- - JULI 1976

A RCHIEF

11

HYDRO- OG AERODYNAMISKLABORATORIUMHYDRO- AND AERODYNAMICS LABORATORY

Lyngby Denmaek

HydrodynamicsSection 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 PRESSVESTER FARIMAGSGADE 31 COPENHAGEN,DENMARK

Lab. v. Scheepsbouwkuntit

Technische Hogeschool

Delft

Analysis of Ship Model Experiments

and Prediction of Ship PerformanceA New Correlation Method

.

HYDRO- OG AERODYNAMISK LABORATORIUMis a self-supporting institution, established to carry out experiments for industry and to conduct research in the fields ofHydro- and Aerodynamics. According to its by-laws, confirmed by His Majesty the King of Denmark, if is governed by acouncil of eleven members, six of which are elected by the Danish Government and by research organizations, and fiveby the shipbuilding industry.

Research reports are published in English in two series: Series Hy (blue) from the Hydrodynamics Section and Series A(green) from the Aerodynamics Section.

The reports are on sale through the Danish Technical Press at the prices stated below. Research institutions within thefields of Hydro- and Aerodynamics and public technical libraries may, however, as a rule obtain the reports free of chargeon application to the Laboratory.

The views expressed in the reports are those of the individual authors.

Series Hy:

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

Hy-1 PROHASKA, C. W. Analysis of Ship Model Experimentsand 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 HeatExchanger for a Small Hypersonic Wind Tunnel 5,00

Analysis of Ship Model Experiments and

Prediction of Ship Performance

by

Prohaska

- - JUU 1976

tip HYDRO- OG AERODYNAMISK LABORATORIUMLYNGBY DANMARK

C W

Introduction.

The 8th International Towing Tank Conference held inMadrid in 1957 decided to abandon the analysis-methodbased on Froudes friction lines and to adopt as an interimmeasure a single friction line, the "ITTC 1957 model shipcorrelation line", defined by:

0.075Cr =

R 2)2

It was obvious that this change would make it necessaryto modify the empirical corrections on horse-power andrevolutions hitherto applied by most tanks. This questionhas been given a great deal of thought and several proposalswere submitted to the 9th International Towing TankConference in Paris 1960, but it was decided that thematter should be further investigated before any decisioncould be taken as to the recommendation of a specificanalysis method for general use.

Until the next conference, which will be held in Londonin 1963, it must therefore be expected that rather differentmethods will be used at the various model basins. Resultsfrom different tanks are therefore not always directlycomparable. This will be clear from the following inwhich a short description is given of the procedure hithertoapplied, of some modifications to it, and finally of a newmethod proposed by the author and now in use at theDanish model basin, [1], [2]*).

Model-ship correlation.

In modern formulation the classical Froude method maybe 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 fromthe results of model experiments, the author describes a new correlation-analysis,already in use at the Danish Ship Model Basin. In this analysis wake scaleeffect is correctly taken into consideration and a logical link is establishedbetween model and ship.

(1)

532.5.07:629.12.07

In Fig. 1 the Froude frictional coefficients for differentmodel and ship lengths are shown as functions of Rey-nolds' number. The curve marked C, represents the total

R.model resistance coefficient C., =

p/2 V2 S' where R7. is

the total resistance, o the density of fresh respectively saltwater, v speed, and S wetted surface. Curve Cr, is thecorresponding curve for the ship.

By means of the propeller and propulsion experimentsthe propulsive coefficients including the propulsive ef-ficiency

1/'7= i - w x 71P

(2)

are found (t being the thrust deduction coefficient, u. thewake coefficient and r. the propeller efficiency).

It has now been customary to neglect the scale effect onpropulsive efficiency. The ordinates of curve Cr in Fig. 1,derived from those of curve C dividing by r, thereforerepresent a horse-power coefficient:

C, = =C. 1 R 1 00108

n X p/2 v2 = X S/7213 X E ,

1000 EHPwith E = A 2/3 v3

0.0108or: Cr X Prv 2/3 with: P

E 1000 PHPP1.

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 theform of a percentage addition varying with ship typeaccording 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 arescaled down and usually given an empirical correction ofa few per cent.

It is. now evident from F.g. 1 that the change overfrom 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 toraise the total ship friction to. such a figure that extraallowances would become unnecessary. This QC-correctionwas thought to cover form and roughness influences. It willbe seen from the following that it must take care also ofscale effect on wake, unless a correction for wake difference:is applied separately.

The best way to check the corrections or allowances tobe applied is of course to compare trial or service resultswith predictions based on such allowances.

