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~~~1301'°'The Revised Solar Array Synthesis
Computer Program
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"ow
Final Report
February 1, 1970
Contract No. NAS5-11669
Goddard Space Flight Center
Contracting Officer: P. VidenieksTechnical Officer: R.Obenschain
Prepared by
RCA CorporationDefense Electronics Products
Astra Electronics Division' Princeton. New JerseyProject Manager: E. Goldberg
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Prepared for
National Aeronautics and Space AdministrationGoddard Space Flight Center
Greenbelt, Maryland
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https://ntrs.nasa.gov/search.jsp?R=19730002318 2018-07-10T03:13:41+00:00Z
FOREWORD
The Revised Solar Array Synthesis Computer Program is a general-purposeprogram which computes solar array output characteristics while accounting forthe effects of temperature, incidence angle, charged-particle irradiation, and
. other degradation effects on various solar array configurations in either circularor elliptical orbits. Array configurations may consist of up to 75 solar cellpanels arranged in any series-parallel combination not exceeding three seriesconnected panels in a parallel string and no more than 25 parallel strings in anarray. Up to 100 separate solar array current-voltage characteristics, corresponding to 100 equal-time increments during the sunlight illuminated portionof an orbit or any 100 user-specified combinations 'of incidence angle and temperature, can be computed and printed out during one complete computer execution.Individual panel incidence angles may be computed and printed out at the user'soption.
Techni~al direction and consultation during the development of the computer program was provided by Mr. Obenchain, Contract Technical Officer, Power SystemsDesign Section, National Aeronautics and Space Administration, Goddard SpaceFlight Center, Greenbelt, Maryland. Technical direction at RCA was the responsibility of Mr. P. Pierce. Mr. P. Hyland of RCA was responsible for computerprogramming.
PRTOOEDING PAGE BIJANK NOT FIT ,M~D
. iii
Section
Preceding page blank _1
TABLE OF CONTENTS
Page
FOREWORD • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • iil
I GENERAL. • e 0 Q • • • • • • ••• 0 •• 0. ....... 1
IT PROGRAM DESCRIPTION ·..................... 5
A. MAIN. - Computer Program Contro~ ........• •••B. PHI - Calculation of DENI 1-MeV Electron Flux • • • •C. DEGRAD - Irradiation Degradation of Solar Cell
1-V Characteristics • • • • • • • • • • • • • • • • • • • • • •D. STASH - Degradation and Temperature Expansion
of Solar Cell I-V Characteristics •••••••••• • • • •." E. STINT - Data Storage and Retrieval • I.' ••••• • •••
F. INCANG - Calculation of Panel Incidence Angles • • •
57
10
111314
lIT USE OF PROGRAM •••••••• • • • 0 • 0 0 • e·. • 0 0 • • 0 • 0 21
A. Date and List Option Card •••••••••••••••••• 21B. STINT Table Title Card •••••••••••••••••••• 21C. STINT Tables •••••••••••••••••••••••••• 23D. Run Label Card. • • • • • • • • • • • • • • • • • • • • • • • • • 24E. NCODE ••••••••••••••••••••••••••••••• 24F. Array Signal Card ••••••••••••••••••••• 0 • 34G. NPARST (No. of Panel Parallel Strings) ••••••• • • 34H. NPANEL (No. of Series Panels). • • • • • • • • • • • • • • 34I. Panel Description Cards ••• I • • • • • • • • • • • • • • • • 34
IV OUTPUT DATA DESCRIPTION AND FORMAT • • • • • • • 5 37
V REFERENCES • • • • • • • • • • • Q a , • • • • e • • • • • • • • • • 41
PRlOOEDING PAGE BLANK ·NOT FILMED.
v
LIST OF ILLUSTRATIONS
Figure Page
1 Solar Array ~ayout ••••••••••••••••••••••••••• 2
Inertial Coordinate System ••••••••••••••••••••.•• 162
3 Fixed Coordinate System ••••• ......• • • • • • • • .. • • • 17
4 . Program Assembly ••••••••••••••••••••••••••• 22
5 Sample Coding Sheet Showing Format for .a SingleArgument STINT Table ••••••••••••••••••••• , • •• 25
6 Sample Coding Sheet Showing Format for a SingleArgument STINT Table • • • • • • • • • • • • • • • • • • • • • • • •• 26
7 Sample Coding Sheet Showing Format for a Two~
Argument STINT Table. • • • • • • • • • • • • • • • • • • • • • • •• 27
Sample Coding Sheet Showing Fo~mat for a Two-Argument STINT Table •••••• '••••••• '. • • • • • • • • • •• 28
9
10
Format and Description of NCODES ••••••••••••••• '. 29
Format and Description of Array Cards •••••••••• :... 36
LIST OF TABLES
Table Page
Solar-Flare Alpha Particle Flux Format • • • • • • • • • • • •• 10
Damage Factors for Alpha Particles. • • • • • • • • • • • • • •• 13
• • • • • • • • • 0 • G • • • 0 • • • • • • • 0 • 8 •
9
7
8
14
• • • • • • • • • • • • • • • • •
• • • • • • • • • • • • • • • • •
• • • • • • • • • • • • • • • • • •
• • • • • • • • • • • • • • • • • • • • • e , • •
.0. . . . . . . . . . . . . . . . . . . . •. . .Electron Flux Format
Proton Flux Format
Solar- Flare Proton Flux Format
Damage Factors for Electrons •••
Damage Factors for Protons ••••
Shielding Numbers
1
2
3
4
5
6
7
8
vi
SECTION I
GENERAL
The Revised Solar Array Synthesis Computer Program is based upon anoriginal solar array synthesis program developed by RCA and described in GSFCTechnical Report No. X-716-69-390. Two major differences exist between thetwo programs. The first is that the revised program has the capability to compute solar cell array current-voltage characteristics for solar cell panels connected in series, as well as in parallel. Secondly, the revised program enablescalculation of individual panel incidence angles for a variety of array configurations designed for missions in circular or elliptic type earth orbits. Other minordifferences such as number of solar panels per array,~ increased number of arraycomputations per computer execution, and increased versatility with panel incience angles versus solar cell cover-glass thicknesses versus relative shortcircuit current of solar cells are characteristic of the revised synthesis program.A second computer program (Power Systems Computer Program) dev810ped underthe same contract will use the solar array synthesis output to perform energybalance cal~ulations for various photovoltaic power system configurations.
