On weights and volumes of displacement type ships

4 MEl 1973 -

Lab. v.

Scheepsbouw-NAVAL SHIP RESEARCH AND DEVELOPMENT CENTER

W..hlngtOfl 'D.C. 20007

February 1971

ON WEIGHTS AND VOLUMES OF

DISPLACEMENTTY SHIPS

Approved for public release: Distribution Unlimited

SHIP PE.RFORMANCE DEPARTMENT RESEARCH AND DEVELOPMENT REPORT

w-i

DEPARTMENT OF THE NAVY

NAVAL SHIP RESEARCH AND DEVELOPMENT CENTER WASHINGTON, D.C. 20034

ON WEIGHTS AND VOLUMES OF DISPLACEMENT-TYPE SHIPS

Henry M. Cheng

Approved for public release:

Distribution Unlimited

TABLE OF CONTENTS

i

-.7 Page ABSTRACT 1 INTRODUCTION 1

BASIC PHYSICAL RELATIONSHIPS 2

DEFINITIONS OF WEIGHT AND VOLUME COMPONENTS 4

WEIGHT AND VOLUME EQUATIONS

METHODSOF SOLUTION

..

,, 9

11

EQUATIONS FOR ANALYSIS 14

SAMPLE CALCULATIONS 18

CONCLUDING REMARKS 25

REFERENCES 54

LIST OF FIGURES

Figure I - Plot of Furctiois G(ç), K(),

and çK(q) 26

Figure 2 - Plot of Functions P(), J(çfr), and (iJ(&) 27

Figure 3 - Plot of Charac.teristi.ó Length L0 28

Figure 4 - Plot of Equations (45) and (46) . 29

Figure 5 - Sample Ca1cu1ations Showing Effects of Range on

Total. Weight and Power fOr a Tanker 30,

Figure 6 - Sample Calculations Showing Effect on V0 / V of

VaiioUs Parameters for a Large Catamaran Carrier , ' 31

Figure 7 - Sample Calculations Showing Effect on WT of Various

Parameters for a Large Catamaran Carrier 32

Figure 8 Sample Calculations Showing Effect on F of Various

LIST OF TABLES

Table

1 - Tabulation of Functions G(), K(),

E(ç&),

J(),K(çS),andiJ(ç1i)

34

Table 2 - Tabulation of Ciarateristic Length L0

Table 3 - Influence Coefficient Formulae . 45

Sample Calculation, Destroyer DDG2 46

- Sample Calculation, Destroyer DDG-2 Modified 47

- Sample Calculation, 40,000-Ton Tanker 48

- Sample Calculation, Container Ship 49

Table 8 - Sample Calculation, Catamaran, Submarine Rescue Ship 50

Table 9 - Sample Calculation, Catamaran, Cargo 51

Table 10 - Sample Calculation, Catamaran, Large Carrier 52

Table 11 - Sample Calculation, Small Research Submarine 53

Page

Table

4

-Table 5

Table 6

NOTATION

Characteristic beam (L) Block coefficient V/LBD Block coefficient V, /LBd

1

Total drag coefficient' P7. / ( p U2 8)

Influence coefficient (Equation 42a)

Wetted surface constant S/V23

Parameter constant

Parameter cons tañt Y(jj ae R

Parameter constant (u3/y3)(d/D)(Cb/Cfi)

Parameter constant a4 T

/

'4 Parameter constant 05/ y5 Draft (L) Total drag (F) d Depth (L)

E1 Influence coefficient (Equation 42b)

e Weight Of energy source per unit time per unit power(ET 1/LFt)

V Froude number; function defined by Equation 35

Idyn Dynamic lift to displacement ratio

G Function defined by Equation 31

J Function defined by Equation 43b

K Funôtion defined by Equation 43a

Power fraction P/P0

L Characteristic length (V/V0)'"3

L d Dynamic lift (F)

L0 Characteristic length (V0 /V) 1/3

Parameter group (Equation 25)

B C C! Cs Cl 02 C3 c4 C5 p

41 Parameter group (Equation 27)

2 Parameter group (Equation 24)

41 Parameter group (Equation 26)

Parameter group (Equation 16) Parameter group (Equation 15)

m Parameter groups (Equations 17 thru 22)

NM Nautical miles P

Service power (FLT')

P0 Installed power (FLT 1) p

(VT/V)2/(Vr/v)l

M L /M

, an initial condition 1? Range (L) S Wetted surface (L2) Ii Ship velocity (LT 1) V Volume(L3)

V'

Nondimensional volume with respect to total volume

Vb Enclosed huilvolume (L3)

W Weight (F)

ae

e/y2i

a

a1 Volume per unit power (L3 /LFT 1)

a4 Proportionality constant relating 44 to WT

y

Density (FL3)

Density of fluid in which the ship operates (FL 3)

A Displacement (F)

Overall propulsive coefficient Parameter

-Mass density of fluid in which the ship operates (Slug/L3)

a3 _{Proportionality constant relating structural weight to hull}

volume Vb (FL'3)

a5 Proportionality constant relating W5 to VT

Function defined by Equation 29 Function defined by Equation 33 Subscripts refering to volume and weight components:

0 Usable payload

1 Power dependent

2 Power and range dependent

3 Structures dependent

4 Component whose weight proportional to total weight

5 Component whose weight proportional to total volume

6 Void or buoyancy control

A BSTRACT

This paper presents a parametric formulation concerning the volumes and Weights of ships of the displacement type. The formulation is .based on the assumption that the volumes arid weights could be related to certain

rele-vant design parameters in simple relationships. The expressions thus derived

lend themselves conveniently to analytical or graphical solutions that can be readily applied.

Algebraic equations for analyzing the effects of changes in any one

para-meter or group of parapara-meters are also developed. A table of influence

coeffi-cients is presented. Also shown are the results of some sample calculations.

INTRODUCTION

A ship is an engineering entity of considerable complexity. It is designed to meet certain functional and operational re4uirernents. A final design of such a vehicle, like

simi-lar engineering endeavors, is usually evolved through many stages ofdevelopment.

Gener-ally speaking there are four major stages; Conceptual formulation Trade-off evaluation

Preliminary design Final design

At each of these stages many decisions are necessary, and they are usually made by

com-paring the merit of the alternatives based on functional, technological, and economic considerations.

Initially the designer investigates different conceptual designs to establish the suit-ability of the concepts. Among the suitable conceptual designs, he then proceeds to make trade-off evaluations by developing the major performance parameters and by acquiring the overall performance characteristics, using a minimum of detail. Within certain restraints he

will have to decide which of the conceptual designs is best suited for the missions intended

and then proceed to develop a detailed design.

As the design progresses step-by-step from initial concepts toward a final design, many technical questions will arise, and answers Will have to be found. Questions concern-ing the size of the vehicle for a given set of design conditions or the effect of change in cer-tain parameters on the overall size will cercer-tainly be logical ones, especially at the initial stage of the development.

To facilitate the answers to questions of this sort, it is desirable to formulate general relationships that express the overall size in terms of relevant parameters so that the size of the vehicle can be estimated before proceeding to detailed development.

It is the purpose of this paper to analyze this general problem but oily for ships of the displacement type, surfaced or submerged.

The formulations presented are based on the assumptions that the size, i.e., the vol-umes and weights, of such ships could be grouped into a limited number of categories, each of which could be related to some relevant operational and geometrical parameters in tractable relationships. From the formulation algebraic equations are derived for the nondimOnsional characteristic form parameters whose coefficients consist of speed, range, drag, etc. The equations are then solved both algebraically and graphically for the unknown parameters. The solution provides a relatively simple relationship between the characteristic forth parameters and the relevant design parameters.

Based on the elementary principles of calculus, influence coefficients are Obtained which denote the relative change in the nondimensiOnal form parameters caused by a unit rel-ative change of design parameters. These coefficients provide useful tools for analyzing the possible effect of change in any particular design parameter on the characteristic form para-meter. Also shown are the results of some sample calculations, demonstrating the calculation procedureand illustrating the usefulness of the technique presented.

BASIC PHYSICAL RELATIONSHIPS

For displacement ships, surface and submerged, there are two basic relationships con-cerning weights and volumes, namely, (1) the total weight is the sum of all weight components, and (2) the total volume is the sum of all volume components. Using W and V to denote, re-spectively, the weight and volume, algebraically we have

WT J'Wi ( i)

and

T

=vi

(2)

Moreover, it may be assUmed that fOr each weight and volume component a linear relatIonship

exists, i.e.

Wi _{= y} V (3)

where is an average density of weight component W. Substituting Equation (3) in the right hand side of Equation (I), and defining an overall average density

T based on total weight,

i.e., y

_T = W - / V_{T T} , we obtain

Or, we may rewrite equation V = W1 / y and substitUte it in Equation (2), and obtain (5)

Also, the total weight mUst equal all-up forces which usually consist of buoyancy due to displacement and net dynamic lift force due to lifting surfaces or bodies

= A + LdYfl or

= A(l+fdyn)

where A is the displacement and fdyn = L / A

, a

fraction denoting dynamic lift force

relative to total displacement,

For convenience, the following nondimensional volume ratios are formed relative to total volume VT displacement volume V, and usable payload volume V0

From Equation (2) we have

where V1'= V/ V. 1

=g;rj

(2a) and VT

r

(2b) VT Vi (2c)

0_I

0

From Equation (4) we have

1 ' V' (4a) 17T 'Yi V (4b) and

V'YT \

VT 1 'O (4c) v0

4

_'T

The applicahi!ity of these equations depends upon the nature of the problem.

