ncar-tn-47 forces in a cable-restrained balloon …34...ncar tn-47 forces in a cable-restrained...

NCAR TN-47

Forces in a Cable-RestrainedBalloon System

JACK M. ANGEVINEDAVID W. FULKER

February 1970

NATIONAL CENTER FOR ATMOSPHERIC RESEARCHBoulder, Colorado

iii

FOREWORD

Tandem balloon system design and launch circumstances often re-

quire that a cable restraint be used to counteract wind drag on the bal-

loon and maintain the balloon system in a given position over the pay-

load at launch. In order to insure a successful launch with such an

arrangement, it is necessary to determine the optimum balloon/payload/

cable configuration under the prevailing wind conditions. This report

presents a complete analysis of the forces acting on a cable-restrained

balloon launch system and describes computer programs that may be used

to determine optimum system configurations. The computer programs are

applicable to either Stonehenge or vehicle launch systems, and solu-

tions to a typical problem are given. Computer program listings appear

as appendices.

v

CONTENTS

Foreword ............................. iii

List of Figures ........................ . vii

List of Tables .... . .................... ix

List of Symbols and Identifiers .............. xi

I. FORCE ANALYSIS ....................... 1

A. Forces Acting on the Train ............... 1

B. Forces Acting at the Transfer Fitting ......... 4

C. Forces Acting on the Restraint Cable (Stay) .. .... 6

D. Determination of Aerodynamic Force Values Requiredin Numerical Force Integrations. ............ 9

II. COMPUTER PROGRAMS FOR CALCULATING FORCE VALUES ANDCONFIGURATIONS FOR TANDEM BALLOON SYSTEM LAUNCHPLANNING .. ....................... 21

A. Variable Payload-to-Winch Distance ........... 22

B. Fixed Payload-to-Winch Distance ... .. 23

III. SOLUTIONS TO A TYPICAL LAUNCH-PLANNING PROBLEM ....... 25

A. Variable Payload-to-Winch Distance ........... 25

B. Fixed Payload-to-Winch Distance ............ 37

References ........................ .... 59

Appendixes

A. Listing of Program LAUNCH .. ......... 61

B. Listing of Program LNPROC ...... .... ..... 75

C. Listing of Program CLANCH ............... 85

D. Listing of Program GRAPHS ............... 95

vii

FIGURES

1. A cable-restrained balloon system .............. 2

2. Static forces at the lowest train segment .......... 2

3. Forces acting on train segment I ............... 5

4. Approximate train shape and apparent angleof inclination .... 5.............. ..... 5

5. Forces acting at transfer fitting . . .......... 5

6. Forces acting on stay segment J ............... 8

7. Approximate stay shape .......... . ....... 8

8. Forces acting at winch .................... 8

9. Wind profile curves (Eqs. 24 and 25)............. 12

10. Sphere-on-cone bubble .................... 13

11. Gore length as a function of gross lift for asphere-on-cone bubble .................... 13

12. Vertical cross section as a function of gross lift fora sphere-on-cone bubble ................... 15

13. Horizontal cross section as a function of gross lift for asphere-on-cone bubble .................... 16

14. Diameter as a function of gross lift for a sphere-on-conebubble . ................. ........ 17

15. Typical dd80 pictorial, Program LAUNCH (Stonehengepayload support) ... .............. ..... 31

16. Sample output, Program LNPROC (Stonehenge payload support):plots of apparent train angle vs payload-to-winch distancefor increasing increments of train tension ......... 32

17. Sample output, Program LNPROC (Stonehenge payload support):plots of stay length vs payload-to-winch distance forincreasing increments of train tension ............ 33

18. Typical dd80 pictorial, Program LAUNCH (vehicle payloadsupport) . . . . . . . . . . . . . . . . . . . . . . . . ... 38

19. Sample output, Program LNPROC (vehicle payload support):plots of apparent train angle vs payload-to-winch distancefor increasing increments of train tension ......... 39

20. Sample output, Program LNPROC (vehicle payload support):plots of stay length vs payload-to-winch distance forincreasing increments of train tension ............ 40

viii

21. Typical dd80 pictorial, Program CLANCH (Stonehenge payload

support) . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

22. Sample output, Program GRAPHS (Stonehenge payload support):tension at winch vs stay length ............... 45

23. Sample output, Program GRAPHS (Stonehenge payload support):extension line tension vs stay length ............ 46

24. Sample output, Program GRAPHS (Stonehenge payload support):anchor cable tension vs stay length ............. 47

25. Sample output, Program GRAPHS (Stonehenge payload support):train tension at anchor apex vs stay length ......... 48

26. Sample output, Program GRAPHS (Stonehenge payload support):apparent train angle vs stay length ............ 49

27. Typical dd80 pictorial, Program CLANCH (vehicle payloadsupport) .. ........................ 54

28. Sample output, Program GRAPHS (vehicle payload support):apparent train angle vs stay length .. .......... 55

29. Sample output, Program GRAPHS (vehicle payload support):tension at winch vs stay length ............ . 56

30. Sample output, Program GRAPHS (vehicle payload support):train tension at anchor apex vs stay length ......... 57

ix

TABLES

I. A typical launch problem: Balloon system and launchenvironment data ..................... 26

II. Input data cards, Program LAUNCH (Stonehenge payloadsupport ........... ............ ... 28

III, Printout of input data and calculated Stonehenge arraygeometry, Program LAUNCH ................ 29

IV. Sample output page, Program LAUNCH (Stonehenge payloadsupport) ......................... 30

V. Input data cards, Program LAUNCH (vehicle payloadsupport) ......................... 34

VI. Printout of input data, Program LAUNCH (vehicle payloadsupport) .................... ..... 35

VII. Sample output page, Program LAUNCH (vehicle payloadsupport) ................... 36

VIII. Input data cards, Program CLANCH (Stonehenge payloadsupport) ................ 41

IX. Printout of input data and calculated Stonehenge arraygeometry, Program CLANCH ................ 42

X. Sample output page, Program CLANCH (Stonehenge payloadsupport) ................... ...... 43

XI. Input data cards, Program CLANCH (vehicle payloadsupport) ...................... ... 51

XII. Printout of input data, Program CLANCH (vehicle payloadsupport) ......................... 52

XIII. Sample output page, Program CLANCH (vehicle payloadsupport) ......................... 53

xi

SYMBOLS AND IDENTIFIERS

TEXT COMPUTER PROGRAMSYMBOL DEFINITIONS VARIABLE IDENTIFIER

A Length of anchor line (ft) A

AH Area of horizontal cross section oflaunch balloon (sq ft) XSECTH

AS Area of segment of stay (sq ft)

AT Area of segment of train (sq ft)

AV Area of vertical cross section oflaunch balloon (sq ft) XSECTV

b Unit lift of bouyant gas (lb/cu ft)

C Distance from payload to winch (ft) C

CD Drag coefficient for launch balloon PDBCOF

CDS Drag coefficient for stay

CT Drag coefficient for train

C Generalized drag coefficient F

CL Lift coefficient for launch balloon ALBCOF

CLS Lift coefficient for stay

CLT Lift coefficient for train

DIA Diameter of spherical portion oflaunch balloon (ft)

F Aerodynamic force (lb)

FAB Aerodynamic lift force on balloon (lb) FALB, ARLFTB

FAS Aerodynamic lift force on stay (lb) FALS

FAS(J) Aerodynamic lift on segment J of stay ARLFTCAS

xii


FAT Aerodynamic lift force on train (lb) FALT

FAT(I) Aerodynamic lift on segment I of train ARLFTC

FDB Aerodynamic drag force on balloon (lb) FDB, PDRAGBDB

F Aerodynamic drag force on stay (lb) FDSDS

FDS(J) Aerodynamic drag on segment J of stay PDRAGC

F Aerodynamic drag force on train (lb) FDTDT

FDT(I) Aerodynamic drag on segment I of train PDRAGC

g Acceleration due to gravity (ft/sec2) G

G Gross displacement - lift (lb) GLIFTL

H Elevation above ground (ft) HT

HCENT Distance from base of balloon to centerof spherical section (ft) HCENT

H Difference in elevation between payloadand winch (ft) GROUND

H Height of payload suspension fitting(vehicular launch) or height of apex(Stonehenge launch) (ft) HP

L (J) Length of segment J of stay (ft) STEP 2S

LT(I) Length of segment I of train (ft) STEP 1

m Unit mass of air

P Third leg of triangle R,S,P; leg adjacentto 3 (ft) P

PANCH Projected length of anchor lines (ft) PANCH

PARTC Horizontal distance from payload totransfer fitting (ft) PARTC

Q Dynamic pressure (lb/sq ft)

R Radius of anchor circle (ft) RADIUS

xiii


S Triangle leg opposite 3 (ft) S

SB Gore length of launch balloon (ft)

SLOPE Slope of ground from payload to winch(ft/ft) SLOPE

THIK(I) Thickness of train segment I (ft)

TOTALH Vertical height of transfer fitting abovehorizon (ft) TOTALH

TOTC Horizontal distance between payload andrestraint cable segment (ft) TOTC

TOTH Vertical height of restraint cablesegment above horizon (ft) TOTH

TSB Tension in stay at balloon (lb) TSB

Tsw Tension in stay at winch (lb) TSW

TTB Tension in train at transfer fitting (lb) TTB

TTCIN Horizontal distance from payload toinitial segment of train (ft) TTCIN

TTHIN Vertical height of initial segmentof train above horizon (ft) TTHIN

TT(I) Resultant tension in segment I of train T

T Tension in train at apex of anchors orat vehicle holding payload (lb) TTP

TTX Horizontal component of tension insegment of train (lb) TTENX

TTY Vertical component of tension in segmentof train (lb) TTENY

V Wind velocity (kt)

VOL Approximate volume of launch balloon(cu ft)

VW Wind velocity (ft/sec) WINDF(HT)

xiv

TEXT COMPUTER PROGRAMSYMBOLS DEFINITIONS VARIABLE IDENTIFIER

WB Weight of launch balloon (lb) WTB

WF Weight of transfer fitting (lb) WTFF

WS(J) Unit weight of segment J of stay(lb/ft) SDENS

WT(I) Unit weight of segment I of train(lb/ft)

X,Y,Z Coefficients of wind profile polynomial WN(II,NW)

~a Angle between horizontal and bottomsegment of train (") ALPHA

a(I) Angle between horizontal and segment Iof train (°)

oA Apparent angle between horizontal andtrain (°) ALPHAA

aB Angle between horizontal and topsegment of train (°) ALPHAB

3P One-half of angle included betweenanchors (C) BETA

~£ Half angle between anchor lines atapex (°) EPS

o6 Half-cone angle of launch balloon (0)

EB Angle between horizontal and stay atballoon (°) THETAB

06 Angle between horizontal and stay atwinch (°) THETAW

Elevation angle of anchor lines (°) PHI

p Specific weight of air (lb/cu ft) RHO

xv

TEXT COMPUTER PROGRAMSYMBOLS DEFINITIONS VARIABLE IDENTIFIER

Density of anchor lines (lb/ft) ADENS

Number of empty anchors (Stonehenge) ANCHE

Total number of anchors (Stonehenge) ANCHT

Thickness of anchor lines (in.) ATHIK

Desired distance from payload towinch (ft) CWANT

Net vertical force at the transfer

fitting = FAB + L - W -F FBY

Length of train on ground (ft) FTONG

Extension line length (ft) HEXT

Height of attach point on payloadabove horizontal (ft) HPAY

Number of train sections of constantdensity NSECD

Number of train sections of constantthickness NSECTH

Number of wind profiles NWIND

Length of stay (ft) SLNGTH

Width of spreader (ft) SPRED

Thickness of stay (in.) STHIK

Tension in one anchor line (lb) TANCH

Tension in extension line (lb) TEXT

Length of train (ft) TLNGTH

Weight of extension line (lb) WEXT

Weight of payload (lb) WPAY

Extra length in anchor line rigging (ft) XTRA

1

I. FORCE ANALYSIS

A balloon system restrained by a cable (Fig. 1) constitutes a

statics problem with three elements: the restraint cable (stay), the

train (main balloon and parachute), and the launch balloon (bubble).

It is assumed that the launch array is set up parallel to the wind and

that there are no side forces. Calculation of the forces acting on the

balloon system is therefore made in a plane parallel to the wind, pass-

ing through the train, launch balloon, and restraint cable. Rectangu-

lar coordinates are established in this plane with the origin at the

base of the payload and axes parallel and normal to the horizon. The

payload, at the base of the flight train, may be supported by a launch

vehicle or controlled by the anchor lines of a Stonehenge (Angevine,

Sparkman, and Fulker, 1969) array. For force analysis in a Stonehenge

launch, the anchor cables are projected onto the plane and considered

as a single cable.

Forces acting on the balloon system are bouyant lift, aerodynamic

lift and drag, weight, and the restraining tensions of the train and

stay. Calculation of the total forces acting on the train and on the

stay is complicated by variations in lift, drag, and weight along their

lengths. These variations are taken into account by considering the

train and stay as being divided into a finite number of small segments,

each contributing its own weight and aerodynamic characteristics. Force

calculations can be made as accurately as required by varying the size

of these segments.

A. FORCES ACTING ON THE TRAIN

A diagram of the static forces at the payload anchor point (lowest

segment of the train) is shown in Fig. 2; the diagram applies to both

vehicular and Stonehenge launches. Tension in the train at the anchor

point, TTp, acts at angle a. Vertical and horizontal components of

2

tF~i-FAB

LAUNCH-' > FD -WIND (+DIRECTION)LAUNCH—- yB WIND

BALLOON L RANSFER FITTING

/RESTRAINT CABLE

/TRAIN

a , \ \ /WINCH_e PAYLOAD\ HORIZON

F 1 C blost GROUND

Fig. 1 A cable-restrained balloon system.

TT =TTP Sin a 6 TTP

COORDINATES 2 T TTPCOs a(TTCIN, TTHIN)

Fig. 2 Static forces at the lowest train segment.

3

tension in the train at this point are, respectively,

TY = TTP in (1)

and

TX = TTP os (2)

Coordinates of the lowest point of the train are denoted by TTCIN

and TTHIN. The actual position of this lowest segment varies with the

design problem. It may be at the point of payload restraint, as in a

vehicle launch; in a Stonehenge launch, it may be at the apex of the

anchor lines, at the base of the anchor lines before the load line be-

comes taut, or at a distance FTONG from the anchors if the train is not

entirely off the ground.

Each segment, I, of the train, from the lowest segment at the pay-

load to the last segment at the balloon transfer fitting, has weight

WT(I) and length LT(I). Aerodynamic lift FAT(I) and drag FDT(I) act on

train segment I (see Fig. 3).

When a segment is in an equilibrium state in some system configu-

ration (as we will assume each to be for the following configuration

calculations), the vertical and horizontal tension components in that

segment exactly counteract the effects of lift, drag, and weight.

Therefore, tension components in the upper end of segment I in the ver-

tical direction are

TTy(I) = TTy(I - 1) + WT(I) - FAT(I) (3)

and in the horizontal direction are

TTX(I) = TTX(I - 1) + FDT(I) (4)

Resultant tension is

TT(I) = [TYvI + TTX(I) (5)(5)

4

and the angle at which this tension acts on the next segment is

(I + 1) = tan 1 [TT(I)/TT(I)] (6)TY TX

B. FORCES ACTING AT THE TRANSFER FITTING

This process of numerical integration is continued upward through

the train segments until the transfer fitting at the bubble is reached.

Coordinates of the transfer fitting position are the sums of the verti-

cal and horizontal distances covered by segments I of the train. Trans-

fer fitting height is therefore

TOTALH = LT(I) sin a (I) + TTHIN (7)

and its horizontal distance from the coordinate system origin is

PARTC = [LT(I) cos a (I) + TTCIN (8)

The apparent angle of the train (Fig. 4) is

TOTALH - TTHINA = t an L PARTC - TTCIN J

Forces at the transfer fitting (Fig. 5) consist of tension in the

uppermost segment of the train, TTB, lift and drag on the bubble, FAB

and FDB, gross lift in the bubble, GL, weight of the bubble and trans-

fer fitting, WB + WF, and tension in the top segment of the stay, TSB.

Vertical and horizontal components of train tension at the fitting are

TTy(B) and TTX(B); resultant tension acts at angle a. Values of these

variables are calculated as the final step in the numerical integration

of forces along the segments of the train.

At equilibrium in any system configuration, the sum of the verti-

cal forces at the transfer fitting must be equal to zero. The vertical

TTY(I)

TTX(I)

FAT ( )

FD/ TTrain Segment I

^FDT( ) yWINDFD(I)7 I- (+ DIRECTION)

TTX(I-) WT()

TTy(I-I)

Fig. 3 Forces acting on train segment I.

Transfer Fitting

TOTAL H-TTHIN

Segment I

LT(I) L S

aA a(I) L (I)Sina(I)

Base of Train / \ k LT(I)Cosa(l)

-—- Part C - TTCIN

Fig. 4 Approximate train shape and apparent angleof inclination.

FDB -t FAB

GL

Transfer Fitting

wBTTB WF \ TSB

Fig. 5 Forces acting at transfer fitting.

6

component of the tension applied by the stay must therefore be

TSy(B) = FAB + G - W -W TTy(B) (10)SY AB L B F TY

The sum of the horizontal forces at the transfer fitting is also equal

to zero at equilibrium, and the horizontal component of stay tension at

the fitting is consequently

T(B) = FDB + TTX (B) (11)

C. FORCES ACTING ON THE RESTRAINT CABLE (Stay)

Tension at the transfer fitting is

TSB [TS(B ) 2 + TsX(B)2 (12)

The angle of the cable from the horizontal at this point is

e = tan- TSy(B)/TX(B)] (13)

Forces acting along the stay (Fig. 6) are calculated in the same

manner as those acting on the train. The stay is divided into seg-

ments, J, of length LS(J), weight WS(J), and aerodynamic lift FAS(J).

Vertical and horizontal components of tension at the lower end of each

stay segment J are, respectively,

TS(J) =TSy(J - 1) - W(J) - FAS(J) (14)

and

TS(J) = TSX(J - 1) + FDS(J) (15)

7

Resultant tension in segment J is

TS(J) [TSYCJ) + TSXC)] (16)

and the angle at which this tension acts on the next segment is

(J) = tan-1 T (J)/Ts( (17)

Coordinates of the lower end of segment J, (TOTC, TOTH), are determined

by the segment's horizontal distance from the payload

TOTC = PARTC + L(J) cos (J] (18)

and its vertical distance below the transfer fitting

TOTH = TOTALH - LS(J) sin (J] (19)

as shown in Fig. 7.

The calculation process for tension and angle of application is

continued downward along the stay segments to the ground. The ground is

represented as a straight line through the origin with an identifying

slope (SLOPE). SLOPE is positive if the ground is higher at the winch

than at the payload. The elevation, HG, of a point on the ground at

distance TOTC from the payload is

HG = SLOPE x TOTC (20)

Segment J of the stay is above ground only if its vertical coordinate,

TOTH, is greater than the elevation HG of the ground at the winch. As

soon as a segment passes into the ground, it is ignored and the previous

segment is extended in a straight line to intersect the ground line.

This location is the position of the winch, and its horizontal distance

from the payload is denoted by C. The stay leaves the winch (or winch

sheave) at angle 8W equal to the angle from the horizontal of the final

segment of the stay (Fig. 8). Tension in the lowest segment of the stay,

TSW, is applied by this winch.

8

ITSY(J-I )

Tsx (J-) I /Stay Segment J

\^^/ WINDF " - A ((+ DIRECTION)FDS (U) ._____

FAS(J) \

.. t '' A Tsx(J)Ws(J) -

Tsy(J)

Fig. 6 Forces acting on stay segment J.

Transfer Fitting

0

TOTALH-TOTH=

(L(J)x Sin (J)) ()

iLs(J)xSin8j)M,^ ,Ls(J)xSinl(J) — e Segment J

Ls(J) x Cos(J) xWinch

TOTC- PART C= (LS(J)xCos (J))

Fig. 7 Approximate stay shape.

TswS TSX(W)

TSYFig. 8 Forces acting at winch.

Fig. 8 Forces acting at winch.

9

D. DETERMINATION OF AERODYNAMIC FORCE VALUES REQUIRED

IN NUMERICAL FORCE INTEGRATIONS

Evaluation of the foregoing numerical force integrations requires

calculation of values of the aerodynamic lift and drag on the stay,

bubble, and train (FAT FDT FAB, FDB, FAS, FD). To accomplish this,

we consider the general equation for the force produced on a body by

the dynamic pressure of a wind field,

F = qACF (21)

where q is dynamic pressure (force per unit area), A is a characteristic

area of the body, and CF is a nondimensional coefficient which takes

into account body geometry, angle of attack, Reynolds number, and other

pertinent factors. Procedures for evaluating each of these parameters

in any launch problem are given below.

1. Determination of Dynamic Pressure, q

The dynamic pressure, q, of the wind at the launch site is found

by using the kinetic energy of the moving air arrested against a sta-

tionary body,

q = ½ x p/g x VW (22)

where p is the specific weight of the air, g the acceleration due to

gravity, and V the wind velocity. Tables provide the value of p at the

altitude equal to launch site elevation plus balloon system height.

Although density is a function of height, it is generally considered

constant over the length of the system. Since the greatest proportion

of system drag is imposed on the bubble, p is taken to be the density

of air at the height of the bubble.

10

Wind velocity is also a function of height above ground. The

actual wind profile varies with terrain and with the vertical stability

of the wind stratum. For the Scientific Balloon Facility at Palestine,

Texas, when the nocturnal jet is fully developed, the profile can be

approximated by

V/V= H/H 0.35(23a)o o

where V is wind velocity at height H above the ground, and V is the

value of wind velocity at height H . Wind velocity at any height H can

thus be found by

V V /H 0.35]H.35 (23b)

Equation (23a) can be generalized to

V/Vo= H/H z (24)

in which z is a function of the vertical stability of the wind stratum

within a few hundred feet of the surface. By employing an estimate of

z dictated by meteorological conditions, this equation can be used to

approximate the wind profile near the surface. Reasonable values of z

for typical wind conditions are:

(a) Unstable 0.1 < z < 0.14. The temperature decreases with

height at a rate in excess of 30 C/1000 ft. This is most likely to oc-

cur on a hot summer afternoon. Cumulus clouds may result from the in-

stability; extensive stratus clouds will prevent such conditions.

(b) Neutral Stability 0.14 < z < 0.33. The temperature decreases

with height at or near but not in excess of 30 C/1000 ft. This is likely

to occur from mid-morning to late afternoon on a mild, sunny day or on

a mild day with extensive stratus clouds.

11

(c) Stable z > 0.33. Normally when the air is stable, the wind

direction turns clockwise with height. The direction may change as much

as 30° in the lowest 1000 ft. The temperature decreases with height at

a rate less than 1.70C/1000 ft. Temperature frequently increases with

height near the ground on a clear, calm night. A value as large as

z = 0.8 may then be appropriate.

These short descriptions of typical weather conditions associated

with degrees of wind stratum stability are not definitive but may be

used as a guide in the absence of measured wind or temperature profiles.

Equation (24) can be considered a special case of the generalized

polynominal with coefficients X, Y, and z,

V = X + YHZ (25)

where X = 0, Y = V /(H )Z, and z = 0.35. For example, with wind veloc-

ity V = 4 kt at a height H = 500 ft, Eq.

V= + [(500o35 H0 3 5 = 0.454 H kt

Wind profiles generated in this way for wind velocities equal to 4, 8,

10, 14, and 20 kt at a height of 500 ft have been plotted and are shown

in Fig. 9; also shown is a tabulation of values of the coefficient Y for

velocities through 20 kt. The variable X is ordinarily of small value

and can be ignored.

2. Determination of Characteristic Area, A

The characteristic area of a bubble can be well approximated by

assuming a sphere-on-cone shape for the balloon (Fig. 10). For half

cone angles of 30° or more, the calculated shape appears nearly identi-

cal to photographs of actual balloons. In high winds the actual shape

is flattened and deformed and its area departs farther from the model.

12

Wind Velocity vs Height Above Ground) V= 0 + 0.454 H 035 ( V= + 1.590H 035

V =0 + 0.909H 3 () V 0 + 2.272H° 35

800 ( V=0 + .136H 0 5

700

600I f /00 //~~V = X + Y(H) z

//coefficient Ywhen1) I I^~~ I I I~ / //X =0 and Z =0.35

W Velocity1 500 at 500ft. Y? Vo, Kt.

I 0.114> eI I I I I / I L2 0.227

400 3 0.341 4 0.4545 0.568

I I.? I I / / 6 0.682"r'/ / 7 0.795

300 8 O.9O9 9 1.022

1/o /. 136I I 1.25012 1.363

200 13 1.47714 1.59015 1.70416 1.81817 1.931

100/18 2.04519 2.158

/ / 20 2.272

5 10 15 20 25Wind Velocity (kt)

Fig. 9 Wind profile curves (Eqs. 24 and 25).

13

-- — DIA

SB .

Fig. 10 Sphere-on-cone bubble

16_0 ——

140

120 |80 . ___ _ .. .. .. ....

400 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

GROSS LIFT,POUNDS

Fig. 11 Gore length as a function of gross lift for asphere-on-cone bubble; 0 = half-cone angles. Unitlift = 0.0646 lb/cu ft.

^ _-__.~~~ -- - _-_ - _ ,_- ̂^^ ^ / ^ ̂ ̂̂ ^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~.8 ///^~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~,

lift = 0.0646 lb/cu ft.

14

The entire displacement volume of the balloon is assumed to be con-

tained in the spherical portion. For a unit gas lift of b, the volume

of the sphere is

GLVOL =

b

and its diameter is

DIA= [(6/7I)VOL /3(26)

The area of the horizontal cross-section at the diameter is

AH = (DIA) (27)

The area of the vertical cross-section at the diameter is

A (DIA)2 + + cot6) (28)

where 0 is the bubble half cone angle. Gore length of the bubble is

DIA (TrSB + 0 + cot 6) (29)

B 2 2

Figures 11 and 12 show bubble gore length and vertical cross-section

area as a function of gross lift for half cone angles of 30°, 35°, 40°,

50° , 60° , and 80°. Horizontal cross-section area and bubble diameter

are plotted as functions of gross lift in Figs. 13 and 14. All figures

were plotted using a unit lift of 0.0646 lb/cu ft, the standard value at

a typical 720 ft balloon elevation at the NCAR Scientific Balloon

Facility. (Palestine has an elevation above mean sea level of approxi-

mately 400 ft, and the height of the bubble is assumed to be an addi-

tional 320 ft.)

Calculation of characteristic areas of the balloon train and of

the stay is simplified by the assumption that these system components

15

7000

1—6000 — — — — — — — — — — — — — —-— -'-"7 --000

~ ,, ,—————————

14000 '0

~ 5000z ~~—"I —--I- I i-—— i 4--—-I— -.,--

2000

000

0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000GROSS LIFT,POUNDS

Fig. 12 Vertical cross section as a function of gross lift fora sphere-on-cone bubble; 6 = half-cone angles. Unitlift = 0.0646 lb/cu ft.

16

5.001 _ -. ............ .. _... _— ___—: ..... :

i" m _ _ _ X _--" -' -

5500

4500 m I mn4000

z3500

t3000

F2500

(A0

2000

I- 1500 -

5:1000

500

0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000GROSS LIFT POUNDS

Fig. 13 Horizontal cross section as a function of gross lift for asphere-on-cone bubble. Unit lift = 0.0646 lb/cu ft.

17

85 ' - - _ - —

75

70

,7.5F _. __ _. _ __ " —_--— —-- -t-———— .-- ,

. .:.- .- .i _ _ .= ; —=— . — .— .I — . .— _ .. .— I7 ------ ::•--

-- __ _65

— 60

45

40 =

35

30f\ _" —( __ ' __ — . _ _"i .-• __ _- , .: ...--

25

200 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

GROSS LIFT,POUNDS

Fig. 14 Diameter as a function of gross lift for a sphere-on-conebubble. Unit lift = 0.0646 lb/cu ft.

