Form factor equations from regression analysis of Rome - Towing tank historical data base

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Form Factor Equations from

Regression

Towing Tank

Historical Data Base

Giuseppe M. BAILO5

Roberto PENNA

°

Daniele RANOCCHIA

Roberto ROCCHI

°

Rome, September 1991

The opinions expressed in this paper are those

of the authors and do not

necessarily reflect

those of their Istitutlons

Abstract

in this paper arc reported the results of temptatives and ef-forts devoted to the determinatiOn of mathematical model (deduced by regressional analysis) that enables reliable pre-diction of the form. factor (1 + k) value of full ships (CB greater than 0.63), without resorting to its experimental determination. For its application is required the sectional area diagram at effective static trim. The approach by which it had been possible to estimate the (1 + k) value of 24 tanker Bhip modCls, considered target cases as in j27j, with high accuracy (max absolute % errors less than 2.5 and rinse 0.55) must be validated through its application to other samples of experimentaldata. As it is well known it is not so easy to validate a regression equation over other data which are external to theanalysed sample 11,4,61, and we believe it is incorrect too, due to the foundamental fact that each Institution has his own "methodological error rough-ness", where roughness is used here in the same sense as Prof. Abkowitz used in his 1990 paper presented at Madrid [1 The authors believe that it is more correct that each Institution derive their own semi-empirical mathematical model for the (i + k) prediction,from regressions analysis of their own experimental historical data. The authors will be grateful to all Institutionthat will be available for the validation of the proposed approach and make votes for

ample cooperation.

1

NomenclatUre

ABL Longitudinal area of bow bulb foreward section 20 ABT Bow bulb area at section 20

A. Maximum transversal area

B = BWL Waterline beam at maximum transversal séc tion area

r3T=B/T

Italian Navy General Staff -Ship Design Committee LN.S.E.A.N - Rome, Researcher

00 _{1.N.S.E.A.N - Rome, Sen,or Researcher}

-BY = B/VOL1"3

CABL = ABL/Az Lateralparameter for bow bulb

CABT = ABT/Az

Cross-section parameter for bow bulb

CB =VOL/(LOSBT)

CBP =

GB/LB

CBG =CBS/LB

CBS =io.CB/(LB.vT)

CBSS =10 CBS2

CCXL Length of cilindrical body as % of LPP

CM =Az/BT

CPE = A/B LE

Longitudinal prismatic coefficient of entrance body

CPR = Az/B . LR Longitudinal prismatic coefficient of run body

CVPR Volumetric parameterof bow bulb (see Fig. 1) DELTA Displacement in salt water

LB = LOS/B

LE Length of entrance body LOS Length over 8ubmerged LPP Length between perpendiculars LB. Length of run body

LT = LOS/T

LV = LOS/VOL"3 Length-volumeratio

RB. = SV . GB

./(BT/CM)

SV = S/VOL2"3 T Immersion at aft PP T, Immersion at fore PP

TV =T/VOL"3

TVS =iOTV2

VOL Hull volume = DELTA/1.025

Note

Tt and hull form coefficients which ileeds its value (CB, CM, etc.) refers to the effective depth at actual static trim whichcorresponds to the section with maximum area.

--

r r;

es

".if there is an agreement between actualship power

and that predicted from model tests, all the coefficients may have been properly predicted or several of the

co-efficienti mayhave been wrongly predictedv,nlherrors in some coefficients compensating for errors in other coefficients...

¶..in reality, the roughness factor has represented a roughness in the extrapolation process rather then specifically the ship roughness..."

Both sentencies are from "Full Scale Measurements of the Resistance and Powering Coefficients and the Resulting Improvement in the Extrapolation Process from Model to Ship", a paper presented by Prof. Martin A. Abkowitz at the 19" ITTC, Sept. 1990, Madrid.

We hope that the analized tanker ship models, taken from the INS EAN Data Base, are not of such particular geometry referred to by Prof. Abkowitz some lines after:

"...one may buildup confidence in faulty prediction

procedure in that compensating errors may only exists

for that particular ship geometry..."

We declare all our uncertainties and doubts in present-ing a paper on an argument like the form factor: first

of all because we are a lot late (beginning the question roughly fourty years ago) [3]. Second because it is haz-ardous for every one to speek nowdays about form factor: in fact there are so interesting new approachs with which to attach the ship performance prediction problem nowdays

(22,23,24,26).

Many other doubts grewn-up remembering the amount of discussions that accompained and followed the original Hughes's assumption [3). Only recall a detail on this as-pect, we report what said Crago about form factor [2]:

"...imagine the reaction of the shipowners, operators

and builders, our customers, on reading this list of

nine objections to the method and then being asked to pay more for their model tests to cover the experiments necessary to derive form factor...";

or what said Prof. Harvald in his comment to the Report of the ITTC '84 Performance Committee [1]:

"...different methods are applied by towing tanks for determination the form factor r = (1 + k) but the

methods do not give the same results...".

Nevertheless the authors concluded that it would be bet-ter to try.