Suppose that the curve C in Fig. 2 has been derivedfrom trial results. By multiply'ng its ordinates by the ef-fic'ency 7] (eq. (2)), the ship C-curve is obtained, whichafter 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 linerepresents AC. It is therefore obvious that the QC, valueis a function of the efficiency The 71 values found bymodel experiments, carried out in different tanks,, for oneand the same ship are, however, not identical, as themethods of performing the self-propulsion experimentsdiffer from one tank to another. Apart from the classicalBritish and Continental methods, differing in propellerloading during the experiment, new varieties have comeinto 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 bereached 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 forthe model also applied to the ship. Although it has beenclear to the profession for quite a ong time that all thethree propulsive coefficients, f, w and np, could be subjectto certain scale effects, corrections for such :effects havenot been introduced into standard analyses or predictionwork.

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

41'

c0= -

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When at the Hydro- and Aerodynamics Laboratory(HyA) an analysis method had to be selected, the questionwas given much thought. Having no previous statistics wasto some extent a handicap, but it represented on the otherhand the advantage, that with no ties to such statistics,there was ample opportunity to develop a new method ofanalysis.

This new method is based on the fact, that the wakeis subject to a scale-effect, which at least for single screwships is rather heavy. For a ship the wake is often abouttwo thirds of that found for its model. This is logical asthe thickness of the ship frictional belt is only of theorder of one half of the propeller radius, whereas for themodel it is about twice as thick, thus producing a higherfrictional wake for the latter.

For flat plates of model and ship lengths approximatecalculations of the wake differences have been performedfrom data given in [5], and the results are shown inFig. 3.

This method of approach only serves to indicate that

SELF PROPULSION

10 KN1520

KN1520

10KN1520 -

ANDn 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 betweenmodel and ship, but exact figures are not easily derivedby calculation, as the three-dimensional wake field is

difficult to determine for the full size ship. It seemslikely that the actual figures will exceed those for flatplates.

Supposing that in a certain model experiment, a wakeof 040 has been found, then for the ship only about030 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 willtherefore reduce to approx. 0.66 X 1.03 = 0.68 for theship, counting in a 3 per cent rize in alp due to the decreasein propeller loading.

Taking into consideration this drop in total efficiency,it is apparent from Fig. 2, that the application of suchreduced (and more correct) ship efficiencies leads to

lower ACE-values, and actually the ACE-values derivedin this manner seem more reasonable than those foundwhen disregarding wake scale-effect.

As mentioned previously the wake scale-effect is difficultto calculate, but fortunately it can be derived easily fromcomparative analyses of model experiments and trial tripdata. Such analyses of available data were carried out at HyAprior to the introduction of the new method.

If on the open water propeller diagram (Fig. 4), inaddition to the usual Ko-curve, the corresponding curvederived from the self- propulsion experiment is plotted,the ratio of the abscissae to points of equal Ko gives

vtorque 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 observedthat these points define a curve which, in general, is farfrom being identical with the K0-curve from the self-propulsion experiment. The trial trip K-curve indicates amuch lower wake. Wake values thus found can be plottedin a diagram similar to that in Fig. 3, and such wakevalues are used in the new method, which will now bedescribed with reference to Fig. 5.

Fig. 5 shows a logarithmic propeller diagram*), butthe method can be used also with other types of dia-grams**). For simplicity it is firstly assumed that thereis no scale effect on thrust deduction or on propellerperformance, and that the relative efficiency is equal toone. These assumptions will be discussed in the Appendix.

In Fig. 5 is shown K( 1:7, and al from the open-waterexperiment. Further K9- and Kr-values derived from theself-propulsion experiment have been plotted over 1,, =

v . The horizontal distance between points as A and BnD

') The logarithmic propeller diagram has been fully described bySaunders 1.61, Vol. 2, p. 589 pp.

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

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K9-curve, giving K, and I. From the latter the revolutionsare determined and then from the former the horse-power.These data are at HyA plotted in a diagram of the typeshown in Fig. 6.

From the efficiency curve (Fig. 5) it is seen that thepropeller efficiency for the ship is higher than for themodel because of the reduction in propeller loading. Onthe other hand the hull efficiency of the ship has becomeconsiderably reduced, and the propulsive efficiency of theship is lower than that found in the self-propulsionexperiment. As stated above this means that with theproposed method lower C,-allowances must be used thanthose corresponding to the conventional analysis basedon an assumed constant efficiency.

This model-ship correlation method requires, as will beunderstood, two (and only two) empirical values to bedetermined from previous statistics, viz, the wake dif-ference Au. and AC,. It has been explained already thatA w is derived simply from a comparison of K9-curvescorresponding to the trial- and the self-propulsion ex-periments. It is evident that as each K-value on the trialtrip corresponds to a certain value of the load coefficientar (easily derived from the diagram in Fig. 5, where lineHGFE indicates the procedure), this or-value

determines the total specific ship resistance, C,., by meansof formula (4), and thus also AC,.

The trial trip speed values used in this analysis mustof course be corrected for currents along the measuredmile. This is done in the following manner: For eachsingle run a K0-value and the corresponding f-value arecalculated. The former determines a [-value by means ofthe open-water 1<Q-curve, and from this ye is calculated.Deducting from the observed speed (v c), where cis the speed of the current, and plotting the differenceon a time scale, two separate curves are obtained, thedistance of which is 2c, and hence the true speed foreach single run is easily determined. The ve-deductioneliminates from v the arbitrary variations in loading dueto wind etc.

