nasa technical memorandum technical memorandum ... appendix vii -use of the eai 8400 data conversion...

NASA TECHNICALMEMORANDUM

GENERALIZED AERODYNAMIC COEFFICIENT TABLE STORAGE,

CHECK-OUT AND INTERPOLATION FOR AIRCRAFT SIMULATION

Frank Neuman and Neil Warner

Ames Research CenterMoffett Field, California 94035 '

'(NASA-TM-X-62229) GENERALIZE AERODYNAMICCOEFFICIENT TABLE STORAGE, CHECKOUT AND :'INTERPOLATION FOR AIRCRAFT SIMULATION

l(NASA) 107 p SC $7.50 . CSCL 01A

N73-16983

UnclasG3/01 .62296 _

January 1973

, _ . .

.......... '-iaJ.

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https://ntrs.nasa.gov/search.jsp?R=19730008256 2018-07-07T13:21:23+00:00Z

CONTENTS ,'

SUMMARY 1

INTRODUCTION 2

CONSIDERATIONS FOR THE PREPARATION OF TABLES 4

TABLE PRE-PROCESSOR 7

DATA VERIFICATION 15

CHANGE FROM 360 TO 8400 INPUT PUNCH DATA CARDS 23

THE INTERPOLATION SUBROUTINES 26

CONCLUSIONS AND COMMENTS 28

APPENDIX I - PREPROCESSOR PROGRAM LISTINGS 29

APPENDIX II - PLOTTING PROGRAM LISTINGS 49

APPENDIX III - EAI 8400 CONVERSION PROGRAM LISTINGS 65

APPENDIX IV - INTERPOLATION PROGRAM LISTINGS 75

APPENDIX V - USE OF PRE-PROCESSOR 84

APPENDIX VI - USE OF THE PLOTTING PROGRAM 93

APPENDIX VII - USE OF THE EAI 8400 DATA CONVERSION PROGRAM 99

APPENDIX VIII - THE APPLICATION OF THE TABLE LOOKUP PROGRAMS 101

i

GENERALIZED AERODYNAMIC COEFFICIENT TABLE STORAGE, CHECK-OUTAND INTERPOLATION FOR AIRCRAFT SIMUALTION

SUMMARY

._For the last three years the set of programs described in this paper has

-been-used for rapidly introducing, checking out and very efficiently using

aerodynamic tables in complex aircraft simulations.

The preprocessor program reads in tables with different names and dimensions

and stores them on disc storage according to the specified dimensions. The

tables are read in from IBM cards in a format which is convenient to the engineer

or person who reduces the data from the original graphs. During table processing,

new auxiliary tables are generated which are required for table cataloging and

for efficient interpolation. In addition, DIMENSION statements for the tables

as well as READ statements are punched so that they may be used in other

programs for readout of the data from disc without chance of programming

errors. Besides punched card output, there is also a line printer output which

consists of the properly labelled tables. For quick data checking graphical

output for all tables is provided in a separate program.

Linear Interpolation routineswere written which required only onesearch per

argument, independent of the number of lists for each argument. The linear

interpolation routines have been written in FORTRAN to interpolate 1 dimensional,

2 dimensional, and 3 dimensional tables.

The programs described so far have been written to be used for aircraft simulation

on the IBM 360. For piloted simulations of the EAI 8400 computer the same

set of data is required. However, the data input format is quite differgnt.

To save time and reduce operator errors a Program was written that converts the

format for the IBM 360 to a punched card deck in the EAI 8400 compatible format.

-1-

INTRODUCTION

The programs that will be described in the following sections are designed to

speed up the data storage, data check-out, and table look-up for aerodynamic

coefficient tables used in aircraft automatic control simuftions on the IBM

360 and for piloted simulations on the EAI 8400.

On the 360 everytime a new aircraft or spacecraft had to be simulated new data

processing subroutines had to be written, while the 8400 interpolation is not

too efficient in its argument searches. The new table preprocessor program

that will be described does not require any re-writing as function of the table

names, table lengths, or table dimensions. The new interpolation program

performs only one search per argument

independent of the number of argument lists required for the set of tables.

This is further explained below.

For an elaborate 6 degree of freedom aircraft simulation, up to 100 tables

are required. These tables often have common arguments, for instance 'alpha'

the angle of attack, but the list of argument values at which the function

values are stored may be different depending on the shape of the functions which

are approximated as linear segments. These lists are called break-point lists.

During a simulation run each break-point list must be searched for the subscript

of the break-point just below the actual argument value. Therefore, many

break-point lists may have to be searched even though they concern the same

argument. In our table look-up method this.disadvantage is over-come by generating

master lists of all break-points and searching the master lists only. The

subscript of the appropriate break-point for each argument ofeach table is

found in an auxiliary cross reference list. Hence, there is only one search -

per argument. An inefficient search could also be avoided by expanding tables

-2-

by means of interpolation so that they all have the same break-point lists.

If one assumes infinite storage, this is the most efficient method of table

look-up. However, table expansion may increase the required storage by a

factor of 4 to 8 so that a large amount of virtual memory and core swapping

my be required on the IBM 360 which would make the program run inefficiently

although the calculations would be reduced. In the programs that will be

described, the tables are kept at their original size at a cost of a small

amount of computation.

At present, data packages for aerodynamic tables for aircraft simulation are

prepared separately for the IBM 360 and the EAI 8400. This requires two

sets of data decks, each containing different types of data transcription

and key punch operator errors;and therefore, it requires two check-out periods.

Such check-out is very costly in computer and engineer's time. Therefore a

program was written that circumvents double data check-out by converting the

data stored and checked out on the on the 360 to a deck of cards in the format

that is required for the 8400 for aircraft simulation.

-3-

CONSIDERATIONS FOR THE PREPARATION OF TABLES

Often aeronautical tables are generated from graphical data. The following

remarks are intended to aid in speeding up the data reduction process -and

aid in obtaining an efficient table lookup for running simulation programs.

The number of breakpoint lists should be kept small. This can be done by

examining all tables with identical parameters and by selecting a set of

parameter breakpoints that would permit faithful description of all curves

with that set of breakpoints. Then select from this master list a reasonable

number of subsets to describe individual curves with a minimum number of

breakpoints. The maximum number of breakpoint lists .per argument is 20,

but considerable storage and running time is saved for the simulation program

if this number is kept smaller. Greatest care in reducing the number of break-

point lists should be taken for the argument that appears most often in the

tables, usually the angle of attack.

All entries of the tables must be filled. It often happens in graphical data

that all curves on a graph do not span the full range of the parameter on the

abscissa. It is thought that the engineer can estimate a better extrapolation

for the purpose of filling the table than an automatic extrapolation program

could. If no prior knowledge is available, or if the simualtion would be

invalid if it entered the region of the graph for which no data exist, the

engineer can insert extremely large function values, which would make the

simulation fail in a very obVious way.

Effort is saved when the tables are constructed from the original graphs by

using the same convention as the automatic plotting program. Unless specified L--

differently, for an individual table, the plotting program plots the horizontal

breakpoint list as abscissa, the vertical breakpoint list as curve parameter,

and for a three dimensional table, it uses the third breakpoint list as fixed

parameter for each individual graph, see figure 1.

In naming the table it is useful to adhere to a simple convention similar for

all tables. A suggested way is to add a T to the name of a function for the

tabulatedvalues. Then, e.g. the table name for the lift -coefficient CL

would be CLT.

The table parameters may -be named identical to the names given in the

simulation-program. The parameter names in the table processor--are used only

as~phameric data. They aid in labelling the printouts and graphs and are

used in error messages in the simulation program.

-5-

r3 r BPL 3QL2 .

Uo

3

Vori E PL

(a) Graphical data.

srd. BPL 1 1 3r4 BPLo.|

(b) Tabulated data.

Relationship between breakpoint lists and standard plotting convention.

-6-

LO

ar-

'Ho; BPL

-- goors z .?L

-i

L.

W .,

"d IHorz; BPL

-.J

4. FunCt io2...n~t

Figure 1.