Like the original synthesis program, the Revised Solar Array Synthesis ComputerProgram is written in Fortran IV language for use on the IBM computer and hasthe purpose of computing and printing out solar cell array I-V characteristics.Solar cell degradation factors such as temperature, charged particle irradation,isolation and bypass diode voltage losses, and series resistance are taken intoaccount during all array computations. Up to 100 separate' solar array I-Vcharacteristics, corresponding to 100 equal-time increments during the sunlightilluminated portion of an orbit or any 100 user-specified combinations of incidenceangle and temperature, can be computed and printed out during one completeexecution.
In the revised program, an array configuration may be defined as planar (Nimbustype), faceted, or circular and may consist of up 75 solar cell panels arranged inany series-parallel combination not exceeding three series-connected panels in aparallel string and no more than 25 parallel strings in an array. (See Figure 1.)Each panel in a parallel string must have the same number of parallel solar cellstrings, but the number of series-connected solar cells may differ for each panel.Separate user-defined profiles of panel temperature versus time versus sun angleare provided for in the program, as well as profiles of panel incidence angleversus time versus sun angle. Panel incidence angles may be computed andprinted out at the user's option.
1
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PANELBYPASSDIODES
TYPICAL PANEL/ PARALLEL STRING
ISOLATIONDIODES
+,,/ \ r--- - -,
\ I ~,r-
p--- II
II: t>I
- - Io _ -
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III t-
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TYPICAL"POLARITY
TYPICAL "POLARITY
. I PARALLEL STRINGTYPICAL t
SOLAR CELL ••PANEL
SERIES - -ROW t
Figure 1. Solar Array Layout
2
Economical execution of the program results through using only those programsubroutines required for a specific set of run conditions. The program user mayelect to perform solar cell calculations only, or solar cell and solar array calculations. Any number of runs may be chained together to evaluate the effectsof spe~ific or numerous parameter changes.
The revised solar array program has six parts - one main routine from whichfive subroutines are called. The six program parts are:
MAIN - reads input data, performs parameter initialization, callssubroutines as required, computes and stores I-V characteristics forup to 75 panels, computes resulting solar array I-V characteristicsin I-volt increments, prints output data, and punches a two-argumentsolar array STINT table for use in the Power Systems ComputerProgram.
PHI - computes damage-equivalent, normally incident (deni) i-MeVelectron fluxes for each of several kinds of charged omnidirectionalparticles (electrons, protons, solar-flare protonsand solar-flarealpha particles) while accounting for solar cell cover-glass and backshielding thicknesses, sums the individual fluxes into a daily flux,and calculates total mission flux based on the mission duration indays.
DEGRAD - 1. 0 or 10.0 ohm-em base resistivity solar cell 1-V curveinput is degraded for deni 1-MeV electron flux calculated in SubroutinePHI or by a user specified deni 1-MeV electron flux value.
STASH - degrades, stores, and prints solar cell input I-V characteristics from Subroutines DEGRAD or STINT for current and voltagedegradation factors and series resistance effects for up to 15 specifiedtemperatures.
STINT - a table storage subroutine adapted from the IBM SHARE,library STINT routine which supplies on command, the values ofvariables whichare functions of one, 'two, or three arguments.
INCANG - computes individual panel incidence angles from angle andtime data supplied by the MAIN routine for spinning or one revolution'per orbit (RPO) spacecraft solar array configurations in an'ellipticalcr circular earth orbit.
3
SECTION II
PROGRAM DESCRIPTION
Preceding page blank J
B'ecause of the many types of computations required in the execution of theRevised Solar Array Synthesis Program, the program is divided into a mainroutine, called MAIN, and the following subroutines: PHI, DEGRAD, STASH,
. STINT, and INCANG. ' Instructions to the computer are entered by means ofcomputer NCODE instruction cards. NCODE names are shown where the described function or value is used as a computer NCODE instruction.
A. MAIN - COMPUTER PROGRAM CONTROL
The primary purpose of MAIN is to perform all data input and NCODEparameter initialization, print out the input data used (printed out in an E format), call out the other subroutines when they are required, and perform thesolar .array calculations. MAIN will also print out calculated panel incidenceangles (NCODE NWRIT) and punch (NCODE NPUNCH) a two-argument STINT tablecontaining solar array I-V characteristics at the specified time increments.
Up to 100 separate solar array I-V characteristics, corresponding to 100 e9ualtime increments during the sunlight portion of an orbit or any 100 specified combinations of incidence angles and temperatures, can be computed during ,onecomputer execution.
The first function of the MAIN routine is to initialize and read all input parameterscontained in the NCODE's and data tables. Subroutines PHI and DEGRAD arecalled, if applicable, to degrade the input solar cell I-V curve for chargedparticle irradiation. Additional design degradation factors such as series wiringlosses and measurement errors are applied to the radiation degraded solar cellcurve in subroutine STASH at the same time STASH is expanding the cell curveinto a family of 15 I-V curves spanning the user-specified temperature range ofinterest for the ensuing array calculations.
Solar array calculations are initiated in MAIN with the contribution to the totalsolar array 1-V curve of each of up to 25 panel parallel strings calculated individually. An equivalent cell I-V curve is ~onstructed for each string based upon thetemperature and incidence angle profile of each panel in the string. The totalstring current and voltage values are calculated by multiplying the representativecell's current values by the number of parallel solar cell strings and the voltagevalues by the number of active solar cells connected in series. Each panel in aparallel string must have the same number of parallel Bolar cell strings, but thenumber of series-connected solar cells may differ for each panel. Losses of
PRFX:EDlNG PAG~ BLANK NOT FlIJMED 5
voltage due to voltage drops across user-specified parallel string isolationdiodes and those panel bypass diodes which are back-biased because of inactiveseries connected panels are calculated into the string I-V curve. Summation ofthe indi vidual string I-V curves yields the total solar array I-V curve at eachtime increment.
Maxi mum solar array power is computed from the final array I-V c'urve: Iftwo identical maximum power points are calculated, the subsequent power pointcharacteristics of power (watts), voltage (volts), and current (amps) are saved ..Time is incremented after maximum power· point calculations are completed and'the complete solar array is recalculated accounting for those parameters effected by time. A STINT table containing all array I-V characteristics for eachtime increment may be L".omatically punched into a set of STINT table cards bythe computer by initializing NCODE NPUNCl::I. The computer will automaticallycount and punch the total number of argument 1 and argument 2 values on thetable header card. (See Section III.)
