1620_Users_Group_Western_Region_Minutes_of_the_Meeting_196312 1620 Users Group Western Region Minutes Of The Meeting 196312

1620_Users_Group_Western_Region_Minutes_of_the_Meeting_196312 1620_Users_Group_Western_Region_Minutes_of_the_Meeting_196312

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1620 USERS GROUP

WESTERN REGION
MINUTES OF THE MEETING
DECEMBER 11-13, 1963
TEMPE, ARIZONA

ROBERT R. WHITE
WESTERN REGION SECRETARY

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CONTENTS
1.

Letter from Robert A. Ebert to 1620 Users Group

2.

Roster of Attendees

3.

Minutes of the Seventh Meeting of the Western Region 1620
Users Group

4.

Agenda and Abstracts

5.

The Impact of Automation on the Professional Engineer;
Melford E. Monsees

6.

Expotential and Sinusoidal Curve Fitting; E. P. Hilar

7.

Automated Design Engineering; W. W. Rogers

8.

A Payroll and Labor Distribution Program Package; Elias C. Tonias

9.

The lISPIREII System; Gary J. Reed

10.

A 1620 Program for Minimization of Boolean FUnctions, Expressed
as Sums of Minterms; Thomas R. Hoffman

11.

Critical Speed, Stress, and Bearing Reaction Calculations
for a General Shaft, Using Numerical Integration; Ralph B. Bates

12.

Three Dimensional Surface Fit; David G. Kitzinger

13.

Maximum Likelihood Resolution of
tion; Reimut Wette, D.Sc.

14.

Comparison of Two Methods of Finding Significant Contributors
in Multiple Regression; M. J. Garber

15.

Network Analysis; H. N. TYson, Jr.

16.

An Integrated Earth-work System; Cecil L. Ashley

~~o

Mixed Normal Distribu-

17. Hydro System Daily Operation Analysis; C. R. Hebble

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'''WLWN IMiL

1620

PRESIDENT

SECRETARY-TREASURER

us ERS

J. L. DAVIDSON

.(lJ Long
Island Lighting Co.
175 Old Country Road

MARLENE T. METZNER
Pratt & Whitney Aircraft Co.
Fla. Research & Dev. Center
West Palm Beach, Florida

GROUP~

Hicksville, New York

WESTERN REGION PRESIDENT

MID-WESTERN REGION PRESIDENT

EASTERN REGION PRESIDENT

ROBERT EBERT
Spectrol Electronics Corp.
1704 S. Del Mar Avenue
San Gabriel, California

W. A. BURROWS
Dravo Corporation
Neville Island
Pittsburgh 25, Pennsylvania

J. R. OLIVER
Univ. of Southwestern La.
Box 133, USL Station
laFayette, Louisiana

CANADIAN REGION PRESIDENT

EUROPEAN REGION PRESIDENT

D. A. JARDINE
Dupont of Canada
Research Center
Kingston, Ontario

H. TOMPA
European Research Associates
95 Rue Gatti De Gamond
Bruxelles 18, Belgium

December 26, 1963

To the Members of the 1620 Users Group:
It is with sincere regret that I must announce my resignation, effective during
this meeting, as President of the Western Region. The executive council of
the group, acting in accord with the by-laws, has appointed Paul Bickford to
serve the remainder of the current termo
Paul's. appointment was made upon my recommendation, and I feel that his
experience with the group will make him eminently qualified to continue its
growth and activity.
In turning the administration of the Western Region over to Paul, I can only
say that I shall sincerely miss working with all of you, I express my thanks
and appreciation to those of you, too numerous to mention individually, who
have worked to make the meetings which I have conducted successful, and I
extend my best wishes to the officers and members of the 1620 Users Group
for the continued growth and success which you have enjoyed over the last
frour years o
Sincerely,
~

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'Rob'ert A,. Ebert

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1620 USERS GROUP MEETING

TEMPE, ARIZONA
DECEMBER 11-12,13. 1963
ROSTER OF ATTENDEES
USERS
GROUP NO.
1118

1118

INSTALLATION
REPRESENTATIVE
NANCY PAQUIN
U.S. PUBLIC HEALTH SERVICE
ROCKVILLE, MARYLAND
G. ROBERT ORNDORFF

U.S. PUBLIC HEALTH SERVICE
ROCKVILLE, MARYLAND
1216

CARLIS TAYLOR
A F R R I
BETHESDA, MARYLAND

1302

T. R. HOFFMAN
UNION COLLEGE

SCHENECTADY. N. V.
1334

DR. REIMUT WETTE
M.,O. ANDERSON HOSPITAL. AND TUMOR INST.

HOUSTON, TEXAS
1346

ELIAS C. TONIAS
ERDMAN AND ANTHONY - CONS. ENGRS.
ROCHESTER, NEW YORK

3082

PAUL BICKFORD
OKLAHOMA UNIV. NED. RESEARCH COMP. CTR.
OKLAHOMA CITY. OKLA,.

3082

CARA

MITCHELL

OKLAHOMA UNIV. MEO. RESEARCH CQIIP,. CTR..
OKLAHOMA CITY, OKLA.
3166

OR. HERMAN 8. WEISSMAN
UN1VERS I TV OF I L.L lNO I S
CHICAGO, ILLINOIS

3175

HELEN LtGON
BAYLOR UNIVERSITY

WACO. TEXAS
3182

'3240

ROBERT C;. LANGE
AUTOMATIC ELECTRIC LABORATORJ'£'S. ' INC.
NORTHLAKE, ILLINOIS
MELFORD E. MONSEES

U.S. ARMY ENGR. DISTRICT
KANSAS C,I TY •

3261

M I SSOUR I

GREGORY ..J. SHANAHAN

CECO STEEL PRODUCTS CORP.
CICERO.

ILLINOIS

. .'
USERS
GROUP NO.

3273

I NSTAU...AT ION
REPRESENTATIVE

R08ERT C. BABIONE
ACIC
ST.

3273

L.OVI,S.

MISSOURI

CHARL.ES WEISS
USAF AERONAUT leAL, CHART AND I NFO CENTER
ST. LOUJ S,. M 1 SSOUR 1

5001

R. C. WENRICK

ACF INOUSTRI'ES. INC.
ALBUQUERQUE. NEW MEX ICO

5001

G. ..J. REED
ACF lNOUSTRlES. INC.
AL.BUQUERQUE. NEW MEX l'CO

R. e. WE'AY'ER
BEAR CREEk MINING co.
SALT LAKE CITY,UTAH

5014

WALTER DAVIS
GENERAL OYNAMI:'CS/ASTRONAUT lC5
SAN D'IEGO. CAL.IFORN IA

5016

RICHARD W. PUGSLEY
COMPUTEAMAT INC
LOS ANGELES. CALIFORNIA

5019

EDGAR M. BLIZZARD
.JET PROPULSJONLAB
PASADENA, CALIFORNI,A

5020

MARI:LYN DOIG
COLORADO STATE UN IVERS I TV
FORT COt.LJ:'N$,. COL:QRADO

5021

..J. W. LAFON

us

ARMY EN'GINEER D:ISTRICT AL.BUQUERQUE
ALBUQUERQUE,. NEW MEX I CO

5027

MARVIN RUBINSTEIN
ELECTRO OPTICAL SYSTEMS. INC.
PASADENA, CAL.IFORNIA

5032

BOB 'MAMtING
GOOD'Y~AR AEROSPACE
LITCHF'-ELO PARK, ARIZONA

5032

N. A. KUFFEL

GOODYEAR AEROSPACE
LITCHFIELD PARK, ARIZONA

5032

oJ. MOSS

GOODYEAR AEROSPACE

LITCfPIELD PARK, ARIZONA
S-

•

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USERS
GROuP MO.
5032

INSTALLATION REPRESENTATIVE
DAVI'D H. o I HERREN
GOODYEAR AEROSPACE CO

L.ITCtFl£LD PAAc: ARIZ
5041

DAVID KEY

MOTOAOLA
PHOENIX. ARIZQNA
5045

w.

5053

ROBERT L.. SHUTT
SACRAMENTO PEAK

WILCOXSON
U.S. NAVAL CIVIL ENGR. LAB.
PORT HUEPEME. CAL IFORNIA

OBSERVATORY
SUNSPOT. NEW MEXICO

5053

FRANK BJ,RI)
SACRAMENTO PEAK OBSERVATORY
SUNSPOT. NEW MEXICO

5057

DAVID G. K1TZINGER
SAND'IACORP
ALBUQUERQUE, NEW MEXICO

5057

EL.IZABETH L.FROST
SAN))A CORP.
ALBUQUERQUE. NEW MEXICO

5058

BOB BABCOCK
SUNDSTRAN) AVIATION DENVER
DENVER. COLORADO

5064

ALLENL. GRAVITT
SIGNAL., OIL AND GAS CO.

LOS ANGELES. CALIFORNIA
5065

ROBERT W. WILLSON
SALT RIVER PROJECT
PHOE,NIX. ARIZONA

5065

EAJEST NICHOLS
SALT RIVER PROJECT
PHCENIX. ARIZONA

5065

MAX A. MAYES
SALT RIVER PRGUECT

PHOENIX. ARIZONA

5078

o

OR. MOAR I S ..J. GARBER
UN I V. OF CAL t;PORN tA AT RIVERSIDE

RIVERSIDE. CALlFORNIA
5078

THOMAS M. LITTLE
UNIVERSITY OF CALIFORNIA AT RivERSIDE

RIVERSIDE. CALIFORNIA
b

USERS

INSTALLATION

GROUP NO.

REPRESENTATIVE

5079

5084

SAMUEL K. PRINGLE
MAGNOLJ'A P'IPE LINE CO.
DAL.LAS,. TEXAS

E. B. LOOP
UNION OIL CO .OP" CALIF

RODEO. CALIFa.tI,A
508S

ROBERT 0. MOFP'l TT

U.S. AMY ENGR. DIVISION. N.P.
PORTLAND. OREGON
5089

DONALD ..I. MART I N
U.S. PUBLIC MEALTH SERVICE
LAS VEGAS. NEVADA

!5089

DAVft) L. BAER
u.s. PUBLIC-MEAL.TH SERVICE
LAS VEGAS,. NEVADA

5095

HARRY D,. RENICK

WEYERHAEUSER CO
TACOMA .WASttINGTON
5096

5096

e,. MOIiiIR I S
BUREAU orr REQ.AMATION
SACRAMEMTO,. CALIFORNIA

BOYD

u.s.

R., SRUCE

8AOW~I"

U.S. BUREAU OF REQ..AMATIQN
SA'CRAMENTO. CALlfrOANIA

5099

BEVERLY DOl,S

WSMR
WHITE SAM>S. NEW NEXt,cO

5'104

5120

~. A. GUI ...
TEXAS COLLEGE OF ARTS +I'NoUSTRI£S
I( I NG;SV ILLE • TEXAS

' WILLI.b' L. REUTER
,SO. DAJ«)TA SCHOOL OF MINES AND TECM_

RAPID CITY. SOUTH DAKOTA
5'125

5133

CHIN MO LEE
UTAH POWER AND LIGHT CO.
SALTLAKE CITY. UTAH

-'OSE RAMIREZ
MASON AND • .NGER -

S fLAS MASON CO..

t HC

o

AMARILLO. TEXAS
51,39

RICHARD A. HARR I S
NORTH TEXAS STATE

UNIVERSITY

DENTON. TEXAS
7
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USERS

c

INSTALLATION
REPRESENTATIVE

GROUP NO.

5144

.JAMES ..J. STANLEY
U S WEATHER BUREAU RFC

SACRAMENTO. CALIFORNIA

5146

a I L.L.

WOLLENiAUPT

GOLDSTONE TRACkI." STATION
BARSTOW. CALIFORNIA

JOE SIBL!:Y
GOLDSTONE TRACKING STATION
BARSTOW. CALlfI'ORNIA
5150

SAM THOMPSON

51'!50

GEORGE A. LARCAOE
HALL I BURTON CO
DUNCAN. OICLAHOMA

5158

HALL IBURTON co·
DUNCAN. OKLAHOMA

A.-6AALAN)
NECHES BUTANE PAODUCTS

PORT NECHES. TEXAS
5165

co'.

CHARLES R. HE88l.E

CORPS OFENGJNEERS
WAU-A WALLA. WASHt·NGTON

5165

cec 1 L. L. ASHLEY
U S ARMY CORPS OF ENG.1ME£R
WALLA WALLA WASH

5179

5181

L. E. MARYEY

fl'OOTHt u... CGLLEGE
LOS AI... TOS H'ILLS. CAL·J'FOANIA

ROBERT R. _ITE
LOS ANGELES DEPT. OF WATER AND POWER
LOS ANGELES. CALIFORNIA

5183

JOSEPH P. SNOW
UNIVERSITY OF WYOMlHG
LARAMIE. WYOMING

5190

WILLIAM G. LANE
CHICO STATE COLLEGE

CHICO, CALIFORNIA
5195

o

5199

S.V·. BURKS,. JR.
PITTSBURGH PLATE GLASS
CORPUS CHRISTI. TEXAS
CHARLES S. WALKER

SCHOOL. OF ENGIN!ERtNG
TEMPE. AR J ZONA

co. -

CHIEM. DIV.

.,
USI!RS

INSTALLATION

GROUP NO.

