The ship screw as an instrument for determining the ship propulsion data

PUBLIKACIJA BRODARSKOG INSTITUTA

PUBLICATION OF THE YUGOSLAV SHIPBUILDING RESEARCH INSTITUTE

No. 1. ZAGREB

1955-THE SHIP SCREW AS AN INSTRUMENT FOR DETERMINING

THE SHIP PROPULSION DATA

By

Prof. ing. S. ILOVIÓ

and

Ing. M. FANCEV

THE SHIP SCREW AS AN INSTRUMENT FOR DETERMINING

THE SHIP PROPULSION DATA

By: Prof. Ing. S. ILOVI* and Ing. M. FANCEV**

To build a ship, and afterwards not to

in-vestigate her performances in service, for which she is intended, means a fruitless work, and a

hindrance in further technical progress. The analysis of ship's behavour in service alone can give a real guidance when designing new vessels,

and secure such the new ship

to be better of

her predecessor.

There are many existing treatises dealing with the results of measurements on full scale ships. The vast interests for these results is the best guarantee for the improvements in the design of better and more economic ships. When ana-lys.ing the ship propulsion data it is of course

necessary to have the full knowledge of the laws which govern the screw propeller action.

The idea to ,,calibrate" the screw-propeller

and afterwards to use it as an instrument for

measurements, is not a new one. As far as the

authors are aware this idea was first originated

by Teller, and he was the first one to throw light upon the practical side of it (1). It is the

credit of Telfer also that the analysis of ship propulsion data was put on a solid base (1, 2,

3, 4). Baker dedicated many a page to this field of -naval architecture also, and some of his expe-riences are published in his nowadays already classical books (5, 6). Very well known papers by Kempf and Kent considerably extended our knowledge about the behaviour of ships in

ser-vice. Also Kan treats these problems in his book (7). Schoenherr gave in (8) an example of the

application of the laws of screw propeller action

to the analysis of trial trip results. Bonebakker adapted the statistic method to the solution of these problems (9, 10). A very serious study of

3

the subject was published by Brard and Jourdaia in (11). As a pattern of scrupulously carried out measurements on ships, and their analysis, the

authors may mention the works done by Brard, Jourdain and D Mas Latrie (12) and Aertssen (13).

In (14) the authors gave their contribution to the great number of works on this field of science. The purpose of the present publication is to give a brief theoretical background, which justi-fies the use of the screw propeller as an efficient. mean when analysing the ship propulsion data. Certain achievments on this field are pointed

out, and some possibilities, which the screw propeller, as a measuring instrument, offers, are developed and explained.

The performance of a screw propeller, i. e the power which it absorbs as well as that which it delivers - under various speed of revolutions

and speed of advance - can be presented by

two curves in the case that convenient and theo-retically justified expressions are chosen.

All what the screw delivers can be presented in theform of the curve for thrust constant

T

= Q n D4

The part which the screw absorbs is showr by the curve of the torque constant:

Km

fl2 . D5

Both these curves are usually plotted as functions of the speed coefficient:

Ve

nD

*Professor of Naval Architecture, University of Zagreb and Superintendent of Towing Tank (Brodarski In-stitut), Zagreb.

- k_

j

Fig. 1

Characterisijc Curves for Screw Propeller. kt,km, up curves on ?. basis for screw of W. B. B. 3.50.

HID = 1,0.

T, 1, lipa curves on o basis for Thove screw of kg. sec2 D = 2,25 in, w 0,11. Q = 104,5 _m4

(All different symbols are explained in

Nomenclature).

Besides the above two basic curves a third ne is usually added, to express conventionally the efficiency of the screw when taken as useful .uievice; it is usually called efficiency coefficient:

Tve

Mw X

In Fig. i are shown .all these three curves

for the three bladed screw of

the well known

Wageningen series with pitch ratio HID = 1,0 and blade area ratio Fa ¡F = 0,50.