The inclusion of solar cell panels connected in series in an array configurationwith each panel having its own temperature versus time and incidence anglev~rsus time profile will introduce current limiting effects. If a series-connectedpanel has a greater incidence angle than other series-connected panels in apanel string, the entire panel string output current will be limited to the shortcircuit current of the low-output panel. A condition also exists where one of thepanels may be in total darkness and, therefore, limiting the entire panel stringto zero output. This condition is avoided by providing a bypass diode in parallelwith each series panel, which results under the above described condition in a .loss of the voltage output from the bypassed panel and a voltage loss to the remaining active series panels equivalent to the bypass diode voltage drop.
There are occasions, however, where the program user may divide a panel circuit into two or three parts to obtain more accurate solar array output characteristics and not have bypass diodes for each of the circuit subpanels. Anexample of this might be a circular array configuration where each parallel rowof solar cells in each panel circuit has a different incidence angle and theoretically a different temperature profile. The computer program will accept seriesconnected panels without bypass diodes. However, if anyone of the subpanelsbecomes inactive, then the entire panel series string output is set to zero. Theprogrammer may vary the number of series connected solar cells per subpanelin order to determine the maximum array output for the desired orbit.
6
B. PHI - CALCULATION OF DEN! i-Mev ELECTRON FLUX
The purpose of the subroutine PHIl, 2 is to calculate the amount of damageequivalent normally incident (deni) i-MeV electron flux to which the input solarcell will be exposed during its lifetime. This can also be inputted as a userdefined 'constant (NCODE FLUX) in which case PHI is skipped. The deni i-MeVelectron flux of charged particles (electrons, protons, solar flare protons, .andsolar flare alphas) is calculated separately, and the total daily flux is obtainedby summation. Total mission fluxes are calculated in PHI when NCODE DAYSis given a value greater than 1. O. NCODE DAYS must never be set to zero.Control is then returned to MAIN.
Charged-particle population is tabulated in rant;es of millions of electron volts(MeV) and assigned to an energy range number. Tables 1 through 4 presentsample data for the specified energy ranges. Where no particle population isconsidered, a value of zero must be used. See Section III for proper STINTtable preparation.
:TABLE 1. ELECTRON FLUX FORMAT
EnergyRange 6. E (Mev) Electrons/ cm2
Number
1 0.0-0.25 1.28E15
2 0.25-0.50 3.62E14
3 0.50-0.75 1. OE14
4 0.75-1. 0 3.11E13
5 1. 0-2. 0 1.32E13
6 2.0-3.0 1. 21Ell
7 3.0-4.0 4.7E9
8 .. 4.0-5.0 3.61E9
9 5.0-6.0 3.6E9
10 6.0-7.0 1. 22E9
11 >7.0 0
7
TABLE 2. PROTON FLUX FORMAT
EnergyRange l:::. E (Mev) Protons I.c m2
Number..
1 0.0-1. 0 4.38E15
2 1. 0-2. 0 3.4E12
3 2.0-3.0 1. 2E11
4 3.0-4.0 2.48E9
5 4.0-5.0 .. 4.38E8
6 5.0-6.0 2. 92E8
7 6.0-7.0 2.92E7
8 7.0-8.0 2.42E7
9 8.0-9.0 7.3E6
10 9.0-10.0 .5.84E6
11 10.0-11.0 5. 84E6
12 11. 0-12. 0 . 5. 84E6
13 12.0-13.0 5. 84E6
14 13.0-14.0 5. 84E6
15 14.0-15.0 5. 84E6
16 15.0-30.0 1. 75E6
17 30.0-100.0 7.3E3
18 >100.0 7.4E3
Program user-specified cover glass shielding (NCODE CG) and backshielding(NCODE BS) are also used by subroutine PHI. Cover glass shielding values arenormally inputted in terms of mils of fused silica ranging from 0 to 54 mils.Maximum cover glass thickness may go as high as 1200 mils. Backshieldingthicknesses may range from 0 to 1000 mils of aluminum (1000 mils of aluminumis used to approximate infinite backshielding). Any desired thickness of coverglass or backshielding within the limits described above may be specified by theuser.
8
TABLE 3. SOLAR-FLARE PROTON FLUX FORMAT
c
EnergyRange A E (Mev) Protons/ cm2
Number
1 0.0-1. 0 0
2 1. 0-2. 0 6.0E10
3 2.0-a.0 1.5E10
4 3.0-4.0 8.0E9
5 4.0"':5.0 4.5E9..-6 5.0-6.0 2.5E9
7 6.0-7.0 2.0E9
8 7.0-8.0 1.1E9
9 8.0-9.0 7.0E8
10 9.0-10.0 4.5E8
11 10.0-11.0 4.0E8
12 11.0-12. O.. 4.0E8
13 12.0-13.0 4.0E8
14 13.0-14.0 3.0E8
15 14.0-15.0 t.5E8
16 15.0-30.0 1.8E9
17 30.0-100.0 1. 7E9
18 >100.0 2.0E8
Each energy range number is related to a damage factor whose magnitude dependson the type of charged particle and shielding value. These damage factors arelisted in Tables 5,6, and 7. Table 8 lists the stored shielding densities andequivalent thicknesses of fused silica cover-glass and aluminum backshielding.
9
TABLE 4. SOLAR-FLARE ALPHA PARTICLE FLUX FORM~T
.0
Energy AlphaRange 6. E (Mev) Particles/
Number cm2
1 16-18 4.0E7
2 18-20 3.0E7
3 20-22 3.0E7
4 22-25 3.0E7
5 25-30 . 4. OE7
6 30-32 2.0E7..
7 32-35 2.0E7
8 35-40 2.0E7
9 40-45 2.0E7
10 45-47 LOE7
11 47-52 1. 2E7
12 52-57 1.3E7
13 57-60 5.0E6
14 60-80 3.2E7
15 80-100 2.0E7
16 100-200 2.25E7
17 200-400 4.5E6
18 >400 1. OE6
C. DEGRAD - IRRADIATION DEGRADATION OF SOLAR CELL I~V
CHARACTERISTICS
In subroutine DEGRADi , 2 the solar cell I-V characteristics stored in'subroutine STINT as current and voltage vectors, called XIVEC and VVEC, aredegraded for radiation damage by empirical equations. The total deni i-MeVelectron flux in this calculation is an input parameter from either subroutinePHI or NCODE FLUX, along with the solar cell base resistivity NCODE DOHMS(1. () or 10.0 ohm-em).