REPRESENTATIVE

5210

A....L. NIEHUES
PALO ALTO UNI:FI"I!D SCHOOL. DISTRICT

PALO ALTO. CALIFORNIA
!5210

ARt.. I'HE K. ICAPPHAHN

PALO ALTO UNIPIED SCHOOL DISTRICT
PALO ALTO. CALIFORNIA
5211

KEe.tETH ICR lEGE
CAL.IFORNIA STATE .....VTECHN·IC CCLLEGE
POJiIONA t CAL..I;P'ORN IA

5215

AOSE'MARYPETERSEN

UCLA - WESTERN DATA PROCESSING CENTER
LOS ANGELES. CALlFORNIA

7007

A. C. R. NEWBERRY
UHIV£RSITV OF ALBERTA CALGARY

ALBERT A. CANADA
SETH P. EVANS
PHOENI X COLLEGE

PHOENIX. ARIZONA
WARREN BUXTOH

PHOEN I X COL.L.EE
PHOENIX,. ARIZ"A
.JOHN P. MCCALL! STER
U S WEATHER BUREAU

FT. WORTH. TEXAS

IBM

W. H. DUKELOW
IBM
KANSAS C.ITY. MISSOURI

IBM

CHARLES E·. BEARY
IBM - WESTERN REGION OFFICE

L.OS ANGEL.ES. CALliFORNIA
IBM

ROBERT A. EBERT

IBM - WESTERN DATA PROCESSING CENTER
LOS ANGELES. CALIFORNIA
IBM

JAMES E. MCRGAN
IBM - WESTERNRSIOH OFFICE
LOS ANGELES-. CALIFORNIA

IBM

BRUCE

~.

SOCKS

1.814 CORP.
CHICAGO. I t.L INC! S

IBM

ANGELO ARENA

IBM
WHITE PLAINS. N.V.

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USERS
GROUP NO.

l·eM

INSTALLATION
REPRESENT AT I VE

GERALD R _HOGSETT

IBM - WESTERN REGION OFFICE
LOS ANGELES. CALIFORNIA

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WESTERN REGION 1620 USERS GROUP
MINUTES OF THE SEVENTH MEETING

The group assembled on the campus of Arizona State
University in Tempe, Arizona, December 11, 12, and 13, 1963.
All papers listed In the agenda were presented as
scheduled except paper A-l, Generalized SPS Routines for
Handling Simple Problems, by Thomas L. Yates, which was not
given, paper A-2, Expotential and Sinusoidal Curve Fitting,
by E. P. Hilar, which was given at Technical Session "Gil, and
paper G-I, Ray Trace Program for a General Lens System, by
D. H. 0 'Herren, which was given at Technical Session II A" •
Paper E-1, Network Analysis, was presented by Mr. Gerald Hogsett,
IBM, Los Angeles. Paper C-2 was read by Bob Ebert.
Copies of the abstracts and papers presented are
enclosed with the exception of Paper G-l which will be included
with minutes of a later meeting.
The general meeting was opened on December 11 by
President Bob Ebert and after opening remarks was turned over
to Jim Morgan of IBM who introduced the other IBM representatives
to the group. The sound-off session was moved up to this time
to fill in the time for paper A-I. A summary of questions raised
and answers to them follows the minutes of the business meeting.
Business Meeting
December
the floor
in order
referred

The business meeting was opened by Bob Ebert on
12 and under' old business, the request was made from
that the Roster of Members be arranged alphabetically
of the name of the installation. The request was
to Angelo Arena of IBM.

The first item of new business was the resignation
of Bob Ebert as president of the Western Region 1620 Users
Group. This was necessary under the by-laws as he is no
longer connected with a 1620 installation. A letter by Bob to
the Users Group is included with the minutes of the meeting.
The executive council, acting under the provisions
of the, by~laws, apPointed Paul Bickford, Western Region Secretary, to complete the unexpired term of office of President,
and he apPointed Robert R. White to fill the vacant position
of Secretary.

o

With Paul now presiding as President the new business
continued with the selection of Denver, Colorado, as the site,
II

....

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2

and the third week in June, 1964, as the probable date of the
next meeting. It was announced that the next fall meeting will
be a joint meeting with the Midwestern Region, and will probably
be held on the campus of Oklahoma University at Norman, Oklahoma,
on November 9 or 22. The program committee will distribute the
information regarding dates and agenda as early as possible, and
they request abstracts of papers be sent in as soon as possible
to aid them. A list of pre-registrants will be available early
on the first day of the meeting.

Ci

Paul then announced results of the Executive Council
meeting at Pittsburgh and they are as follows:
1.

Jim Davidson is soliciting suggestions for
methods for removing programs from the library.
A criterion for value of the program and a means
for the removal of inadequate programs is needed.

2.

The cost of running the users group has risen.
Dues paid by each region to the National 1620
Users Group were $.25 per registrant at each
regional meeting. This has now been raised to
$.50. Most of this increased cost has been in
publication of the Newsletter. This must now
be distributed to over 1,000 members while the
average number of registrants at each meeting
has not risen. It was stated that the registration fees for the meetings may have to be
increased.

This concluded the new business and the busfness meeting was adjourned.
After an excellent luncheon, Mr. Melford E. Monsees,
ADP Co-ordinator" U.S. Army Engineer District, Kansas City,
Missouri, spoke on "The Impact of Automation on Professional
Engineering." A copy of the talk is enclosed.
Two special interest groups met for discussion of
mutual problems. The Civil Engineering group was presided over
by Elias C. Tonias of Erdman and Anthony, Consulting Engineers,
Rochester, New York, and minutes of the discussion are enclosed.
The Power Utilities Engineer group was very informal but of
benefit to all participants.
Sound-Off Session and Comments
It was announced that Version 2 of FORTRAN/FORMAT is
available and has these advantages over Version 1 1.

Multiple Format Specifications (also in the
Pre-Compiler)
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2.

Source decks are available (on magnetiC tape)

3.

There are more subroutine options.

Ninety hours or more are required for field installation
of 1311 disk drives.
Some operating difficulties with the disk were discussed
and these pOints were brought out.
1.

In order to use a FORTRAN lID or SPS lID object
deck the Monitor I must be on a working drive.
This is because no loader or subroutines are
punched.

2.

There is no current provision in Monitor I to
load object decks to disk unless they are
Monitor I compiled. It is therefore necessary
to recompile all programs.

There is a great deal of interest in FORTRAN/FORMAT.
Requests were made for a disk version and a version to batch
compile. It can now be changed to allow free form input similar
to the first 1620 FORTRAN compiler. Chuck Berr.y of IBM Wilshire
office can supply instructions for this change.
Requests were made for the following from IBM:

c

1.

Relocatable I/O and arithmetic subroutines for
FORTRAN so only those used would be called.

2.

A reduction in nOise level on the Model 2 1622.

3.

A FORTRAN pre-compiler which would give indication of the amount of storage the compiled
program takes.

4.

A

5.

A loader for Systems Output Format decks punched
under Monitor I control.

6.

FORTRAN processors to take advantage of extended
machine capabilities.
.

7.

A Report Program Generator for the 1620-14431311 combination.

8.

COBOL for 1620

9.

ALGOL tor 1620

10.

Tabulate command in FORTRAN.

FORTRAN IV.
13

--~-----------.------

---------

------~-

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4
Some of these requests were answered in the comments
session by Jim Morgan and the other IBM representatives. The
questions answered are:
1.

Processors specifically designed for larger
machine configurations are being investigated.

2.

There are no present plans for IBM written
COBOL, ALGOL, or Report Program Generators,
however, there is an ALGOL processor available
from Southern Illinois University.

3.

The request for FORTRAN IV was noted and Jim
asked for more opinions on the need for 1t.

The new hardware announced for the 1620 since the last
Western Region meeting is the CalComp Plotter in two models,
binary capabilities for the Model 2 - 1620, and index registers
for the Model 2 - 1620.
It was noted that the FORTRAN II sine subroutine does
not handle small angles correctly. IBM programming systems is
working on the problem now.
Angelo Arena discussed the program library and said
that the KWIC index is still in the process of being developed
and may be changed even further, so that it will be easier to
find programs by number. It will be published every six months with
supplements issued every month. It will be 3-hole punched.
Angelo requested that when programs are ordered, unless the user
1s sure the program f1ts his need, he order only the documentations. IBM can supply this quickly while program decks and tapes
take longer. More descriptive titles for programs would also
help this p~oblem.
There is now available from IBM a manual which lists
the RPQ1s available (A26-5799). Some of these mentioned were:
1.

The ab1lity to punch one character on paper tape.

2.

A real time clock. The clock IBM is now installing on all equipment is an elapsed time clock
only and is not addressable.

3.

An

future.

addressable IR-2.

Version 2 of FORTRAN II will be available in the near

The 1443 print commands are handled in the same manner
as 7000 series machines with Column 1 being used for carriage
control.
In order to get IBM publications without fail, have
the IBM Systems Eng1neer put the installation name on the SRL

o

5

list. Mailing is then automatic. Be sure that the installation
receives the 1620 Bibliography, A26-5692.
The meeting was concluded with a demonstration of a
Model 2 - 1620 with a 1311 disk file, on the evening of
December 12, at the IBM Phoenix office and tutorial sessions
on December 13 for MONITOR 1, FORTRAN II, and SPS 1620/1710.

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1620 USERS GROUP WESTERN MEETING
PHOENIX, ARIZONA, WINTER 1963
CIVIL ENGINEERING SESSION
WEDNESDAY. DECEMBER 11. 1963. 3:30 PM

The highlights of this session were discussions
on the disc file, the use of Fortran VB. SPS in Civil
Engineering programs, the introduction of COGO and the use
of the CALCOMP plotter.
It was the general consensus of the participants
that SPS provided a better and faster object program than
Fortran; Fortran however may be considered as the language
for installations where speed in programming is preferred
over speed in program runs.
The use of COGO in Civil Engineering installations
should be reserved to engineers who are neophytes in the
field of electronic programming and should not by any means
replace existing programs or prevent the development of
special programs.
Also of great interest was the use of the CALCOMP
plotter now adopted by IBM. Successful programs have been
written for contour plotting either with or without photogrammetric equipment and in plotting cross sections and
profiles. It has also successfully been used in structural
design in such cases as in the plotting of influence lines.
Another field of successful use is that of hydraulic engineering
and hydrology. The use of other plotting de.vic:es such as the
Digital Scale and the Wilde T7 has tremendously helped in
reducing conventional type of work and in tightening the interrelationship of photogrammetry, plotting and computing.

ELIAS C. TONIAS

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1620 USERS GROUP
WESTERN REGION
AGENDA FOR 1963 WINTER MEETING
ARIZONA STATE UNIVERSITY
TEMPE, ARIZONA
DECEMBER 11, 12, 13, 1963
WEDNESDAY -- DECEMBER II, 1963
8:00 - 10:00
9:00

Welcome and Opening remarks - R. Ebert, Regional President,
and IBM Representatives

10:15

Coffee Break and informal Ifget acquainted" session

11:00

Technical Session "Alf
A-I
Generalized SPS Routines for Handling Simple
Problems.
Thomas L. Yates, Director, Statistics Computing
Lab., Oregon State University, Corvallis, Ore.
A-2

12:00
1:30

3:00

o

Late Registration

Exponential and 3inusoidal Curve Fitting.
E. P. Hilar, Goodyear Aerospace, Litchfield Park,
Ariz.

Break for Lunch
Technical Session liB"
B-1
Automated Design Engineering.
W. W. Rogers, IBM, Los Angeles, Calif.
B-2

A Payroll and Labor Distribution Program Package.
Elias C. Tonias, Erdman and Anthony, Consulting
Engrs., Rochester, N.Y.
Richard C. Devereaux,
IBM, Rochester, N.Y.

B-3

The SPIRE System - Salaried Personnel Information
REtrieval.
Gary J. Reed, Proj. Engr., ACF Industries,
Albuquerque, New Mexico

Coffee Break
Technical Session "c"
0-1
A 1620 Program for Minimization of Boolean Functions,
Expressed as Sums of Minterms.
Thomas R. Hoffman, Prof. of Elect. Engr., Union
College, Schenectady, N.Y.

17

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............. _..

__ ..- _._"----_._-_. __ .__ ....................__.........

__.

Agenda - Tempe - Page 2
WEDNESDAY -- DECEMBER 11, 1963 (Cont'd.)

5:00

C-2

Critical Speed, Stress, and Bearing Reaction Calculations for a General Shaft, Using Numerical
Integration.
Ralph B. Bates, Mgr. of Engr. Computing, Industrial
Div. of American Standard, Detroit, Mich.

C-3

Three Dimensional Surface Fit.
David G. Kitzinger, ACF Industries, Albuquerque,
New Mexico

Adjournment of Day's Sessions.

8:00 p.m.

New Users Meeting, t~J:)~ followed by Sound-Off
Session at Approximately 8:30.

THURSDAY -- DECEMBER 12, 1963
9:00

Technical Session liD"
D-l
Maximum Likelihood Resolution of Two Mixed Normal
Distributions.
Reimut Wette, D.Sc., Asst. Biometrician, The
University of Texas, M.D. Anderson Hospital and
Tumor Inst., Houston, Texas
D-2

Comparison of Two Methods of Finding Significant.
Contributors in Multiple Regression.
M. J. Garber, Director, Computing Ctr., University
of California, Riverside, Calif.

10:15

Coffee Break

10:45

Technical Session "E"
E-l
Network Analysis.
H. N. Tyson, Jr., IBM, Los Angeles, Calif.

11:15

BUSINESS MEETING

12:00

LUNCHEON "The Impact of Automation on the Professional
Engineer"
MelfordE. Monsees, ADP Co-ordinator, U.S.
Army, Corps of Engineers, Kansas City, Mo.

1:30

Technical Session "F"
F-1
An Integrated Earth Work System.
Cecil L. Ashley, ADP Co-ordinator, U.S. Army
Engineering District, Walla Walla, Wash.
F-2

Hydro-System, A Daily Operation Analysis.
Charles R. Hebble, Civil Engr., U.S. Army Corps
of Engineers, Walla Walla, Wash.
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Agenda - Tempe - Page 3

~

THURSDAY -- DECEMBER 12, 1963 (Cont l d.)
3:00

Coffee Break

3:30

Technical Session uG"
G-l
Ray Trace Program for a General Lens System.
D. H. 01Herren, Goodyear Aerospace, Litchfield
Park, Arizona

4:00

IBM Reports and Discussion of Sound-Off Session.

5:00

Adjournment of Day's Sessions.

