Computer added design of ship form

TECHNISCHE HOGESCHOOL DELFT

AFDELING DER SCHEEPSBOUW- EN SCHEEPVAARTKUNDE

LABORATORI UM VOOR SCHEEPSHYDROMECHANICA

Rapport No. 436

-COMPUTER AIDED DESIGN OF SHIP FORM

-I. Grubii

dipl.ing.

-june 1976

Iç

tUi

Deift University of Technology

Ship Hydromechanics Laboratory

Mekelweg 2 Delft 2208 Netherlands

SUMMARY

In this work a method of the ana1iticaldsign of ship form is presented. An equation combining Arch functiòn and the olynoin of 4thdegree. was

developed for the description of sections.The parametres affecting sections were longitudinaly distributed by using 6t'Ìdegree parabola for the sectional

area and waterline curves and 3degree. parabola for other parametres. Example of the design of fast container ship with bulb is presented.

INTRODUCTION

The process of ship design usualy follows the well known design spiral.

At the certain stage of work it is necessary to develop the preliminary drawing of the ship form that satisfies all design parametres previously defined.The designer has various possibilities for performing that task. Often the soliution is found by adapting lines of the similar ship to the new requirements.The method presented in this paper generates the table of offsets fromthe design parametres directly.Simiiar ideas were. allready employed by various authors(Taylor,Kuiper,Reed).This paper is a contribution to the development of program by which it will be possible

to develop añd generate all variety of ship forms.

METHOD

Method used in this work is to define the hull surface by sections.

The parametres of the sections are longitudinaly distributed by polinomials. Polynomials are defined by design parametres such as:length,breadth,prismatic coefficient,position of the centre of boyancy,etc.It was not allways possible

to use only wellknown parametres normaly used in ship designing. Some arbitrary

parametres had to be included to anabie more influence on the form of the ship.The process proceeds in the following steps:

1.definition of the input parametres

2.generation of the longitudinal distribution of section

parametres

3.definition of the section parametres

4.calculation of the section equations and table of offsets

To increase the possibility of the description of various forms,secti.ons are divided in few parts.IIorizontal keei,flat incli.ned(deadrise)part of

1

bottom and flat side are separated.Curved part of the section is further divided in the underwater and the abovewater part.(Fig. I a&b)

V

-2-The underwater curved part can have various forms represented by Fig. 2 _a,b,c,d Similar division for the definition of the sectional area curve and waterline

is performed(Fig.4 for the waterline and Fig.5 for the sectional area curve) The end of the forward 1)art of the waterline is defined by the circle

with radius and angle of entrance defined (Fig.6).

Other parametres were longitudinaly defined using the combination of the straight line and the 3'degree parabolas(Fig 7 a&b).

-3---ç'_{iLL i I ui: o}

Variour equations for sections have 1'cen tried. and fina

the following was accepted:

For the underwater part of the section:

Y=Arch(x+c)-Fc2ax+c3x2+c4x+c5x4

Solving for thefollowing conditions gives:

x=O and y=O

c2=.-rch(c1)=

-ln(c1-i-SOT(c12--l))

x=O dx/dy=B c1=SOR'f((B/(l-Ba))2l)

x=l and y=i

_{l=Arch(l+c1)-Arch(c1)+a+c,+c4±c5}

x=l dy/dx=S

_{S=l/SQRT((l+c1)2-l)+a+2c3+3c4+4c5}

x=l

jdxA

_{A=(l+c1)Arch(l+c)-c1Arch(c)-3oRT((1+c1Y1)±}

6

SQRT( c12-i)-ln(

C1+SQRT( c -1)

_{)+a/2+c3/3i-c4/4±c5/5}

After substituting and rearanging of ecations:

c3±c1+c5=K1 2c3+.)c/+4c5=K2

c3/3+cA/4+c5/5K3

where,

]

-a- n

c1+SQRT(c12-l)

K0=S-i/SQRT((i+c, )2-l)-a i±c1+SQRT((c1+l)2-1) 2 K=A-a/2--(c1+l)ln( 2 )SQRT((1+c1) -i)-c1-i-SQRT(c1 -IL)

SQRT( c12-l)

In this equations (a) repesents free coefficient.The value of

this coefficient is chosen arbitrarily.Its: effect is to shift the whole curve giving more U or V shape.

Solving the three ecuations for three unknowns:

c3=3(-4K1+K2/2+ILQK3)

c41=4(

_{l'2 -}

15K9)

-f

--,-.-,

-4--Fina].y the equation for the underwater part of the section is: X+C +cPï( (x+c1 2

y:aX+C3x+C1X

-i-c5x +ln (

-c1+B/(I-aB)

various curves obtained from the equation are represented in fir( ₂

he ahoveater part of the section is. described by 4tuidegree

parabola jitii tangent and the second derivative aL the i..rater line

adapted to the underwáter part.

The ecuat ion is usde dimensionles _{according to the}

underwater part,i e drauht=l and half breadth of the designers

waterline=1.

The second derivative of the underwater part is:

U=2C+6Cii+12Cr(i±Ci)(Ci2+2Ci)(_3/2) _{on the waterline.}

Equation is: _O

4

ya1+a2x+a3x-i-a4x +a5x

Solving for the conditions:

xl and y=l

1=a1-Fa2+a7+a4±a5

x=]. dy/dxS 3: _{a2+2a,-i-3a4±4a5}

x=l

d2y/dx2=U 2a3+6a+l2a5

x=x and

Y=a1+a2x+a3x2+a4x3+a5x4

x=x dy/dx=T T=

_{a+2a3x1+3a4x2+4a5x3}

Matrix of the coefficients:

Solution cf the set of eou.tions is performed using subroutine

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a d.d,ree parabola is used. for entrance and _{run separe tely.} quation, is. made dimensionless after _{eparatin: parts i.i1e}

paralel midlebody and nose roundinr.

quabion is of the foro:

2 3 5 6

ya1+a0x-Fa.7x +a,1x +a5x ±a6x +a7x

Solving for the boundary conditions:

x=O x=O dy/dx=O

xO

d2y/dx2=O x=1 y=O x=1 dy/dx=-T x=1

fyx=

x=1 _JYXC1X=AXT

ilr±then in the matrix form:

-8-a1=I a9=Q a3=O a4+a5±a6+a7=-i 3a4±4a5+5a6+6a7=-T a/4+a5/5 -i-a6/6±a7/7=A-1 a4/5+aS/6±a6/7+a7/8=AXT_1/2

This sistem of equations is solved using subroutine SISIT

ina1 form of the equation is:

y=1+a4x3-Fa5x4+a6x5+a7x6

Polynom of the

6tdegree

_{can haveas much as 4 points of inflection.}

is one of them is eliminated by prescribing d2y/dx2=O for x=O that leaves still three possibilities for inflection points.To overcame

this disadvantage a systematic search for eliminating undesirable shapes was performed.hor each combination of free arametres

value of the ordinate, firtt and cecond derivative were celculated

a Le:s of 1/] t) for x. ve va Inc was test.e for the uncervi. c.d

caracteristi,c i.e. y negative,y exceeding. 1,dy/dx positive and

d/dx2 changing

sign more than once.Tho diagram fig(

_{3 )}

wa prepared

to serve as a guidance for acceptable combinations ofparametrcs

1 1 1 a, -1

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For the nose

rouncIiriJ: of the

waterline a circle j used.

the following

eauations

were developed:

L'auation of the positive part of the circle wiLh the centre at x

y=SOPT(R2-(x-x)2)

First derivative for the part between x and x iR

o o

x-x

o

SQRT (F2 ( )

2)

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¿ydx=+((b_x)SRT(R2(bx)2(a_x)3T(R2_(a_x)2)±

+R2(arcsin((b-x)/R)-arcsin((a-x)/R))

1oment about position"a"

b

Syxdx=-1/3(ScJRT(R2-(b_x)2)

i/3(SORT(R2(ax

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Q

-

U

-9rdEGP.

