may show an appre-ciable range of draughts. In this case it will be preferable to compute one regression equation including a draught term.

Estimating a ship's regression equation

The following regression equation, computed from service performance data only, has already been mentioned:

SHP(ship) = (O.lN)3 (0.0694 Sa+ 1103N2+ 5.992).

The regression equation of the corresponding

model is

DHP = (0.1N)3 (0.090 Sa + 5.00).

It is quite a common case that, even if we have numerous and reliable service data at hand, their restricted range of sa-values renders them useless as a basis for computing a regression equation. Under such circumstances it might be justified to accept the coefficient c1 of the model equation as an approximate value for the ship equation. In the case of the vessel mentioned above the influence of Sa would be overestimated to the extent of

0.0900-0.0694

>< 100% = 30%.

0.0694

The turbine-installation of this vessel has a normal

output of 2700 SHP at N = 70. Taking shaft

friction losses at 3%, friction-HP can be

represen-ted by

1 .1 56N, and the estimated regression equation becomes

SHP = (0.lN) (0.O9Sa ± ll56N-2 + c). The constant c can be computed from the available service performance data, because

X [SHP/(0.1N) - 0.095,, 1 156N-2]

number of records In our case c = 5.52 and hence

SHP = (0.IN)3 (0.O9Sa + ll56N-2 + 5.52) In actual service the slip values of this vessel's pro-peller range from 15% to 30%, the slip being based on the virtual pitch H5.

Within this range the maximum difference be-tween SHP/(0.1N)3 values computed from the service regression equation and those resulting from the estimated equation amounts to about 2.3%

at 15% slip and + 1,6% at 30% slip. At 23%

slip there is exact agreement.

Weather conditions: wind, waves and swell

Service performance data, including records taken both under favourable and adverse weather con-ditions, are the foundation of a ship's regression equation. In this paragraph the influence of gra-dually changing weather conditions ori horsepower, speed, revolutions and slip will be investigated. Let it be assumed that the setting of the fuel or steam inlet valves is kept fixed. In that case the torque will remain approximately constant over a fairly wide range of speeds.

On a voyage commencing under ideal weather conditions, the engine will settle down to a certain number of revolutions which will not show any

C =

fluctuations as long as the fuel or steam inlet and the weather conditions remain the same.

What will happen when this ship meets a gradually increasing headwind? The wind will increase the ship's resistance and reduce her speed. If the pro-peller revolutions remained constant, the reduction in speed would cause an increase in slip. Keeping revolutions constant at increasing slip necessitates an increase in torque. Consequently, at constant torque, any increase in the ship's resistance will cause a reduction in propeller revolutions and a

reduction in engine output. This reduction in

engine output will cause a further drop in speed. In fig. 9, curves of SHP, propeller revolutions and

Fig. 9

slip at constant fuel or steam inlet have been plotted to a base of ship's speed. In the same diagram curves of DHP and model propeller revolutions

are also shown.

This is a first step towards assessing approximate service performance allowances, viz.

SHP(service) - DHP(tank)

x 100% DHP (tank)

This procedure does look rather attractive at first sight. Differences in propeller revolutions between model and ship, at the same speed, are read off at a glance. The differences between SHP(service) and DHP( tank) can be split up further.

Shaft-13 3000 - 30 _120

0RVlCE/

2500 - 25 -

/

- 110

/-2000 20.. - 100 Ç., - --L-

--I-

- z -- 90 1500 15 -1000 10 80 11 12 13 y

friction HP can be ascertained either as a constant percentage, or calculated by multiplying N by the coefficient b of the service regression equation. Differences in frictional resistance between ship and model can be calculated approximately. The remaining differences are caused by weather con-ditions and scale effect.

Unfortunately, an accuracy in ascertaining the ship's speed through the water is required which

is unattainable with present day ship's logs. If

numerous data are avaiable, service performance allowances in % of DHP(tank) can be computed for every set of simultaneous records. For speed intervals of half a knot, cumulative frequency distribution curves of these percentages can be prepared for each interval, see fig. 10. From these

Fig. lo

curves we take the most probable

service per-formance allowance % for the mean speed of each speed interval. These percentages, plotted to a base of speed, will lie on a fair curve, provided that the basic records were taken whilst the enignes were

Trial and service performance predictions are usually prepared by the staff of the experimental tank. They work out from model experiments and previous experience the engine output that will be required to attain a stated speed under fine weather conditions, and the number of propeller revolutions at which that engine power will be

de-running at constant fuel or steam inlet; see fig. 11.

