Analysis of ship model experiments and prediction of ship performance

- -

JULI 1976

A RCHIEF

11

HYDRO- OG AERODYNAMISK

LABORATORIUM

HYDRO- AND AERODYNAMICS LABORATORY

Lyngby Denmaek

Hydrodynamics

Section

_{Report NO Hy-1}

_{December 1960'}

BY

C. W. PROHASKA

Reprint from

INGENIOREN, Internationa:1

Ed.; Vol. 4 1960, No.,, 4

IN COMMISSION,

DANISH TECHNICAL PRESS

VESTER FARIMAGSGADE 31 COPENHAGEN, DENMARK

Lab. v. Scheepsbouwkuntit

Technische Hogeschool

Delft

Analysis of Ship Model Experiments

and Prediction of Ship Performance

A New Correlation Method

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Series Hy:

No.: Author: Title: Price: D. Kr

Hy-1 PROHASKA, C. W. Analysis of Ship Model Experiments

and Prediction of Ship Performance 5,00

Series A:

No.: Author: Title: Price: D. Kr.

A-1 TEJLGARD JENSEN, A. An Experimental Analysis of a Pebble Bed Heat

Analysis of Ship Model Experiments and

Prediction of Ship Performance

by

Prohaska

- - JUU 1976

tip

HYDRO- OG AERODYNAMISK LABORATORIUM

LYNGBY _DANMARK

Introduction.

The 8th International Towing Tank Conference held in

Madrid in 1957 decided to abandon the analysis-method

based on Froudes friction lines and to adopt as an interim

measure a single friction line, the "ITTC 1957 model ship

correlation line", defined by: 0.075

Cr =

R 2)2

It was obvious that this change would make it necessary to modify the empirical corrections on horse-power and revolutions hitherto applied by most tanks. This question

has been given a great deal of thought and several proposals were submitted to the 9th International Towing Tank Conference in Paris 1960, but it was decided that the

matter should be further investigated before any decision

could be taken as to the recommendation of a specific analysis method for general use.

Until the next conference, which will be held in London

in 1963, it must therefore be expected that rather different methods will be used at the various model basins. Results

from different tanks are therefore not always directly comparable. This will be clear from the following in

which a short description is given of the procedure hitherto applied, of some modifications to it, and finally of a new

method proposed by the author and now in use at the Danish model basin, [1], [2]*).

Model-ship correlation.

In modern formulation the classical Froude method may

be explained as follows: The specific ship resistance is

derived from the specific model resistance at the cor-responding speed by deducting from the latter the

dif-ference between the model and ship frictional coefficients.

After reviewing existing methods for predicting ship performance from

the results of model experiments, the author describes a new correlation-analysis,

already in use at the Danish Ship Model Basin. In this analysis wake scale

effect is correctly taken into consideration and a logical link is established

between model and ship.

(1)

532.5.07:629.12.07

In Fig. 1 the Froude frictional coefficients for different

model and ship lengths are shown as functions of

Rey-nolds' number. The curve marked C, represents the total

R.

model resistance coefficient C., =

p/2V2 S' where R7. is

the total resistance, o the density of fresh respectively salt

water, v speed, and S wetted surface. Curve Cr, is the

corresponding curve for the ship.

By means of the propeller and propulsion experiments

the propulsive coefficients including the propulsive

ef-ficiency

1/

'7= i - w x 71P (2)

are found (t being the thrust deduction coefficient, u. the

wake coefficient and r. the propeller efficiency).

It has now been customary to neglect the scale effect on propulsive efficiency. The ordinates of curve Cr in Fig. 1,

derived from those of curve C dividing by r, therefore

represent a horse-power coefficient:

C, =

C.

=

1 R 1 00108 n X p/2 v2

=

X S/7213 X E , 1000 EHP with E = _{A 2/3 v3} 0.0108 or: Cr _{v 2/3} X Pr with: PP1. E 1000 PHP A2/3 v3 (3) from which the horsepower*) is easily found.