.! 3rd B PLI 1

TABLE PRE-PROCESSOR

READING IN THE TABLE DATA AND DESCRIPTION OF THE PROGRAm4 FLOW

The table pre-processor consists of a main program and 5 subroutines all

written in FORTRAN (for listings see appendix I). Their operation will be

explained by means of a small example. Figure 2 shows the data deck for the

example, which includes short 1, 2, and 3 dimensional tables in arbitrary

order. The cards are numbered and anotated for the purpose of discussion

only.

The main program T READ, reads in the NAMELIST "Input", which contains only

the variable IPUNCH. Table storage and card punching is controlled by IPUNCH;

when it is '0' only line printer output occurs. It is advisable to run the

program in this manner until one is reasonably sure of the correctness of the

data format and table dimensions. Finally, set IPUNCH to '1' to store the

data on disc and obtain a deck of DIMENSION and READ cards for all tables and

auxiliary arrays.

TREAD then calls subroutine TABCOM. TABCOM reads two key cards, (1) and

(2), which contain the number of arguments for all tables to be read and the

alpha-numerical names of all arguments. For reading each table TABCOM calls

TABIN. Each table has a header card, (3), (7), (20). The header card contains,

in order, a user's comment field, the table name, the names of the arguments,

and the lengths of the individual breakpoint lists which are also the table

dimensions. As can be seen, for the examples of the 2 and 3 dimensional

tables, the tables are constructed in a conventional fashion with one breakpoint

list written horizontally across the top, (9), (15), (21, and the other

,: ;brea.kpoint list. vertically on the left (first. column of numbers). The ., :

breakpoint for the third dimension are given at the head of each 2-dimensional

subtable, (8), (14). This arrangement requires repetition of breakpoint lists

-7-

3

ALPHA DA tiACH

CM ALPHA 1 3

I C20. -. 25. 0.610. .

iCLDA ALPHA DA MACH 3 4 2

-,,,o :--% . 5r.~ 5. lo.

-. i0.o . 1 .1 .10 . .3 .2 .115. .50 1 .302 .420. 8 4 .598

> O. 05. O0.-10. .05 .048 .05.0 .146 .1 .09815. .46 .15 .220. .39 .20 .31

CLilN 0 4 ALPHA 3 3 1

Figure 2. Card images with explanations of a sample set of inputpre-processor. (Blank cards were inserted for printout clarity

argurment YamrneS

4

Table I

I d.;nerisional

Table 2

3 dceasior,al

Table 3

2 J'. rvelO'nal

data to theonly.)

-8-

(2)-

(3)'

(4)(5)(6)

. I

(7)

(8)(9)

(I Oa)(I I)

(13).

(I 4).O S)

(I 6).tl7)( 8)(I 9)

(20)

(22)(Za 3)(Z 9)

no. o ar'uonie"ts

for 3-dimensional tables, but it aids the visual check of the data cards

before processing. The corresponding function values are located at the

intersection of one element in the vertical breakpoint list and another element

.in the horizontal breakpoint list.

In addition to the above, TABCOM stores the function elements and saves the

name of the table and the names of the arguments associated with the break-

point sublists. Next, once per table, TABCOM calls TABOUT which i's a 'subroutine

that writes out the table. The output for the example in Figure 2 is shown

in Figure 3. TABCOM also compares the new breakpoint lists with those already

stored and adds them to the already stored breakpoint lists, unless an identical

breakpoint is already in storage. Furthermore, TABCOM assembles breakpoint

identification lists which identify the required breakpoint lists as function

of the table number and first, second, and third table dimensions as appropriate.

After all tables have 'been read in, TABCOM prints out all breakpoint lists as

shown in Figure 4(a). Control is then turned back to the main program.

The last job to be performed by the table pre-processor is to generate the

lists that are required for a more efficient table look-up. First the main

program calls subroutine MLIST. MLIST generates a master list for each argument

that occurs in the tables. (A master list is an ordered list of all values

that occur in the sublists for one particular argument). These master lists

are required for searching each argument that occurs in the tables. The master

lists are printed out as shown in Figure 3(b). Finally, subroutine NBLIST is

called. This subroutine generates cross reference lists which will allow table

look-up by only searching the master list for each argument. After these

lists are constructed they are printed out as shown in Figure 5(a) for the

-example. The INBPL lists define the corresponding element in the breakpoint

list for each argument and each table. When the breakpoint list for a given

-9-

_,. ,...... . _; .. . . .s....:_.........,.. .,,- . _ _ , , , , __,__,,.

.UBER OF VARIABLES4HA- DA ___-- MAC.H

i

3

TABLE 1 CM ( ALPHA )