_{I1:J$O]A UShD FOR THE LONG iTUD:rI.AL}

D] STG1I]TITJCN OF

FAi

Two kinds o the third degree parabola ero used for the longitudinal distribution of parametres as:anglc of deadris,

shear. line,deck profile ec.Eoth equations _{were ìracle dimensionless.}

J irst -a]+a2x+a3

TI

solving for the boundary conditions:

a.7=T-3 a -2- T final equation: y=l+(T-3)x2+(2-T)x3 Second: x=O _y=ï x=O dy/dx=O x=l y() x=l d.y/dx=-T a1=l a2=O O=a1+a2-i-a±a4 -T=a2+2a7+3a4

solving for the boundary conditions:

x=O y=O a1=O

x=O dy/dx=O

a=O

x=1 y=l 1=a3+a x=l dy/dx=T _T=2a3-f3a4 a3=3-T

a1=2

.ina

_ccuaion:

. y=(3-T)x2+(T-2)x3 .

1f T. equals 2 both eqUations become second degree parabols..

CONCLUSIONS

1.The proposed method is acceptable for the preliminary design of the

underwater. body of the. common ship forms.

2,.Variety of the. possible forms is sufitient for the purpose.

3.Description of the ahovewater part is not satisfactory because of the high sensitivity of the 4thdegree parabola to minor variation of the parametres. 4.It is possible to generate several designs at the acceptable expense. 5.Somè experience with the method is necessary,and after it is gained a predictable alterations of the form are easiI obtidned.

6.This method is suitable for the implementation in the computer equiped with the graphical terminal(screen),Interactive design anabled by that device would considerably ease the design since anny change of the input prametres yelds quick response and new adjustments are easily performed. 7.Intention is to proceed by the further improvement of the method by adding the description of the abovewater part by waterline method and

by implementing thè program on the graphical terminal' to make it possible to design the form interactively.

ACKNOWLEDGEMENTS

This paper was prepared during Authort s visit to the Shipbuilding Department

of the Delft University(april 1976.).The visit was enabled through the schoolarship by the Ministry of education and it is kindly acknowledged.

Numerous suggestions by Prof.Ir.J.Gerritsma and Mr..A.Versluis were valuable

contribution to this work and the Author wants to acknowledge this help.

REFERENCES .

1.D.W.Taylor,Ship Calculation,Resistance and Propulsion,San Francisco 1915. 2.A.Wiliams,Mathematical Representation of Ordinary Ship Forms,SSST 1962. 3.G.Kuiper,Het voorontwerp van een lijnenplan met behuip van een rekenautomat,

NSP 1967. . . .

4.A.Reed and H.Nowacki,,Interactive creation of Fair Ship Lines,,Journal of Ship Research,june 1974.

5.C.Kuo,Computer Methods for Ship Surface Design,Longman 1971.

6.A.Versluis,Ontwerpen en tekenen van scheepsvormen door middel van een

rekenautomaat erl een x-y plotter,T;H-Delft,July F976. 13

-DESCRIPTION OF THE. INPUT DATA LWL -length on the waterline Loa -length over all

BNL -breadth on the waterline

BM -max.breadth of the ship

TM -draught

Cp -prismatic coefficient

Cm -midship section coefficient Cv -designers waterline coefficient

lcb/LWL -longitudinal position of the centre of boyancy as the fraction of LWL lcf/LWL -longitudinal position of the centre of flotation ' H ti

R -radius of the forward end of the waterline

PBR -distance from the mid.sect. to the after point of para'lel mid.body

PBE ii ti it It it ti fo'e H ti

PSE - " ti _after " " watetline

PSR ti ii it ' after ti ti

PDE " i'

"

_" fore '

deck

PDII I '' _after ii ii it

DP - " " ti _{foremost point of the bow}

RTW -breadth of the transom/BWL at. the DWL (if anny)

ALK -angle of run(degrees) ALP -angle of entrance(degrees)

CWR -nondimensional area of the run :water]ine

RVTR -noniinensonal abscissa of the centre of gravity of run-waterline CR -nondimensional area of the run for sectional area curve

RTR -nondimensional abscissa of the centre of gravity of run for sec.area

RT -irmnersed transom/mid.sect area ratio

RS -area of bulb at F.P./mid.sect.area ratio

ATE -nondimensional tangent to the fore part of the sect.area curve

ATR ii ii after it il ii it

BALK -angle of the after part of the flat bottom .curve(deg.)

it _fore t ti lt it ti

FBP -distance of the fore point of the flat bottom curve FR -length of the after part of the flat bottom curve

BEM -maximal breadth of the flat bottom

BK -breadth of the horizontal fIat keel

RK -radius of the cruiser stern(if anny) DALP -angle of entrance at the deck level DALK -angle of run at the deck level DR -length of the run at the deck level

BT -breadth of the transom at the deck level(if anny)

RSD -rounding of the fore point of the deck -radius

HFM -height of the lower point of flat side on the mid.sect.

FB -freeboard aft

FM - ". mid.sect.

FF - " forward

AKUT -nondimensional angle of the fore point of the shear line

RPM -rise of floor angle at the mid.sect.

RFS ii it ti F.P.

RFA lt ti it A.P.

tab -nondimensional angle of the after, part of rise of floor angle curve TFB -

-ti

"

' _fore ii it it ii tt ti

WEM -angle of the section at the wate-rlin at mid.s-ect.

WFS ' " ' "

F.P.

-WFA it ii it ti ti lt A.P.

TAN -nondimensi.onal angle of the fore part of the WL-angle -curve

TFW ti it "

aft il It lt ti

15

-DFM -angle of the section at deck at mid.sect.

DÈS

-.t, ii F .1.

DFA ii it ti A.P.

TAD nondimensional angle of the aft part of the deck-angle curve

TFD I fore

it it ii

ASR -UV-fact.at the mid.sect

AFWD F.P.

ABACK ii

A.P.

TANB - nondimensional angle of the aft point of UV-fact.curve

TANF it It il ii fore

ti i ii

F2 -height of the lower transom point above WL

BHK -distance of the aft point of horizontal keel from mid.sect.

FHK fore ti It it

It it

WBN -angle of the stern profile at the waterline level

WFN " stem it ii ii ti ti

-

stern keel level

FAN " stem ti

It ii ii

UVA -UV-fact.for the stern profile UVI? -UV-fact.for the stem profile

CBLP -nondimcnsional area of the stern lateral profil

CFLP II ti stem

- it

CAF -angle of the stem profile at the deck level

GAR stern ti it or at the transom

NR -number of sections for which table of offsets is to he calculated

NZ -number of waterlines for which table of offsets is to be calculated

IZ -indicator:if IZ1 - transom stern,if 1Z0 - cruiser stern. Z(i) -array of heights of waterlines

X(n) -array of longitudinal abscissas of the sections(mid.sec. X0)

Input form provides an useful guide for the arangement of input data.All

formats except for NR,NZ,]IZ,are F1O.O.That makes punching of input cards easier.

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18

-EXAMPLE

The result of the application of the presented program to the creation

of the fast container ship form.