3

The ITTC '78 Extrapolation

Procedure

As happen in other Institutes also at INSEAN the form factor methodology had been adopted following the ITTC reccomandations, and included in its Acquisition Data Sys-tem. But before 1978, at INSEAN the experimental de-termination of the form factor had been considered as an extension to lower speeds of the routine calm water tests [7]. Models were all made in wood and equipped with a

2

standard row of pins. Customers were never asked to pay more for it because, as said by Prof. Jourdain in [7):

"...Hughes is cheaper than Prohaska, since the runs at

the moderate speeds are useless, as the CTmnim,i

ii

normally into the field of the usual runs...".

Some experimental research have been developed spe-cially for very full form ships (CB from 0.830 to 0.900) during the seventhies [19]. In 1983 started a general re-analysis of the collected form factor data according to eight different Prohaska-modified procedures, and results were presented in [17). The report includes more than 50 twin-propeller merchant ships and more than 60 single twin-propeller ships (bulk-carriers, tankers, cargo, GPL ships).

A first regressional analysis of above said data, in which only the foundamentals hull form coefficients as in [4,6) were included, had been performed in 1985 and the results reported in [18].

4

The Regression Analysis

Per-formed in 1985-87

In the last analysis [18), regressions were performed with all data sample and with samples derived according to a specific criteria: derive an procedure for the experimental form factor determination to be assumed as a standard in ruotine towing tests for ship performance predictions according to ITTC '78 Method. Or, in other words:

"...to decide on a method of form factor

determina-tion having the least possible experimental errors and is practicable in normal routine work..." page 180(4).

From the 1985 analysis it resulted possible to select the procedures FFAI (n. = 4, Fm = 0.10 0.20) for twin-screw ships and FFC1 (n = 4, Fm = 0.10 0.18) for single screw ships.

The eight procedures were the following:

Proc. n Fn values -FFA1 4 0.10 0.20 FFBI - 4 0.12 - 0.20 FFC 1 4 0.10 0.18 FFD1 4 0.12 0.18 FFA2 variable 0.10 0.20 FFB2 variable 0.12 0.20 FFCI variable 0.10 0.18 FFD2 variable 0.12 0.18

where n is the exponent of Fn power in the well known equation:

CT Fm"

The selection was made comparing standard deviations, rrnse, maximum % differences between each of the eight

results and the (1 + k) values obtained by the INSEAN standard procedure of the CT,,,,,, and performing t and W statistical tests.

The 8ampie made-up with the data of single-screwships of GPL, tankers and bulk-carriers permitted to

obtin the

following regre8sion equation ]A]:

Equation [A]

(1 + k)est = +LT 0.02553 + CM 22.37842 + -CBC .9.56988 + CBSS 0.15180+ +BTS 0.28198

with MCC =0.924, SE=0.034, TMIN= 2.56, interval of confidence= 5.5%

The ranges of the hull form parameters and coefficients, that give some idea of the applicability of the proposed equation are:

The sample made-up with the data of twin-screw (fer-ries, supply-vessels, passengers, etc.) allowed to derive this equation:

(1 +k)est +RRS P0.22803 + TVS 1.23866 - 1.07656 with MCC= 0.925, SE = 0.071, TMIN= 8.5, interval of confidence

=

10.5%

The RR variate has been derived in 1985 by R.Rocchi starting from free-surface water channel hydrodynamic con-siderations briefly as follows:

S

=

BS . LOS (fiat plate) S

=

RS - ir . LOS from which

RS

_{- ir-LQS}

AX=

CM.

. T (area max transv.) AX= p2 ir/2, from it:

p2

=

CM B T 2/ir

dividing [1]/[2] and semplificating like in [61, we ob-tain (after the introduction of SV LV LB LT):

RR

=

SV . CD. RRS =RR2/10

5

The Regression Analysis

Per-formed after 1985-87

With the scope to better taste the effectiveness of other more elaborated hull form parameters, like those intro-duced by Taniguchi [61, in their ability to read-up the phys-ical interrelation between the form that disturbs the uni-form flow that Washes the ostacle and the effects of such

disturb - in this case (i±k) - the following variates were intro4ce4 in thö regressions:

CPR, CPE and CBB, CZB, CLPR,

CCPR, CABT, CABL for bow bulb form characterization [81, seeFIGURE 1.

All cases considered in the sample are tanker-ship mod-éls as proved in routine tests. It contains the tanker-ships data from the sample congidered in 1987analysis and other collected during last years. It had beenconsidered a sample of 19 data, keeping 5 apart for validation. The selection of this sample takes account of the fact thatthe form factor is more inifuent on slow full ships. In one hand, the more the effects of the form on the resistance at moderate and low speeds, the more the difficulties in trying to explain it via regressional analysis (specially when the sample dimension is low). In the other hand: being greater the phenomenum, if we can ensure absence of laminarity and separation as, is in the case we are considering, if new variables are re-ally good for the job, they have to be able to build-up an equation that permits to make very accurate estimates of (H-k).

The best data-fit equation we could derive fromthe anal-ysis of the above said sample comprehensive of only the data of tanker ship hulls with bow-bulb, rudderand single-screw bossing, see FIGURE 2, is the following equation [B]:

Equation [B]

(1±k)est

= -CABT .0.18767 + CPE . 0.32882 ± -CB . 0.64598 + CM 12.48494 + +CABL . 0.04224 + CPR 0.32408 ± +CVPR 0.08133 - 12.19436

with MCC = 0.945, SE=0.032, MAX % err: -2.6 3.4 We do not propose this equation for any reliable predic-tion because it is a good one only for sample data fitting, since, in spite of good values of MCC, SE, etc. it contains a form coefficient characterizedby a too low significativity (sig t= 0.18).