These thrust and torque constants are

dimen-ionless. In different, but geometrically similar systems their relation to the speed coefficient

iernains unchanged - and for that reason they

.are called constants. For any given screw pro-peller, with known dimensions and working in the same fluid, the before said lawfullness

remains valid if for any practical reasons

-in the expressions of the constants the density of

the fluid and the dimensions of the screw are omitted. Therefore the thrust constant may be

ieplaced by: T

t =

N2 o

Iauu .ai

'z

/U.UII

!'URiLIII

o

T"1I

°'

UUllV.

and the torque constant by

M1

=

_IV

-Instead of the accustomed dimension for the torque M (kgm) with help of which the power is expressed by

DHP

_{= 716}

M N (metr. HP)

we prefer here for practical reason such a

di-mension for torque which will satisfy the equation:

DPH = M3. N (metr. HP) Therefrom it follows

M5 DEIP (metr. HP/rpm)

Further on this dimension shall be used for the torque; it becomes therefore

M3 DHP

= N2

N3

Instead of the speed coefficient, for practical reason, we introduce the relation:

V

where V denotes ship speed in knots.

The physical meaning of the coefficient r

follows from the relation

Ji (knots Nm/h Nm

N rpm rpm 60 revs

i. e., o represents the distance in nautical miles

covered by the ship during the time in which

the screw makes 60 revolutions.

It is well known, that the water behind the

ship and at the position of the screw is in mo-tion - normally in the same direcmo-tion in which

the ship is sailing. The intensity of this motion

(= wake) is expressed in terms of ship speed, and known as wake fraction:

wake vdocity = V

Va = wV

where:

V= the

ship speed relative to the

water far ahead of the ship, Va (mean) speed of the ship, and

i

screw too, relative to the

sur-roundig water behind the ship, on

the position where the screw is

placed.

The speed coefficient used, has to correspond to the speed coefficient X and must therefore be based upon Va instead of V; this means that to

A corresponds:

V9

(1w)V

N N

_(lw).o

In the case of constant value of the wake

fraction, what may be supposed by slower ships speed coefficient o can be directly used in place

of A.

Once the values of

i, t

and o are known it is possible to develop the expression for the

apparent efficiency of the screw. This equation is:

T.V.O,5144

3

t.N2.V

lpa _{- 75 . DHP} 10 6,859

N'

3lpa 1O . 6,859

1

This expression is based on the ship speed V, which can be measured, instead of unknown and problematic speed V9, by which the real screw efficiency is defined. The apparent

effi-ziency proves to be more practical for use, though it looses on the adequacy of the expression.

The difference between the real screw effi-ciency and the apparent one is shown by relation:

ip= (lw) 1lpa

As an example the values of p, t, _{ipa as}

function of o are derived from the curves of Km, K, r1-, (in Fig. 1.) plotted against A, and that for a screw diamter D = 2,25 m and wake fraction w = 0,11. The same example will be used and further developed in the later considerations.

In the practical work one has to start from the measured values of the ship speed, numbers of revolutions, power on the propeller shalt and, eventually, thrust. These measured values are to be recalculated to the values of p, r, o and then plotted in order to find their interdependence.

Fig. 2. is an example of presenting results in such a way. The plotted values in Fig. 2. refer

j

p._$I.5l6FO'

-II o -o %Q0O 0%

.00.

o ¿o I o Io 90 Fig. 2

Measurement Data Shown in the Form o on o basis.

to the measurements carried out by Brodarski Institut, Zigreb, aboard a vessel during her ser-vice. These measurements are more elaborately

described in (14).

Of all the range of A or a values, within

which the screw propeller may work by merchant vessels merely a restricted range comes into

con-sideration. In this restricted range Km and Kt

curves, or i and

t

curves, can be approximated to a straight line _{without any loose of the} accuracy.

In that case, for the range under

considera-tion, it can be written:

Km = - a' A + b'

Kt =zrc'X±d'

or also:

- (1 - w) a + b

t =

(i -

w) ca + d

For a fixed value of the wake fraction,

t

_and s can be expressed more simply by:

= - a1 a + b

t

= - c1 o + d

From these equations follows that only coef-ficients a1 and c1 depend on the value of wake fraction whilst coefficients b and d, though with-out any physical meaning, do not depend

at all

'5

5

on the wake fraction. Furthermore this means

also that for a given screw, all straight lines of

and t for different values of wake fractions

plotted against o, have one common point; with increasing value of wake fraction they become

less steep. In fig. 3. the straight lines of .t and

-r for different values of wake fraction are shown, using the same screw data as in Fig. 1.