Similarly, nondimensional weight ratios may be formed based on Equations (1) and, (5). Since they can he obtained directly from the volUme ratios, we shall not express them here.

DEFINITIONS OF WEIGHT AND VOLUME COMPONENTS

To proceed with the formUlatiOn it is necessary to provide more details concerning

each of the weight and volume components and to provide definitions for them. We shall

attempt to catagorize these components in a gross fashion in order to present a general out line of the approach. For cases where a detailed analysis is necessary, the treatment could

be refined following the general approach presented here. Let the subscript i denotethe

fol-lowing categories of weight and volUme: Subs en Pt 0 1 2 3 4 5 Category Usable payload Power dependent

Power and range dependent Structures dependent

Other, whose weight is proportional to total weight

Other, whose weight is proportional to total volUme

Void or buoyancy ëonttol

We shall now discuss each of these categoried weights and volumes and express them in

I nondimensional parameters.

PAYLOAD

The payload of a ship is that portion of usable volume or weight for which the ship is

designed. Of course, for different ships the payloads are defined differently, e.g., for a bulk carrier the payload is the deadweight tonnage of bulk cargo with a certain density; for a small submersible, the payload is probably the weight of one or two persons, special instruments

and equipment, and space for adeqUate operation. In any case,the payload W0 and either

V0 or should be clearly defined.

POWER DEPENDENT

This categOry pertains mainly to the propulsion machinery. It is reasonable to assume that the volume and weight are functions of the installed power P. For simplicity it is

further assümGd that they are directly pioportionaI to the powerinstalled, he., V1 = a1 P0

where a1 is a proportionality constant (an average volume per unit of installed power) that

has a unit of L 2 _{T / F and a value that varies depending upon type} of propulsion system.

This V1 could be expressed in terms of operating conditions. The derivation is as follows:

V1 = a1 P/k,,

= a1 DTU /

=aDU

= a (DT/A)

=

Cd C F

L U (6)

where P is service power (FLT 1),

is power fraction P /P0

is overall propulsive efficiency,

a

= a1 / kri average

volume of power dependent component per unit of

effective power (L2 TF 1),

U is ship velocity (LT 1),

Cd is total drag coefficientbased on S,

S is wetted surface (L2),

C3 is wetted surface cOnstant (circle S),

s/v2"3

is Froude number based onV,

UiJv", and

DT is total drag (F)

Nondirnensionalizing Equation (6) with V., V, and V0 we obtain

V1,.=.C1 CdCsF(V/Vo)2/3(Vo/VT)

(6a)

and

where C1. y a U.

For convenience, a Froude.nurnber

_,

_V/fgV

based on V0 is intrOduced.

POWER AND RANGE DEPENDENT

This category consists of those items which are dependent upon both power and range. The derivation of an expression fOr V2 is similar to that for V1

V2 =

/

e (R/U) Ply2

= eRD /y2

=a DR

_T

=a(D/L\)AR

= 2 ae R Cd C0 (7)

where e is unit weight of energy soUrce per unit of work output (L 1),

I? is range (L), and

ae = e/( y2 ii), average volume per unit of "effective" work output (L2 V) Analogously, V isnondimensionalizedwith V,V,and V0

F'

(v/ i

)2/3 _{(Vo /VT)} and where C2

_aeR.

'1 1

=C C

V0 2 V0)2"3 (6c) =

!C2

_{C Cs F' (V0 /V)"3}

V C CdCs

/)2/'3

1 2 d 7a) (7.b) (7c)

STRUCTURES DEPENDENT

In a gross term the weight of ship structures is assumed to be proportional to the enclosed hull volume Vb, i.e.,

W3 = a Vb

Here, a3 is a proportionality constant and has a unit of FL It is dependent on theship

configUration, structural design, and constructipn material. The enclosed hull volume is de-fined as the total volume Under the uppermost deck, which extends approximately the total

length and width of the ship. Associated with it is an enclosed volume (block) coefficient

Cb which is defined as

Cb = Vb/ LBd

where L, B, and d denote length, beam, and the uppermost deck height above baseline,

re-spectively. The quantities are tq be defined to suit specific cases. Consequently, the

volume maybe expressed as

V3

d Cb

(8)

where D is draft, and CB is the traditionally defined block coefficient.. We have assumed

that thecharacteristi.c length and beam are the salme for both Cb and CB.

The nondimensional ratios are

V3. = V/ VT and V3 = C3v/Vo 0 where C3 = (ci3d Cb / y3 V CB) OTHERS

The remáiniñg volumes and weights;are expediently grouped in two major categories:

those components whose weight is proportional to ttal weight, and those components whose

weight iS proportional to total volume, i.e.

W4a4WT

where a4 isa proportionality constant and has a unit of force per mit of force, and

W5=a5V

where a5 has a unit of FL3. It followsthat

W4 = aW./ Y4 = a4 VTYT / V4 and its nondimensional.rates are

vo = C4

-

C VT/V

and V4 C4 VT/V0 0 where C4 = a4 _{T / V4} Similarly; V5 =

V/y5

_('°)

.V'= C5

(ba)

V5 Cc VT/V (lOb) V5

yr/V0

(lOc) Where. C5 = VOIDS

A broader meaning is applied to the term void. It includes all usable spaces which

havenot been used, e.g., accesses, hallways, ballast tanks, etc. For void spaces the

den-sityy6-O,

TOTAL

It should be noted that the term "total volume" implies all usable spaces. It includes not only those volumes:bounde4 by hull structures sUôh as cargo holds but also spaces utilized

above deck such as containers stowaged on the uppermost deck, and, there, the boundaries are not ship structural members but the cargos. In general

but for a submersible

and

V.>V>V

= Vb = V

WEIGHT AND VOLUME EQUATIONS

Equation (4b) may be rearranged to explicitly express V6 /V in terms of other corn-ponents

5

V6

_{YTT- 'ç-'}

-

v

y6

Sübstitutiñg Equation. (11) into Equation (2b) we have

VT

r

1

pi

-V

Here a density parameter Pj

= (.' -

'6) / T is introduced.

Using the expressions for V /Vderived previously, Equations (6b), (7b), (8b), (9b), and (lOb), and substituting them in Equation (12), we obtain a cubic equation of the nondimensional

char-acteristic length L0, which is defined

=

(V/V)"3

(13)

as follows

+ M1L0 (14)

where M1 and M0 are parameter groups which relate to the previously defined parameters in the following manner

=

(m m2)/m

M0 = - _{(PT -}

-

m5)(V/V) - m3] /m0

where m0 = p0 m1 = - C Cd C5 Pi 1 m2 = ' C2 Cd Cs ö0 P2 m3 - C3 p.3 m4 = C4 p4 rn5 C5 p5

and V. /V (or y7. / ye), a function of ship type, is considered to be a design criterion. For

example, for submerged vehicles V = 1, for surface ships V. /V> 1, and generally

(VT /V)catamaran> (VT /V)monohull

container

An equation similar to Equation (14) in terms of VT/V0 may be derived, having a form as follows L'03 + '2 + M0'= 0 (14k) where

L= 1/L0 = (V/V0)3

(23) (24) h1 = - - m - mS)(VT /V0) - /m3 (25)

In Equation (25) VT/VO (or YTO)' like VT/V in Equation (16), isalso considered to be a design criterion.

For submerged vehicles since VT /V0 =V/V0 = (L.)3 , Equation (14a) may

here-arranged

-+ ₀ (1.4b)

(VT/V)monohull bulk

For Equation (14) M 1/3 1/3 L0 =

k0

{[ô+(1+1/2]

+ whOre 6=+M0/1M01

Froth this we obtain the volumeratio of V0

V

(29)

(SQ) The new coefficients M'2'and M"are defined as

M'=-(m1 +m2) /(pT-m3_m4

m5) (26)

- mO/(pT-m3-ñz4-mS)

(27)

The nondimensional characteristi,c length L0, which is a form parameter expressing the ratio of payload to displacement,, is now algebraically related to Other relevant design parameters. The solutipns to Equation (14) or Equations (14a) and (14b) would explicitly express -either this form parameter or its reciprocal in terms of the various design parameters1 'the methods used to obtain such expressions are discussed in the following section

METHODS OF SOLUTION

Equations (14), (14a), and (14b) are cubic equations which can be solved either

alge-braically or graphically We shall discuss both of these methods presently Since Equation

(14a) is redundent to Equation (14) there is no need to discuss its solution

ALGEBRAIC SOLUTION

All cubic equations encountered herein are standard forms with coefficients consising of varioUs parameters that ,are assumed'to be known or can be arbitrarily assigned. There-fore, the solutions can be obtained readily.using standard formulas.