The new correlation method has been described withrelation to torque wake. If thrust is measured, the sameProcedure could be used &Rally well in relation to thrustwake. Up to now most tanks have used thrust wake or adirect 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 torquewake should be used as a standard. It provides a naturaland logical link between model experiment and trial trip.

The same link also extends to the service data, fromwhich it is eaually simple to calculate corresponding

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

will show that after some years of service the K11-curvewill 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 ISOREy4,

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 diagramat .8', where A'B' = AB. A similar procedure holds ofcourse for thrust wake (see distance TC, which for theassumption made about the relative efficiency, must beequal to AB). The point C lying vertically above point Bgives the KT-value corresponding to the K9-value at Aand B. A normal to the a1.-scale drawn from C intersectsthe scale at D, and the a7.-value can be read on the scale.This is an a,-value corresponding to the self-propulsionexperiment at the speed in question. Assuming now thatthe CT-value for the ship has been estimated for thecorresponding speed (curve C. in Fig. 2), then the loadingof the ship propeller is easily calculated. As:

a. =pl2 v 2 F

=.(1 t) (1 w)-

SIF, X

RX CT (4)

pi2 1,2 S (1 t) (1 w)2

where S = wetted surface and F = disc area, ar can becalculated when proper values of ship t and u. have beendetermined. At HyA three per cent is added to the cal-culated load coefficient to take account of air- and steeringresistance.

Suppose that t is taken from the self-propulsion experi-ment*), and te. corrected for scale-effect, an a.-value, pointE, is obtained, which again corresponds to the K,,- andK9-values in F and G. From the latter point, GH is setout horizontally, with GH = Gr' on the bottomscale 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 givesdirectly 1t on the vertical scale in Fig. 5.

.

I

1

-

-

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= =

-

4

0

both due to the increased roughness of the shell. Aftereach docking of the ship the curve will tend to movedownwards, then rise upwards again. A large size diagramof this type can therefore represent the complete history ofthe propulsion characteristics of a ship. Comparison of suchdiagrams will give the relationship between shell roughnessand proper service values of Au. These will be lowerthan those for trial trips and may even become negative.

The correlation method described is in no way restrictedto the use of the ITTC 1957 model ship correlation line,but is equally well applicable if other friction lines shouldbe adopted in the future. The Au-values and AC,,.-valuesfound in the present analysis can easily be corrected toany other friction line formulation including the so-calledthree dimensional systems, and data corresponding also tosuch systems are at present collected at the Hydro- andAerodynamic Laboratory for future use.

Appendix :Scale effect on the remaining propulsive coefficients.

The model-ship correlation method described has takenaccount of scale effect on wake only, but it will be seent hat, when at a later date sufficient is known on thesubject of scale effects on the remaining propulsivecoefficients, these effects can easily be dealt with withoutany fundamental change in the method:

. Suppose that the full size propeller has a higherefficiency than the model propeller. As an example letus assume that its Kr-curve is situated 2 mm higherthan the model-Kr-curve (Fig. 5) and the K(-curve1 mm lower. Line FG will be shifted approx. 15 mmto the right and GH about the same amount down-

wards, whereby increases approx. 2 percent and thehorse-power is reduced 5 to 6 per cent, correspondingto the same increase in propeller efficiency. Such animprovement on propeller efficiency of 6 per cent isprobably much on the high side and the error introducedin neglecting this scale-effect is in most cases without

great importance.

If the wc,- and CT corrections to be used have beenderived 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 papersread at the »Symposium on Ship Trials and Service Per-formance Datao, Newcastle, March 1960, Trans. NECInst., 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 9thInternational Towing Tank Conference, Paris 1960.D. I. Moor & A. Silverleaf: A Procedure for Resistanceand Propulsion Experiments with Ship Models, Paperread at the Symposium on Towing Tank Facilities, Zagreb1959.H. Lindgren & C. A. Johnsson: The Correlation of ShipPower and Revolutions with Model Test Results, Publ. ofthe Swedish State Shipbuilding Experimental Tank, No.46, 1960.S. A. Harvald: Wake of Merchant Ships, Copenhagen1950.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 modelexperiment is greater than one. A horizontal line frompoint T would then intersect the vertical BC in a

point 0 situated above point C. A normal from C' tothe a,-scale would indicate a higher ar-value, meaningthat 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 tothat of the model. If it is lower, point H will moveslightly 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 iseasily taken account of in the calculation of the ship-a5..Point E moves downwards to the right and so do thepoints F, G, and H. The number of revolutions in-creases and the horse-power is reduced as the hullefficiency 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 highvalues of relative efficiency sometimes found in modelexperiments are due to inadmissible differences in

experimental conditions for the open water and thebehind tests, for instance different propeller im-

mersions.

'3.

4.

6.