The equation it is possible to give for reliable predictions resulted the following:

Equation [C]

(1 + k)est = -CABT - 0.17039 + DV 0.38210 + +CB- 1.23499 + CM- 11.35831 + +CABL .0.04669 - 11.19620

-vith MCC = 0.909, SE = 0.032, MAX % err: -4.0 + 4.0 TMIN= 2.05 (sig t =0.0616)

The % error of estimates over the 19 sample data are listed in TABLE 1, after the text, in column EC.

LV SV CPR LB BT miii. 5.0 6.1 0.50 5.2 21 max 6.2 7.1 0.60 7.6 4.8 LT CB CM CABL mm. 14.0 0.630 0.992 0.75 max. 29.0 0.800 0.995 2.30

The Introduction of Sectional

Area Diagram in the Analysis

of (1+k) Value

The introduction of the variates that permitted to obtain equation [C] enable to make more accurate and reliable

predictions than those with equation [A], and it may be considered a good result. But we tried to go over resort-ing to the results obtained in the regressional analysis of the residuary resistance of displaceant ships, with the in-troduction of some groups of variables derived in aspecial way from the CPCTJRVE, as originally made by R. Rocchi and reported by him in [13,14,151.

We considered then the oportunity to enface the analysis, of the form factor according that kind of approach. This fact brings on the table the following question: Why the CF CURVE?

One may answer remembering for instance the consider-ation made by Gross at page 583 in [4]

"...it can be staled that trim in the ba!la.!i condition and the hitherto unknown effect of the differences in stern contour shapes and other ship form parameters, the effect of bulbous bow or stern bulbous, not compre-hended in main ship form parameters, lead to a great scatter..."

This would be a good answer because all them are intrin-sically accounted for into the CPCURVE. But we believe the answer may be this another:

o the influence of the hull-form on theform resistance, is a function of both Fn and Rn (among others see [10]). More over the troubles about their interdepen-dencies are so extended that Prof. Harvald declares

- "The rn.ethod is built on Froude 's law, but there can be doubts about the validity of this law. Per-haps a scale effect on the wave resistance should be added in the future", page 104 [11].

we consider all that is right, but. it's also true that at moderate and low speeds too, the form of the object (the hull) generate - in spite of the fact if we arc able or not able to take account of- an extended pressure gradient, here we don't care if viscous or not viscous, see Robb ]9], due mainly to the form of the obstacle that alters the state of uniformity of the, flow that surrounds and washes it.

At higher relative speeds the existence of the pressure gradient is clearly evident by one of its moreobservables phenomena: the waves generated by the hull, Robb [9]. At low speeds the pressure gradient is not so clearly observ-able: one way to have an evidence of its existence is the excess in resistance over that determined for the equivalent flat plate. This excess may also be considered as residuary resistance: it is only a question of words. The old concept of the viscous belt, takes account of the additional re-ciprocal effect of the form in the sense that viscosity alters

i the original form of the obstacle [20]. We have to

con-clude saying that we are lucky because we are analysing the phenomena at low speeds: when the development of 4

the viscous belt is not so much developed. We can say that we are at speed values at wich there are only secondary differences between the form of the hull at rest an the form of the hull in movement.

Summarizing we consider that the effect of the hull form on the resistance at low and moderate speeds is mainly due to the alteration of the indisturbated field of pressures of the flow, and only in minor part due to the alteration of the hull form by the viscosity of the fluid. If it is. so, the variables that demonstrated to be so strongly related to the CPCURVE in the evaluation of the residuary resistance (at higher speeds made-up mainly by the generated wave) should enable to derive regression equations affected by very low errors of estimates.

In the regression analysis of the low speed CRV coef-ficients of tanker-ships performed by R. Rocchi inst july 1991 according to his own approach (the CPCURVE co-efilcients included among the independent variables, [13, 14, is]) on same sample of data analysed in 1989 (12], re-sulted that the CPCURVE approach permitted to derive regression equations characterized by very small standard errors.

In example, at FNV

=

0.40 we report the proposed equa-tion for the extimate of residuary resistance:

CRy40 = +AA.A 17.39015 + BBB . 0.99305 +

+CCC 20.87215 + DDD- 1.16517 +

EEE 1.79153 - FFF 11.68160 +

GGG 0.34251 - CB 14.18355 +

+FWD 0.70240 + 8.97731

with MCC= 0.993, SE=0.146, MAX% err: -0.92 1.14 TMIN= 2.69 (sig t=0.023), rmse =0.55. To note that the corresponding relative speed is Fn= 0.16: clearly into the speed range at which normally the (1 + k) is experimentally determined [71.