8:00 p.m.

FRIDAY

o

Demonstration of the 1620, Model II, with 1311
Disc Pack at the Phoenix IBM Branch Office.
(Transportation will be arranged).
DECEMBER 13, 1963

9:00

Workshop Session "A"
A-I
MONITOR I

1:00

Workshop Session "B"
B-1
FORTRAN II
B-2
SPS 1620/1710

4:00

Conclusion of WorkshOp Sessions, and Final Adjournment
of Meeting.

'0

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1620 USERS GROUP
WESTERN REGION
ABSTRACTS FOR 1963 WINTER MEETING
ARIZONA STATE UNIVERSITY
TEMPE, ARIZONA
DECEMBER 11, 12, 13, 1963
NO.

TITLE, AUTHOR, ABSTRACT

A-l

GENERALIZED SPS ROUTINES FOR HANDLING SOME SIMPLE PROBLEMS.
Thomas L. Yates, Director, Statistics Computing tab.,
Oregon State University, Corvallis, Ore.
Two-way frequency distributions; output editing and
formattingi card reproducing. (No further abstract
available.)

A-2

EXPONENTIAL AND SINUSOIDAL CURVE FITTING.

E. P. H1lar, Goodyear Aerospace Corp., Litchfield Park,

Arizona.
A specified number of exponentials are fitted to
given equally spaced data pOints. The frequencies of
the exponentials can be a mixture of real frequencies
and complex conjugate pairs. The least mean square
error criterion is used to find both the frequencies
and the coefficients of the exponentials. The program
is written in FOR'1'RAN language. The limitations of the
program will be discussed.

o

B-1

AUTOMATED DESIGN ENGINEERING.
Rogers, IBM Corp., LOs Angeles, Californ1a
A presentation of Automated Design Engineering and
how to achieve it. The role of a computer, ability to
capture design logic, use of decision tables, comparison
to manual design methods, and considerations involved
with establishing Automated Design Engineering will be
discussed.

B-2

A PAYROLL AND LABOR DISTRIBUTION PROGRAM PACKAGE.
Elias c. Tonias, Head of Data Proc. Dept., Erdman &
Anthony, Consulting Engineers, Rochester, N.Y., and
Richard C. Devereaux, IBM Corp., Rochester, N. Y.
The objective of this paper is to demonstrate how
some free 1620 time may be utilized in a relatively
small scientific or engineering installation through
the use of a package of commercial programs. The
successful operation of such a program package since
the first of this year (1963) has helped to justify
the installation of a 1620 in another firm. This
package, designed for use with the basic 20K 1620

w. w.

(Cont Id.)

Abstracts - Tempe - Page 2
Computer, with paper tape 1/0 and without any peripheral
equipment, produces the payroll reports, and complete
labor cost distribution and breakdown reports. Written
in FORTRAN for easy maintenance, the ideas from this
program package might prove a worthwhile tool in justifying the installation, or in increasing the production
ratio of a 1620 in a small scientific or engineering
account. With few or even no alterations, parts of the
package may be used to handle other various time and
cost distributions.
B-3

C-I

THE· It SPIRE" SYSTEM - SALARIED PERSONNEL INFORMATION RETRIEVAL.
Gary J. Reed, Project Engineer, ACF Industries, Albuquerque,
New Mexico
The Albuquerque Division of/ACF Industries has developed a powerful management tool/for use in personnel
administration. This tool is the SPIRE system, utilizing
an IBM 1620.
The system involves over 30 programs designed to
utilize information from a master file of information
maintained on magnetic tape. This master file contains
over 300,000 different items of information. By judicious
choice of information blocking, search time has been kept
to a minimum for all applications.
The SPIRE system current applications include: inplant recruitment, providing resumes of personnel qualified
to-fill vacant positions; preparation of quarterly reports
containing information on employees eligible for merit
cons.1derations; creation of summary reports on salary
increases for any time period; man power inventories;
prOjections for salary budgeting; preparation of data for
salary surveys; current salary status reports; and many
other similar reports.
The information contained in the SPIRE system has
proved to be complete for all applications thus far. The
approach and system layout have provided an economic way
of producing information that no hand techniques could
supply at any cost. In the applications where the ~esults
could be obtained by clerical methods, enormous cost
savings have resulted.
The SPIRE system has been operational since February
1963. The use of existing programs and the creation of
new applications consistently increase reflecting overwhelming management acceptance.
A 1620 PROGRAM FOR MINIMIZATION OF BOOLEAN FUNCTIONS,

EXPRESSED

AS

sill4S OF MINTERMS.

Thomas R. Hoffman, Prof. of Elect. Engr., Union College,
Schenectady, N.Y.
A FORTRAN program implements a major portion of the
Boolean minimization problem by reducing a sum of minterms
to a logically equivalent set of prime.implicants.
Minterms are entered as 3-digit octal-coded fixed
pOint numbers. With the help of a special table, digit
comparisons at the octal level reveal terms combinable
according to the Boolean identity XA + X1t = X. Systematic
(Cont I d.)
~I

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Abstracts - Tempe - Page 3

o

determination of all possible combinations of this type,
coupled with a bookkeeping system that keeps track of
the different subsets produced, leads to the desired
result. Prime implicants are printed out in octal code,
to complete the processing.
The program can handle minterms having as many as
nine variables, although the 1620 memory capacity (20K)
may be exceeded in problems involving both large numbers
of variables and long lists of minterms.
C-2

CRITICAL SPEED~ STRESS~ AND BEARING REACTION CALCULATIONS
FOR A GENERA! HAFT, U ING NUMERICAL INTEGRATION.

Ralph B. Bates, Mgr. of Engr. Comput1ng, Industrial Div.
of American Standard, Detroit, Michigan
Critical speed, stresses, and bearing reactions can
be calculated on a digital computer for a general twobearing shaft, any number of cross sections, variable
loading, and any length.
Besides eliminating the tedious labor of the calculations, the computer provides flexibility. A number of
calculations may be rapidly made to optimize design, or
to check out application variations on a standard design.
The method 1s illustrated 1n detail by an example
calculation. Briefly it consists of dividing the shaft
into increments of length, determining the load and shaft
moments of inertia in each imrement and the computer
calculates critical speed, stresses, and bearing reactions.

C-3

D-I

M-15l, THREE-DIMENSIONAL SURFACE FIT.
David G. Kitzinger, ACF Industries, Albuquerque, New Mexico
This code uses multiple interpolation techniques in
combination with extenSive transformation of variables to
effect accurate fits of most smooth functions of three
variables. With limited experience in selecting the form
of curve fits in two dimensions, the programmer can fit
complex three-dimensional surfaces. Output is designed
to facilitate successive better approximations to the
function in terms of additional transformation of variables.
Second and third order fitting of functions is aided b~ a
statistical error analysis. Two magnetiC tapes and a 60K
memory are reqUired, although modifications can be easily
made for smaller machines.
MAXIMUM LIKELIHOOD RESOLUTION OF TWO MIXED NORMAL
DIS1'RlliUTIoNS •

o

Reimut Wette, D.Sc., Asst. BiometriCian, Univ. of Texas,
M.D. Anderson Hospital and Tumor Institute, Houston, Texas
Iterative estimation of the five parameters from a
sample taken from two normal distributions by the method
of maximum liklihood seems preferable over the method of
moments, because generalization to more than two parent
distributions appears easier. Two approaches to estimate
the maximum likelihood information matrix were abandoned
in favor of the third, which cut down on computing time
(Cont 1 d.)
014

Abstracts - Tempe - Page 4
(1620 FORTRAN II) for the complete estimation procedure
considerably. Computing time is, aside from variations
due to behavior of the procedure depending on goodness of
initial estimates and structure of the sample, directly
proportional to the size of the sample. Therefore, a
grouping-of-data program was developed specifically for
this problem,/and large samples, preceding the estimation procedure and reducing computing time to reasonable
limits.

D-2

COMPARISON OF TWO METHODS OF FINDING SIGNIFICANT CON-

TRIBUTORS IN MULTIPLE REGRESSION.
M. J. Garber, Director, Computing Ctr., University of
California, Riverside, Calif.
(No abstract available.)

E-1

NETWORK ANALYSIS.
H. N. TYson, Jr., IBM Corp., Los Angeles, Calif.
Discussion will center about the general technique
of network analysis, and the capabilities of a system of
the 1620 programs utilizing this technique for the analysis
of electronics circuits. The programs operate under MONITOR
I on a 40K 1620. The capabilities allow for AC, DC, and
transient analysis.

F-l

AN INTEGRATED EARTH-WORK SYSTEM.
Cecil t. Ashley, ADp Co-ordinator, U.S. Army Engineering
District, Walla Walla, Washington
(No Abstract Available.)

F-2

HYDRO SYSTEM DAILY OPERATION ANALYSIS
C. E. Hildebrand, L. A. DUristan, c. R. Hebble, R. D. Moffitt,
U.S. Army Engr. District, Walla Walla, Washington
The program is a mathematical model of a system of
hydro-electric projects. It is a general program applicable to any river system and scheme of development. It
is capable of accurately simulating the hour-by-hour
operation of a hydro system for as long a real time period
as desired. It will determine the effects produced by
eXisting hydro stations in regards to reservoir levels,
river stages, and alternative distributions of system
load among a group of hydraulically and electrically
integrated hydro stations. The program makes it possible
to determine the operating characteristics of planned
future projects in regards to backwater encroachment on
upstream reservoirs, pondage reqUirements, the effect of
peaking discharges on downstream river stages and reserVOirs, and effects of added power installations. Two
versions of the program exist: One for an IBM 1620 with
40K memory, and one for an IBM 1620 System with 60K in
the IBM 1620 and 4K in the IBM 1401.

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Abstracts - Tempe - Page 5
G-l

RAY TRACE PROGRAM FOR A GENERAL LENS SYSTEM.

D. H. QIHerren, Goodyear Aerospace Corp., Litchfield

Park, Arizona
This program, written in FORTRAN with Format, and
requiring 40K core storage, is designed to trace rays
through complex lens systems, outputting intersection
points at selected surfaces in the system. Cylindrical,
conic, and toric surfaces can be handled and can be arbitrarily oriented with respect to the optical axis. Lens
surfaces can be virtually any contour describably by
second degree (or less) equations or at least divisable
into sections which can be so described. A sample ray
tracing problem is given to illustrate the use of the
program.
The compiler workshOp sessions to be held on Friday will
assume that those attending will have a working knowledge of the
externals of the programming systems (i.e. how to write programs
in FORTRAN or SPS, etc.). The p'urpose of these sessions will
be to present some of the "Hows' and "Whys" of the internal
workings of the compilers. The session on MONITOR I will include
more information on using the monitor, as well as delving into
some of the internals.

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THE IHPACT OF AUTOM..I-\TION ON PROFESSIONAL ENGINEERING

A PAPER PRESENTED
AT
ARIZONA STATE UNIVERSITY
TEMPE, ARIZONA

12 DECEMBER 1963

BY
MELFORD E. MONSEES
LWP COORDINATOR
U. S. L\RMY ENGINEER DISTRICT
lZANSAS CITY, MISSOURI

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'eCL 'W;;' AbW '''.W1t&l! '''lL''g '1Ibt'!\I"\ il"\'/il"IL:"'I'M1i,!!,),Lr,',\\"LL\'/""111'1""/ ,L,L""!"')'\L,'l''''I'",

SOCIAL t\ND ECONOHIC ASPECTS OF AUTOH.A.TION

There are many differing views regarding the impact that the electronic computer 'will have on the development of our social and economic
lives, but most of us can agree that the potentialities of automatic
data processing (ADP) are limited only by the boundaries of our individual imaginations.

The outlook, therefore, is open to wide-ranging

speculations.
The truly great impact of digital computation will be a dramatic
speedup in the rate of technological progress -- and concurrently in the
evolution of our social and economic lives.
Electronic data processing is one of the most pO"t-lerful catalysts of
technological development yet discovered.

This is so because ADP has

the ability of extending the capabilities of man's intellect.
The human mind is the most

powerf~l;

most versatile, most useful

natural gift bestowed upon man by his Creator.

Any instrument that can

substantially increase its capabilities is certain to have a profound
effect on our future development.
Han succeeded in building our technology to an extraordinarily sophisticated level during \.j'orld

~var

II without an aid to his

bility even remotely approximating the power of ADP.

~intellectual

capa-

Now, with the aid

of computers that increase the productivity of his intellect in many
areas by factors running into the tens of thousands, we are certain to see
significant adva.nces in the tempo of technological, economic and social
progress.

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•

Another broad area of impact will be in fields of. business, industry and communications.

We are all familiar with the progress ADP has

already made in automating the business office.

And computers are now

being used increasingly in manufacturing--not only in process control
applications, but also as an aid to the efficient management of the overall manufacturing operation.
We are entering a battle for our very survival in the market places
of the world.

Much emphasis is being placed on economic development.

Technological progress, rising productivity and ascending standard of
living are the true sources of economic strength.

They are vital to

national survival in today's competitive world.
As we move forward, we will encounter the problems always inherent
with social and economic change.

These problems should in ·no way warrant

artificial restrictions on technological development for this is vital
to the success of any business in a free economy.
It may well turn out that the efforts of the new technology will
be far more lastingly felt in its impact on many of the traditional principles and practices of management.

Many traditional personnel practices

are obviously going to be automated or abolished and various leader
groups will change in power and prestige.
While there are no precise means as yet of measuring the speed of
technological change, it is reasonable to assume that by the mid-1960's,
as those born during the Second World War establish families and the

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challenge of foreign competition becomes more intense, the present rate
of change will increase.

At the present time, productivity increases in

the nonfarm sector amount to roughly 2.5 percent a year.

Even a moderate

speedup in this rate would mean that by 1990, a relatively short span of
less than 30 years, industry could double its production with the same
labor as it employs today.l
THE ENGINEERING EMPLOYMENT SITUATION2
Engineering, the second largest profeSSional occupation, is exceeded
in size only by teaching; for men, it is the largest profession.