I

I ALPHA CM

0.000000 -0.200000

5.0O000 0.600000

10.000000 0.800000

TABLE 2 CLDA . ALPHA , DA , MACH

MACH = 0.500000

ALPHAO0.000000 5.000000 10.000000

DA

-10.00000OO 0 OOOOO O.1OO0O O.1h 0O000

0.000000 0.300000 0.200000 0.100000

15.000000 0.501000 0.302000 0.400000

20.000000 0.800000 0.400000 0.598000

Figure 3. Printed tables from the preprocessor.

- ~~~F. igure 3. Printed tables from the pre-processor.· -

-10-

MACH = 0.900000

ALPHA0.000000 5.000000 10. 000000

DA

-10.000000 0.050000 0.048000 0.050000

0.000000 0.146000 0.100000 0.098000

15.000000 0.460000 0.150000 0.200000

20.000000 0.390000 0.200000 0.310000

TABLE 3 CLMN ( DA , ALPHA

DA-9.000000 10.000000 18.000000

ALPHA

0o.000000

6.00000

1.0.0 00000

0. 000120

0.200000

0.400000

0.200100

0.600000

1. 000000

0.410000

0.800000

1 .2 000o00

(b)FIGURE 3-(concluded).

10a

i

I

iI

i

I

I

iI

ALPHA5.00000 10.000006.00000 10.00000

-10. 00000_Q nnnn

DA0.000001n. nnnnn

15.000001 R.0 0000

20.00000

I ULMN t__ -_ ___ ____ ________VVVVV _

0.50000MACH

0.90000

(a) Break-point lists, none repeated, with the table number and name whereeach list first occurred.

MASTER LISTS

4 ALPHA0.000 5.000 6.000 10.000

7 DA-10.000 -9.000 0.000 10.000 15.000 18.000 20.000

2 MACH0.500 0.900

(b) Break-point master lists with number of elements and name ofargument. /

Figure 4. -Auxiliary arrays from pre-processor.

-11-

1 CM3 CLMN

O .000000.00000

2 CLDA'l i Mm -

2 CLDA

NBPL LISTS FOR

1·23

-- 4 34

5.000

6.00010.000

ALPHACM CLM"N

1 1cm _1_M'

2 12 23 3

NBPL LISTS FOR DACLDA CLMN

1 -10.000 1 -12 -9.000 1 13 0.000 2 1-4 10.000o 2 ..2-.. 5 15.000 3 26 18.000 3 07 20.000 4 0

NBPL LISTS FOR MACHCLDA

1____ 00 1,_0_2 0.900 2

(a) NBPL cross reference lists.

CROSS REFERENCE LISTSJ NTDIM NJ1 NJ2 NJ3 NK1 NK2 NK3 NL1 NL2 NL31 1 1 1 32 3 1 2 3 1- -1 1 3 4 23 2 2 1 2 2 3 3

Mi. 8 i mey ay- . bra*-on ~- r . leq, ;+l~r eacl~o4'i r tht4e_ ag breek-p4,.vt I1,sts

(b) Cross reference lists indicating the correct breakpoint list for eachargument of each table.

16 DIMENSION CARDS WERE PUNCHED.

18 READ CARDS WERE PUNCHED.NOTE ** ON TSS, THESE CARD IMAGES ARE STORED IN THE DATA SET

ASSIGNED TO FT07FOO1 BY A DDEF CARD.

" S.SEE THE TABLE PROCESSOR USERS GUIDE.

·~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .· -. ., ....·.. . ..-

,- ' ."'.-(c) Message giving number of access card images stored.. ' ' ,,. '

Figure 5. Final output from the pre-processor.

-12-

=- ----

table does not cover the whole range of the master list, for points outside

the range, a'-l' is inserted when the value is below the range and a '0'

is inserted in the NBPL list when the value is above the range. (See the

DA NBPL list for table CLMN). As will be shown later, this permits the inter-

polation subroutines to determine, with a single IF statement, whether an

argument is outside the range of the table.

'Other cross-reference lists that are reui-fred are shown in figure 5(b). At the

beginning of the main program, under symbol explanation, the meaning of the

important variables and tables are given. Sufficient comment cards are

inserted into the programs to make them self-explanatory. Also given in the

main program are the ranges of the subscripts, which are determined by the

dimension statements presently in the program. The program as it stands

can handle 25 different independent variables and a maximum of 20 different

breakpoint lists per argument. It is of computational and storage advantage

if the numbers of breakpoint lists per argument are kept to a minimum. The

maximum length of a master list must not exceed 35 elements. These limits, of

course, can be changed by simply changing the dimensions of the arrays.

Since the pre-processor has stored all arrays efficiently, the remaining

programs could not be written in complete generality. However, the only

change that must be made as function of the type of tables to be processed

is to take the dimension cards and read statements which are provided by the

table pre-processor (see Figure 6) and insert them at the beginning of the

main programs. Note that the READ cards must remain in the correct order.

-.. - ,..

-13-

DI!,'ErISO,' C.i (' 3) D . 1DIi'ENSION CLDA ( 3, 4, 2) D 2DIMENXSION CLMIN ( 3, 3) 0 3REAL;:8 VARN 1i( 3) O 4DIM ENS I Oi'! BPL( 3, 2, 4) D 5DIi'ENSION NLENTH( 3, 2) D 6DIiMiENSION! NTABLE( 3, 2) D 7REAL*8 TNi'JME( 3) 0 8DIM ENSION JTN ( 3) D 9DIMIENSION NTDI[1( 3) . D 10DIMiENSION NBPL.( 3, 7, 2) D 1].D'IOWEN S ION NNMAST ( 3) D 12DIIMENiSION AMAST( 7, 3) D 13.DIMENS ION NJ( 3, 3) D 14DIMIENSION NK( 3, 3) D 15DIMENSION NL( 3, 3) D 16READ (2 )CM 1.READ (2) CLDA 2READ (2 ) CLMN 3READ ( 2) NUMTBL - 4READ (2) NOVARS 5READ (2) VARNM 6READ (2 ) BPL 7READ (2) NLENTH 8READ (2) NTABLE 9READ (2) TN;'fE . 10READ (2 ) JTN 11READ (2) NTDIM1 12READ (2) NIlBPL 13READ (2) NMiAST 14.READ (2) AHAST 15READ (2) NJ 16READ (2 ) NK .17READ (2) NL 1l

Figure 6. Listing of the DIMENSION and READ cards provided by the pre-processor.These cards must be inserted into the graphics program, the 8400-card punchprogram, and the interpolation-program.

," :. :. "". "': . "- ... . : .' -. t -' . . . . " " " :. 'f ."; ." - :.:" ' :: ' -- - " - .... ."'': ":"'' ... ' . '

DATA VERIFICATION

Although the tables are printed out in easily readable form, it is still

tedious to compare the data with the original graphical aeronautical data.

This process is simplified by graphical output of all tables that have been

stored. A main plotting program and some subroutines are included in this

table processing package to plot the tables stored by the pre-processor.

Hardcopy 8 x 8 - inch plots are produced on the S-'C 4020 cathode-ray-tdbe

plotter.

Sample plots of the example tables described previously are seen in figures

7(a) through 7(g). Figure 7(a) shows a 1 dimensional table, CM. Figures

7(b) and 7(c) show a 3 dimensional table, CLDA, which is plotted with the

variables in order as stored by the pre-processor and has been automatically

scaled on the stored data. Figures 7(d), 7(e) and 7(f) show the table CLDA

plotted where the plotting program options are used. The plotting order has

been changed so that the variable DA is now plotted as the abscissa. The

3 variables can be plotted in any order the user desires.

Another option illustrated is specification of the minimum and maximum values

of the function CLDA to be used on the graph. Figure 7(g) shows the format

for a 2 dimensional table and further illustrates results of specifying the

minimum and maximum graph values for the function CLMN and the variable DA.

Instructions for specifying the options desired and the cards used for figure 7

are described in Appendix VI.

Listings of the programs to produce the data verification graphs are presented

in Appendix II. Detailed instructions for their use are in Appendix VI.

-15-

i, ,- i I rI I r r rI T=

PtI -.H i- -F t t- z-tI

AL'HA

Figure 7(a). One dimensional table plotted as stored.

-16-

. 7C X

1111rIIl l

'j1 7 71 STOL 'U'!

I I O.-~>- X 4g

LIt-L-LTLL

.401

-4-I

-jF

.0

.T--ti E

-I

r

F

---- I

0.50

[4-#-

U7/2.7/71 >STOL t',2 I

I ' I -If I-T ] ?

HH1 "HirTiT111ITil IIi

.60 ., - - ! -,I u ___ It M4TMI}-+51 -[-

.50

iT.L

IN.20

I

I,Lh

+1il

vv -I rt

71:1-- t-f -tttttIL.LL24-4.4 LIII i II iW! i i i : I i i ii 1 1 1 1 " ! ." " " : : " : " " ; .IB11 a ". A U

S.0. S.L0ALPHA

Til7.0 8.0

Figure 7(b). Three dimensional table (part 1) plotted as stored,

and ..tomat'cally s~ai-...

I;' ' '.... . - and automatically scaled.

-17-

.80MACH

Fl t FF-H liI I I I ILLiL.LI

tf-t-M-

tLL1111I~ I 1111 ;1, 111 111 111, 1 1

: L - *ii~:?' ii:-iL

T I ?--i'- ,i-K i ], t

11[ l} It I! -I I II I I i --- t-l !111 tt t~it -I - i-i

......... .,,il.,,,ii I I I a I -l| I LLLL

Pk~i'-

I Lt

I~l i'-i-- ~- 4 ,X +-IilliT

t1-4-bi' -rH _ 1- *iU l i i:_

_ FFF n 41 ItFF:;11

lI

TIS

.35o

, I L

e.uo

Ltt

� 1

.80 MACH

.60l

°'4t

~~~1

.40

.sommm-FtI

.~ 45J t

edit, ~~~~I -- i-tWL G oi * - -- l 1 1 -11 _

2.0 4.0

ALPHA6.0 7.0 8.0

Figure 7(c). Three dimensional table (part 2) plotted as stored

. . . . . and automatically scaled .

... ., .. ...

-18-

0.907/2 7/71 I TCL

LiM1 ID ]V

;F I -

I .- i

f#1# -1.0 10.0

t m St Aht I

A.: X 1j, .. t: T onrntn,- l9-,I

.?70L

i *!

.

ALPHA 0.00

-t

-. .--.YE.w t-6 -6 -4 -2 0 2 4 6

DA "'8 12 t4

-I \57/2?T/? W-Ttk !A.Jl\

;I

[flP1171

16 i8

Figure 7(d). Three dimensional table (part 1) showing a change in

- .plotting order from th graphs of figure 5(b) a.nd (c).

New minimum and maximum values of the function CLDA

were also specified.

-19-

:---- _-

I

-. - - -, i

tO

1.00

0. ? 4 6

DA^'8 1L 12

fI

I. I .1

57/2?/71 -II

INV I -4-1 %,

-tTH---4"-4 _ 'dI_1=

14 16 18 2t

Figure 7(e). Three dimensional table (part 2).

-20-

ALPHA 5.00

�I2i

.I

_.4

Ii iV;

P-4-P

-10 -8 -6 -4 -Z

I iv: ! i i

L./27/ ?I ST.X 's' 6

-2Xy^H-~ 'i

ALPHAA 10. 00

4-:4 r_- Ft -- -_

-4

7 A- - -~

=2> ::-z

=I:+A7 F--

-8 -6 - 4 -2 0 2 4 _4

DA^-

IZ

U{ -- Hi

6 8 10 12 14 16 18

Figure 7(f). Three dimensional table (part 3).