In the case of normal merchant vessels it is correct enough to assume the wake fraction to be practically constant: under this assumption for a screw propeller, the coefficients

i and t when

plotted on base of o, fall each in one line only. There are of course, considerable changes in wake fraction when the ship is a great deal fouled or sailing in ballast. In ballast condition there may

be, in eddition, a further decrease of

t and t

-values due to the reduced immersion of the screwS

The assumption of constant wake fraction values is not even anymore valid for fast ships. Ey high speeds, it can be expected, that to every speed belongs a different wake fraction value. Accordingly, for every speed, there is a separate

ji and t line above o. Thus it may be supposed

that every and t line in Fig. 3. refer to a cer-itain speed of a fast vesseL

Thus far on basis of our considerations we may conclude: under the assumption of constant 'wake fraction values, for the normal speed range

of the ship screw, the screw performance can be

expressed by two single straight lines, i. e., t and t lines plotted against o. Any combination of the three main quantities: power, number of revolutions and ship speed, when measured under the service conditions must satisfy the equation:

ji

= - a1

+ b

If in a peculiar single case the measured

point may not satisfy this equation - the only

valid conclusion is, that there must be something wrong with our measurements. The same may be

said for the thrust also, but as in the practice

the greatest importance is usually laid upon the output of the propelling machinery and the fuel consumption, we shall proceed our investigation mainly in this dircction.

Replacing ji

and o by the values they

re-present, we obtain: DHP V N and also: DHP = - a1 VN2 + bN' where:

DHP = power absorbed by the screw

It could be supposed that up to a certain

point, the losses along the propeller shaft are

--- .'-.- ... p.(7-w)a. Q-eh

2---_-ior i.,.

///

-(/w)e. red WOJ1(VV) (VJ L I I ; 3 4 5 6 7 8 g 11 Fig. S

r and o Relation for Shipscrew.

proportional to the number of revolutions; the-ref ore

shaftiosses = K N

The shaft horse power is thus defined by

this expression:

SHP = - a1 VN2 + bN3 + KN

Once the shaft losses factor K, along the whole shaft, is known, it is possible with this

expression to calculate the brake horse power

BHP of the main motor also.

Further, when the screw characteristics a1 and b are once determined on basis of the

mea-surement results on trial trip or on endurance trials, it is possible to form a simple, generalized

expression for the shaft horsepower SHP as a

function of the ship speed and number of

revo-lutions. In a similar manner a generalized

ex-pression. for the screw thrust could be derived also.

Thus the measurements carried out on ships

may be used for the calibration of screw

pro-peller as an instrument, which later can serve in service - with known speed and number of re-volutions - to determine the power absorbed by

the screw as well as the developed thrust The

experience proves that the screw propeller is.

really suitable as such an instrument ; the results already obtained in this way are precise enough for practical purposes. Unfortunately it seems that until now in general the screw has not been used adequately with this aim in view.

It is very simple and useful to represent

graphically the generalized expression for shaft

horse power SHP, or if we take all the losses

along the whole shaft, the expression for brake horse power BHP. Since three different inter-dependent quantities must be shown, the best

way seems to bring each of them on either axis of a rectangular reference frame and to induce the third one as a parameter, i. e., by a constant value of the third quantity, the interdependence of the first two is given.

In his book (7) Kan shows the relation

between numbers of revolutions and speed by

constant power. Naval architects are more

accusto-med to the curves of power plotted against ship speed, because for their relation they are mostly

interested. For this purpose the most practical

7

solution was found by Telfer (1), giving the-generalized power diagram in the form of the

relation between speed and power, by constant number of revolutions. Marine engineers mostly use the diagram of motor performances in which the relation between motor output and number of revolutions is shown. Making use of the gene-ralized expression for power, it is possible to plot in such a diagram the lines of constant ship speeds also, since, due to the screw, which is acting as a regulator, the relation between power and number of revolutions is unambiguosly fixed only if the ship speed is taken into account too. The procedure of the generalization will he explained on the earlier example.

Assuming the wake fraction w == 0,11, frora

Fig. 3. the following equation for

t - line is

obtained:

= - 1,635 i0e + 16,06 .

10-e or:

DHP = - 1,635 .

10 VN2 + 16,06 i0 N3 Here, for example, to receive the characte-ristics of the i. straight line the results from the open water tests of the screw model (from Fig. and 3.) were used - assuming a certain fixed value for the wake fraction.

As stated already before and shown in Fig-. by full scale ships the relation between p. and o is received from the results of measurements carried out on the ship. But even when analysing the results of measurements on a full scale ship,. it is very useful to draw such a pattern of p.