The

approximately 875,000 engineers in the United States in mid-1960 have
made major contributions to the design, construction, and efficient
utilization of the machines, equipment, roads, and buildings used by
the .Nation's 180 million people.

Engineers provide technical, and fre-

quently, managerial leadership in industry and Government.

They develop

new products and processes, design many types of machines and structures,
and contribute in countless other ways to the technological progress of
the country and to the national defense.
The outlook is for continued rapid expansion of the engineering
profession.

Engineering has been one of the fastest growing professional

lJoseph A. Raffaele, "Automation and the Coming Difussion of Power
in Industry," Personnel, (May-June 1962), 30.
2U. S. Bureau of Labor Statistics, Employment Outlook for Engineers,
(Washington: U. S. Government Printing Office, 1961), pp. 101, 103-104.

0·'
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occupations in the United States in the past 50 years, and there is every
indication that the demand for engineers will continue to grow.

c

As in

recent years, there will probably be a particular need for engineers with
advanced degrees to teach and to do research.
Some of the major factors expected to raise the demand for engineering personnel are:

Continued high levels of Government spending for

defense, accentuated by the increasingly large amount of engineering
time necessary for the development of modern weapons; growth of population and expansion of industry; increasing complexity of industrial
technology, as such the trend toward automation of industrial manufacturing
processes; and further growth in expenditures for research and development.
In particular, the large sums spent for research and development in recent
years by both industry and Government -- total research and development
expenditures in the United States amounted to more than $13 hi1lion in
1960-61 -- have broadened existing areas of employment for engineers and
opened up new ones, such as those concerned with computers, missiles, and
nuclear energy.

As scientific frontiers are extended, more areas of work

for engineers will be provided.

5

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THE EMERGENCE OF AUTOMATION IN ENGINEERING
That the systems concept is having a reaction in the engineering
field is generally recognized.

The question is how much.

The change in

a lot of features surrounding the engineering profession is beginning to
assume large proportions and that rate of change is increasing rather
than leveling off.
For instance, we are told that the amount of engineering information
and scientific information which is directly relevant to engineering
problems has doubled within the last fifteen years.

Even now the volume

of knowledge related to engineering is so great that no one man can
possibly know it all, even though he does nothing but study from boyhood
to senility.

For us engineers that means two things.

We must specialize

more than was formerly necessary or desirable, and second, we must be
diligent students throughout our active lives.

If we fail to study and

keep abreast of the developments which directly apply to our

chos~n

fields of engineering, we shall quickly become back numbers and soon thereafter become useless to an advancing civilization.
As a civil engineer, I am more familiar with the developments in that
field than in some of the others.

I recall the observations I have made

and the discussions I have had with various men over the past 25 years,
relative to the extreme reluctance of engineers to adapt labor-saving
devices in their

~

work.

Our fellow engineers were accomplishing much

in the industrial world in devising and perfecting labor-saving equipment,
6

o
30

but we civil engineers were extremely slow in demanding any sort of

o

machinery or equipment that would make our work easiero
For example, up to a few years ago, we were using the same methods
of surveying that had been devised in ancient times.

The transit was a

little better than the old surveyor's compass, but the long and tedious
process of making ground surveys was basically unchanged for 3,000 years.
Now electronic measuring devices for survey parties are becoming standard
equipment.
The electronic computer is an item which cuts across all the fields
of engineering arid many of the areas of science as well.

They have been

in use now for only about 15 years, but in that time they have increased
the computational ability of mankind one million timeso

The industry has

grown in 15 years from zero to the production of a billion dollars worth
of equipment during the year 1960.

Since that date there has been an

upsurge in the number of manufacturers of electronic computers.

Competi-

tion has become keener than it was a few years ago and we can confidently
look forward to a greater variety of computers, composed of more dependable pieces of equipment, at a cheaper price than they command today.3
The electronic computer systems have eliminated much of the routine
drudgery that has long been the bane of an engineering office.

Also, they

have eliminated the need for those men who were fitted for nothing more
than routine work.

There will be less and less need for the man who can

only run a calculator or a slide rule, and who has been noted in an office

3Murray A. Wilson, "Change or Progress," American Engineer, (June,
1962), 29.

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primarily because he could remember all the formulae that applied to his
line of work, able to recall and use them accurately as the occasion
demanded.

This work, the machine can do better and much more rapidly.

The other feature is that the computer can solve the basic, theoretical equation and eliminate the necessity for the approximations and shortcuts that have been in common use in so many phases of design, simply
because the basic formulae were so long and complicated that the process of
solving them longhand took so long that no one could afford to use them.
On the other hand, the new facilities will put a premium on imagination
and ingenuity.

These have always been desirable qualities in an engineer,

but in the past a great many engineers have been kept gainfully employed
on jobs that require little of either.

This situation is changing and

the prizes in the future are going to those men who are well endowed with
these two important attributes.

EFFECT OF AUTOMATION ON ENGINEERING EDUCATION
Actual and tangible changes in the practice of the art and science
of engineering are being reflected in our schools and are under constant
discussion in publications, so it seems probable that we have created a
new concept of the profession of engineering, or if you please, a new
image of the engineer.

The curricula in our colleges are in a state of

fluidity with considerable differences in their means of meeting the
challenge of the changing conditions.'

On one thing all seem to agree--

that is, that the engineer of tomorrow and the day after, will need to be

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more thoroughly grounded in the basic physical sciences than was thought
necessary for his predecessor.

Others have felt that an equally important

need of the coming engineers is a knowledge of the past such as is gained
through a study of the "humanities. 1f

In an attempt to make room for these

additional courses in a curriculum already overcrowded, something had to
give, so the subprofessional subjects such as shop practice, material
testing, laboratory work of various kinds, surveying and similar courses
are being eliminated.

The logical justification of this elimination is

that these functions are actually to be performed by subprofessional men
anyWay, or as we propose to call them, the engineering technicians.
Modern problems of engineering are no respecters of traditional
boundaries between the specialities.
by schools of engineering.

Accordingly, changes are being made

It is understood that Dr. Keith Glennan has

made broad moves which will go far to establish interdisciplinary approaches
in engineering education at Case Institute of Technology.

At the under-

graduate level he has consolidated the departments of chemical, civil,
electrical and mechanical engineering into a single administrative unit
the Engineering Division.

The engineering faculty are re-grouping in a

natural way according to their common professional interests such as
systems, design, energy conversion, materials, information processing
and other emerging fields.
Degrees in electrical, mechanical, civil and chemical engineering
will continue to be granted, but a new degree at Case -- probably named
Bachelor of Science in Engineering -- will be offered.

It will give the

student the opportunity to plan his elective program -- with faculty

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advice -- to suit his career interests.

Such a program can be designed

to lead more effectively into advanced work.
There is little doubt that the four-year graduate will continue to
play an important role in industry, but there is an ever increasing need
for the engineer with the depth of knowledge and experience produced by
work at the advanced graduate level.
Also, Dean B. R. Teare, Jr. of the College of Engineering and Science,
Carnegie Institute of Technology, said recently in a letter to me -"The electronic computer has certainly made an impact on the individual
courses in our engineering programs but it has not yet been the reason
for extensive curriculum changes.

Some engineering departments, pressed

with the lack of time in a four-year program, have had to decide between
continuing courses in engineering graphics and courses in computer 10gic.,,4
The electronic computer is also having its impact on the curriculum
at M.I.T.

In a letter I received last January from Dean Gordon Brown's

office some of the directions in which the computer was leading were outlined. 5

For example the inclusion in the curriculum at M.I.T. of the

following subjects:
Digital Computer Programming Systems
Mathematical Methods in Civil Engineering
Digital System Application.

4B• Ro Teare, Jr., Carnegie Institute of Technology, in letter to
author dated January 3, 1963.
5Gordon Baty, Adm. Asst. to Dean of school of Engineering, M.I.T.,
in letter to author dated January 18, 1963.

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Other related subjects have been included in the curriculum, but it
pointed out that the automatic computations is not presented as an end in
itself, but as another tool of analysis in the engineer's kit.

The subjects

merely focuses upon the techniques available to the engineer for exploiting
the power of electronic computations •
. Dean Brown's office also advised me that the impact of the computer
upon research activities has been enormous.

A copy of the semiannual

Report, available from the MoI.T. Computation Center, can give you some
idea of its magnitude.

Yet, however important these computer-related

activities have become to the School, there is a danger involved in
attributing any of them simply to the availability of computer technology.
For this is only one of the influences which have converged to create many
of our most exciting research projects and subject offerings.

Others include

new methods in statistics and operation analysis, systems analysis and
synthesis, theory of learning, and the information technologies.
TANGIBLE BENEFITS FROM AN ELECTRONIC COMPUTER SYSTEM
First hand knowledge of the impact of automation on professional eng ineering has been obtained as a member of the staff of the U. S. Army
Engineer District, Kansas City, Missouri.

This Corps of Engineers office

has civil works engineering and construction in

St~tes

of Kansas, Missouri,

Nebraska, Iowa, and Colorado, and military engineering and construction in
the States of Kansas and Missouri.

The total work of this district averages

about 70 million dollars per year and includes the design and construction
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of large multipurpose dams, levees, £loodwa11s, channel

i~provement

works,

pumping plants, and necessary utilities, highways, railroads, bridges, etc.,
required to be relocated in connection with flood control projects.

Also,

included in the assigned work of the district is the construction of
military facilities and structures for the Army and Air Force.
Computer facilities for engineering applications have been available
since January 1958.

The initial computer was the Burroughs E-l02, which,

although of limited capability, was used until replaced in December 1960
with an IBM 1620 paper-tape system.

Utilization of the paper-tape system

for engineering applications increased rapidly and in January 1962, the
system was augmented to provide for high speed punched card input-output.
During this period, the utilization of electronic computer systems has
provided tangible benefits through reduced cost of construction, savings
in engineering and clerical manpower, and by providing a superior endproduct or flood control structure.

To date the major effort in implementing

ADPS procedures has been directed toward high-benefit engineering applica..;
tions.

Only preliminary phases of planned implementation of ADPS in areas

of personnel administration, property accounting, real estate activities
and fiscal responsibilities has been possible.

As of December 1963, over

75 computer programs were being used in the fields of mechanical engineering,
structural engineering, hydraulic engineering, hydrology, reservoir regu1a. tion and earthwork and soil mechanics.
The currently installed system in the Kansas City District Office has
provided the following:

0·'·"
,J

12

36

f~
\,--",)

a.

Improvement of the engineering and design product.

b.

More timely and accurate data which is fully responsive to the

needs of management and engineering, including data previously not economically obtainable.
c.

Savings in costs by maintaining continued evaluation and balance

of equipment and personnel.
d.

Savings in costs and engineering manpower by application of ADP

principles.
e.

Simplified and reduced manual data handling and eliminated dupli-

cation of files, reports, and entrance of source data.
Further benefits are being obtained through realization of the following objectives:
a.

Expansion of hydropower and pumped storage-power

stu~y

programs to

be used in connection with reservoir regulation, hydrology and hydraulic
engineering programs used for design, construction, and operation of nrultipurpose projects.
b.

Expansion and refinement of structural design analysis programs

used for preliminary and final design of various civil engineering projects.
c.

Expansion and refinement of earthwork and soils mechanics programs

used for quantity computations and stability analysis of large and small
embankments.
d.

Implementation and expansion of Critical Path Scheduling techniques

to be used for coordination of construction activities as well as coordination and scheduling of engineering and design programs.

13

J7

c

'" ·j·.eWH&S5'#RMFfiWibij"j·6"·'·_·-J···_'

o

··I--··r

...-

[

j.

m.li5W··t-·SW 17·'·····"'_· ·--WW·-Tb-r---··-r ...

I~·

-[I··

I!·

wtirf'

if

ffffdijwW&ii8\i,ifj·jijiH8itftF#ihti#i5·j"¥#r1ftFj·... ··bHW·#*fjdttT···P·-...·SIW#tftiij"j¥€fHfbiWfj"¥##iii·· ·rIll ¥····.±ifril#8fiff"*e·ttH·ritiiRi.i••··fijHiHM;r····.···d±·ijt··j·····WftiF"

e.

Refinement of personnel administration and reporting procedures.

f.

Implementation of one additional phase, of the engineering budget

management data to eliminate manual posting and to provide more accurate
readily accessible data for management and estimating purposes.
g.

Exploitation of the principle of "management by exception" through

the potentialities of data processing equipment and techniques by continued
education and training of personnel in the use of machine oriented reporting procedures and elimination of duplication of detail.
h.

Full utilization of presently installed data processing equipment

by insuring that all data processing activities are essentially highbenefit programs.

CONCLUDING OBSERVATIONS
Last year, 1962, was a year which may very well be recognized as the
beginning of the first plateau of maturity for the industries that automatic
control has helped to create.
Signs of maturity are also evident among the scientists and engineers
who created these new industries and who must continue to act as whole
partners with management and finance in continuing to create and exploit the
new scientific breakthroughs which will firmly establish automatic control
in its ultimate pOSition as the greatest servant of mankind.

This maturity

takes a number of forms:
a.

The number of engineers and scientists enrolled in post-graduate

or extension courses in management is testimony that the importance of

o

14

market and management factors in technical decisions is not widely recognized
by the technical exper.ts.

C)

The idea of technical performance, cost, schedule,

physical characteristics, an4 reliability has now
a factor in technical decisions.

beco~

widely accepted as

Finally, an increasing number of scientists

and engineers has come to realize that their technical brilliance is wasted
if their ideas cannot be sold, and that it is a hollow satisfaction to be
able to prove that something new and wonderful can be done unless means are
found to ensure that it will be done.
b.

Electronics engineers, dynamicists, and even civil engineers have

discovered the benefits of computers; and the electrical, mechanical, and
field service engineers are recognizing the importance of automation in
the translation of their diagrams and equations into operating realities.
c.