Fig. 11

A specimen calculation of cumulative frequency distribution curves is given in appendix C.

Roughness of the ship's bottom;fouling; scale effect

Assuming again that numerous reliable data are

available, these can be grouped according to

weather intensity. Restricting the following in-vestigations to fine weather data, the influence of wind and sea on performance is eliminated. Ap-plying the procedure mentioned at the end of the preceding paragraph, the differences between SHP (service) and DHP(tank) include only three elements:

shaft friction losses,

differences in frictional resistance between ship and model,

scale effect.

In the case of a liner trading between Rotterdam and Indonesia, an analysis of accumulated data showed conclusively that the service performance allowance under fine weather conditions increases gradually in a ship's lifetime, quite apart from fluctuations caused by fouling, and differences in the quality of the bottom coating.

IV. TRIAL AND SERVICE PERFORMANCE PREDICTIONS

veloped. Service performance predictions are res-tricted to an average engine output for an average sea speed under average conditions; such predictions can only be checked roughly when the ship has been in service for over 12 months, in order to eliminate seasonal influences.

The accuracy and reliability of trial performance

Z loo -< 90: -

BO-9ll:

w 50 30_ O 20

I

-10 100 10.2 110 11.2 120 I 1,5 99.9 99.5 12<12.5 11.5<12 I 5<11

0IiIIii

20 30 40 I 50 60 ¡ ¡ ¡ I I 70 80 90 LL0WANCE % 100 I 110 I 120 130 140 ¡ ¡ ISO

predictions depends largely on the accumulated

trial performance data collected by the tank

authorities.

Well fcunded predictions for speczjìc external con-ditions - including fine weather trials - will be based on the regression equations of numerous vessels and their models. Ultimately it will be possible to estimate the performance allowance required for any particular vessel at any specified weather factor. The corresponding propeller revo-lutions can be ascertained as follows.

Take for example the single screw turbine steamer nr. 5 of tables 4 and 5. Her regression equations for the loaded condition are

DHP = 0.0l383N - 0.0423N2 V (model) DHP = 0.01293N3 0.0333N2 V (ship)

The data underlying the ship-equation were

collected within one month; the influence of

changes in the degree of fouling can be neglected. From these equations two curves can be derived, showing DHP's (ship and model) for a service speed of (say) Il knots at overloads ranging from zero to 80% for the model. These powers have been plotted in fig. 12 to a base of revolutions. Estimating the service performance allowance at 35%, the service horsepower for 11 knots speed

Further investigations are required on the following subjects:

The development of apparatus for recording a vessel's behaviour, i.e. amplitudes and periods of her three rotative movements - rolling, pitching and yawing and their angular accelerations.

Such apparatus, based on the principle of the

gyroscope, belong to the standard equipment of airplanes. They can be modified to suit the move-ments of ships.

Preliminary experiments have been carried out; they seem to be promising.

The causes of the dispersion in c'1 and c' values

(table 3). More service performance data and

overloaded model experiments should be sub-mitted for analysis, including the preparation of

V. CONCLUDING REMARKS 3500 -3000 2500 -2000 1500 DHP = 2560 65 N 70 FIODEL: 0H? 0.01383 N-0.0423 NV (DERIVED FR011 OVERLOADIEST AT 11 KN) SHIP 0H? =0,01293N'=.0.0333N'V

(DERIVED FR011 SERVICE DATA)

Fig. 12

will be 1.35 >< 1900 DHP = 2560 DHP. From fig. 12 it will be seen that the corresponding pro-peller revolutions will be 70.8 (model) and 69.4 (ship).

diagrams similar to those shown in figures 9, 10 and 11.

The recording of meteorological data - wind

force, wind direction; direction, period and height of waves and swell should be standardized. The nautical staffs of several shipping companies are actively interested in this subject.

A study of the influence of scale effect on the com-ponents of screw propulsion remains a subject of primary importance. This heading covers subjects such as the quantitative investigation of variations in wake and thrust deduction, and of the influence of changes in roughness and fouling. New

approa-ches are being developed and tested, and it

is believed that they may contribute to the ultimate solution of these fundamental problems.

15

DERIVATION OF THE REGRESSION FORMULA

It is assumed that a linear connection exists be-tween M Km

=

and A =

--nD

This linear connection is

represented by the

equation

Kmao+aiA

(1)

a0 and a1 being constants.

Whether this

assumption holds good can be

verified by considering the diagrams of the

Wage-ningen B series of screw propellers.