-lines, for different values of wake fraction, de-. riving them from the open water test of the screw

model.

Our example deals with one of two screws.

on a twin screw motor ship, propelled by twG

directly coupled Diesel motors, each developing 1000 BHP by 250 rpm.

Supposing that all shaft losses under normal

motor output and revolution come to 2%, the

losses factor K amounts

0,02 BHP 0,02 1000

K

=

=

250

- 0,08 HP/rpm

For any other regime of revolutions the total shaft losses are:

BHP

Adding this value to the former expression for DHP, we receive:

BHP = - 1,635 . 10 V N2 + 16,06

10 N3 + 0,08 N

When ship speed and number of revolutions are known, this equation defines unambiguously the output of the propelling motor.

The last expression is worked out graphi-cally in the generalized power diagram and

-shown in Fig. 4., with number of revolutions as parameter. So, for instance, the equation of the

straight line, which corresponds to N = 200 rpm, takes the following form

BHP = - 65,40 V + 1300

Other straight lines, corresponding to diffe-rent numbers of revolutions are constructed in Fig. 4., in the same manner. In the diagram are

10 11 12

Fig. 4

Generalized BHP-dia gram.

shown also curves of the constant apparent slip which is given by the expression:

Sa ico

(i

_{_.-) %}

Taking in account that

V =

N

the relation between apparent slip and is de-fined by the equation:

Sa = 100 (i - 30,864 %

It is evident that for a given screw, apparent slip Sa and o mean in fact the same thing, i. e., the ratio between ship speed and rpm: V/N. In practical work the apparent slip is generally used, and therefore as the diagram is intended for such a practical use it is based on apparent

Table 1. - CONTROL OF FUEL CONSUMPTION BY THE AID OF

DFC

DIAGRAM

M. V.: VOYAGE No.: 2/1953 (A) I (B) (C) Mean rpm N rpm Total 196.309 194.280

Fe-FL

Difference: 100 . + 1 04% FL

9

-CARRYING OVER 83.905 81.500 18. IV. 13,5 122,5 8460 18 45 18,75 0,781 6607 4700 19. IV. 13,2 123,0 8925 15 00 15,00 0,625 5578 460) 21. IV. 13,7 119,0 7260 16 00 16 00 0,667 4842 5000 22. IV. 13,3 1200 7940 6 00 6 00 0,250 1985 1400 23. IV. 13,5 120,5 7890 2 20 2,33 0,097 765 700 24. IV. 13,2 120,0 8035 5 00 5,03 0,208 1671 3700 28. IV. 12,8 121,0 8720 14 00 14,00 0,583 5084 5000 2. V. 14,0 120,0 7270 6 00 6,00 0,250 1817 2250 3. V. 13,7 122,0 8125 23 35 23,58 0,982 7979 8560 4. V. 13,3 120,1 7980 24 00 24,00 1 7980 8600 5. V. 13,5 121,1 8060 24 00 24,00 1 8060 8500 6. V. 13,7 120,9 7830 24 00 24.00 1 7830 8500 7. V. 13,3 121,0 8225 11 15 1125 0,469 3857 3900 8. V. 13,0 1210 8525 24 00 24,00 1 8525 8500 9. V. 12,7 120,5 8370 19 00 19,00 0,792 6867 6750 11. V. 13,0 121 0 8525

ii

40 11,67 0,486 4143 3820 12. V. 13,2 121,2 8390 17 00 17,00 0,708 5940 5880 13. V. 13,6 _120,5 7790 24 00 24,00 1 7790 8603 14. V. 13,6 121,0 7930 9 00 9,00 0,375 '2974 2930 17. V. 13,5 120,0 7750 3 50 3,83 0,160 1240 920 18. V. 14.0 120,0 7270 9 40 967 0403 2930 2970 19. V. 13,6 120,2 7700 11 30 11.50 0,479 3688 3300 20. V. 13,7 120,5 7710 4 20 4,33 0,180 1388 1100 21. V. 13,7 123,3 8500 8 05 8,08 0,337 864 2600 Daily fuel consumption from DFC

- diagram

Time

at

sea Fuel consumption Calcu-lated Shown up engin, log F FL Fd (F)124 (D) X (G)

kg per day hrs min hrs day I kg kg

(D) (E) I (F) (G) I (H) I (i) Date 1953. Me an speed V kn

slip. The expression for apparent slip is formed in such a way, that notwithstandig of different screws and different service conditions, its value remains within fixed range - from 0% do 40%, while otherwise o changes considerably in case of different screws. Furthermore it may be worth mentioning, that in the case of adverse weather

conditions, fouling of the ship-hull, etc, it becomes

necessary for the same ship speed, to encrease the number of revolutions of the screw.