TABLE 0F LONGITUDINAL DISTRIBUTION 0F .PARIMTRE5

X AR YWL B-FLAT Y-DECK H-FLAT

H-DECK R F-A N GL E WI-ANGLE Uy-FACT H-KEEL DECK-ANGLE

21.71399

35.00000

52.00000 0.0 0.25098 0.0 Z1077399 27,86421 38.20412 0.0 3.09360 0.0 27.17399 .21.56790 26.53062 0.0 0.0 0.0 27.77399 16.11111 16.97960 0.0 000 0.0 27. 77399 11. 49 383 9.55103 0.0 0.0 0.0 27.77399 7.11605 4.24490 0.0 000 0. u 27. 77399 4.77178 1.06123 0.0 0.0 0.0 27.77399 2.67901 0.0 0.0 0.0 0.0 27.11399 1.41975 000 0.0 000 000 27.77399 1.00000 000 0.0 0.0 0.0 27.77399 1.00000 0.0 0.0 0.0 0.0 27.77399 1.00000 1.37800 0.0. 0..0 0.0 27,77399 1.00000 4. 90400 0..0 0.0 0.0 27.77399 1.00000 9.66600 0.0 000 0.0

27.77399

1.00000

14.75200

0.0

0.. 0

27.77399

10co,0,00

19.25000

0.0

0.0

06'U, 27.77399 lo ZiO 000 22. 24 LOO 0.00006 . C.D 0. .5 bU

21.i799

21.77399 1.00000 1.00000 ZZ.83400, 20.09599 1.r8v'ao 9.00137 0.0 0.0 3D ;ì-'1.32 7. 44931. 27.77399 1.000.00 13.12198 29.81232 0.0

13.16322

27.77399 1.00000 1000000 70.00000 0.25098 22.00000. -J. 340 18999 2.62820 1.84004 0.0 9 92263

27.

77399

-120. 71100

340 16687

583294

0.0

.12 b 4990 27.77399 107o 35199 84.93315 9.30746 0.35638 14.91509 27.77399 -93.93300 134.89018 12.15459 1.54148 16 01921 27.77399 -80.5 L 399 171.9789]. 14.23046 3.2933.3 16.07999 23.26897 -6T. 09499 213.94841 15.47776

533925

16.0 ! 999 17. 55476' -53.67599 243. 16859 15.99872 7,40506 16.07999 12078228 -40.25699 264.42505 16.07999 9.22057

16.01999

9. 14000 -26.83800 215.69175 16.07999 10.50961: 16.07999 608 1641 -13. 41900 277.92212 16.07999 11.00000 16.07999 6.00000 0.0 274. i33 545 16 07999 1.0.18519 16.07999 9.13999 13.41900 258,68848 15.89073 8.14815 16.07999 16. 58421 26.83800 228.13231 14.91537 5.50000 16.07999 25. 36929 40.25699 186.76489

l309?10

Z. 85186 16.07999

21.11399

53.67599 148. 15311 10.77460 0.61481 16.07999 27. 77399 67.09499 112.42255 8.35794 0.0 16 .07999 27. 77399 80.51399 84.42397 6.13179 0.0

1563419

27.77399 93.93300 63.45543 4. 18 528 0.0 13093436 27.17399 107.35199 46.57317 2.46962 0.0 11.24639 27. 77399 120. i_moo 31. 46742 0.982 11 0.0 7.81491 21.77399 134. 18999 20.8 7447 0.00271 0.00 4.12399 27, 77399 k

TABLEIDF SEALAÑ SECTION

WLATZ=

OFFSETS MC LEAN

>-134.190-120.711-107.352 -93.933 -80.514 -67.095 -53.676

-40.257

-26.838 -13.419

000

0.910

0.0

0.0

1.111

2.846

4.281

6.380

9.038

11.274

12.540

12.946

12.542

1.0

0.3

0.3

2.504

4.486

6.649

9.032

11.300

12.996

13.169

13.94.

13.859

2o i 't 'J' ' s

0.0

2.951

5.597

8.110

10.619

12.722

14.219

14.645

14.624

14.835

3.660

0.0

0.810

3.420

6.556

9.391

11.831

13.799

15.150

15.301

15.135

15.511

4.73

0.0

1.525

4.063

7.509

10.458

12.811

14.606

15.792

15.764

15.Ot

16.08

-

5.4;C

0.0

2089

4.975

8.544

11.464

13.644

15.202

16.080

16.045

15.772

16.u80

6.4Ò0.

0.0

2.809

6.112.

9.68

12.395

14.337

15.602

16.080

16.080

16.080

iô.08O

7.320

0.0

3.78?

7.378

10.706

13.2.4

14.898

15.845

16.080

16.080

16.080

16.00

8.230

0.0

4.691

8.538

11.612

13.881

15.290

15.961

16.080

16.060

lo.O80

1608C

9.140

0.0

.o33

.9.307

12.155

14.230

15.478

L5.999

j..6.030

16.080

160080

16.00

.SECTIÒN X=

_13.419

_26.838

_40.257

_53.676

_67.095

_83.514

_{93.933 101.352 120.771 134.190}

WL.ATZ=

0.910

11.210

9.224

6.957

4.888

3.481

2.616

2.192

2.602

2.456

0.0

1.830

12.686

10.731

8.58

6.392

4.760

3.632

3.092

3.481

3.264

0.0

2.740

13.702

11.783

9.513

7.339

5.571

4.297

3.601

3.547

.138

0.0

3.660

_14.464

_12.531

_10.245

_8.038

_6.156

_4.162

_3.660

_3.188

_2.527

_0.0

4.570

15.017

13.125

10.848

8.6L2

6.60?

,.079

3.944

2.691.

1.783

0.0

5.490

_15.408

13.638

11.406

, 9.115

6.994

5.302

3.922

2o245

1.13

0.0

6.400

15.658

14.081

11.932

9.596

1.346

5.468

30864

1.986

0.730

0.0

7.320

15.600

14.463

12.426

10.58

7.692

5.623

3.839

1.961

0.618

0.0

3.230

_{1.854. 14.754}

_l2.3&

10.46

8,030

5.o30

3.921

2.15.

u..753

0.0

i:

.

7

.

=7 :

;1T7O

i

i:

FORE

:

T1

.

I

-, L SHIP SECTiONS i -.

:L

L

_ITIT:TiiI

TH::

±r:ï

j

±

. :JT: L F 1[

I

L:

::--T

:LT

T

:):

I--:: - rT '

H

:: : . H

:

4Hti:

;

LT

i:r:

j T _L :-j

i

j I :f:

-- -_

:: : . r t

a--,--r

:

:H.:

.

: .t:

:

±

, .'FTERSfiI' SECIONS

i

T I __J_'- -. _j

I

---

--.---,- -

---ÌL

_I-L1

I -TTt -i-i--

.f

F

r

s ± =

-:I

I;) ::::

UIi

:::I

- _L - --j_

- i-;--H'

-

-,

--

-I -j I Vi - - --- -I - I I

-t.

j

-L

H-I

:

--- s: s: -I : .:..:5 --s:. .5.: :j:;

.--

!-.-.-I

'i ...

...j --- i

_J..