The overriding importance of reliability in concept, design, manu-

facture, operation, and maintenance of automatic control systems has been
thoroughly recognized.
d.

Our new ability to use high-speed, high-capacity digital computers

as controllers for automatic control systems, plus the advent of microminaturization, has provided the flexibility for universal application to
systems of almost any complexity, involving almost any combination of
scientific disciplines.

This new flexibility provides the base from which

automatic -control can be adapted to applications ranging from space vehicles
to automatic factories -- from complex air-traffic-control systems to the
most microscopic of biological measurements and processes -- from the unmanned
vehicles of oceanological exploitation to the complex man-machine systems
of industry and sociology.

15

3~

o

I

o

e.

In the areas of technology, today, because of the broadening appli-

cation of this industry into all fields, the engineer and the automatic
control technologist must be able to understand and communicate with technologists from almost every field of endeavor.

This universality of automatic

control science application has brought about a lowering of the barriers
of disciplinary specialty to permit an intermingling of the most widely
diversified technologies.
Finally, there is no doubt that the electronic computer has had its
effect and will continue to have an impact, not only on professional
engineering but on the curriculum and educational program in our schools of
engineering throughout the United States.

c

16

40

,

4

c

o
BmLIOGRAPIIY

Josepb A. Raffalle. tlAutomation alld the Coming Diffusion of
Power in Industry," Personnel, (May - June 1962).
Frank W. Reilly. "Policy Dec~isions and EDP Systems in the
Federal Government," Public Admini.stration Review,
(September 1962).

u. S. Bureau of Labor Statistics.
Engineers, (Washington:
Office, 1961).

!n.m.t2L'UlE'~

Outlook for

U. S. Government Printing

Murray A. Wilson. "Change or Prl.>gress,"
(June, 1962).

~mer.ican

Engineer,

B. R. Teare, Jr. Carnegie Institute of Technology, ltr.
dated January 3, 1963.
PaulO. Roberts. :?Computer MOdels of Future Roads,"
(The Technology Review, December, 1962).
Mart in Greenberger. Management 8.nd the r.ompu ter of the
Future, (New York: John Wiley & Sons, Inc., 1962).
Glenn Murphy. "Whither Engineering Education," Journal of
Engineering Education (November, 1962).
R()ger W. Bo1z. UAutomation as a Social Problem, H American
Engineer, (March, 1962).

o
44

Lfl

o

o
GOOOfiE4R
GOODYEAR AEROSPACE
COR P () HAT ION
ARIIONA

OI\ISION

LllCHI-'IE.l.D PARK,

Expo:m~lTIAL A~JD

sr:usotnAl

Af-(IIO~~A

CrEVE FITTING

E. P. Hilar

AAP- IRB!.:)

o

Ncvember 20, 1963

·
,

o

c

LIST OF REFERENCES

(1)

Dr. F. A. Willers, :~actical Analysis, Graphical and
~'!t1m€'r:tcal Methods, Dover Publications, Inc., 19L8

(2)

Louis vJeisner, Introduction to the Theory of Equations,
The MacMillian Co.

(3)

1620

Po~om1al Rootrinder

J. W. Wentzien,

o

ra~

b.Y BarstowB Method,

1620 Library (lt20 -

07.0.oLo)

INTRODUCTION

This paper presents a program written around the method of fitting exponental
curves to data as given by F. A. 1'.'i1lers in his book, ttpractical Analysis .. l •
The program fits exponentals with either real or complex conjugate pair fre~lencies.
The frequencies and the coefficients of the exponentals are fitted
using the leas t mean square error criteria. The rrumber of 'exponentals to
be fit.ted is specified as part of the in~t data. The program is written
in Fortran language o

---~------------~---

~~-

~--.~

~~--~-~~.~~~

o

THEORY OF METHOD

Given N observations equally spaced in the independent variable :x by an
amount h and originating at ~ • 0, it is desired to fit a sum of n exponentals

to them.

The obBervations will be represented by the dependent variable y.

The desired fit will be written

n

y(x) • Co +

L1

where the coefficients, C, are real,

(1)
3f!d

the frequencies, a, are real or

occur in complex conjugate pairs which give rise to terms of the form
C e n + 1

The derivation of the method of fitting the
begin

ttl

exacUy.

~xponerta1s

to the data will

assuming that the pain ts actually fit the exponental repreS'entation
An expression involvi.ng only the frequencies, a, and the successive

diffel'ences of the data points will be derived.

The fiction of an exact fit

will then be removed by introducing an error term into this relationshipr;
The above assumption may be written
n

y(~)

• Co +

L

(L)

1

where y(m) is the roth data point.
Defining the difference between successive data points as

D(j) • y(j+l) - y(j)

o

( 5)

Using Equation (L), Equation (S) may be written as

-1-

b
n

D( j ) .

Cj ( e U

il

-1) e c j (m-1) h

(6)

1
Defining
(7)

(3)
Equa tion (6) may be written

D( j ) .

t

(U(j)-l) t(j)

(9 )

Using Equations (5) throup,h (8)

D(m+k) • y(m+k+1) -y(m+k)
n

~

f(j)

(U(j)-l) U(j)k

(10)

Now n+l equations of the form (10) will be wTitten out
D(m)·

L f(j)(U(.j)-l)

•
•

(11)
where the sum runs from lto n on j.
Under the assumption that t.he curves are an exact fit, all of these
equations (11) hold true.

Now i f we consider them as n+l equat.ions

in the n unknown f( j) then the determinate of the equat;.ons nrust be
zero.

This restriction on the determinate yields the following

equation

o
-2-

WY"·., . b.··· "•.. i "ifF""" . .... F f #It-·" f"i "iF, %&R£&if&:fbtfHf8iHii'*fdfia-Wtiftidw' iP9i&HA-liHHiit8fC"*fWiiWiiWMHi'iiiiT """/T-' rx

o

_.. .

TSWl"""W' ET¥2f""F"""T-- E wPY W··-7 I ¥

- '"""iF

n
•

Tn r···'srzW'fIK"%fZTWmpmarEP?l'Pwrnm

ewes

n

(12)

D (m+k) S(n-k) • 0

The functions S( j) are the s:/Il1Tletric functions and are defined in the two
")

equivalent fo~~ shown below

L
•

S(o) • 1
n

S (1)·

--

~

U( j )

1
n

~1

(13)

•
•
o

or, given an n

th order polynomial whose zeros are the U(j)s, then the

pc lynomial can be wri t ten as

n

~

S(k)Zn-k

• 0

(1),)

ft.
o

where 5(0) • 1
In the problem of fitting the exponentals to the data we do not know the
value of the symrlletric functions before hand.
frequt?ncies could be calculated from them.

If we did the required

but by removing the fiction of

an exact fit throt .gh introrluc.ing an error tenn into Equation (12) and
1

writing it as

o

n

. ~ D(m+k) S(n-k) •

f (m)

(15)

o

47

. -3-

C\

the error can be minwzled by the proper choice of the symmetric functions.
The means of choosing them will be the least mean square error criteria.

(15) and summing over the permissible values of m yields

Squaring Equation

(~
S~ce

it is the symmetric

2
D(m+k) S(n-k»)

~lnctions

•

t(n+l)
m

f{m)

2

(16)

that are being fitted, the partial

derivatives with respect to the symmetric funct.ions of the left hand side
of Equation (16) are equated to zero yielding n equations of the form
n

~
o

(L;

D(m+{) D(m+k»)

S(n-k)

•

0

(17)

where .R.. runs from 1 ton and all s urns on m run from 1 to ~! - ( n+1) unless
otherwise noted.
The n( j)s are calculated from the data and the n sOO1 taneo11S Equations (17)
are used to solve for the bestf1t symmetric functions. Equation (14) is
then solved yielding for its roots the U(j)s. For a real root the frequency

,
i

is calculated from

in
aj •

U(j)

1

(18)

n

For a complex conjugate pair of roots of the form

(19)

ntib

the

corresponJi~ng

frequencies are calculated from

I

1
2 2
a· ~ inCa +b )

~l

~.

(20)

~
~

1

(21)

• h arctan (b/a)

where the corresponding terms in Equation (1) are

no~

of the form (2).

0

1,

I

I
-4-

-,I

o

Onoe the frequencies have been found the fitting of ' the coefficients of
Equation (1) to the data 1s a straight forward problem using the least
mean square error criteria on the following equation:
Co + )lJ~
~

cje(tj(m-l)h

-y(m) •

€(m)

(22)

where the coefficients, C, are now to be fitted. The development from
this point on is Fortran oriented and will be presented in the discussion
of the program itself.

o
-5-

METHOD AND PROCEIlJRE

The description of the program will e'mphasize the means used to speed up
the calculations of the various portions of the problem. Once these are
understood the listing becomes self-explanatory.

The first major task is to generate the coefficients of the symmetric
functions in Equations (11). To accommodate the DO loops the following
definition will be made

D~(j) ~ D(m+j-l) • y(m+j+l) - y(m+j)

(23 )

In the program the symbol is written

DE(j) and the value of m is kept track of by a DO loop.
Now defining
(2L)
The n equatiors (11) may be written

1
( 25)

where j runs from Ito n
The desired coefficients are the sums

•

(26 )

A rapid method of calculating these coefficients will now be described.

This method makes use of the following properties which are easily derived
from Equations (23) and (2L).
~'o

o
-6-

t?+l

j,k

.

~
j+l,k+l

(28 )

•

~,j

(29)

E~,k

•

~ ~,j

(30)

The quantities DE, E, and ;; E are stored as they are calculated. The
procedure is as follows: m is set to one, and all the required values
of the DEs and the Es are calculated and stored. The values of the Es
are entered into the coefficient sums of the form (26) as the first term.
Then m is set to 2 and the DEs are shifted one s pace to the left using
the property shown in Equation (27). The missing term is calculated from
Equation (23). The stored Es are shifted up and left one space using the
property shown in Equation (28). The missing terms are calculated using
Equation (2L). The values of the Es are entered into the coefficient sums
as the second term. The program proceeds as for m • 2 until all the terms
of the coefficient sums have been entered. A separate but concurrent aspect
is that of storage. The properties of Equations (29) and (30) show that
only terms on and to the right of the diagonal need be calculated. The
remaining space is used for storage. The terms ~ k are stored in E(j,k+l)
and the terms

~ ~,k are stored

in E(k,j).

At the end of the procedure
described above Equation (30) is used to complete the arr~ of coefficients.
The n simultaneous linear Equations (25) are solved by a Gaussian reduction
routine. The solution yields values for the n s.rmmetric functions (13).

o

The nth order polynomial (le) is now-solved using a stripped down version
of the Barstow method3 o The roots of Equation (lL) may be either real
or occur in complex conjugate pairs. In the program the roots are stored
in the following manner: Two fields R(j) and M(j) are defined where j runs
from 1 to n. If the jth root of Equation (lL) is real then it is stored in
R(j) and M(j) is set to zero. If the jth and j+l roots are a complex conjugate pair then the real part of the roots is stored in R(j) and M(j) set
to one and the imaginary part of the roots is stored in R( j+l) and M( j+l)
is

8Pt to

two.

The field M(j) serves to identifY the contents of the field R(j).

SI

-7-

•

t,

The prot:ram does not use the variable S(j) directly but st,ore::;: the solutions
of the n linear equations in the field ::( j) wl :E're

S(j) • x(n+l-j) 0 < j ~. n

(31)

The entry into tr.Le polynomial solver places the symmetric functions in the
field A( j) where
A(j) • S(j-l) • x(n+2-j) 1 < j ~ n, A(l) • S(O) • 1

(32)

The transfer from x to A is done directly.
Once the roots have been found the frequencies may be calculated using the
following form of Equations (lS), (20) and (21)
aj •

~ .R n ( R( j

a

122
2h
,in(R( j) + R( j+l) )

whBn M( j)

))

=0

or

j

•

1

Pj +1

• Ii

Jwhen

I

H(j+l) \

arctan (

.

\

R(j)

M( j) .. 1

and M( j+1) • 2

J
If a real root or the real

p~}rt

of a complex root is negative then the

remainder of the program cmmot give meaningful results and the program halts o

The remainder of the program

i5:3.

straight-forward detE'rmination of the

The di~cussion will be concerr1ed with a

coefficients of Equat.ion (22).

rapid way of ,g€lierating the nt)ecied numbers.
n :: J will be considered here.

straight-forward.

Co
+

+

The generalization of the results is quite

Equation (22) is rewritten

C e~(m-l)h
1

+

e a 2(m-l)h Cos(P3(m-l)h)
2

c

c e a 2(m-l)h sin(~J(m-l)ll)
3

The most gerleral form for

-y(m) • t(rn)

(3L)

-8-

o

o

nefinl!i?, 00 loop notation
m

V(l). 1

V(2)

=

eal(m-l)h

m ~ e a~(m-l)h
) )
V(3)
~
Cos(~3(m-l h

VeL) =
m

v( S)

e a 2(m-l)h

(35)

Sin(~3(m-l)h)

=-y(m)

x( j+1) • C.::
J

wherE-; m is a supers~ript

on V.

Using Equation?(35) Equation (3L) is "1Titten as

m

m

m

m

m

x( 1) *V(l)+x( 2) ~~V( 2 )+x(3) ~~V( 3 )+x( L) --:v( L)+v( 5) •

(36)

£ (m)

Fittine the Cs or the xs by the least mean squarf) error cr-i teria as in the

first part of this re~rt yields n+1 1irlear simultar)eous equations of the

form
n+l

~
1

~

m

m

V(j)*V(k)

*X(k») +

~

m

m

(37)

V(j)*V(n+2)· 0

(

where j runs from 1 to n+ 1 and all the sums on m now run from 1 to N url1ess

otherwise noted.
Defining

m

E(j,k)

m

m

• V(j) * V(k)

(38)

where m is a superscript.

o

Equations (37) become

-9-

n+l

?

l~

m

\~

\

\

m

L!!l E

E(j,k») *:x(k) +

(j,n+2)·

(39)

0

where j runs from 1 to n+l.
Now the Va may be calculated frclm equations of the form (35) for each m
but the amount of time spent doing so is prohibitive.