Threre-fore the ratio V/N decreases, i. e. o is decreasing.-and Sa is increasing.

It may be supposed that in the

working-range of marine Diesel motors, their daily fuel

consumption is a linear function of the motor output.

Analitical form of that function is:

Fa = e BHP + f

(kg/d)

Combining the above expression with the

generalized expression for BHP (or also SHP),

:7200 /6 12

4'

¡

iT

---L

k I- E-800

iii Mia

---..

oAi/IjIi#TT/

r

BHP 600

4

-

-,!

A

->'

_- -200

/.1íi-:::

- M 25

f----

12 16 9 o 5C 700 ¡50 200 250 300 Fig. 5

it is possible to come to a generalized expression

for daily fuel consumption. On behalf of this

latter expression the diagram for the daily fuel consumption can be finally drawn (DFC - dia-gram). This diagram resembles the diagram in Fig. 4., the only difference is that the scale for power is changed to the scale for daily, or hourly,

fuel consumption.

One type of such a diagram is given in (14) together with the explanation of its application

in practice. The result obtained by the use of

this diagram were satisfactory.

From the results of measurements, carried out on one ship only of a series of sister-ships

owned by Jugoslavenska Linijska Plovidba

-Rijeka, such a DFC-diagram has been calculated out by Brodarski Institut, Zagreb, and put at the disposal of the ship-owners for their practical use. Table 1. contains the formulary used to

re-gister data, taken during the voyage of each of

these ships, in behalf of which the actual fuel

consumption is compared with that received from the DFC-diagram.

If there are at disposai the detailed data of the motor bedtrials also it may be useful a dia-gram of the form shown in Fig. 5. wich is worked out for the same example as the diagram in Fig. 4. The bedtrial diagram usually contains the curves of specific fuel consumption plotted as a

function of BHP and rpm. From these curves

the new ones of constant daily fuel consumption -were derived. For instance for the constant daily fuel consumption of 3.500 kg/d, and for the specific fuel consumption of 162 gr/BHP/h, the brake horse power of the motor amounts

BHP

_{- 24}

1000 Fd (kg/d) 1000 . 3500 f (gr/BHP/h) = 24

162 =

= 900 HP

For the same daily fuel consumption, but

with the specific fuel consumption of 165 gr/B1-IP/h

we receive: BHP = 884 HP; and with the spe-cific fuel consumption increased to 170 gr/BHP/h,

the brake-horse power of the motor is BHP =

= 858 HP, etc. - Through the

points,

calcu-lated in such a way, the curve of the constant

daily fuel consumption of 3.500 kg/d is drawn.

Analogous procedure is applied to construct the

11

-curves for other values of the constant daily fuel consumption.

The curves of the constant ship speed are

also drawn in the diagram on Fig. 5. They have been calculated from the earlier developed gene-ralized expression for BHP:

BHP = 1,653 10 V 1V + 16,06

. 10.

Z'P + 0,08 N

changing the numbers of revolutions for a given speed V. Thus, for the speed V = 10 knots, the expression for BHP has the form:

BHP = - 16,35 . 10e N2 + 16,06 . ¡e-5 . N3 +

+ 0,08 N

and changing numbers of revolutions the curve for that constant speed can be calculated.

The diagram of the type Fig. 5 makes it

possible to read off BHP, motor-loading, daily

fuel consumption and specific fuel consumption, when ship speed and number of revolutions are known. The above mentioned data are the most

interesting ones in the exploitation of a ship. However there exists the possibility to show also the curves for constant apparent slip, or, what is the same, the lines of cons-tant screw efficiency too, but in this case the diagram should loose on

its clearness; therefore it is recommendable to trace these curves in different colours.