To this so called tank horse-power a certain correction (allowance) has been applied by most tanks, usually in the

form of a percentage addition varying with ship type

according to the experience of the tank. The curve marked

D Figures in brackets [ ] refer to the bibliography at the end of he D The numerical coefficient refers 1,,eel nc horsc-power (1 HP =

article. 75 kgm/sec.).

INGENIOREN INTERNATIONAL EDITION _{VOLUME 4}

Analysis of Ship Model kxperiments and Prediction of

Ship Performance

A nen' correlation method in use at the Hydro- and Aerodynamics Laboratory, Lyngby, Denmark

by C. W. Prohaska, D. Sc.

(log.

by

S

± allowance therefore corresponds to the trial trip, prediction. The revolutions found in the experiment are

scaled down and usually given an empirical correction of a few per cent.

It is. now evident from F.g. 1 that the change over

from the Froude lines to the ITTC-1957 line will neces-sitate new corrections, or the allowances will be unreason-ably high. It has been proposed to apply an additive

cor-rection, QC,, to the ship frictional coefficient so as to raise the total ship friction to. such a figure that extra allowances would become unnecessary. This QC-correction was thought to cover form and roughness influences. It will

be seen from the following that it must take care also of

scale effect on wake, unless a correction for wake difference:

is applied separately.

The best way to check the corrections or allowances to be applied is of course to compare trial or service results

with predictions based on such allowances.

Suppose that the curve C in Fig. 2 has been derived

from trial results. By multiply'ng its ordinates by the ef-fic'ency 7] (eq. (2)), the ship C-curve is obtained, which

after deduction of the CR-values (C, C, C,) derived!

from the model experiment gives the curve marked C, QC,. The distance between this curve and the ITTC line represents AC. It is therefore obvious that the QC, value

is a function of the efficiency The 71 values found by

model experiments, carried out in different tanks,, for one

and the same ship are, however, not identical, as the

methods of performing the self-propulsion experiments

differ from one tank to another. Apart from the classical

British and Continental methods, differing in propeller

loading during the experiment, new varieties have come into use [3] or have been proposed [41.

F.g. 1. The Froude-method.

Each tank will therefore have to establish its own

AC,-statistics for prediction work, or agreement must be

reached on a standard method. The new niethod,

From the above it is seen, that it has been customary to take it for granted that the propulsive efficiency found for

the model also applied to the ship. Although it has been clear to the profession for quite a ong time that all the

three propulsive coefficients, f, w and np, could be subject to certain scale effects, corrections for such :effects have not been introduced into standard analyses or prediction

work. 0.00 Log Re Fig. 2. Definition of c i 7 hhhh's F U ., =LP' +/--O C -I- ALLOWANCE 1 P 1 lb,

---,/

(","p__,. 1 , L ='..hl L= 6:4 > tO X 0.. 0 qoo2,__ ,--I '

-_ % II T IC 19

ROUDE L.25i

iv%

ill' I I 11C7 z-N.` III . k. ,.. ...

41411110ill

/

..--S r 41%44104 52 = . m L-7- 15001 - S n M 16,0 ' II LOG Fl 0 9,5 I 11-- li, 70 [ II I 8,0 II 9 t 18,5 1 4 0-, I 1 , 1 1 7 71 171 SI 34 L5) ; , Cile q 41. IR I [ I Cm IITTC I C, C +AC 1 a

Mil 4-4

G OA CC

1960, No. 4 ANALYSIS OF SHIP MODEL EXPERIMENTS AND PREDICTION OF SHIP PERFORMANCE 115

41' c0

=

-0.004 7,5 I I I I I 8.0

KG

8 m MODE

.05

50 160 150 200 250m

L

Fig. 3. Approximate wake scale effect.

When at the Hydro- and Aerodynamics Laboratory

(HyA) an analysis method had to be selected, the question was given much thought. Having no previous statistics was to some extent a handicap, but it represented on the other

hand the advantage, that with no ties to such statistics,

there was ample opportunity to develop a new method of

analysis.