Comming again to (i + k) regressional analysis per-formed with the concurrence of the group of variables de-rived from the CPCURVE permitted to obtain the equation

[E]: -Equation (F,] (1 +k)est

= +AAA

2.97797 -.BBB 1.17127 + CCC 2.092 25 - DDD . 2.88771 + +RRS 0.01331 + EEE .0.77929 + +CABL 0.08349 + CPR . 0.55954 + +1.2 1489 MCC=0.972, SE=0.021, TMIN

=

3.40 .(sig t=0.007), MAX % errors

=

-2.3 +1.7.

Over the target sample data the accuracy of the predic-tions made with this equation is twice that of equation [C]. The intervals of confidence beeing 6 % and 3.7 % for fE]

equation, at a level of confidence fixed at 0.95.

To compare the superiority of the variables AAA,BBB, etc. derived from CPCURVE in relation to CPR, CABT, etc., the equation [C] may be compared with equation fD] that has also k= 5:

Equation [D]

(1 + k)est = +CPR - 0.72425 - CCIL .0.24510 + -AAA- 1.4 1532 + CABL 0.08689 + +BBB 1.56650 + 0.51120 MCC= 0.940, SE= 0.026, TIvUN= 2.03 (sig. t= 0.022), MAX % errors = -2.7 3.1.

7

Other Implementations and

the Question of Validation

When one has to do with validation of regression equa-tions, many people is convinced that the only way to do it s: get a group of external data; apply them the equation under consideration; verify if the errOrs of the estimates are into the range of the interval of confidence that characterize the equation. If it does not succeed: Why?.

Everyone who had been involved with regressional anal-ysis knows that hO will succeed if the external data is well surrounded by the data of' the analysed sample . in the analytical space at k-dimensions - k beeing the variables that are in the regression equation considered there. If we do not succeed, it does not mean that the proposed equa-tion is wrong: it only tells us that the external data is in someway - and generally we do not know at a first glance which that way is - non omogeneous with the sample data. In other words: we are trying to apply the just equation in the wrong place.

Our thought about the validation question is: one has to validate the kind of approach, not the single equation. How to do it?. It can be done applying the same approach to another sample. If also with this new sample it is possible to derive a good regression equation the approach may be declared OK. In the following we will report what may happen when one is engaged with validation of regressional equations as the basis of external cases.

In the N

= 19 considered sample, cases identified by NN1 equal to 16, 17, 18, 19 refers to the same ship model at level trim, but at four different displacements. Their main dimensions and coefficients:

Note: T

= (Tj + T)/.2 all four cases at level trim. The % errors of estimates of (i+k) made with equation [E] are listed in Tab.1 under EE. The cases NN1 equal 43, 44, 45, 46, 55 are:

external to the analysed sample N = 19 employed to obtain equation IE];

the value of main hull form parameters and coeffi-cients are into the ranges of values of the sample

data (excluded: mm LV, in SV, mm CM each for small differences);

the cases with parameter values a little bit out-range are: NN1 43 (SV, LV with an % error 1.57), and NN1 55 (CM with an % error .7.2); see Tab.1;

as it may be seen there are no formal justificable reason for the estimate % error of NN1 46 equal to -7.7%; neither for NN1 44, error -5.5 %.

All questions will became clear if are observed the foundamental facts of the five cases on which we pretend to test the regression equation [E] new proposed approach. We have to look the values of following table:

Five External Cases for Validation

where CM*, T*, CB*, are fOr actual trim (as we believe it has to be done); whereas T = (T1 + T)/2, CB, CM compu ted with T values (as was right to do for the N=19 sample analysed, because all data of the sample were all for level trim condition).

The foundamental reason by which it is inadmissible any consideration nor any inference about the five exter-nal cases, is the fact that they refer to trimmed condition whereas the regression equation [El had been derived from a sample in which this "state factor" was not included. It would be interesting to taste a dicotomous variable for trim condition but, apart this curiosity, we hope there is none who would try to introduce in regression analysis CM value greater' than unity. We are convinced that definitions are to be applyed with a lot of "common sense".

The group of variates derived from the CPCURVE take account of all this particular details 1241, because the CPCURVE for the five external cases are determined at effective trim. This question is shown in FIGURE 3, from which it is evident the great mistake anyone would make in substituting CPCURVE at the actual static trim, with that for level trim at the same displacement. We have to remember that cases NN1 43 44 45 46 55 are, as NNI 16 17 18 19, experimental determinations of form factor of the same physical model (the same wooden tanker model) tested at very different conditions.

NN1 LOS DELTA T T CB CB* 43 277.1 190000 16.90 18.65 0.764 0.692 44 283.8 190000 16.94 17.28 0.744 0.730 45 286.0 190000 16.98 17.76 0.737 0.705 46 286.8 190000 ' 17.02 18.82 0.733 0.663 55 273.1 110000 10.32 11.10 0.735 0.683 NN1 SV LB CM* (1 ± k)ezp TRIM CM 43 5.85 5.35 0.991 1.246 -6m 1.094 44 5.89 5.48 0.990 1.265 -Im 1.010 45 5.95 5.52 0.975 1.295 +4m 1.020 46 5.98 5.54 0.977 1.353 +9m 1.080 55 6.77 5.27 0.963 1.295 +4m 1.036 NN1 LOS DELTA S CB LB T 16 349.65 302330 27542 0.791 6.75 20.59 17 338.61 190000 22077 0.797 6.54 13.26 18 285.22 183482 19312 0.731 6.50 16.58 19 271.89 114210 15750 0.740 5.25 10.09