21

-IV G LEVEL

21 MAIM

OATE = 16170

18/15/4

DIMENSIÜÑ XR(45),YW(45),ARB(45),BRF(45),YD(45),HFS(45),HPS(45) ,8ET.f

£A(45),SW(45),AGW(4i),RKL(45),V(41,45),Z(41),UP(41),U((41),OPIS(20)

£,CF(5),GAMA(45)

COMMON /bLÜKl/RLVL ,R

L0AVLB0A,TM,CP,CMvCW, RLCB

,RLCF,RSTPPaR,PbE,; £PSE,PSR,PDE, PDR,DP £ /ELOK2/RîW,ALK,ALPWWC,WWT £

/ßLCK3/WC,WTRS,RTATE,ATR

£ /BLOK4/BALK,BALP,FBP,FR,BRM,BK £ /BLOK5/RK,DALP,DALK,13R,BT,RSD £ /BLOK6/HFM,F,FM,FF,AKUT L /8L0K7/RFM,RFS,RFA,T4B?TFB £ /bLOK8/FM,WFS, WFA,TAW,TFW £ /BLOK9/ASR,AFWD,AACK,TANE,TANF ,PFUV £ /8LOKA/FZ,8HK,FHK,WNVWFN,aÂN,FAN,UVA,UVF,CBLP,CFLP,GAF,GAK £ /I3LOKB/DFM,DFS,DFA,TAD,IFD

1R5

xw=6 SR3.14l59/180.

DO 30 TJ141

DO 30 J11.,45

Y(IJ,JI)0.

READ(TR,62UOPIS(K),K1,20)

62 FORMAT(20A4) REAO(IR,201)RLVL,RLOA,BVL9BOA,TM,CP,CM9CW F&EADCIR,201)RLCB,RLCF9RST,paR,PaE,PSE,PSR READ(IR,201)PDE,PDR,DP EAD(IR,20flRTW,ALK,ALP,WWC,WWT READ(IR,20])WCpWT9.RSRTpATE,ATR READ( IR201)BALK,BALP,FP VFRVBRM,BK

READ(IR,201)RK,DALP,DALK,D1,BT,aSD

READ( IR, 20 1) KFM, F8 ç FM, FF, AKUT

READ( 1R,201)RFM,RFS,FA,TAB,TFB READ(1Rç201)WFM,WFS,WFAçTAWçTFW READ(IR,201)DFM,DFS,DFA,TAD,TFD

READ(IR,2Oj)AS,AFWD,ABACKTAME,TANF,PFUV

IR, 201) FZ,E}1K,FHK ,WfN, WFN,BAN, FAN

READ( IR,ZQ1)UVA,UVF,CBLP,CFLP,GAF.,GAR READ(IR,202)NR,NZ,IZ READ(IR,201)(Z(I),11.,Nl)

READ(IR,2O1)(X(N),N4,M)

201. FORMATIBF1O.3) 202 FORMAT(512) CALL WLONG(XR,YW,NR) CALL ALONG(XR,ARB,NR) CALL FLONG(XR,BRF,NR) CALL DLONG(IZ,XR,YD,N) CALL SIDEU(R,HFS,HPS,NR) CALL BANGLE(XR,BETA,ÑR)

22

-N IV G LEVEL

21 MAIN

DATE = Th170

18/l'i,',

CALL WAGLE(XR9SW,NR)

CALL DA4GLE(XRVGAMA,NR)

CALL APLE(XR.,AGW,NR)

CALL PROFI (XR,HKL,NR,Z,ÑZ,UP,UK)

WRITE (IW,221)

W.ITE( 14,220)

WRITE(IW,222)(xR(N),ARB(N)yW(I\I),ßRF(M),yD(N),HFs(N),HpS(N)ßETA(N

SW( N) , AG W( N) ,HKL (N ) , GAMA(N) ,Nl,NR)

221 FORMAT(1H1,' TABLE OF LONGITUDINAL DISTRIBUTION OF PARAMETRES

',

X AR YWL

aFLAT

VDECK

HFLAT

£HOECK RFANGLE WLANGLE WIFACT

HKEEL DECKANGLE°)

222

FOU4AT(1X,12F10.)

WRITE( 14,220)

WRITE(IW,201)RLVL,RLDA,B'/L,BOA,TM,CP,CM,CW WRIÏECIW,201)RLCB,RLCF,RST9PBR,PBE,pSE,PSR WRI1E(IW,2Ol)PDEPDR,DP WRITE(IW,201)RTW1ALK,ALP,WWC,WWT WRITE(IW,201)WC,WT,RS,RT,ATE,ATR

WR IlE ( 1W, 201,) fALK, BALP FR ,I'iRM,BK WRITE(IW,201)RK,DALPeDALK,DR,BT,RSD WRITL(IW,201 )HFM,FB, FM,FF,AKUT

WRITE(IW,201 )RFM,RFS,RFA,TAB,TF8

WRITE(IW,201)WFM,WFS,WFA,TAW,TFW

WRITE(IW,201 )DFM,DFS ,DFA, TAD,TFt)

WRITE (IW,201)ASR,AFWi,A8ACK,TANa,TANF, PFUV

WRITE(IW,201)FZ,BHK,FHK,.WBN,WFN,BAN,FAN WRITE( 14,201 )UVA,UVF,CLP,CFLP,GAF,GAR

WRITE(iW,202)NFt,NZ,IZ

G=TM

DO loo N1,NR

XUXR(N)

ARARB(N)/2.

ALF=SW(N) BE T =BETA (N BR=BRF(N)

BVYW(N)

PYD(N)

.1 HK=Htc.L(N) t-IF HF S (N ) HP =HPS C N) Uy AG W C N ) GAM=GAMA (N) WRITE(IW,220) 220 FORMAT(1X,130(''))

WRITE(IW,51)XU,AR,ALF,BET,GAM,BK,BR,EsV,Bp,IjK,HF,Hp,UV

51 F0RMAT(2F8.3,3F5.2,8F6.) IF(ABS(xu)RLVL/2.+RLVL/2000.)150,15o,100 150 CONTINUE :4

23

-Ñ IV G LEVEL

21 MAIN DATE Th170

18/15/4

PDTAN( SRtsEÏ)

PAHK+(BR-13K)*PD

PBRbK

PC =3VBR AK=BK*( GHK)

4F=PB((GHK)--PB*PD/2.)

1F ( GHF 1 909919 94 90

XP=(HFPA/(GPA)

'fP(BPBR)/PC

T=TAN(GAl4*SR)(GPÂ)/PC

GO TO 92 91 XP=1. YP=1. T= 0 92

A=(ARAK--AF)/PC/(GPA)

=PD*PC/(G-PA)

S=TAN(ALF*SR)(GPA)/PC

GO TO 93 94

ABPC*(GHF)

A(ARAKtFA8)/PC/(HFPA)

=PD*PC/(HFPA)

s=o.

1=00 xP=1. YP=1

93 CALL FRAME(A 9S,ß,T,XP,YP,UV,C,CC,CCC,CF) IF(T10000q)99 91009 100 99 CONTINUE DO 111 I=1,NZ ¿Z=Z( I) IF (ZZHK) 111,54,54 54 IF(ZZPA)55,55,5& 55 IF(PD)50,50,49 50 Y(I,N)=BR GO TO 111 49 Y(I,N)=BK+(ZZHK)/PD GO TO 1.11 5E. IF(ZZ-+IF)51,56,58 58 IF(ZZHP)59,59,111. 59 Y(1,N)=BP GD TO 111 57

IF{GHF)80,61,61

80

IF(ZZG)&1,82,60

81

X=(ZZPA)/(GPA)

Q=SQRT((B/(1.B*UV))**2+1.} FUV*X+X*X*(C+CC*X+CCC*X*X)+ALOG((X+Q+SQRT((X+Q)**2.-1.))/(Q+B/(10

£B*UV)))

VC I ,N)=F*PC+BR

24

-N IV G LEVEL

21 MAIN

DATE = 76170

10/15

GO TO 111 60

SS=CF(l)

X(ZL-PA)/(G-PA)

DO 35 LL2,5

35

_{SS=SS+CFCLL)*X*(LL-1)}

VC I,t'4)=SS*PC+BR

CO 10 111

61

IF(U-HF)81,02,82

82

V(1,N)=BV

111 CJNTINUE 100 CONTINUE

OD 400 1=1,41

DO 400 .J1,45

IF(Y(I,J)}401,402,402

401

Y(i,J)=0.