.2] -

-21 -

H

Hr

I>

I1

a-10

I

t-=

_ I

!i.9I ? i *9 .1I -

-6 -4 -2

2.0

4

OA0 12 I$ 6 . -a . ta .

I

Figure 7(g). Two dimensional table showing results of user specification

of minimum and maximum values for both axes.

-22-

_1

--go

I

$-

CHANGE FROM 360.TO .84QO NiUTPcUCH DATA CARDS

As has been discussed in the introduction, a different set of punched table

data cards is needed for the 8400. In the 8400 the breakpoint lists must

be entered se.parately and identified with different names for each breakpoint

list although they concern the same argument. The function values for each

table must be entered separately in a specific format which separates individual

numbers by commas. Also, a slash is used as termination indicator for each

table. The program that does the conversion from the 360 to the 8400 format

consists of a main program (P84o00) and a subroutine (FTOB) which converts

floating point numbers to a short alpha-numeric array representing the same

number in the shortest possible format followed by a comma.

As shown in Figure 8 for the example tables, the output of the program provides

a listing and a deck 'of cards with the following fuhbtibons. There is onie

THRUPUT card for each table, which gives the name of the table as well as the

arguments in the order in which they are stored. kEach THRUPUT card printed

image is followed by a line of comment which will aid in associating the names

of the breakpoint lists on the THRUPUT cards with the proper breakpoint list.

Secondly, all breakpoint lists are given and the name of the argument for each

breakpoint list is defined. In addition, a comment card is included. Since

each breakpoint list must have a different,name in the 8400 program, a suggestion

for accomplishing this is given at the head of the printout for this program, as

shown in Figure 9.

NONE'OF THE BRREAKPOINTLISTS PUNCHED IS DUPLICATEDAS INITIALLY PUNCHED ALL BREAKPOINTLISTS ARE CALLED BY THE SAME NAME,

- SINCE WE CANNOT PREDICT WHAT THE NAMES OF THE INDIVIDUAL BREAKPONTLISTS WILL BE.SUGGESTION=CHANGE CARDS AS PER EXAMPLEFROM=- THRUPUT FAFB(CJA ,DA )TO = THRUPUT FAFR(C(JA1 ,DA1 )aCCF1RD)I'NG TO THE NUJMBER OF THE BRE/)KPOINTLIST FOR THE GIVEN TABLE. -*RT" , - - - -....--..-

-TTHI S NlJU'fBER IS (;GIVEN IN T:HE COMMHIENT LINE.,THE VARBPT CARDS MUST BE CHANGED IN A SIMILAR MANNER

FIGURE 9. Printout from Data Conversion Program

-23-

.THRUPUT CM (ALPHA )COMMENT, BK PT LIST NO. 1

THRUPUT CLDA (ALPHA ,DA ,MACHCOMMENT, BK PT LIST NOS. 1 1 1

THRUPUT CLMN (DA ,ALPHA )COMMENT, BK PT LIST NOS. 2 2

*THIS IS BK PT LST NO. 1 FOR VARIABLE ALPHAALPHA VARBPT

.0,5.,10.

/*THIS IS BK PT LST NO. 2 FOR VARIABLE ALPHAALPHA VARBPT

- vO..0,6. -O./

*TH-IS IS BK PT LST NO. 1 FOR VARIABLE DADA VARBPT

-10.,.0,15.,20.

*THIS IS BK PT LST NO. 2 FOR VARIABLE DADA VARBPT

-9. ,10.,18.

/*THIS IS BK PT LST NO. 1 FOR VARIABLE MACHMACH VARBPT

.5, .9/

CM POINTS

-.2,.6,.8/

CLDA POINTS* MACH = 0.50000

.1.,. 1, .1

.3,.2,.1

.501,.302, .4

.8,.4,.598* MACH = 0.90000

.05T4 , zq,.05

.146,.1,.098

.46,. 15, .2

.39,.2,.31/

CLMN POINTS.00012,.2001, .41.2,.6,.8.4,1.,1.2

/_ __ _ _ _ _ _ _ _ _ _ _ _

Fi-gure 8. Line printer output from the 8400 data conversion program.. ~ ~~~~~~~~~~~~~~~~~~ . _

-24-

One appends a number to the name- of'thye, variable- for each breakpoint list"

according to the number of the breakpoint list for the given variable. The

comments automatically identify which breakpoint list number belongs to the

variable for the given table. One must-append this number to the name of

the'variable in the THRUPUT card. We intentionally did not automatize this

process, since the choice of the name for the breakpoint list is up to the

user, and he may choose completely different names for the individual break-

point lists.

There are no changes required for card output of the function values them-

selves. The proper comment cards are inserted for 3 dimensional tables. The

function elements are ordered as specified in the THRUPUT statements with the

fastest argument on the left and slower varying arguments successively to

the right. The punched cards are identical to the line printer output, but

in the 026 card punch format which is required for the EAI 8400 computer.

Appendix VII describes use of this program and shows a set of control cards

for the TSS System. Again, the main program, shown in Appendix III must be

recompiled for each card punch job because of the DIMENSION and READ statements.

With the availability of the data conversion program, the table preprocessor,

and the plotting program it is hoped that in the future all function tables

will be punched in the manner required for the pre-processor and coverted

to the 8400 format by the conversion program. This should provide a faster

data check-out, even if were not desired at present to put the aircraft

simulation on the IBM 360. Also, hard copy graphical documentation of the

tables that are being used for simulation are obtained. If, at a later date,

the program for an aircraft simulation is to be transferred to the 360, further

benefit is derived from using the simple data card format for the pre-processor.

-25-

THE.. INTERPOLATION SUBROUTINES

The interpolation subroutines are used to interpolate 1, 2 and 3 dimensional

tables. Interpolation efficiency is increased by a search'subroutine (SEARCH)

which takes advantage of the cross-reference list NBPL, see Figure 5(a).

At the beginning of each programming cycle the master lists are searched by

the subroutine SEARCH. This subroutine determines the subscript of the master

list breakpoint if the nearest value is lower than the argument and calculates

the proportionality constants PFAC for all breakpoint lists which are needed

to interpolate the functions.

PFA = Ar.urrent - brea_-lo, t rPFAC.Nleares t burl_ IrhLerest lowern

L~~reak-po; L #., Lta k-in

First, however, the limits of the master lists are checked against the actual

value of each argument. The argument is reset to the nearest limit when it

is outside the limits and PFAC is set to zero. In this case a message is

printed out indicating the facts.

The acutal interpolation of the tables is accomplished by three function

subporgrams. FOUTID interpolates one dimensional tables; FOUT2D interpolates

two dimensional table; and FOUT3D interpolates three dimensional tables.

The three subprograms and interpolation equations are structurally similar.

The one dimensional interpolation equation is:

F- F(Qt neArest .- ro1 + PFAC Fjat hear.t kor) - F('at ne-rest )ve) ]brea.pv^t / L brea kapo;- btre a' r@Fvt .nt

For the purpose of storage efficiency the subrpograms are not written in complete

generality. The dimensions in the DIMENSION statements must be changed to

match, the array sizes required for a specific aircraft simulation. Since the

breakpoint lists of some tablesdo not cover the complete range of the master

lists, each interpolation subprogram must check if the corresponding arguments

, ~-26-

are within their limit. This is accomplished very quickly with the

aid of the cross reference list NBPL, as explained in appendix VIII

Auguments outside the breakpoint list limit are reset to the appropriate limit forthat table.For increased computational efficiency by a factor of four, the two'

and three dimensional table interpolation subprograms were written

in one dimensional array lookup form. Listings of the search and

interpolation subprograms are given in appendix IV. These sub-

programs must be recompiled for each aircraft simulation to have the

proper DIMENSION 'statements. Source programs may be obtained from

the authors. Also, the READ cards from the pre-processor program have

to be incorporated into the simulation to read in the tables. In

appendix VIII an example is given of the programming required.