1/31

where the function G() is defined as:

113

()

_={E

+(1+c)h/2J

+

Ea.(i+)h12]1'3J

₍₃₁₎

The values of function C() for 3 = + 1, i.e., iIf <0 are given in Table 1 and in Figure 1.

For cases where (1 + ) <0, the solution expressed in Equation (30) still holds, except that

the function G () is defined differently.

(3a)

where

cos

(_.)l/2

and a is a constant which assumes 0, 2ir/3 or 4rr/3 For Equation (14b) (Submerged Vehicles)

1/3 2/3 2/3

L=

{E( 1 +

b)2

+

i]

+[i

+ çfr)1' /3} ₍₃₂₎ where fr = (M;'./ 3) / (M1'./4) (33)

Similarly we express the volume ratio / V0 for submerged vehicles as a function of çtr

V0 4 (34)

where

=

{[i

+

)'

+

1]'

[(1 + )1/2

]

1/3} (35)

The values of function F(i1') are also shown in Table 1 and in Figure 2. These expressions for submerged vehicles are similar tO those shown in Reference 1.k

With an assigned valuéfor VT /.V and other parareters, and withtle solution for volume

ratio V0 /V thus obtained, we can proceed to solve for other volume components, using

ap-propriate equations previously derived.

r

Here, we collect a set of relevant equations for thevolume ratios:(form parameters)

V2 m2 VT p2 V5 m5 VT PS

5v

E;

VT i I (6a) (7a)

We have seven equati.ónsfor. seven nondimensional volumes, which may be called

design-form parameters. It should be noted that some of the parameters are form dependent,,

there-fore., an iterative procedureis necessary. GRAPHIC SOLUTION

The form of Equation (14) suggests.that the unknown form parameter (volume ratio) is

to be fOund in termã of the coefficients; i.e.

V0

= (hi

hi

TI TI O 1

"r

'T

Since the coefficients are functions of parameter groups:m, which in turn are functions of

other parameters: , general, we may express

(36) 1/3

(PT_m4-m5) (VT/V)-m3

(14) V m V mo 1/3 Vt .m1fV0

-=

---VT p1 VT (8a) TTT p.3 VT V4 m4 (9a) VT P4

VT VT

(Li lL2,(L3, . _{. )} (37)

Theoretically, cürvés of V0 /v may be plotted in a multidimensional i space. For simplicity,

let us illustrate the graphic solution of quation (14) in two dimensions, i.e., in the two

pa-rameter groups M1 and .M0. The results are shown in Figure 3. It is noted that the rate of

change in is greater for small values of and H0. For M values larger than 10, the

change in L0 is nearly linear For a more accurate estimation, tabulated values are pre-sented in Table 2 for values of i1 and W0 up to 20, with an interval of 0 5 for H0 and of

1 for M For intermediate values use interpolation

For a weight-limited or volume-limited vehicle, the value of the form parameter V0 /V

(or L0) is required to be more than a certain minimum For a given such requirement, Figure

3 shows the bonds imposed on H1 and H0 For example, if (L)min = 0 6, for a given value

of ''o of 5, the value for H1 has to be 8 or lower, likewise, for a given value of H1 of 8, the value for H0 has to be 5 or higher.

EQUATIONS FOR ANALYSIS

In studies that deal with problems of a bräad, general nature it is always important to study the effect on the whole of a change in any one parameter. To facilitate this kind of

analysis it is necessary to formulate mathematical models for the problem on hand an to

pro-ceed with the analysis by changing either one parameter or a combination of parameters at ,a time to see what effect the change has on the whole.

Analyses for small changes in parameters are often called sensitivity analyses.

For-mally, we may state as follows. For a function f =f (x , x2 , x, . . , x,), which is a

func-tion of variables x1 , x2, x3, . . . , x, the total differential is

df

=

L

(38)

1= 1 /

fOr small discretechanges in x1, the total change in f may be approximated by the following Af

&f

=.4

A x.

and the relative change in fin terms of relative changes in x1., is, therefore

where C1 is:an influence coefficient which denotesthe contribution to the relative change in f due to a unit relative change of

X13f

C.=L_

(41)

fax1

Now we can apply this concept totheproblem on hand. Take Equation (30), for

ex-ample. Here, we have V0 / V expressed in terms of M0 and , both functions of variable

parameters p.s. It therefore follows that the influence coefficient for V /V may be formally

expressed 1.

C1= K()1

+ (42a) Where (43a)

Similar equations may be derived for submerged vehicles based on Equations (34)

a.

.L

3M'.

E1= J(;/i) + (42b) Where 1

ap

- )Th

(43b)

The values of the functions K and J are tabulated in Table 1, and they are plotted in Figures 1 and 2, respectively.

For given small changes in any of the variable parameters , we can calculate

ana-lytically all other required quantities in Equation (42a) or (42b) and obtain a corresponding

value of C1, or E1 for a submerged vehicle. The expressions derive for C and E1 due to

change in parameter groups m0 through m5 are tabulated in Table 3

The concept pf influence coefficients can be very useful for cases where the changes in the parameters:are relatively small. It is not suitable for cases where the changes are relatively large, however. The large changes may result from a choice of system components that had considerable volume and wOight difference or may be assigned arbitrarily to simulate potential advancement in certain areas of technology to see whether the effects are

suffi-ciently attractive to justify future research efforts. For these cases the following approach may be applied.

with

= m1

= - [(P,_m4_ri5)(VT/V)

where additional subscripts 1 and 2 have been introduced for identification, 1 denotes a

given condition, 2 a new condition. Combining them, since is assumed to be the same,

we obtain m02 X12

=(1+q)L__

m01 X11 or X12

_r

m02 X02-1

- 1(1 + q) - --. I I q

Xii

_L m01 X01J/

where q denotes a given ondition q = M11 L0 /41

For given values of q and M /M , the relative changes in X0 and X1 ace

in-versely proportional to each other. Case 1 - Effect on Design Forms

The effect on design forms may be obtained in a straightforward manner. First,

cal-culate a new set of parameter groups M's, based on other given parameters, then solve,, either

analytically or graphicaI1y, for the fOrm parameter V0 /V.

Case

2 -

Effect on Other Parameters for

a Given Form Parameter

When the form parameter is to remain unaltered,, we are interested in investigating the

effect of one parameter on the other. The relationships may be derived as follows. Based

on Equation (14), we write two equations for the form parameter V0

/V(or

L0) for two

dif-ferent sets of coefficients.

L -1-(X11/m01)L0- 0

(X12 ) L ₂ 0

(44 a)

Special Cases

1. When the coefficients M1 and are independent of each other, a simplified

relation-ship may be obtained

MO2 fM12

-'= 1 -

1

\

ii

= 1

M11

These two equations provide simple relationships between the relative changes in H0 and

,one expressed in terms of the other, for a given condition H1 . These simple

e*pessions provide answers to such questionsas how much effect ,a change in H0 (e.g., due

to change in structures) would have on H1 (e.g., range) or vise versa. They are also pre-sented in Figure 4.

2. For the effects of changes in one parameter on another parameter within the same pa rameter group M

Effect of change in m1 on m2 or vise versa, with no change in H0

rn12 _{/ m22}

-- 1 - q1(

-1

m11 \m21 where m2

ql -

_m11

This linear relationship is similar to Equation (45a), and Figure 4 may be used for various values of q1.

Since the parameter groups m (themselves parameters) are functions of L,any change in them could be considered as Ohanges in one or more j's; consequently, the previously de-scribed relationshipscould help in evaluating, for examples theeffect of reduction in machin-ery weight (change in m) on increae hi range (change in m2).

Effect of change of m3, m4, and rn5 on each other (H1 remains constant).:

m32 / 1 - rn42 - rn52

=i+q2(.

p-i

m31

\i_rn41 m51

or M12 (46) (47a)

)

(45 a) (45b)

where 1 - rn41 -rn51

_fVr)

or or 1

I

V\

(Vr\

p Cl

/1

in52

-Ip-\1 -rn51 m31 m41 (Vr./ 1 -rn41 q5 m5 rn3 rn51( VT/V)1 SAMPLE CALCULATIONS

To demonstrate the usefulness of the techniques developed, a few sample calculatiOns are presented in this section. For convenience, a simple computer program has been w:ñtteh. SURFACE, SHIP - DESTROYER

In his discussion of the factors that affect tIe size of destroyers, the author of Refer ence 2 presents data for volumes and weights of two destroyer designs, DDG-2 and DDGFY67,

(47b) (47c) rn52 1

fl_rn42

= I ± p m51 _L

\1-rn41

where q3 rn5₁ = m 1

If we are interested in the effect of increasing range and payload on the fôPm param-eter V0 /V, all other paramparam-eters being the sathe, we cn perform a new set of calculations. Table 5 shows the result of such a computation. It should be noted that four input quantities have been changed:

which have resulted in a different set of answers, the major ones. being: BASE. TABLE 4 MODIFIED TABLE 5 V0 / V 0.45945 0 .5 8021 Displacement in tons A 4730 7170 Total Volume in _VT cubic feet x10'5 7.2026 11.794 Payload in tons 450 650 Payload density in ye pounds/cubic feet. 13.25 10.0 VT/V 4.35 4.7

Range at full power in NM 2200 2700

BASE MODIFIED

TABLE 4. TABLE 5

Total power in horsepower 71684 94582

It is wOrth notingthat the major differences between the DDG-2 and the study made for

DDG-FY 67 as reported in Reference 2 are the payload and range. Had the other differences been taken into account,, one would be able to estimate the general characteristics of a ship which may resemble the DDG-FY 67.