18

are made up of cylindrical sections. The rectangular cross-section

area of train segment I is

AT(I) = THIK(I) LT(I) (30)

where THIK(I) is the diameter of the segment and LT(I) its length. The

cross-section area of segment J of the stay is

As (J) = STHIK(J) L (J) (31)

3. Determination of Coefficient CF

Coefficients of lift and drag for flexible sphere-on-cone shapes are

not well documented. Some wind tunnel testing has been carried out con-

sidering pitching moments and angle of attack (Sherburne, 1968).

For a flexible bubble with bouyancy, the full-scale tests so far

have shown that pitching moment and changes in angle of attack can be ne-

glected under the conditions encountered to date. One such test yielded

a drag coefficient value of 0.6 for C (Angevine, 1968; pp. 47 and 115),

and a lift coefficient value of 0.1 for CL . For the Reynolds numbers

which are encountered with large balloons, the drag coefficient might be

expected to be as low as 0.1 (Hoerner, 1958; p. 3-8, Figs. 10 and 11).

Differences between laboratory tests and field experience are great and

probably attributable to lack of similarity in shape, flexibility, sur-

face finish, bouyancy, and instrumentation.

Coefficient values for inclined cylinders simulating the train and

cable have been published (Hoerner, 1958; p. 3-11, Fig. 18). Drag co-

efficient on inclined cylindrical train section I at Reynolds numbers

below critical (about 2.0 x 10 s ) is given as

CDT(I) = 1.1 [sin a (I)] + 0.02 (32)

Drag coefficient for segment J of the inclined cable is

CDS(J) = 1.1 [sin 0 (J)] + 0.02 (33)DS

19

Lift coefficient for inclined segment I of the train is

CLT(I) = 1.1 [sin a (I [cos a (I) (34)

Lift coefficient for inclined segment J of the cable is

CLS(J) = 1.1 [sin (J)] [cos (J)] (35)

4. Evaluation of the Required Aerodynamic Force Variables

Drag on the bubble is found using

FDB (p/2g) x V 2 x CD (36)

from Eqs. (21), (22), and (23). The value of AV can be taken from

Figs. 11 and 12 or Eq. (29). CD is found by experiment; for conserva-

tive design, a coefficient of 1.0 may be used as an initial estimate.

VW can be taken from Fig. 9 or calculated with Eq. (25). Height of

the center of the spherical portion of the bubble may be substituted

as height H in Eq. (25). Although this height does not necessarily

represent the center of pressure, it is a close approximation. Spher-

ical center height can be calculated (Figs. 4 and 10) according to

HCENT =2 Dn (37)

and therefore

H = TOTALH + HCENT

Lift on the bubble is found similarly using the horizontal cross-

section area,

FAR = (p/2g) x VW2 X A X C (38)

20

Drag on segment I of the train is calculated from

FT(I) = (p/2g) V 2 x AT(I) x CDT(I) (39)

derived from Eqs. (21), (22), (23), (30), and (32). Wind velocity is

taken at the height of the segment, using Eq. (25). Lift on segment I

of the train is given by

FAT(I) = (p/2g)V x A(I) CLT(I) (40)

Drag on segment J of the stay is

DS (J) (p/2g)V2 x AS(J ) X CDS (J) (41)

Wind velocity is taken at the height, TOTH, of stay segment J. Lift on

segment J of the stay is

FA(J) (p/2g)V x A(J) C(J) x (42)AsW S LS

21

II. COMPUTER PROGRAMS FOR CALCULATING FORCE VALUES AND

CONFIGURATIONS FOR TANDEM BALLOON SYSTEM LAUNCH PLANNING

The balloon launch planner has two primary responsibilities in

effecting a successful launch: he must recognize that point in the

launch procedure at which the balloon system has attained a desirable

launch configuration, and he must plan to maintain stability in the

system during its erection to that configuration.

The actual configuration of a balloon/payload/cable system at the

moment of launch is a compromise between the preplanned, desirable

force distribution, and the physical realities of the launch situation.

Before the field site team attempts the launch, the launch planner must

define the desirable distribution of forces acting on the system, and

plan the balloon system configurations which will achieve that distri-

bution of forces under the various wind conditions possible at the

launch site. (The definition of a desirable force distribution varies

with launch circumstances, but it has been found during NCAR launches

that a "desirable" balloon system configuration is one which maximizes

pre-launch load in the train, thus reducing acceleration shock in the

payload at release.)

Stability in the balloon system during erection to the planned

launch configuration is a function of wind velocity and gross system

weight in the train. Enough tension must be maintained in the train

to prevent whipping damage from gusts or crosswinds. (A successful rule

of thumb has been to maintain tension at the base of the train equal to

at least 50% of payload weight, except in the very early stages when

tension is building from zero.) Instability can be casued by too high a

proportion of weight in the train, or high winds; a given system with

its particular weight distribution has a maximum wind level beyond

which the system configuration is unstable. The launch planner must

describe system configurations that will maintain the desired train

tension (and therefore stability) as the balloon system is erected.

To aid the launch planner in choosing a desirable launch configu-

ration and in evaluating stability of the system, a computer program

22

has been developed at NCAR which provides him with a list of balloon

system configurations in advance of actual launch operations. The

listed configurations describe, for specified wind conditions, the posi-

tions and tensions assumed by the elements of the balloon system. The

computer produces such descriptions by applying the force analysis pre-

viously described to the actual parameters of the balloon system and to

variables reflecting wind conditions that can be expected at the launch

site. The launch planner can use these theoretical descriptions of bal-

loon system configurations to choose operating limits for wind velocity

and to guide the launch team in positioning payload and winch and paying

out cable to achieve the desirable distribution of forces for launch.

The computer program has been adapted for two possible types of

launch situations. In some cases, the distance between winch and pay-

load, as well as cable length, can be varied to achieve system stabil-

ity during erection to launch position; Program LAUNCH describes system

configurations as both cable length and payload-to-winch distance are

allowed to vary. A modified program, CLANCH, describes system config-

urations for a fixed distance between payload and winch. The two

launch-planning programs are applicable to both Stonehenge and vehicle

launches.

Although the programs were set up with the wind blowing in the

positive direction (from the winch toward the payload; Figs. 1, 3, and 6),

they will operate and give valid results if the wind direction is taken

as negative (blowing from the payload toward the winch).

A. VARIABLE PAYLOAD-TO-WINCH DISTANCE

The more complex method of maintaining stable system configura-

tions in the process of reaching a desirable launch position is to al-

low payload-to-winch distance to vary, as well as cable length. The

variable-distance control system can be manual (paint marks on pavement

and cable) or automated (Anderson, et al., 1967), but in either case the

necessity of controlling two variables complicates the launch operation.

23

Program LAUNCH (Appendix A) calculates for given wind profiles the

payload-to-winch distance associated with each of six incremental train

tension values (near-zero tension, and 20% increments of payload weight).

The calculation is an integration of forces acting upward through the

train segments and downward through the cable segments to the ground.

The result is a table of distance vs incremental train tension for given

wind velocities and for each chosen level of tension in the train.

Cathode-ray tube (dd80) output may be called from the program to

give side-view scale drawings of the configurations (payload-to-winch

distance and cable length for a given wind profile and train tension).

An auxiliary program, LNPROC (Appendix B), draws plots of the values

from the data tape generated by Program LAUNCH. Such plots can be in-

corporated into a launch operation plan and used to establish maximum

wind velocity limits for launch, to determine the optimum launch posi-

tion for prevailing wind conditions, and to check the stability status

of the system as the launch progresses.

B. FIXED PAYLOAD-TO-WINCH DISTANCE

A simpler method of balloon system positioning in the field is

that of fixing a constant payload-to-winch distance, and deploying the

cable to achieve the required system positions. Only one control var-

iable is involved in assessing changing tension in the train, i.e., the

amount of winch cable payed out. This can be determined by coded paint

marks on the cable.

The computer program, CLANCH (Appendix C), used for planning this

type of launch integrates force calculations up the train and down the

cable to find the payload-to-winch distance necessary for system equi-

librium for given train tension and wind values. This calculated dis-

tance is compared with the predetermined fixed payload-to-winch dis-

tance required for the launch. If the calculated and required distances

differ, the program adjusts the train tension value according to a nu-

merical root-finding procedure, and the calculation is made again. The

24

process continues until the distance between payload and winch, with

some modified value of train tension, is within an acceptable margin

of the desired distance.

Pictorials of the system configurations (cable length and train

tension) calculated by Program CLANCH for various wind profiles can

be called as dd80 output. Using the tape generated by Program

CLANCH, Program GRAPHS (Appendix D) plots cable and train tension

and angle of train elevation for given wind profiles with the desired

constant payload-to-winch distance. These curves are employed in

prelaunch planning.

25

III. SOLUTIONS TO A TYPICAL LAUNCH-PLANNING PROBLEM

The following samples of launch planning, using computer programs

to describe balloon system configurations, employ data from a test

flight conducted at the Scientific Balloon Facility, Palestine, Texas,

under NASA Contract NASr-185 (Angevine, 1968). Balloon-system and

launch-environment data for the actual test flight (a fixed payload-to-

winch distance--Stonehenge launch) are given in Table I. Data from this

test have been modified to serve as input data representing a theoretical

balloon flight with vehicular payload support. The computer programs

(fixed and variable payload-to-winch distance) are illustrated with

both Stonehenge and vehicular payload-support input data. Comparison

of the results of the Stonehenge test at Palestine and the computer-

derived balloon system configurations for that case verified the valid-

ity of the computer model.

A. VARIABLE PAYLOAD-TO-WINCH DISTANCE

Program LAUNCH determines configurations of the balloon system for

each of four sample wind profiles included in the test data; the payload-

to-winch distance is allowed to vary as necessary to maintain the re-

quired train tension.

All information for both Stonehenge and vehicular launches is input

to Program LAUNCH in floating point format (usually F15.5), except for

the values of variables NSECTH, NSECD, and NWIND, which are integer for-

mat (19). Values for each train segment's thickness and length, and

weight and length, appear on separate cards in 2F15.5 format. Coeffi-

cients of the wind profile polynomial (Eq. 25) are input in the se-

quence X, Y, z as WN(1), WN(2), WN(3) format 3F10.5. Train length on

the ground, FTONG, and the angle of inclination of the train's lowest

segment, a, are supplied (in any desired increments) on cards of

format 3F15.5. The incremental percentages of train on the ground must

be arranged in decreasing order, and the last value of train length on

the ground, FTONG = 0, must appear before any values of a. Angle of

26

TABLE I

A Typical Launch Problem: Balloon System andLaunch Environment Data

For both Stonehenge and vehicular payload handling:

Payload weight: 3780 lb

Total train length: 403 ft

Parachute riser and shroud lines: 85 ft

Parachute canopy: 50 ft

Main balloon: 268 ft

Weight distribution along train:

Risers and shroud lines: 60 lb

Parachute canopy: 120 lb

Main balloon: 1088 lb

Launch balloon weight: 232 lb

Gross lift (including 15% free lift): 6089 lb

Launch balloon horizontal cross-section: 2500 sq ft

Launch balloon vertical cross-section: 2680 sq ft

Cable thickness (diameter): 5/8 in.

Cable unit weight: 0.72 lb/ft

Four winds representing 0, 9, 10, and 11 mph at 500 ft were considered.

Transfer fitting weight was considered zero; there was no transfer fit-

ting in the actual test. Connection between launch balloon and train

was made by hardware of negligible weight.

For vehicular payload handling only:

All computer variables referring to Stonehengearray dimensions are set to zero.

Height of payload support: 25 ft

27

inclination increments must be arranged on the data card in increasing

order to simulate a rising balloon system. The final data card for

Program LAUNCH must read 1000 in format 3F15.5.

1. Stonehenge Payload Support

Data cards with sample input from the Palestine test for Program

LAUNCH, with Stonehenge payload support, are listed in Table II; input

cards to the program must be arranged in this sequence. Column numbers

identify positions on the cards for the data and descriptions (data de-

scriptions are complete to avoid ambiguous identification of the data).

A printout of this input data is supplied by Program LAUNCH and appears

in Table III. A sample printout page of balloon system configurations

for the givenwind profiles, with Stonehenge payload support, is

illustrated in Table IV. A typical dd80 sketch from Program LAUNCH

appears in Fig. 15, and represents the enclosed block of data in

Table IV. The pictorials are optional at the discretion of the program-

mer. Curves drawn by Program LNPROC for wind profile number four are

given in Figs. 16 and 17. Each curve represents train tension values

in 215.452 lb increments, approximately 20% of payload weight.

2. Vehicle Payload Support

Input data to Program LAUNCH for vehicle payload support does not

require the geometry data necessary for the Stonehenge array at launch,

and all such Stonehenge-related variables are set to zero. There is no

provision for calculating the various draped configurations the train

might take lying over a vehicle and along the ground. Data cards must

start assuming no train on the ground (FTONG = 0). Table V shows the

input data used to plan a vehicular launch of the test system with var-

iable payload-to-winch distance. Printout format is identical to that

of Program LAUNCH used with a Stonehenge array; printout of the input

data for the sample problem is given in Table VI. Table VII is a sample

output page with anchor line tension (TANCH) equal to zero, and exten-

sion (TEXT) equal to TTP (train tension); these values reflect the lack

28

Table II

INPUT DATA CARDS, PROGRAM LAUNCH

(STONEHENGE PAYLOAD SUPPORT)12345678901234567890123456789012345678901234567890123456789012345678901234567890

LAUNCH EXAMPLE-STONEHENGE CABLE RESTRAINED LAUNCH.0736 DENSITY OF AIR IN POUNDS PER CUBIC FOOT.------- ------------ ..~ - f fE ---- Xf R76--6N- SI- H- §AIOI......................-------...----------..........6 COEFFICIENT OF AIR DRAG ON THE BALLOON

0.1 COEFFICIENT OF AIR LIFT ON THE BALLOON50. RADIUS OF ANCHOR CIRCLE IN FEET 24. TOTAL NO. OF ANCHORS.-------... . ... _.. _.... . _..5. NO. OF INCLUDED EMPTY ANCHORS.625 .THICKNESS OF ANCHOR LINES IN INCHES

*72 DENSITY OF ANCHOR LINES IN POUNDS PER FOOT2.1667 WIDTH (FT.) OF SPREADER AT APEX OF ANCHOR LINES0 0 LENGTH (FT) BETWEEN ANCHOR LINE CONFLUENCE AND EXTENSION LINE END

15. HEIGHT OF PAYLOAD IN FEET--- ------.-...-._ _ -.. ..... .. .. ........-.............................-.............-

3780. WEIGHT'OF PAYLOAD IN POUNDS33.337 LENGTH OF EXTENSION LINE IN FEET"""15, - -WEIGHT OF EXTENSION LINF IN POUNDS - -------------.008 GROUND SLOPE (FT./FT.) + IF WINCH ABOVE PAYLOAD

403. TOTAL TRAIN LENGTH IN FEET1.0 INTEGRATION STEP SIZE FOR TRAIN SIDE IN FEET3 NO. OF SECTIONS F CO'NSTANT THICKNESS .1. 85* THICKNESS (FT.) AND LENGTH (FT.) OF SECTION

'-...- ...-'-.----'--'---------'-50'. '-' THICKINESS (FT.'-- AN--L-ENGTH--('FT.---UF--SE-CTTrON -------'--.6666 268. THICKNESS (FT.) AND LENGTH (FT.) OF SECTION

3 NO. OF SECTIONS OF CONSTANT DENSITY60. 85. TOTAL WEIGHT (LBS.) AND LENGTH (Ft.) OF SECTION

..1. .....20.' -- - 50. TOTAL WEIGHT(LBS.) AND LEN'GTHT"-(FT- -F- ' T ECTrfCN 1088. 268. TOTAL WEIGHT (LBS.) AND LENGTH (FT.) OF SECTION

0. '-0 .'WEI'GHT OF TRANSFER FITTING IN POUNDS 232. WEIGHT OF TOP BALLOON IN POUNDS

6089 . GROSS LIFT IMN POUNDS—- --_--_ __2500. HORIZONTAL CROSS SECTION OF BALLOON IN SQUARE FEET2680o .- VERTICAL CROSSSECT'ION OF BALLOON IN SQUARE-FEET -" -----

.625 THICKNESS OF STAY IN INCHES

..72 DENSITY OF STAY IN POUNDS PER FOOT10_ INTEGRATION STEP SIZE FOR STAY SIDE IN FEET.4 . NUMBER-OF WINDS

0. 0. 0. COEFFICIENTS OF WIND PROFILE POLYNOMIAL0. .878 .35 CO'EFFICIENTS -OF'WI'ND PROFIIE--PULCYNOMIAL-'- 0. .986 .35 COEFFICIENTS OF WIND PROFILE POLYNOMIAL0. 1.083 .35 COEFFICIENTS OF WIND PROFILE POLYNO-I'AL.-'--..

_99 DECIMAL FRACTION OF TRAIN ON GROUND..95 " DECIMAL FR'-CTION--'OF-TRA'N ON '" GROUND . -..-- ---.9 DECIMAL FRACTION OF TRAIN ON GROUND.8 DECIMAL FRACTION OF TRAIN ON GROUND.7 DECIMAL FRACTION OF TRAIN ON GROUND.6 DECIMAL FRACTION OF TRAIN ON GROUND.5 DECIMAL FRACTION OF TRAIN ON GROUND.4 DECIMAL FRACTION OF TRAIN ON GROUND.3 DECIMAL FRACTION OF TRAIN ON GROUND

2 DECIMAL FRACTION OF TRAIN ON GROUND.1 DECIMAL FRACTION OF TRAIN ON GROUND.01 DECIMAL FRACTION OF TRAIN ON GROUND

0o0 DECIMAL FRACTION OF TRAIN ON GROUND0.0 0 ALPHA IN DEGREES1 .0 ALPHA IN DEGREES5. ALPHA iN DEGREES10. ALPHA IN DEGREES15. ALPHA IN DEGREES20. ALPHA IN DEGREES25. ALPHA IN DEGREES30. ALPHA IN DEGREES35.0 ALPHA IN DEGREES40. ALPHA IN DEGREES45. ALPHA IN DEGREES50. ALPHA IN DEGREES55. ALPHA IN DEGREES60. ALPHA.IN DEGREES65. ALPHA IN DEGREES70. ALPHA IN DEGREES75.0 ALPHA IN DEGREES76. ALPHA IN DEGREES77. ALPHA IN DEGREES78. ALPHA IN DEGREES79. ALPHA IN DEGREES80. ALPHA IN DEGREES

1000. THIS CARD INDICATES END OF ALPHA FILE

29

Table III

PRINTOUT OF INPUT DATA AND CALCULATED

STONEHENGE ARRAY GEOMETRY, PROGRAM LAUNCH

LAUNCH EXAMPLE-STONEHENGE CABLE RESTRAINED LAUNCH

INPUT RHO = .07360 DENSITY OF AIR IN POUNDS PER CUBIC FOOT

PDBCOF = .60000 COEFFICIENT OF AIR DRAG ON THE BALLOONALBCOF = .10000 COEFFICIENT OF AIR LIFT ON THE BALLOONRADIUS = 50.00000 RADIUS OF ANCHOR CIRCLE IN FEET

ANCHT = 24.00000 TOTAL NO. OF ANCHORSANCHE = . 0.00 0QO NO, QF.A.INCLUDED. EMPTY ANCHORS . .ATHIK = .62500 THICKNESS OF ANCHOR LINES IN INCHESADENS = .72000 DENSITY OF ANCHOR LINES IN POUNDS PER FOOTSPRED = 2.16670 WIDTH (FT.) OF SPREADER AT APEX OF ANCHOR LINES

XTRA = 0O LENGTH (FT) BETWEEN ANCHOR LINE CONFLUENCE AND EXTENSION LINE ENDHPAY = 15.00000 HEIGHT OF PAYLOAU IN FEETWPAY = 3780.00000 WEIGHT OF PAYLOAU IN POUNDS ._ _.HEXT = 33.33700 LENGTH OF EXTENSION LINE IN FEETWEXT = 15.00000 WEIGHT OF EXTENSION LINE IN POUNDS

SLOPE = -. 00800 GROUND SLOPE (FT./FT.) + IF WINCH ABOVE PAYLOAD

GEOMETRY OUTPUTPHI . 53.81698

PANCH = 59.88711S = 35.35534

EPS = 29.78150A = 69.00025

INPUTTLNGTH 403.00000 TOTAL TRAIN LENGTH IN FEET

STEP1 = 1.00192 INTEGRATION STEP SIZE FOR TRAIN SIDE IN FEETNSECTH 3 NO. OF SECTIONS OF CONSTANT THICKNESS

TTHIK = 1.00000 85.00000 THICKNESS (FT.) AND LENGTH (FT.) OF SECTIONTTHIK = 2.00000 50.00000 THICKNESS (FT.) ANO LENGTH (FT.) OF SECTIONTTHIK .66660 268.00000 THICKNESS (FT.) AND LENGTH (FT.) OF SECTIONNSEC = 3 NO. OF SECTIONS OF CONSTANT DENSITYTDENS = 60.00000 85.00000 TOTAL WEIGHT (LBS.) AND LENGTH (FT.) OF SECTIONTDENS = 120.00000 50.00000 TOTAl WEIGHT (LBS.) AND LENGTH (FT.) OF SECTION1DENS = 1088.00000 268.00000 TOTAL WEIGHT (LBS.) AND LENGTH (FT.) OF SECTION

WTF = 0 WEIGHT OF TRANSFER FITTING IN POUNDSWTB = 232.00000 WEIGHT OF TOP BALLOON IN POUNDS

GLIFT = 6089.00000 GROSS LIFT IN POUNDSXSECTH = 2500.00000 HORIZONTAL CROSS SECTION OF BALLOON IN SQUARE FEETXSECTV = 2680.00000 VERTICAL CROSS SECTION OF BALLOUN IN SQUARE FEETSTHIK = .62500 THICKNESS OF STAY IN INCHESSDENS = .72000 DENSITY OF STAY IN POUNDS PER FOOTSTEP2 = 1.00000 INTEGRATION STEP SIZE FOR STAY SIDE IN FEETNWIND = 4 NUMBER OF WINDSWIND = 0. 0. 0. COEFFICIENTS OF WIND PROFILE POLYNOMIALWIND = 0. .87800 .35000 COEFFICIENTS OF WIND PROFILE POLYNOMIALWIND = 0. .98600 .35000 COEFFICIENTS OF wIND PROFILE POLYNOMIALWIND = 0. 1.08300 .35000 COEFFICIENTS OF WIND PHOFILE POLYNOMIALTTP = 214.4 3994.4 756.0 lNITIAL,FINALgINCREMENTAL TENSIONS AT PAYLOAD

30

Table IV

SAMPLE OUTPUT PAGE, PROGRAM LAUNCH

(STONEHENGE PAYLOAD SUPPORT)ALPHA = 1.00 FTONG = 0

WIND PROFILE 1 ALPHA = 1.000 FTONG = 0_IITP _ 214.452 970.360 1726.360 2482.360 3238.360 99436-

ALPHAB 82.622 55.504 39 386 29.918 23.985 19,996TTB 1397.059 1697.646 2225.829 2858.254 3539.487 4246.102

TOTALH 367.781 199.445 135.538 102.067 82.042 68,881PARTC 182.835 358.510 396,544 410.317 416.599 419,943

TSB 4475.106 4560,361 4765.925 5076.865 5475.238 5943.485THETAW 87.557 77.421 68.365 60.306 53.321 ....... 3

TSW 4209.653 4414.783 4666.039 5001.002 5413.840 5891.380SLNGTH 369.682 207.487 149.445 121.529 106*753 98.546

C 198.113 402.967 451.060 470.065 480.006 486.392ALPHAA 59.446 26.920 17.464 12.930 10*313 8.623

TEXT = . 0. 0. 0. 0 0.TANCH = 123.543 559.011 994.532 1430.053 1865.574 2301-,95.

FALB = 0. 0. 0. 0. 0 0.FBY = 5857,000 58570 000 58 000 57,000 5857.000 5857.000FDB = 0 0. 0. 0 0 0

WINDB = 0. 0. 0. 0. 0 0,

WIND PROFILE 2 ALPHA = 1.000 FTONG = 0OTTP = 214.452 970.360 1726.360 2482.360 3238.360 3994.360

ALPHAB = 81.562 55.294 39.324 29.895 23.974 19.991TT8 = 1392.301 1696.795 2225.696 2858.295 3539.575 4246.203

TOTALH = 366.322 199.179 135.459 102.036 82.027 68.873PARTC = 187.386 358.791 396.595 410.331 416.604 419.945

TSB = 4546.825 4636.836 4846.243 5160.051 5560.127 6029.074THETAW = 83.600 75.114 66.762 59.141 52.453 46,712

TSW = 4281.987 4491.246 4746.155 5084.451 5498,849 5976.992SLNGTH = 370,307 209.267 1510.94 122.949 107.970 99.597

C = 227.374 411,684 455.583 472.929 482.037 487.938ALPHAA = 58.8?2 26.873 T7.452 12.926 10.311 8,622

TEXT = 0. o 0. 0. 0.TANCH = 123.543 559.011 994.532 1430.053 1865.574 2301,095FALB = 42.138 29.076 23.405 20.186 18.149 16.756

FBY = 5899.138 5886.076 5880.405 5877,186 5875,149 5873.756FnH = 271. 32 187.016 150.543 129.834 116.735 107.772

WINDS = 7.187 5.970 5.357 4,975 4.717 4.K32

WIND PROFILE 3 ALPHA = 1.000 FTONG = 0.

TTP = 214.452 970.360 1726.360 2482.360 3238.360 3994.360ALPHAB = 81.288 55.239 ;9.308 29.889 23.972 19.989

TT8 = 1391.038 1696.573 2225.662 2858.305 3539.598 4246.229TOTALH = 365.935 199.109 135.438 102.028 82.024 68,871

PARTC = 188.553 358.865 396.608 41.).334 416.605 419.946TSH = 4568.621 4657.913 4867.792 5182.105 5582 495 6051.550

THETAW = 82.595 74.527 '66.354 58.840 52.228 46.545TSW = 4304.312 4512.716 4768.007 5106,12] 5520.828 A999,610

SLNGTH = 370.717 ?09.779 151.540 123.326 108.291 99.872C = 234,845 413.935 456,754 473.673 482.565 488.340

ALPHAA = 58,662 26.861 17.449 12.924 10.310 8,622TEXT = 0. n. 0. . 0. 0.