-27-

CONCLUSIONS AND COMMENTSi

A unified approach has been presented to table processing, checkout

and table interpolation for aircraft simulation. Complete program

listings are included in this report for documentation and to permit

changes and additions by the user. The programs were specifically

written with Ames computers and computer operation in mind, but portions

of the programs could easily be adapted to other users' needs.

Listings of the programs used in this table processing package are given

in Appendices I through IV. Detailed information for their use on

the TSS system is given in appendices V through VIII. For further

information on the control cards, users are referred to "A Guide

to TSS/360 Batch Job Processing" and other TSS manuals available

from the Computational Division library. ,

The computer programs comprising this table processing package have

been compiled and stored in the authors' job library. This job lib-

rary has been set up to be shared by all TSS users. Information

on accessing it is given in Appendix V.

-28-

APPENDIX I

PRE-PROCESSOR PROGRAM LISTINGS

This appendix contains listings of the computer programs used to

process and store the aero tables. The programs (main and sub-

routines) are in the following order:

1. TREAD (main program)

2. TABCOM

3. TABIN

4. TABOUT

5. NBLIST

6. MLIST

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APPENDIX II

PLOTTING PROGRAM LISTINGS

Data verification by plotting

using the following programs:

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

with the S-C 4020 plotter is done

Main

PLOT1D

PLOT23

SCLIM

FLIP2

FLP213

FLP321

FLP132

FLP231

FLP312

The subroutines

Ames package of

PLOT1D and PLOT23 make use of subroutines in the

programs for the S-C 4020 plotter.

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EAI 8400 CONVERSION PROGRAM LISTINGS

The following programs convert the tables to the proper format

for input to the EAI 8400:

1. Main

2. FTOB

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INTERPOLATION PROGRAM LISTINGS

The following programs perform table look-up and interpolation:

1. SEARCH

2. FOUT1D

3. FOUT2D

4. FOUT3D

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- 8 3 -

APPENDIX V

USE OF THE PRE-PROCESSOR

General Information

This appendix provides information to allow users to prepare their

input cards and to process them with the table processing package

described in this working paper. It is written to be a self-contained

users guide. Consequently some of the information is similar to that

given in the main body.

The table processing package has been compiled and stored in a job

library of the authors' TSS/360 library. A PERMIT command has been

issued so that-anyone can access the package ol a read-only basis.

Before the user can access the package, he mus;t issue -a SHARE command

of the form

SHARE DSNAME=MY.TABPROC,USERID=FSMDNWfl,OWNERDS=LIB.TABPROC

where the underscored data set (job library) name is assigned by the

user as desired. This SHARE command needs to be issued only once. It may

be placed after the LOGON card for the first computer. run. The user must

include a DDEF card for his job library (e.g., MY.TABPROC) each time he

makes a computer run using any part of the shared package.

USE OF THE PRE-PROCESSOR

The pre-processor set of routines is used to read in aerodynamic coefficient

tables, process and store them, and generate auxiliary arrays for use in

other parts of the table processing package.

The first step in the process is to have the tables punched into

IBM cards in the formats shown in figure V-1. This general format is

similar to one commonly used when manually tabulating aero data from

graphs. The card data fields are 8 columns wide, although such

exceptions as table dimensions on the header cards should be noted.

The table entries themselves are in floating point format and, for

ease of card punching, are left justified. Note that everything is

left justified in the fields except the integer values, which must

be right justified. Floating point values must have a decimal point.

The table header cards (cards (3), (7), (20) of figureM (a) are

set up as follows. The first field of 8 characters is a user's

comment area. If desired for future reference, table numbers may be

put here. For cataloginrpurposes, the Pre-processor assigns table

numbers sequentially as the tables are read in. User's labeling of

table numbers should follow this convention. The next fields contain

the table name, up to 3 argument names as needed, and the break-point

list lengths in the following order:

Field Columns Contents

9-16 Table Name17-24 Horizontal break-point list name25-32 7 Vertical break-point list name33-40 Third break-poin*list name for 3rd tables41-44 Length of horizontal break-point list45-48 Length of vertical break-point list49-52 Length of third break-point list

Names are alphanumeric and are left justified. Lengths are integerand are rqight justified. Table names should be different from thefunction names they represent; for instance,CLT instead of CL. Break-point list names may be the same as the related variable names.

8e-

I 1C ALPHA 1 3 1_~~~~~ .IO.5.

-. 20. 6

10. .8

CLDA ALPHA DA MlACH 3 4 2

-. 5. 10.-10. . 1 1ol .1O. .3 .2 .115. .501 .302 .4

.8

.9 --M

. 4 .598

I Dtable

3 Dtable

;--. o. - 5. 10.-10. .05 .048 .05.0 .14 6 .1 .0981 5. .46 .15 .220. . 39 .20 . 31

L Jl lN O1DA ALPHA _ 3 3 1 3_1

YO.6.1 0

-9.0.000 12.2.4

8I9

10..2001.6!.0

17

18..41.81.2

25 e1 9Sal

2Dtaije

FIGURE V-l(a). Card formats with a sample set of input data.Blank cards were inserted for clarity only.

-86-

Car

(I

(2)

(3)

(5)(6)

(7)

(9)Cia)(I 0o)

(,9)I 02)

O t.) .

(16)(')(I 8)

(I 5,)

(2c)

(2.)

(z .)

Colu_.a I

20.

57 ,.~~@ 80

I

i 1

.i

I i

61

62

a1 a2 a3 a4 a5 a6 a7

10 11 12 13

F2,10F2,11F2,12F2,13

FIGURE V-l(i). Extended Format.

a 8 a 9

F,1 1,2 F1,3 F1,4 F1 ,5 F1 ,6 F1 ,7 F1 ,8 F1 ,9

1,10 Fl,llFl,12Fl,13

F2,1 2,2 F2,3 F2,4 F2,5 F2,6 2,7 2,8 2,9

If the 1st breakpoint list has more than 9 members this format applies.

The table entries are punched left justified into 8 column fields as

in figure1l(a). One dimensional tables are punched so that the first"

field contains the break-point (argument) value and the second field

contains the corresponding function value, cards (4), (5), and (6).

On 2 dimensional tables, the first card contains the horizontal break-

point list starting in the second field, (21). Following cards have

a vertical break-point value in the first field and corresponding

function values across the card, (22), (23), (2.). If a table has

more than 9 horizontal break-point values and related function values,

then overflow cards are made as in figureY:(b). Three dimensional

tables are made up similar to 2 dimensional ones except that each

2 dimensional group is preceded by a card with the corresponding third

break-point value in second field, cards (8) and (14) or figureVl(a).

The format in figurers must be strictly adhered to. Only a few

checks are written into the program itself. Errors in column dis-

placement are avoided for the floating point number entries by using -

a program control card (program 1) for the 029 card punch as shown

in figureV2 and by visually checking off-line listings of the data

cards. For the table ID cards, one switches to program 2 of the pro-

gram card. Program 2 is punched in such a manner that it is correct

for 2 digit integers and for the alpha-numeric information for a three

dimensional table. Hence, one must insert a leading blank or 0 for

one digit integers and skip once or twice on tables with smaller

dimensions. As a further restriction the horizontal break-point

I . - .