10
TABLE 5. DAMAGE FACTORS FOR ELECTRONS
Energy Shielding NumberRange
Number 0.0 1.0 1.5 3.0 6.0 9.0 200.0
1 0.01 0.0 0.0 0.0 0.0 0.0 0.0
2 0.06 0.03 0.02 0.0 0.0 0.0 0.0
3 0.18 0.13 0.08 0.03 0.0 0.0 0.0
4 0.38 0.30 0.20 0.10 0.02 0.0 0.0
5 1.3 1.15 1. 02 ." 0.75 0.47 0.25 0.0
6 2.9 u 2.70 2.50 2.05 1. 55 1.10 0.0
7 4.35 4.15 3.92 3.38 2.85 2.15 0.0
8 5.5 5.30 5.15 4.60 4.10 3.30 0.0I9 6.5 6.15 6.10 5.70 5.30 4.60 0.0
10 7.4 7.30 7.30 6.80 6.50 5.85 0.0
11 7.8 7.80 7.80 7.70 7.50 7.0 0.0
D. STASH - DEGRADATION AND TEMPERATURE EXPANSION OF SOLARCELL I-V CHARACTERISTICS
The purpose of Subroutine STASH3 is to receive a set of I-V characteristicsfor a single solar cell at a temperature defined by NCODE TNOT, degrade it forcurrent and voltage degradation effects (NCODES DI 1 through DI 4 and DV 1 andDV 2 respectively), and expand it into a family of curves for 15 equally spaced(NCODE DELTT) temperatures. Current and voltage temperatures coefficientsare established in NCODES SIGISC and SIGVOC respectively. AVOCO is theNCODE for the open-circuit voltage of the input, undegraded solar cell whileNCODE THETA is the open-circuit voltage degradation factor. NCODE AVPMOis the undegraded input solar cell maximum power point voltage and NCODEAIPMO is the maximum power point current.
Subroutine STASH prints a list of 50 current-voltage pairs at each of the 15 temperatures along with maximum power point values with associated maximum.power current and voltage values, and ISC and OCV values. There I-V pairs arealso stored for ready reference when solar cell information is called for byMAIN.
11
TABLE 6. DAMAGE FACTORS FOR PROTONS
Energy Shielding NumberRange
Number 0.0 0.5 1.0 1.5 3.0 6.0 9.0 200.0.1 20000.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
2 10000.0 0.0 0.0 0.0 0.0 0.0 0.0 0.. 0
3 7000.0 6000.0 0.0 0.0 0.0 0.0 0.0 0;0
4 5400.0 5400.0 0.0 0.0 0.0 0.0 0.0 0.0
5 4500.0 4500.0 3000.0 0.0 0.0 0.0 0.0 0.0
6 3900.0 3900.0 3700.0 2000.0 0.0 0.0 0.0 0.0
7 3500.0 3500.0 3500.0 3100.0 0.0 0.0 0.0 0.0
8 3100.0 3100.0 3100.0 3100.0 200.0 0.0 0.0 0.0
9 2800.0 2800.0 2800.0 2800.0 1400.0 0.0 0.0 '0.0..10 2700.0 2700.0 2700.0 2700.0 2000.0 0.0 0.0 0.0
11 2600.0 2600.0 2600.0 2600.0 2100.0 0.0 0.0 0.0
12 2500.0 2500.0 2500.0 2500.0 2100.0 100.0 0.0 0.0<,
13 2500.0 2500.0 2500.0 2500.0 2100.0 1000.0 0.0 0.0
14 2500.0 2500.0 2500.0 2500.0 2000.0 1400.0 0.0 0.0
15 2500.0 2500.0 2500.0 2500.0 2000.0 1500.0 100.0 0.. 0
16 2500.0 2500.0 2500.0 2500.0 2000.0 1800.0 1500.0 0.0
17 2300.0 2300.0 2300:0 2300.0 2000.0 2000.0 2000.0 0.0
18 1000.0 1000.0 1000.0 1000.0 1000.0 1000.0 1000.0 0.0
Subroutine STASH spreads the solar cell I-V characteristics over the specifiedtemperature range using a linear interpolation' method. This procedure is basedon solar cell temperature coefficient data obtained in the temperature range -60°Cto +800C and is considered accurate within these limits. Reasonable accuracy hasbeen obtained with this program at temperature range e"Xtremes of -170° C and+100° C by assuming linear temperature coefficients within this range'.
12
TABLE 7. DAMAGE FACTORS FOR ALPHA PARTICLES
Energy Shielding NumberRange
Number 0.0 1.0 1.5 3.0 6.0 9.0 200.0.1 20000.0 10000.0 0.0 0.0 0.0 0.0 0.0
,.
2 15000.0 13000.0 0.0 0.0 0.0 0.0 0.0
3 14500.0 14000.0 7000.0 0.0 0.0 0.0 0.0
4 13700.0 13700.0 11000.0 0.0 0.0 0.0 0.0
5 12500.0 12500.0 12000.0 0.0 0.0 0.0 0.0'.,
6 11500.0 11500.0 11500.0 2500.0 0.0 0.0 0.0
7 11000.0 11000.0 11000.0 5200.0 0.0 0.0 0.0
8 10400.0 10400.0 10400.0 7200.0 0.0 0.0 0.0
• 9 9800.0 9800.0 9800.0 7900.0 0.0 0.0 0.0
10 9500.0 9500.0 9500.0 8000.0 1700.0 0.0 0.0
11 9500.0 9500.0 9500.0 7800.0 3650.0 0.0 0.0
12 9500. o· 9500.0 9500.0 7700.0 5300.0 0.0 0.0
13 9500.0 9500.0 9500.0 7600.0 5700.0 1600.0 0.0
14 9400.0 9400.0 9400.0 7600~0 6300.0 4000.0 0.0
15 9200.0 9200.0 9200.0 7600.0 7000.0 6400.0 0.0
16 8600.0 8600.0 8600.0 7700.0 7400.0 7100.0 0.0
17 7000.0 7000.0 7000.0 7000.0 7000.0 7000.0 0.0
18 4000.0 4000.0 4000.0 4000.0 4000.0 4000.0 0.0
E. STINT - DATA STORAGE AND RETRIEVAL
Subroutine STINT is used many times throughout the program to obtain information from input data tables and the panel temperature and incidence angleprofile tables. The name stands for Standard Table Interpolation; it is an adoptionof the STINT routine which is a part of the IBM SHARE library.