402

IF(Y(I,J)-BOA/2.)400,400,403

403

Y(I,JJ=BOA/2.

400 CONTINUE WRITE(IW,71)(opIs(K),K=1,20)

71.

FORMATCIHI,' TABLE OF OFFSETS,/,20A4)

RITE(iW,63)(XR(K),K=115}

63

_{FORMAli' SECTION X=',15F8.3,/,' 14L AT Z}

',/,1X,130('-'))

DO 65 K=1,Z

65

WRrTE(Iw,o4)z(K),(y(g.,1),r=1,5)

64

FORMAT(1X,F103,15F8..3)

IF(NR-15)70,70,66

66

WR1TEUW,71)(OPIS(lÇ),K=1,20)

WRITE(Iw,63)(xR(lç),K=1o,30)

DO 68 K=I,Nl

68

_{WRITE(IW,64)Z(K),(Y(K,I},I=].6,30)}

IFLNR-30)Ì0,70,67

67 WRITE(IW,7])(OPIS(K),K=I,20) WRITE(IW,63)(XR(.K),K=31,45) DO 69 K=1,NZ 69 _{WRITE(IW.,&4)ZiK),(y(K,I),r=3],45)} 70 COÑTINUE END

25

-'J TV G LEVEL 21 WLONG DATE 76170 18/15/4

SUSRDUTU.IE WLcmG(XY,NR)

DIMP4S)ON ((45),'((45),CFR(5),CFE(5)

CORN1ON /BLOK1/;LVL,RLOAPBVLTOAITMVCP,CM,CW,RLC8 9RLCF,RST,PBR,PßE,

£PS E PSR, POE, PDR, OP L /i3LOK2/RT,ALK,ALPWWC,WWT SR =3.14159/180. B V= bV L / 2. RXN-RST/RLVL*(1.SIN(ALP'SR)) RS =RST/B V*COS C AL SR ) RPS=(PSE+P SR)/RLVL RE=(RLVL/2.PSE) /RLVLRXN RR=(RLVL/2.PSR)/RLVL RAVS=RSTRST/4.*(3.14159-2.*ALP*SRS1N(2.*ALP*SR))/RLVLIBV / RMVS=RST**3*((COS(ALP*SR))t*3/3.+(SIN(ALP*SR)-1.4LVL/RST)/(3.14l5 L9-2.*ALP*SRSIN(2.*ALP*SR)))/RLVL/RLVL/BV

CVWWC

CVE=(CRRRTRE*RSRPSNAVSCVR*RR*(1.RT))/RE/(1.RS}

RVTR=WWT

RVTE=((0.5+RLCF)*CWRMVSRDRR*RR/2.RPS*(Rt+RPS/2, )RE*RS*(RR+RPS

£+RE/2.)RR*RR*(j.kT)VCVE4(RR+RPS)*RE*(1.--RS)

£+RR*RR*CVR*( 1.RT)*RVTR)/CVE/RE/kE/ (1.RS) EE=TAN(ALPSRJ*RE*RLVL/í3V/(10RS) ER=TAN(ALK*SR)RRRLVL/ßV/ (1.Rr) WRITE(f,401)RAVS,RMVS,CVE,RVTE,EE,ER

401 FORMAT(' (DVL)RAVS RMVS CVE RVTE EE ER °,6F10.5) CALL SESTA(CVE,RVTE,EE,CFE) CALL SESTA(CVR,RVTR,LR,CFR)

DO 11 N1,NR

U=X(N)/RLVL 1F(ABS(U)O. 500001)2,2,1 i Y(N)=O. GO TO 11 2 PR-0.5--RR+U 1F (P R )3,4,5 3 BXR=PR/í(R BY =1. DO 6 1=1,4 6 _{BY=BY+BXRc*CI+2)*CFR(I)} N ) =BV* (B ( 1.RI) +RT ) GO TO 11 4 Y(N)=BV GO TO 11 5

PE=REO.5+U+RXN

7 IF(UO.5+RXN)9,B,8 IF(PE)4,4,7 q 9 BXR=PE/RE BY=1. 30 10 1=1,4 10 YBV+BXR**(t+2)*CFE(I) ) _3'.( 3* (I ,;s )+..S ic ii b -11 CONTINUE RETURN END

IV G LEVEL 21. ALONG DATE = 16110

1B/l5/s

SUBROUTINE ALÍJNG(X,V,NR)

oINENSÏO x(45),Y(45)vCFR(5),CFE(5)

COMMON /BLûK1/RLVLvRLOA,BVL,BOA,TM,CP,CMvCW,RLCB ,RLCF,RST,PBR,PbE,

L PS E PSR , POE , PDR, OP £ /bLCiK3/iC,WT,RS,RT,ATE,ATR.

SR3a

14159/180. CR WC RI R W T

RR=0.5PBR/RLVL

RE=0.5PBE/RLVL

RPM(PßR*PcE)/RLVL

RPSRPM

AM-BVL*T4*CM

CE=(CPRT*RRRPMRE*RSCR*RR(1.RT})/RE/(1.RS)

RTE=(CP*(O .5.RLCa)RR* RRT/2.RPS*RPS/2 6RR*RPSRE*RS*(10--RE/2. )..

£CR*RR*RR*(1._RT)*(1.RTR)CE*RE*(1RS)(1.RE))/CE1RE/RE1(1oRS)

EE=ATE/(AM(10RS))

ERATRI(AM*(

i.RT) I

WRITE (6,402)CE,RTE,ER,EE

402 FORMAT( (AREALA) CE RIE ER EE ',4F10.5)

CALL SESTA(CE,RTE,EECFE) CALL SESTA(CR,RTR,ER,CFR) DO 11 N=1,NR U=X(N)/RLVL I.FIABS(U)-0.i000O].)2,2,1 Y(N)=O. GO TO 11 2 PR=0.5RR4-U I F ( PR ) 3 4, 5 3

[XRPR/RR.

t,

00.6 1=1,4 b

Y=2YBXR#(1#2)*CFR(I}

Y(N)=AM*(BY*(1 .RT)+RT) GO TO 11 4 Y(N)=AM co io 11 5

PE=REO.5+U

IF(PE)4,4,9 _'1 9 ÌF(U.500001)7,7,1 7 IXR=PE/RE BY=1.