5CCCCC&D7GGGGGGG7GGGG5GGGGGGIGGJ7GGGGGGu7G&DEC&D5C&DECCC3CCCCCCC3CCCCCCC3CCCCCCC

1 2 3 4 5 G 7 8 9 1011 12131415IS17 la 19 20 2122 23 24 2 27 23 29 30 312 33 24 29 29 37 3 39 43 4142 47 44 4, 4, 47 4 $ 49 N 52 53 54 79 56 57 60 Cl 62 63 64 65 96 67 68 69 70 71 72 73 ; 75 7E 77 78 79 t

*22:-22222222 22222 22222222222222222222222222222222222222222222222222 22222222222222

333333333333333333333333333333333333333333333333333333333333333333333S3333333333

4i 411:L.4 :'::.'4 4 4 4 4 4 4 4 4 4 .4 .i

-- :-[!: ss555555 ssss55sssss5sssssss555ss55ss55555555555ssss 55 . . .' . '. ; 1 !li'

6 666666666666666666 666666666666666666666666666666666666666666666666 666666666

77777777 7 . . . . . . . 7 777777777777777777777777777777777777

888 88 8 888 888 8 8888888888888 e8 888888Pi838888Es8$CC88888 88888d88888e sa868a 1

9 9 999 9 999999999 9 9 9 9 99999 59 9 9 9 9 9 9 9 9 9 9 999999999 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 9 99999 .9 9 9 9 9 9 9 9991 2 3 4 5 6 7 8 9 10 11 12 13 1415 16 17 i 197 213 21 2. 2' 25 26 27 28 29 27 32334 3 37 33 4341 4243 4534 , 47 443 *3 751 2 r3 54 5 56 57 3 U 6) 61 CZ 3 S4 E5 67 G67 8 6 3 1 1 72 /34i 7 7G71 70 79 so

508 BSSC

FIGURE ¥-2..029 Program Control Card

Figure V-1(a) (;lists must increase from left to right A(9 ), (15), (21); the vertical

break-point lists must increase downward; and the break-point list

elements for the third variable of a three dimensional table must in-

crease in the order of appearance (8), (14).

After the data cards are punched, one or more computer runs are

made for initial checking of the tables. FigureY-3 shows a sample

deck of TSS/360 control cards for the computer run.

! :

(I) LOGON U.SZ±JalJf 99 JO.HN DOE STOP 99 PH ,3999(-) DDEF DDNAME=TABIIB,DSORG=VP,DSNAME=MY.TABPROC,OPTION=JOBLIR(3) LOADTRE AD$$ $--(+) DDEF DDNAME=FTO2FOOl,DSORG=VS,DSNAME'-TABLES(S5) DDEF DDNAME=FTO7FOO1,DSORG=VS,DSNAME=DIMREAD(6) CALL TREAD$$

&INPUT(7) IPUNCH=1,

' 'l _ IPU.NC H=C H _O__&END

(8s) *, TABLE DATA CARDS GO HERE

} ~~**"- *at******

) %END(O) LOGOFF

Figure-V-3. TSS/360 control cards for computerrun using the Pre-processor

Unerlined words should be changed to conform to the user's naming

conventions. Card (1) is the standard users LOGON, card. Cardy

(2) defines the user's job library which contains the table processing

package. The data set name (DSNAME) should be identical to that -

specified by the user in the SHARE command. The data set name in

-9o-

card (4) specifies where the processed tables and related data are

to be stored. Card (5) names the data set where the DIMENSION andto be

READ card images areAstored. The second of the NAMELIST "INPUT"

cards (7) determines whether the tables and the DIMENSION and

READ card images are to be stored (IPUNCH=l) or not stored

(IPUNCH=O). The user's table data cards go at (8). The %END

at card (9) must be present to signal the end of the data cards.

It is suggested that off-line listings of the data cards be examined

for such things as blank cards, duplicate or missing cards, and the

use of wrong columns. Further, it is suggested that the user make

computer runs with IPUNCH=O to conserve computer time until all of

his tables and the auxiliary arrays are printed out correctly. Some

errors which may cause premature run termination include missing

cards in a table and incorrect dimensions on a table header card.

After all tables have been printed out, they should be examined

carefully for errors. Error message printouts should be noted and

their causes remedied. Causes of errors can be determined by examination

of the printout and the data cards.

After all apparent errors are corrected, another computer run should

be made with IPUNCH=l to store the tables and the DIMENSION and

READ card images in their respective data sets. The DIMENSION andTSS

READ cards can be punched using the,\command

PUNCH DSNAME=DIMREAD,STARTNO=l,ENDNO=80

where the data set name is the same as specified on the DDEF card (5)

*1l-

of figure V-3. A printed listing of the DIMENSION and READ statements may

be obtained by using the TSS command

PRINT DSNAME = DIMREAD, PRTSP = 1,

STATION = RMT02,!

where RMT02 is for RJE station 2. These commands can be put before the

LOGOFF card (10), run as a separate batch job, or entered conversationally

from a terminal. The DIMENSION and READ cards should have interpreted and

separated according to type for use in the plotting main program. They are

numbered to aid in keeping the READ cards in order.

-92--

APPENDIX VI

USE OF THE PLOTTING PROGRAM

The plotting program is written to provide hardcopy plots of 1,2, or

3 dimensional -tables on the S-C 4020 plotter. All necessary sub-

routines are shared in the TSS job library described in Appendix V.

The main program, however, is data dependent and must be changed by

the user to include DIMENSION and READ cards for his stored tables.

A copy of the main program may be obtained from the anthors. The

required DIMENSION and READ cards are obtained during use of the

pre-processor as described in Appendix V. Comment cards in the main

program indicate where these cards are to be placed. The main program

may be compiled separately or during the plot job.

The plotting program provides the user with several options for

plotting the tables. The options and data cards to specify them are

described with reference to figure VI-1. Card (1) transmits information

to identify the plot job and to specify the user's tape number. Columns

1 to 66 are printed on the first and last frame of the plot job.

Columns 69 to 72 are printed on the upper right hand corner of each

plot frame. The user must have a 7 track magnetic tape assigned to

him for this purpose. The plot option cards, (2) through (6), specify

the table to be plotted, whether the variable order for 2 or 3 dimensional

tables to be plotted differs from the order in storage and, if so, what

order is desired. The other option specifies special scaling limits desired.

Special plot instructions can be largely eliminated by following certain

corrections for the table construction as explained in the section

3-7

users v ae, Wm'/ stOr .... .. ,/ ' , ?... ..

JOHN DOE STOP 99 PH 3999

(A) Plot iJ'e ' " :ca ;to ca

I o RZ N£

( )¢Io ~ No.

i1

V ,arlea arder\ar. I Var 2

I JkjD

for rOTF IO(

PLOT JOB

h ; [1 C a tpu h b Plot tapID peeI l o/

T99 a 99 (E1LT999 X/<9 9 999991

hr~ ~ e. . I.~ . I . . ..

a-rd~ (mvaut be dis a ta card).'

opt.rtI3)

•,V~3

Funct ;r VI L-. I 'In

m I max.e, "" cat'rs Var. IM I fl .M;n

SCa, iI .aX

0 2I 2 A MACH A LPHA 3 L,

O01 3 .. .__ ,_, - nz o. _-_-i1

(-b) TaBLe ptot o rlo cardsO

FIGIJREV-1. 7 EXAMPLE OF USER SUPPLIED INFORM.ATION FOR TABLE PLOTTING

-94 -

"Considerations for the Preparation of Tables".

A logical variable called IORDER can be set to either -1, 0, or +1

(column 8). If IORDER is equal to -1, all of the tables are plotted

in the order in which they have been stored on the disc by the table

pre-processor, see figure VI-2. In this case variable 1 is on the

abscissasvariable 2 is always plotted as the fixed parameter for a

given curve, and variable 3 is always plotted as fixed parameter for

each set of curves for 3-dimensional tables. The scaling is automatic.

If only a few tables are to be plotted from all the tables that are

stored, IORDER may be set equal to O. In this case more specifications

must be given. The second number (right justified column 16) will be

the table number. As an optional feature, the next two numbers define

the maximum and/or minimum value of the function to be plotted on the

ordinate (columns 41 and 49) and the last two values designate the

minimum and maximum of the first argument _ that is plotted as the

abscissa (columns 57 and 65). Omission of these values results in

automatic scaling of the data points as stored-. No scaling, of course,

is needed on the second and third arguments. As mentioned before, the

arguments may not have been stored in the order as one wants to plot

them out. In this case the logical variable IORDER is set equal to 1.

In addition to the information that is needed when IORDER equals 0,

one also must read in the order of the variables to be plotted by giving

the names of the 2 or 3 variables in the proper order (columns 17,25, and

33 as_on__card4)).