The purpose of this routine is to store in tables, then supply on command, thevalues of variables which are functions of one, two, or three arguments. Apackage of STINT tables consists of a stack of individual table card decks, each
13
TABLE 8. SillELDlNG NUMBERS
Shielding Density 0.0 0.016 0.033 0.05 0.1 0.2 0.3 *,
(gm/cm2)
Equivalent mils 0.0 3.0 6.0 9.0 18.0 36.0 54.0 ~200.Q
of fused silico, cover glass
Equivalent mils 0.0 2.5 5.0 7.5 15.0 30.0 45.0 1000.0*of Aluminum
Shielding Number 0.0 0.5 1.0 1.5 3.0 6.0 9.0 200.0for Computer "
Lookup
>:CSimulates infinite backshielding
.beginning with a descriptive header card. In the loading mode, STINT will loadsuch cards until it finds a blank card instead of a header. It will then exit backto the control point. The first use of the STINT routine, which occurs in MAIN,
, is to load all data tables.
Subroutines PHI and DEGRAD are essentially the same as those used in theMOPS Power System Computer Program, developed for NASA-MSC by RCAunder Contract No. NAS 9-5266. A detailed technical discussion of the techniques employed in these two subroutines is contained in References 1 and 2. 'Subroutine STASH is essentially the same as Subroutine STASH used in theNimbus B Energy Balance Computer Program, developed for NASA-GSFC byRCA under Contract No. NAS 5-9668. The techniques employed by STASH aredescribed in Reference 3.
F. INCANG - CALCULATION OF PANEL INCIDENCE ANGLES
In Subroutine INCANG, individual panel incidence angles are calculatedfrom angle and time data supplied by the MAIN routine. Incidence angles arecalculated for solar array configurations of planar, faceted, or circular incircular or elliptical orbi ts. The elliptical equations are used for any of theabove spacecraft array configurations in an earth locked one revolution perorbit (RPO) elliptic orbit only. One revolution per orbit spacecraft in a circular orbi t will use circular orbit type equations. A spinning spacecraft ineither an elliptic or circular orbit will use circular orbit type equations sincethe spin rate is uniform and not affected by the characteristic elliptical orbit
14
anomalies described later in tllis text. The computer program does not providefor checking spacecraft spin rates versus orbit types. Therefore, the programuser must select either an elliptic or circular orbit using NCODE NTYPE.Elliptic orbits are usedonly when the spacecraft spin rate is 1 RPO.
Vector 'analysis of two separate coordinate systems, fixed and inertial, is thebasis for calculating a panel incidence angle beta (f3) at any time t. The panelincidence angle is defined as the angle between the sun vector and panel normal.Each coordinate system reference point (~and S{' axes) may initially be parallelor separated by an angle zeta t (NCODE ANGLO), which provides the programuser with accurate real-time solar array calculations~ For example, if solararray data is to be used in subsequent power system energy balance computations and a portion of the spacecraft orbit is in earth eclipse, then a real-timedifference exists between the theoretical beginning of orbit referenced at startof eclipse in the energy balance program and beginning of daylight which isdefined at time zero in the solar array program. The spacecraft referencepoint shall have shifted an amoWlt equal to the eclipse duration in minutes(NCODE TN) times the spacecraft spin rate (NCODE DEGTOT) for circular oneRPO orbits and spinning spacecrafts. Spin rates for one RPO elliptical orbit
~ .spacecraft are nonuniform and, therefore, special equations described later inthis test must be used.
The first coordinate system is defined as the inertial system. The xaxis isreferenced in the orbit at the start of earth eclipse and the £ axis is parallel tothe orbit normal while the inertial system origin is located at the earth's center(Figure 2). Vector analysis of the sun vector ~ in this system gives the following equation
~ = sin () cos A ~ + sin () sin A Y+ cos () Z
where angle theta «() is the orbit n9rmal to SWl vector (NCODE ETA) andlambda (.A) is the orbital phase angle referenced to the start of earth eclipse(NCODE TANGLE). Lambda (A) is fixed with respect to time and is equal tohalf the angle zeta described above. If NCODE TANGLE is initialized to -1.' 0,the computer will automatically calculate lambda. Either or both N;CODESANGLO and TANGLE may be initialized to -1. O.
Vector analysis of the second system which is fixed with respect to the space.craft, (Figure 3) gives the following equation:
p = cos ep cos €~, + sin ep sin € y' + cos ~';
15
SUN -EAHTH INTERSECTION
1\X
S
OHBIT PLANE
INERTIALCOORDINATE
SYSTEM
.:'
X1\Z
1\Z
1\S
1\k----:--- Y
ECLIPSE
,START OFECLIPSE
16
Figure 2. Inertial Coordinate System
~, /\P
."
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FIXEDCOORDINATE
SYSTEM
../\
. X'/\S
1\X
II
~-~
x-yORBITPLANE
Fixed Coordinate System
17
where p is the panel normal vector, ¢ is angle between p and the spin axis,and E: is the angle between p projected onto the orbit plane (x' - y') and thespacecraft reference point. Figure 3 also shows the relationship of these twosystems at time zero.
Turnin'g the inertial coordinate system into the fixed system at any time t andsolving for the cosine of the incidence angle {3 gives the following simplifiedrelationship: .
{3 = cos-1 [sin () sin ¢ cos «E: + ~ (t» - A) + cos () cos ¢)
where ~ (t) is defined as
~ (t) = ~o + "6 t, and
Ws is the spin rate (NCODE DEGTOT) of the spacecraft in the degrees perminute. The above described general equation is used for panel incidence anglecalculations of earth locked one RPO spacecraft in a circular orbit and spinning
.sp..acecraft in either a circular or elliptical orbit. This same equation is usedfor earth locked one RPO spacecraft in an elliptical orbit with one exception.