SURFACE SHIP - TANKER

In Table 6 a set of calculations was made for a typical 40,000-ton tanker. All the in-put data were estimated based on References 3 - 5.

It is interesting to note that ,for this tanker, due t. the nature of the cargo carried and

the proportion of cargo to total ship, the influence coefficient Cm is 0.95615, which

indi-cates that al-percent change in in0 (say cargo density ) will cause a 0.95-percent change in

the form parameter V0 / V; whereas, for the destroyer case the effect is 039 percent as shown

The ttal volume-to-displacement volume ratio used in the computation was 1.464. To investigate the effect of this quantity on the form parameter, additional calculations were made for VT/ V values, ranging from 1.3 to L7. The effect for this particular ship, shown as fol-lows, seems to be very small but this observation must not be generalized; see discussion on

Also calcUlated were two additional c-ases havingdifferent values of total drag

coef-ficients: Cd = 0.00238 and 0.00288. The former is 10 percent lower than that assumed in

the previous calculation, and the latter is 10 percent higher. The effect on the form

param-eter V0/Vis shown as follows.

The effects of Cd on the form parameter could also be estimated based on the influence

coefficients. Since the Cd value affects only the parameter groups m1 and m2

propor-tionately, the influence coefficients C'm and Cm for the base case, which are 003605 and

0.089147, respectively, are each multiplied by 10 percent and are added t.gether to estimate.

the total effect. The values thus obtained area +1.2525 2 percent, which are rather close to.

those obtained from the separate calcUlations.

The table also shows:the changes in power. Normally, for a 10-percent difference in

drag, all other things being unchanged, one would get a 10-percentcorresponding difference

in power. Whereas, the calculated values, though very close to 10 percent,. do show the inter-.

play between the overall size of a vehicle and themachinery component.,

Percent increase Percent increase Percent increase Cd in Cd V0/V in V0/V P0 in P0 0.00238 -10 0.75853 1.25 17886 -10.7 0.00262

-

0.74917 20022

-0.00288 10 0.73990 -1.24 22192 10.8 large catamaran. TABLE 6 VALUES VT / V 1.3 1.464 1.5 1.7 Percent of change in V./V -11.2 +2.5 + 16.1 Vo/V 0;75105 0.74917 0 .74877 0.74648 WO/WT 0.70411 0.70235 0.70197 0.69982 wT 39767 39866 39888 40010 Percent of change in W7. - 0.250 + 0.055

+0.36

To investigate the effects of range on the major characteristics of the ship, two addi-tional sets of calculations were made, one for range of 5,000 NM (naUtiëal mile) and the other for 15,000 NM. The results are shown as follows

The total weight and power are plotted in Figure 5. Their relationships with the range are. bout, but not exactly, linear. For a relatively smaller change in range, the influence

coef-ficient Cm could be used, since it affects only the parameter group m2.

SURFACE SHIP.- CONTAINER SHIP

A fictitious container ship was concocted, using basically the same data as were used.

for the tanker, except that the cargo density was reduced by half, i.e., y0 = 30

lb/ft3

in-stead of 60, which means that the cargo volume was doubled. This is to be facilitated by the

Use of space on the main deck. The total volume-to-displacement volume ratio is changed

from 1.464 to 2.21. The calculated results are shown in Table 7. Compariig the results for this fictitious container ship and those fOr the tanker, we find the major differences as folloWs

5000 0.78309 38140 19439

10000 0 .74917 39866 20032

15000 0.71630 41696 20630

Tanker Container Ship

Payload density in pounds/cubic feet 60 30

V0/V 0.74917 1.4813

Total volume in cUbic feet x 10 2.0427 3.119 1

Range _{V0 /V} WT P0

NM Ton F'

p

W5 in tons 652 995

The change in W5 is simply due to the assumption that some of the weights are directly pro-portional to the total volume. Since there is considerable difference in VT, the value of W5 is proportionately changed.

SURFACE SHIP - CATAMARAN

Submarine Rescue Ships

The submarine rescue vessel PIGEON (ASR-21), which is presently being built, is of the twin-hull type. The general characteristics are known, and the weight components hav2 been estimated. Based on these available data we'can estimate the other essential input

It should be noted that the main "payload" for this particular ship is a rather spe-ôilized cargo; the four deep-submergence rescue vehicles (DSRV) and the associãtéd handling gears.

It should also be noted that the primary reason for adopting the catamaran configuration for this service was to solve the unique handling problems associated with the rescue vessel; consequently, the other advantages offered by a catamaran sUch as inôreáseddeck area were not fully capitalized.

Cargo Catamaran of 4500 Ton

To illustrate the special feature 9f carrying low-density cargo, a fictitious catamaran is contrived using the ASR as a basis. It is assumed that this ship has the same general characteristics as the ASR, except that it carries a much lighter cargo by fully utilizing the space above the main deck, and some of the capacities, which were fOr special services, have been converted for general cargo purposes. This results in an increase in payload from 260 to 1200 tons. Assuming the cargo density to be 11.25 lb/ft3 instead of 19.4 as for the ASR case, and making appropriate adjustments in categories 4 and 5, we obtain a new set of input fOr computation. The results are shown in Table 9.

Comparing Tables 8 and 9, we find the differences in the major characteristics between this cargo-carrying catamaran and the basic special-service ASR are:.

ASR Catamaran

Cargo-Carrying Catamaran

Payload in tons 260 1200

Payload density in lb/cubic foot 19.4 11.25

V0 / V 0. 1918 1.5396

Displacement in tons 4472 4434

Power in horsepower 6012. 5978

0.28662 0.01806

Also, it should be noted that the calculated influence coefficients are tharkedly differ-ent owing to the differences in ç values, which reflect the significant role played by the pay-load density y0

Large Catamaran

The catamaran type of ship, owing to its unique features, has been considered for such military applications as aircraft carriers. Extensive studies have recently been made. It is therefore considered appropriate to include one sample calculation for a large catamaran which may represent a possible carrier.applicatilon. The results are shown in Table 10.

To investigate the effects of some of the important input parameters on the form pa-rameter V0 /V, total weight WT , and installed power P0 a series of calculations was

per-fOrmed with variations in the parameters of V. /V, range, ruel rate, payload, payload density,

machinery space specific volume a1 , average machinery space density y1, and overall

pro-pulsive coefficient i; results are shown in Figures 6-8. Mst of the curves shown are

al-most, but not exactly, linear with respect to the abscissa, representing percentagechange in

input parameters. For the range of variations shown, similar estimates of V0 /V could be

made using the influence coefficients shown in Table 10. The fact that, for example, the curves labeled 2 and 3 for changes made in range and fuel rate, respectively, almost coincide with each other could be expected. Had the influence coefficient Cm been used, a single

straight line would have been obtained, irrespective of the source of v2ariation, whether range

or fuel rate, since both affect the parameter m2 in similar manner. Also evident are the ef fects of a1 and y1 both of which, for this particular example affect the parameter group rn1 in the same way as shown by the curves labeled 6 and 7 in Figures 6-8k

Comparing the influence coefficients in Table 10 with those of the tanker in Table 6, we find that they are markedly different because the weight distributions are very different for the two ships. This is significant for estimating the general characteristics of the ship

in question. For example, the values in Cm and Cm for this large catamaran are much

larger than those for the tanker. As a result, the effects of change in the total volume-to-displacement volume ratio Vt/Von the general characteristics as shown in Figures 6-8 are no longer small as in the tanker case. The curves labeled 1 on these figures, which al-most coincide with curves 2 and 3, demonstrate that the role played by VT/V is now as

signif-icant as change in range or fuel rate. (It should be noted that this Observation is coincidental. It is true only for this particular ship and for the particular set pf input data used).

SUBMERGED SHIP

-SMALL RESEARCH SUBMARINE

The formulation presented is intended to be applicable also t. submerged vehicles.

To illustrate, a small two-man research submarine will be considered. This

vehicleisas-sumed to be self-propelled, t. be capable of operating at a velocity of 10 fps, and t. have an

endurance of 50 miles. It is assumed that buoyancy material having an average density of

25 lb/ft3 is used, if needed, and the payload consists of personnel and equipment for the mission. The calculated results are shown in Table 11. The so-called fuel rate printed in the input is really the specific weight of the battery, or any other kind of energy source, per unit of work output. The results indicate that the total vehicle weight is 5.9791 tons, the payload is 19.568percent of the total weight, and the payload is 47.8percent of the ttal

vol-ume. It also shows that to achieve a neutral buoyant condition, 1,535 lb (0.68533 tOn) of

From the calculated influence coefficients, we find that both C_m2 and C_m3 are rela-tively larger than the others, which means that the size of the vehicle is predominately af-fected by the parameter groups m2 and m3. This indicates that for the set of design

param-eters and requirements used to substantially reduce the overall size, improvements will have

to be made in the cOmponent parameters, which make up the parameter groups such as lighter

energy source or lighter construction material.