8

Implementation

We modified the original N=19 sample including the five external cases obtaining the N=24 sample. This data had been submitted to regression analysis according to the new approach (CPCURVE as indipendent variables) and we derived the equation [F] which PC-SPSS output sheet is reproduced in FIGURE 4, whereas FIGURE 5 presents the (i+k) estimates for all 24 cases (XXX), the % er-rors (EXXX); the estimates made with Gros-Watanabe (KW84) equation, and the % errors (EKW84) cbmpare for same values at column EGW in TABLE 1. Data under CC says there are cases at full load and at light load; CEB says that the sample is made-up Only by bow bulb ships;

APPsays all data have appendices (rudder and single screw bossing) and EN says all are single screw ships.

The % errors of the estimates for the old external five data are here reported again:

The values at column F are XXX values of FIGURE 5. We report also the max and mm % errors of estimates of data of the old N=19 sample;

The Gross & Watanabe formula being:

k = 0.017 + 20 LB2

It can now be said that the new approach permits to ob-tain accurated predictions which are statistically reliable. The example here reported may be considered the first val-idation according to the proposed criteria. We do votes of obtaining from other tankery people a collection of data to be performed according to our new approach. We will be grateful at all who will adhere and help us in the valida-tion or the refusal of this new approach for the analytical (semi-empirical) form factor determination in such a way as never again be forced to ask our customers more money for it experimental determination: We Hope!.

Some notes about equation [E]:

We believe it had been answered to the arguments of Mr. Gross at page 583 [4] before reported in our page 4.

among the conventional hull form coeffi-cients/parameters the only one that still remains in the regressions is CABL, which takes account of the

6

longitudinal blountness of the bowbuib; but in the equation it has the least significativity (least BETA coefficient);

with small BETA but with higher significativity then CABL resulted CCIL;

the RR variate mantains it significativity, being its BETA= 0.72962 (see Fig. 4);

all other variables in the equation are those derived from the CPCURVE;

to validate even more the new approach it is needed to have more samples to be performed.

In the following table the variables included in the equa-tions (A], (C], (DJ, [Ej, [FJ are listed according to theirsig-nificativity in the equation (BETA coefficient decreasing):

Eq.n Variables according decreasing w - w/o value of BETA coeff.

A

LTCMCBGCBSSBTSV

w/o

C CABT CD BY CM CABL w/o

D AAABBBCPRCABLCCIL w

E AAABBBCCCDDDRREEE w

CABL CPR

F

AAA BBB CCC RRS FFF

w

GGG

mni

DDD EEE CCIL

CABL

9

Final Considerations

We are convinced that perhaps one right way to read into the intricated question of form factor could be the one that remember Hughes's conception of k basically intented to take care of the 3D-form that disturbs the uniform flow. About "flat plate" we all heard some time ago about certain Mr. Froude and the consequences of the Greyhound full scale data analysis.

Tankery people ever have in their mind the famous nine trubles connected with the form factor determination. We recall them a.s,made by Tamura K. [21]:

separation on a model may give too low a form factor;

laminar flow on a model may give too low a form

factor;

wave breaking may disturbe the linearity of the re-sistance coefficient;

a bulb may also disturbe the linearity;

interaction between propeller and hull may influence the form factor;

it may be difficult to take the appendages into

ac-count;

tank blockage may influence (i+k);

the form factor is dependent on the Froude number;. (H-k) may be dependent on the Reynolds number. We do votes that the tendencies of last decades, in times where there are a lot of computational codices and capa-bilities, money and time to spend too, will not bring also

NN1 (1+k)exp C D E F W 43 1.246 -9.9 -0.8 1.6 0.4 4.9 44 1.265 -9.8 -4.8 -5.5 -1.0 2.6 45 1.295 -26.3 -5.0 -2.5 2.4 -0.6 46 1.353 -29.6 -10.9 -7.7 -1.6 -5.6 55 1.295 33.4 -10.3 -7.2 1.1 -3.9

Eq. K type max % err.

C 5 w/o CPcurve -4.0 +4.0

D 5 w CPcurve .2.7 - +3.1

E 8 w CPcurve -2.3 +1.7

F 11 w CPcurve -1.8 +1.7

a lot of papers reporting about temptatives done in trying to solve the same problem following the opposite way. The temptatives done according to the direct old way, we may say "from small to big", taken to tankery people inore than 150 years. How long will take the opposite way from big to small?.

Perhaps the "global approach to the status" like those of Prof. Schmiechen and those of Prof. Abkowitz, both plenty of so revolutionary ideas will give at tankery peo-ple one chance more to solve the old problems. Also the increasing attention devoted by mathematicians to hydro-dynamic problems may, in spite of the questionable doubts appeared among tankery people like Abkowitz, Morgan, Wen-Chin-Lin, Van Oortmerssen [25, 231 and as reported in recent reports of the ITTC Performance Committee[24],

shut some inside look to the central problem connected with the disturbed viscous flow representation in presence of a free surface. In the meantime we apologize for our old fashioned way to do things.