There is no special need to mention that in case the ship may not be sailing full 24 hours, the readings of the fuel consumption from this diagram have to be multiplied by the factor:

Nut-ober of hours in sailing

24

Moreover it must be mentioned that this

dia-gram is valid only for one quality of the fuel,

with the caloric value q0 cal/kg, while for any

other fuel quality with a different caloric value q, the readings from the diagram must be multi-plied by

q0

q

If there comes to greater changes in the tem-perature of the ambient or in barometric pres-sure, those facts must be taken into account by the final balance of the fuel consumption,

pro-durer. Using this diagram, the behaviour and the

changes in performances of the motor, over a longer period o time, can be discovered and studied.

As emphasized earlier, in this treatise we

operate

with the ship speed in regard to the

water. It is clear that this speed is made up from: ship speed in regard to' the land ± water current-velocity. The sign + is applied when a

ship is sailing against current, and the sign -when sailing with current. There are certain seas with strong currents which can not be neglected, when the ship speed is computed.

Generalized power diagram as well as gene-ralized fuel consumption diagram can serve

ex-ceedingly when analysing the ship behaviour

under service conditions, by analysing the ship economy, as well as to predict the fuel costs for a planed voyage.

The screw efficiency can be computed from model tests or from thrust measurements on the

full scale ship. Up till now but few ships only

are equipped with thrust-meters. Furth more, they may not be too reliable instruments.

Here is shown how to determine the thrust of the ship screw and the generalized expression for thrust as well, when once at the ship speed V0 (lower than normal speed) and with other conditions remaining the same, the following data are known:

number of revolutions N0 for the ship in

the free running confition.

number of revolutions iV1 for the ship, when towing an object of the known

re-sistance

T.

number of revolutions N, when the ship has in tow another object of the known

resistance L T.

Of course in all three said cases the general outside conditions must remain unchanged. On the trial trip therefore three progressive trials

should be carried out: free running condition,

towing condition No. I, and towing condition No. 2. Th towrope forces could be measured by dynamometers, which are more precise than the to-days thrustmeters. The above programme of

trials would be worth the trouble on the first vessel from a series of sister-ships, but

also in the case when there is the desire, to know as much as possible about a certain ship. As

sta-ted before, such a programme of trials would

provide a solid base for the generalization of the screw performances and of the propelling

machi-nery.

Namely, usual trial trips supply a too

re-strictad range of a - values (or slip-values),.

insufficient for a thorough generalization, while

the towing condition would extend this range

con-siderably. Moreover, the towing condition could partly give an idea of behaviour of the ship pro-pelling machinery under the service conditions,

which on a normal trial trip can not be easily

achieved.

Further follows a brief description of the method, how the thrust and the generalized

ex-pression for thrust can be deduced from the

results of the trial programme outlined above. In free running condition t0 _amounts:

T0 T0

= T2 =

m

where:

T0 = thrust developed by the screw to overcome the ship resistance at ship speed V0, and

- c3rresJonding to N0 rpm.

(Thus: = V0 IN0 or N0 = V0/a0)

Supposing that for the same ship speed V0

same thrust T0 is necessary to overcome the ship resistance in free running condition as well as in towing conditions (assumption of equal thrust deduction fractions in both cases),

t will

consist

of two parts ; the first one being the thrust T0,.

the second one the measured tow-rope force thus: T

_T0+AT

T0 LT Ñ N

N2+N2_

= to' ± 'r' For to' = T0 LV0 VØ

with the speed V0 = const. we have:

to, N N V02 V02 N T0 T0 V02 T0 J7 T0

= --

= m6 V0

t =

Accordingly in towing condition:

t

to' ± t' = m + t'

The basic equation for the screw thrust

coefficient is of the form:

t = -

o + d

and there from:

c10 ± d = nzo2 + T' or:

mo2 + c10 - d + t'

O

In these equation the unknown factors are:

-in, c1, and d. The three conditions: when free

running, towing condition No. 1. and towing con-dition No. 2. render possible to form three such equations, by means of which the solution of all the three unknown is found.

These three equations are:

Free running condition: m 0o2 + C1<10 d ± O = O

Towing condition No. 1.: m 2 + c1o1- d + t1' = O

Towing conditionNo. 2.: m22±c1a2 d+t2' O

where: __vo VO LT1 Ti =

vo

(12

- N2

x T., -N12 N92 n Ji--,

c.r.

"

Q; Fig. 6

Quantities under consideration are represented

graphically in Fig. 6.

13

-.&i2 4rr

r --

V.rv,$f V.

N V.'