The interval with which we are concerned in

actual practice is small in comparison with the total range of the diagrams.

We can write:

DHP =

2Mn

or M =

75DHP (metric units)

75

2n

Substituting this in K,

₌

gives:

pDHP

(2) (0.1 N)3 61 x 75

p =

being constant.

2D0

further: y,,

v(l)

nD nD

orA=A'(1p).

. . . (3)

DERIVATION OF THE MULTIPLE REGRESSION FORMULA

Given is a set of N observations of the variables

Y, X1, X2, Xn Y is to be predicted from X1, X2, APPENDIX A. in which: A'

flDflHD(S

y y H H . . (4) D Substituting (2) en (3) in (1) gives DHP

P(01 N)3=ao+a1A(l_

(5) and with (4) DHP H (0.1 N)3

a0 + a1 (1 sa)b(l

p) (6) or DHP (0.1 N)3 = ciSa + c (7) in which

=

a3 (1

)-H

20DH

_{a1 (l)}

- 60>< 75

c=±Í

pl

+ a1 (1 - v)

bi =

Hl

2000 itD5J

Hl

= 603x 75

a0+a1 (1

Equation (7) will be referred to as ,,the regression formula".

The application of this formula to overload pro-pulsion tests shows that for modelexperiments it can be assumed that c1 en c are constants (viz. table 3). Hence, variations in can be neglected in this case.

Regression analysis enables us to find those values of c1 and c which will ensure the closest agreement between DHP/(0.1 N)3 computed from (7) and DHP/(0.l N)3 from records.

APPENDIX B.

Y* is the predicted value of the corresponding observed value Y.

From the equation

\7*_

_{b0 + b1X1 + b2X2 + . .} .

bX (l)the

constants b0. . . .b are to be calculated in such a

a(162)

ab,,

=0(6)

values of Y and the values predicted by the partial regression equation: Y" is given by the multiple correlation coefficient R:

162

R2==l_=l_

2 _L'y2

for a

=

1/162

₍₌

_{standard deviation of 6)} i /L'y

= V N =

standard deviation of y). It can be shown that R 1.

For 162

=

O (and L'y2O): R

=

In this case there is a functional relation between

Y,X...X,.

For 162>0: R < 1.

The smaller 162 is compared with L'y2, the closer R will approach to R

=

L

With respect to (5) and (8) R becomes:

R

₌

J L'y2 \/L'x12.1y2. 100 1/x62 100

'L'y2(l_R2)

F=YN2

N-2

n=2

Y* = b1X1 + b2X2 + b0 17

R=

b1E1 + b2X2 +.

. . . b,,L'yx,, L'y2

To get an impression of the differences between Y and Y* we can calculate the mean deviation F.

162 F

=

- N-n-1

or expressed as a percentage of Y, which is the mean value of Y.

F=1/E6

0/ V _N-n-1 162 (From R2

=

i -

we find 162) L'y2

In our analysis of ship performance data, we are mainly concerned with the cases where n

=

and n

=

2.

The standard equations, R and F are given for these values of n.

n=l

=

b1X1 + b0; L'xy b1L'x12

b Xxy

b0=b1X1

formula (1)) differ as little as possible from the emperical values of Y (observed).

,,As little as possible" is specified mathematically by the postulate that

N N L'(Y - Y*)2

=

E 2 be minimum

. . . (2) I I

in wich 6=Y_Y*.

Substituting (1) in (2) we get: 162_ L'(Y b0 b1X1

b,X2 -.

- bX)2to be minimum

(3)

It is convenient to use the following expressions

-

L'Y

Y=y+Y in wich Y

N Xl

=

xl + X1 XX1 (4) -Xn = -Xn + X,

Xn

Substitution of (4) in (3) gives

L'62=X(yb'0--b1x1.

. b,,x,,)2 to be minimum (5) in which: b'0

=

b0 + b1X1 + b2X2 +

.. . . b,,X,, - Y

During the process of regression analysis

b0,

b1. . . . b,, are to be considered as variables

be-cause the minimum condition is to be satisfied by finding the correct values for these coefficients. For this, it is necessary that the partial derivates with respect to b0, b...b,, be zero,

a(162)

-.