3 rad BPL.

r

UCIL14

Ho-', SPL

(a) Graphical data

3rd BPL II

\~~ .'\ Hor; z L

-j

0 Fv nc t sic to,D~~~~~~~~~~~~~~

_S..

.:

U

-0I

Horie DPL

L3r- BPL.J

_' Hor, BPL

_JQ _ t

L. Func t ion 2.i.

(b) Tabulated data

FIGURE VI-2. RELATIONSHIPS BETWEEN BREAKPOINT LISTS AND STANDARD

PLOTTING CONVENTION

[3 ,- rJ, I

The TSS control cards required for the plotting computer run are shownin figure VI-3.

(I)'. LOGON USER ID,JOB ,99(7) JOHN DO STOP 92 PH 3999ERASE SOURCE.MHYPLOT$$, FTN MYPLO'F$SISD=N

********* !*n**********t **n*

.. * ,.

(2) .SUPdLIED MAIN PROGRAM WITH USER'S DIMENSION AND READ CARDS INSERTEDGOES HERE FOR COMPILATION

* * ar ,--,- ,*- *. *r *Y *-*** ,-, ,--r-* ,-, * *r. R,-v .r ,. * ** *a

(3) DDEF DDNAME=TABLIPBDSORG=VP,DSNAME=MY.TABPROCOPTION=JOBLIB() AMES SC4020

(") lOAD-'MYPLOT$$(6) DDEF DDNAME=FTO2FOO1,DSORG=VSDSNAME=TABLES? i MTMSG

(7) P'LEASE OBTAIN-99999'---7-TRA-CK W-I-TH -- R-I-N'G- '(8) CALL MYPLOT$s

~-~----~--- * * * ,,,ie * * ** ~* ***

(9) ' * . PLOT OPTION CARDS GO HEREI * t** _ _ .-

(I0) %END(Ii) LOGOFF

Figure VI-3. Control Cards for Plotting Job.

Underlined parts of the cards are to be changed by the user as necessary.

An estimate of time required, for the LOGON card, can make based on the

authors' experience in plotting the number-of tables below during

1 job run.

No. of Tables Time (sec)

3 1532 132

Use of the plotting options affects the time used, so it is suggested

that 10 - 30% additional time be specified to avoid premature termination

of the job. Portions of a job cannot be saved if the tape writhing job is

terminated due to underestimation of time. The plotting main program,

with the user's DIMENSION and READ cards from the pre-processor, are

put at (2) with the FTN card for.compilation. The DDEF card (3) specifies

the user's job library which contains the shared program modules. Card (4)

provides access to the Ames library of plotting routines. The LOAD card (5)

-q 7-

must specify the main program named at (2). The user's stored tables

to be plotted are specified by card (6). Card (7) specifies the user's

7-track magnetic tape. Card (8) starts writing the plotting tape.

The plot identification card and plot option cards described previously

go at (9). Card (10) signals the end of the data cards. The printer

listing received after the job run will specify which tables were

plotted and the number of plot frames made.

The plot run described above generates plotting data on the user's

magnetic tape. To get hardcopy plots made, the user must send a card,

as in figure VI-4, to the operations room, N233. The card is self-

explanatory. 0ff-line production of the plots from magnetic tape

takes approximately 24 hours.

SC-4020 PLOTTER /AAMD C/MP STOP

TEL. . 99 MAIL STOP ___;~~-- -- _______ _,,,,,_,,_

H.C. FRAME ON H,.C. FRAME OFF TIME ON-__ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ - - - - - - - - - - - - - - - -

MICRO FRAME ON MICRO FRAME OFF

TAPE NO.IC.P./J.O. 1iOn. OFINn. OFITYPE OF COPVIYXD1OI ICOPIESIFRAMESIHARDI MICRO IMC OEITIME-FF…I …I------ I--- I .... I

I I------ - - -e -_L - -e__! - ..-... I-TIME-ON

I I t I 1 - - - - I…I …I … I… .-I t ..I…. t 1..

H.C. FRAME ON H.C. FRAME OFF----------- ----------- TiME OFF

MICRO FRAME ON MICRO FRAME OFF

Figure VI-4. Request for SC 4020 Plots.

-98-

APPENDIX VII

USE OF THE EAI 8400 DATA CONVERSION PROGRAM

This appendix describes the use of the programs which convert the tables

stored on disc by the Pre-processor to a punched card format which

can be read directly by the EAI 8400 computer. Only a small amount

of manual work, as described, is necessary on the punched cards.

The main program is data dependent and must be recompiled by the user.

A card deck copy of it may be obtained from the authors. A set of the

DIMENSION and READ cards produced by the Pre-processor is inserted

in the main program at the place denoted by comment cards. The main

program may then be compiled alone or as part of the computer run

to punch "8400" cards.

(1) -'LOGON L.SERIDJO_, 99' JOHN DOE L_--S'T-OP 9__- P-H - -9(2) ERASE SOURCE.MYP84$55 FTN MYP84$SIISD=N

;.~. 4.-· -..4.4 .4.,. .... 4. 4 -..'. . ..,. - ,.4.~ . 4.., 4. 4.o,

(3) * SUPPLIED MAIN PROGRAM WITH USER'S DIMENSION AND READ CARDS INSERTEDGOES HERE FOR COMPILATION

4r 4.** * ** * ** 4* ** **

) DDEF DDNAME=TABLIB,DSORG=VP,DSNAME=?MY.TABPROC,OPTION=JOBLIB(5) LOAD MYP84.$ -' ( D) DEF DDNAMiE=FTO2FOO1,DSORG=VS,DSNAME=TABLES

(7) DDEF DDNAME=FT07FOO1,DSORG=VS,DSNAlME=.CRD84..8) CALL -'MYP84 $$-_---

t9) PUNCH DSNAME=CRD84,STARTNO=1,ENDNO=80(to) LOGOFF

Figure VII--. Control- cards for punching data cards for EAI 8400.

_ ~/q-

The TSS control cards used compile the main program and to execute it

are shown in Figure VII-1. Underlined parts are to be changed by the

user as necessary. Card (1) is the user's LOGON card. Card (2)

is for compilation of the main program which is placed at (3). Its

module name may be chosen by the user and used on cards (2), (5), and

(8). The DDEF card (4) specifies the user's job library which contains

the shared program modules. Card (6) specifies the user's tables

which were stored by the Pre-processor. Card (7) specifies the

dataset where card images of the converted tables aretobe stored. These

cards are punched by card (9), which may be used here, run separately,

or entered from the conversational terminal.

The printed output from the computer run gives card image printouts

which should be examined by the user. All breakpoint and table

values punched out will be between 0.0001 and 9999.9. If a table entry

should be outside this range, the number will be replaced by a series

of slashes (////), which can be easily recognized and can be replaced

by the proper number. Further information about changing the punched

cards to obtain a running deck for the 8400 program is given in the

main body of the report.

-/00-

APPENDIX VIII

THE APPLICATION OF THE TABLE LOOKUP PROGRAMS

The use of the table lookup programs is illustrated by means of an

example. The tables to be interpolated are those saved and plotted

previously. The sample program is shown in figure VIII-1. First, the

DIMENSION and READ cards from the table pre-processor must be inserted

in the simulation program to make the tables and auxiliary arrays

available to the simulation program (cards 500 to 3800, not shown

on the figure). In addition, the common blocks "ARGS" and "CATLOG"

must be put into the user's simulation program. Before calling

the SEARCH routine, the table arguments must be placed in the proper

order into the array ARG (cards 4400 to 4600). SEARCH resets the value

of any member of the array ARG to the closest tabulated limit if

the argument was outside the tabulated range of the master list. A

statement is then printed to this effect. Figure VIII-2 lines 9 and

10 are examples of this output. The lower limit for APLHA in the tables

was 0. and the upper limrlit for MACH was 0.9. Note that SEARCH does

not reset the actural arguments ALPHA, MACH and DA as shown in line

12 of figure VIII-2. Other computations in the simulation program

would therefore be based on the actual values of the arguments. This

non-reset of actual arguments feature of the simulation can be traded

for a small amount of increased computational efficiency by putting

the actual argument list in the labelled common block ARGS in the proper

order; COMMON/ARGS/ALPHA, DA, MACH

-toI-

'. 'I i

_., -. C-

X..i 9 ' C 001i

4000/7. i fl --

4200430 04i 3 i) (i.