CONCLUDING REMARKS

The technique presented in this report provides a simple tool for estimating form

pa-rameters that depicts the general characteristics of a ship for a given set of nondimensional

design parameters and design requirements. Though the formulation is simplified, and

ad-mittedly in some areasthe approaches have been overly gross, it does serve a useful purpose, especially at the initial stages of developing a design.

It is contemplated that some refinements will be made to the formulation to provide

more accurate initial estimates. A similar, but much broader treatment of problems of this

general nature has been presented in Reference 6. It may be of interest to the reader since it provides a comprehensive, systemati,c exposition of engineering design procedures.

It should also be noted that the general approach adapted, specifically the formulations

developed here for sensitivity studies, can hO very useful, to research administrators in

tI

Figure 1 - Plot of Functions G (), K (q),

and K (ç) 0 -5

I0

0 -4 1 2 3 4

120 100 0 .-80 60 40 20

iiaiui

ill.."

I_1iiiuuupp

1ppr"

lii

4111111

1

Figure 2 - Plot of Functions F(), J(q),and çbJ()

2.4

2.0

1.2

0. 8

0.4

1 2 4 140 2,. 8

2.8: .2.4

2.0

1.6 1 2.

0.8

0.4

dlli

...:II!1P1

--S...

1 2 .3 6 10 12 15 20 10 15 20 MJ

2 1 2 1/5 1/2 2 4 10 10 2 qUM11L0/M01 -

A

q OR q

- V

q1.m21/m11 -:1

£4112.

11

0 M12/M11-1

Figure 4 - Plot of Equations (45) and (46)

(I)

z

o 42000 40000 0 38000 5000 10000 RANGE, NM

Figure 5 - Sample Calculations Showing Effects of Range on

Total

Weight and Power for a Tanker

15000

10 _-10 5 6,7 CURVE CHANGE IN. 1

v/v

2 RKNGE 3 FUEL RATE 4 wo 5 6 o.i 7 1 8 3 4 5, 8 6,7 2 20 10 -20 -10 0 PERCENT CHANGE Figure 6

1b 0 _-10 CURVE CHANGE IN 1 7 8 6,7: PERCENT CHANGE

Figure 7 - Sample Ca1culations Showing, Effect on WT of

Various

Parameters for a Large Catamaran Carrier

20

10

0

-10

5, o _-5 CURVE CHANGE IN 1 VIV 2 RNGE 3 FUEL RTE 4 w 5 6 8 1 3, 6,7 0 PERCENT CHANGE

Figure 8 - Sample Calculations Showing Effect on

P0 of Various

Parameters for a Large Catamaran Carrier

30 20

z

10 C.) 0 0 r. 0 a.

z

-10 u.s C,

z

200

z

30 -20 -10 10 20

TABLE 1

Tabulation of Functions G(qS), K(qS), F(/'), J(oli), çSK(ç5),and çrJ(&)

C K F J K IpJ 0. u.233)O0 01 0.250006 CC C.4C0030 01 C.ICCCCE 00 C. 0. 0.031 i.l64S80 Cl -0.669360 72 U.466C92 11 0.142251 20 0.069361-Cl 0.142250 00 0.002 3.156156 Cl -0.427980 C2 0.512336 01 0.923220 02 -0.655570-Cl 0.164640 00 0.003 0.152826 Cl -0.325941 02 0.531030 01 0.715056 02 -c.9e03I-Cl 0.215720 CC 0.004 ).l4580 Cl -0.27'.536 C2 C.548031 Cl 0.603C00 02 -0.139016 CO 0.241231 00 3.005 2.142331 01 -0.238146 C? C.562150 CL 0.526636 02 -0.119070 CC 0.263316 00 0.006 3.139146 Cl -C.Z&2070 C2 0.574560 Cl C.471661 02 -0.127240 CC 0.263011 00 2.007 3.036360 Cl -0.l2320 02 0.566671 31 0.429900 02 .0.134626 CC O.3C0951 00 0.003 0.130870 CI -0.176721 C2 C.597560 01 C.096640 02 -0.141760 CC 0.317471 00 0.009 0.131611 Cl -0.164033 02 0.637041 31 c.365070 02 -0.147630 CO O.!32B91 00 0.001 0.129540 01 -2.153471 72 C.61754E 01 0.347390 CO -0.153470 CC 0.347580 CC 0.011 .0.121636 Cl -0.144521 CO 0.626921 Cl C.2t25E 02 -0.150576 Co 0.361091 00 0.012 ).12505( 00 -0.136611 02 C.6356S0 31 0.311761 00 -0.164170 CC 0.374110 00 0.013 0.124162 Cl -O.IOCCO6 C2 C.644236 01 C.257350 02 -0.165110 CO 0.306550 CO 0.014 9.122600 01 -0.124061 02 C.652471 01 0.284621 02 -0.173620 CC 0.398470 00 0.015 2.121130 Cl -0.118890 CO 0.660440 31 0.273290 32 -0.178730 CC 0.609930 00 7.016 3.115738 Cl -0.114161 02 .668100 01 0.263116 02 -0.162668 CO 0.420980 00 C.017 2.119430 71 -0.105SCE CO C.675706 01 C.253916 02 -0.186830 CC 0.631650 00 0.018 2.117126 Cl -0.116C30 C2 0.683048 01 0.245546 02 -C.19C850 CC 0.441970 00 0.019 2.I1SQIO Cl -0.130491 02 2.690190 01 0.237996 02 -0.194130 CO 0.451990 00 0.020 0.114750 Cl -0.992490 Cl C.69719E 01 C.23C660 32 -C.ISO5CO CO 0.461720 00 0.021 3.113631 Cl -C.9626C0 Cl 0.706046 01 C.224376 02 -C.202151 CC 0.471180 CO 0.022 3.112560 Cl -0.934960 01 C.710750 01 0.218366 02 -0.205691 CC 0.460400 CC

0.023 j.Il1521 Cl -o.9q29E CI 0.717536 01 0.21218E 02 -0.209140 CC 0.489386 CO

0.024 3.11 .J530 Cl -o.e05361 Cl 2.123191 01 C.207571 02 -C.212490 CC 0.698160 Co 0.025 3.135570 Cl -0.663050 CI 0.702150 Cl 0.202690 02 -0.215766 CC 0.036738 CO 0.026 2.138646 CI -0.84213E 71 C.7364C6 00 0.198126 02 -0.218951 CC C.315125 00 0.007 0.107741 01 -0.822486 01 0.742551 01 C.l532E 02 -0.222070 CC 0.023328 00 0.026 3.106660 Cl -0.823980 Cl C.748621 Cl 0.l8977E 22 -0.220111 CC 0.031360 CO 0.029 3.106020 Cl .0.786531 Cl 0.754596 tI 0.105951 02 -C22O09l 70 0.309256 CO 0.030 0.105230 01 -O.17CO30 Cl 0.760450 01 0.182330 02 -0.231016 CC 0.546986 00 0.031 2.104400 CI -0.154412 CI C.76631E 01 C.170851 02 -C.233871 CC C.054571 00 0.032 .103600 Cl =0.739581 CI 0.172050 01 C.175650 CO -0.230670 CC 0.062036 CO 0.033 3.152861 Cl 0.705490 Cl 0.777130 01 0.172536 02 0.235410 CC 0.369350 CC 3.034 3.102136 01 -,O.112C8E Cl 0.787340 01 0.109570 32 -0.242110 CO 0.576950 00 0.035 2.131410 Cl -0.659296 01 0.788081 Cl 0.106756 02 -0.244756 CC C.58364 00 0.076 .l3J1lE CI -0.66719E 01 3.794371 Cl 0.164060 02 -0.27350 CC 0.590610 CO 2.037 0. 17.,000 21 -0.675426 Cl 3.rqqecE 01 0.181466 02 -0.249910 CO 0.597460 00 3.038 0.993570 CC -0.664266 Cl C.605170 01 C.15501E 02 -0.252421 CC 0.604241 00 0.039 .98735E CC -0.653586 01 C.812591 Cl 0.158640 02 C.204896 CC 0.610900 00 0.040 2.987671 CC -0.643308 Cl 7.815771 01 0.154371 02 -0.257321 CC 0.611466 00 0.041 3.974438 00 -0.630438 Cl 0.820991 01 0.152181 02 -0.259710 CC 0.623946 00 0.042 3.968328 CO -O.63398E 01 0.826070 01 C.I5C060 02 -0.262076 CC 0.630326 00 0.043. 3.962340 CC -0.614876 01 0.831306 01 C.186056 02 -0.264391 CC 0.636626 CO Ci244 .956400 CO -0.626090 01 c.6563g0 01 0.146101 02 -0.261680 CC 0.642841 00 2.045 0.550751 CO -0.59764E 01 0.841440 01 0.144220 02 -0.268946 CO 0.288971 Co 0.046 0.945021 CO -0.585481 Cl C.84645E'bl 0.142400 02 -0.211161 CC 0.055006 00 0.041 0.535606 CO -0.581601 Cl C.851428 01 C.l40640 C2 -0.273350 CC 0.061026 CO 3.048 0.534190 CO -3.514C00 Cl C.85636E 01 0.138340 02 -0.275028 CC 0.066536 00 0.049 u.920e80 CC -0.568640 Cl C.861251 01 0.137306 02 -0.217600 CC 0.072170 CC 0.057 3.923666 CO -0.559536 Cl C.866121 Cl 0.135111 02 -0.279766 CC 0.678506 CC 0.051 3.916540 CO -0.55264E 31 3.670951 Cl 0.134170 02 -0.281848 CC 0.864260 CC C.052 0.918510 CO -0.543960 Cl 0.875740 Cl 0.132671 32 -O.2839C1 CO O.0699CE CO