The rate of change of the spacecraft fixed reference point (x' axis) is non':'uniform. Angle anomalies are introduced and dependent upon the orbit radiusof apogee ra (NCODE APOGEE) and perigee r R (NCODE PERIGE). Therefore,wst of ~ (t) = ~o + wElt is defined in terms of the true anomoly ~~ in the following relations.
~ (t) = ~ + ~ ando e
tan -1 (1- e2) j /2 sin E~e = ----..;.--::----
cos E - e
where
e = (orbit eccentricity)
18
E = M + e sin E (eccentric anomaly)
M = 27r t (mean a~omaly)Po
t = elapsed time
Po = TD + TN is the orbit period, TD is orbit daytime duration, and TN is theorbit nighttime duration.
The eccentric anomaly relationship is derived from the basic laws of Keplerianmotion and is adequately called Kepler's equation. (Kepler's equation is morecommonly shown as M = E - e sin E.) In order to solve for the eccentricanomaly, an iterative Newton-Raphson formula is used and shown below•.
where
En + 1 = En +M- E + e sin En n
1- e cos En
E1 ::c M and iterating until .
. .where
1 - < y, and
Y is a tolerance set to to- 1•
Selecting the type of spacecraft orbit is accomplished by means of NCODE NTYPE.This NCODE is automatically set by the computer. The program user shall callfor elliptic orbit type computations only if he has a one RPO spacecraft in anelliptical orbit. Spacecraft spin rate (NCODE DEGTOT) is not used in ellipticorbit computations. NCODE NANG allows the progra~ user to either computepanel incidence angles or call for a table lookup in STINT. Panel incidence angleversus time vs sun angle table numbers are recorded on panel description cardsdiscussed in Section III of this reporf. It:lcidence angles which are calculated may'also be printed out at the option of the program user by means of NCODE NWRIT.
19
Preceding page blankSECTION III
USE OF PROGRAM
Assembly of the complete program as it is submitted to the computer isshown in Figure 4. This assembly bascially consists of two parts -- a programdeck and a data deck. The program deck, which can be used in either Fortran IVor binary form, is always used and is placed first in the assembly. It containsthe MAIN routine and all of the subroutines used in the program (STINT, PHI,DEGRADE, STASH and INCANG) and does not require any card changes to perform its function.
The data deck contains all the numerical information the program requires forcomputation and defines the user- selected options for each run. Consequently,the data deck must be prepared specifically for each run, or series of chainedruns, to be made. Cards and tables in the data deck must be positioned in theorder shown in the program assembly in Figure 4. The data deck descriptionand format are presented below in the proper assembly sequence.
A. DATE AND LIST OPTION CARD
Col. 1-2
Col. 3-4
Col. 5-6
Col. 9
Col. 9
Number of month
Number of day
Number of year
o- Input data (STINT) tables not printed out
1 - Input data (STINT) tables printed out in exponential format
B. STINT TABLE TITLE CARD
Col. 1
Cols. 2-72
Blank
Any alpha-numeric information
PRIDEDING PAGE BLANK NOT FILMED
21
BLANK CARD
LABEL CARDFOR LASTRUN IN CHAIN
BLANK CARD
STINT TABLES
STINT TABLESTITLE CARD
NCODES FORFOH RUN NO.1
DATE CARD &NLIST OPTION
LABEL CARD
END OF STINT __._r-'--F-O-R-H.....;U--N---N.....;O--.-,l
TABLES CARD
PROGRAM DECK
SOLAR ARRAYDESCRIP.
NUMBEH OF SEHIE~ 0CONNECTED PANELS. FIHRT
SOLAR ARRAYPAHALLEL STHING DESCRIP.
NUMB EH OF PAN EL __-,,.J-_-n~0;.:0~3__-,PARALLEL STRINGS 002
999..
NUMBEH OF SEHIESCONNECTED PANELS. SECOND
PAHALLEL STHING
.Figure 4. Program Assembly
22
C. STINT TABLES
The STINT tables are stacked one behind the other in the data deck inascending numerical order. The 10 tables listed below must be presented inthe data deck, in the order shown for each computer execution:.Table No.
1
2
3
4
5
6
7 ,••
8
9
10
(Variable'Data)
Table Name
Solar Cell I-V curve
Relative Solar Array Current vs Incidence
Angle vs cover glass thickness
Orbital Electrons Particle Flux....Orbital Protons Particle Flux
Solar Flare Proton Particle FluX
Solar Flare Alpha Particle Flux
Damage Factors for Electrons
Damage Factors for Protons
Damage Factors for Alpha Particles
NMVTBL Curve Shape Volts vs PHI
The maximum number of STINT tables that the program will accept is 200, the10 tables listed above plus, starting with Table No. 11, a panel incidence angleversus time versus sun angle table and a temperature versus time versus sunangle table for each of the 75 panels comprising the solar array. If fewer thanthe maximum number (75) of panels is specified, fewer STINT tables are required. More than one panel may use the same angle or temperature tablestored in STINT.
The first card of each STINT table is a header card, which must be prepared inthe following format:
Cols. 1-8:
Cols. 9-12:
Cols. 13-14:
Any alpha-numeric characters can be used fora date
Table number. Cannot be zero. Fixed pointand right justified
Number of argument1 values. Cannot be zero.Fixed point and right-justified
23
Cols. 15-16:
Cols. 17-19:
Cols. 20-70:
Cols. 71-72:
Number of argument2 values. Cannot be zero,is 1 for a function of one argument. Fixed pointand right-justified
Not used
Any alpha-numeric characters desired. Usuallyused for table title
00
After the header card, each card in the table uses 10 fields of 7 columns each forthe argument values and the function values. The first card contains the firstnine argument1 values in fields 2 through 10. lIi"the following cards, field 1 contains an argument2 value, and fields 2 through 10 contain corresponding functionvalues. Mter all the argumen~values have been spanned, the whole series of anargument1 card followed by argumen~ cards can repeat until all the function valuesare used. If there is an argument3 value for the table, it goes into field 1 of theargument1 1 card. Columns 71 and 72 on each card must contain a sequence number, starting with 01 for the first card. Figures 5 and 6 show typical STINT tablecoding sheets for a single argument (current as a function of voltage and computerdata table 3) STINT table. Figures 7 and 8 show a two-argument STINT tableformat for computer data table 7, and a typical panel tempera:ture table.
Mter the last STINT table in the data deck, there is a card labeled END OF STINT,TABLES, starting in Col. 21., Cols. 9-12 and' 71-72 must be left blank on thiscard.