4500I-, f, 0

RP:-A L 'AC H .Cf- '-F!-r}J, /A F-',S/ ?,P (3)

tCti.~'S~ ,'It f i¢l T:-...ll i RI/:F CAr D.RS .C, C; ltRF-.-0~ ijC FsSl.p R0.:?,A :G SX~~~~~ -

10-0FL T 7 -E9=0 -- PHADA,,'. - C .. .:.X

1 00 R E A) (5 I E1r- O)= 5 00) A L P H. i, A C H] i ,.i i- !) '! I i .i- ) F _ ,

C PUT C\ RGUiO E'F-ITS I ,iT ' CIO !H ', i 0 IN! tAP. F-\Y Il! TH-E S/:4, t. F)E ,, Fi.'TE-.F- 'IT ,Cr THE !ATA, ST'?li'\.-e PROQQRAji '

.:\PG(2) = )AA, D C ' -i ) = ;,I A' ,-,

-Y0-L~o 0~.E 7K~PT7-'-I-i) ~ C, --f--T j' i ) 4-17It- ,Sti 'T-= -Tr tR % 1 1 I cr I FF T 7(TT Wi ; 1 ! : L I -4800 CALL SEARC H4900 C II--FEP.POL/;TE- THE TA!3LES

5100 CicA = F7UTO)(Ci r! ))

5200 CL = U FT 3T( CLr)3A 2)-, 33-3TO C-.....r-T-fZ[ D(C.E-vi;, )r540n C P OI;'T fU.T THt RES!!LTS:550f0 ?!i TE (6 2) ALPHA, Ai4, FACH- , C;-iACLIDCOR5f-n-'F--Tl. P " ! -, -- -'%F i, o T = '6 L A o e / 57 105800

5 6000 -60~ 0 !: i0

cI.' = It 6 ,FAo3,/"(CL r = ' ,F6.o39/ OU) = I , 0 I,)CO TO 100

- !) - -1"1l/ -

E ,'..~ 1

Figure VIII-1. Sample interpolation program.

A1L:i.PHA = L, !0O I) = 0 . 1ion iAACH = 0. 510

(,,'4 at = !) AC-Tr

Cl_) = 0 .96

C-= 0 347

7tX1 , _ . ' e'-T-' 0 ... ()A - 4. (O T---H = t). 700

Cr; 0 = .12(0

CLi) = 0 .243

C'TR' = I. o e'Z-zF9-"!.PHA, =' -!io)0000C0 UiUTSI OE THE;','CH. = 1. ,0nn000 OUTSIT)E THE

T'" r.~ . ...... _' .'_' _T< T ~qy i-7,

LowER SUBLIS'r LIMT!1 Pi,',. = -_],OQ|) O< !00 = --9.500'

r-:i& = -0,o 2-00

C' i -t''' '"~''- .....('' ~'jl-- T-- -- ---"- __

'iASTFR LIST LI`ITS,RFST Tr-i lT T', ASTER ·LIST IlI,,TS,~S-. FT Ti' I TI:,T

= --~ .o:-..~ OfSo'P t1 5 A'.I( r-MI 7l i'T- S!-: P TI'

i<'ACH = 1000

(;'. R = .Q q )

Figure VIII-2, Outputs from the sample interpolation program._-/g9 _--

!

The function values are obtained when needed by function calls as shown

on cards 5100 to 5300 in figure VIII-1. -Lines 1 to 8 on the next

figure show the argument values and results from the table lookup

when all arguments are within the proper limits. If an argument is

outside the proper limits of a specific table and withinthe range of

the master list, a call to an FOUTxD function will result in an output

as shown on line ll,,figure VIII-2 and the function value will be set

to the proper subist limit as indicated on line 14.

The structure of the NBPL list makes the above check very efficient.

The appropriate NBPL element is tested with an algebraic IF statement.

When the NBPL element, which normally determines the subscript for the

breakpoint list, is negative, the argument is below the range of the

breakpoint list for the given table. When the NBPL is '0' the argument

is above the range of the breakpoint list. In either case the follow-

ing information is printed out: the number and namfe of the table

and the name ond the value of the argument which exceeds the limits

of the breakpoint list.

In some cases, it may be desirable to suppress the above error messages.

To do this one can add a two value dummy table, which will not be used

in the actual program, but which serves to establish a breakpoint

list for the parameter in question that spans the whole range of the

parameter. ]An example/might-be the parameter 'altitude' for ground

effect calculations. A second method to remedy the situation which

is not quite as efficient, is to use logic statements in the running

-/o3-

program to permit ARC(J) for the given parameter to take on values

only within the specified limits.

The table lookup routines are data dependent and must therefore

be recompiled by the user after insertion of the proper DIMENSION

statements. Card deck copies of these subprograms-SEARCH, FOUTID,

FOUT2D, FOUT3D-may be obtained from the authors.

All 4 of these subprograms have identical COMMON blocks and DIMENSION

statements, as shown in figure VIII-3. Most of the DIMENSION statements

are provided by thile pre-processor as described in appendix V. The

sizes of the arrays ARG, LSUB, and PFAC are dependent on the sizes

of VARNM and BPL as shown by the arrows in figure VIII-3. The

values of the array LSUB must be initialized to 1 at load-time.

This may be done in a BLOCK DATA subprogram as in figure VIII-4

or by a DO loop in the user's initialization program.

I

400 ICfiAII lj / I -[J L F ' /',LL -&C .SL S)JCf0 f. /CATLOOT'IC{:,.LI TITO, ;,,i' T i VF [..',Vi... T' ,: . T\P, P NST .'A .-t Ar.iST NJp, .,iK

---~T?') ~.i,-.-i ixti / a P,('S'-] t(:,

8O00 C SIZE (7)- .ARR<AYS ARFE PR.GRlAi l-.DFPEi[,FlI'T-9OI- C-T-A'T T Ii',lEm I ' s"-' nT-.!' ---'P iE - P't7< uL .' ' il, . I PH

1000 REAL:.;8 V/AI;,i i( 03 )t1100 0 hIi,' FiSI in",.L PPL M, 2 I )l200 R¥L'--8Ti 'hiI-( /3)

* ~1300F I i:F S' I -i' ! Jl'.i 3) _l4f)() OtI~,f--_'iS fC!.s F, \BL ( 3, 7, 2) "

1500 I)Ii'.,I- 'j' ] ,"!%'! T (Po ' 3 ) .1(600 DI iF"'!SiI :'S! ,/!, ST( 7,- 3)17 00 I t," F i\! S I li\ i\l ( 3, 3 )

71, i(IT) /\)lI lEN SI O lN 3S 3) I21900 nIlMFI ! I 0SiN i'iLR ( 3) 2200 () C l) 1 !'v T E T - E NI - F ! t H F\!l ) F I T … …12 ()Y'O C t)1I~E!",!SIF'1'' STiA'Et.~j_ '"-~~ '-,. . ''~--IR)' EW~uSAfll/,!)F'lT'! .2i0) I')I,':t-EIX'SIfx! AR,((;(.~),L.SIJ! .'....I---;!,' I f:

2 0 0. C, ... ..._... .,,,.,.. ,, .. ...,,,,,,, . . ,,,,,,,,,,,,,,,,, , ,,,,,,,,,,;

Figure VIII-3.

] 00200

- OT-400500

COMMON and DIMENSION statements used in table lookup

subprograms SEARCH, FOUT1D, FOUT2D, FOUT3D.

Rl OCK D)ATAC. ":r-iN / I;I -PL / PFAC, L StJB'T':T Exrs 7-- L-...-TT ' :-TTFC-,.'T-1TC, ETKF-TTT0 PTh.3TTM3D A TA L S II B/ 3-: 1. /F i\! I')

Figure VIII-4. Initialization of LSUB array.

nasa technical memorandum technical memorandum ... appendix vii -use of the eai 8400 data conversion...

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