0.053 9.90856E CO -0.535450 01 C.88031E 01 C.l'l22E 02 -0.285931 CC 0.293480 00

0.054 u.903736 CO -0.533226 01 C.085250 01 0.129626 02 -0.287546 CC 0.701011 CO 0.055 3.898936 CC -0.527130 Cl 0.885950 01 0.178450 22 -C.28S92E CO 0.706471 CC 0.036 2.894730 CO -0.501216 01 0.894630 Cl 0.127122 00 -0.291880 CC 0.711880 CO 0.057 .0.889600 CO -0.315478 Cl C.899281 01 Ol20836 02 -0.253820 CC 0.717230 CC 0.058 0.885001 CC -0.539880 Cl 0.903906 01 C124571 02 -0.293738 CC 0.722520 00 0.059 2.883580 CO -0.504456 01 0.908560 CI 0.123300 02 -C.297636 CC 0.727771 CC 0.060 0.876176 CC 0.499l70 01 0.913C70 00 O.l22l6E 02 -0.299300 CC 0.732966 00 0.061 0.871830 CO -0.494031 01 C.Sl7tlE CI 0.121000 02 -0.301366 CC 0.736100 00 2.062 0.867550 CO -0.469021 Cl 3.922131 01 0.119871 02 -0.303198 CC 0.743190 00 0.063 0.860340 CO -0.466136 CI 0.926633 Cl C.11677E 02 -0.305CC0 CC 0.746240 00 0.064 0.659198 CO -0.479386 01 0.931106 01 .C.l1769E 02 -0.306800 CC 0.753230 CO 0.065 0.655116 CO -0.4 01 3.935566 01 0.116640 32 -0.308580 CC 0.350150 00 0.066 0.851078 CC -0.470210 01 0.909950 01 0.115620 02 -0.310341 CO 076309E 00 0.067 2.847126 CC -0.465800 Cl 0.944406 Cl 0.118620 02 -C.312C8O CC 0.767960 CO 3.i168 0.043180 00 .0.461480 Cl 0.948790 Cl 0.113646 32 -o.ol3ell CC 0.772766 CC 0.069 0.855320 Co -0.457270 01 0.953150 01 0.11269E 32 -0.715520 CC 3.777561 00 0.070 0.835506 CO -0.433166 Cl 0.957301 01 0.111760 02 -0.317210 CO 0.782301 00 0.071 0.831751 Co -0.449141 Cl 0.561836 Cl C.11084t 22 -0.310890 CC 0.787006 00 0.072 2.028030 CO -0.445210 Cl 0.566140 01 0.109950 32 -0.320550 CC 0.791661 CO 0.073 3.824370 CC -0.441370 Cl 0.970440 01 5.109080 02 -0.322200 CO 0.796280 00 C.074 0.823760 CO -0.437616 Cl 0.97471001 C.1C8220 02- -0.323830 CC 0.800660 CO 3.075 0.817151 CO -0.433930 01 0.978570 01 0.607390 02 -0.320456 CC 0.805411 00 0.076 3.813660 CO -0.432341 .31 3.983210 Cl 0.106570 02 -0.327050 CC 0.809921 00 0.077 3.81)180 CO -0.426016 Cl 0.987431 01 0.105770 02 -0.320641 CC 0.814350 00 0.078 0.836756 CC -0.423360 01 C.99l64E 01 C.104966 02 -0.330226 CC 0.818830 00 0.079 0.803350 CO -0.415980 35 0.995830 00 0.1C421E CO -0.331780 CC 0.027240 00 0.090 2.800006 CO -0.416671 01 0.100031 02 0.133450 02 -0.333301 CC 3.827618 00 0.081 0.056690 CO -0.413420 01 0.100620 02 0.102711 32 -03334876 CC 0.831951 00 0.082 0.790416 CO -0.410246 CI u10083E 02 C.101986 02 -0.336390 CC 0.836280 CC 0.083 3.790181 CO -0.437121 Cl C.101241 02 C.1C1271 02 -0.337910 CC o.e40531 CO 0.084 0.786980 CO -0.404001 CII 0.101650 02 0.100570 C2- -0.339410 CO o.e4478E Co 0.080 2.783820 CO -0.4llC50 01 C.IJ2C6E 02 0.598810 01 -0.34C891 CC 0.648590 00 0.086 0.780691 CO -0.398105 01 0.132471 02 C.992078 Cl -0.042571 CC 0.653106 CC 0.087 0.777608 O -0.395210 21 2.102888 02 0.580440 01 -0.343831 CC 0.857330 00 0.088 0.774541 CO -0.392371 Cl 0.133250 02 0.578931 01 -0.345291 CC 0.861460 00 0.089 0.771521 CO -0.389080 CI C.10365E 02 0.972531 01 -C.346736 CC 0.865550 00 03000 0.768516 CO -0.306851 01 0.124090 02 0.986251 01 -0.548066 CC 0.069621 CC 0.091 2.765581 CO -0.364160 01 0.104330 02 C.96007E 01 -0.349581 CC 0.873661 CO 0.092 0.762650 CC -0.361516 Cl O.1O4SC6 02 C.553591 01 -O.35Cq5E CC 0.877600 CO 2.093 0.759766 CO -0.378910 Cl 0.105300 02 C.940020 01 -0.352398 CC 0.081660 00 O094 0.756090 CO -0.376366 Cl 0.135370 02 0.942150 01 -o.3537e1 CC 0.085620 00 0.095 0.754061 CO -0.373850 01 C.106C50 02 0.936301 UI -C.055160 CC 0.069560 CC 0.096 0.751250 CO -0.071381 Cl 0.106450 C2 0.530651 01 -C.352531 CC 0.853470 00 0.097 0.748481 CO -0.368966 Cl 0.106086 02 0.920101 01 -0.357898 CC 0.897350 00 0.098 0.745738 CO -0.366570 Cl 0.107280 02 0.515600 01 -0.359260 CO 0.901211 00 0.099 0.743018 CO -0.364220 Cl C.10767E 02 C.514190 Cl -0.360580 CO 0.505040 00

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00 00 0 ---0 0000000000000000000000000000000000000 00000000000000000000000000000000000000000000000 0000000000000000 00dS0*W004000N040O0*N0W0014W...0040NW*.I0000N4'14#.W.-00I.I 0004,$10 4001440000 041.0h40 fl 00-iNG.00140Iaw0 odOa.-00ao.-0000,.-0004000014,a.SOO4I-d0040.40001400a000000014,00000.000000 000000000000000000000000000000000000000000000000000 000000000000000000000000.0000000000000000000000000 0 00 0000 0000000 0 000000000 0000000000000 00000000000 000 00 0 00000 000000000.0 000 00 0 000000000000 00000000 00000 -, '0NW *0.404410*0.1000000 ---14*0*0000 .d.4a000IuaJIaGs041aI0a 0-ac0.-.0an.

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-g ggggggggg gggggggggggggggg gggggggggggggg g gg gg g.gggg g g 00000000000000004000000000000000000000000000 0'O 0000000000000000000000000,0 000000.000000000000000000000000000.0 00 00 000 00 000 0 0 00 0 0000 0 0 0 0 00 000000 0 00 0000 0 000 0 000000 0 00 00 0 0 00 0000 000 000 0 0 0 0 00 0000 0 00 00 0000 0 00 0 00000.00 00 000 00 0 0 00000 0 000 0 000 0 00 010004100000Sl 414' 01 00000,0 4' 41 0000 0000000.0 00 0 000.00041*04000*0400000*004' 0*' *140 0.00.000 00 0 0000 00 00 000 00000000000000000000000 no 00000000000000000000000000000000000 Co 00000000000000000000000000000000000000000

TABLE 3

Influence Coefficient Formulae

j

Parameter Group C E 0 m0

-[I4K()]

-[I+4J(W)] I m1 3m1K()/(M1m0) -3M0m19J(P)/(M2m0) 2 m2 3m24K(t)/(Mim) -3M0m24J(f)/(M2m0) 3! m3

[I-2K()]m3/(M0m0)