Recursion formulas

may be developed for the Vs by noting that Equations (33) lead directly to

R(j)

• e

ajh

when M(j) • 0

and
R(j) • eajh

{When M(j)

cos (f3j+lh)

• 1

(40)

and M( j+l) • 2

R{j+l) • eajh sin (~. lh)
J+

Now from Equations (35) and (40) it is obvious that

m+l

m
(41)

Vel) • Vel) • 1
m+l

m

m

V(2) • V(2) e~h • V(2)* R(l)

(42)

I

V(2)·

(L3)

1

The recursion formulas for V(3) and

veL) are obtained wit.h

the help of

well known trigonometric identities as

m+l
V(3)

•

e02

mb

(cos(~3(m-l)h)

m

cos

~3h -

sin

(~3(m-l)h)

sin

~3h)

m

• V(3)* R(2) - V(L)*R(3)
1
V(3) • 1

(LL)

and

m

m

• V( L)-:tR (2) + V(3 ) ~R (3 )

(45)

1

veL) •

o

0

The generalized recursion relationships are

-10-

o

m+l
Vel)

•

1

•

V(j)*R(j-l) wl~en M(j-1) • 0

m+l
V(j)

m

m

m+l
or

V(j)

m+I
V

m

(46)

• V(j)*R(j-1) - V(j+1)*R(j)

m
m ) when M( .i-I) •
(j+l)· V(j+I)*R(.j-l) ... V(j){~(j) ) and M(j)
•

0
2

m+l
-y(m+l)

V(n+2)·

and the vaJ.ues for mel are

V(l)· 1
V(j) •

when M(j-1)

1

• 0, 1

or

(41)
v( j) =-

0

when M(j-l)

•

2

V(n+2) = -y(l)

T'nc program calculates the sums
The value of m is set to

OIle

01,

m in Equations (39) somewhat as bofore.

and the initi.a1 values of the Vs are calcu-

lated from Equations (L7) using M( j) to control the choice of equations.

Tho Vs are stored and the Es are calculated 'Using equation (38) and entered
dil"e~tly into

of

l'!l

the sum on 'm of equations (39) as

th(~

first term.

The value

is then set to two and Equations (L6) used to calculate the new Va

with M(j) as the control.
as before.

The Es are calculated and entered into their sum

The program fJ'oceeds as for m • 2 until the aulTlS are complete.

As in the early part of this paper only the terms

01)

and to the rirjlt of

the ditlf,onal need be calculated fJtep-by-step.

The sarna subprogram is used to calculate the xs of ~quations (39) as with

o

Equation

(25). The coefficients

of E~ation (1) and form (2) are then

calculated using

-11-

Co • x(l)
C

j

C

i

• x(j+l)

when M(j) • 0

=V

when M(j) • 1

x( j )1)2 + x( j+2)2

¢ j+l • arctan ( x( j+2) )

and M(j+l) - 2

x(j+l)
The method of calculating the two variance termfj is discussed in
F. A. Willer 's bOOkl.

o
-12-

o

AUTOMATED DESIGN ENGINEERING

W. W. ROGERS
IBM
LOS

ANGELES, CALIFORNIA

o

';iMRit~ ~i·u·wiji·Hi 'j \~it"'%fl

o

*'¥'5dtw"";;' rB&fill"ifHRfiFi'S6"¥iWw'--' "jW"'" a'SWUTS'T,m E'V""'''W-YW'WP
i8

r

W·-S····TiF···W'n "WJ-" TriPliWW"

Gentlemen:

I would like to talk to you today about a new computer application, Automated Design Engineering.

A. D. E. is the use of the computer in the design of nonprototype products, the type of engineering commonly referred to as
custom engineering, application engineering, or product engineering.
Specifically, A. D. E. can benefit your company through significantly
reducing your engineering lead time, increasing your engineering
productivity,

and decreasing your engineering costs.

These and the

other advantages of the application can, in turn, result in an improved
competitive position for your company in your industry.

First, I would like to tell you what A. D. E. is.
will discuss where A. D. E. applies.
on how A. D. E. works.

Second, I

Third, I will spend a little time

Fourth, I would like to cover in more detail

the advantages of A. D. E.

Computers have been used, in the past, in the design of many
products for industry.

Computers have been utilized successfully in

the design of circuits, missiles, motors, transformers, and telephone
equipment, to name just a few.

In each case, the use of the computer

has resulted in great savings and great increases in efficiency and

o

productivity for the companies involved.

Now a newly

develop~d

computer application, Automated Design Engineering, vastly increases

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

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the power of the computer as an engineering tool. With A. D. E., the

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computer can now be used to solve more engineering problems on a
wider range of products.

Conceptually, A. D. E. involves the sto:r:ing of cfesign

~ogic

in a computer so that the computer can accept customer orders as
input and automatically generate complete designs.

The input to the

system would be the same type of orders you now receive from your
customers.

The completed design would contain the same type of

information normally given by your engineers to your manufacturing
department; such things as product characteristics, part numbers,
assembly numbers, bills of material, purchases parts list, drawing
numbers and so forth.

The principles of A. D. E. can best be described by using an
example.

An A. D. E. system for a company that manufactures

pumps, for instance, would receive customer requirements in the
form of orders or requests for bids. In this case, the customer needs
0

a pump to pump 150 Fahrenheit carbonic acid at the rate of 100 galIons per minute with a head of 40 ieet and he wants the pump motor
wired for 220 and, 440 volts.

These requirements would be entered into

the computer and the completed design would be printed out.

These requirements would be entered into the computer, would
be processed by the computer with the aid of the stored design logic,

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and the completed design would be produced.

The completed design

information can be in many different forms ... such as part numbers,
assembly numbers, drawing numbers, manufacturing instructions,
etc.

In this example the completed design information consists of

the pump frame number, FQ 6; the model number CXR; the suction
and discharge pipe diameter, 3 and 4 inches, respectively; the impeller diameter, 8 3/4 inches; the motor speed, 1750 RPM; etc. ,
etc.

In short, the completed design would consist of the information

needed by manufacturing to build the product.

Now that we have discussed what A. D. E. is, where does it
apply?

Automated Design Engineering applies primarily to "cus-

tom" or "product" design which can be defined as "non-prototype
custom design variations of a standard product line to meet your
customers' requirements on a continuing basis." Even though some
of the tools, techniques, and methods available through A. D. E. are
applicable to prototype design, the major impact of A.D. E. will be
in the custom or product design area.

There are many companies in industry today which produce
custom designed variations of a standard product line in response to
customer orders or requests for bids.

"Custom" or "product" de-

sign is common in such products as pumps, motors, generators,

4.
switch gear, transformers, electrical measuring equipment, indus-

o

trial furnaces, switchboards, engineering and research instruments,
heat exchangers, steam turbines, conveyors, and air compressers,
to name just a few.

Let us look at the problem of the "custom" or ' 'product"
engineer.

In industry today, customer orders for products will

come to the design engineer.

His problem is three-fold:

First, he must determine what to build to satisfy customer
requirements.
Second, he must translate these customer requirements
into workable parts and assemblies and their drawings.
Third, he must prepare the complete paperwork for manufacturing.

It has been determined through actual experience in

industry that these problems can be solved on a computer with
great savings of time and money and great increases of efficiency
and productivity.

Now to help you visualize what a system would look like in
your company, let us look at a typical Automated Design Engineering
System in operation.

A customer order coming in would go tb the

Engineering Department where two functions would be performed.
First, the order would be edited to insure the completeness and
validity of the customer order.
ing would be performed.

Second, any necessary pre-engineer-

Once the order editing and pre-engineering

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has been completed, the customer order would go to the key punching room where the customer requirements would be transcribed
onto cards and fed into the computer.

The computer is programmed with design logic and has
available to it tables, standards, and reference information.

The·

output of the system would be completed design which would then
be reviewed by the engineering department and passed on to manufacturing.

Now that we have covered what A. D. E. is, and where it

applies, and what an operating system would look like, how does an
Automated Design Engineering System actually work?

The key to

Automated Design Engineering is the ability to capture the design
logic by which customer requirements are translated into product
spe cific ations.

We have developed new tools, new techniques and new
methodologies which will assist you in developing an A. D. E. system
for your company.

One of the most important tools, and the heart of

this new system, is Decision Tables, a technique for capturing the
design logic that comprises custom or product design.
to capture design logic is the key to A. D. E.

The ability

Before we discuss

Decision Tables, let us clarify what we mean by design logic.

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What is design logic ... ? Design logic is the complex
decision-making process through which the engineer proceeds in
designing a product to meet a particular customer's requirements.
The engineer reads the customer order and then, through the medium
of design logic, proceeds to design and select the various parts and
assemblies required to satisfy the customer's requirements.

The

result is the completed design of the product.

Let us look at a sample of design logic and how this design
logic can be captured using decision tables.
example the armature for a voltmeter.

We will use as our

If we were to ask an

engineer working for a company that manufactures voltmeters how
he designs the armature for a voltmeter, he might say: "Well: if
thre(-customer requires DC service for a speed application and asks
for a single phase instrument with villivolt rating, then I know I have
to use a moving coil.

~

two windings are needed, which

is the case, then the part number will be -12526A.
A26A will be used in this case.

frequently

Drawing number

If the rating value specified is be-

tween 76 and 200 millivolts and we need a moving coil, the main
winding will use Aluminum wire 16 mils in diameter.

•

The number of

turns and the number of layers will come from these two formulas
which relate to each other.

Based on the case we're using, we'll

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have 13 turns on the main winding and one layer.

Again, I have to

look up the drawing number ... it's 012526-1A.

Now the coil will

also need a damper winding which for a 76 to 200 millivolt rating and
a scale size specified as four inches, will take 8 mil Copper wire and
half the number of turns on the main winding which is also shown on
drawing number 012526-1A."

This complex decision-making pro-

cess can be captured by use of a new tool called decision tables.

A decision table consists of four quadrants.

In the top two

quadrants are the customer requirement names and values.

In

the lower two quadrants are product specifications, names and values.
This decision table is a summary of part of the data given to us
by the voltmeter design engineer.

In the upper left hand quadrant

is a list of customer requirement names ... service, application, rating
units and number of phases.

Values which the customer might specify

for these requirements are given in the upper right hand quadrant ...
DC, speed, millivolt, 1, etc.

In the lower right hand quadrant are

values for these product specifications ..... moving coil, inductive,
1 plus the number of phases, etc.

The decision table is read as

follows: If the service is DC, and if the application is temperature,
then the type of armature needed is amoving coil, and tables number
2 is the table to which we should go next.

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Rule 4 would be read as follows.

7.
If the service is AC, and if the rating units are milliamps, and if the
number of phases is 1, then the type of armature required is inductive,
and the number of windings is calculated as being ONE PLUS the number
of phases, and the next table is number 2.
which can exist is called a rule.
sets of conditions or six rules.

Each different set of conditions

In this case there are six feasible
Once the decision table is established,

programmed and entered into the computer, the computer will automatically select which rule applies to each individual customer order.

It takes hundreds of decision tables to capture and store the
design logic for an entire product or product line.

When all of the

required decision talbes have been programmed and placed in the
computer memory, customer orders can be entered into the computer
design in a logical stepwise manner.

Now that we have covered what A. D. E. is, where it applies,
and have gone into a little detail on how it works, let us turn our attention
to what an A. D. E. system can do for you, or the advantages of an
A. D. E. system.

We have already indicated that you can reduce

your engineering costs and at the same time, obtain increased productivity
and efficiency from your engineering force. Overall lead times can,
in addition, be significantly reduced through a reduction of design
engineering time, materials procurement time and manufacturing lead
time.

The design time, for example, can be reduced from weeks or

even months to a matter of minutes.

This reduction in design time

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will allow you to give faster response to customer orders and requests

o

for bids.

Faster response to bids, on the one hand, can have a significant

effect on your profits if there is a high correlation, as exists in many
industries, between speed of your response and acceptance of your
bids.

Faster response to orders, on the other hand, can result in

faster deliveries and improved customer relations.

And furthermore,

A.utomated Design Engineering can provide a significant increase in
your business activity by allowing you to respond to more bids if you
now find yourself unable to resp::> nd to all of the requests for bids that
are made to your company - - due to the lack of available time in your
engineering department.

In addition, faster response to bids can have

a significant effect on your profits if there is a high correlation, as exists
in many industries, between speed of your response and acceptance
of your bids.

Also, bid costs can be reduced because A. D. E. can

reduce the out-of -pocket cost incurred when bids are designed but not
won, since the engineering cost per bid can be greatly reduced.

Material savings are another potential advantage of Automated
Design Engineering.

By calculating exactly how much material is required

for each job, A. D. E. can reduce overdesign and waste.

Another way

in which material savings can be realized is through reducing the number
of parts in inventory with the same specifications but different part
numbers.

0,
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As you develop your A. D. E. system, these duplications

will become readily apparent and can be eliminated.

The consistent

I'",

use of the best design practices eliminates the proliferation of methods

9.

and materials and insures a design commensurate with requirements.

o

All too often today, the pressures of competition and of constantly
shrinking delivery times tend to result in over-design or in picking
a design which is perhaps more expensive than the specifications
actually call for and the result is loss of profit.

Bid and orde'r cost-

ing can be incorporated into your Automated Design Engineering
system to allow you to not only design but also to price both labor
and material for your design.

Through the automatic generation of

engineering paperwork much of the clerical burden which wastes so
much of the time and talent of engineers today can be alleviated.

A,utomated Design Engineering also provides an improved
error-checking facility.
are many.

The sources of errors in engineering today

These errors can creep in through the customer order,

through the sales engineers, through engineering errors or material
list preparation.

Errors can result in the wrong material, too much

material, or too little material being available at assembly points.
They result in wrong design and in over-design.