TANCH = 123.543 559.011 994.532 1430.053 1865.574 2301.n95FALB = 53.107 36.661 ?9.515 25.456 22.888 21.131FRY = 5910.107 5893.661 5886.515 5882.456 5879.888 %878.131FDB = 341.583 235.806 189.841 163,732 147.217 135.914

WIND8 = 8.069 6.704 6.015 5586 5.297 5.090

WIND PROFILE 4 ALPHA = 1.000 FTONG = 0.TTP = 214,452 970.360 1726.360 2482.360 3238.3b0 3994.360

ALPHA8 = 81.017 55.185 39 292 29.883 23 969 19,988TTB = 1389.771 1696.353 2225.627 2858.316 3539.621 4246.256

TOTALH = 365.548 199.040 1,5.417 102.020 82.020 68.R89PARTC = 189.709 358.937 396*622 410.338 416.606 419.946

TSB = 4591.565 4679.370 4889.506 5204.224 5604.875 6074.007THETAW = -81.605 73.945 ^5.952 5b,546 52*009 46, 75

TSW = 4327.140 4533.882 4790,025 5128.474 5543.389 6021.687SLNGTH = 371.220 210.307 151.990 123.703 108.611 100.146

C = ?42.223 416.168 457.919 474.412 483.090 488.739ALPHAA = 58.503 26.848 17.446 12.923 10.310 8H.22

TEXT = .n. O. (. OTANCH = 123.543 559.011 994.532 1430.053 1865.574 2301,095

FALB a 64.027 44.221 35.605 30.710 27.612 25.493FRY = 5921.027 5901.221 5892,605 5887.710 5884.612 5882.493FDB = 411.821 284.426 279.011 197b524 177.603 163.969

WINDB = 8.860 7.363 6.607 6.136 5.818 5.R90

31

LAUNCH EXAPLE-STOrEINGE CABLE RESTRAINED LAU'CH710

NIND PROFILE 4 ALPHAA 59 TTP = 214 SLNGTH = 371 FTONG · 0 JJ

600

500

O0

of -- _. 0 0

2 00 -

100 -

*t00 . . . I . . . -I * I I * a a A I I I I I I

DISTANCE FROM PAYLOAD, C, FT

Fig. 15 Typical dd80 pictorial, Program LAUNCH (Stonehengepayload support).

32

SLOPE - - .807. WIND PROFILE 4 LAUNCH EXAMPLE-STONEHENGE CABLE RESTRAINED LAUNCH90 '\I N

70

.-i

~4o

1,0I-—------.-------------.-1~~4d50~ ~ ~ ~ ~~~

_ ,oo 920 Soo 400 6o 100 1 700 00 90 ,0o_DISTANCE PAYLOAD TO .INCH, C, FT

o I^lI t~ltl ITI___ -_____-

-o__I IIIIIII IuIIldi 1

X _ _ I10 20 90 40 6 1 0 g\ 11 TIl 70 60 90 _(00 __Z__ _ I I I I I DISTAC PAYOA TO9 1 1 WINCH,_Z C, _FT _____

Fig.T ll 16 Sampl oupt.1 Progra LNPROC (Son- eg _ala support):_ __ ___ ploItsII T_ apprent 1ri 111 l 111/ palat-ic distance ___ ___ ___

20__ IIII _ for IIU 1/rasn inrmet of trai _tension.__ ___ ___

33

SLOPE - .807. WIND PROFILE 4 LAUNCH EXAMPLE-STONEHENGE CABLE RESTRAINED LAUNCH

i ' '''• " \ j -T ^ ' ' i h i «I i 0 .. . . i •

900

-00

-_ - -..J t

F-^ 6 00

(I)'

:^_ 500

Z

2:0

' 5 100 200 s00 400 500 600 00 S00G 900 0 00

DISTANCE PAYLOAD TO WINCH, C, FT

Fig. 17 Sample output, Program LNPROC (Stonehenge payload support):plots of stay length vs payload-to-winch distance forincreasing increments of train tension.

34

Table V

INPUT DATA CARDS, PROGRAM LAUNCH

(VEHICLE PAYLOAD SUPPORT)12345678901234567890123456789012345678901234567890123456789012345678901234567890

LAUNCH EXAMPLE-CABLE RESTRAINED LAUNCH BY VEHICLE.0736 DENSITY OF AIR IN POUNDS PER CUBIC FOOT.6 COEFFICIENT OF AIR DRAG ON THE BALLOON

'0.*1 COEFFICIENT OF AIR LIFT ON THE BALLOON0. RADIUS OF ANCHOR CIRCLE IN FEET0. TOTAL NO. OF ANCHORS0. NO. OF INCLUDED EMPTY ANCHORS0. THICKNESS OF ANCHOR LINES IN INCHES0. DENSITY OF ANCHOR LINES IN POUNDS PER FOOT0 WIDTH (FT.) OF SPREADER AT APEX OF ANCHOR LINES0. LENGTH (FT) BETWEEN ANCHOR LINE CONFLUENCE AND EXTENSION LINE END

25. HEIGHT OF PAYLOAD IN FEET3780. WEIGHT OF PAYLOAD IN POUNDS

0 LENGTH OF EXTENSION LINE IN FEET----„ --„ ------ ------ -----.---- ----0. WEIGHT OF EXTENSION LINE IN POUNDS

-.008 GROUND SLOPE (FT./FT.) + IF WINCH ABOVE PAYLOAD403. TOTAL TRAIN LENGTH IN FEET

1.0 INTEGRATION STEP SIZE FOR TRAIN SIDE IN FEET..3 - NO. OF SECTIONS OF CONSTANT THICKNESS1 -85. THICKNESS (FT.) AND LENGTH (FT.) OF SECTION

-------- · --------- 5o -c,------fCNI-cfNE'(FT;-f7--Nb--L-EN-GTH--TFT;T-IUF-S-E-CTrON.6666 268. THICKNESS (FT.) AND LENGTH (FT.) OF SECTION

3 NO. OF SECTIONS OF CONSTANT DENSITY60. 85. TOTAL WEIGHT (LBS.) AND LENGTH (FT.) OF SECTION----------------------------------------120. 50. TO.TAL WEIGHT (LBS. ) AND LEN-T-'-H (FT - OF- E-T-fON----

1088. 268. TOTAL WEIGHT (LBS.) AND LENGTH (FT.) OF SECTION0."" 0 WEIGHT OF TRANSFER FITTING IN POUNDS

232. WEIGHT OF TOP BALLOON IN POUNDS6089. GROSS LIFT IN POUNDS2500. HORIZONTAL CROSS SECTION OF BALLOON IN SQUARE FEET2680. VERTICAL CROSS SECTION OF BALLOON IN SQUARE FEET

.625 THICKNESS OF STAY IN INCHES*72 DENSITY OF STAY IN POUNDS PER FOOT

1.0 INTEGRATION STEP SIZE FOR STAY SIDE IN FEET4 NUMBER OF WINDS

0. 0. 0. COEFFICIENTS OF WIND PROFILE POLYNOMIAL0. .878 .35 COEFFICIENTS OF WIND ROFI--E PO-LYNO-MAL0. o986 .35 COEFFICIENTS OF WIND PROFILE POLYNOMIAL0. 1.083 .35 COEFFICIENTS OF WIND PROFILE-PO-LYNOMIAL

0.0 DECIMAL FRACTION OF TRAIN ON GROUND0.0 ALPHA IN DEGREES1.0 ALPHA IN DEGREES5. ALPHA IN DE GREES - :---

10. ALPHA IN DEGREES_..-...A-LPH- I DEE-- ----------------------.-----------------------------

1520 ALPHA IN DEGREES25. ALPHA IN DEGREES30. ALPHA IN DEGREES30. ALPHA IN DEGREES

40- ALPHA IN DEGREES

50- ALPHA IN DEGREES ____.....50. ALPHA IN DEGREES65. ALPHA IN DEGREES60. ALPHA IN DEGREES

50. ALPHA IN DEGREES70. ALPHA IN DEGREES75. ALPHA IN DEGREES77. ALPHA IN DEGREES78. ALPHA IN DEGREES

79. ALPHA IN DEGREES80 _ALPHA IN DEGREES_ ____________


35

Table VI

PRINTOUT OF INPUT DATA, PROGRAM LAUNCH

(VEHICLE PAYLOAD SUPPORT)

LAUNCH EXAMPLE-CABLE RESTRAINED LAUNCH BY VEHICLE

INPUTRHO .07360 DENSITY OF AIR IN POUNDS PER CUBIC FOOT

PDBCOF .60000 COEFFICIENT OF AIR DRAG ON THE BALLOONALBCOF .10000 COEFFICIENT OF AIR LIFT ON THE BALLOONRADIUS 0. RADIUS OF ANCHOR CIRCLE IN FEETANCHT 0 TOTAL NO. OF ANCHORSANCHE = 0. NO. OF INCLUDED EMPTY ANCHORSATHIK 0 THICKNESS OF ANCHOR LINES IN INCHESADENS = 0. DENSITY OF ANCHOR LINES IN POUNDS PER FOOTSPRFD - 0 WIDTH (FT.) OF SPREADER AT APEX OF ANCHOR LINESXTRA = 0 LENGTH (FT) BETWEEN ANCHOR LINE CONFLUENCE AND EXTENSION LINE ENDHPAY - 25,00000 HEIGHT OF PAYLOAD IN FEETWPAY - 3780.00000 WEIGHT OF PAYLOAD IN POUNDSHEXT 0 LENGTH OF EXTENSION LINE IN FEETWEXT = O0 WEIGHT OF EXTENSION LINE IN POUNDS

SLOPE - -o00800 GROUND SLOPE (FT./FT.) + IF WINCH ABOVE PAYLOADTLNGTH - 403.00000 TOTAL TRAIN LENGTH IN FEETSTEPI 1.00000 INTEGRATION STEP SIZE FOR TRAIN SIDE IN FEETNSECTH = 3 NO. OF SECTIONS OF CONSTANT THICKNESSTTHIK = 1.00000 85.00000 THICKNESS (FT.) AND LENGTH (FT.) OF SECTIONTTHIK = 2.00000 50.00000 THICKNESS (FT.) AND LENGTH (FT,) OF SECTIONTTHIK = .66660 268.00000 THICKNESS (FT.) AND LENGTH (FT.) OF SECTIONNSECD = 3 NO. OF SECTIONS OF CONSTANT DENSITYTDENS 60.00000 85.00000 TOTAL WEIGHT (LBS.) AND LENGTH (FT.) OF SECTIONTDENS 120.00000 50.00000 TOTAL WEIGHT (LBS.) AND LENGTH (FT.) OF SECTIONTDENS - 1088.00000 268.00000 TOTAL WEIGHT (LBS.) AND LENGTH (FT.) OF SECTION

WTF = 0. WEIGHT OF TRANSFER FITTING IN POUNDSWTB = 232.00000 WEIGHT OF TOP BALLOON IN POUNDS

GLIFT 6089.00000 GROSS LIFT IN POUNDSXSECTH = 2500.00000 HORIZONTAL CROSS SECTION OF BALLOON IN SQUARE FEETXSECTV 2680.00000 VERTICAL CROSS SECTION OF BALLOON IN SQUARE FEETSTHIK = ,62500 THICKNESS OF STAY IN INCHESSDENS = .72000 DENSITY OF STAY IN POUNDS PER FOOTSTEP2 1.00000 INTEGRATION STEP SIZE FOR STAY SIDE IN FEETNWIND = 4 NUMBER OF WINDS

WIND 0 . 0. 0. COEFFICIENTS OF WIND PROFILE POLYNOMIALWIND 0. .87800 .35000 COEFFICIENTS OF WIND PROFILE POLYNOMIALWIND = 0. .98600 .35000 COEFFICIENTS OF WIND PROFILE POLYNOMIALWIND = 0. 1.08300 .35000 COEFFICIENTS OF WIND PROFILE POLYNOMIALTTP = 100.0 3880.0 756.0 INITIALFINALINCREMENTAL TENSIONS AT PAYLOAD

36

Table VII

SAMPLE OUTPUT PAGE, PROGRAM LAUNCH


ALPHA = 50.00 FTONG = 0.WIND PROFILE 1 ALPHA = 50.000 FTONG = 0.

TTP = 100.542 856.541 1612.541 2368.541 3124.541 3880.541ALPHAR = 87.263 74.038 67.511 63.716 61.256 59,537

TTR 1346.140 2000.875 2708.871 3437.373 4175.663 4919.335TOTALH - 410.836 378 330 365.656 358.560 354.029 350.889

PARTC = 86.612 185.272 211.390 223.913 231,252 236.067TSR = 4512.853 3971.565 3510.539 3165.046 2975.603 2972.203

THETAW = 89.127 81.443 71.385 58.399 42.357 23.254TSW ' 4216.965 3697.950 3246.038 2904.782 2717.408 2714.530

SLNGTH = 411.622 384.234 386.982 418.637 507.159 757.392C = 92.676 240.423 330.151 434.039 589.492 902.423

ALPHAA = 77.348 62.329 58.1i9 56.127 54.899 54.081TEXT s 100.542 856.541 1612.541 2368*541 3124.541 3880.541

TANCH 0. 0. 0. 0. 0. 0.FALB 0. 0. 0. 0. 0. 0.

FBY 5857.000 5857.000 5857.000 5857.000 5857.000 5857.000FDR = 0. 0. O. 0. 0. 0O

WINoR 0, .00 0


TTP = 100.542 856.541 1612.541 2168*541 3124*541 3880.541ALPHAR = 85.787 73.253 66.976 63.315 60.935 59.271

TT 8 1341.503 1996.518 2705,678 34343934 4173.727 4917.755TOTAIH - 409.153 377.079 364.732 357.835 353.435 350.386

PARTC = 95. 70 188.115 213.081 225.104 \232.167 236.808TSR = 4580.892 4077.937 3658.595 3158,663 3212.261 3240.349

THETAW = 84.757 77.041 66.930 54.240 39.080 21.412TSW = 4286.1?9 3805.208 3394.566 3n98.904 2954.465 2982.774

SLNGTH 411.814 388.465 396.980 436.955 537.569 807.429C= 132 061 272.175 362.832 470,315 632.479 959.442

ALPHAA A 76.004 61.885 57.904 55.929 54.744 53.954TEXT = 100.542 856.541 1612.541 2q68.541 3124.541 3880.541

TANCH 0 . 0 0. 00 0 0.FAI R = 45.201 42.916 42.023 41.520 41.198 40.974FRY - 5902.201 5899.916 5899.023 5898.520 5898.198 5897.974FoB = 290.732 276,036 270,289 267.056 264.984 263.545

WINDR = 7.444 7.253 7.178 7.134 7.107 7.087


TTP s 100-542 856.541 1612.541 2368.541 3124.541 3880.541ALPHAR = 85.408 73.049 66.838 63.211 60.852 59.201

TTR = 1340.182 1995.374 2704,844 3434.297 4173.222 4917.343TOTALH = 408.683 376.751 364 490 357.645 353 279 350.255

PARTC = 98.082 188*849 213.519 225.413 232.405 237,001TSR = 4602.522 4108.958 3700.130 3411.446 3275.357 3310.806

THETAW = 83.647 75.939 65.833 53.240 38.310 20.986TAW = 4307.585 3836.703 3436.151 3151.759 3017.595 3053.171

SLNGTH = 412 177 3899869 399,865 441.934 545.519 820.092C = 14?.093 280 273 371.164 479.548 643,379 973 737

ALPHAA = 75.660 61 769 57 832 55.877 54 703 53,921TEXT = 100.542 856.541 1612.541 2368A541 3124.541 3880.541TANCH 0. 0 0, 0 0 O,

FALRB 56.963 54.093 52.974 52.345 51.942 51.662FRY = 5913.963 5911.093 5909.974 5909.345 5908.942 5908 662FOP = 366.386 347.929 340.730 336.684 334.091 332.290

WINnR = 8.357 8.143 8.0~9 8.011 7.980 7,958

WINn PROFILE 4 ALPHA = 50,000 FTONG = 0

TTP 1= 00.542 856,541 1612.541 2368*541 3124,541 3880,541ALPHAR = 85.033 72*848 66.700 63,107 60.769 59,133

TTR = 1338.823 1994.231 2704,012 3433.663 4172.719 49169932TOTALH = 4n8.203 376.423 364,248 357.457 3539125 350,124

PARTC = 100.383 189,578 213.954 ?2 5721 232 642 237,193TSR - 4625.608 4141 149 3742.635 3464.895 3338 728 3381 197

THETAW = 82.556 74.858 64.768 52 278 37 574 20 593TSW = 4331.306 3868.746 3478.767 3205.309 3080.986 3123.708

SLNGTH - 412.660 391 382 402.842 446 963 553 436 832 544C = 151.989 ?88.268 379.390 488*658 654*115 987.749

ALPHAA = 75 .21 61.655 57.762 55 826 54.663 53 888TEXT - 100.542 856,541 1612.541 2368.541 3124.541 3880,541

TANCH 0 0O 0. 0 0. 0.FALR = 68.671 65.2?4 63.883 63.130 62.647 62,312

FRY = 5925.671 5922.224 5920.883 5920.130 5919.647 5919.312FORB 441.b89 419.5E2 410.897 406.051 402.948 400.792

WINoR = 9.175 8.942 8,850 8.797 8.764 8.740

37

of Stonehenge anchor lines, and the consideration of the anchor lines'

extension as the initial train segment.

In dd80 pictorials of the launch designs, the payload-supporting

vehicle is represented as a post to which the base of the train is

attached (Fig. 18). Curves drawn by Program LNPROC (Figs. 19 and 20)

for a vehicular launch are analogous to those for the Stonehenge launch,

but display no values for the length of train on the ground. Vehicular

launches are considered initiated with the train already off the ground

(FTONG = 0).

B. FIXED PAYLOAD-TO-WINCH DISTANCE

For the sample launch problem, Program CLANCH produces lists of

forces and positions of the balloon, train, and cable associated with

various wind conditions while a constant payload-to-winch distance is

maintained. Input data cards for CLANCH are nearly identical in se-

quence and format to those of Program LAUNCH. An additional data card

defining the desired constant payload-to-winch distance is inserted

between the wind profile data and the first value of variable FTONG.

1. Stonehenge Payload Support

Table VIII gives the input data to Program CLANCH used for the

Palestine test launch problem with Stonehenge payload support, and

Table IX the input printout with Stonehenge array geometry. Table X

displays a sample calculation printout page. The train tension values

associated with each of the given wind profiles for the predetermined

payload-to-winch distance appear as variable TTP in the printout.

Figure 21 illustrates a dd80 pictorial representing the block of en-

closed data in Table X which is supplied by Program CLANCH. The curves

drawn by Program GRAPHS for each wind profile variation are given in

Figs. 22-25, with wind profiles numbered according to the order of their

input to the program. Figure 26 shows the plot by Program GRAPHS of

train elevation angle vs cable length. In this case, the family of four

curves is identical; in some cases a distinct curve for each wind profile

will be apparent.

38

LAUNCH EXAMPLE-CABLE RESTRAINED LAUNCH BY VEHICLE700 . I , , , I ' , , I I , , , I I , , . I I ... I I I .. I I .X

WIND PROFILE 4 ALPHAA = 55 TTP - 3125 SLNGTH « 553 FTONG 0

600

500

-t~/ \ '&La

3

t200

1300

_D _ AC o o C F

A A A A A A A A DISTANCE FROM PAYLOAD, C, FT

Fig. 18 Typical dd80 pictorial, Program LAUNCH (vehicle payloadsupport).

39

SLOPE - - .807. WIND PROFILE 4 LAUNCH EXAMPLE-CABLE RESTRAINED LAUNCH BY VEHICLE. .. . -. . .. .-.. . _ ._.. _ _ _ ~ ........ 1-1--.-—-.-. - ...- .

------ -I i_ - I _ .- _ + : -r--450

I tH H 5 H t H H E H 2ta. k HH t J' t

0 100 20o Sol 40 Soo 600 _oo 1f o 00 I o:

DISTANCE PAYLOAD TO WINCH, C, FT

for increasing increments of train tension.

z _ __ __- __ -__ __-: -_----- .. -- II--I rIrTI Ir ::::: _::::: ::::_^; ::::::: _::::::::_ 2I___ 1_z IiI t11111 -

::::::::::::::::::::: ^_ __ 1_ L_ 1:_:__:f:::::::::::::::::: 1 1 1

40

SLOPE - - .807 WIND PROFILE 4 LAUNCH EXAMPLE-CABLE RESTRAINED LAUNCH BY VEHICLE

900

700

3= 600

z

fg 1 4 W 0 W X 4 4 W 4 4 T44..........

so 0

I/.

500 _ _ _____ _- _--_______ _ _-_-_. _ . _. _ . ·- - - --

:¶1 ~ 0 0 61 · ' 0

F ig. 20 Sample output, Program LNPROC (vehicle payload support):

plots of stay length vs payload-to-winch distance for

»--—- _.-- ___ _'_ _-- - - - - - -- --'- ---N -_ W I / I

^/ F ::::::::::211^ ;:/:::::: :::Z:::::::::::::

200 r .. . . . . . . .

/ 0 9O 200 *0 o 40 .0 600 7fo 100 o0 OOOt DISTANCE PAYLOAD TO WINCH, C, FT

Fig. 20 Sample output, Program LNPROC (vehicle payload support):plots of stay length vs payload-to-winch distance forincreasing increments of train tension.

41

Table VIII

INPUT DATA CARDS, PROGRAM CLANCH

(STONEHENGE PAYLOAD SUPPORT)1234567890 12 3456789012345678901234567890123456789012 34567890 12345678901234567890

CLANCH EXAMPLE-STONEHENGE CABLE RESTRAINED LAUNCH.0736 DENSITY OF AIR IN POUNDS PER CUBIC FOOT·6 COEFFICIENT OF AIR DRAG"ON THE BALLOON

0.1 COEFFICIENT OF AIR LIFT ON THE BALLOON50. RADIUS OF ANCHOR CIRCLE IN FEET ——24. TOTAL NO. OF ANCHORS

5. NO. OF INCLUDED EMPTY ANCHORS.625 THICKNESS OF ANCHOR LINES IN INCHES.72 DENSITY OF ANCHOR LINES IN POUNDS PER FOOT

2.1667 WIDTH (FT.) OF SPREADER AT APEX OF ANCHOR LINES0.0 LENGTH (FT) BETWEEN ANCHOR LINE CONFLUENCE AND EXTENSION LINE END


33.337 LENGTH OF EXTENSION LINE IN FEET15. WEIGHT OF EXTENSION LINE IN POUNDS . ... .. ...-. 008 GROUND SLOPE (FT./FT.) + IF WINCH ABOVE PAYLOAD

403. -TOTAL TRAIN-'LENGTH"I'N FEET-- -10o INTEGRATION STEP SIZE FOR TRAIN SIDE IN FEET3 NO. OF SECTIONS OF CONSTANT THICKNESS1. 85. THICKNESS (FT.) AND LENGTH (FT.) OF SECTION2. 50. THICKNESS (FT.) AND LENGTH (FT.) OF SECTION

.6666 268. THICKNESS (FT.) AND LENGTH (FT.) OF SECTION3 NO, OF SECTIONS OF CONSTANT DENSITY

60. 85. TOTAL WEIGHT (LBS.) AND LENGTH (FT.) OF SECTION120. 50. TOTAL WEIGHT (LBS.) AND LENGTH (FT.) OF SECTION'

1088. 268. TOTAL WEIGHT (LBS.) AND LENGTH (FT.) OF SECTION0.0 WEIGHT OF TRANSFER FITTING IN POUNDS

232. WEIGHT OF TOP BALLOON IN POUNDS.6089. GROSS LIFT LN POUNS S ......- ..... ..... .. 2500. HORIZONTAL CROSS SECTION OF BALLOON IN SQUARE FEET2680. VERTICAL CROSS SECTION OF BALLOON IN SQUARE FEET

.625 THICKNESS OF STAY IN INCHES

.72 DENSITY OF STAY IN POUNDS PER FOOT1.0 INTEGRATION STEP SIZE FOR STAY SIDE IN FEET

NUMBER" OF WINDS..0. 0. 0. COEFFICIENTS OF WIND PROFILE POLYNOMIAL0. .878 .35 COEFFICIENTS OF WIND PROFILE POLYNOMIAL0. .986 .35 COEFFICIENTS OF WIND PROFILE POLYNOMIAL0. 1.083 .35 COEFFICIENTS OF WIND PROFILE POLYNOMIAL

425. DISTANCE FROM PAYLOAD TO WINCH IN FEET.99 DECIMAL FRACTION OF TRAIN ON GROUND.95 DECIMAL FRACTION OF TRAIN ON GROUND.9 DECIMAL FRACTION OF TRAIN ON GROUND.8 DECIMAL FRACTION OF TRAIN ON GROUND.7 DECIMAL FRACTION OF TRAIN ON GROUND.6 DECIMAL FRACTION OF TRAIN ON GROUND.5 DECIMAL FRACTION OF TRAIN ON GROUND.4 DECIMAL FRACTION OF TRAIN ON GROUND.3 DECIMAL FRACTION OF TRAIN ON GROUND.2 DECIMAL FRACTION OF TRAIN ON GROUND.1 DECIMAL FRACTION OF TRAIN ON GROUND.01 DECIMAL FRACTION OF TRAIN ON GROUND

0.0 DECIMAL FRACTION OF TRAIN ON GROUND0.0 ALPHA IN DEGREES1.0 ALPHA IN DEGREES5. ALPHA IN DEGREES10. ALPHA IN DEGRFFS15. ALPHA IN DEGREES20. ALPHA IN DEGREES25. ALPHA IN DEGREES30. ALPHA IN DEGREES35.0 ALPHA IN DEGREES40. ALPHA IN DEGREES45. ALPHA IN DEGREES50. ALPHA IN DEGREES55. ALPHA IN DEGREFS60. ALPHA IN DEGREES65. ALPHA IN DEGREES70. ALPHA IN DEGREES75.0 ALPHA IN DEGREES76. ALPHA IN DEGREES77. ALPHA IN DEGREES78. ALPHA IN DEGREES79. ALPHA IN DEGREES80. ALPHA IN DEGREES


42

Table IX

PRINTOUT OF INPUT DATA AND CALCULATED

STONEHENGE ARRAY GEOMETRY, PROGRAM CLANCH

CLANCH EXAMPLE-STONEHENGE CABLE RESTRAINED LAUNCH

INPUTRHO = ,07360 DENSITY OF AIR IN POUNDS PER CUBIC FOOT

PUBCOF = ,60000 COEFFICIENT OF AIR nRAG ON THE BALLOONALBCOF = .1000o COEFFICIENT OF AIR LIFT ON THE BALLOONRADIUS = 50.00000 RADIUS OF ANCHOR CIRCLE IN FEETANCHT = 24.00000 TOTAL NO. OF ANCHORSANCHE = 5.00000 NO. OF INCLUDED EMPTY ANCHORSATHIK = .62500 THICKNESS OF ANCHOR LINES IN INCHESADENS = .72000 DENSITY OF ANCHOR LINES IN POUNDS PER FOOTSPRED = ?216670 WIDTH (FT.) OF SPREADER AT APEX OF ANCHOR LINES

XTRA = O. LENGTH (FT) BETWEEN ANCHOR LINE CONFLUENCE AND EXTENSION LINE ENDHPAY = 15.00000 HEIGHT OF PAYLOAU IN FEETWPAY = 3780 OO000 WEIGHT OF PAYLOAU IN POUNDSHEXT = 33.33700 LENGTH OF EXTENSION LINE IN FEETWEXT = 15.00000 WEIGHT OF EXTENSION LINE IN POUNDS

SLOPE = -.00800 GROUND SLOPE (FT./FT.) * IF WINCH ABOVE PAYLOAD

GEOMETRY OUTPUTPHI = 53.81698

PANCH = 59.88711S = 35.35534

EPS = 29.78150A = 69.00025

I NPUTTLNGTH = 403.00000 TOTAL TRAIN LENGTH IN FEET

STEP1 = 1.00192 INTEGRATION STEP SIZE FOR TRAIN SIDE IN FEETNSECTH = 3 NO. OF SECTIONS OF CONSTANT THICKNESS

ITHIK = 1.00000 85.00000 THICKNESS (FT.) AND LENGTH (FT.) OF SECTIONTTHIK = 2.0000 50.00000 THICKNESS (FT.) AND LENGTH (FT.) OF SECTIONTTHIK = .66660 268.00000 THICKNESS (FT.) AND LENGTH (FT.) OF SECTIONNSECD = 3 NO. OF SECTIONS OF CONSTANT DENSITYTDENS = 60.00000 85.00000 TOTAL WEIGHT (LBS.) AND LENGTH (FT.) OF SECTIONTDENS = 120.00000 50.00000 TOTA.. WEIGHT (LBS.) AND LENGTH (FT.) OF SECTIONTUENS = 1088.00000 268.00000 TOTAL WEIGHT (LBS.) ANU LENGTH (FT.) OF SECTION

WTF = 0. WEIGHT OF TRANSFER FITTING IN POUNDSWTB = 232.00000 WEIGHT OF TOP BALLOON IN POUNDS

GLIFT = 6089.00000 GROSS LIFT IN POUNDSXSECTH = 2500.00000 HORIZONTAL CROSS SECTION OF BALLOON IN SQUARE FEETXSECTV = 2680.000000 VERTICAL CROSS SECTION OF BALLOON IN bQOJARE FEETbTHIK = .62500 THICKNESS OF STAY IN INCHESSDENS = .72000 DENSITY OF STAY IN POUNDS PER FOOTSTEP2 = 1.00000 INTEGRATION STEP SIZE FOR STAY SIDE IN FEETNWIND = 4 NUMRER OF WINDSWINl = 0. O. .. COEFFICIENTS OF WIND PROFILE POLYNOMIALWIND = 0. .87R00 .35000 CUEFFICIENTS OF WIND POHFILE POLYNOMIALWIND = 0. .98600 .35000 COEFFICIENTS OF wIND PHOFILE POLYNOMIALWINU = 0. 1.08300 .35000 COEFFICIENTS OF WINU PROFILE POLYNOMIAL

CWANT = 425.00000 DISTANCE FROM PAYLOAD TO WINCH IN FEET

43

Table X

SAMPLE OUTPUT PAGE, PROGRAM CLANCH

(STONEHENGE PAYLOAD SUPPORT) ----

ALPHA 55.00 ... FTON --------------NWIND 1 2 3 4

.___TP-_. -7 6-- ...... _ .......5 .. 2-42.2989 —-- 2074.q09 200511 _1ALPHAB = 66.916 67.346 67 468 67.595

.TTB. 3522.285 3260.686 ....319267Q .. 312 ..... .Q 02TOTALH = 397.480 398.168 398.365 398,570

PARTC 198.902 197.515 19-7 113 .. 49..-..TSB = 2958.790 3277.497 3360.713 3443.666

ITHETAW sa58858 58.910 58916 . 58.13 TSW a 2670.357 2988.758 3072.064 3154.496

SLNGTH 460.310 461.580 461.947 462.33..C = 425.001 425.000 425.000 425.000

ALPHAA 60.331 60.551 60.615 ..... 6,81..8..TEXT a 84.201 74.944 72.534 70.136

TANCH. 1347,592 1199.436 1164L 3 ... . 1.12289 FALB 0 44.424 56.043 67.634

FBY 5857.000 5901.424 5913.. 43 5-9.24a3_...3FOB o. 285.735 360.467 435.021

WINDB 0. 7.380 8.289 ... ......