[tPJ()-I]M0m3/m0--PJ(')M2m3/(fli1+fl2) 4 m4 [I_2K(4)]m4VT/(MornOV) [9'J (9')- I]M0m4/m0-'I'J('P)M2m4/(m1+m2) 5 m5 [I-2K()]m5V1/(M0m0V) [ipJ('p)-I]M0m5/m0-'PJ(W)M2M5/(m1+m2)

SPEED, KNOTS PAYLOAD, TONS

PAYLOAD DENSITY,L8/FT*3

TOTAL VOL/C ISPI VOL DYN LIFT FACTOR V 1/PCWER

POWER FRACT!ON KP PROPULSIVE EFF

TOTAL DRAG COEFF EASEC ON S WET SURF CONSTANT

DENSITY G1,LB/FT*3 FUEL RATE,L8/IIP-HR DENSITY G2,LBIFT*3 RANGE, N M SIGNA3,LB/FT**3 DENSITY G3,LB/FT**3 DEPTH/DRAFT BLCCK CCEFF RATIO AL PH A4 DENSITY G4,LB/FT**3 S IGMA5 DENSITY G5,L8/FT'3 DENSITY G6,L8/FT*3 INITIAL WO/WT OLTPUT CATA TABLE 4

Sample Calculation, Destroyer DDG

SURFACE SHIP-DESTROYER CCG2

PAYLOAD 450 TONS 22CONM RANGE AT FULL POWER

INPUT DATA

INFLUENCE CCEFFICIEKTS WITI PHI$K(PHI) -O.61720E CC

CRC -0.38280E CO CML -0.7287'.E CO CM2 -o.1122gE 01 CM3 -O.11483E 01 CM'. -0.20122E CO CM5 -0.44036E CO FVC**2 ALE CS O.21410E 01 ö.81803E08 o.z8isoE CC ALP R O.66032E-02 0.1!316E 08 Cl C2 0.22841E 02 C.70028E 01 E C3 0.303C3E-0t o .3 80'. 6E-0 1 RHCO RHC2 RHC 4 O.90059E C O.39q66E 01 0.18623E CC SMO SM2 SM'. 0.SCU-it Cc a.1572qE 01 0.SCCCOE-01 RHO1 RHC3 RHCS 0.79523E OQ 0.3225E 02 C.38063E CO Sel SP3 SR 0.102C8E 0.124L2E 0.1CS'.3E 01 01 CC CAP MO VO/DISPI VT P0 V -O.26819E 01 0.45945E DC O.72026E 06 O.71684E 05 CAP ML LC GT FVEL$*2 O.288C1E 01 0.17164E 00 Ô.1'.113E 02 0.16521E Dl PHI DISPL WC/bIT VC/VT V .49210E 00 .1655 06 0.95121E-Cl C.10562F 00 CIFHI:) CISPL WI VC 0.34264E 0.473C8E 0.473C8E C.76075E CC C'. CA CS '11/VT V3/VT VS/VT WI O.22771E 00 0.87461E-02 0.28750E CO 0.85668E 03 Vi '13 V W2 O.16401E 06 0.629S5E 0'. 0.20708E 06 O.132C0E 04 V2/VT VA/VT V6/VT h3 0.698.15E-01 0.26848E 00 C.32125E-01 0.13AS9E 04 '12 VA '16 WA C.50285E 0.15338E 0.23138E 0.236548 CS çt CS 03 wS 0.51769E 03 W6 0. VK C.32C00E 02 IC C.45C00E 03 GO 0.13250E 02 VTVEL 0.43500E 01 FOYN 0. ALl O.41600E-C2 PK o.ICCOOE 01 ETA 0.63CCOE Cc CC 0. 7C cc cE-c? CS C.75COOE 01 GI 0.11700E 02 FR 0.6COCCE Cc G2 O.5PRCCE 02 RANGE 0.22000E 04 SIG3 C.S9ICOE 01 G3 0.48CCOE 03 CD 0.20600E 01 CØCB O.15CCOE 01 ALA C.5CCCOE-C1 C'. 0.274C0E 01 SIG5 C.L6ICOE 01 G5 C.5bCCOE 01 C6 0. bCWTO C.98C00E-01

SPEEO,NOTS

P A VI C AD IT ONS

PAYLOAD DENSLTY,LB/FT$*3 TOTAL VCL/DISPL VOL

0Th LIFT FactoR

V 1/POWER

PObER FRACTION kP PROPULSIVE EFF

TOTAL DRAG COEFF OASED CN S

WET SURF CONSTANT DENSITY GI,L8/FT**3 FUEL RATE,L8/HP-HR DENSITY G2,LB/FT**3 RANGE, S IGMA3,LB/FT3 DENSITY G3,LBFFT*'3 DEPTH/DRAFT BLCCK CCEFF RATIO AL PH A 4 DENSITY G4,LB/FT3 S IGMA5 DENSITY G5,LB/FT*3 DENSITY G6,L8/FT**3 INITIAL WO/WT OUTPUT CATA TABLE 5

Sample Calculation, Destroyer DDG-2 Modified

SURFACE SHIP-DESTROYER DOG1 MODIFIED

PAYLOAD 650 T PAYLOAD CENSITY 10 RANGE AT FP 2100 NH

IIPLT DATA VK 0.320001 02 WO 0.650001 03 Ga 0.100001 02 VTVEL o..47ccoE 01 FDYN 0. *11 0.416C0102 Pk 0.100001 01 ETA 0.63000E CO CC 0.700001-02 CS 0.75000E 01 Ci 0.117001 02 FR .C.6COCOE 00 G2 o.se8eoE 02 RANGE 0.270001 04 SIG3 0.59100E 01 G3 0.480001 03 CC 0.206001 01 C8CB 0.150001 01 AL4 0.500001-01 G4 0.214C0E 01 SIGS 0.16100E 01 05 0.560001 01 G6 0. WONTO 0.800001-01

INFLUENCE COEFFICIENTS WITH PHI*MPHI) -0.626281 CC

CMC -0.313721 00 CH1 -0.64989E 00 CH2 -0.12289E 01 CN3 -0..11763E 01 CM4 O.2O6i2E CO (MS -0.48740E 00

FVOS*2 O.17244E 01 ALP 0.66032E02 Cl 0.228411 02 1 0.303031-06

ALE 0.81003E-08 A 0.164161 00 C2 0.85944E 01 C3 O.30C46E01

C5 0.28750E 00

RHOO 0.734376 OC SMO 0.134371 00 RHO1 0.859226 00 SP1 3.ee831E cc

RHO2 RH04 0e43181E 01 0.201221 00 SPZ SM', 0.16199E 01 0.S0000E-0i RHC3 ANtS 0.352506 02 O.41125E 00 S3 SPS 0.13411E ci 0.110231 CC

CAP HO -0.349711 01 CAP Ml 0.3 451,3 E 01 PHI 0.518151 00 G(PHI) 0.331021 CC

VO/OISPL VT V O58O21E 00 0.11794E 01 10 CT 0.834051 00 0.136176 02 DISPL NO/WI V 0.250941 06 C.90658E-01. CISPL NT 0.7169aE 04 0.716901 04 P0 0.945821 05 FVEL**2 0.143836 01 VO/VT 0.123451 00 VC 0.145601 C6 V 1/VT 0.183486 ₀₀ Vi 0.21640E 06 V2!VT 0.690386-01 V2 0.814276 05

V3/VT 0.80948E-02 V3 0 95'.73E 04 V4/VT 0.24849E 00 V4 0.29307E 06

V5FVT 0.207901 00 VS 0 339091 06 V6/YT 0.795531-01 V6 0.942991 03

Wi 0.113031 04 W2 0.21374E 04 W3 0.204991 04 W4 0.350491 03

TABLE (

arnp1e Calculation, 4OOUO-Ton Tankor

40000-TON TANKER RARGE.L 0000.

INPUT DATA

SPEEO,KNOTS VK O.187C0E 02

PAYLOAD,!CNS hO O.28C00E 05

PAYLCAC CENSITY,L8/FT°'3 GO C.60000E 02

TOTAL VCL/DISPL. VOL VTVEL 0.14640E 01

0Th LIFT FACTOR FOYN 0.

V1/PCWER AU C.2C000E-01

PObIER FRACTION NP PK 0.IOOCOE 01

PROPULSIVE EFF ETA 0 6OCCOE Co

TOTAL ORAG COEFF BASEC CN S CC Oo26200E02

WET SURF CCNSTANT CS 0.645C0E 01

DENSITY G1,L8/FT*3 Gi 0.10730E 02

FUEL RATE,Le/14P-HR FR 0.545001 CC

DENSITY G2,LB/FT**3 G2 O.60480E 02

RANGE, t RANGE 0.IC000E 05

SIGMA3,LB/FT*3 SIG3 0.16700E 01

DENSITY 63,LBIFT**3 G3 O.48C00E 03

DEPTHFORAFT CC 0.131301 01

BLOCK COEFF RATIO CBCB 0.110001 01

ALPHA4 L4 0.164001-01

DENSITY G4,LB/FT**3 G4 C.54340E 01

SIGMA5 SIG5 0.71500! CC

DNSITY G5,LBIFT**3 G5 C.52400E 01

DENSITY G6,L8/FT**3 G6 0.