With an Automated

Design Engineering System these functions are performed automatically.

Error checkipg capabilities are built into the computer to catch

and eliminate such miscalculations, which are the real problem in
industry today.

Greater management control is possible because

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management policies can be incorporated in an Automated Design
Engineering System with the design logic, to insure that management
policies on engineering are carried forward.

Now that we have discussed the advantages of A. D. E., I
would like to show you how we can assist you in developing and implementing an Automated Design Engineering system in your company.
IBM has available tools, techniques, and methods to help you in
developing your system. There are two steps in the development of
an operating Automated Design Engineering system.

These are the

Survey and the Implementation. The survey represents
step.

th~

first

Its purpose is to determine the applicability of the A.. D. E.

system to your product lines.
of your present system.

It will provide you with a:n analysis

It will determine the requirements of the

new system and will give you a preliminary design of the new system
as it can be applied specifically to your company.

Lastly, upon com-

pleting the survey, you will be able to measure the advantages that
will accrue to your company through the use of Automated Design
Engineering.

The new tools have been developed to prepare an

analysis of your present design engineering operation from four related but different standpoints: Those of time, cost, accuracy, and

o

operations.

After the survey is completed you are ready for the

next step, implementation.

The purpose of the implementation phase

11.

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is to develop a completely tested and operational A.utomated Design
Engineering system.

In order to do this, an analysis of your cus-

tomer specifications, and an analysis of your product structure
must be prepared.

The techniques and tools which IBM will provide

will also enab Ie you to capture the design logic of your product line
onto decision tables, to perform the detailed systems design, the
programming, the testing, the conversion and finally the initial
operation of your Automated Design Engineering system.
techniques and methods are tested and proven.
in the form of printed material.

These tools,

They are available to you

For example, the A. D. E. General

Information Manual will introduce you to the survey and implementation phases of this new system.

In addition, we have prepared a de-

tailed reference manual to provide your engineers with the "How To
Do It" information necessary to develop an A. D. E. system.

I:
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A PAYROLL
AND
LABOR DISTRIBUTION
PROGRAM PACKAGE

by

ELIAS C. TONIAS

and
RICHARD C. DEVEREAUX

December 1963
ERDMAN & ANTHONY

82 St. Paul Street
Rochester 4, New York

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TITLE

A Payroll and Labor Distribution
Program Package

AUTHORS

Elias C. Tonias of Erdman & Anthony,
Consulting Engineers, 82 St. Paul Street,
Rochester 4, New York
and
Richard C. Devereaux of IBM Corporation,
540 Main Street East, Rochester 4, New York

DIRECT INQUIRIES TO

EliasC. Tonias

ABSTRACT
The objective of this paper is to demonstrate
how some free 1620 time may be utilized in
a relatively small scientific or engineering
installation through the use of a package of
commercial programs. The successful
operation of such a program package since
the first of this year (1963) has helped to
justify the installation of a 1620 in another
firm. This package, designed for use with
the basic 20k 1620 Computer, with paper.
tape 110 and without any peripheral equipment,
produces the payroll report,. and complete
labor cost distribution and breakdown reports.
Written in FORTRAN for easy maintenance,
the ideas from this program package might
prove a worthwhile tool in justifying the
installation, or in increasing the production
ratio, of a small account. With a few or
even no alterations, parts of the package may
be used to handle other various time and cost
distributions.

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TABLi£ OF CONTENTS

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I.

Introduction

•••••••••••••••••••••••••••••••••••••••••••• 1

II.

Systems Analysis and Design

III.

The Programs

••••••••••••••••••••••••••••• 2

.................................... 4
B. Payroll Register .................................... 5
C. Payroll Checks ......................................
D. Payroll Deductions Register ......................... 6
E. Labor Distribution Data Sorting ..................... 6
F. Labor Cost Distribution ............................. 8
G. Labor Cost Breakdown Bi weekly .................... 10

A. Data Preparation

6

H. Labor Cost Breakdown

Accumulati ve

IV.

Timing Considerations and Limitations

V.

Swmnary

VI.

Appendix

.................

10

................. . 11

..................... .......................... . 12
'

•...•.........................•...
Time and Expense Account Sheets ...•..........
Payroll Master ........•......................

A. General Flow Chart

14

B. Sample

16

C. Sample

18

D. Table of Addresses for the Data Preparation Program ••• 19

............................. 20
F. Sample Payroll Check ................................ 21
G. Sample Payroll Deductions Register .................. 22
.............. 23
H. Sample Labor Cost Distribution
I. Sample Labor Cost Breakdown Reports .................. 26

E. Sample Payroll Register

~eports

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INTRODUCTION

It is no secret that the 1620 is not designed for excessive
data handling and the IBM Corporation definitely is not marketing it
for commercial uses. In fact it is a small scientific computer and
as its many users will attest, it performs with excellence in this role.
Despite the machine's fine record in the field, its inability to handle
excessive data (especially the basic 1620 with paper tape) produces
one distinct problem area which can present itself during the selling
phase or after the installation of the system. It is known as 1Il8chine
utilization.
Present day engineering or scientific establislunents do:have
considerable, if 1 not abundant, amounts of commerical (accounting) type
of work which could be automated and thus increase the utilization of a
computer. This problem of the 1620 utilization is not as predominant
in a large data processing oriented company as it most probably has a
commercial computer system. In such a company the 1620 is being looked
upon for the engineering or research and development departments. A
large company would presumably not expect high utilization on a machine
which would be operated in an open shop atmosphere. Their objectives
would be more intangible, such as the release of engineers for more
creative type work and the increase in speed of routine computations.
On the other hand, in a small engineering account, where the
rental cost of $1,600 per month represents a large investment, the subject
of machine utilization is of great concern. Even though a two or three
hour run a day can justify the installation of a 1620 in such an account
there still is the feeling that more should be gotten for this kind of
money. It is for such an establishment that this paper is primarily
intended.
The comPAny for ahich these programs were developed has a
bi-weekly payroll for two offices, one of ninety and the other of forty
employees. It takes about two days (16 hours) of the computer's time
every other week to produce the complete payrolls and labor cost distri~
bution. The operation of these pregrams since January 1, 1963 has helped
to increase the average utilization of the computer to 40 hours per week.
As for economic value of these programs, it cannot, be measured in dollars
and cents. It places valuable up-to-date information about the cost,
progress and estimation of projects in the fingertips of management in a
matter of a few hours. Neat reports may be produced in a moment's notice.
It may be said that these programs in addition to increasing machine
utilization do contribute in improving management operation.

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SYSTEMS ANALYSIS AND

DESIGN

In trying to analyze and successfully design a payroll and
labor cost distribution program package the following must be taken
into account: the memory capacity of the computer, the presence or
absence of special features, the type of input-output and the method
of operation of the shop including personnel availability. The concern
where these Payroll and Labor Cost Distribution Program Packages were
developed employed the basic 1620 with a 20k memory, without any special
features, and with paper tape input-output hardware. This concern, a
consulting engineering outfit, operates on a semi-open shop basis without
a specialized machine operator. One cannot start any simpler than that
nor can one have any more handicaps as far as the 1620 is concerned.
Of the three major languages of the 1620, machine, SPS, and
Fortran, the latter was chosen by the authors because the programs could
very easily be maintained and revised according to the needs of the
company. In addition, Fortran offers a lot easier means of programming
and debugging and to the best of the author'S knowledge such a task would
be a first. It must be noted here that all of the following programs
(see exceptions later in this paper) were originally written in Fortran
with Format and later changed to UTO Fortran. For those unfamiliar with
UTO Fortran, it was developed by Mr. E. Stewart Lee and Mr. James A. Field
of the University of Toronto, Ontario. UTO in general is similar to Fortran
with Format except that it brings the program origin down to 06950, is
slightly faster, the subroutines are about 10 per cent shorter, the use
of EXECUTE PROCEDURE n statements (similar to CALL statements) facilitate
programming and save memory when properly used, and has quite a flexible
input fonnat (input data does not have to be in strict accordance with the
fonnat statement).
One question that had to be answered early in the planning stages
was the availability of checks for the 1620 typewriter. Cardboard checks
were out becaU5e they necessitated a typewriter RPQ. Paper checks were
chosen and designed by IBM. A picture of a check appears in the appendix
of this paper.
The check is of the high-low design with the stub under the
check proper. The perforation of the right .an be placed any where.
When designing a pay check the following hints should be considered:
(1) When designing the check, it is advisable to make the
spacing between the printed lines a multiple of two or three. This means
that at program time during the carriage control operations, the typewriter can be run in double or triple space mode and thereby save a
considerable number of carriage returns •

•

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(2) Hint (1) may be accomplished with statements of the
form 1000 FORt\1A T (f/) or if using UTO Fortran with the CONTROL 102
statement. In UTO the statement CONTROL +08 may be used for tabulation.
(3) The check should be designed so that variable alphameric
data appears only on the left edge. Note the example check where the
two dates (XX/XX/XX) and the name are all left adjusted. This is very
important in a situation such as the following. The employees name is
part of the master record and must be the first data in that record.
For example, the name and year to date gross, FICA, and withholding
taxes would read in as:

0

ACCEPT TAPE 100, YGR, YFICA, YF\vT
100 FORMAT (ISH EMPWYEE NAME F9.2,F7.2,F8.2)
The variable alphameric name is stored in the format statement
itself. When saying PRINT 100, the name alone will be printed out. If
the name were not left-adjusted in the master record and in the Format
statement, it would be impossible to get it out alone. Another technic
that could be used is to carry the name all by itself in a separate
master record.
The payroll system for which these program packages were
designed is based on the following criteria:
(a) Employees are to be paid bi-weekly with time being
reported on two time sheets (the programs may easily be changed to
any other pay system).
(b) Reported time is to be reported by each employee by
operation. (also referred as activity herein) for each project.
(c) There are three types of paying systems (pay codes):
straight salary (code 1), straight time (code 2) and time and a half
for overtime (code 3).
(d) There may not be more than 130 employees. This company
uses 20 activities only. If need be this number may be increased at
the expense of running time.
(e) Three master records are to be kept:- (1 )the payroll master
tape containing the name, number, rate, pay code, dependents, year-to-date
gross, FICA, tax withholdings and expenses, quarter-to-date gross, FICA,
tax withholdings, social security number, hospitalization, bonds, savings,
life insurance, pension, and miscellaneous deductions; (2) the project
master tape containing the project number and todate totals on direct labor,
expenses, and indirect labor (sick leave and vacation); (3) the activity
Master tape containing to-date totals for each activity for each project.

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As mentioned in the introduction the biggest handicap in
this opera~ion is that of handling data. Because of this, changes
to any of the master tapes should be kept to a.minimum as the slightest
revision requires the reproduction of the entire tape. Master tape edit
programs may be written to facilitate tape revisions, especially massive
ones such as the zeroing of the registers at the end of a quarter or the
year.
the data.
II I.

The other case where data handling enters the picture is in
This is discussed in the following section.

THE PROGRAMS

Below is a general description of the programs in the Payroll
and Labor Cost Distribution Programs.
A.

Data Preparation

Considerable thought was given to the input data since this
was the start of a chain of events which would produce all of the payroll and labor distribution reports. As part of this paper's appendix
one will find the time sheet used for reporting work time and expenses.
Since this data form the basis to both packages it is typed into the
Data Preparation program. The sequence of this data is composed of a
minimum of three records per employee. The first contains the employee's
number and the remaining contain the activity, number of hours or
personal expenses and the number of the project. A negative activity
denotes the end of a time sheet. For a bi-weekly payroll two negative
activities are required. The program immediately punches on tape the
accepted data in a similar format. This is the Labor Distribution
Data Tape. Then it proceeds to compute the regular and overtime hours
and personal expenses on a weekly basis which is stored in memory for
ea.ch employee. This information will l~lter produce the Payroll Data
T~pe.
To do this the Payroll Haster Tape containing the employees'
pay codes is read into the program at the start of the run storing each
employee'S number and pay code. It should be mentioned here that
activities 18, 19 and 20 are reserved by the programs for vacation,
sick leave and personal expenses.

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One bit of logic that might be helpful in the prog~m is a
technique for being able to go into memory and make corrections after
all data is typed in and while the payroll dat~ tape is still stored.
This could be accomplished by assigning a storage cell number to each
employee as he is entered into memory for the first time. This storage
cell nmnber would teen represent the position in all four arrays (man
number, regular hours, overtime hours, expenses) where this particular
employee's data could be found. The number, along with a memory map of
the arrays would then give the exact location of any data in question.
A portion of such a table is included in the appendix. If an error were
made in the typing of data for the say ninth employee the table will show
that this employee's number, regular hours, overtime hours and personal
expenses would be found in addresses ,19750, 18450,17150, and 15850
respectively (see table in appendix).

5

It will be advantageous in the Data Preparation Program to
have a dump of grand totals at the end showing regular hours, overtime
hours and personal expenses. These totals should balance back to an
adding machine tape which should have been taken when auditing the
time and expense sheets. The totaling routine should be programmed so
that it may be "branched to" after any corrections to the memory table
have been made. At this point if everything balances, the Labor
Distribution Data Tape may be removed from the punch and the punching
routine of the Payroll Data Tape initialized.

•

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This marks the end of the combined operation between the
Payroll and Labor Cost Distribution Programs.
B.