/

When solving these equations we have:

i

/

ti t2' m i

\°o°i

0009

c1 2'

+ o)

00 - (19 d = ?fl0Y02 +c1

Once the value of in is known, the thrust TOE

corresponding to the speed V0 is given by: T0 = V02 m

With constants c1 and d we are able to make

a very useful generalized expression for the

thrust:

T = - c1 o + d

or:

T=c1J/N+dN2

By means of the above expression it is

pos-sible to form the generalized thrust diagram, similar to the generalized power diagram, shown in Fig. 4.

Unfortunately, as far as we know until now

there had not been any ship trials carried out

according to the suggested programme, thus there are no available results to illustrate the proposed

method.

However it must be kept in mind, that the resistance of the towed object should _{not be} ex-cessively high. The high resistance of the towed object may make impossible for the ship to reach

e-range would be too wide and the assumption of the linear relation between r and s is no more valid.

Once, the equation for the absorbed power by the screw is obtained in the form:

- a1 + b

or:

DHP--a1J7N2 +bN

it can be treated in the same way as any other

mathematical expression. So for instance, the

slight increase in power may be replaced by the total differential of the expression for power, i. e.

A DHP = - a1 NO2. AV+ (-2a1V0N0 +

+ 3bNO2). L\N

Index o denotes the quantities before any change in their values took place, but which were

subsequently subject to slight change. If the speed remains constant, than AV = O and:

A DHP ( 2a1 V0 N0 + 3b NO2) A N = (- 2a V0 NO2 + 3b N01)

jo

A N (2 DHP0 + bN01) N0 or: ADHP

AN'

b

DHPJ = N

(,2 + -) V being constant

Now, if it may be required to compute the change in the number of revolutions from a

known percentual change in DHP the following equation is valid:

AN ADJIP

= Dill'0

Ib

The value of the ratio depends upon slip. By merchant vessels this ratio lies between 2 and 3 (with higher and lower slip, respectively) so that the change of rpm in % amounts about 1/

to % of the change in absorbed power.

If the change in power is caused by the

change in ship displacement D, it can be assumed

that at a certain constant speed, the power varies with D2/s. Consequently, for a small change in

displacement A D, the expression for the change in power becomes:

ADHP AD02l

2 AD

DHP0 D02I

-and the expression for the change in rpm:

AN2AD

I

NO3

These expressions are precise enough for practical application when necessary to reduce the measured quantities to a standard condition

This standard condition, of course, should not

differ much from the condition under which the measurements have been carried out.

Here follows the example to show how the-former equations could be applied in order to

de-duce the power of a twinscrew ship to the common

number of revolutions. Namely, it is a general

case that during the measurements on a twin-screw ship, the screws, as a rule, never run on

the same number oF revolutions, as a consequence the power absorbed by each screw differs still more. It may be sometimes interesting to find out what power wauld be absorbed by the

port and what by the starboard screw, if

at a

given speed, they should run at the same number of revolutions.

Earlier it was stated that for a small change in absorbed power owing to a small change in rpm, both of them occurring at a constant speed,. the following equation is valid:

A DHP = (- 2 a VN + 3 bN2) . A N = _rV2(2Ib

b). AN

or one may write:

A DHP = p. A IV where, for a measured point:

p = \J2 (2 t b) = cons t.

The constants PL for the port screw respec-tively PR for the starboard screw can be received from the results of measurements. The measure-ments supply also the

data for the power L

absorbed by the port screw, corresponding to the number of revolutions NL of the same port screw,.

respectively the power R absorbed by the

star-board screw, corresponding to the number of re-volutions NR of the same screw.

Therefore we can write: A L = PL A Nr. A R = PR A NR

The assumption may be justified, that, with the same number of revolutions of both screws, the

total power necessary to reach the same ship

speed remains unchanged, i. e.

L' +R'L +RL +AL +R+ AR

ApDstrophed symbols reffer to the common equal number of revolutions. From the above it

follows

AL = - AR

PL A NL =

- PR

A NR

and further on:

ANL

PR

Denoting the common equal number of

revo-lutions with Nc, one may write

N = NL + ANL = NR + ANR

accordingly:

ANR

ANL + (NLNR)

Comparing both expressions for

N it

fol-lows that:

NRNL

ANL i PR Telfer: Telfer: Telfer: Telfer: Baker: Baker:

15

-And using this expression in connection with the expression for the increase of.power absorbed

by the screw:

AL_PL. ANL

we receive finally the power absorbed by the

port screw, at the common equal number of revo-lutions N = NL + NL

L' = L + AL

and finally:

R'=R+R=R+pR.