ALPHA = 60.00 ......... ... _.T.ONG =_ __NWIND = 1 2 3 4

TTP 2607.511 2329.873 2257.487 2185.,....ALPHAB = 69.709 69.933 69.997 70.063

TTB = 3759.476 3483.332 3411.366 3339.6 7-TOTALH = 410.772 411.054 411.136 411.220

FARTC = 174.245 ]73.559 173-361- l...13-55TSB = 2670.682 3021.566 3113.177 3204.498

THETAW = 56.668 56.871 s6.905 ..-.. 54 2TSW = 2372.654 2723.706 2814.763 2906.135

SLNGTH = 484.?69 484.845 485.013 1.3- 485-.88 ..C = 425.000 425.000 425.000 424.999

ALPHAA 64.323 64.429 64459..-.... ,4 ...TEXT = 475.706 425.055 411.849 398.693

TANCH a 1272.219 1136.758 lnl .440 1066.,56FALB a O 45.335 57.181 68,994

FBY = 5857.000 5902.335 5914.181 5925.994..FDB 0. 291.593 367.787 443.768

WINDB = 0. 7.455 8.373 9.197

ALPHA = 65.00 FTONG = ._NWIND a 1 2 3 4

TTP 22828.539 2538.897 2463.254 2367. 846.ALPHAB = 72.673 72.714 72 726 72.738

TTB = 4013.672 3724,386 3648.839 3573.526TOTALH a 422.461 422.465 422.466 422.466

PARTC = 148.127 148.083 1489070 148,057TSB = 2351.915 2734.551 2834.487 2934.117

THETAW = 54.237 54.638 54.723 548.01TSW = 2045.387 2428.037 2527.978 2627,615

SLNGTH = 508.128 508.110 508.109 508.109C = 425.000 425.001 425.001 425.001

ALPHAA = 68.400 68.406 68.408 68.409TEXT = 929.214 834.063 809.213 784.441

TANCH = 1166.477 1047.030 1015.835 984.737FALB = o. 46.135 58.183 70.193FBY a 5857.000 5903.135 59 15.183 5927,193FOB = 0. 296.738 374.230 451.484

WINDB = o. 7.521 8.446 9.276

44

CLANCH EXAt:PLE-STO-EENGE CABLE P£STRAIED LA' CHi i i , ' I § '' ' I I I i , I I i t · I i i * * ; ' I I" . l , I,, , ,_

WIN PRO 4 ALPHAA , 68 TTP - 2588 SLNGTH - 508 C - 425 FTONGS ·

600

..

9-00

o00

I -

loo - \ \ :DISTANCE FROM PAYLOAD, C, FT

Fig. 21 Typical dd80 pictorial, Program CLANCH (Stonehenge payloadsupport).

45

CLANCH E:;ArPLE-STONH-ENGE CABLE RESTRAINED LATCH C- 425

51l ————— — — —— — — ——— — — — — ——1

I-m.,~~~~~- [

I00

Z F000 W < 2 P F1 E -1

LC _ 4 I—I--- -..-I 11--0 1

0 ---- 0-0-lg 200 So -400 0oo 600 o00

MAIN STAY LENGTH, SLNGTH, FT

</r)2 ——00—


Fig. 22 Sample output, Program GRAPHS (Stonehenge payload support):tension at winch vs stay length.

46

CLANCH EXAMPLE-STONEFNGE CABLE RESTRAINiED LAUNCH C= 425

3zSIO————— ———— -———oo —— .————————0-I

z 33200-

,.-_ _ _ _ _ _ _ _ __ 7; r_ _~~~~~~~~~V I I '

z -__ ____ _ ___________ __ __-_ = ___—__ —- _- _. —- .-.

za _-- ____-_-__-____ __ __ _ _ _ ---- -

2- —- ——— -..............

_^ ____ __ __ __ __ _ _ __ _______.__ _ _ Z-_____._- __.___. -I I -:l::.l

oo

z———- -- ----.

o J '100 200 500 - 400 o00 600 700


Fig. 23 Sample output, Program GRAPHS (Stonehenge payload support):extension line tension vs stay length.

47

CLANCH EXAIPLE-STONEHENGE CABLE RESTRAINED LAUNCH C= 4251600 .........

ID

LI /- 1 _ -7 _~7 _ __

o.. .. .--- _ . __ _ __ _____ _ _ _ ,.... .^ _ -... _.....

()•I 0 _---…..... _-

-1

400

200

0 t0oo 200 500 400 oo0 600 7MAIN STAY LENGTH, SLNGTH, FT

Fig. 24 Sample output, Program GRAPHS (Stonehenge payload support):anchor cable tension vs stay length.

48

CLANCH EXAPPLE-STONI-INE CABLE RESTRAINED LAUNCH C= 425

J- ° ° ° 'ii 1 I I i WIN

--- ------------- - _-'---,.. m 1 1 1 /,~: R 1 1ILI

: /

'_L--0 0 0

W3000o —_ _ _ ,—_- _ _ _ __ __ __I .-.

0 100 200 300 40 60 Soo 79tMAIN STAY LENGTH, SLNGTH, FT

Fig. 25 Sample output, Program GRAPHS (Stonehenge payload support):train tension at anchor apex vs stay length.

49

CLANCH EXAMPLE-STONEHENGE CABLE RESTRAINED LAUNCH C= 425

'o . . 71.-i . ..

Ieo -

——60 - — - - --

4 .-o --..--. -- -....-. I

I--- - - —~

-. .-------.........


Fig. 26 S=mple output Program GRAPHS (=-__ __ T-Ipay =loa=d =uort:1-

*e tp aet tri anl vs sa ln f I

I-- -f

60 I3 9! !00 000 see 400


Fig. 26 Sample output, Program GRAPHS (Stonehenge payload support):

L~~paettananl ssa egh

50

2. Vehicle Payload Support

Input data for Program CLANCH using vehicle payload support is near-

ly identical to that of the Stonehenge launch, with the circle radius

and other Stonehenge-related variables set to zero (Table XI). Table XII

gives the input data printout of Program CLANCH. A sample output page

for the problem is shown in Table XIII. A post represents the vehicle

in the dd80 pictorial of Program CLANCH (Fig. 27). Program GRAPHS draws

three pertinent curves for this case: apparent train angle, stay ten-

sion at winch, and train tension at the anchor apex (Figs. 28-30).

51

Table XI

INPUT DATA CARDS, PROGRAM CLANCH

(VEHICLE PAYLOAD SUPPORT) ---- -

12345678901234567890123456789012345678901234567890123456789012345678901234567890

CLANCH EXAMPLE-CABLE RESTRAINED LAUNCH BY VEHICLE.0736 DENSITY OF AIR IN POUNDS PER CUBIC FOOT.6 COEFFICIENT OF AIR DRAG ON THE BALLOON

0.1 COEFFICIENT OF AIR LIFT ON THE BALLOON0. RADIUS OF ANCHOR CIRCLE IN FEET0. TOTAL NO. OF ANCHORS

0. NO. OF INCLUDED EMPTY ANCHORS0. THICKNESS OF ANCHOR LINES IN INCHES0. DENSITY OF ANCHOR LINES IN POUNDS PER FOOT0. WIDTH (FT.) OF SPREADER AT APEX OF ANCHOR LINES0. LENGTH (FT) BETWEEN ANCHOR LINE CONFLUENCE AND EXTENSION LINE END


0. LENGTH OF EXTENSION LINE IN FEET0. WEIGHT OF EXTENSION.LINE IN POUNDS-.008 GROUND SLOPE (FT./FT.) + IF WINCH ABOVE PAYLOAD

403. TOTAL TRAIN LENGTH IN FEET1.0 INTEGRATION STEP SIZE FOR TRAIN SIDE IN FEET"3 " NO. OF SECTIONS OF CONSTANT THICKNESS1. 85. THICKNESS (FT.) AND LENGTH (FT.) OF SECTION2. 50. THICKNESS (FT-) AND LENGTH (FT.) OF SECTION.6666 268. THICKNESS (FT.) AND LENGTH (FT.) OF SECTION

3 NO. OF SECTIONS OF CONSTANT DENSITY60. 85. TOTAL WEIGHT (LBS.) AND LENGTH (FT.) OF SECTION

120. 50. TOTAL WEIHT (LBS.) AND ENGrHTT.-T F--OSECTTON -1088. 268. TOTAL WEIGHT (LBS.) AND LENGTH (FT.) OF SECTION

0.0 WEIGHT OF TRANSFER FITTING IN POUNDS232. WEIGHT OF TOP BALLOON IN POUNDS

6089. GROSS LIFT IN POUNDS2500. HORIZONTAL CROSS SECTION OF BALLOON IN SQUARE FEET2680. .VERTICAL CROSS SECTION OF BALLOON IN SQ-UARE FEET

.625 THICKNESS OF STAY IN INCHES.-.------.. 72 DENSI TY OF STAY IN POUNDS PER FOOT-------

1.0 INTEGRATION STEP SIZE FOR STAY SIDE IN FEET4 NUMBER OF WINDS

0. 0. 0. COEFFICIENTS OF WIND PROFILE POLYNOMIAL—o ~0.--.— � -F-C"88E- ----- -.i -F- I----CO-E'-F- -C I1NTS- FE--P-rL . ..... -AO E"P NOMA0. .986 .35 COEFFICIENTS OF WIND PROFILE POLYNOMIAL0. 1.083 35 COEFFIC IENTS OF W-IND PRO-FILE--P-OY-NOMI-AL---------------

425. DISTANCE FROM PAYLOAD TO WINCH IN FEET0.0 DECCIMAL FRACTION OF TRAIN ON GROUND 0.0 ALPHA IN DEGREES1 .0 ALPHA IN DEGREES5. ALPHA IN DEGREES

10. ALPHA IN DEGREES . . ... ..-.15. ALPHA IN DEGREES—20. ALPHA IN DEGREES25. ALPHA IN DEGREES30. ALPHA IN DEGREES..-. ...35.0 ALPHA IN DEGREES40. ALPHA IN DEGREES45. ALPHA IN DEGREES50. ALPHA IN DEGREES55. ALPHA IN DEGREES60. ALPHA IN DEGREES65. ALPHA IN DEGREES70. ALPHA IN DEGREES75.0 ALPHA IN DEGREES76. ALPHA IN DEGREES77. ALPHA IN DEGREES78. ALPHA IN DEGREES79. ALPHA INDEGREES80. ALPHA IN DEGREES


52

Table XII

PRINTOUT OF INPUT DATA, PROGRAM CLANCH

(VEHICLE PAYLOAD SUPPORT)CLANCH EXAMPLE-CABLE RESTRAINED LAUNCH BY VEHICLE

INPUT

RHO 0 .07360 DENSITY OF AIR IN POUNDS PER CUBIC FOOTPDBCOF * .60000 COEFFICIENT OF AIR DRAG ON THE BALLOONALBCOF a .10000 COEFFICIENT OF AIR LIFT ON THE BALLOONRADIUS X 0o RADIUS OF ANCHOR CIRCLE IN FEET

ANCHT * O0 TOTAL NO, OF ANCHORSANCHE s O. NO. OF INCLUDED EMPTY ANCHORSATHIK * 0 THICKNESS OF ANCHOR LINES IN INCHESADENS 0O DENSITY OF ANCHOR LINES IN POUNDS PER FOOTSPRED 0 0. WIDTH (FT.) OF SPREADER AT APEX OF ANCHOR LINESXTRA * O0 LENGTH (FT) BETWEEN ANCHOR LINE CONFLUENCE AND EXTENSION LINE ENDHPAY = 25.00000 HEIGHT OF PAYLOAD IN FEETWPAY * 3780.00000 WEIGHT OF PAYLOAD IN POUNDSHEXT a 0 LENGTH OF EXTENSION LINE IN FEETWEXT s 0 WEIGHT OF EXTENSION LINE IN POUNDSSLOPE * -.00800 GROUND SLOPE (FT./FT.) + IF WINCH ABOVE PAYLOAD

TLNGTH * 403.00000 TOTAL TRAIN LENGTH IN FEETSTEP1 1.00000 INTEGRATION STEP SIZE FOR TRAIN SIDE IN FEET

NSECTH a 3 NO. OF SECTIONS OF CONSTANT THICKNESSTTHIK * 1*00000 85.00000 THICKNESS (FT.) AND LENGTH (FT,) OF SECTIONTTHIK 2 2.00000 50*00000 THICKNESS (FT.) AND LENGTH (FT.) OF SECTIONTTHIK .,66660 268.00000 THICKNESS (FT.) AND LENGTH (FT.) OF SECTIONNSECD * 3 NO. OF SECTIONS OF CONSTANT DENSITYTDENS a 60.00000 85.00000 TOTAL WEIGHT (LBS.) AND LENGTH (FT.) OF SECTIONTDENS a 120,00000 50.00000 TOTAL WEIGHT (LBS.) AND LENGTH (FT.) OF SECTIONTDENS a 1088.00000 268.00000 TOTAL WEIGHT (LBS.) AND LENGTH (FT.) OF SECTIONWTF O0 WEIGHT OF TRANSFER FITTING IN POUNDSWTB * 232,00000 WEIGHT OF TOP BALLOON IN POUNDS

GLIFT = 6089.00000 GROSS LIFT IN POUNDSXSECTH = 2500.00000 HORIZONTAL CROSS SECTION OF BALLOON IN SQUARE FEETXSECTV = 2680e00000 VERTICAL CROSS SECTION OF BALLOON IN SQUARE FEETSTHIK * .62500 THICKNESS OF STAY IN INCHESSDENS = ,72000 DENSITY OF STAY IN POUNDS PER FOOTSTEP2 = 1.00000 INTEGRATION STEP SIZE FOR STAY SIDE IN FEETNWIND - 4 NUMBER OF WINDS

WIND 0. 0 O0 COEFFICIENTS OF WIND PROFILE POLYNOMIALWIND = 0 .87800 .35000 COEFFICIENTS OF WIND PROFILE POLYNOMIALWIND = O. .98600 .35000 COEFFICIENTS OF WIND PROFILE POLYNOMIALWIND = 0. 1.08300 .35000 COEFFICIENTS OF WIND PROFILE POLYNOMIALCWANT = 425.00000 DISTANCE FROM PAYLOAD TO WINCH IN FEET

53

Table XIII

SAMPLE OUTPUT PAGE, PROGRAM CLANCH


ALPHA 5 0. FT-ONG- .. .NWIND 1 2 3 4

TTP * 1562-942 1445.369 141i4513 1383.694ALPHAB = 39.052 41 181 41 769 42.369

TTB = 2012.613 1922.599 1899.454 1876,549TOTALH = 138.361 145.309 147.256 149,257

PARTC = 376.146 372 688 371.680 370.626TSB 4847.856 4885.991 4896.731 4907.795

THETAW 70.774 70.393 ...70 -.2 .18TSW * 4746.430 4779.360 4788.815 4797.923

SLNGTH a 149 943 i57.642 159.814 162.052C = 425.000 425.001 425.000 424.999

ALPHAA z 16.771 17,891 18.208 18,534TEXT m 1562.942 1445.369 1414.513 1383.694

TANCH = . .oO 0FALB 0. 24.318 30.894 37,550FBY a 5857.000 5881.318 5887.894 5894.550FDB o 0. 156.413 198.709 241.519

WINDB = 0. 5.460 6.154 6.785

ALPHA = 1.00 FTONG s 0.NWIND 1 2 3 4

TTP = 1545.375 1427.448 1396.515 1365,662ALPHAB = 39,966 42.086 42.672 43.268

TTB = 2016.027 1925.587 19n2.341 1879.365TOTALH = 145,144 152.078 154.021 156.014PARTC = 374.059 370.463 369.416 368.324

TSB = 4816.589 4858.644 4870417 4882.524THETAW s 70.848 70.434 70.311 70,180

TSW = 4709.663 4747.224 47579720 4767,880SLNGTH = 157.036 164.766 166.946 169.190

C a 425.000 425*000 425.000 425,000ALPHAA = 17.807 18,933 T9.252 19.581

TEXT a 1545.375 1427.448 1396.515 1365.662TANCH = 0. 0 0.FALB = 0. 24,937 31.671 38.483FBY = 5857.000 5881.937 5888.671 5895.483FDB = 0o 160.393 203.709 247.526

WINDB 0. 5.529 6.231 6.869

ALPHA = 5.00 FTONG = 0.NWIND 1 2 3 4

TTP = 1508.904 1386.496 1354.495 1322.554ALPHAB = 42.956 45.041 45.615 46,201

TTB a 2053.759 1958*317 1933.840 1909.618TOTALH = 169.800 176.615 178*521 180 479PARTC = 365.720 361.662 360,485 359.258

TSB a 4704.103 4760.635 4776.221 4792.127THETAW = 70.839 70.334 70.184 70.033

TSW = 4579,443 4631.594 4645.259 4659.93pSLNGTH = 183.064 190.833 193,023 195,278

C = 425.000 424.999 425.000 425.000ALPHAA 21.600 22.744 ?3.068 23.402

TEXT = 1508.904 1386.496 1354.495 1322,554TANCH o 0 0. 0 0.FALB 0. 27.127 34.421 41.787FBY = 5857.000 5884 127 5891,421 5898,787FDB = 0 174.480 221.398 268,775

WINDB 0. 5.767 6.496 7.157

54

CLANCH EXABPLE-CABLE RESTRAIlED LAUNCH BY VEHICLE

WIN PRO 4 ALPHAA - 19 TTP - 1384 SLNGTH - 162 C · 425 FTONGS

*..-d 0 S-LU.

too

0 o

9 .

199Z. O -

DISTANCE FROM PAYLOAD, C, PT

Fig. 27 Typical dd80 pictorial, Program CLANCH (vehicle payloadsupport) .

55

CLANCH EXAMPLE-CABLE RESTRAIND LAUNCH BY VEHICLE C- 425

. t....-......----—…......-... . . . . -.i-. . .

0

L64

J. - == =- _ = - r .--- - —.

^50 o - _ _ _ _ _--- - _ _ -r- --

., I

[ E_4-- I IIIIII— I I III—II-Z- -.- I-—-�-_— —_—— ——-1.-.-

__ __ ... =_.__... ...... _ ......

.-I~~~~~~~~~~~~~~~~~AJ

9= 0 — -- 2050-400 . . . 0

^ ^-_-___-______....

Lai

CJ

2 Soo 4oo Soo 60o ?10MAIN STAY LENGTH, SLNGTH, FT

Fig. 28 Sample output, Program GRAPHS (vehicle payload support):apparent train angle vs stay length.

56

CLANCH EXAMPLE-CABLE RESTRAINED LAUNCH BY VEHICLE C= 425

....... __ .. . _ __ . . .. . . T _ _- .....

--- z--^ _-^ __ _ _-^--^^ ^ , _ _ _ ... _ . .1, .. _. ....

5000

:,in 0 — 00 200 500 0—5tO k— — , —00

v,^~~~~~~~~~~ ,

t3~ 820 9 40 9 6


Fig. 29 Sample output, Program GRAPHS (vehicle payload support):tension at winch vs stay length.

57

CLANCH EXAPLE-CABLE RESTRAINED LAUNCH BY VEHICLE C= 425

---- A ........... l :l

4000 — —

X^ 30 0 m r 010m _ __.__._._ __ _ ___ __._ __ I I _ ._ -_—--. ......

C.-

Z" : _ _ _ _ , 4 . I ._ I....

0x.

I-oo X0200 MMU00X/WIND

0 00 200 500 400 oo0 600 70oMAIN STAY LENGTH, SLNGTH, FT

Fig. 30 Sample output, Program GRAPHS (vehicle payload support):

train tension at anchor apex vs stay length.

a:

train tension at anchor apex vs stay length.

59

REFERENCES

Anderson, J. A., L. E. Colombe, J. Heinsen, and L. J. Lloyd, 1967:Some Notes on Heavy PayZoad BaZZooning. NASA Particle PhysicsProject, Memo No. 46, Lawrence Radiation Laboratory, Universityof California, Berkeley, Calif.

Angevine, J. M., 1968: Test Report: Stonehenge Launch Test,27 October 1967. (Internal report, Scientific Balloon Facility,NCAR, Boulder, Colo.)

Angevine, J. M., J. W. Sparkman, and D. W. Fulker, 1969: Design of theStonehenge Launch System. NCAR Technical Note-40, 89 pp.

Hoerner, S. F., 1958: Fluid Dynamic Drag. (Published by author,148 Busteed Dr., Midland Park, N.J.)

Sherburne, P. A., 1968: Wind Tunnel Tests of Natural Shape BalloonModel. Goodyear Aerospace Corp., Scientific Report No. 1, GER-13731;AFCRL-68-0123, 37 pp.

61

APPENDIX A

Listing of Program LAUNCH

63

RUN 0527R*FORTRANPROGRAM LAUNCH

CC CABLE LAUNCH - FLOATING DISTANCE TO WINCHC USE PROGRAM LNPROC TO PLOT CURVES FROM THIS TAPEC REVISED OCT 1968C

-000002. CQMMON/APARTS/SLOPEWND(3)tALPHATTH(20000)TTC(2000) ALPHABt1THETABTHETAWTTFNS(1000) TSBtSTENSBALLH»PARTCISTEPTTHIN,2TTCINMIN19MAXltSTEP1,Wl(1000),TTHIK(lOOO)oCFBYHCENTXSECTH,3XSECTV9FDB9FBYMIN29MAX2,STEP2,W?2STHIKWINDB

000002 COMMON/AIR/G.RHO9PDBCOFALBCOF000002 DIMENSION PRINT (18910)000002 DIMENSION LABT(20)9LABX(20),LABY(20),IDENT(5),IUESC(8)000002 DIMENSION TDENS(lU),9MEAS(ln),THIK(10),TMEAS(10)000002 DIMENSION WN(3 91)000002 DIMENSION BSHAPX(?3),BSHAPY(23),RSX(23),BSY(23)000002 DATA LABX/28HDISTANCE FROM PAYLOAD, C. FT/000002 DATA LABY/23HHEIGHT ABOVE GROUND, FT/

C CONVERSION BETWEEN DEGREES AND RADIANS000002 DATA PI/3.14159265358979/, CNVIN/.0174532925199433/9

1 CNVOUT/57.2957795130R23/000002 DATA(G=32.1725)000002 DATA BANG/45./, HELFT/64.6/

C CONVERGENCE CRITERION FOR C000002 DATA CRIT/.001/

C ITERATION LIMIT000002 DATA ITLIM/40/000002 IFM = 6H(F6.0)

CC DD80 = 0. MEANS NO PICTORIALS OF APPARATUS

000003 DD80 = 1,C

000005 IF (DD80.NE.O.) CALL GRDFMT(IFMTIFM)000010 READ 1008,(IDENT(I),I=1,5)000021 1008 FORMAT (8A10)000021 PRINT 10099(IDENT(I)I=1i5)000032 1009 FORMAT (1H1,8A1O)000032 PRINT 1002000035 1002 FORMAT (1HO,5HINPUT)000035 READ 1014,RHO *(IDESC(II),II=1.7)000050 1014 FORMAT (F15.596AUO,A5)000050 NAME = 6H RHO000052 PRINT 10159NAMERHO ,(IDESC(II),II=197)000067 1015 FORMAT (IH 9A692H =,F15,55XX7A1;)000067 READ 1014,PDBCOF,(IDESC(II),II=1.f)000102 NAME = 6HPDBCOF000104 PRINT 10159NAMEPDBCOF,(IDESC(II),1II=17)000121 READ 1014,ALBCOF,(IDESC(II)lII=l7)000134 NAME = 6HALBCOF000136 PRINT 10159NAME,ALBCOF,(IDESC(II)II=197)000153 READ 1014,RADIUS,(IOESC(II),II=l,7)000166 NAME = 6HRAOIUS000170 PRINT )O15,NAMERADIUS,(IDESC(II),II=197)000205 READ 1014,ANCHT ,(IDESC(II),II=1.7)000220 NAME = 6H ANCHT000222 PRINT .015,NAMEANCHT ,(IDESC(II),II=1,7)000237 READ 1014,ANCHE ,(IOESC(II),II=1,7)000252 NAME = 6H ANCHE000254 PRINT 10159NAMEANCHE ,(IDESC(IIi,II=197)000271 READ 1014,ATHIK ,(IDESC(II),II=1.7)000304 NAME = 6H ATHIK000306 PRINT 10159NAME*ATHIK ,(IDESC(II),II=1,7).000323 ATHIK = ATHIK/12.000325 READ 1014,ADENS ,(IDESC(II),II=1I7)000340 NAME = 6H ADENS000342 PRINT 10159NAMEADENS ,(IDESC(II),II=197)000357 READ 1014,SPRED ,(IDESC(II),II=1,7)000372 NAME = 6H SPRED000374 PRINT 10159NAMESPRED ,(IDESC(II),II=1,7)000411 READ 1014,XTRA ,(IDESC(II),II=1,7)