(L')

-ab'0 -

'

ab1

-or,

b,,x) =0

X(y - b'0 - b1x1 -

- b,,x,,)x

=

0 (7)

L'(y - b'0 - b1x1 -

- bx,,)x,,

=

O hence b'0

=

O and L'yx1

=

_{b11x12+b2L'x1x2+ +b,,Xx1x,,} L'yx2=b11x1x2+b21x22+ +b,,Ex2x,, (8) Eyx,, = b1Xx1x,, -f- b 21x2x,, +. . . + b,,L'x,,2

These equations are called the ,,standard equa-tions" and they are to be solved for b1, b2. . b,,.

Substitution of these values in

b0

=

Y - b1X1 - b2X2 -.

- . b,,X,, gives b0

and thus the ,,partial regression equation" is:

=

b0 + b1X1 +.... + b,,X,,

The degree of correlation between the observed

Eyx1 = b1Xx12 -f-- b2Xx1x2

Eyx2 = b1Ex1x2 + b2Ex22

b0=Y-b1X1- b2X2

R ]/b1ETX1 + b2Eyx2 100 J/Ey2 (1_R2) _0/

F=

_N3

°

To calculate Ex2, Exy etc. it is convenient to use the following expressions:

Ex2 EX2 (EX)2

N

- EXXY

andEyx=EXY-

_N

Modern calculating machines enable us to get EX and EX2 values in one operation.

SAMPLE CALCULATION I SHP Service data (0.1 N)3 ciSa + C or \'*= b0 + b1X1 EY= 248.68; EY2= 1936.5472;

-

248.68 32 = 7.77; 248.682 1y2 1936.5472 32 = 3.9928. R 46.391 VEx12. Ey2 V658.99 x 3.9928 = 0.908

b0=-b11; b0= 7.770.0709x22.0 =

6.21 1.97% (0.1 N)3 Xx1y Y X1 SHP (0.1N)3 SHP Sa % SHP,. SHPf-SHP (0.IN)3 2820 355 7.94 25.4 2844 ± 22 2120 261 8.12 24.8 2080 - 40 1730 221 7.83 21.9 1715 - 15 2350 294 7.99 26.1 2370 ± 20 2480 289 8.58 31.0 2430 - 50 2330 267 8.73 31.6 2256 - 74 1780 222 8.02 26.2 1792 + 12 2535 318 7.97 24.5 2528

- 7

2830 371 7.63 21.3 2864 ± 34 2400 320 7.50 20.0 2442 -+- 42 2420 322 7.52 18.6 2425

± 5

2310 311 7.43 17.2 2311 H- 1 2790 366 7.62 17.0 2716 - 74 2080 270 7.70 16.6 1995 - 95 2110 274 7.70 17.5 2041 - 69 2200 268 8.21 30.1 2235 + 35 3000 371 8.09 27.0 3013 ± 13 1795 218 8.23 28.0 1788

- 7

1760 216 8.15 25.8 1737 - 23 2390 302 7.91 25.8 2428 ± 38 2405 321 7.49 22.4 2504 ± 99 2860 368 7.77 21.7 2852

- 8

2850 379 7.52 20.8 2911 + 61 2490 331 7.52 20.3 2532 ± 42 2360 314 7.52 20.2 2399 ± 39 2400 320 7.50 18.8 2413 ± 13 1240 168 7.38 18.1 1258 + 18 2320 314 7.39 17.8 2346 ± 26 2240 306 7.32 16.3 2255 + 15 2800 373 7.31 16.5 2753 - 47 2020 268 7.54 16.4 1975 - 45 3000 408 735 19.4 3097 ± 97 241.68 705.1 705.1 _thus SHP F

=

(OlN)3_OO7O9Sa Y*== 100 0.0709 X1 + 6.21 + 6.21

=

EX12 EX1=705.1; =16190.43; =22.0; 705.1 or Xx12=l6l9O.43 =653.99 32 EYX1 = 5525.899; Eyx1 = 248.68x705.1 = 5525.899 - 46.391 /Ey2(1R2) 100 N-2

=

32 46.391 Eyx1 = b1 Xx12; b1

=

= 0.0709 p3.9928 (1_0.9082) 7.77 30 653.99 SHP

SAMPLE CALCULATiON II SHP - cjSa + d1N-2 + C (0.1 N)3 -or Y' = b0 + b1X1 + b2X2 Service data

SHP = Shafthorsepower from service records.