DO 8 11,4

8

BYY+BXR**(I+2)*CFE(I)

Y(N)=AM*(BY*(1.RS)+RS) 11 CONTINUE RETURN EN D -

26

27

-J IV G LEVEL 21 FLUNG DATE 76170 18/15/4

SUBROUTINE FLOG(X,Y,NR)

DIMENSION X(45),Y(45)

COMMON /BLOKI/RLVL ,RLOA,VL,BOÀ,TM,CP,CM,CW,RLCB ,RLCF,RST,PBRVPBE,

£PS E , PSR, PDE, POR, OP £ /6LOK4/BALK,BALP,FfP,FR,BRM,8K FE -FBP-PBE FPS=PBE+PBR SR=3. 14159/180. IF ( iWM-B(-O.0OO1)9 9, 10 9

DU 11 N1,NR

1]. Y(N)=BK GO TO 111 10 CONTINUE EE=TAN( BALP*SR)*FE/(P,RM-BK) ER TAN ( BAL SR ) *FR/( BR M-B K ) DO 111 N=1,NR XX t N IF(FR+FPS+FE-FEP+XX) 1,2,3 i V(N)=0. GO TO 111 2 Y(N)=BK GO TO 111 3 IF(FPSFE-F8P+XX)4,5,6 4 _{XB-(FPS+FE-FBP+XX)/FR} YB=1.+(ER-3.)*XB*X8+(2.-ER)*XB**3 Y(N)=YB*(BRM-BK)+BK GO TO 111 5 Y(N)=BRM GO TU 111 6 IF(XX-FBP+FE).5,5,7 7 1F(XX-FBP)8,2,1 8 Xa=(Xx-FBP+FE)/FE YB1±(EE-3. )*x13*Xß+(2.-.EE)*XB**3 Vt N) 5RM-BK) +8k iii CONTINUE RETURN END

28

-IV G LEi1EL

21 DLDNG

DATE = 76170

18/15R

SUBROUTINE DLONG(IZ,X,YNR)

DIMENSION X(45hYC45)

COM1ÜN /ßLOKi/RLVLRLOA,bVL,ßOA,TM,CP,CM,CW,RLCBRLCF,RSWPBR,PBE, £PSE,PSR, POEPDR,DP £ /t3LOK5/RK,DALP9DALK,DR,3T,RST SR=3. 14159/lbO. XN=RST*( 10SIN(DALP*SR)) D=R LOA B=ßOA/2.

DE=-DPXNPDE

DO 111 N1,NR

XXX(N)

1F(DDP+XYJ111,1,1

i

Ip(IZ)2,111,3

2

_/

XK=RK*(10SIN(DALK*SR))

IF (DDPXKXX)4,4,3

's XP=(DP--RK+XX) Y( N) =SQRT (RK'RKXPXP) GO TO 111 3

XKRK*(1.SIN(DALK*SR))

IF

(DDPDRXK+XX) 5 6 ,7

XA=DDP--DRXK

Xß=DDPXK

XP

=(

DDPi)R--XK+XX ) / (XBXA)

IF(ÏZ)12,111,13

12 BT=RK*COS(ALK*SR) 13 Bß=B-13T TP=TAN(DALK*SR)*(X8--XA )IBB

Y(N)(1u+(TP3e)*XP*XP+(2eTP)*XP*XP*XP)ßß+BT

GO TO 111 6

Y(N)B

GO TO 111 7

IF(XX(DPXNL)E))6,698

S

IF(XX(DPXN))9,10,10

9

XA=DPDEXN

X=DPXN

XP(XXXA)/(XBXA)

SS =R S T*COS C DAL P*SR )

BBt3BS

TP=TAN(OALP*SR)*(XBXA)/BB

Y(N)=(10(TP-3.)*XP*XP+120TP)*XP*XP*XP)*BB+13S

GO TO 111 10

IF(XXDP)11,11,111

11

Y(N)=SQRT(RST*RST(XXDPFRST)**2)

111 CONTINUE RETURN EN D L' 1:1

I IV G LEVEL 21 17 HF(N)=HP(t4) 16 CÙNTINUE 222 RETURN EN D 29 -SiDE

OTE

= 76173 11/29/2 E SLJiROUTINE SiOE(X,HF,HP1tR) DIMENSiON X(45hHF(45) ,H1'(4) COMMON

_{/LGKI/RLVL,LOA,VL,ßOA,TM,CP,CM,CW,RLCß,RLCF9RST,pB,pBE,}

£PSEPSR,PDE , PDR1DP

/BLOK/HFM,FB,FMFFAKUT

DO 111 N=1,NR

XXX(N)

0= RL OA IF(DDP+XX)111,1,1 i

IF(XXDP)22,111

2 IF(PDR+XX)3,4,5 3

X=(PuR+XX)/fc--DPPDR

HP ( N) =XEP.XB*( F hFM )+FMi- TM GO TO 111 4

HP(N)=FMTM

GO TO 111 5

IF(XXPDE)4,4,6

6 XB=(XXPDE}/(OP--PDE) H°(N)=((3.AKUT)*X8*Xß+(4KUT-2,)aXß*Xß*xB)*(FFFM)+FM.TM 111 CONTINUE

DO 7 N1,NR

7 I-IF(N)=HP(N) IF(PSR+PSEO.0001)222,222,8 8

DO 11 N=iNR

XXX(N)

IF(PDR4XX)11,11,9 9 _{JF(XXPDE)1O,I1,11} 10 1F(PBR+XX)12,13,14 12 ALFA=0.

Y3TÑ+FM

XBXX

CALL TRIPO(XB,PBR,HFM,PSR,TM,PDR,y3,ALFA,HFA) HF (Ñ)=HFA GO TO 11 13

HFN)=HFM

GO TO 11 14 IF(XXPhE)13,I3,15 15 4LFA=O. Y3=TM+ FM CALL TRIPD(XX,PB[,HFM,PSE,TrI,PDE,Y3,ALFA,HFA) HF(N)=HFA 11 CONTINUE 00 16 N=1,NR IF(HF(N)HP(N))16,16,17 V t

t

F PI

30

-SUOUTINE BANGLE(X,Y,NR)

QIMENSIOiJ X(A5),Y(45)

COMÚN /BLUK l/RLVLRLOABVL,BUA,TM,CP 9CM,CW, RLCB ,RLCF,RST,PBR,PÔE,

PSL,PSR,PÚPDR,DP

£ /BLOKÎ/RFM,RFS,RFA,TAB,TFB

DERLVL/2.-P3E

DRRLVL/2 .-P3R

DO 111 N1,NR

XX=X(N) CALL ANGLE(XX,RFM9RFA,RFS,RLVL,DE,DR,TAB,TFB,YY) 11]. Y(N)=YY RETURN EN D SUbROUTINE WANGLE(X,Y,NR)

DIMENSION X(45),Y(45)

COMMON IBLUKL/RLVL ,RLOA,B VLBOA,TM,CPpCM,CW,RLCB ,RLCF,RST,PBR,PBE,

L PS E ,P SR, POE, PDR, OP £ /BLOK8IWFM,WFS,WFA,TAW,TFW

DERLVL/20-PSE

DR=RLVL/2.-PSR

DO ill N1,NR

XX(N)

CALL ANGLE(XX,WFM,WFA,WFS,RLVL,DE,DR,TAW,TFW,YY) 111 Y(NJ=YY RETURN EN D SUBROUTINE DANGLE(X,Y,NR)

DIMENSION X(4),Y(45)

COMMON /BLOK1/RLVL,RLOA,VL,BOA,TM,CP,CM,Cj,RLCB ,RLCF,RST,PBR,P8E,

£PSE ,PSR,PDE,PDR,DP £ /BLOKB/DFM,DFS,DFA,TAD,TFD DE RLVL/2 .-PDE DR=RLVL/2.-PDR DO 111 N-1,NR XX-X(N) CALL AÑGLE(XX,DFM,DFA,DFS,RLVL,DE,DR,TAD,TFD,Yy) 111

Y(N)YY

RETURN EN D SUBROUTINE APLE(X,V,NR) DIMENSION X(45),Y(45)

COMMON /BLCK1/LvL,RLßA,vL,BQA,TM,Cp,CM,cw,

_{RLCB,RLCF,RST,PBR,pE,}

L PS E , PSR, POE, POR, £ _{/BLOK9/ASR,AFWD,ABACK,TANB,TANF,PFUV}

DEaLVL/2.-PFUV

D R = R LV L / 2 -P R DO ill N=l,NR ÁLL 11].