64

000424 NAME = 6H XTRA000426 PRINT 10159NAMEXTRA ,(IDESC(II),II=197)t0QQ443 READ 10144HPAY ,(IOESC II),II l.7)000456 NAME = 6H HPAY000460 PRINT 10159NAMEHPAY ,(IDESC(II),II=17)000475 READ 1014,WPAY ,(IDESC(II),II=1s7)000510 NAME = 6H WPAY000512 PRINT 1015-NAMEWPAY ,(IDESC(II),II=1,7)00Q0527 READ 1014,HEXT ,(IDESC(II),II=17)000542' NAME = 6H HEXT000544 PRINT 10159NAME,HEXT ,(IDESC(II) II=17)000561 READ 10149WEXT , IDESC(II), II=,7)000574 NAME = 6H WEXT000576 PRINT 1015,NAMEWEXT ,(IDESC (II, II=17)o00061a3 READ iol.-4tSLOPE *(IDESC(II),.II=17)000626 NAME = 6H SLOPE000630 PRINT 1015,NAMEtSLOPE 9,(IDESC(II )II=17)

CC RADIUS = 0. MEANS NO ANCHOR LINES ARE USED - EVERYTHING ISC CALCULATED FROM THE TOP OF THE PAYLOAD. IF RADIUS *NE. 0. ANCHOR

C GEOMETRY CALCULATIONS ARE MADE AND PRINTED HERE.C

000645 IF (RADIUS) 2,2,3000647 2 PHI = CNVIN*90.000651 PANCH = 0,000651 P = 0.000652 NNDX = 0000653 NRAD = 1000654 TTHIN = HPAY000655 TTCIN = .000656 MINI = 100QQ657 MINIS = 1000660 GO TO 4000660 3 PRINT 1003000663 1003 FORMAT (1HO,*GEOMETRY OUTPUT*)000663 NRAD = 2000664 HP = HPAY+HEXT00Q666 BETA = CNVIN*(360.*(ANCHE+1.)/(2,*ANCHT))000674 P = RADIUS*COS(BETA)000676 PHI = ATAN2(HPgP)000702 VALUE = CNVOUT*PHI000703 NAME = 6H PHI000705 PRINT 1001,NAMEVALUE000714 1001 FORMAT (1H 9A692H ,3F15.5)000714 PANCH = P/COS(PHI)-XTRA000721 NAME = 6H PANCH000722 PRINT 1001,NAME*PANCH000731 S = RADIUS*SIN(BETA)000734 NAME = 6H S000736 PRINT 1001,NAME,S000745 S = S-SPRED/2.000750 EPS = ATAN2(S,PANCH)000753 NAME = 6H . EPS000754 VALUE = CNVOUT*EPS000756 PRINT 100l NAMEVALUE000765 A = S/SIN(EPS)000770 NAME = 6H A000772 PRINT 1001,NAMEA001001 PRINT 1005001004 1005 FORMAT (1HO5,HINPUT)001004 4 READ 1014,TLNGTH,(IDESC(II),II=1.7)001017 NAME = 6HTLNGTH001021 PRINT 10l15NAMEgTLNGTH,(IDESC(II)IIl=17)001036 READ 1014,STEP1 ,(IDESC(II),II=11 7)001052 TOTL = TLNGTH+PANCH+XTRA001054 MAXI = INT(TOTL/STEP1)001056 STEPI = TOTL/FLOAT(MAX1)001060 NAME = 6H STEP1001061 PRINT 10159NAMESTEP1 ,(IDESC(II)III=17)001076 IF (RADIUS) 99,59

65

CC FOR ANCHOR CASE THE ANCHORS ARE TREATED AS 1 LINE 8ISECTING THEC ANGLE BETWEEN THE REAL ANCHORS. THIS FORMS ONE SECTION OF THEC TRAIN WITH THICKNESS DOUBLE THAT OF THE ANCHOR LINES AND DENSITYC EQUAL THE WEIGHT OF BOTH ANCHORS DIVIDED BY THE LENGTH OF THISC IMAGINARY SECTION PANCH.C

001100 5 I a 1001101 THIK(I) = ATHIK*?.001104 TMEAS(I) _ PANCH+XTRA001106 TDENS(I) = ADENS*A*2.001111 NSEC = INT(TMEAS(I)/STEPl+,5)001114 SECT = FLOAT(NSEC)-1l001116 WW * TDENS(I)/SECT001121 DO 6 K=iNSEC

D11T31 TTHIKI(K). THIK(I)001132 W1(K) = WW001132 6 CONTINUE001133 NNDX = NSEC001135 WI(NNDX) a WEXT001137 MINIS = NNDX

CC READ IN THE DENSITY AND THICKNESS CONFIGURATION OF THE TRAIN ANDC SET UP CORRESPONDING ARRAYS. EACH INTEGRATION STEP OF THE TRAINC SIDE IS ASSIGNED A WEIGHT W1(I) AND THICKNESS TTHIK(I).C

001140 9 READ 10129NSECTH (IDESC(III) II1,7)011153 1012 FORMAT (I996X,6AlOA5)001153 NAME = 6HNSECTH001155 PRINT 10139NAMENSECTH,(IDESC(II),II=17)001172 1013 FORMAT (1H 9A692H =,I9,11X97Alo)001172 NSECTH = NSECTH+NRAD-1001174 NDX = NNDX001175 NAME = 6H TTHIK001177 DO 10 I=NRADNSECTH001200 READ 1016,9TIK(I),TMEAS(I)9(IDESc(II)gIIl=15)001215 1616 FORMAT (2Fl5.5,5A10)001215 PRINT 1011,NAME,THIK(I),TMEAS(I),(IDESC(II),II=i5)001234 1011 FORMAT (1H 9A692H =,2F155,5X,5AI0)001234 NSEC = INT(TMEAS(I)/STEP1+*5)001240 DO 11 J=1,NSEC001251 K = J+NDX001252 TTHIK(K) = THIK(I)001252 11 CONTINUE001255 NDX = NDX+NSEC001256 10 CONTINUE001261 READ 10129NSECD ,(IDESC(II),II=1,7)001274 NAME = 6H NSECD001276 PRINT 10139NAMENSECD ,(IDESC(II),II=197)001313 NSECD = NSECD+NRAD-1001315 NOX = NNDX001316 NAME = 6H TDENS001320 DO 12 I=NRAD.NSECD

-001321 READ 1016,TOFNS(I),DMES((I),(IOESC(II),II=1,5)001336 PRINT 1011,NAMETDENS(I),DMEAS(I),(IDESC(II) II=lb)001355 NSEC = INT(OMEAS(I)/STEPl+*5)001361 14 SECT = FLOAT(NSEC)001362 WW = TDENS(I)/SECT001365 DO 13 J=1,NSEC001373 K = J+NDX001374 W1(K) = WW001374 13 CONTINUE001377 NDX = NDX+NSEC001400 12 CONTINUE001403 NOXER = MAX1-NDX001404 IF (NDXER) 15,16,15001406 15 NDX = NDX-NSEC001407 NSEC = MAXI-NOX001410 I = NSECD001411 GO TO 14001412 16 CONTINUE001412 READ 1nl14,TF .(IDESC(II).II=1.7)

66

001425 NAME = 6H wTF001427 PRINT 1015,NAMEWTF 9(IDESC(II),II=1,7)001444 READ 10149WTB ,(IDESC(II),IIs,7)001457 NAME = 6H WTB001461 PRINT 1015 NAMEgWTB ,(IDESC(II) II=17)001476 READ 10149GLIFT ,(IDESC(II),II=l.7)001511 NAME = 6H GLIFT001513 PRINT 10159NAMEGLIFT ,(IDESC(II),II=1l 7)001530 CFBY = GLIFT-WTB-WTFQ01533 READ 10149XSECTH,(IDESC(II),II=1,7)001546 NAME = 6HXSECTH001550 PRINT 1015 NAME XSECTH (IDESC (II) II=17)001565 READ lo149XSECTV,(IDESC(II)II1,7)001600 NAME = 6HXSECTV001602 PRINT 10159NAMEXSECTV9(IDESC(II)gII=17)001617 READ 1014,STHIK ,(IDESC(II),II=1,7)001632 NAME = 6H STHIK001634 PRINT 1015,NAME,STHIK ,(IDESC(II),II=17)001651 STHIK = STHIK/12.001653 READ 1014,SDENS ,(IDESC(II),II=1,7)001666 NAME = 6H SDENS00.1670 PRINT 1015,NAMEgSDENS 9(IDESC(II),II=1l7)001705 READ 1014,STEP2 ,(IDESC(II),II=l,7)001720 NAME = 6H STEP2001722 PRINT 1015,NAME,STEP2 ,(IDESC(II),II=1,7)001737 READ 101-2,NWIND ,(IDESC(II),II«1,7)001752 NAME = 6H NWIND001754 PRINT 10139NAMENWIND ,(IDESC(II),II=197)001771 NAME = 6H WIND001773 DO 17 NW=1,NwIND

CC FOR EACH NW, WN CONTAINS 3 COEFFICIENTS FOR THEC FUNCTION REPRESENTING A WIND PROFILE AS FOLLOWS -C IF HT IS THE HEIGHT IN FEET THEN THE WIND IN KNOTS ISC WN(1,NW)+WN(29NW)*(HT)**WN(39NW)C

001774 READ 1017,(WN(IINW) ,II=193) ,(IDFSC(II) ,II=15)002014 1017 FORMAT (3F10.5,5A1 O)002014 PRINT I018,NAME,(WN(II,NW),II=),3),(IDESC(II) II=1,5)002036 1018 FORMAT (1H ,A692H =,3F10.,5X,5Aio)002036 17 CONTINUE

CC COMPUTE TENSION VALUES.C

002041 T1 = 2.4A*ADENS+WEXT+100.002045 T2 = TIlWPAY002047 TINC = WPAY/5.002050 NAME = 6H TTP002052 PRINT 1020 9NAME,TI,T2,TINC002065 1020 FORMAT (1H ,A6r2H =,3F1 O.1I3X*INITIALFINALgINCREMENTAL TENSIONS A

QT PAYLOAI*)CC WRITE RUN IDENTIFICATION ON MAG TAPE (UNIT 2)C

002065 WRITE (2) (IDENT(I), I=15),SLOPE,NWINDCC COMPUTE 3ALLOON PROFILEC

002102 VOLUME = 1000.*GLIFT/HELFT002104 BRAD = (3.*VOLUME/(4.*PI))**(l./3.)002114 BANG = BANG*CNVIN002116 HCENT = BRAD/SIN(BANG)002121 ANGMIN = -BANG002122 ANGMAX = PI+BANG002124 ANGINC = (ANGMAX-ANGMIN)/20.002126 BSHAPX(1) = 0.002126 BSHAPY(1) = 0.002127 ANGLE = ANGMIN002130 DO 101 I=2,22002132 BSHAPX(I) = BRAD*COS(ANGLE)002136 BSHAPY(I) = RRAD*SIN(ANGLE)+HCENT002143 ANGLE = ANGLE+ANG-NC002145 101 CONTINUE

67

002147 BSHAPX(23) = O.002147 BSHAPY(23) = 0... . C

C THESE MINS AND MAXS ARE THE END POINTS FOR THE INTEGRATION.C

002150 MIN2 = MAX1+1002152 MAX2 a MIN2+1200002153 MAXIS = MAXI002154 MIN2S = MIN2002156 MAX2S = MAX2002157 W2 = SDENS*STEP2002161 ALPHA = 0.002162 ,ALPHSV = 0.

CC READ IN FTONG = FEET ON GROUND UNTIL A 0. VALUE IS REACHED. THENC START READING IN ALPHA = ANGLE AT STARTING POINT OF INTEGRATION.

002163 201 READ 10009FTONG002170 1000 FORMAT (3F15.5)002171 MINISS = INT(FTONG*FLOAT(MAX1))002173 STPONG = FLOAT(MTINSS)002174 MINiSS = MIN1SS+1002176 FTONG = STPONG*STEP1002177 IF (FTONG) 1*,1202

C002200 1 READ 1000,ALPHA002205 IF (ALPHA.EQ.1000.) GO TO 99002207 ALPHSV = ALPHA002210 ALPHA = CNVIN*ALPHA002211 202 CONTINUE002211 NPAGE = IH1002213 PRINT 1004,NPAGE,ALPHSVFTONG002224 1004 FORMAT ( A1,25X,8H ALPHA =,F6.2]OX,8H FTONG =,F6.1)002224 IF (RADIUS) 19,199210002226 210 IF (ALPHA-PHI) 2119220,220002230 211 TTCIN = FTONG-P002232 TTHIN = TTCIN*SLOPE002233 IF (TTCIN.LT.u.) TTHIN=O.002235 MINI = MIN1SS002237 GO TO 19002237 - 220 TTHIN = HPoQ2aQ.. ..... TTCIN = 0.002241 MINI = MINlS+l002243 DO 18 I=1,MINIS002251 TTH(I) = 0.002252 TTC(I) = -P002252 18 CONTTNUE

CC NWIND = NUMBER )F wIND PROFILES

002253 19 DO 200 NW=1*NWIND002255 DO 20 I=1,3002263 20 WND(I) = wN(INw)002265 PRINT 1006,NWAI.PHSVFTONG002276 1006 FORMAT (1H 910X,14H WIND PROFILF,I4,10OX8H ALPHA =,F10.31OX,8H F

1TONG =*F0o.3)002276 TTP = Tl002277 NT = ]002301 30 IF (TTP.GT.T2) GO TO 300002305 TTPSV = TTP002305 IF (RADIUS) 40940,31002307 31 IF (ALPHA-PHI) 3?,40940

CC FOR ALPHA .LT. PHI IN THE ANCHOR CASE9 FIND A TENSION VALUE WHICHC INPUTED AT THE BEGINNING OF THE INTEGRATION RESULTS IN A TFNSIONC AT THE APEX OF THE ANCHOR CONFIGURATION APPROXIMATELy EQUAL TO TTPC

002311 32 MINI = MIN1SS002312 MAxl = MINIS002314 IF (MIN1.GE.MAX1) GO TO 39002316 MAX2 = MIN2002317 TTENIN = TTP002321 DO 33 I=1,3

68

CC FIND THE TENSION AT THE APEX AND USE IT TO CALCULATE A BETTERC STARTING TENSION TTENINC

002323 CALL NTGRAT(TTENTNC)002325 TTENIN = TTENIN-(TTENS(MAX1)-TTP)002331 33 CONTINUE002333 MAX1 = MAXIS002334 MAX2 = MAX2S012353 GO TO 41002336 39 MAX1 = MAX1S002337 MAX2 = MAX2S

CC IF THE..INTEGRATION STARTS AT OR REYOND THE APEX TTENIN = TTPC

002341 40 TTENIN = TTP002342 TTENS(MINIS) = TTENIN002345 41 CONTINUE

CC CALL THE INTEGRATION SUBROUTINE. MOST OF THE ARGUMENTS AREC CARRIED THROUGH COMMON BLOCK APARTSC

002345 CALL NTGRAT(TTENINgTOTC)CC THE OUTPUTED TTP IS THE TRAIN TENSION AT THE APEx.C

002362 TTP = TTENS(MINIS)002364 PRINT(1 NT) = TTP002365 PRINT(2,NT) = CNVOUT*ALPHAB002367 PRINT(39NT) = TTENS(MAX1)002371 PRINT(4,NT) = BALLH002372 PRINT(5,NT) = PARTC002373 PRINT(69NT) = TSR002374 PRINT(79NT) = CNVOUT*THETAW.002376 PRINT(RNT) = STENS002377 420 MMAX = ISTEP-1

CC COMPUTE THE STAY LENGTHC

002401 STEPLS = SQRT((TTC(ISTEP)-TTC(MMAX))**2+(TTH(ISTEP)-TTH(MMAX))**2)002410 SLNGTH = STEPLS+FLOAT(MMAX-MAXl)*STEP2002415 PRINT(99NT) = SLNGTH002420 IF (ALPHA-PHI) 140,1409130

CC FOR ALPHA .GT. PHI THE TENSION Is DIVIDED RETwEEN [HE ANCHORS ANDC THE AXTENSION. THE APPARENT TRAIN ANGLE IS CALCULATED FROM THEC APEX.C

002423 130 ATOP = P002424 TEXT = TTP*(SIN(ALPHA)-COS(ALPHA)*TAN(PHI))002435 TANCH = TTP*COS(ALPHA)/(2?.*COS(EpS)*COS(PHI))002450 VDB = BALLH-HP002451 HDB = PARTC002453 GO TO 150002454 140 ATOP = PANCH*COS(ALPHA)002457 IF (RADIUS) 141,141,142002461 141 TEXT = TTP002462 TANCH = 0.002463 VDB = BALLH-HPAY002465 HOB = PARTC002467 GO TO 150

CC FOR ALPHA .LE. PHI IN THE ANCHOR CASE TEST TO SEE THAT THE APEX ISC WITHIN THE EXTENSION DISTANCE FRoM THE PAYLOAD. IF IT IS NOT SETC TEXT = INFINITY AS A FLAG. THE APPARENT TPAIN ANGLE IS CALCULATEDC FROM THE ANCHORS.C

002467 142 TEXT = 0.002470 IF (TTH(MIN1S).GT.HP) TEXT:37764noO00000000000002475 TANCH = TTP/(d.*COS(EPS))002502 VDn = BALLH002503 HDB = PARTC+S002510 150 C = TOTC

69

002511 PRINT(10,NT) = C002512 TLNGA = SQRT(VDB**2+HDBR*2)002516 ALPHAA = ATAN2(VDBQHUb)002533 ALPHAA = CNVOUT*ALPHAA002535 PRINT(11,NT) = ALPHAA002536 PRINT(12,NT) = TEXT002537 PRINT(139NT) = TANCH002540 FALB = FBY-CFBY002543 PRINT(14,NT) . FALB002544 PRINT(159NT) = FRY002544 PRINT(16,NT) = FDB002545 PRINT(179NT) = WINDB

C002546 IF (DD80.EQ.O) GO TO 49

CC TILT BALLOON PROFILE WITH WINUC

002547 ANGLE = ATAN2(FDB8FBY)002552 DO 102 I=1923002553 BSX(I) = BSHAPX(I)*COS(ANGLE)-BSHAPY(I)*SIN(ANGLE)002562 BSY(I) = BSHAPX(I)*SIN(ANGLE)+BSHAPY(1)*COS(ANGLE)002573 102 CONTINUE

C DRAW CRT PLOT OF THE CONFIGURATION.C

002574 CALL FRAME002575 CALL PWRT( 112910089IDENT,5o02eO)002601 CALL PWRT( 3249 12,LARX9e81ln)002605 CALL PWRT( 129 3729LABY,23,191)9_Qi-_.?1 - -._ENCQDE .(.6. 101.0 LABT) NW ALPHAA,TTPSLNGTH,FT ONG002630 1010 FORMAT (13HWIND PROFILE tI2,2X,9HALPHAA = ,F2.092Xt6HTTP = iF50.

Q2Xt9HSLNGTH = ,F3.0,2XbHFTON( = ,F3.0)002630 CALL PWRT( 1009 950,LABT96891t0)002634 CALL SET(.06, 96 .06, 969-100 .700.,-100 .700. 1)002643 CALL PERIML(8959895)002646 CALL FRSTPT(-100.,0.)002650 CALL VECTOR(700,O.)002652 CALL FRSTPT(0.,n.)002654 CALL VECTOR(O.,HPAY)002656 CALL FRSTPT(-P,0.)002662 CALL VECTOR(TTCIN,TTHIN)002664 DO 104 I=MIN1lISTFP002666 CALL VECTOR(TTC(I),TTH(I))002670 104 CONTINUE002673 CALL FRSTPT(PARTCBALLH)002675 DO 103 I=1923002700 X = BSX(I)+PARTC002701 Y = BSY(I)+BALLH002704 CALL VECTOR(X,Y)002706 103 CONTINUE002710 49 CONTINUE002710 160 TTP = TTPSV+TINC002712 NT = NT+i002714 GO TO 30002715 300 CONTINUE002715 NT = NT-1002717 PRINT 10079((PRINT(IJ)tJ=l1NT)iT=1l,7)002736 1007 FORMAT (IH 9RH TTP =,6F15.39/

11H ,aHALPHAB =,6F15.3t/21H ,8H TTB =96F15.39/31H 9RHTOTALH =6F15.39/31H ,8H PARTC =96F15.3,/31H 98H TSB =96F15.39/31H ,8HTHETAW =s6F15.39/31H 98H TSW =96F15.39/31H 98HSLNGTH =96F15.39/31H ,8H C =96FI5.39/31H ,8HALPHAA =,6F15.3,/31H ,8H TEXT =96F15.3,/31H 98H TANCH =96Fl5.3,/31H 98H FALB =96F15.39/31H .8H FBY =96F15.39/3]H ,8H FOR =96F.5.3./31H .8H WINOD =96F15.3,/)

70

002736 WRITE (2) ALPHSVqFTONG,NW,((PRINT(IJ),l=1913),J=1,NT)002763 200 CONTINUE002766 IF (FTONG) l.12o1002770 99 CONTINUE002770 IF (DD80.NE,0.) CALL FRAME002772 END FILE 2002774 END

LENGTH OF ROUTINE LAUNCH004656

SUBROUTINES CALLEDGRDFMTINPUTCOUTPTCCOSATAN2SINOUTPTRRBAREXNTGRATSQRTTANFRAMEPWRTOUTPTSSETPERIMLFRSTPTVECTORENDFILEND

VARIABLE ASSIGNMENTSWND - OOO1COlC TTH - 000005C01 TTC - 003725C01 TTENS - 007650C01W1 - 011632C01 TTHIK - 013602C01 PRINT - 003667 LABT - 004153LABX - 004177 LABY - 004223 IOENT - 004247 IDESC - 004254TOENS - 004264 DMEAS - 004276 THIK - 004310 TMEAS - 004322WN - 004334 BSHAPX - 004372 BSHAPY - 004421 BSX - 004450BSY - 004477 PI - 004526 CNVIN - 004527 CNVOU1 - 004530G - 000000C02 BANG - 004531 HELFT - 004532 CRIT - 004533I1LIM - 004534 IFM - 004535 DD0O - 004536 I - 004537RHO - 000001C02 II - 004540 NAME - 004541 PDBCOF - 000002C02ALBCOF . 000003C02 RADIUS - 004542 ANCHT - 004543 ANCHE - 004544ATHIK - 004545 ADENS - 004546 SPRED - 004547 XTRA - 004550HPAY - 004551 WPAY - 004552 HEXT - 004553 WEXT - 004554SLOPE - OOOOOOC01 PHI - 004555 PANCH - 004556 P - 004557NNDX - 004560 NRAL) - 004561 TTHIN - 011625C01 TTCIN - 011626C01MINI - 011627C01 MIN1S - 004562 HP - 004563 BETA - 004564VALUE - 004565 S - 004566 EPS - 004567 A - 004570TLNGTH - 004571 STEP1 - 011631C01 TOTL - 004572 MAX1 - 011630C01NSEC - 004573 SECT - 004574 WW - 004575 K - 004576NSECTH - 004577 NDX - 004600 J - 004601 NSECD - 004602NUXER - 004603 WTF - 004604 WTB - 004605 GLIFT - 004606CFBY - 015552C01 XSECTH - 015554C01 XSECTV - 015555COI STHIK - 015564C01SUENS - 004607 STEP2 - 015562C01 NWIND - 004610 NW - 004611T1 - 004612 T2 - 004613 TINC - 004614 VOLUME - 004615BRAD - 004616 HCENT - 015553C01 ANGMIN - 004617 ANGMAX - 004620ANGINC - 004621 ANGLE - 004622 MIN2 - 015560C01 MAX2 - 015561C01MAXIS - 004623 MIN2S - 004624 MAX2S - 004625 W2 - 015563C01ALPHA - 000004C01 ALPHSV - 004626 FTONG - 004627 MINiSS - 004630STPONG - 004631 NPAGE - 004632 TTP - 004633 NT - 004634TTPSV - 004635 TTENIN - 004636 C - 004637 TOTC - 004640ALPHAB - 007645C01 BALLH - 011622C01 PARTC - 011623C01 TSB - 011620C01THETAW - 007647C01 STENS - 011621C01 MMAX - 004641 ISTEP - 011624C01STEPLS - 004642 SLNGTH - 004643 ATOP - 004b44 TEXT - 004645TANCH - 004646 VDB - 004647 HDP - 004650 TLNGA - 004651ALPHAA - 004652 FALB - 004653 FBY - 015557C01 FDB - 015556C01wINDR - 015565C01 X - 004654 Y - 004655

71

SUBROUTINE NTGRAT(TTP,C)CC SUBROUTINE TO DETERMINE THE CONFIGURATION OF A CABLE LAUNCHINGC APPARATUS.C

000006 COMMON/APARTS/SLOPEgWND(3),ALPHA,TTH(2000),TTC(2000),ALPHAB,1THETABTHETAWTTENS(1000),TSBgSTENSBALLH9PARTCISTEPTTHIN,2TTCINMMINl.MAX1,STEPo1WlO(1000)TTHIK(O1000)CFBYHCENTXSECTH,3XSECTVFDBgFBYgMIN2,MAX2,STEP2,W2,STHIKgWINDB

00000Q 6 COMMON/AIR/GRHOPDBCOFALBCOFCC THIS ARITHMETIC FUNCTION DEFINES THE WIND AS A FUNCTION OF HEIGHT.C WIND IN KNOTS IS GIVEN BY WND(1)+WND(2)*(HT)**WNO(3)

._ .._ -. .THIS FUNCTION ALSO CONVERTS IT TO FEET/SECOND.000006 WINDF(HT) = (WND(1) + WND(2)*AMAX1(HT90.)**WND(3))*1.15155*5280

Q /3600.CCC THIS ARITHMETIC FUNCTION GIVES THE DRAG IN POUNDS UN A BALLOON

_-__......C __HAVING A VERTICAL CROSS SECTION oF XSECT SQUARE FEET WITH THEC WIND GIVEN IN FEET PER SECOND

OQ0.0Q21 PDRAGB(WINDXSECT) = (RHO*WIND*ABS(WIND)*PDBCOF*XSECT)/(2.*G)C

... -- C .