NLNR

PL

REFERENCES:

,,The Practical Analysis of Merchant Ship Trials and N. E. C. I. E. S. Vol. 43 1927._{p. 63.}

The Reduced Speed Running of Merchant Ships", Trans. Economic Speed Trends", Trans. S. N. A. M. E. Vol. 59 The Power-Loss Factor in Ship Service _{Performance",}

Navales, 1953.

,,Ship Design, Resistance and Screw Propulsion" Vol. II. ,,Ship Efficiency and Economy" Liverpool _1946.

L'L+PL

NRNL

PL

accordingly:

There are great many other problems, which could be solved in a similar _{manner; any further} considerations on the subject would go beyond the scope of this paper. The only _{scope of it was} to show some of the possibilities, which thescrew

propeller offers, when considered

_{as an}

instru-ment for determination and for analysis of ship propulsion, and further to indicate the _{way how} to tackle these problems. More detailed _and si--stematical works in this field may develop further

possibilities, and give _{answer to others, up till} now not yet answered questions, creating thus _a new discipline, under the name of: Applied

ship-propulsion.

Service Performance" Trans N. E. C. I. E. S. Vol. 51 1935.

1951.

Centre Belge de Recherches.

Liverpool 1951. or:

A R _{PR A NR}

i

+p_

PR

In the same way for the starboard _screw: NL - NR

Kan: Rossell, Chapman Bonehakker: Bonebakker: Brard, Jourclain: Brand, Jourdain. De Mas Latrie: Aertssen: iloviá, Fancev: a, a', a1 b', b BHP C, C', ej EL', d d D DFC DHP e f fs F Fa Fd H K Km Kt L M Ms

,,Design and Cost Estimating of All Types of Merchant and Passenger Ships", London

1948.

,,Principles of Naval Architecture", Vol. II. p. 183 New York 1949.

The Application of Statistical Methods to the Analysis of Service Performance Data", Trans N. E. C. I. E. S. Vol. 67. 1951.

,,Analysis of Model Experiments, Trial :and Service Perforirance Data on a Single-. Screw Tanker, Trans. N. E. C. I. E. S. Vol. 7, 1954. p. 475.

,,Criique des Essais a la Mer', A. T. M. A., Vol. 5. 1953. p. 63. A. T. M. A.. Vol. 52, 1953. A. T. M. A., Vol. 53, 1954.

Sea Trials on a Victory Ship. AP 3. in Normal Merchant Service', Trans. I. N. A. 1953 p. J 21.: and ,Sea Trials on a 9500-ton Deadweight Motor Cargo Liner', Trans. I. N. A.

1955.

,,Measurements on M. V. Rijeka with Thelr Attempted Practical Application", Trans I. N. A., 1955.

= Constant

= Constant

= Brake Horse Power

= Constant = Constant

= Abbreviation for day (e. g. kg/d = kg per day)

= Diameter of screw (m or ft)

= Daily Fuel Consumption = Deliverd Horse Power

Constant = Constant

= Fuel rate

= Screw disk area

= Developed blade area of screw = Fuel consumption per day = Screw pitch

= Constant = Torque constant

Thrust constant

= Power delivered at port shaft. Also

suffix for port. Constant

= Torque (kg. m or lbs. ft) = Torque (HP/rpm)

NOMENCLATURE

= Revolutions per second = Revolutions per minute

= rpm of port or starboard screw respecti-vely

= Constant

= Caloric value of fuel

Power deliverd at starboard shaft. Also as suffix for starboard

= Apparent slip

= Shaft Horse Power = Thrust (kg or lbs)

= Ship speed (rn/sec or ft/sec) = Ship speed in knots

= Speed of advance of screw through wake (rn/sec or ft/see)

Speed of advance in knots = Taylor wake fraction = Screw efficiency

Apparent Screw efficiency

= Speed coefficient of screw ve / nD = Torque coefficient

= Density of medium

= Apparent speed coefficient of screw V/N = Thrust coefficient

Angular velocity of screw

n N NL, NR p q R Sa SHP T V V Ve Va w lip pa X as Q a t (i)