Y(N)YY

RETURN END

31

-I' G LEvEL

21 IROFI DATE = 76110 _{1B/15/' j}

SUBROUTiNE POF1(XY,N,Z,NZ,UP,UK)_

DIMENSION X(45hY(45h1(41),UP(41),UK(41 ),XI(10].),YB(101),YF(1O1),

£CFB(5) ,CFF(5)

COMMON /HLK1/FLVL,RLOA,aVL,3OA,TM,CP,CM,CW, RLCRLCF,RST,PBR,PBE

£PSE,PSR ,PDE.,PDR,DP £ /BLOK6/HFM,FB,FM,FF,AKUT £

/bLOKA/FL,BK,FHK,W,WFN,tAN,FAN,UVA,(JVF,C8LP,CFLP,GAF,GAR

DRLOA

KLIK1

SR=3.14159/180.

IF (DDPRLVL/2.) 1,1,2

IFCFfl3,3,i11

3 PAB=TM+FZ

PBß=RLVL/2BHK

IF(PAB)4,4,5

4 ¡

KL1KO

GD TO 7

5 STAN(WBN*SR)*PAb/PBB 8B=TAN(uANSR)*PBb/PAß

T0.

xP = i e YP = 1. CALL FRAME(CBLP,S,BBT,xP,YP,UVA,CA,CB,CC,CFB)

GaTO?

2 IF(FZ)111,]i1,6 6

PABTM

J

PBB=RLVL/2.BHK

S=TAN(WaN*SR)*PAB/PBB t BB=TAN(BANSR)*P3B/PAB T=TAN(GAR*SR)*P48/P&B XP(TM+FZ)/PAt

VP(D-DPBHK)/PbB

ÇALL FRAME (CLP,S,8B,T,XP,YP,UVA,CA,CB,CC,CFB)

7 CONTINUE PA TM

PB=RLVL/2.FHK

S=TAN(WFN*SR)*PA/P8 BF=TAN(FAN*SR)*Pa/PA T=TAN(GAF*SR)* PA/PE

XP(TM+FF)/PA

YPIDPFHK)/Pb

CALL FRAME(CFLP,S,BF,T,XP,YP,UVF,CD,CE,CF,CFF) Q3=SQRT((BB/(1.bB*UVA))**2+1.) CF=SQRT((BF/(1.BF*UVF))**2+i.)

DO 8 11,iCl

V=FLOAT(Ii)/1OO.*KLIK

XI(I)=V

YB(I)=UVA*V+V*V*(CA+CB*V.CC*V*V)+ALOG((V+QB+SQRT((V+QB)**2i.))/R

't_'t

32

-IV G LEVEL 21 PROFI

DATE = 76170

18115/4.

&B+BB/(l.-3B*UVA))) VFLOAT( 1-1)1100. XI (1 )V £F+BF/(l.BF*UVA)}) B CONTiNUE

DO loo N1,NR

XX=X(N) IF(RLVL/2. -XX) 100,9,9 9 IF(HK+XX)10,1].,12. 11 Y(N)=0. GO TO 100 10

XZ=(XXBHK)/(RLVL/20BHK)

IMAX=l0l

CALL PAA32(XZ,Th, X. ,IMAX,YZ)

V(N)=YZ*PAB GJ TO 100 12 IF(XXFHK)13,13,14 13 Y(N)=04

W TO loo

14 IF(XXRLVLI2.)15,16,l00 15 _{XZ=(XXFHK)/(RLVL/2.FI-IK)} .1 M AX 101

CALL PARAB2(xZ,YF,XI,IMAx,yZ)

Y(N)=YZ*PA

GO TO 100 16

Y(N)TM

100 CONTINUE

DO 222 I=1,NZ

ZZZ(I)

ZBZZ/TM

IF(ZZTM)40,4].,42

40

_{UP(I)=(UVF*Zb+ZB*ZB*(CD+CE*LB+CF*ZB*ZB)+ALOG((LB+QF+SQRT((ZB+QF)**}

GO TO 222 41

UP(I)=LVLf2.

GO TO 222 42 POM=CFF(1)

00 43 J2,5

43 _{POM=POM+ZB**(Jl)*CFF(J)} UP(I)=POM*PBs-FHK 222 CONTINUE

DO 111 l=1,NZ

ZZ=Z( I)

I F (Z Z T M ) 20,24,22 20

IF(ZZTMFZ)23,24,24

23

IF(FZ)27,29,29

27

Z3=ZZ/(TM+Fz)

33

-N IV G LEVEL 21 PROFI DATE = 76170

GO TO 28 29 LB-ZZ/TM 28, GO TO 111 24 UK(I)=RLVL/2. GO TO 111 22 IF(FZ)24,24,21 21 IF(ZZ-TM-FZ)25,26,26 26 UK(I)=D-DP ;o TO 111 25 ZB=ZZ/TM

PO=CF8(I)

DO 30 J2,5

30 POM=POM+ZB*(J-1)*GFB(J) UK(I}=POM*PBB+BHK 111 CONTINUE RETURN END r.

-

34

-IV G LEVEL 21 FRAME DATE 16170 18f 15/

SUBROUTINE FRAME(A ,S,B,I,Xb9YP,UV,C,CC,CCC,CF)

DIMENSION c;(5,5),CF(!)

1W6

Q=SQRT((B/(1.BUV))'*2+1.)

W=SQRT((Q+1)**2-1. I POM=(1.04-w)/(Q+b/(1.B*UV)) IF(PÛM)20,20,2]. 20

WRITE(IW22)

22 FORMAT(° LOG OF NEGATiVE OR ZERO SKIPPED') T=IC0010 GO TO 4& 21 CONTINUE

E1.UVALOG((1.+Q+W)/tQ+i3/(1.B*UV)))

/EESUV-1./W

/

EEE=AUV/2.b[/(1QB*UV)+W(Q+1.)*ALOG((1o+Q+W)/tQ+B/(leB*UV)))

C3o*(4.*E+EE/2m+1O.*EEE)

CC 4 C 7.

*

EE E-15. *E EE I CCC=5.*(-3_*E+EE/20+6.*EEE) WRITE(IW,3)B,S,A

3 FORMAT(//,' RISE OF FLOR F7e3 WATER LINE TANG.',F7.3,' AREA

*

=',F1.3) IF(XP-1. 146,46,5 5 CONTINUE U=20*Cô.*CC+12.*CCC( i+Q)f(Q*Q+2.*Q)**(3./2,)

ITERÌO

NN=5

DO 33 L1,NN

G(1,L)=l. &(2,L)FLOAT(L-1)

_r-.

4, L) =XP**( L-1) 33 _{G(5,L)=FLOAT(L-13*XP**CCL-2)} G(3 ,1)=O. G(3,2)=0. G(3,3)=2. G(3,4)=6. G(3,5)=12. CF( 1)=1. CF (2)

CF(3)U

CF (4) =YP

CF(5)T

CALL SISIT(NN,G,CF,ITER.) WRITE(IW,36).P,YP,T,U

36 F0RMAT(' OWL TO DECK PART',f,' XP ,F193p YP ',F7.3,' DECK TANG £.=',F7.3,' SECOND DERIV.DVL=',F1O.3)

DISK36.cF(4)**2-96.*CF(3)*CF(5)

IF ( DISK )40 41,42

35

-N 1V G LEV[L 21. FRAME _{UATE = 76110}

43 FORMAT(' NO INFLECTiON POINTS AEOVE OWL') G3 TO 46 41 1(-6.*CF(4))/240/CF(5) O TE) '.4 42 _{X1(&o*CFi4)+SQRT(DÀSK))/24./CF(5)} X2=(-6.*CF(4)--SQRT(o1SK))/2401cF(5) WR1TE( IW,45)X1.,X2 (;O TU 46 44 WRITE(IW,45)X1.