For the authors this paper ought to be concluded by the words of Prof. Lèif N. Persen, to whom we are in debt:

"Here the agreement between theory and experiments

IS not as gooda. one might hauc wished, but the

die-crepancy 13 not as jeriou, as itmay look"

The Professor is right, what he says do not need valida-

10

tion at all:. it is sufficient to look the percent variations of PD and N for the different values of predicted form factor 1.

according to the listed equations and the CT,,num ex-perimental value: see FIGURE 6 which reports the results for two cases. For whom that are not frequently involved with ship performance prediction according to the ITTC 2. '78 procedure we report the FIGURE 7, taken from [211.

For the very next future it is scheduled to go on as fol-lows:

external enhancement: expand the boundaries of ap. plicability; define "ad hoc" ship forms, do

experi-ments;

internal enhancement: by regressional and clustering analysis derive analitically "internal" new cases; verify and take account of the actual trim if needed: dynamic actual trim, not only the static one;

try to correlate form factor with full forms and nom-inal wake (aLso with effective wake) and resistance

augmentation do to propeller;

implement proposed form factor predictor according the results from previous items.

Here we understand that with "external enhancement" will be possible to cancel the queslion of the applicability of regression equations. For it we only need the shipyard designers, naval architects and tankery people cooperation in the determination of the "ad hoc" hull forms.

In mean time there exist one way towards the implemen-tation of (1 + k) predictor:

derive from the CPcurve the values of variables to be included in regressional analysis for the target new cases;

Reference

Harvald Sv. Aa., "Remarks Regarding the Form

Factor", Comments to the Report of the

Perfor-mance Committee, 17th ITTC, Goteborg, 1984.

Crago W. A., "On Form Factor", Comments to:

the Report of the Performance Committee, l7

ITTC, Goteborg, 1984.

Hughes, "Friction and Form Resistance in Tur.,

bulent Flow and a Proposed Formulation for Use in Model and Ship Correlation", Trans. INA, vol. 96, 1954.

Gross A., "Form Factor", Appendix 4, Report of the Performance Committee, 14th ITTC, Ottawa,

1975.

Prohaska C. W., "A Simple Method for the

Deter-rnination of the Form Factor and the

Low Speed

Wave Resistance",

Written Contribution,

Re-port of the Performance Committee,

ll' ITTC,

Tokyo, 1966.

Gross A., Watanabe K.,

"Form Factor",

Ap-pen(lix 4, Report of the Performance Coniinittce, 13t!i _{ITTC, l3erliui/llainburg, 1972.}

Jourdain M., "On the Form Factor Evaluation",

Proceedings, 18th ITTC, vol. 2, pg. 139, Kobe, 1987.

Hoyle 3. W., Cheng B. H., "A Bulbous Bow Dc-sign Methodology for High-Speed Ships", Trans. SNAME, vol. 94, pg. 31 56, 1986.

I

select from the Data Base those cases which more resamble the target-one and statistically "surround the target";

S perform regression and derive equation;

.

verify how wrong is the prediction with the experi-mental value.

Acknowledgement

The authors are in debt with all tankery people of

I.N.S.E.A.N., whom during the decades are devoted

themselves to do their job with such a high

parteci-pation: if data were not so good it was sure no

equa-tion would be possible to obtain at all. Worth of note

are the collaboration the authors obtained from Mr.

Chierici L. and Mr. De Biase F. both of tecnical staff

of I.N.S.E.A.N., for collection of experimental data,

analysis and C)Pcurve determination. The authors are

very grateful to the Authorities of their own

Institu-tions for the encouragement received. The (1 + k) data. reanalysis were determined under the I.N.S.E.A.N. '84

Robb A. M.

, ¶Iheory of Naval Architecture", 23.

Charles, Griffin & Co.Ltd. London 1952.

Holtrop J.,

4A Statistical Resistance Prediction

Method with a Speed Dependent Form Factor",

Proceedings of he l7° Session of the SMSSH,

24.

vol. 1 paper 3, Varna, 188.

Harvald Sv. Aa., aResistance and Propulsion of

Ships", Wiley Interscienze Publication, John Wi-ley & Sons, 1983.

Genov E., Rocchi R., "A Statistical Power

Pre-,li.e,.',i ?t(r.(Io.l f.,, l',,,Ar, .hip.i

\Tarn.l., I ¶)9.

11. U*,cihi IL, ".1 ."(a(Is(I,:ol p.Purr l',r.JH:IIIfl /tfe:I/'o.l

for I )ee:,iu (.'o,H ) 1'4.4/I ui e:s,els ', I 7'" M ; II,

V.LulI1, I 08g.

V

II. fltit-iIii II., lIIt)tglt4zzII I)., ll,ill /1i:uI,vLee: ,I,Ld

.tre:d !)iiijii&vi&

lii:otIi,igi oi tl,o

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';( l4,,1.:(s.,zl 'J',J,'l for ll'ClIUbl( l'rr:l,r V

CI(',L.l of 1/IC .S1(Ci1V ( u,'ve: for /:lhe:'In.,,

IC3.ICLS ,

i'"I''I' I", Ai,,o,i, I.i) I

V Id.