C THIS ARITHMETIC FUNCTION GIVES THE LIFT IN POUNDS ON A BALLOON_,__ ._._ .... HAVING A HORIZONTAL CROSS SECTION OF XSECT SQUARE FEET WITH THE

C WIND GIVEN IN FEET PER SECOND000033 ARLFTB(WINDOXSECT) = (RHO*WIND**#*ALBCOF*XSECT)/(2,*G)

C-CC THIS ARITHMETIC FUNCTION GIVES THE DRAG IN POUNDS ON A CYLINDRICAL

__-.... C. BODY HAVING A LONGITUDINAL CROSS SECTION OF XSECT SQUARE FEET ANDC AN ANGLE OF ATTACK PARALLEL TO THE WIND OF ANGLE RADIANS WITH THEC WIND GIVEN IN FEET PER SECOND

000044 PDRAGC(WINDXSECTgANGLE) = (RHO*WIND*ABS(WIND)*XSECT*i (1.1*ABS(SIN(ANGLE))**3+.n2))/(2.G)

C

C THIS ARITHMETIC FUNCTION GIVES THE LIFT IN POUNDS UN A CYLINDRICALC BODY HAVING A LONGITUDINAL CROSS SECTION OF XSECT SQUARE FEET ANDC AN ANGLE OF ATTACK PARALLEL TO THE WIND OF ANGLE RADIANS WITH THEC WIND GIVEN IN FEET PER SECOND

000067 ARLFTC(WINDXSECTgANGLE) = (RHO*WIND*ABS(WINU)*XSECT*1 (1.*SIN(ANGLE)*ABS(SIN(ANGLE))*COS(ANGLE)))/(#.*G)

C000114 ALPHAB = ALPHA000115 TOTH = TTHIN000117 TOTC = TTCIN000121 TTENY = TTP*SIN(ALPHA)000124 TTENX = TTP*COS(ALPHA)

CC INTEGRATE ALONG TRAIN SIDE (UPWARD)C

000131 DO 400 ISTEP=MINI,MAX1000133 TOTH = TOTH+STEP1*SIN(ALPHAB)000137 WIND = wlNOF(TOTH)000141 TTH(ISTEP) = TOTH000144 TOTC = TOTC+STEP1*COS(ALPHAB)000150 TTC(ISTEP) = TOTC000150 XSECT = TTHIK(ISTEP)*STEP1000154 FDT = PDRAGC(WINOXSECTALPHAB)000162 FALT = ARLFTC(WINnXSECTALPHAB)000171 TTENY = TTENY+wl(ISTEP)-FALT000174 TTENX = TTENX+FDT000176 TTENS(ISTEP) = SQRT(TTENY**?+TTENX**2)000203 ALPHAB-= ATAN2(TTENYgTTENX)000210 400 CONTINUE000213 IF (MAX2-MIN2) 500n500,401000215 401 BALLH = TOTH000216 PARTC = TOTC

CC COMPUTE BALLOON FORCESC

72

000220. WIND = WINDF(BALLH*HCENT)000223 WINUB = WIND*3600./(5280,*l1,5155)000225 FDB = PDRAGB(WINO,XSECTV)000227 FALB = ARLFTB(WINDnXSECTH)000232 FBY = CFBY+FALB000233 STENY = FBY-TTENY000235 STENX s TTENX+FDR000237 TSB = SQRT(STENY**2+STENX**2)000243 THETAW = ATAN2(STENY*STENX)000247 THETAB = THETAW

CC INTEGRATE ALONG WINCH LINE (DOWNWARD)C

0.00247 XSECT = STHIK*STEP2000252 DO 410 ISTEP=MIN29MAX2000255 TOTH = TOTH-STEP?*SIN(THETAW)000261 WIND _ WINDF(TOTH)000263 TOTC = TOTC+STEP?*COS(THETAW)0.00270 GROUND = SLOPE*TOTC000271 IF (TOTH-GROUND) 4209420,408000275 408 TTH(ISTEP) = TOTH000276 TTC(ISTEP) = TOTC000300 F.DS = PDRAGC(WINDXSECTgTHETAW)000305 FALS = ARLFTC(wINnDXSECTTHETAW)Q0Q314 STENY - STENY-W2-FALS000316 STENX = STENX+FDS000D320 STENS..- SQRT(STENY**2+STENX**2) . ..000324 IF (STENS) 4119411,409000327 409 THETAW = ATAN2(STENYSTENX)000333 410 CONTINUE000336 411 CONTINUE

CC INTERSECT LAST STEP wITH THE GROUND.C

000340 420 MMAX = ISTEP-1000341 TOTC = (STENX*TTH(MMAX)+STENY*TTc(MMAX))/(STENX*SLOPE+STENY)000350 TTC(ISTEP) = TOTC000351 TOTH = SLOPE*TOTC000352 TTH(ISTEP) = TOTH000353 C = TOTC000354 IF (ATAN2(SLOPE,1.)+THETAW) 50195019500000363 500 RETURN000365 501 C = 1.E1CO000366 TTC(ISTEP) = C000367 TTH(ISTEP) = TTH(MMAX)-C*THETAW000372 RETURN000373 END

LENGTH OF ROUTINE NTGRAT000530

SUBROUTINES CALLEDRBAREXSINCOSSORTATAN2END

AHITHEMETIC FUNCTIONSWINDFPDRAGBARLFTBPDRAGCARLFTC

73

VARIABLE ASSIGNMENTSWND - OOOOO1COl TTH - 000005C01 TTC - 003725C01 TTENS - 007650C01W1 - 011632C01 TTHIK - 013602C01 RHO - 000001C02 PDBCOF - 000002C02G - 000000C02 ALBCOF - 000003C02 ALPHARB 007645CO1 ALPHA - 000004CO1TOTH - 000511 TTHIN - 011625C01 TOTC - 000512 TTCIN - 011626C01TTENY - 000513 TTENX - 000514 ISTEP - 011624C01 MINI - 011627C01MAXi .... 011630C01 STEP1 - 011631C01 WIND - 000515 XSECT - 000516FDT -- 000517 FALT - 000520 MAX2 015561C01 MIN2 015560C01BALLH - 011622C01 PARTC - 011623C01 HCENT 015553C01 WINOB - 015565C01FOB - 015556C01 XSECTV -015555C01 FALB - 000521 XSECTH - 015554C01FbY - 015557C01 .CFBY . 015552C01 STENY - 000522 STENX - 000523TSB - 011620C01 THETAW - 007647C01 THETAR - 007646C01 STHIK - 015564C01STEP2 __- 01562Cn l GRQUND.--. 000524 SLOPE . OOOO00CO-1 FDS 0-00525FALS - 000526 W2 - 015563C01 STENS - 011621C01 MMAX - 000527

' TOTAL CORE USED 035151

ENTRY POINT LOCATION ROUTINE ORIGIN... .LUNCH _ 003 00300

NTGRAT 025454 025450ALOG 026201 026200EXIT 026250 026250END 026250 0262R0STOP 026250 026250.INPUTC 026253 026253KODER 026623 026623KRAKER 027506 027506OUTPTC 030315 03n315SIN 031003 030777COS 030777 030777SQRT 031066 031066TAN 031120 031117ATAN2 031212 031212ENDFIL 031321 031321OUTPTB C31343 031343INPUTB 031405 031343OUTPTS 032561 032561SET 033073 033060PSCALE 033136 033060PORGN 033142 033060FRAME 033156 033060FLUSH 033171 033060OPTION 033200 033060DASHLN 033213 033060FRSTPT 033220 033060VECTOR 033225 033060POINT 033231 033060PSYM 033235 033060PWRT 033264 033060AXES 033453 033060GRDFMT 033466 033060MXMY 033472 033060GRI[ 033477 033060GRIDL 033502 033060

_ __PE I . ...- _33507 .. . _ . J3060 _ _ __ .._.___._ . .PERIML 033514 033060LABMOD 034011 033060TICKS 034110 033060HALFAX 034114 033060LINE 034124 033060CURVE 034132 033060FLASH1 034146 033060FLASH2 034160 033060FLASH3 034175 033060FLASH4 034213 033060RBAREX 035011 035011

COMMON BLOCKS LOCATIONAPARTS 007656AIR )25444

75

APPENDIX B

Listing of Program LNPROC

77

RUN 05278*FORTRAN 10/24/68PROGRAM LNPROC

C USED TO PLOT CURVES FROM TAPE GENERATED BY PROGRAM LAUNCH090002 DIMENSION IDENT(5)9ALPHA(200),FTONG(600),NWP(200)000002 DIMENSION TTP(1200)tALPHAB(1200),TTR(1200),TOTALH(1200),PARTC(1200

1) TSB(1200) tTHETAW(1200) TSW(12nO) SLNGTH(l200) C(1200) ALPHAA(12020),TEXT(1200),TANCH(1200)

o000o 2 NT « 6000003 READ (1) (IDENT(I),la195),SLOPENW000020 J 0.090021 1 B NT*Ji900024 IE . IXBNT-1

0QOQ05 J = Jli000026 READ (1) ALPHA(J)tFTONG(J),NWP(J),TTP(I),ALPHAB(I)tTTB(I),TOTALH

l(I)tPARTC(I) TSB(I) THETAW(I),TSW(I) SLNGTH(I) C(I) ALPHAA(I) TEXT2I) 1TANCH(i)1 tIB9IE)

O00076 IF (EOF,1) 10,1000101 10 NA = (J-1)/NW000105 CALL CVSL.IDENTSLOPENWNTNANWPCSLNGTH)000113 CALL CVSA(IDENTSLOPENWNTNANWPCALPHAA)000121 END

LENGTH OF ROUTINE LNPROC037657

SUBROUTINES CALLEDINPUTBIFENDFCVSLCVSAEND

VARIABLE ASSIGNMENTSIDENT - 00o132 ALPHA - 000137 FTONG - 000447 NWP - 000757TTP _ 001267 ALPHAB - 003547 TTB - 006027 TOTALH - 010307PARTC 012567 TSB - 015047 THETAW - 017327 TSW - 021607SLNGTH - 024067 C - 026347 ALPHAA - 030627 TEXT - 033107TANCH - 035367 NT - 037647 I - 037650 SLOPE - 037651NW - 037652 J - 037653 IB - 037654 IE - 037655NA - 037656

78

SUBROUTINE CVSL(IDENTSLOPENWNTNAtNWPgCSLNGTH)000017 DIMENSION NWP(NWNA)gC(NTgNWtNA)gSLNGTH(NTTNWMNA)000017 DIMENSION LABT(20-)LABX(20),TDENT(5),LABS(20)000017 DATA LABX/32HDISTANCE PAYLOAD TO WINCH, C, FT/090017 DATA LABS/28HMAIN STAY LENGTH9 SLNGTH, FT/90017 SLP = ABS(SLOPE*100.)6o0021 NSGN = iH,900022 IF (SLOPE.LT.O) NSGNlIH-000025 XMIN a O.000026 XMAX = 100l .000027 YMIN = 0.900030 YMAX a 1000.000031 DO 10 IW=l,NW000033 ENCODE (90 10109LABT) NSGNSLPNWP(IW,1),(IDENT(I)I=1,5)900072 .110 FORMAT (9H SLOPE " ,A1F4.2,20H ASS 1 WIND PROFILE,13,3X,5A10)900972 CALL AUTOGD(XMINXMAXYMIN,YMAX,1,LABX,329LABS,28,LABT990,1)000104 DO 20 IT1l,NT090111 CALL FRSTPT(C(ITIW,l),SLNGTH(IT,IW,1))000136 DO 40 IA=2,NA090137 CALL VECTOR(C(IT,IWIA),SLNGTH(ITlWIA))000163 40 CONTINUE000165 2 0 CONTINUE00167 10 CONTINUE000171 CALL FRAME900172 RETURN000173 END

LENGTH OF ROUTINE CVSL006334

SUBROUTINES CALLED

OUTPTSAUTOGDFRSTPTVECTORFRAMEEND

VARIABLE ASSIGNMENTSLABT - 00QZ26 LABX - 000252 LABS - 000276 SLP - 000322NSGN - 000323 XMIN - 000324 XMAX - 000325 YMIN - 000326YMAX 000327 IW - 000330 I - 000331 IT - 000332IA - 000333

79

SUBROUTINE CVSA(IO ENTSLOPENWNTNANWPCALPHAA)oo0017 DIMENSION NWP(NWNA),C(NTNWNA),ALPMAA(NTNWNA)

000017 DIMENSION LABT(20),LABX(2O),IDENT(5),LABA(20)000017 DATA LABX/32HDISTANCE PAYLOAD TO WINCH, C, FT/000017 DATA LABA/33HAPPARENT TRAIN ANGLE9 ALPHAA, DEG/000017 SLP u ABS(SLOPE*100.)

00o21 NSGN a= IH000022 IF (SLOPE.LT.O) NSGN1=H-0Qo025 XMIN * 0.000026 XMAX = 1000V00027 YMIN = 0.00030 YMAX = 9 0q_0'o032 60 iO IWW1,NW000033 ENCODE (90,10109LABT) NSGNtSLPNWP(TW91),(IDENT(I)Iz=195)oo0072 1610 FORMAT (9H SLOPE i ,A1,F42t,20H AS5 1 WIND PRoFILEI3,3X,5A10)000072 CALL AUTOQD(XMINXMAXYMINYMAX,1 LABXt32,LABA,33,LABT,90t1)000104 DO 120 IT=1iNT000111 CALL FRSTPT(C(ITIW91)tALPHAA(ITIW,1))000136 DO 140 IA=s2NA090137 CALL VECTOR(C(ITIW.IA),ALPHAA(ITIW9IA))090163 140 CONTINUE000165 120 CONTINUE000167 110 CONTINUE000171 CALL FRAME000172 RETURN000173 END

LENGTH OF ROUTINE CVSA000335

SUBROUfINES CALLEDOVTPTSAUTOGDFRSTPTVECTORFRAMEEND

VARIABLE ASSIGNMENTSLABT . 000 2 27 LABX - 000253 LABA - 000277 SLP - 000323NSGN - 000324 XMIN - 000325 XMAX - 000326 YMIN - 000327YMAX - OQ0330 IW - 000331 I - 000332 IT - 000333IA - 000334

80

SUBROUTINE AUTOGD(XMINXMAXYMINYMAXLINLOGLABXNCHXgLABYNCHY,iLABTOP.NCHTOPISZTOP)

C THIS ROUTINE SETS UP A SCALED AND LABELED GRIDCC XMIN9 XMAX, YMINN AND YMAX ARE THE RESPECTIVE LIMITS OF THE X AND YC VALUES. IN THESE VARIABLES ARE RETURNED THE ROUNDED VALUES WHICHC ARE THE LIMITS OF THE GRID. IF THE ROUTINE IS RE-ENTERED WITHC THESE ROUNDED VALUES THE SCALING IS SKIPPED, AND AN IDENTICAL GRIDC IS SET UP (EXCEPT FOR LABELS).C LINLOG 1 IS LINEAR-LINEAR, 2 IS LINEAR-LOG, 3 IS LOG-LINEAR,C a 4 IS LOG-LOGC LABX! NCHX, LABY, AND NCHY ARE THE RESPECTIVE X AND Y LABELS AND THEC NO. OF CHARACTERS IN EACHC LABTOP, NCHTOP, ISZTOP ARE THE TOP LABEL9 NO, OF CHARACTERS, ANDC CHARACTER SIZE. IF LABTOPaO NO FURTHER PARAMETERS NEED BE LISTED9C AND NO TOP LABEL IS WRITTEN*CC ISIZ IS THE CHARACTER SIZE OF THE X AND Y LABELS

000023 DATA ISIZ/i/000023 DATA ISZN/O/Q00023 DATA NFRST/1/,LNLGSV/O/90023 IF (NFRST.EQ.O) GO TO 1000024 NFRST = 0000025 INC a 8+((ISIZ*2)/3)*2**(ISIZ+1)Oq007 INCN 8+((ISIZN+2)/3)*2**(ISIZNl)000503 1 CALL FRAME000054 NFLGX a 10Q0055 NFLGY a 1900056 IF (LNLGSV.NE.LINLOG) GO TO 5000064 IF (XLOLDEQ.XMIN.AND.XHOLD.EQ.XMAX) NFLGXaO!00074 IF (YLOLD.EQ.YMIN.AND.YHOLD.EQ.YMAX) NFLGY30000105 5 LNLGSV = LINLOG000106 YB · 1.000107 IF (LARTOP.EQ.0) GO TO 10000111 INCT * 8*((ISZTOP+2)/3)*2**(ISZTOP+1)090124 YB a YB-FLOAT(INCT+INC)/1023.000130 MY = 1Q24000131 MX = (1024-NCHTOP*INCT)/2+10Q0137 CALL PWRT(MX,MYLABTOP,NCHTOP,ISZTOP90)000147 1n MY = 19Q0150 MX = (i024-NCHX*INC)/2+l090156 CALL PWRT(MXMYLABXNCHXISIZO)090162 MX 1 i000163 MY a (1024-NCHY*INC)/2000170 CALL PWRT(MXMYLABYNCHYISIZ,1)090174 IF (NFLGX.EQO.) GO TO 100000201 IF (LINLOG.LT.3) GO TO 300002 Q2 CALL L(RND(XMIN,XMAXMJDVXMNDVX,NDXNFORMX)000211 XLOLD a XMIN000211 XHOLD = XMAX050213 GO TO 100090213 30 CALL LNRND(XMIN,XMAXMJDVXtMNDVXNDXNFORMX)000222 XLOLD XMIN000222 XHOLD a XMAX000224 150 IF (NFLGY.EQ.0) GO TO 200000225 IF (MOD(LINLOG,2).GT.O) GO TO 130000231 CALL LQRND(YMINYMAXMJDVYMVYMNDVYNDYNFORMY)000240 YLOLD a YMIN000240 YHOLD a YMAX000242 GO TO 200000242 130 CALL LNRND(YMINYMAXMJDVYMNDVYNDYNFORMY)000252 YLOLD = YMIN090252 YHOLD = YMAX000254 200 IF (INCN((MJDVX+1)*(NDX+2)+6).LT.1023) GO TO 230000264 IXOR = 1000264 YA a FLOAT(INC*NDX*INCN)/1023.000270 XB · 1.000272 GO TO 250090273 230 IXOR = 0000274 YA = FLOAT(INC*3*INCN)/1023.000277 XB = 1.-FLOAT(NDX*INCN)/(2.*1023.)000304 250 XA = FLOAT(INC+NDY*INCN)/1023.000311 CALL LABMOD (NFORMXNFORMYNDX,NDY, IZN, ISZN,00 IXOR)

81

000320 CALL SET(XAtXB.YAtYBXMINXMAXtYMINtYMAXtLINLOG)000334 CALL GRIDL (MJDVXMNDVX,MJDVYMNDVY)000337 RETURN

100340 -END

;LENG -VROUTINE-- "'* eT -A000432

SUBROUfINES CALLEDISBAEXFRAMEPWRTLGRNDLNRNDLABMODSETGRIDLEND

VARIABLE ASSIGNMENTSISIZ . 000375 ISZN - 000376 NFRST - 000377 LNLGSV - 000400INC 000401 INCN - 000402 ISIZN - 000403 NFLGX - 000404NFLGY 000405 XLOLD - 000406 XHOLD - 000407 YLOLD - 000410YHOLD _ 000411 YR - 000412 INCT - 000413 My - 000414MX - 000415 MJDVX - 000416 MNDVX - 000417 NDX - 000420NFORMX 000421 MJDVY - 000422 MNDVY - 000423 NDY - 000424NFORMY 0 Q0425 IXOR - 000426 YA - 000427 XR - 000430XA - 000431

82

SUBROUTINE LNRND(ZMINiZMAXMJDVOMNDVeNDtNFORM)000015 IF (ZMAX-ZMIN) 10,900,20000017 10 FLAG' * -I..000021 GO TO 30000021 20 FLA' G .-000023 30 ZMIN » FLAG*ZMIN

M»^ --~~~7AX)T FLAGZa X -000025 ZVAR » ZMAX-ZMIN-0-06 T- IF "VAR- E-2g90) 'GO TO 900000030 NEX = -INT(ALOG1O(ZVAR))

6oja 6 ~ - F -I-VAR-.LTYi4 X NENEXi"'I0Q0043 VAR · ZVAR*10.**NEX0000a4.-6-... -'" ''-' ZINFC - .- e- '-— -' '.'.- -.00050 MNDV · 5

q91o!I . rF' VAR;GE.5 ) GO TO 60OQ0053 ZINC a .5000054. IF (VAR.GE.2.5) GO TO 60000057 ZINC a .1000060 IF (VAR.LE.1.2) GO TO 60000062 ZINC a *2Q00063 MNDV a 4

000070 60 MJDV = INT(o998*VAR/ZINC) +1oQ0074 ZMIN a ZMIN*10.*NEX00075 ZMAX a ZMAX*10.**NEX000076 RMIN = AINT(ZMIN)0O0077 - IF (ZMIN.LT.O) RMIN=RMIN-1.000104 ZMIN a ZMIN+.UO1*VAR000105 ZMAX a ZMAX-.OO1VAR000106 RMIN = RMIN+ZINC*AINT((ZMIN-RMIN)/ZINC)Q00112 70 RMAX = RMIN.ZINC*FLOAT(MJDV)'00115 MJDV =.MJDV+l000116 IF (RMAX.LT.ZMAX) GO TO 70000120 MJDV · MJDV-1000120 Z = AMAXI(ABS(RMIN),ABS(RMAX))000126 LGZ . iNT(ALOG10(Z))000136 ND = LGZ+2-NEX000140 NDA = .+NEX-INT(ZINC)000142 IF (NDA.LT.O) NDAO -

000144 IF (NDA.GT.O) ND=ND+NDA+I000150 IF (ND,GT,10) GO TO 800000153 IF (NDA.GT.4) GO TO 800000156 IF (ND-NDA.GT.7) GO TO 800000161 NTYP 1IHF000162 GO TO 950000162 800 ND = LGZ*8-INT(ZINC)000165 IF (ND.GT.12) ND=12000170 NDA = ND-7000171 NTYP = 1HE000173 GO TO 950

C THIS SECTION DEALS ONLY WITH ARRAYS HAVING VERY SMALL VARIATION000174 900 IF (ABS(ZMIN),LT.1.E-290) GO TO 910000177 ZMIN = ZMIN-10.**(INT(ALOGIO(ABS(ZMIN)))-1)000213 ZMAX = ZMAX+ZMAX-ZMIN000215 GO TO 20000216 910 ZMIN = -1.000217 ZMAX = 1.000220 GO TO 20

C000221 950 ENCODE (7O1000,NFORM) NTYP9NDNDA000240 1000 FORMAT (1H(,AlI12,1H.tIl,1H))000244 ZMIN = FLAG*RMIN*10***(-NEX)090246 ZMAX = FLAG*RMAX*10.**(-NEX)000250 IF (MJDV.GT.10) MNDV = 2000253 RETURN000254 END

LENGTH OF ROUTINE LNRND000342

SUBROUTiNES CALLEDALOGIORBAIEXOUTPTSEND

VARIABLE ASSIGNMENTSFLAG _ 055327 ZVAR - 000330 NEX - 000331 VAR - 000332ZINC - 000333 RMIN - 000334 RMAX - 000335 Z - 000336LGZ - 000337 NDA - 000340 NTYP - 000341

83

VERSION D

ENTRY SERCH0'O000 00`000iO000000o00000 SERCH CON 0000001 56210 SA2 Bi

6310 SA3 B110620 BX6 X2

. ........... 1T30 BX7 X3000oo2 111000016o SAI B1*l

--- . - b6111000001 SB1 BI+I000003 37416 LOOP 1X4 Xi-X6

l-611100oo001 SB1 81+31571 FX5 X7-X1

000000 0324o000005 PL X4,TMAX10610 BX6 XI

000005 0325000006 TMAX PL X5,FETCH10710 BX7 Xl

000006 5611i0 FETCH SAI B10621000003 GE B2lRI1LOOP

56630 SA6 B3000007 56740 SA7 84

0200000000 JP SERCHEND

84

VERSION D

TOTAL CORE USED 051445

ENTRY POINT LOCATION ROUTINE ORIGINLNPROC 003003 003000CVSL 042671 042657CVSA 043225 043213AUTOGO 043566 043550LQRND 044212 044202LNRND 044236 044226SERCH 044570 044570ALOO 044601 044600EXiT 044650 044650END 044650 044650STOP 044650 044650KODER 044653 044653ALOGO0 045537 045536BACKSp 045611 045611IFENDF 045711 045611REWINM 045614 045611IBAIEX 045726 045726OUTPTB 045756 045756INPUTB 046020 045756OUTPTS 047174 047174SET 047506 047473PSCALE 047551 047473PORGN 047555 047473FRAME 047571 047473FLUSH 047604 047473OPTION 047613 047473DASHLN 047626 047473FRSTPT 047633 047473VECTOR 047640 047473POINT 047644 047473PSYM 047650 047473PWRT 047677 047473AXES 050066 047473GRDFMT 050101 047473MXMY 050105 047473GRID 050112 047473GRIDL 050115 047473PERIM 050122 047473PERIML 050127 047473LABMOD 050424 047473TICKS 050523 047473HALFAX 050527 047473LINE 050537 047473CURVE 050545 047473FLASHi 050561 047473FLASH2 050573 047473FLASH3 050610 047473FLASH4 050626 047473RBAIEX 051424 051424

85

APPENDIX C

Listing of Program CLANCH

87

RUN 05278#FORTRAN 10/24/68PROGRAM GRAPHS

C USED TO PLOT CURVES FROM TAPE GENERATED BY PROGRAM CLANCH000002 DIMENSION IDENT(6),TAPE(14,8)000002 DIMENSION ALPHA(100l 8),FTONG(100,8),WIND(10098)tTTP(10098)9

1ALPHAB(109Q8) TTB(100t8) BALLH(10098) .PARTC(10098) TSB(100,8),2THETAW(10098),STENS(100,8),SLNGTH(100,8),C(1008),ALPHAA(10098)93TEXT(10098) TANCH(100,8)

000002 DIMENSION LABX(10),LARYI(10),LABY2(10),LABY3(1o0)LABY4(10)000002 DIMENSION LABY5(10)000002 DATA LABX/28HMAIN STAY LENGTH, SLNGTH, FT/000002 DATA LABYi/33HAPPARENT TRAIN ANGLE, ALPHAA, DEG/000002 DATA LABY2/41HTENSION IN TRAIN AT ANCHOR APEX, TTP, LBS/000002 DATA LABY3/35HTENSION IN ANCHOR CABLE, TANCH, LBS/000002 DATA LABY4/36HTENSION IN EXTENSION LINE* TEXT, LBS/000002 DATA LABY5/36HMAIN STAY TENSION AT WINCH, TSW. LBS/

00002 1000 FORMAT (F4.1)000002 READ (1) (IDENT(I),I=1,5),SLOPECWANTNW000021 ENCODE (6,1001 IDENT(6)) CWANT000030 1o01 FORMAT(2HC=,F4.0)000030 DO 10 NN=1,100000032 READ (1) ALPHT,FTONT,((TAPE(IJ),I=1,14),J=1*NW)00054 IF (EOF,1) 15,5000057 5 DO 10 J=1,NW000117 ALPHA(NN,J) = ALPHT000120 FTONG(NNJ) = FTONT000122 WIND (NN»J) a TAPE(01,J)000124 TTP (NNJ) = TAPE(02,J)000126 ALPHAB(NNJ) = TAPE(03,J)000130 TTB (NNJ) - TAPE(04,J)000132 BALLH INNJ) = TAPE(05,J)000134 PARTC (NN,J) = TAPE(06,J)000136 TSB (NNJ) = TAPE(07,J)000140 THETAW(NNJ) = TAPE(08,J)000142 STENS (NNJ) = TAPE(09,J)000144 SLNGTH(NNJ) = TAPE(10 J)000146 C (NN,J) = TAPE(1,J)000147 ALPHAA(NNJ) = TAPE(129J)000151 TEXT (NNJ) = TAPE(13,J)000152 TANCH (NN,J) = TAPE(14,J)000154 10 CONTINUE000200 15 MAX = NN-i090202 CALL AUTOGD(0.700. *0.*90.*91LABX,28,LABY1i33IlDENT,60*2)000214 DO 20 J=1,NW000216 CALL CHKCRV(SLNGTH(1,J),ALPHAA(1,J),MAXC(1, J),TEXT(1,J),CWANT)000226 20 CONTINUE000231 CALL AUTOGD(O.,700.0.,t 5000o.1lLABX928,LABY2*4l1IDENT,60*2)000243 DO 30 J=1,NW000245 CALL CHKCRV(SLNGTH(19J), TTP(1,J),MAXC(19J),TEXT(1,J),CWANT)000255 ENCODE (4,1000,LABW) WIND(19J)000266 CALL MXMY(MXMY)000270 MX = MX+6000272 CALL PWRT(MX,MY,LABW,4,0,0)000276 30 CONTINUE000301 CALL AUTOGD(0.,700*.,90 1500'.OlLABX,28,LABY3, 359IDENT96092)000313 DO 40 J=1,NW000315 CALL CHKCRV(SLNGTH(19J), TANCH(1,J),MAXC(1,J).TEXT(1J),CWANT)000325 ENCODE (4,10009LABW) WIND(1IJ)000336 CALL MXSRCH(TANCH(19J),MAXMXC(1,J),TEXT(1,J),CWANT)000346 CALL FRSTPT(SLNGTH(MXJ),TANCH(MXJ))000354 CALL MXMY(MXMY)000356 MY = MY+8000360 MX = MX-4000362 CALL PWRT(MXMYALABW,4(090)000366 40 CONTINUE000371 CALL AUTOGD(0O.700.0sO o 4000.,19LABX928,LABY49369IDENT*60,2)000403 DO 50 J=1NW000405 CALL CHKCRV(SLNGTH(1,J), TEXT(19J),MAXC(1,J)ETEXT(19J),CWANT)000416 ENCODE (4,1000*LABW) WIND(1*J)000427 CALL MXMY(MXY IY)000431 MA = MX+6000433 CALL PWRT(MX,MY,LABW,4,0,0)