D. RUN LABEL CARD
Following the END OF STINT TABLES card is a card containing any desiredalpha-numeric information in cols. 2-72, which usually describes the first run tobe made.
E. NCODE
Following the Run Label Card are the 37 NCOD~ cards. The card number,or NCODE, is right justified against col. 3. The numerical value of the NCODEvariable is left-justified against col. 5 and must have a decimal point. Figure 9shows the NCODE names, the NCODE numbers, the NCODE values and a briefdescription of each NCODE for a sample computer run. Only the NCODE (item)number and its numerical value are punched on the NCODE cardsj the other datain Figure 9 are for information only. All 37 of the NCODEs are initially loaded
24
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into memory, thus a single run or the first of a series of chained runs must contain all the NCODE's in the data deck. Each of the NCODE's listed in Figure 9are described below:
1. TD is the orbit suntime duration in minutes.
2. DELTAT is the desired orbital time increment between solar arraycalculations starting at zero minutes. Up to a maximum of 100 solararray I-V curves may be printed out for each run.
3. SIGISC is the input solar cell short-circuit current temperature coefficient expressed in amperes per degree centigrade.
4. SIGVOC is the input solar cell open-circuit voltage temperature coefficient expressed in volts per degree.:centigrade and is punched onthe card as a positive number. The computer program will automatically assign the proper negative sign.
5. DI 1 is a short-circuit current degradation factor.
6. DI 2 is a short-circuit current degradation factor.,7. DI 3 is a short-circuit current degradation factor.
8. DI 4 is a short- circuit current degradation factor.
9. DV1 is a maximum power point voltage degradation factor.
10. DV2 is a maximum power point voltage degradation factor •
. 11. AVPMO is the input solar cell maximum power point voltage.
12. AIPMO is the input solar cell maximum power point current.
13. AVOCO is the input solar cell open-circuit voltage.
14. THETA is the open-circuit voltage degradation factor.The DI's, DV's, and THETA are used for some of the followingreasons:
Reason
Standard Cell Error
illumination Intensity Veriation
Measurement Error
Ultraviolet Degradation
* short-circuit current
Effect
ISC*
ISC
ISC
ISC
31
Reason
Series Wiring Loss
Thermal Cycling Degradation
Voltage Measurement Error
Effect
VPM*
VPM
OCV**
...
1,
!,
15. TNOT is the input solar cell reference temperature.
16. ADIODE is the panel series string isolation diode. drop specified bythe user. A value of 0.0 is punched if no isolation diode drop isdesired in the output solar array curves.
17. DELTT is the temperature increment .. between solar cell I-V curvecalculations in subroutine STASH.
18. ADDT is the difference in temperature between the highest STASHtemperature and TNOT.
19. FLUX is punched as 0.0 if no charged particle irradiation damage is. to be considered, in which case subroutines PHI and DEGRAD do not
compute. If FLUX has a value of i-MeV equivalent flux (Example:2.6 X 1014 is punched as 260000000000000.0 on the card) subroutinePHI is bypassed and MAIN will calculate the mission flux based onDAYS. Subroutine DEGRAD will then degrade the solar cell for themission i-MeV flux. If flux is given a value of -1.0, subroutine PHIwill compute a value of i-MeV flux from tables of omnidirectionalparticle fluxes that the user must supply in table locations 3,4,5 and6. This value of i-MeV flux will be multiplied by the number of daysspecified in NCODE DAYS and will then be automatically sent to subroutine DEGRAD for the appropriate solar cell corrections.
20. CG is the solar cell cover glass thickness in mils of fused silica.
21. BS is the solar cell backshielding thickness in equivalent mils ofaluminum.
22. BOHMS is the input solar cell base resistivity.
23. NDGRAD must be set·to 1.0 in the first run. This causes the machineto automatically degrade the solar cell and expand it for temperaturein subroutine STASH as specified by the degradation and temperatureparameters in the NCODES. When chaining additional runs, if thesolar cell degradations are not changed, NDGRAD should be set to0.0 in the second run. By setting NDGRAD to 0.0 needless repetitivecomputations in the solar cell subroutines are eliminated.
-* maximum power point voltage** open-circuit voltage
32
24. NEND must be set to either 1.0, 20, 3.0 or 4.0 for each run, anddetermines which of the following options is selected:
NEND = 1.0
NEND = 2.0
NEND = 3.0
NEND = 4.0
Do solar cell calculations only (PHI,DEGRAD and STASH) and stop.
Do solar cell calculations and read newset of run instructions.
Do solar cell and solar array calculationsand stop.
Do solar cell' and solar array calculationsand read new set of run instructions.
25.
,-
26.
27.
28.
29.
30.
31.
32.
33.
DAYS is the total number of mission days. This value is used to setthe daily i-MeV flux calculated in PHI to total mission flux whenNCODE 19 is set to -1.0. Equivalent fluxes greater than 0.0 set inENCODE 19 are also converted to total mission fluxes. DAYS shouldnever be set to 0.0.
PBYPAS is the voltage drop of all series panel bypass diodes. Avalue of 0.0 is punched if no bypass diode drop is desired.
ANGLO i~ the angle between the hvo coordinate system referencepoints at time zero. This allows the program user to arbitrarily setthe spacecraft reference point at any time in the orbit. It is nor- 'mally used when a portion of orbit nighttime is encountered. Theorbit will always start at the start of nighttime (eclipse). A value of-1.0 is used for automatic calculation of ANGLO by the program.'
ETA is the angle between the sun vector and the normal to theorbital plane (or spacecraft spin axis).
TANGLE is the orbital phase angle referenced to the start of eclipse.A value of -1.0 may be used for automatic calculation by the program.
DEGTOT is the spacecraft spin rate and is used when circularorbital calculations are called for byNTYPE.
APOGEE is the eliptic orbit radius of apogee including the earth'sradius.
PERIGE is the eliptic orbit radius of perigee including the earth'sradius.
NTY PE is used to select the type of orbit. 0.0 is punched when acircular orbit is desired or when the spacecraft spin rate (DEGTOT)is greater than 1 RPO. . ,.,
33
· I
34. NANG allows the program user to call for panel incidence angle calculations (punched as 1. 0) or for a panel incidence angle lookup inSTINT (punched at 0.0).