NIiI,4IIlI,t S., It,i:,:i,-liiii:i

., l,.t,iu IL,

tII1T4.I1'1t4( .1i1 j'.,tI,i,e: ,lu l'.littlIl Tin! ''II, ,.i,1( I/o

I '.0 (1,1 l.,l&C I 'I''l( '1.": .1,4 (I/li I ,If I !,'u.i H ill Ii ,IeII,i

'II.1s,1 d$ IV(11t4'/l :'V 'MI, Veuii*.', I

ip'r

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If. lC.,t,.l*:,l%il I li'.i/Jr.'ti(.' .'.'pr,u,ieII loin

dci /"olt.,r, iii fr'oruii dl iVvi ,-1;no.r.itcL C i/ic!"

i4I J'tI't''l is jIrc4.s,, I 'INSF.,l iv ', IN S l' A N 'l'c.:I, ii ietI IC cptnI. 19S5-7.

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,,(sV ,.;,fl(: ,&t,ils lr , /& Ito, ,i& /', ,,,,i ', IN S I' A N

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/'r..';'H/.loTi C ,lc.lIc ( :,UI(/l IVO II, ,1,i ( -irii:' N .poIi

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'!)cini'jte:riii:ri I 'J l'o,,,i !.I,.tI,,V

.' Ic(/i't'l ,i,a.i

iii

1 r,ibir,ti t.' Pie: i,,I,u:,l ",

.ictioiis Vest. Japan Soc.

NivaI Aic!i., No.79,

NI LII II I '

21. lepott ot I'eiIotmaucti

4,ulliIIiI.Lc:, "De.ctip1zon

of 1 ll(

Y 1 'crft) r,nt 7ZcC (,o ,n,,t&tIe:

Itul /

'rcdit: hori

1'ri( 1 'rIHJr(I

U A I0II x I,

1.11 Ii, 1075.

2'2. A likow iI.z NI ..t ., "l"lLll .'"c,ilc i', lca.i tire' uie: II Cs of ihe: if ssl,i,&ec 144141 1'ou.'eti.j '..e./Jzi:ic:tii 11711/ ic .it/CstiJ !i,Lpi.)I'Ci/ICTZt iii 1/IC /,i1,ilJ.4)/ii(&i'7L 1', I:c:I jt-,,l4 ,f,l,1ri 1.' .'ehi1' ', (') /i III(, I',,%Vl'ilIt ,iis,

III 111411*1' ('.' CII 4 NI..cIi i,I

Morgan W.B., Linn W.-C. "Computational FlOW

Dynamics, Ship Designed and Model Evaluation",

4th mt. Congress of the I.M.A.E.M., Proc.s pp.

32.1,32.8, Varna 1987.

Oortmerssen, Van G.,

"Pre4icting the

Hydrody-namic Performance in Ship Design:

Tests or

Cornputations",CFD & CAD in Ship Design, Else-vier Science Publishers B. V., 1990, pp.233±245 25. Sasaki N., Kawakämi Y., "On the Scale Effect of

Form Factor", RF-8 Performance Committee 18th

ITTC '87, pp.4346.

2d. ScIi it,i,t:Iit' it NI., IVe.ke 'Ihrust I)cduc hioti fruTn

(jtitit ys te:ady i'roji uls i,,i I'cs Cs °, I PS'" 11:"I.(VV 'S7,

IiI ,*:(:4l liii :l 'Vol I .( I I I.

27. ScIi IIIIHCIII!il NI., 7he, Mc/iod of ç'uusysrady

I 'rup ,jl. 1074 u iid

i/i

l'riol on Hoard of l'tVIC 1ur

VWS

I(;,ut

I IM-I/YI, U4rljui Molt:I Il.,nui,

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r

I

uber of cases read : 24 Number of cases listed 24

SPSS/PC:co egw:100*(watagr-ffl/ff.

SPSS/PC:co watagr:1.017+2Otcb/( ( lb2t2)*(bt*(J.5)).

PSS/PC:1is flfli ff ec ed ee eg e ap cob.

1.135 1.23 .22 -.74 7.77 0 1 2.433 S 1.250 1.75 .21 1.5S -3:5 0 1 .922 10 1.235 2.47 .55 -1.60 -.s: 0 1 L1B6 11 1.320 -1.62 -1.18 .65 -6.76 0 11.643 :12 1.095 -1.61 -.35 1.11 0 12.643 13 1.130 3.29 1.19 1.16 7.26 0 11.7(16 14 1.250 .38 -1.32 -.16 -1.45 0 11.932 15 1.270 -1.35 .71 -.13 -4.5 0 1 1.532 :16 L32 -.S9 -2.15 .5? -0.73 ii I .903 17 1.230 3.05. 1.06 .16 -1.97 0 1 .503 16 1.230 -.06 3.03 .60 4.66 8 1 .903 19 1.270 -1.99 -2.71 -1.30 -.70 0 1 .903 43 1.246 -9.92 -.76 3,5? 4.93 0 1 1.805 44 1.265 -9.76 -4.61 -5.45 2.59 0 11.805 '45 1.295 -26.25 -4.96 -2.49 -.5" 0 11.805 MORE $1 PP EC ED EF EG El APP CBB 46 1.353 -2.61 -10.91 7.65 -5.5? 0 11.805 55 1.295 -33.35 -10.31 -7.20 -3.85 0 1 1.805 EF EC ED EE !10FE EC E1 APP CBF :211 -3.37 .63 -1.72 2.2 1: 1.962 :191 45 .6 1.50 i.4 I I 1.953 I I I

11

-,1 .02 -154 5 1 1.129 1.161 3.95 3.11 1.45 .:4 .0 12.356 4, I Cr-It .' Ci -1 "p u ''. _.1it

L.ENQnI PARAJETER

-LPR'LP DEPTH PARAI.TER C10 1. flOSS.SLCTIOH PAflA1ER

-L&TEHALPAR.AEIER c,__a_ -. Vou..&in PARAI.EIEfl - VPIVM. Fig. Bow'bulb pairnIef$

FG2

4;

4.