45 FORMAT( ABSCISSAS OF THE POINTS OF INFLECTION e,2F1003) 46 CONTINUE

RETURN

END

36

-4 1V G LEVEL 21 SISIT DATE

7170

18/15

SUEROUTINE SISIT(N,E,X,1TER) DIMrNSION A(5,5),E(5,5),X(5),B(5),F(5)

00 1 11,N

FC I)=X(I)

DO i J1,N

I.

A(I,J)E(I,J)

1)3 5 I=1,tl

DO 4 J1,N

4 X(J)=A(1,J) CALL MAXIM(X,N,U,J) 5

B(1)U

00 16 L1,N

IF(L-1)3,3,2 2 00 6 I=L,N

DO 6 J2,L

6 _{A(I,L)=A(I,L)-A(I,J-i)*A(J--1,L)} 3

DO 1 1L,N

T X(I)=A(I,L)/B(I) CALL MAXIM(X,N,U,J) IF(U)1O,10,J.5 10 ITER=-1 RETURN 15 IF(N-L)16,16,8 B DO 9 I=1,N X ( I ) 0. UECL, I) EC L,I)=E(J,I)

E(J,I)U

UA(L,I)

A(L,I)A(J,1)

9 A(J,I)-U U=8(L) BC L) =8 (J)

B(J)U

UF (L) FC L ) F (J) F(J)=U K L + i

DO 12 1K,N

IF(L-1) 12,12,13 13

DO 11 J2,L

11 A(L,I)=A(L,I)-A(L,J-1)*A(J-].,I) 12 A(L,I)=A(L,I)/A(L,L) 16 CONTINUE DO 20 I=1,N 20

B(I)F(I)

ITER=ITER+1 W=i.E38

37

-N IV G LEVEL

21

SISIT

DATE = 76110

18/15

DO 22 JTER1,ITER

BC 1).B( 1)IA( 1,1)

DO 26 12,N

DO 71 J=2,I

71

S( i )=B( £)-A(I,J-1)*t3(J-i)

26

B(I)E3(IJ/A(I,I)

DO 27 12,N

M=N-I+2

00 27 J=M,N

27

_{B(M-1)i(M--1)-A(M-1,J)*B(J)}

IF(JTE-Z)34,3]., 31

31

DO 45 I=l,N

45

B(I)=B(I)+X(I)

u=o.

f

DO 42 11,N

/

VF(I)

DO 48 K=1,N

48

V=V-ECI,K)B(K)

U=U+ABS(V) 42 CONTINUE

IF(U-4)44,43,43

43 ITER=JTER-1 RE TURN 44 W=U 34

DO 35 I1,N

35

X(I)=B(I)

00 37 t=1,M

B( I)=F(I)

DO 37 K=1,N

37

B(I)=B(I)-E(I,K)*X(K)

J 22 CONTINUE 38 ITER=JTER RETURN END

38

-N IV G LEVEL

21 1AXIM

DATE = 16170

16/15

SU[sROUTINE MAXIM(X,N,U9J) DIMENSION X(5)

U0.

DO 2 I1,N

1F (U--AbS(X(I)) )1,2,2

UAíS(X(I))

J=I

Z CONTINUE RE1'URN END

2

-

39

-('J IV G LEVEL 21. PAAt32 DATE 76170

1.8/15 SUBROUTINE PARAB2(Z,X,Y,IMAx,yz) DIMENSION X(1O1),Y(1o1) DO 11 I=1,1MAX IF( X( I )-XZ.) 11, 12,13 11 CONTINUE 12

YZY(I)

GO TO 25 13 J=I-i. IF t J-1.) 14,14,15 14

XAX(1)

YA=Y( 1) XB=x(2) YB=Y(2) XC 3) YC=Y(3) CALL LAG3(XL,XA,YA,X8,yB,xC,yC,yz) GO TO 25 15

_{IF(IMAX-J-1)16,1&,17}

16

XA-X(IMAX-2)

YA=Y(IMAX-2)

XB=X(IMAX-I)

YB=V( IMAX--1) XC=X(IMAX) YC=Y( II4AX) CALL LAG3(X1,XA,YAVXB,Y8,XC,YC,VZ) GO TO 25 17 XAA=X(J-1) YA A Y C J-1) XAB=X(J) 'fABY( J) XAC=X(J+1) YAC Y(J'-l) XBA=X(J) YB A = Y C J)

XBB=X(J+1)

YBB=Y(J+1) XBC=X(J+2) YBC=Y(J+2) CALL _{LAG3(XZ,XAA,YAA,XAB,YAB,XAC,YAC,YAZ)} CALL LAG3( XZ ,XBA,YBA,XBB,yt3B,XBC,yßC,yßz)

YZ=(XZ-XAB)/(XAC-xAB

_{)*(YBZ-YAfl+YAZ}

25 RETURN END SUBROUTINE LAG3(X,XA,YA,XB,yB,XC,YC,y) Y=YA*(X-xB)*(X-xC)f(XA-xB)/(XA-xC)+Y6*(x-XA)*(x-xC)/(xB_xA)/(xB £)+YC*(X-XA)*(X-XB)f(XC-XA)/(XC-XB) RE TURN END

40

-SUbROUTINE ANGLE(X,RFM,RFA,RFS,RLVL,DE,DR, TA13,TF,Y) xB=XIRLVL

IF (ABS(XB).500Oi)1 ,i ,ii

1F(LVL/2.DR+X)2,394

2

xB=(RLVL/a.DR+X)/OR

3 .TAB )*X3*X+ (TA.-20 ) *XB*X8*XB y=yß*(RFARFM)+RFM GO TO 111 Y=RFM

GOTO ILL

JF(XRLVL/20+Dt)3,3,5 XB=(XRLVL/2.+DE)/DE

YB(3.TFB)*XBXß+(TFB-2.)*XB*Xb*XB

Y=YB*(RFSRFM)+RFM GO TO li]. it Y=0o iii RETURN EN D

SUBROUTINE SESTA(A,XT,t,C)

DIMENSION C(5),EC5,5) N=4

DO i 11,N

E( i,I)=1. E(2,I)=FLOAT(I+2) E(3,I)1./FLOAT(I+3) E(4,I)=I./FLOAT(Ii-4) C(1)=-1.

C(2)=T

C(3)Ai.

C( 4)#*XT.5

ITER=iO C#LL S1SITCN,E,C,ITER) RETURN END

SUBROUTINE TRIPO(X ,X1,Y1,X2,Y2,X3,y3,ALFA,y) XM=(X2--x1)/(X3xi) YM=(Y2yl)I(y3--Yi} T=TAN(ALFA*3.14159/180. )*(X3Xl)/(Y3Y1)

XB=CXXI)/(X3X1)

Q=(I.T)/(XM-1.)

W=(YMT*XM)/IXM-1.)/XM/XM Y3-.XB (T+( xM*QW)*XB+(wQ) *X1XB) i'Yz#(Y3Y1)+Y1 END