INITIAL WCWT NONTO 0.700001 CC OUTPUT CATA

FVCS*2 0.30526E 00 ALP Q.33333E-01 CI 0.673801 02 E 0.275251-06

ALE o.75852E-0a R 0.608001 08 C2 0.29516E 02 C3 0.230191-01

C5 0.136451. 00

RHCO 0.137251 01 SNO 0.L3725E 01 RHCI 0.24545E CO SI 0.42657E-C1

RHC2 0 13835E 01 SN2 0 105321 00 RHC3 C 10980102 SP3 0 2534CE CC

RHC4 0.12430E 00 SN4 O.I6400E01 RHOS 0.119861 00 SNS 0.16356E-01

CAP NO -O.84110E 00 CAP NI O.10782E 00 PHI 0.258761-03 GPhII 0.17688E 01

VOIOISPL V O.14911E 00 IC O.9C823E 00 DISPL V o.i3q53E 07 CISPI 0.398661 05

VT 0.204271 07 CT 0.437161 02 NC/NT C.70235E 00 NT 0.358661 05 PU, Vt/VT 0.20022E 01 O.10782E 00 FVEL**2 VI 0.277241 00 O.22C24E 06 NO/VT V2/V1 0.5U73E 00 0.472291-01 VC V2. 0.104531' 07 0.964761 CS V3/Vf O.15164E-01 V3 0.32202E 5 V4/VT 0.131941 00 V4 0.265511 06

VS/VT 0.i3645E 00 VS 0.278731 06 V6/VT 0.49074E-01 V6 0.1CC2E 06

111 0 105501 04 112 0 260481 04 113 0.69004E 04 11'. 0.653801 03

W5 0.65203E 03 6 0.

INFLUENCE COEFF!CIENTS WITH PHIKIPHI) O.41751E-0t

CNO -0.958251 CO cpa -o.36105E-C1 cM? -0.891411-01 043 -0.23616E CO 044 0.223751-01 CM, -0.223151-01

SURFACE SII IF-CONTAINER

SAPE AS THE TANRER EXCEPT PAYLOAD 1rPUT DATA

SP EEC, K NUTS

PAYLOAD, TONS

PAYLOAD DEP4SITY,L8/FTS3 TOTAL VCL/DISPL VOL

Dvw LIFT FACTOR

VI / POWER

PONER FRACTION KP PROPULSIVE EFF

TOTAL DRAG COEFF ØASEC ON S

WET SURF CONSTANT

DENSITY G1,Lb/FT"3 FUEL RATE,LB/4PHR DENSITY G2,LB/FT*t3 RANGE, N P SIGMA3,LB/FTS*3 DENSITY G3,LB/FTS3 DEPTH/DR AFT BLOCk COEFF RATIO

ALPHA'. DENSITY G4,LB/FT**3 S IGMA5 DENSITY DENSITY INIT IAL G5,LB!FT**3 G6,LB/FT'3 WC!WT

Sample Calculation, Container Ship

CENSITY3C. VII O.187C0E 02 NO 0.28000E 05 GO C.3C000E 02 VTVEL O22100E 01 FCYN 0. ALL C.2C0001-01 Pk O.1C000E 01 ETA C.60000E Co CC O.26200E-02 CS O.64500E 01 Gi 0.107301 02 FR 0.545001 00 G2 C.60480E 02 RANGE O.IOOCOE 05 SIG3 0.767001 01 03 0.48000E 03 CD 0.131301 01 CBC8 0.110001 01 AL'. O.1600E0I C'. 0.543401 01 TABLE 7 $105 0.715001 CC 05 O.52'.00E 01 G6 C. NONTO 0.700001 CC OLTPUT tATA FVC*2 ALE 0.242281 00 0.758521-08 ALP a 0.33333E-01 0.6C800E 08 CI C2 0.673801 02 0.295161 02 1 C3 C.27525E-0 0 .230191-Cl C5 O.L3b4SE GO RKCO RHO2 RHO'. 0.103591 01 0.208841 01 0.187641 00 SMO SM2 SN'. 0.103591 01 O.1261g1 00 O.L6400E-Oi RHC 1 RNC 3 RHC5 0.370 52 00 0.165751 02 C .180941 00 SF1 SF3 SR 5 0.SIIOSE-01 0.382531 CC 0.246901-01 CAP MO VC/DISPL VT PC V -0.167641 01 0.148131 ₀₁ 0.31191E 07 0.201751 05 CAP Ni LC GT F VEL *$ 2 0.1 71151 00 0.113591 01 0 .2 89591 02 O.27615E Co PHI DISPL NC/NT VO/VT V 0.26428-03 0.141141 91 C.6943PE 00 0.670281 00 CESPL vC 0.L7672E 01 0.4C325E CS 0.403251 CS O.209C7E 07 Vt! VT V 3! VT VS/VT WI 0.711501-01 U. 104431-01 .O.136'.51 00 0.106311 04 Vi V3 VS 0.22 12E 06 0.32572E 05 0.25601 06 0.262481 04 V2/VT V4,VT v6/VT W3 0.311671-01 0.874C0E-01 -0 .68894E'-02 0.697981 04 V2 V4 V6 N'. 0.972141 05 0.272611 06 0.21489E 05 0.661321 03 W5 0.995611 03 -0.

INFLUENCE COEFFICIENTS NITH PHISKIPHI) -O.'.2057E-01

CRC -O.95794E Co CR1 -0.3637C1-C1 CR2 -0.898011-01 CR3 -0.23879E CO CR4 -O.22625E-01 CR5 -O.34062E-01

T13LE 4

anipIe (iIciiIation Catamaran, Suh.rnari ne Re cue ship

SURFACE SHIP-CATAMRAN

ASP INPUT DATA

SPEEC,KNOIS VK O.L630CE 02

PAYLCAO,TCNS C O.26000E 03

PAYLOAD DENSIIY,LB/FT**3 CC 0.19400E C2

TOTAL VC1/PISPL VOL VTVEL C.157COE 01

DYN LIFT FACTCR FCYP4 O.

-VIFPCIdER ALl C.15200E-Ol

POhER FRACTION'KP PK C.93300E CO

PROPULSIVE FF ETA C.A0000E CO

TOTAL DRAG COEFF EASED (N S CC C.48500E-02

WET SURF CCNSTANT CS C.6TCCOE 01

DENSITY G1,LB/FTA*3 Gi O.lC500E 02

FUEL RATE,LE/HP-HR FR 0.600CCE CC

DENSITY G2,IB/FT$S3 G2 0.6CCCCE 02

RANGE. N RANGE O.66000E 04

S:LCMA3,L8/FT*3 SIG3 0.16500E 02

DENSITY G3,LB/FT3 G3 c.4RccoE 03

DPTI1FDRAFT CC 0.L4450E 01

BLCCK CCEFF RATIO CBCB C.97500E cc

ALPIIAA AL'. C.22'.COE 00

DENSITY G4,LBIFT°3 G4 O.30000E 02

SIGMA5 SIG5 0.666C0E CI

DENSITY G5,LB/FT**3 G5 C.32200E 02

DENSITY G6LB/FTé3 G6 0.

INITIAL C/Wt bCWTO 0.58000E-0l

OLTPUT CATA

FVC*$2 O.72914E CC ALP O.27153E-01 Cl O.46q61E, 02 1 0.3C3C3E-Ot

ALE O.841751-08 R 0.40128E 08 C2 0.21618E 02 C3 0.484301-01

C5 0.206831 CC

RHCO o.47591E 00 SI'C 0.Al5qiE 00 RHC1 0.25158E CO SP1 0.143421 CC

RHC2 0 147191 01 SM2 0 377261 CC RHC3 C 11775E 02 SP3 C 57026E CC

RHO'. 0.735941 CC SPA 0.224C0E 00 RHC5 0.789911 Cd SP! 0.16338E cc

CAP O -0.822151 00 CAP MI O.1C941E 01 PHI 0.28662E CO GIPPI) 0.4t624E CC

VO/OISPL V 0 l9L8uE 00 IC 0 S7670E CO DISPL V 0 15652E 06 CISPL 0 4472CE CA

VT 0 2457'.E C6 GI 0 40764E 02 WCIWI 0 581391-01 WI 0 441201 CA

PC 0.601191 0'. FVEL**2 o.A2CeAE öOvCivT 0.12217E 00 VC 0.3CO21E 05

0.20452E 00 Vi 0.502601 05 V2/VT 0.941491-01 V2 0.231361 C5

0.308471-01 V3 0.758031 04 V'./VT C.30437E CO VA O.74fl6E 05

0 206831 00 VS 0 50827E 05 V6/V1 0 37107E-0L V6 0 91187E 04

O.23559E 03 W2 0.Aicl2E 03 W3 0.162441 0'. bA 0.LCOITE CA

O.73063E 03 WA 0.

INFLUENCE COEFFICIENTS WITI PHIKIPHI) -0.52363E CC

CIlO -0.476971 CC CR1 -O.A322CE CC CR2 -0.113691 Cl CR3 -0.297991 CI CR4 -O.18377E Ci CR5 -0.13AOAE 01 V1/VT V 3/VT V5/VT Wi W5