35. NWRIT is used to printout calculated panel incidence angles and ispunched as 1.0. If no print out is required, 0.0 is punched on thecard.
36. NPUNCH is used to punch the solar array I-V curves on cards in aSTINT tables format, and is punched as 1.0. If no array STINT tablesare required 0.0 is punched on the card. STINT table sequence numbers are punched in columns 71, 72, and 73.
37. TN is orbit nighttime duration in minutes.
F. ARRAY SIGNAL CARD
If NCODE 24 has been punched with a 3.0 or a 4.0 immediately followingthe NCODE 37 card must be a card containing 999 in columns 1-3. This cardtells the' computer tilat solar array information is to follow.
G. NPARST (No. of Panel Parallel Strings)
Following the Array Signal Card is the NPARST card, which contains thenumber panel series strings connected in parallel in tile array (maximum number of parallel strings is 25). This number must appear right justified in colurns 1-3. A decimal point is not required.
H. NPANEL (No. of Series Panels)
Following the NPARST card is the NPANEL card, which contains thenumber of series panels in the first panel parallel string of the array (maximumnumber of series panels is 3*). This number must appear right justified in columns 1-3. No decimal point is required.
I. PANEL DESCRIPTION CARDS
Following the NPANEL card is a panel description card for each solarpanel in the first parallel string. The number of these panel description cardsmust agree with the vaiue of NPANEL. Each card contains six fields of ten columns each, in floating point format (requires decimal point).
* Panels connected in series shall have the same number of solar cells connectedin parallel on each panel.
34
Columns
1-10
11-20
21-30
31-40
41-50
51-60
Variable
No. of Series-Connected Solar Cells perPanel
No. of Parallel Strings per Panel
Panel Angle to Spacecraft Spin Axis (1))
Panel to Spacecraft reference pt. (E)
Panel Incidence Angle vs Time vs Sun AngleTable Location in STINT
Panel Temperature vs Time vs Sun AngleLocation in STINT ',.
Typical Value
30.0
10.0
45.0
0.0
11.0
12.0
Following the Panel Description Cards is another NPANEL card describing howmany series panels are in Parallel String No.2. The number of panel description cards following the NPANEL card must equal the value of NPANEL. Thissequenc~ is repeated for each parallel string. The number of NPANEL cardsmust agfee with the value of NPARST.
Following the Panel Description Cards is a blank card. This tells the computerto stop reading in data and to start computing. If it is desired to chain an additional run, a new Run Label Card and only those NCODES and Panel DescriptionCards that contain changed or new information should be placed after the blankcard. As many runs as are desired can: be chained in this manner, ensuring thateach new run starts with a Run Label Card and ends with a blank card. Referagain to Figure 4 for the proper sequence of card positions for chained runs.Figure 10 shows the format for the Array Signal Card, NPARST card, twoNPANEL cards and six Panel Description cards.
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SECTION IV
OUTPUT DATA DESCRIPTION AND FORMAT
The information that the computer prints out after a run consists of thefollowing items:
(1) STINT Table Listing Option .
There is an option in the program to list all the STINT tables.This is done by taking the date card at the beginning of the datapackage and either punching a one (1) 'or a zero (0) in column9. Punching a one (1) will pro'duce a listing of the STINTtables in an E format. A zero (0) will not produce a listingof the STINT tables.
(2) Input Data Page
(a) Run number and date.
(b) Run comments as specified on input card.
(c) Listing of NCODE numbers, names and values.
(d) Number panel parallel strings.
(e) Panel parallel string number.
(f) . Solar array description: panel number, number of seriessolar cell rows, number of parallel solar ~~ll strings,panel angle to spin axis, panel angle to SC referencepoint, number of STINT table which contains the panelincidence angle, number of STINT table which containsthe panel temperature-time profile.
(3) Subroutine PHI (The fluxes are in equivalent i-MeV electrons/cm2.)
(a) The computed electron flux
(b) The computed proton flux
(c) The computed solar flare proton flux
(d) The computed solar flare alpha particle flux
(e) The computed total daily flux
(f) The computed total mission flux
37
(4) Subroutine DEGHAD
(a)' The solar cell I-V curve irradiation degraded
(b) Short-circuit current
(c) Current at the maximum power point
(d) Open-circuit voltage
(e) Voltage at the maximum power point
..
(5)
(6)
Subroutine STASH
Values of temperature for which the degraded solar cell I-Vcurve has been prepared are listEid in a row across the page. 'Values of maximum-power voltage and current, open-circuitvoltage and short-circuit current appear in columns undereach temperature. Values of every other calculated currentand voltage pair comprising the I-V curve and stored in thecomputer memory are listed in columns under eachtemperature.
Solar Array Data
(a) Time in orbit sunlight (up to 100 time increments startingwith 0.0 min.)
(b) Array short-circuit current
(c) Array open-circuit voltage
(d) Maximum power
(e) Maximum power current
(f) Maximum power voltage
(g) Solar array voltage in i-volt steps from 0 volts up to100 volts
(h) Total solar array current at each voltage above for eachtime increment; a maximum of .100 solar array I-V curvescan be produced per computer run.
38
(7) Panel Incidence Angle Data,
(a) Time
(b) Panel parallel string number
(c) Panel number (1, 2, or 3)
(d) Incidence angle
,.
(8) Solar Array STINT Table
(a) Header Card with number of argument! and argumentzvalues.
(b) Voltage versus current versus time data cards. STINTtable sequence numbers are also punched on the data cardsin columns 71, 72, and 73.
39
'i
'I
SECTION V
REFERENCES
1. Rasmussen, R., "Calculation of i-MeV Electron Flux and IrradiationDegradation of Solar Cell I-V Curves by Computer, " presented at theSixth Photovoltaic Specialists Conference, Cocoa Beach, Fla., March28-30, 1967.
2. "Manned Mission Photovoltaic Power System Study," Vols. II and Ill,NASA Accession No. N67-31837 and N67-31832. Report prepared forNASA-MSC by RCA on June 9, 1967 under Contract No. NAS 9-5266.
3. Harmon, H. and Rasmussen, R., "Temperature, Illumination Intensityand Degradation Factor Effects on Solar Cell Output Charcteristics, "presented at the IEEE Aerospace and Electronic Systems Conference,.geattle, Wash., July 1966.
P~EDING PAGE BUNK NOT M.vm,41
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