This new method is based on the fact, that the wake

is subject to a scale-effect, which at least for single screw

ships is rather heavy. For a ship the wake is often about two thirds of that found for its model. This is logical as

the thickness of the ship frictional belt is only of the

order of one half of the propeller radius, whereas for the model it is about twice as thick, thus producing a higher frictional wake for the latter.

For flat plates of model and ship lengths approximate calculations of the wake differences have been performed

from data given in [5], and the results are shown in

Fig. 3.

This method of approach only serves to indicate that

SELF PROPULSION 10 KN 15 20 KN 15 20 10KN 15 20 -AND n n

Fig. 4. Typical K-curves from open-water test,

self-propul-sion experiment and trial trip for a single-screw vessel.

quite appreciable wake differences must exist between model and ship, but exact figures are not easily derived

by calculation, as the three-dimensional wake field is

difficult to determine for the full

size ship. It seems

likely that the actual figures will exceed those for flat

plates.

Supposing that in a certain model experiment, a wake

of 040 has been found, then for the ship only about

030 can be expected. This means that the hull efficiency

1-04

6

1

-will be reduced in the proportion

=

or by approx.

7

14 per cent. A total model efficiency of say 077 will therefore reduce to approx. 0.66 X 1.03 = 0.68 for the

ship, counting in a 3 per cent rize in alp due to the decrease in propeller loading.

Taking into consideration this drop in total efficiency,

it is apparent from Fig. 2, that the application of such

reduced (and more correct) ship efficiencies leads to

lower ACE-values, and actually the ACE-values derived

in this manner seem more reasonable than those found when disregarding wake scale-effect.

As mentioned previously the wake scale-effect is difficult

to calculate, but fortunately it can be derived easily from comparative analyses of model experiments and trial trip

data. Such analyses of available data were carried out at HyA

prior to the introduction of the new method.

If on the open water propeller diagram (Fig. 4), in

addition to the usual Ko-curve, the corresponding curve derived from the self- propulsion experiment is plotted,

the ratio of the abscissae to points of equal Ko gives v

torque wake as 1 - =- = (-. This value applies

to the model. After subsequent plotting also of the

K9-values derived from the trial trip data, it will be observed

that these points define a curve which, in general, is far from being identical with the K0-curve from the

self-propulsion experiment. The trial trip K-curve indicates a much lower wake. Wake values thus found can be plotted

in a diagram similar to that in Fig. 3, and such wake values are used in the new method, which will now be

described with reference to Fig. 5.

Fig. 5 shows a logarithmic propeller diagram*), but

the method can be used also with other types of

dia-grams**). For simplicity it is firstly assumed that there

is no scale effect on thrust deduction or on propeller performance, and that the relative efficiency is equal to

one. These assumptions will be discussed in the Appendix. In Fig. 5 is shown K( 1:7, and al from the open-water experiment. Further K9- and Kr-values derived from the self-propulsion experiment have been plotted over 1,, =

v . The horizontal distance between points as A and B

nD

') The logarithmic propeller diagram has been fully described by

Saunders 1.61, Vol. 2, p. 589 pp.

*) The diagram must contain a curve of the propeller load

coeffi-T

(dent:

el2 V2 X

P

z

P

j

o : 0 3 -I 0 7 10 ," .3 PROPELLER COEFFICIENTS ADVANCE NON DIMENSIONAL ENGLISH UNITS TO. PT, HP, KNOTS, RPM U. lICE

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SPEED OF WATER AT PROPELLER: V, = KNOTS

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PROP E ILER DIAGRAM

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6000_ 5000_ 4000_ 3000_ 2000_ 1000_ 4600 BHP' <SOSPHP AT 170 r.vAin

K9-curve, giving K, and I. From the latter the revolutions are determined and then from the former the horse-power.

These data are at HyA plotted in a diagram of the type

shown in Fig. 6.