SHPf = Shafthorsepower computed with the regression formula. EY = 248.68; 'y2= 1936.5472;

-

248.68 32 7.77; 248.682 Ey2 = 1936.5472 = 3.9928 32 EX1 = 705.1; EX12 = 16190.43;

- 705.1

= 32

= 22.0; 705.12 Ex12 = 16190.43 = 653.99 32

- 7240

EX2 = 7240; EX22 = 2669662; X2

= 32

= 226; 72402 Ex22 = 1669662- = 31612 32 EYX1 = 5525.899; 248.68 X 705.1 Eyx1 = 5525.899 - = 46.391 32 EYX2 = 56362.21; 248.68 x 7240 Eyx2 = 56362.21 = 98.36 32 EX1X2 = 160443.8; 7240>< 705.1 Ex1x2= 160443.8 = 914.9 32 Standard equations:

Eyx1 = b1Ex12 -]-b2Ex1x2 or 46.39 1 = 65399b1 + + 914.9 b2

Eyx2 = b1Ex1x2 -j- b2Ex22 98.36 = 914.9 b1 + + 31612 b2

b0 = Y- b1X1 - b2X2

b1 = 0.0694 b2 = 0.001103

b0 = 7.77-0.0694 x

><22.0-0.001103>< x 226=5.99

R =

Vb1t1 +

b2Eyx2 Ey2 R

=

J,/0.0694x46.391 +0.001103x98.36=0.914 3.9928 thus *== 0.0694 X1 + 0.001103 X3-f- 5.99 SHP or (01 N)3 = 0.0694Sa + 1103 N-2 + 5.99 100 Ey2(1-R2)

F=

_y

_V

N-3 100

=

j/3.9928 (1 _0.9142)29 SHP = 1.94% (0.1 N)3

Note: in previous publications the mean deviation of SHP was computed; it is believed that the mean deviation of SHP/(0.1 N)3 is to be preferred. 19 Y X1 X, SHP (0.1N) SHP Sa 1O'N SHPf SHPf-SHP (0.1N)' 2820 355 7.94 25.4 199 2829

+ 9

2120 261 8.12 24.8 245 2083 - 37 1730 221 7.83 21.9 273 1726

- 4

2350 294 7.99 26.1 226 2367 ± 17 2480 289 8.58 31.0 229 2422 - 58 2330 267 8.73 31.6 241 2256 - 74 1780 222 8.02 26.2 273 1800 + 20 2535 318 7.97 24.5 215 2522 - 13 2830 371 7.63 21.3 194 2849 + 19 2400 320 7.50 20.0 214 2435 ± 35 2420 322 7.52 18.6 213 2420 0 2310 311 7.43 17.2 218 2308

- 2

2790 366 7.62 17.0 195 2701 - 89 2080 270 7.70 16.6 239 2001 - 79 2110 274 7.70 17.5 237 2047 - 63 2200 268 8.21 30.1 240 2235 + 35 3000 371 8.09 27.0 194 2998

- 2

1795 218 8.23 28.0 276 1796 ₊ I 1760 216 8.15 25.8 278 1747 - 13 2390 302 7.91 25.8 222 2425 + 35 2405 321 7.49 22.4 213 2497 H- 92 2860 368 7.77 21.7 195 2837 - 23 2850 379 7.52 20.8 191 2896 + 46 2490 331 7.52 20.3 209 2526 ± 36 2360 314 7.52 20.2 216 2396 ± 36 2400 320 7.50 18.8 214 2410 + 10 1240 168 7.38 18.1 328 1278 + 38 2320 314 7.39 17.8 217 2342 + 22 2240 306 7.32 16.3 220 2252 + 12 2800 373 7.51 16.5 193 2742 58 2020 268 7.54 16.4 241 1981 - 39 3000 408 7.35 19.4 182 3076 H- 76 248,68 705,1 7240

APPENDIX C.

CALCULATION OF THE MOST PROBABLE

SERVICE ALLOWANCE %

FOR A SPEED

INTERVAL

12 kn. <V < 12.5 kn.

The values of

.'

frequency % are plotted to a base of allo wance % on ,,probability paper" (fig. 10). The intersection of this line with 2' frequency % = 50% gives the most pro-bable allowance percentage, i.e. 39.5%.

Allowance 0/_/0 frequency Efrequency Frequency 0/ /0 £frequency 0/_/0 15 <20 1 1 0.63 0.63 20 <25 2 3 1.27 1.90 25<30 11 14 6.96 8.86 30 < 35 25 39 15.82 24.68 35 <40 47 86 29.75 54.43 40<45 39 125 24.68 79.11 45 <50 17 142 10.76 89.87 50 <55 13 155 8.23 98.10 55 <60 3 158 1.90 100.00 L= 158 L=100%