88

000437 50 CONTINUE000442 CALL AUTOGD(0.9700.90.9 6000.91LABX,28,LABY5936 IDENT,602)0004r4 DO 60 J=1,NW000456 CALL CHKCRV(SLNGTH(1,J), STENS(1,J),MAXtC(19J),TEXT(1,J).CWANT)000466 ENCODE (4,1000,LABW) WIND(1.J)000477 CALL MXMY(MXMY)000501 MX = MX+6090503 CALL PWRT(MXMYtLARW94,090)000507 60 CONTINUE090512 CALL FRAME000513 END

LENGTH OF ROUTINE GRAPHS

032110

SUBROUTiNES CALLED

INPUTBOUTPTSIFENDFAUTOGDCHKCRVMXMYPWRTMXSRCHFRSTPTFRAMEEND

VARIABLE ASSIGNMENTSIDENT - 000612 TAPE - 000620 ALPHA - 001000 FTONG - 002440WIND - 004100 TTP - 005540 ALPHAB - 007200 TTB -010640BALLH - 012300 PARTC - 013740 TS8 - 015400 THETAW - 017040STENS - 020500 SLNGTH - 022140 C - 023600 ALPHAA - 025240TEXT - 026700 TANCH - 030340 LABX - 032000 LABYl - 032012LABY2 - 032024 LABY3 - 032036 LABY4 - 032050 LABY5 - 032062I - 032074 SLOPE - 032075 CWANT - 032076 NW - 032077NN - 032100 ALPHT - 032101 FTONT - 032102 J - 032103MAX - 032104 LABW - 032105 MX - 032106 My - 032107

89

SUBROUTINE MXSRCH(XNgMXCTEXTCWANT)Q00015 DIMENSION X(1)

000015 DIMENSION C(1),TEXT(1)000015 CCHK AINT(CWANT+*5)000017 XMAX = X(1)0000?0 MX = 1000021 I = 000022 1 I = I+1000024 IF (I-N) 2,2,4000025 2 CONTINUE

000025 IF (TEXT(I).EQ.37764000000000000000) GO TO 1000030 IF (AINT(C(I)+.5).NE.CCHK) GO TO 1000035 IF (XMAX-X(I)) 3,1,1000040 3 XMAX = X(I)00.042 MX = I000043 GO TO 1000044 4 RETURN000045 END

LENGTH OF ROUTINE MXSRCH060063

-SUBROUTINES CALLEDEND

VARIABLE ASSIGNMENTSCCHK - 000060 XMAX - 000061 I - 000062

90

SUBROUTINE CHKCRV(XY,NCTEXTCWANT)000015 DIMENSiON X(1) Y(1) C(1) TEXT(1)000015 CCHK = AINT(CWANT+*5)000017 SLNGTH = 0000020 NSTRT = 1000022 DO 10 i=1,N000023 IF (AINT(C(I)+.5).NE.CCHK) GO TO 10000030 IF (TEXT(I).EQ.37764000000000000000R) GO TO 10000033 IF (X(I)oLT.SLNGTH) GO TO 10000036 IF (NSTRT.EQ.O) GO TO 8000037 CALL FRSTPT(X(I),Y(I))000051 NSTRT = 0600052 GO TO 9000052 8 CALL VECTOR(X(I),Y(I))000064 9 SLNGTH = X(I)000066 10 CONTINUE000071 RETURN000071 END

LENGTH OF ROUTINE CHKCRVo00011

SUBROUTINES CALLEDFRSTPTVECTOREND

VARIABLE ASSIGNMENTSCCHK - 00o105 SLNGTH - 000106 NSTRT - 000107 I - 000110

91

SUBROUTINE AUTOGD(XMINXMAXtYMINYMAXLINLOGgLABXNCHXgLABYNCHY,ILABTOPNCHTOPISZTOP)

C THIS ROUTINE SETS UP A SCALED AND LABELED GRIDCC XMIN, XMAX, YMIN, AND YMAX ARE THE RESPECTIVE LIMITS OF THE X AND YC VALUES. IN THESE VARIABLES ARE RETURNED THE ROUNDED VALUES WHICHC ARE THE LIMITS OF THE GRID. IF THE ROUTINE IS RE-ENTERED WITHC THESE ROUNDED VALUES THE SCALING IS SKIPPED, AND AN IDENTICAL GRIDC IS SET UP (EXCEPT FOR LABELS).C LINLOG = 1 IS LINEAR-LINEAR, = 2 IS LINE4A-LOG, a 3 IS LOG-LINEAR,C - 4 IS LOG-LOGC LABX, NCHX, LABY, AND NCHY ARE THE RESPECTIVE X AND Y LABELS AND THEC NO. OF CHARACTERS IN EACHC LABTOP9 NCHTOP, ISZTOP ARE THE TOP LABEL9 NO, OF CHARACTERS, ANDC CHARACTER SIZE. IF LABTOP=O NO FURTHER PARAMETERS NEED BE LISTED,C AND NO TOP LABEL IS WRITTEN.CC ISIZ IS THE CHARACTER SIZE OF THE X AND Y LABELS

000023 DATA ISIZ/1/000023 DATA ISZN/O/000023 DATA NFRST/1/,LNLGSV/O/000023 IF (NFRST.EQoO) GO TO 1000024 NFRST = 0000025 INC = 8+((ISIZ+2)/3)*2**(ISIZ+1)000037 INCN = 8+((ISIZN+2)/3)*2**(ISIZN+1)000053 1 CALL FRAME000054 NFLGX = 1000055 NFLGY = 1000056 IF (LNLGSV.NE.LINLOG) GO TO 5000064 IF (XLOLD.EQ.XMIN*AND.XHOLD.EQ.XMAX) NFLGX=O000074 IF (YLOLD.EQ.YMIN.AND.YHOLD.EQ.YMAX) NFLGY=O000105 5 LNLGSV = LINLOG000106 YB * 1.000107 IF (LARTOP.EQ.0) GO TO 10000111 INCT = 8+((ISZTOP+2)/3)*2**(ISZTOP+i)000124 YB = YB-FLOAT(INCT+INC)/1023.000130 MY = 1024000131 MX = (1024-NCHTOP*INCT)/2+1000137 CALL PWRT(MXMYLABTOPNCHTOPISZTOP90)000147 10 MY = 1000150 MX = (1024-NCHX*INC)/2+1000156 CALL PWRT(MX,MY,LABXNCHX,ISIZ,0)000162 MX = 1000163 MY = (i024-NCHY*INC)/2000170 CALL PWRT(MXMYLABYNCHYISIZ,1)000174 IF (NFLGX.EQ.O) GO TO 100000201 IF (LINLOG.LT.3) GO TO 30000202 CALL LQRND(XMINXMAXMJDVXMNDVXNDXNFORMX)000211 XLOLD = XMIN0002 11 XHOLD = XMAX000213 GO TO 100

92

000213 30 CALL LNRND(XMINXMAXMJDVXMNDVXNDXNFORMX)000222 XLOLD XMIN000222 XHOLD = XMAX000224 100 IF (NFLGY.EQ.O) GO TO 200000225 IF (MOD(LINLOG92)eGT.O) GO TO 130900231 CALL LGRND(YMINYMAXMJDVYMNDVYNDYNFORMY)000240 YLOLD = YMIN000240 YHOLD = YMAX000242 GO TO 200000242 130 CALL LNRND(YMIN9YMAXMJDVY9MNDVY, NDYtNFORMY)0Q0252 YLOLD = YMIN000252 YHOLD = YMAX000254 200 IF (INCN*((MJDVX+1)*(NDX,2),6).LT.1023) GO TO 230000264 IXOR = 1000264 YA FLOAT(INCNDX*INCN)/1023.000270 XB = 1.000272 GO TO 250000273 230 IXOR O 0000274 YA = FLOAT(INC+3*INCN)/10230000277 XB = 1.-FLOAT(NDX*INCN)/(2.*1023.)000304 250 XA = FLOAT(INCNDY*INCN)/1023.000311 CALL LABMOD(NFORMXNFORMYINDOXNDYISZNISZN,900,IXOR)000320 CALL SET(XAtXBgYABYBoXMINXMAXtYMINYMAXLINLOG)000334 CALL GRIDL (MJDVXMNDVXMJDVYtMNDVY)000337 RETURN000340 END

LENGTH OF ROUTINE AUTOGD066432

SUBROUTINES CALLEDIBAIEXFRAMEPWRTLGRNDLNRNDLABMODSETGRIDLEND

VARIABLE ASSIGNMENTSISIZ - oO37'5 ISZN - 000376 NFRST - 000377 LNLGSV - 000400INC - 00O401 INCN - 000402 ISIZN - 000403 NFLOX - 000404NFLGY - 000405 XLOLD - 000406 XHOLD - 047 LOL - 000410YHOLD - 000411 YB - 000412 INCT - 000413 MY - 000414MX - 000415 MJDVX - 000416 MNDVX - 000417 NDX - 000420NFORMX - 000421 MJDVY - 000422 MNDVY - 000423 NDY - 000424NFORMY - 000425 IXOR - 000426 YA - 000427 XB - 000430XA - 000431

93

SUBROUTINE LNRND(ZMINZMAXMJDVMNDVND9NFORM)000015 IF (ZMAX-ZMIN) 109900,20000017 10 FLAG = -i.000021 GO TO 30000021 20 FLAG = 1.000023 30 ZMIN = FLAG*ZMIN000024 ZMAX = FLAG*ZMAX000025 ZVAR = ZMAX-ZMIN000026 IF (ZVAR.LT.1.E-290) GO TO 900000030 NEX = -INT(ALOGiO(ZVAR))000034 IF (ZVAR.LT.I1) NNEXNEX+000043 VAR = ZVAR*10.**NEX000046 ZINC = 1.000050 MNDV = 5000051 IF (VAR.GE.5.) GO TO 60000053 ZINC = .5000054 IF (VAR.GE.2.5) GO TO 60000057 ZINC = .1000060 IF (VAR.LE.1.2) GO TO 60000062 ZINC = .2000063 MNDV = 4000070 60 MJDV = INT(.998*VAR/ZINC)+1000074 ZMIN = ZMIN*10.**NEX000075 ZMAX = ZMAX10.**NEX000076 RMIN = AINT(ZMIN)000077 IF (ZMIN.LT.O) RMIN=RMIN-1.000104 ZMIN = ZMIN+OO01*VAR000105 ZMAX = ZMAX-.OO1*VAR000106 RMIN = RMIN+ZINC*AINT((ZMIN-RMIN)/ZINC)000112 70 RMAX = RMIN+ZINC*FLOAT(MJDV)000115 MJDV = MJDV+I000116 IF (RMAX.LT.ZMAX) GO TO 70000120 MJDV = MJDV-i000120 Z = AMAX1(ABS(RMIN),ABS(RMA X))000126 LGZ = INT(ALOGlO(Z))000136 ND = LQZ+2-NEX000140 NDA = I+NEX-INT(ZINC)000142 IF (NOA.LT.O) NDA=O000144 IF (NOA.GT.O) ND=ND+NDA+I000150 IF (ND.GT.i1) GO TO 800000153 IF (NDA.GT.4) GO TO 800000156 IF (ND-NDA.GT.7) GO TO 800000161 NTYP = 1HF000162 GO TO 950000162 800 ND = LGZ+8-INT(ZINC)000165 IF (ND.GT.12) ND=12000170 NDA = ND-7000171 NTYP = 1HE000173 GO TO 950

C THIS SECTION DEALS ONLY WITH ARRAYS HAVING VERY SMALL VARIATION000174 900 IF (ABS(ZMIN).LT..lE-290) GO TO 910000177 ZMIN = ZMIN-10.**(INT(ALOGIO(ABS(ZMIN)))-1)000213 ZMAX = ZMAX+ZMAX-ZMIN000215 GO TO 20000216 910 ZMIN = -1,000217 ZMAX = 1.000220 GO TO 20

C000221 950 ENCODE (7,1000,NFORM) NTYPNDNDA000240 1000 FORMAT (lH(,Al1I2,1H.lI1IlH))0Q0244 ZMIN = FLAG*RMIN*IO.l (-NEX)000246 ZMAX = FLAG*RMAX*10.**(-NEX)000250 IF (MJDV.GT.10) MNDV = 2000253 RETURN000254 END

LENGTH OF ROUTINE LNRND000342

SUBROUTINES CALLED

ALOG10RBAIEXOUTPTSEND

94

VARIABLE ASSIGNMENTSFLAG - 000 3 27 ZVAR - 000330 NEX - 000331 VAR - 000332ZINC - 000333 RMIN - 000334 RMAX - 000335 Z - 000336LGZ - 000337 NDA - 000340 NTYP - 000341


ENTRY POINT LOCATION ROUTINE ORIGINGRAPHS 003003 003000MXSRCH 035120 035110CHKCRV 035203 035173AUTOGD 035322 035304LGRND 035746 035736LNRND 035772 035762ALOG 036325 036324EXIT 036374 036374END 036374 036374STOP 036374 036374KODER 036377 036377ALOG10 037263 0372628ACKSP 037335 037335IFENDF 037435 037335REWINM 037340 037335IBAIEX 037452 037452OUTPTB 037502 037502INPUTB 037544 037502OUTPTS 040720 040720SET 041232 041217PSCALE 041275 041217PORGN 041301 041217FRAME 041315 041217FLUSH 041330 041217OPTION 041337 041217OASHLN 041352 041217FRSTPT 041357 041217VECTOR 041364 041217POINT 041370 041217PSYM 041374 041217PWRT 041423 041217AXES 041612 041217GRDFMT 041625 041217MXMY 041631 041217GRID 041636 041217GRIDL 041641 041217PERIM 041646 041217PERIML 041653 041217LABMOD 042150 041217TICKS 042247 041217HALFAX 042253 041217LINE 042263 041217CURVE 042271 041217FLASHi 042305 041217FLASH2 042317 041217FLASH3 042334 041217FLASH4 042352 041217RBAIEX 043150 043150

CPU TiME = 2 SECONDS

95

APPENDIX D

Listing of Program GRAPHS

97

RUN 05278*FORTRAN 10/24/68-....... ..-----.-. ROGRAM CLANCH

CC CABLE LAUNCH - FIXED DISTANCE TO wINCHC USE PROGRAM GRAPHS TO PLOT CURVES FROM THIS TAPE

....-- C REVISED-OCT 1968C

0000 2 - C---OMNA TS/TSLOPE--.NDo (3-) ALPHAT,4TTH.(2 T 0-+T TC 2400.)ALP HAR8 1THETABoTHETAwTTENS (1000) TSBgSTENStBALLHgPARTCt ISTEPTTHIN

'--- 2TTCIN-+MIN-1,MAX1+-STEP 1 W1 410-00)- -TTHIKO( 10-O)--CF-RY HGCNTf-*XSECTH,3XSECTVgFDBgFRYMIN29MAX29STEP2.W?,STHIKWINDB

040002 - COMtON/AIR/G RHOPDBCOF ALBCOF 000002 DIMENSION PRINT (18.10)

40 00002 - --- - MEN-f S ION AT-C 2L LAX-(2 ,-LA- 4 Y-(--2(. +-I0 ET-. -C 4-84- -000002 DIMENSION TDENS(lU),DMEAS(1O)9THIK(10)*TMEAS(10)

30Q0002 DIMENSION-TEN(5),C(5) WN(3,10)000002 DIMENSION BSHAPX(23) ,USHAPY.(23) ,RSX(23) ,BSY(23)'000002- DATA-L-ABX/28HDISTANCE FROM PAYLOAD, C* FT/ -000002 DATA-LABY/23HHEIGHT AROVE GROUND, FT/

C —CONVERSION--BE.TWEEN. -DEGREES ANU RADI ANS ..... ....... ...... ...................000002 DATA PI/3,14159265358979/, CNVIN/.0174532925199433/9

3----- -- - . -CNVOUT/57*295779513023/ .- 000002 DATA(G=32.1725)

,000002--. - DATA. BANG/45,/9 HELFT/64.6/ C CONVERGENCE CRITERION FOR C

s0i000 2 DATA CRITT/ O, /. ./ . .... .... .............C ITERATION LIMIT

.00-002..------ - DA ITLIM/4/ .. .. ..I. . ..000002 IFM = 6H(F6.0)

, ....... .... . ... . ... ...------------.--........... . .

C DD80 = 0 MEANS NO PICTORIALS OF APPARATUS'000003 n" .DDaO s l .---- --.. .... . .....-..- . .... .............. _ - .

C400 -Q5 . .- -IE--(D8Da .NE.O.) CALL GRDFMT(.IFM- IFM) -. --...- - ...- -..000010 READ 1008,(IDENT(I)gI=1l5),4002.0-1- ....L--.O --- -F--ORA-AT-- 8A 1 0... .. .. - ... .000021 PRINT 1009,(IDENT(I)9I=195)0000d 32 100 FORMAT (1Hl1B A ..................... - ....000032 PRINT 1002-0L-035 .-----1.002 FORMAT..(1 O-- 5HINPUT) 000035 READ 10149RHO ,(IDESC(II),II=1*7):0Q050iS---..1014 ...F.ORMAIT- (F- 5.s54-6ATGA5) 000050 NAME = 6H RHO00on_;2 PRINT i1n0I5NAMEgRHO .(IDESCLII),II=1,7) .000067 1015 FORMAT (1H 9A692H =,F15,55XX7A1*)00067 ----------..READ--.1 Ol4.PBCEOQF, (IDESC (I.l) , I=-l 1 ) -)

000102 NAME = 6HPDBCOFA0.010-4--- -- ..- P-INT.-1-01-5 NAME-tP-BCQF, (IDESC (I I) + I I 1, 7) .000121 READ 1014,ALBCOF,(IDESC(II),I=1,.7)000134 NAME = 6HALRCOF .__ _ . ........ . .. .000136 PRINT 1015,NAME,ALBCOF,(IDESC(II),II1,7 7)-004-153--- .--READ- -114-RAD1IUS.(-I DESC I )-I., Ill , -I -I000166 NAME = 6HRADIUS-000Q1 -- ..-..---PNI .LO1S5NAMELARADIUS_. (.DESC t I) .I l 1i 7.L .000205 READ 1014,ANCHT ,(IDESC(II),II=If)Q00020n NAMF = 6H ANCHT _.- .. ..000222 PRINT 1015,NAME,ANCHT ,(IDESC(II)"II-=17)-00237 . . READ ...1014,ANCHE , ¢IESCUII) ,Ill^7)000252 NAME = 6H ANCHE4400254 -- .-....PR- -- 1-0 1-SNAME4ANCHE--+ 1 I-U)ESC( I I.) I I=-t 7 --000271 READ 1014,ATHIK ,(IDESC(II),II=1,7)000304 NAME = 6H ATHII000306 PRINT 10159NAME*ATHIK (IDESC(II),II=197)

dlQa323------ --- A.TLT A- c_/_- T. . ..... ......000325 READ 1014,ADENS (-IDESC(II),II=l1.7)

?00034 -...............-- NA ME-. _ .A.NS .- . .. ... ........000342 PRINT 10159NAME,ADENS ,(IDESC(II),II=197)Qf00357 READ 10l41SPREi... O-(IDFSC(l 4tI+5.lz7 7.., .......... ...000372 NAME = 6H SPREDQ0-0037-4 ..-..---.. PRINT ._115LNAMEtSPRED ,I DESC.(l) II..,7) .000411 READ 1014,XTRA ,(IDESC(I-I),II=1.7)

98

000424 NAME = 6H XTRA000426 PRINT 1015,NAME.XTRA ,(IDESC(II),II=197)000443 READ 1.014,HPAY ,(IDESC(II),Il=1.7)000456 NAME = 6H HPAY000460 PRINT 10159NAME9HPAY (IDESC(II)'I1I=1 7)000475 READ O1149WPAY ,(IOESC(II),II=1, 7)000510 NAME = 6H wPAY000512 PRINT 1015,NAMEWPAY ,(IDESC(II),II=l17)000527 READ 1014,HEXT ,(IDESC(II),tII=,7)000542 NAME = 6H HEXT000544 PRINT nl05NAME*HEXT (IDESC(II).Il=1,7)000561 READ . 14-EEXT (IUESC(II),I I1=17)000574 NAME = 6H WEXT000576 PRINT 1015,NAMEpWEXT ,(IDESC(TIIII=1*7)000613 READ 1l014.SLOPE ,(ILESC(II),l111.7)000626 NAME = 6H SLOPE000630 PRINT 1015,NAMESLOPE ,(IDESC(II).II=1 7)

CC RADIUS = 0. MEANS NO ANCHOR LINES ARE USED - EVERYIHING ISC CALCULATED FROM THE TOP OF THE PAYLOAD. IF HADIUS ,NE. :). ANCHOR

- C

C GEOMETRY CALCULATIONS ARE MADE AND PRINTED HERE.C

000645 IF (RADIUS) ,2,*2000647 2 PHI = CNVIN*9n.000651 PANCH = !,.00651 P = 0.000652 NNDX = 00U0653 NRAD = 1000654 TTHIN = HPAY000.655 TTCIN = O.000656 MINI = 1O0Q0657 MINIS = 1000660 GO TO 4000660 3 PRINT 1003000663 1003 FORMAT (IHf, *GE(MFTRY OUTPUT*)000663 NRAD = 2000664 HP = HPAY+HEHXT000666 BETA = CNVIN*(36'.*(ANCHE+*.)/-(2.*ANCHT))000674 P = RADIUS*COS(HETA)000676 PHI = ATAN? (HPP)000702 VALUE = CNVOIJT*PHI000703 NAME = 6H PHI000705 PRINT 10019NAMEVALIJE000714 1001 FORMAT (1H 9A69,H =,3F15.5)000714 PANCH = P/COS(PHI)-XTRA000721 NAME s 6H PANClH000722 PRINT 1001 NAMEN ANCH000731 S = PADIUS*STN(UETA)000734 NAME = 6H S000736 PRINT 1001,NAMES000745 S = S-SPREU/?.000750 EPS = ATAN?(S<PANCH)000753 NAME = 6H EPS000754 VALUE = CNVOUT*EPS000756 PRINT 1001,NAME.VALUE000765 A = S/SIr(EPS)000770 NAME = 6H A000772 PRINT 1001,NAMEA001001 PRINT 1005001004 1005 FORMAT (1HOSHINPUT)001004 4 READ 11(4,TLNGTH,(IDESC(II)) II= 1.7)001017 NAME = 6HTLNGTH001021 PRINT 1015,NAMEtTLNGTH,(IDESC(IIII=197)001036 READ 10149STEP1 ,(IDESC(II)II=l.7)001052 TOTL = TLNGTH+PANCH+XTRA001054 MAX1 = INT(TOTL/STEPI)001056 STEPI = TOTL/FLOAT(MAX1)001060 NAME = 6H STEP1001061 PRINT 1015lNAMESTEPl ,(IDESC(II) ,II-17)001076 IF (RADIUS) <Q9,r

99

CC FOR ANCHOR CASE THE ANCHORS ARE TREATED AS I LINE BISECTING THEC ANGLE BETWEEN THE REAL ANCHORS. THIS FORMS ONE SECTION OF THE

___ .... C TRAIN W...ITH THICKNESS DOUBLE THAT OF THE ANCHOR LINES AND DENSITYC EQUAL THE WEIGHT OF BOTH ANCHORS DIVIDED BY THE LENGTH OF THISC IMAGINARY SECTION PANCHOC

001100 5 I - 1001101 THIK(I) = ATHIK*2.001104 TMEAS (IL_ P ANCH XTRA001106 TDENS(I) = ADENS*A*2.O-lllll ...-....... .NSEC. INT (TMEAS(I)./STEP 1+,5)001114 SECT « FLOAT(NSEC)-1.fl11i.6-l. -..... TD.IWW _ DENS(I -/SECT

001121 DO 6 K=1,NSEC001131 TTHTK(K) s THIIK--.-- .... . ......001132 W1(K) = WWQ01132 ----_6 iCONTINUE ..... ..-....001133 NNDX * NSEC0.115 ----_---- ND __. EXT . .. ... .

001137 MINIS = NNDXCC READ IN THE DENSITY AND THICKNESS CONFIGURATION OF THE TRAIN AND

EJ------------- .. _.._ElUPC ORRESP-ONDIN GARBAY-S-.--_EACH-_ INERAT ILQTN-_- SIE- -TRINC SIDE IS ASSIGNED A WEIGHT Wt(I) AND THICKNESS TTHIK(I),

----------C---......-. __------------- ---------001140o 9 READ 1012,NSECTH,(IDESC(II), II1,7)n115F 101_2 FORMAT ttrIQ.6X bAA!G )001153 NAME - 6HNSECTH601155 -.-S - - -P.RINYT-_ l 1l3l3NAME9-NSEC-THI__liDESC_[ II s ---II_.L--tZ .-091172 1013 FORMAT (1H 9A692H ,19,1X,7A1o)01j 7------- NSECTJ-H_ NSECTJ-R_+AD-_ 1------- - ----------------------------

901174 NDX « NNDX101175 NAME = 6H TTHIK01177 DO 10 ImNRAD,NSECTH

JLOJ_20. . ... ......-_- READ OlO6_TIKILL .TIEASlj_ LQEScCll-j-lLmLtS ..5..001215 1016 FORMAT (2F15.5,5Alo)012l5 B----rPINJ_ LO 14NAMEJIT-I KLIIMEAS.) i I.lESCIl).l-IPl.5s) -- _i..--..