From the efficiency curve (Fig. 5) it is seen that the

propeller efficiency for the ship is higher than for the

model because of the reduction in propeller loading. On the other hand the hull efficiency of the ship has become considerably reduced, and the propulsive efficiency of the

ship is

lower than that found

in the self-propulsion experiment. As stated above this means that with the

proposed method lower C,-allowances must be used than

those corresponding to the conventional analysis based

on an assumed constant efficiency.

This model-ship correlation method requires, as will be

understood, two (and only two) empirical values to be

determined from previous statistics, viz, the wake

dif-ference Au. and AC,. It has been explained already that A w is derived simply from a comparison of K9-curves

corresponding to the trial- and the self-propulsion ex-periments. It is evident that as each K-value on the trial

trip corresponds to a certain value of the load coefficient ar (easily derived from the diagram in Fig. 5, where line

HGFE indicates

the procedure), this or-value

determines the total specific ship resistance, C,., by means

of formula (4), and thus also AC,.

The trial trip speed values used in this analysis must of course be corrected for currents along the measured

mile. This is done in the following manner: For each

single run a K0-value and the corresponding f-value are calculated. The former determines a [-value by means of the open-water 1<Q-curve, and from this ye is calculated.

Deducting from the observed speed (v c), where c

is the speed of the current, and plotting the difference on a time scale, two separate curves are obtained, the distance of which is 2c, and hence the true speed for

each single run is easily determined. The ve-deduction

eliminates from v the arbitrary variations in loading due to wind etc.

The new correlation method has been described with relation to torque wake. If thrust is measured, the same

Procedure could be used &Rally well in relation to thrust

wake. Up to now most tanks have used thrust wake or a

direct or weighted average of thrust and torque wake.

As thruit at present is very rarely measured on ship-board,

whereas revolutions and torque (or horse-pourer) are

determined fairly accurately, it is proposed that torque

wake should be used as a standard. It provides a natural and logical link between model experiment and trial trip.

The same link also extends to the service data, from

which it is eaually simple to calculate corresponding

values of K, and v . A plotting in Fig. 5 of such data

nD

will show that after some years of service the K11-curve will have moved upwards and to the right in the diagram, indicating for each speed higher wake and higher loading,

118 INGENIOREN INTERNATIONAL EDITION VOLUME 4

50 100 ISO

REy4,

Fig. 6. Trial trip prognosis.

on the two K9-curves represents the influence of wake,

and 1 wo can be read on the bottom scale of the diagram

at .8', where A'B' = AB. A similar procedure holds of

course for thrust wake (see distance TC, which for the assumption made about the relative efficiency, must be

equal to AB). The point C lying vertically above point B

gives the KT-value corresponding to the K9-value at A

and B. A normal to the a1.-scale drawn from C intersects the scale at D, and the a7.-value can be read on the scale.

This is an a,-value corresponding to the self-propulsion

experiment at the speed in question. Assuming now that

the CT-value for the ship has been estimated for the

corresponding speed (curve C. in Fig. 2), then the loading of the ship propeller is easily calculated. As:

a. =

pl2 v 2 F =. (1

t) (1

w)-SIF

, X

R X CT (4) pi2 1,2 S (1

t) (1

w)2

where S = wetted surface and F = disc area, ar can be

calculated when proper values of ship t and u. have been

determined. At HyA three per cent is added to the

cal-culated load coefficient to take account of air- and steering

resistance.

Suppose that t is taken from the self-propulsion experi-ment*), and te. corrected for scale-effect, an a.-value, point

E, is obtained, which again corresponds to the K,,- and K9-values in F and G. From the latter point, GH is set

out horizontally, with GH = Gr' on the bottom

scale corresponds to 1

w,,

being the ship wake.

The point H thus is a point on the predicted trial trip

nR,

") It is the prnulice HIM to plot n curve of 0<nzx-D4 below

and correspoluling to the ti,,-curve from the self-propulsion experi-ment. The vertical distance between the two curves TR= T'Er gives directly 1t on the vertical scale in Fig. 5.