Ii

'I

//

2; 'ii (

7

I

I

I

11 TTc A

Nultiple R R Square Adjusted R Square Standard Error

F:

Variable RRS CA9L. GC' EEE FFF CC I HHH 989 CCC (Constant)

ttt$ HULTIPLE REGRESSION

It

Equation Number I Dependent Variable.. FF

26.07504 Signif F

tltt MULTIPLE REGRESSION

ttt

.Eqution Number Dependent Variable.. FF

Variables in the Equation .97972 95984 .92303 .01989 Sum of Squares 10239 00428 B SEB .01756 2..72938E-03 -.01489 3.94275E-03 .06882 01666 -1.96213 .61596 -.05125 01 102 -1.80231 .24 876 -.34334 ('8284 -1.64747 .67365 .0497! .7.24512E-03 -.37068 .06113 2.52539 .66572 1.64195 .12809 B ta .72962 -.56('94 .38432 - 60455 -.72673 -. 52734 -. 57479 1.01243 -1. 0 7804 .85251 Mean Square .00931 0O('36 6.434 -3,776 4.130 -3.186 -4.650 _7 -4.144 '1 _i 6.861 -6.064 3.793 12.818 T Sig I .0(1(10 .0026 .0014 .1)078 (1006 .0000 0014 (1308 0(101 V ' L (10(1(1

flC;;.4

Analysis of Variance DF Re r e ss ion 1.1 Residual 12 MORE MORE

FF

NNI F XXI EXIX KWR4 EKW84 CC COB APP EN

46 !.3$3 i.139? -1.51 1.78 -5.51 1 1.805 I 0

55 I.25 I.30L6 .09 1.24 -3.89 01.805 1 0

Nubpr of cases read 74 Number of cases listed 24

Cun! Midpoint o I.O& o I.OB 7 3 4 5 HickQram Frequency 1.50 1.10 prr CcunI Microint -I .70 _Y I

-I"

-W4fP-'I I

Gross-Ya1anabc - C'!'

II1i11ilflO P l.20 1.30 (I CT mlrdrne ________ 2 4 Iii! (r.qrs FreqilerIcy 1.40 t.50

±L

w --P

HNI rr ETIX Kt404 EKWB4 CC COO APP EN

I 1.210 1.71086 .07 1.74 2.72 1 1.962 I 0 71.190 1.20599 1.34 1.73 3.49 I 1.953 I 0 31.720 1.23321 1.09 1.23 .49 1 1.16? I 0 4 1.140 1.1197? -1.78 I.?? 6.65 I 2.079 1 0 51.160 1.16599 .52 1.23 6.14 0 2.356 1 0 61.140 1.14036 .03 1.18 3.73 I 1.015 1 0 7 1.270 1.71161 -.69 1.30 6.66 1 2.116 I 0 81.135 1.17927 -.50 1.?? 1.13 I 2.433 I 0 9 1.250 1.24812 -.10 1.?! -3.75 1 .9?? I 0 10 1.235 1.23388 -.09 1.23 -.52 1 1.186 1 0 II 1.370 1.31209 -.60 1.23 6.16 I 1.643 I 0 121.075 1.10251 .69 1.17 1.10 12.643 1 0 13 1.130 1.13614 .60 1.21 1.26 1 1.706 1 0 14 i.?50 1.25347 .71 1.?? -2.45 I 1.93? I 0 IS 1.710 1.24946 -1.62 1.7! -4.85 0 1.93? I 161.375 1.30363 -1.61 1.24 -6.73 I .903 I 0 Il 1.230 1.75072 1.68 1.21 -1.97 0 .903 1 0 lB 1.730 I.23I1 .14 1.?? 4.86 I .903 I 0 IV 1.770 I.?64 -.43 1.26 .10 0 .903 I 0 '3 1.746 1.25060 .31 1.31 4.93 .1 1.805 1 0 44 1.765 1.75213 -1.0? 1.30 ?.59 I 1.805 I 0 45 1.295 1.37574 7.31 I.?? -.51 1 1.805 I 0 1.10 -'5 3 1.1? 1.14 1 - . .__: .1;,, I 1.16 - . r.v 0 .05 1.20 7 .30 3 I.?? c 4 1.24

I--

_{I .80} I...J_ 3 1.26 - -.

'---7 i 2 1.18 1.30 ry I (I 1.30 1.55 ________________ UIJ.L_M.__.. .LL,._J.1 .I.J..4..IJ' 7 1.3? I I M--.-J -P 1.34 I 1.36 A 1.30 2.30 I