001234 o1011 FORMAT (1H ,A692H ,2FT5.5S5X95A1O).0134 _ NSEC a INT(TMFAS{T)/STFP!+*5) .......:1240 DO 11 J-1,NSEC

· 01251 .N.-- XX.....__-__ ....0 01252 TTHIK(K) u THIK(I)001252. _11 CONTINUJE .. ..001255 NDX s NDX+NSECi01256 a1 CONTINUE _ __ 001261 READ 1012,NSECD ,(IDESC(II),II11,7)Q00_12_74 NAME_ . 6H.NSECD001276 PRINT 1013,NAMEiNSECD ,(IDESC(Ii),I=1,)7)

13.13-.-3- _ .... NSECa _NS E_ CD-ANRGa-l- .......... . .... .. ..............001315 NDX = NNDX001316 NAME = 6H TDENS001320 DO 12 INRADNSECDiQ13-I -- EA LD6iIDENS__ lt MEASIIi_,IDSC IIt._-_t-001336 PRINT 101ONAMETDENS(I),DMEAS(I),(IDESC(II),II=1l5)QQ01_355_.....--NSEC = .IN.T (DMEAS.t Il}/STEPI t .,5)......-...... .... ........ .001361 14 SECT = FLOAT(NSEC)001362 WW a TDENS(I)/SECT_ .__.......001365 DO 13 J=1,NSECbQ1373 ---- K. . .. ...... _-_______ ..... . .. ....001374 W1(K) = WW00137 3----CONTINUE----------------------001377 NDX = NDX+NSEC

01004on 17 CNTTNtJF001403 NDXER t MAX1-NDX

.Q1_40L4-------- - ..--.15---I__tN£-E_- 1_541 _-5-- ------------_001406 15 NDX a NDX-NSECI1-40 - N--------------EC_--AXI---D------------------------

001410 I a NSECD,1~o1&11 ~ '~n Tn 14001412 16 CONTINUE,_OQ12 _ -REA__ lDi._EJ_--IDESIT._LII L__-1. _. __ _

100

001425 NAME b 6H WTF,14_-21— ---- PRINlT__1lStDlNAtM TF . --- t.i SC Il.,.Ii-L7--_--..001444 READ 1014,WTB ,(IDESC(II),II-l,7),0Q14%7 NAMF = 6H WTB001461 PRINT 1015,NAMEWTB ,(IDESC(II),IIu1,7)Ql .t.---Q ---- 4.A_ -_L4 J QL LEI__ lDESCLiI --E-.-ZLI001511 NAME = 6H GLIFT

11. i - PRINT 115tNlAMiEJ___J. ESCIl .LL7±_-001530 CFBY a GLIFT-WTB-WTF;0013 RF3 rAn 11,4 XSFrTH ( TnF _ C( tI) TTIm 1 7)001546 NAME u 6HXSECTH.I1a55aP J I---------- PRNT--P4al&T--NQ.1tAMESEJ CH ESCLIs .-- -001565 READ 1014,XSECTV,(IDESC(II),II1,97)

_Q-0A..l.....-----NA MEJ i-XS-ECV—-—---001602 PRINT 10159NAMEXSECTV,(IDESC(II),II-17)Q00167 RFAD 101_4QSTHTK ,'TnDEsC(TT),I.lm 7)001632 NAME * 6H STHIK

A,0163-4 - P--- R_ -- PJNT-15lsNAHME.,STH IKI--_sLDESClll),.IitL7-L -- --001651 STHIK « STHIK/12,

-01-653 -- READ-4 -- +SENS-. + -DESC II-)-4-tL-- -----001666 NAME u 6H SDENS0f01670 PRINT 1015,NAMFESDFNS ,(TnDFC(TI), _7) -_001705 READ 1014,STEP2 ,(IDESC(II),II11,7)O2----------NAME__6tL-SLEP _2---------------..----

001722 PRINT 10159NAMESTEP2 ,(IDESC(II),IIu17)01-7.L3- RE -- 12 L- ----- ......QE..S..-.... .001752 NAME = 6H NWIND,001754 PRINT 1 l1 NAMENwTIND_ T nE C ( TI) IlT 7 ........001771 NAME = 6H WINDD-_QlI73 17- IS -l__L---7__-ilD .......................... . ..........___ ..

C-------- ----- -C F-OR-EACH-Kwt__ L CONTAINS-3-CO3EEF-ICIENTJS-_FQR-OR E-- -

C FUNCTION REPRESENTING A WIND PROFILE AS FOLLOWS -C IF HT TS THF HEIGHT IN FFET THEN THE WIND IN KNOTS ISC WN(1,NW)+WN(2,NW)*(HT)**WN(39NW)

001774 READ 1017,(WN(II,NW) ,II=1,3), (IDESC(II), II=15)11020L 4 — - 1017-- FORMAT C3 .5 5A ) . .........................

002014 PRINT 1018,NAME,(WN(II,NW),lIIi,3)9(IDESC(II),II1195)002036 li1 FORMAT (1H ,A6«2H =,3FlncX_._SXAfo)002036 17 CONTINUEQ0041 ..-- REA___I___ A__ l_ iMT DC I I) _ I_....- . ...002054 NAME = 6H CWANT02.DOS6 ...-. ...--.. 1.RIN1T.J1 15i NAME.CWANT , (IDESC ( I ), I I=1, 7)

CC WRITE RUN IDENTIFICATION ON MAG TAPE (UNIT 1)C

00207-3.. WRITE.I1) (IDENT(I) I=15) SLOPECWANTNWINDCC COMPUTE BALLOON PROFILEC

002112 2.... .... _.V aYLUME. = 1 000.*GLIFT/HELFT002114 BRAD = (3.*VOLUME/(4.*PI))**(1./3,)002124 BANG = BANG*CNVIN002126 HCENT = BRAD/SIN(BANG)002131 ANGMIN - -BANG002132 ANGMAX = PI+BANG0021 34 A N G N. _.N C_ .. (ANGMAX. ANC MIN /2 0002136 BSHAPX(1) = 0..0213........ SHAPY ( 1 ) -- 0 .002137 ANGLE = ANGMIN00214.0 ..DO 101. I =2,22 002142 SSHAPX(I) = BRAD*COS(ANGLE)0 02146 ..... BSHAP.Y ) . .RADt NIANIANGLE) +HCENT002153 ANGLE = ANGLE+ANGINC002155 101 CONTINUE002157 BSHAPX(23) = n.002157 .BSHAPY(23) = 0....

C____..__C COQMPUITE ..TES IOQN VALUES:C

OQ2160 TEN1 = 0.002160 TEN2 = 2.*A*ADENS+WEXT+WPAY+1000.

101

cC THESE MINS AND MAXS ARE THE END POINTS FOR THE INTEGRATION.C

00216b MIN2 = MAXI+I002170 MAX2 = MIN2+1200002172 W2 = SDENS*STEP?002174 ALPHA = C.002174 ALPHSV = 0.002175 NT = 1

CC READ IN FTONG = FEET ON GROUND UNTIL A 0. VALUE IS REACHED. THENC START READING IN ALPHA = ANGLE AT STARTING POINT OF INTEGRATION.

002177 201 READ 1000,FTONG002204 1000 FORMAT (3F15.5)002205 MINiSS = INT(FTONG*FLOAT(MAX1))002207 STPONG = FLOAT(MINtSS)002210 MIN1SS = MINISS+1002212 FTONG = STPOhG*STEPi002213 IF (FTUNG) 1, 1 ,2."2

C002214 1 READ 1000,ALPHA002221 IF (ALPHA.E.1000,) GO TO 99002223 ALPHSV = ALPHA002224 ALPHA = CNVIN*ALPHA002225 202 CONTINUE002225 NPAGE = 1H002226 IF (MOD(NT,3).EQ.1) NPAGE=lH1002235 PRINT 1004,NPAGEALPHSV FTONG002246 1004 FORMAT ( A1,2?SXH ALPHA =,F6.,?10X98H FTONG =oF6.1)002246 NT = NT+I002250 IF (RADIUS) 199199210002251 210 IF (ALPHA-PHI) 211,220,220002253 211 TTCIN = FTONG-P002255 TTHIN = TTCII*SLOPE002256 IF (TTCIN,LT,n.) TTHIN=0,002260 MINI = MINISS002262 GO TO 19002262 220 TTHIN = HP002263 TTCIN = C.002264 MIN1 = MINIS+I002266 DO 18 I=1,MIN1S002274 TTH(I) = U.002275 TTC(I) = -P002275 18 CONTINUE

CC NWIND = NUMtER OF wIND PROFILES

002276 19 DO 200 NW=1,*NoINn00i2300 DO 20 I=1,3002306 20 WNO(T) = WN(TINw)002310 PRINT(1,NW) = Nq002313 ITER = C002314 T1 = TEN1002315 T2 = TEN2002317 29 TEN (1) = T002320 TEN(2) = T2002322 DO 30 NTN=1'2002324 CALL NTGRAT(TEN(NTN)C (NTN))002326 ITER = TTEP+I002330 30 CONTINUE

CC PERFORM INTERVAL HALVINGC

002332 DO 35 I=1,6002333 TEJ(3) = (TEN(1)+TEN(2))/2.002336 CALL JT(RAT (TEN (-),C ( 3))002340 ITER = ITER1+002342 INuX = 1002342 IF (C(3).GT.CwANT) INDUKX00234 TEN,(IINUX) = TEN(q)002350 C(INI)X) = C(3)002352 35 CONTINUE002354 TI = TENl(I)002355 T? = TEN(2)0O2356 TTENS(MTiiJ]S) = TFN(()

102

CC USE SECANT METHODC

002360 36 IF (ITER.GT.ITLIM) GO TO 40002364 IF (ABS(C(1)-C(2)).LT.1.E-ln) GO TO 40002370 TEN(3) = TEN(2)*(TEN(1)-TEN(2))*(CWANT-C(2))/(C(1)-C(2))002375 IF (TEN(3).LT.T! ) GO TO 29002377 IF (TEN(3).GT.2.*T2) GO TO ?9002403 TTENS(MINIS) = TEN(3)002405 CALL NTGRAT(TLN(3),C(3))002407 ITER.= ITER+1002411 INDX = 1QZ4... .. AL1. = ABS(C(1)-CWANT)002414 VAL2 = AHS(C(2)-CWANT)002Q41.7 IF (VAL2.GT.VAL ) INDX=2002422 TEN(INDX) = TEN(3)002424 C(INDX) = C(3)

CC ...... ...IF C FC IS CLOSE ENOUGH TO CWANT STOP ITERATING

002426 IF (ABS(C(3)-CWANT)-CRIT) 40,409,6CC THE OUTPUTED TTP IS THE TRAIN TENSION AT THE APEX.C

002444 40 TTP = TTENS(MINIS)00Q446 PRINT(2,NW) = TTP002447 PRINT(39NW) = CNVOUT*ALPHAH002451 PRINT(4,NW) = TTENS(MAX1)002453 PRINT(5,NW) = BALLH002454 PRINT(6,NW) = PARTC002455 PRINT(7,NW) = TSR002456 PRINT(8,NW) = CNVOUT*THETAW002460 PRINT(9,NW) = STENS002461 MMAX = ISTEP-1

CC COMPUTE THE STAY LENGTHC

002463 STEPLS = SQRT((TTC(ISTEP)-TTC(MMAX))**2+(TTH(ISTEP)-TTH(MMAX))**2)002475 SLNGTH = STEPLS+FLOAT(MMAMA-MAX1)STEP2002501 PRINT(1 ,NW) = SLNGTH002502 IF (ALPHA-PHI) 140,140,130

CC FOR ALPHA .GT. PHI THE TENSION IS DIVIDED RETWEEN THE ANCHORS ANOC THE AXTENSION, THE APPARENT [RAIN ANGLE IS CALCULATED FROM THEC APEX.C

002505 130 ATOP = P002506 TEXT = TTP*(SIN(ALPHA)-COS(ALPHA) TAN(PHI))002517 TANCH = TTP*COS(ALPHA)/(?.*C)S(EPS)*COS(PHI))002532 VDB = BALLH-HP002533 HD8 = PARTC002535 GO TO 15C002536 140 ATOP = PANCH*COS(ALPHA)002541 IF (RADIUS) T41,141,142002543 141 TEXT = TTP002544 TANCH = 0.002545 VDB : BALLH-HPAY002547 HDb = PARTC002551 GO TO 150

CC FOR ALPHA .LE, PHI IN THE ANCHOR CASE TEST T0 SEE IHAT THE APEX ISC WITHIN THE EXTENSION DISTANCE FROM THE PAYLOAD. IF IT IS NOT SETC TEXT = INFINITY AS A FLAG. THE APPARENT TRAIN ANGLE IS CALCULATEDC FROM THE ANCHORS.C

002551 142 TEXT = O.002552 IF (TTH(MIN1S).GT.HP) TEXT=37764000000000O00000R002557 TANCH = TTP/(,.,*COS(EPS))002564 VDO = BALLH002565 HOB = PARTC+S002567 150 CONTINUE002567 PRINT(11NW) = C(3)002572 TLNGA = SQRT(\/VD**2+HDB**2)002577 ALPHAA = ATAN?(VDB,HDR)002614 ALPHAA = CNVOUT*ALPHAA

103

002616 PRINT(12,Nw) = ALPHAA002617 PRINT(13,NW) = TEXT002620 PRINT(14,Nw) = TANCH002621 FALB = FBY-CFqY

02i624 PRINT(15tNW) = FALB002625 PRINT(16,Nw) = FRY002625 PRINT(179NW) = FOB002626 PRINT(18,Nw) = WINDH

C002627 IF (DD80.EQ.O) GO TO 49

CC TILT BALLOON PROFILE WITH WINDC

002630 ANGLE = ATAN?(FDB,FBY)002633 DO 102 I=1,23002634 BSX(I) = BSHAPX(I)*COS(ANGLE)-BSHAPY(I)*SIN(ANGLE)002643 BSY(I) = BSHAPX(I)*SIN(ANGLE)+RSHAPY(I)*COS(ANGL£)002654 102 CONTINUE

C DRAW CRT PLOT OF THE CONFIGURATION.C

002655 CALL FRAME002656 CALL PWRT( 11]210089IDENT,50o2,0 o002662 CALL PWRT( 3249 12,LABXe8,1,n)002666 CALL PWRT( 12, 372,LABY,23,1*1)

q.00?2672 .-- _ENCQDE (7291010,.LABT) NW,ALPHAA,TTPSLNGTH,C(3) FTONG002713 1010 FORMAT (8HwIN PRO ,12,2X,9HALPHAA = ,F2.0,2X96HTTP = ,F5.0,

12X99HSLNGTH = 9F3.0,2X94HC = 9F3.092X98HFTONG = ,F3.0)002713 CALL PWRT( 1009 950,LABT972,10):002717 CALL SET(.06,.96,.06, .969-100.,700o.-100..700..1)002726 CALL PERIML(8,95985):0.02731 CALL FRSTPT(-LO0.,O.)002733 CALL VECTOR(700.,O.)4Q02735 CALL FRSTPT(o.,O.)002737 CALL VECTOR(O.,HPAY).002741 CALL FRSTPT(-P. .)002745 CALL VECTOR(TTCINTTHIN)002747 DO 104 I=MIN1,ISTEP002751 CALL VECTOR(TTC(I),TTH(I))002753 104 CONTINUE002756 CALL FRSTPT(PARTCBALLH)002760 DO 103 I=19,3002763 X = HSX(I)+PARTC002764 Y = BSY(I)+BALLH002767 CALL VECTOR(XY)002771 103 CONTINUE002773 49 CONTINUE002773 200 CONTINUE002776 PRINT 10079((PRINT(IJ)J=1,9NW),T=1l18)003015 1007 FORMAT (1H ,8H NWIND =94(Fllo 4X)*/

11H ,RH TTP =94F15.39/11H 98HALPHAH =94F]5.39/21H ,8H TTB =,4F15.3,/31H ,8HTOTALH =94F15.39/31H 8RH PARTC =94F15.39/31H 98H TSB =94F]5.3,/31H 98HTHETAW =94F15.39/31H ,8H TSW =94F15.39/31H 98HSLNGTH =,4F15.39/31H ,8H C =94F15.39/31H ,8HALPHAA =94FI5.3,/31H ,8H TEXT =94Fl5.39/31H e 8H TANCH =94F15*39/3]H 98H FALB =94Fi5.3,/3)H ,8H FBY =9,F15.3/31H 98H FUB =94F15.39/31H ,8H WINOB =94F15.3/)

003015 WRITE (1) ALPHSVFTUNG,((PRINr(I,J),I=1914),J=1lNW)003040 IF (FTONG) 1,1 2il003042 99 CONTINUE003042 IF (DD8O.NE.O.) CALL FRAME003044 ENO FILE 1003046 END

104

LENGTH OF ROUTINE CLANCH004742 ...

SUBROUT.INES CALLED ..GRDFMTINPUTC OUTPTCCOSATAN2SINOUTPTBRBAREXNTGRATSQRTTANFRAMEPWRTOUTPTSSETPERIMLFRSTPTVECTORENDFILEND

VARIABLE ASSIGNMENTSWND 000001C01 TTH - 000005CO1 TTC - 003725C01 TTENS - 007650C01W1 .- 011632C01 TTHIK - 013602C01 PRINT - 003741 LABT - 004225LABX - 004251 LABY - 004275 IDENT - 004321 IOESC - 004326TUENS - 004336 OMEAS - 004350 THIK - 004362 TMEAS - 004374TEN 004406 C - 004413 WN - 004420 BSHAPX - 004456BSHAPY - 004505 RSX 004534 BSY - 004563 PI - 004612CNVIN - 004613 CNVOUT - 004614 G - 0000OOOOOC02 BANG - 004615HELFT - 004616 CRIT 004617 ITLIM - 004620 IFM 004621DU80 - 004622 I - 004623 RHO - 000001C02 II - 004624NAME - 004625 PDBCOF - 000002C02 ALBCOF - 000003C02 RADIUS - 004626ANCHT - 004627 ANCHE - 004630 ATHIK - 004631 ADENS - 004632SPRED - 004633 XTRA - 004634 HPAY - 004635 wPAY - 004636HEXT - 004637 WEXT - 004640 SLOPE 000000CO1 PHI - 004641PANCH - 004642 P - 004643 NNDX - 004644 NRAU - 004645TTHIN - 011625C01 TTCIN - 011626C01 MINI - 011627C0O MINIS - 004646HP - 004647 BETA - 004650 VALUE - 004651 S - 004652EPS - 004653 A - 004654 TLNGTH - 004655 STEP1 - 011631C01TOTL - 004656 MAX1 - 011630C01 NSEC - 004657 SECT - 004660WW - 004661 K - 004662 NSECTH - 004663 NDX - 004664J - 004665 NSECD - 004666 NUXEH - 004667 WTF - 004670WTB 004671 GLIFT - 004672 CFBY - 015552C01 XSECTH - 015554C01XSECTV - 015555CO1 STHIK - 015564C01 SDENS - 004673 STEP2 - 015562C01NwIND - 004674 NW - 004675 CWANT - 004676 VOLUME - 004677BRAD - 004700 HCENT - 015553C01 ANGMIN - 004701 ANGMAX - 004702ANGINC - 004703 ANGLE -004704 TEN1 - 004705 TEN2 - 004706MIN2 - 015560C01 MAX2 - 015561C01 W2 , 015563C01 ALPHA - 000004C01ALPHSV - 004707 NT - 004710 FTONG - 004711 MIN1SS - 004712STPONG - 004713 NPAGE - 004714 :ITER - 004715 TI - 004716T2 - 004717 NTN- - 004720 INOX 004721 VALI - 004722VAL2 -0-04723 TTP - 004724 ALPHAB - 007645CO1 BALLH - 011622C01PARTC - 011623C01 TSR - 011620C01 THETAW - 007647C01 STENS - 011621C01MMAX - 004725 ISTEP - 011624C01 STEPLS - 004726 SLNGTH - 004727ATOP - 004730 TEXT - 004731 TANCH - 004732 VOD - 004733HUB - 004734 TLNGA - 004735 ALPHAA - 004736 FALB - 004737FbY - 015557C01 FDB - 015556C01 WINDO - 015565C01 X - 004740Y - 004741

105

SUBROUTINE NTGRAT(TTPC).. _ . C

C SUBROUTINE TO DETERMINE THE CONFIGURATION OF A CABLE LAUNCHINGC APPARATUS.C

000006 COMMON/APARTS/SLOPEWND(3),ALPHA4TTH(2000) TTC(2000) ALPHAB,1THETABTHETAWTTENS(1000) TSBgSTENSgBALLHgPARTCtISTEPTTHIN,

___ -..... .... 2TTC.IN.MIN19MAX1,STEPIgWl.(1O00) TTHIK(1000),CFBYgHCENTXSECTH,3XSECTVFDBFBYMIN29MAX2,STEP2,W?,STHIKWINDS

000006 COMMON/AIR/GRHOPDBCOFALBCOFCC THIS ARITHMETIC FUNCTION DEFINES THE WIND AS A FUNCTION OF HEIGHT,C WIND IN KNOTS IS GIVEN BY WND(1)+WND(2)*(HT)**WND(3)C THIS FUNCTION ALSO CONVERTS IT TO FEET/SECOND,

000006 WINDF(HT) = (WND(1) + WND(2)*AMAX1(HT90.)**WND(3))*1.15155*5280Q /3600.

CCC THIS ARITHMETIC FUNCTION GIVES THE DRAG IN POUNDS ON A BALLOONC. HAVING A VERTICAL CROSS SECTION oF XSECT SQUARE FEET WITH THEC WIND GIVEN IN FEET PER SECOND

000021 PORAGB(WINDXSECT) = (RHO*WIND*ABS(WIND)*PDBCOF*XSECT)/(2.*G)CCC THIS ARITHMETIC FUNCTION GIVES THE LIFT IN POUNDS ON A BALLOONC HAVING A HORIZONTAL CROSS SECTION OF XSECT SQUARE FEET WITH THEC WIND GIVEN IN FEET PER SECOND

000033 ARLFTB(WINDqXSECT) = (RHO*WIND**p*ALBCOF*XSECT)/(2**G)CCC THIS ARITHMETIC FUNCTION GIVES THE DRAG IN POUNDS ON A CYLINDRICALC BODY HAVING A LONGITUDINAL CROSS SECTION OF XSECT SQUARE FEET ANDC AN ANGLE OF ATTACK PARALLEL TO THE WIND OF ANGLE RADIANS WITH THEC WIND GIVEN IN FEET PER SECOND

000044 PDRAGC(WINDXSECTgANGLE) = (RHO*wIND*ABS(WIND)*XSECT*1 (1.l*ABS(SIN(ANGLE))**3+.n2))/(2.*G)

CCC THIS ARITHMETIC FUNCTION GIVES THE LIFT IN POUNDS ON A CYLINDRICALC BODY HAVING A LONGITUDINAL CROSS SECTION OF XSECT SQUARE FEET ANDC AN ANGLE OF ATTACK PARALLEL TO rHE WIND OF ANGLE RADIANS WITH THEC WIND GIVEN IN FEET PER SECOND

'000067 ARLFTC(WINDXSECTANGLE) = (RHO*wIND*ABS(WIND)*XSECT*1 (1,I*SIN(ANGLE)*ABS(SIN(ANGLE))*COS(ANGLE)))/(?. 4 6)

C000114 ALPHAR = ALPHA000115 TOTH = TTHIN000117 TOTC = TTCIN000121 TTENY = TTP4SIN(ALPHA)000124 TTENX = TTP*COS(ALPHA)

CC INTEGRATE ALONG TRAIN SIDE (UPWAPD)C

000131 DO 400 ISTEP=MIN1, MAX1000133 TOTH = TOTH+STEP!*SIN(ALPHAB)000137 WIND = WINDF(TUTH)000141 TTH(ISTEP) = TOTH000144 TOTC = TOTC+STEPItCOS(ALPHAB)000150 TTC(ISTEP) = TOTC000150 XSECT = TTHIK(ISTEP)*STEP1000154 FDT = PDRAGC(WINDXSECTALPHAB)000162 FALT = ARLFTr(wlNnXSECT,ALPHAR)000171 TTENY = TTENY+wl(ISTEP)-FALT000174 TTENX = TTENx+FDT000176 TTENS(ISTEP) = SQRT(TTENY**)+rTEiX**?)000203 ALPHAB = ATANI(TTENYTTENX)000210 400 CONTINUE000213 IF (MAX2-MIN?) 500,5009401000215 401 HALLH = TOTH000216 PARTC = TOTC

CC COMPUTE HALLOON FORCES

106

C000220 WIND = WINDF(BALLH+HCENT)000223 WINDH = WIND*3600./(5280.*1.15155)000225 FDd = PURAGB(WINDXSECTV)000227 FALB = ARLFTB(WINoXSECTH)000232 FBY = CFBY+FALB000233 STENY = FBY-TTENYQ .002a53 . . STENX = TTENX+FDR000237 TSB = SQRT(STENY.**2+STENX**?)000243 THETAW = ATAN2(STENY, STENX)000247 THETAB = THETAW

CC INTEGRATE ALONG WINCH LINE (DOWNWARD)C

000247 XSECT = STHIK*STEP2000252 DO 410 ISTEP=MIN29MAX2000255 TOTH = TOTH-STEPP*SIN(THETAW)000261 WIND = WINDF(TOTH)000263 TOTC = TOTC+STEP2*COS(THETAW)000270 GROUND = SLOPE*TOTC000271 IF (TOTH-GROUND) 4209420,408000275 408 TTH(ISTEP) = TOTH000276 TTC(ISTEP) = TOTC000300 FDS = PDRAGC(WINDXSECTTHETAW)000305 FALS - ARLFTC(WINnDX5ECTTHETAW)000314 STENY = STENY-W2-FALS000316 STENX = STENX+FOS000320 STENS = SQRT(STENY**2+STENX**2)000324 IF (STENS) 4119411,4C9000327 409 THETAW = ATAN2(STENY.STENX)000333 410 CONTINUE000336 411 CONTINUE

CC INTERSECT LAST STEP wITH THE GROUND,C

000340 420 MMAX = ISTEP-1000341 TOTC = (STENX*TTH(MMAX)+STENY*TTC(MMAX))/(STENX*SLOPE+STFNY)000350 TTC(ISTEP) = TOTC000351 TOTH = SLOPE*TOTC000352 TTH(ISTEP) = TOTH000353 C = TOTC000354 IF (ATAN2(SLOPE,1.)+THETAW) 5039501,500000363 500 RETURN000365 501 C = 1.E100000366 TTC(ISTEP) = C000367 TTH(ISTEP) = TTH(MMAX)-C*THETAW000372 RETURN000373 END

LENGTH OF ROUTINE NTGRAT000530

SUBROUTINES CALLEDRBAREXSINCOSSORTATAN2END

ARITHEMETIC FUNCTIONSWINDFPDRAGBARLFTBPDRAGCARLFTC

107

VARIABLE ASSIGNMENTSWND - 000001C01 TTH - 000005C01 TTC - 003725C01 TTENS - 007650C01Wl - 011632C01 TTHIK - 013602C01 RHO - 000001C02 PDOCOF - 000002C02G - 000000C02 ALBCOF - 000003C02 ALPHAR - 007645C01 ALPHA - 000004C01TOTH - 000511 TTHIN - 011625C01 TOTC - 000512 TTCIN - 011626C01TTENY - 000513 TTENX - 000514 ISTEP - 011624C01 MINI - 011627C01MAX1. - 011630C01 STEPI - 011631C01 WIND - 000515 XSECT - 000516FOT - 000517 FALT - 000520 MAX2 - 015561C01 MIN2 015560C01BALLH - 011622C01 PARTC - 011623C01 HCENT - 015553C01 WINOB - 015565C01FOB - 015556C01 XSECTV - 015555C01 FALB - 000521 XSECTH - 015554C01FbY - 015557C01 CFBY - 015552C01 STENY - 000522 STENX - 000523TSB - 011620C01 THETAW - 007647C01 THETA8 - 007646C01 STHIK 015564C01STEP2. - 015562C01 GROUND - 000524 SLOPE - 000000C01 FDS 0 000525FALS - 000526 W2 - 015563C01 STENS - 011621C01 MMAX - 000527


ENTRY POINT LOCATION ROUTINE ORIGIN........- LANCH 003003 003000

NTGRAT 025540 025534ALOG 026265 026264EXIT 026334 026334END. 026334 026334STOP 026334 026334

........ INPUT.C 026337 026337KODER 026707 026707KRAKER 027572 027572OUTPTC 030401 030401SIN 031067 031063COS 031063 031063SQRT 031152 031152TAN 031204 0312n3ATAN2 031276 031276ENOFIL 031405 031405OUTPTB 031427 031427INPUTR 031471 031427OUTPTS 032645 032645SET 033157 033144PSCALE 033222 033144PORGN 033226 033144FRAME 033242 033144FLUSH 033255 033144OPTION 033264 033144DASHLN 033277 033144FRSTPT 033304 033144VECTOR 033311 033144POINT 033315 033144PSYM 033321 033144PWRT 033350 033144AXES 033537 033144GRDFMT 033552 033144MXMY 033556 033144GRID 033563 033144GRIDL 033566 033144PERIM 033573 033144PERIML 033600 033144LAdMOD 034075 033144TICKS 034174 033144HALFAX 034200 033144LINE 034210 033144CURVE 034216 033144FLASH1 C34232 033144FLASH2 034244 033144FLASH3 034261 033144FLASH4 034277 033144RBAREX 035075 035075

COMMON BLOCKS LOCATIONAPARTS 007742AIR 025530

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