. I 1

-SIF

-

-=

=

-4

0

both due to the increased roughness of the shell. After each docking of the ship the curve will tend to move

downwards, then rise upwards again. A large size diagram of this type can therefore represent the complete history of

the propulsion characteristics of a ship. Comparison of such diagrams will give the relationship between shell roughness and proper service values of Au. These will be lower

than those for trial trips and may even become negative. The correlation method described is in no way restricted to the use of the ITTC 1957 model ship correlation line, but is equally well applicable if other friction lines should be adopted in the future. The Au-values and AC,,.-values

found in the present analysis can easily be corrected to

any other friction line formulation including the so-called three dimensional systems, and data corresponding also to

such systems are at present collected at the Hydro- and

Aerodynamic Laboratory for future use.

Appendix :

Scale effect on the remaining propulsive coefficients. The model-ship correlation method described has taken account of scale effect on wake only, but it will be seen

t

hat, when at a later date sufficient is known on the

subject of scale

effects on the

remaining propulsive

coefficients, these effects can easily be dealt with without any fundamental change in the method:

. Suppose that the full

size propeller has a higher

efficiency than the model propeller. As an example let

us assume that its Kr-curve is situated 2 mm higher

than the model-Kr-curve (Fig. 5) and the K(-curve

1 mm lower. Line FG will be shifted approx. 15 mm

to the right and GH about the same amount

down-wards, whereby increases approx. 2 percent and the

horse-power is reduced 5 to 6 per cent, corresponding to the same increase in propeller efficiency. Such an improvement on propeller efficiency of 6 per cent is

probably much on the high side and the error introduced

in neglecting this scale-effect is in most cases without

great importance.

If the wc,- and CT corrections to be used have been

derived from trial trip statistics with no regard paid to

such scale-effect, it is logical also to neglect it in

prognosis work.

Bibliography:

C. W. Prohaska: Contribution to the discussion of papers

read at the »Symposium on Ship Trials and Service Per-formance Datao, Newcastle, March 1960, Trans. NEC Inst., vol. 76, Part 8, p. SD 27 p.p.

C. W. Prohaska: Model-Ship Correlation at The

Hydro-and Aerodynamics Laboratory. Paper presented at the 9th International Towing Tank Conference, Paris 1960.

D. I. Moor & A. Silverleaf: A Procedure for Resistance and Propulsion Experiments with Ship Models, Paper

read at the Symposium on Towing Tank Facilities, Zagreb 1959.

H. Lindgren & C. A. Johnsson: The Correlation of Ship

Power and Revolutions with Model Test Results, Publ. of the Swedish State Shipbuilding Experimental Tank, No.

46, 1960.

S. A. Harvald: Wake of Merchant Ships, Copenhagen

1950.

Harold E. Saunders: Hydrodynamics in Ship Design,

New York 1957.

1960, No. 4 ANALYSIS OF SHIP MODEL EXPERIMENTS AND PREDICTION OF SHIP PERFORMANCE 119

b. Suppose next that the relative efficiency in the model

experiment is greater than one. A horizontal line from

point T would then intersect the vertical BC in

a point 0 situated above point C. A normal from C' to

the a,-scale would indicate a higher ar-value, meaning that the points D and E would move slightly upwards.

to the left but the vertical FG would not change,

provided the ship's relative efficiency corresponds to

that of the model. If it is lower, point H will move

slightly to the left on the trial trip curve.

C. Suppose finally that the ship thrust deduction

coef-ficient, t,

is lower than that of the model. This is

easily taken account of in the calculation of the ship-a5..

Point E moves downwards to the right and so do the

points F, G, and H. The number of revolutions in-creases and the horse-power is reduced as the hull

efficiency has gone up.

In general the above effects will be of little importance,

and especially when compared with the heavy scale-effect on wake found in single-screw ships. The high values of relative efficiency sometimes found in model

experiments are due to inadmissible differences in

experimental conditions for the open water and the

behind tests, for instance different propeller

im-mersions.

'3.

4.