Payroll Register

The first step in the Payroll Program Package is to obtain
the payroll register showing all incomes and deductions for all employees
of the current period. This, the Payroll Register Program, necessitates
as input the Payroll Master Tape and the Payroll Data Tape as well as the
starting check number and period ending date which are entered via the
typewriter. The payroll data is stored in four arrays - employee number,
regular hours, overtime hours and expenses. The Payroll Master Tape is
then read in, the arrays are searched for a match, and the pertinent data
from the master and detail are combined to calculate the net pay for each
individual. Two lines of printed output appear for each employee· showing
the standard payroll register items • Accumulative totals are kept for
each item and at the end of the report these totals are crossfooted for a
check against the accumulated net .pay.
In this program as well as in the next there is the problem of
half adjusting and truncating a product. Let it be. assumed that a. straight
time employee waged at $4.375 per hour has wori{ed 48.50 hour$. Hence

PAY • 4.375 x 48.50 • 212.18750

For obvious reasons the employee should be paid $212.19. Fortran
however will carry it as 2121875003. When several such products are
accumulated there is going to be a disagreement between the actual
swns and those of Fortran. This may be remedied by the following
statement:
PAY • RATE x HOURS + 0.005 + 100000.0 - 100000.0

which will be executed
PAY
PAY
PAY
PAY

•
•
•
•

8S

4.3750000
212.18750
212.19250
100212.19

follows step by step

x 48.500000
+ 0.0050000
+ 100000.00
- 100000.00

•
•
•
•

212.18750
212.19250
100212.19
212.19000

When completed the payroll register should be spot shecked by
the"personnel responsible to insure complete accuracy. There is no punched
output to this program.

I

oj
I

17

wm

. -'JWoof

6

C.

o

Payroll Checks

As soon as the pay~ll register is checked and accepted the
Payroll Checks Program may be used to produce the paychecks. Basically
this program is similar to the previous one using the same input (instead
of the check number the check date is entered). In addition to the checks
this program updates the Payroll Master Tape concurrently with the checks
and at the end it produces an Adjusted Pay Rates tape. Such a rate is merely
the employee's gross pay divided by the number of hours worked.. This will
affect only the straight salary and time and a half employees. For example,
a straight salary employee who is always paid for 40 hours and ha.s a rate
of $4.375 has worked 48.50 hours. To give a more complete picture in the
distribution reports all of the 48.50 hours should be considered. Thus
this employee's adjusted pay rate is
Adjusted Pay Rate • 4.375 x 40.00/48.50 • 3.6082474
Had the employee being paid time and a half for overtime then his adjusted
pay rate would be
Adjusted Pay Rate • (4.375 x 40.00 + (4.375 x 1.5) x 8.5)/48.50 • 4.7996134
This adjusted rate may later be used to distribute dollar increments of the
48.50 hours over the various projects on which the employee worked. This
rate can be calculated at the same time as the employee's check and stored
in memory. Since the Payroll Master tape is updated during the production
of the checks the Adjusted Pay Rates will have to wait until the end of the
program to be dumped on tape. These rates are later used with the labor
cost distribution programs.
D.

Payroll Deductions Register

Because of memory and output limitations not all deductions are
itemized in the payroll register. These deductions, bonds, savings,
hospitalization, etc. are itemized for each employee by the Payroll
Deductions Register Program utilizing the just updated Payroll Master Tape.
E.

Labor Distribution Data Sorting

Having completed the payroll phase of the operation we may
proceed with the labor cost distribution phase.
It was stated under the Data Preparation Program that data
read directly into the program from the time sheets were divided ·into
the Labor Distribution Data Tape and the Payroll Data Tape. Since it is
possible for an employee to report time under several activities for several
pro jects time data will have to be sorted in one way or another. Such a sort
would be easy for a card machine. For a tape machine though it is a
different story. Data could be sorted manually before the Data Preparation
Program run but this would defeat payroll automation. As a matter of fact it
would be a rather involved affair. Also mentioned earlier was the Project
Haster Tape containing all projects of the company with their respective costs.

o

---~---'-----------~"''"-'''''-'''"'--~'~=~=----=----=----=-----=--=---,

7

It is possible for the operator to type an erroneous project number
that is not included in the Project Ha.ster Tape or that a new project
had been added without the master being updated. For these reasons two
programs were developed in machine language to utilize memory space.
These are the Project Completeness Test and The Labor Distribution
~ Sorting programs.
The Project Completeness Test program first reads the Project
Master Tape and stores the project numbers only; then it reads the Labor
Distribution Data Tape and compares each project number with the table
previously stored in memory. If a match does not occur the project
number on the Labor Distribution Data Tape is printed on the typewriter.
At the end of the run the number of projects and number of records are
typed. The number of records re fers to the records of the Labor Distribution Data Tape containing an activity, hours or expenses and a project
number. When this test has been made the Labor Distribution Data Tape
may be corrected if need be through a tape correction utility program.
The Labor Distribution Data Sorting Program does a little more
than just sort data. First it counts records to insure that no unauthorized records have been dropped or added while correcting the Labor
Distribution Data Tape. Second it sorts data. The program inserts the
employee number to each of his records, changes each record from an
alphameric mode to numeric mode dropping all decimals and arranging them
in the format shown below:

XXXXX XXX XXXXXXX

...

J

\
whe re 1:
2:
3:
4:

______

2:3

•

.,

4

:t-

pro ject numbe r
employee number
activity number
hours or personal expenses

Each record contains a total of 16 characters including the record mark.
These records are stored in memory beginning in location 19999 and working
on downwards. The sorting of the -records begins when all records have been
stored. It is a simple replaceable sort routine which starts at the top of
memory and keeps comparing two adjacent storage cells (records). If the
upper is less than or equal to the lower, no replace takes place. If the
upper is grea,ter than the lower, the two records .are interchanged, a switch
is set and the program steps down one record to compare the next two. This
continues until one complete pass on the records has been made. At this
point, the switch is checked. If it is on (meaning at least one record
out of sequence), it is turned off and the comparing routine is repeated.
When the switch is finally off after a complete pass, the internal sort
is considered terminated. It should 'be emphasized here that during the
compression phase (changing data from alphameric to numeric) where data
is edited in the input area and placed in a cell, the comparing field can
be set up as one field and still get three breakdown levels - activity,
within man, within project - providing the field is arranged as described
in the previous paragraph.

o
1

~!

II·'.,',

'

II!

8

o

Third, at-the completion of the sorting routine the program
will commence reading the adjusted pay rates which were produced at
the end of the payroll check production. The rates and employee numbers
are converted into numeric characters and the memory cells are searched
for an employee number match. When the match occurs the rate is multiplied
by the corresponding hours (no multiplication is perfonned for activity
20 - personal expenses) and the hours are now replaced by the cost. Each
employee number of the Adjusted Pay Rates tape searches the entire memory
map as it is possible for one employee to appear in several records.
Fourth, when all hours have been convered into costa the
program will type the total direct and indirect labor cost which should
agree with that of the payroll register. It is obvious that the adjusted
pay rates of personnel other than those of straight time will not be the
same with their original base pay. These adjusted pay rates may contain
as many as eight significant digits. This problem is similar to that of
the payroll register and payroll checks of rounding or truncating products.
To compensate for this each product (rate times hours) is half adjusted to
the nearest penny and all truncated parts are accumulated to form the
truncation or rounding error. This which may be negative is assigned to
project one, administration, to activity one, general, and to employee
zero, fictitious. Hence the gross payroll figure plus the rounding error
of this program should equal that of the payroll register.
Fifth and last the fields of each record are changed back to
alphameric and are punched on tape to produce the Sorted Labor Distribution Data Tape.
F.

Labor Cost Distribution

This program is essentially a listing with some accumulating
of the sorted labor data tape. This tape is now in project sequence.
Within each project are the records of each man who worked on that
project during the last pay period. Within each man are the operations
which he performed on that project as well as the distributed money.
There are actually three phases to this program which give three separate
reports.
The first report shows by employee number all the employees
who worked on each project this current period. All the activities
for each employee are accumulated and this accumulated money total is
segregated into direct and indirect labor and personal expenses.
The second report of this program is merely a listing of the
totals lines for each project. It gives a neat, condensed, summary
report of what the projects did this period. This is accomplishee by
storing project number, total direct labor, total' expenses and total
indirect labor for each project while producing the first report.

0 ",:
,

,

--------.-----~--.

9

The third report is the pro ject sta'tus report showing all
pro jects of the company whether work was done or not on all of them.
For this the Project Master Tape is used. As the master is read in the
project number from the tape searches the memory (see previous paragraph)
for a match. If a match does occur the figures are combined and the
master is updated. If no match occurs (no work done on this project
this week) the figures remain the same. There may be printout options
at this point. One which the user would probably want is a project-todate report showing three totals for each pro ject. Line 1 shows project
totals to-last period, line 2 shows project totals of this period (zeroes
may be present) and line 3 shows the updated project totals (sum of lines
1 and 2).

~~.,

I,

~

point of interest to this program as well as to the last of
this series is that of the grand totals appearing at the end of the
various reports. Fortran handles only eight significan figures thus
limiting totals to $999,999.99. If the elements of a total added to
more than a millien dollars the machine computed total would be a
truncated figure sometimes several dollars off the actual sum. This
problem may be eliminated using Fortran in the following manner. Let
SUM represent the accumulative value of an item and COST the value of
anyone element of the same item so that
A

SUM •

L COST

Before incrementing SUM by COST, COST is compared with the difference
between 999,999.99 and SUM. If the cost is smaller than the difference
the addition is performed. If not a carry-over factor is incremented
by one and the sum reinitialized by the difference between COST and the
first difference. Thus in UTO Fortran a procedure could be set up as
follows:
BEGIN PROCEDURE 100
DIF - 999999.99 - COST
IF(DIF-COST) Ill, 110, 110

110 SUM - SUM + COST
RETURN 100
III KARRY - KARRY + 1
SUM - COST - DIF - 0.01
END PROCEDURE 100
where KARRY indicates the millionth carry-over factor. Note the penny
(0.01) in the last statement of the procedure to take care of the
difference between a million and 999999.99.

o
'hI

I

I'i
Ii
I

\

"l

10

G.

o

Labor Cost Breakdown - Bi weekly

This program merely rearranges data from the Sorted Labor
Distribution Data Tape. That is, it reads in all the details for a
project number, accumulates the amounts by activity nuulber, and punches
out a new tape, the Labor Cost Breakdown Tape, which contains the project
number followed by each of the operation numbers and their respective
monies. This is done for the entire input tape, so that the output tape
contains all the project numbers followed by all the activity numbers
and amounts. This program generates a new activity code number for each
project Activity 21 representing an accumulative total of all the money
from all the other operations on that project.
There is also an optional print-out to this program. Any or
all projects may be printed showing money spent by each emPloyee under
each activity for a project. Because of space limitations and the extend
of the arrays only eight employees are to be included on a page. Thus
several pages may be needed for one project.
H.

Labor Cost Breakdown -

Accumulativ~

This is the last of the Labor Cost Distribution series of
programs. As one may recall the third report of the Labor Cost Distribution Program updates a Project Master Tape showing labor breakdown
by direct labor, personal expenses and indirect labor. This last
program gives the labor breakdown by operation within project. Because
there are 21 possible operation under each project, the Activity Master
Tape is actually composed of three reels of tape. The first carries all
the projects with activities 1 through 7. The second aarries all projects
with activities 8 through 14 and the third carries all projects with
activities 15 through 21. As a reminder activity 21 represents the
total cost of activities 1 through 20 inclusive.
This program is executed in three passes. At the beginning
of each pass the Labor Cost Breakdown Tape is loaded and the program
selects and stores activities 1 - 7, 8 - 14 and 15 - 21 depending whether
it is pass one, two or three. Having stored this information the
corresponding Activity Master Tape is passed printing the breakdown
report and punching the updated Activity Master Tape. The report may
take a similar form to~hat of the project status mentioned under the
Labor Cost Distribution Program. The company that developed these
programs however chose to eliminate from this report the top line
showing project-to-last period totals.
This final report is an extremely comprehensive breakdown
of the allocation of funds on the various projects. When a project
is completed, the final master records become an invaluable reference
,to be used in the future for estimating costs of similar jobs and in
a way to predict or forecast job progress and man power alocation.

11
IV.

TIMING CONSIDERATIONS AND LIMITATIONS
Below is a list of limitations to these programs:

0

(a) The number of employees is limited to 130 in anyone
run. Slight variations in paying systems and in state or local taxations may increase or decrease available memory and thus introduce
new limitations on the number of employees.
(b) In the Labor Distribution Data Sorting Program there
is room for 1048 records.
(c) An increase in the number of activities will increase
the number of passes in the Labor Cost Breakdown Accumulative Program.
(d) The following timings are based on 90 employees working
on 35 pro jects at anyone time and reporting their time in about 500
records. The total number of projects being reported on the distribution
and breakdown reports are 70. It should be kept in mind that these
figures of time are for a bi-weekly payroll.
1. Time and expense sheets are turned in by Friday night.
2. Time and expense sheets are audited Monday morning.
3. Revisions and adjustments to the master
tapes ••••••••••••••••••••••••••••••••••••••••• 1.00 hours
4. Data Preparation Program

.••••..............•...

5. Payroll Register Program

....................... 0.75

2.50

"
II

6. Payroll Checks Program ••••••••••••••••••••••••• 2.25

n

7. Payroll Deductions Register Program •••••••••••• 0.50

II

................ 0.75

ff

Report #1

....................................... 1.00

II

Report #2

...................................... 0.25

II

8. Labor Distribution Data. Sorting
9. Labor Cost Distribution Program

Report #3 (project status) ••••••••••••••••••••• 0.75

"

10. Labor Cost Breakdown - Bi weekly
without any print-out •••••••••••••••••••••••••• 0.50
(allow 5 minutes per project
print-outs)

"

11. Labor Cost Breakdown - Accumulative •••••••••••• 2.25

It

12. Average minimum total •••••••••••••••••••••••••• 12.50

It

G

ZUMTfi'IYW

12

o

The secret to a smooth and fast run is to avoid last minute
changes, and to train the employees to report their time and expenses
properly thus eliminating corrections and revisions while a $1600 a
month machine is running doing nothing but tape corrections.

v.

SUMMARY

It was the purpose of this paper to present guide lines and
documentation for implementing a payroll and labor distribution application
on a basic paper tape 1620. It takes but a little imagination to develop
additional utility programs to handle information developed by these
programs to prepare special reports such as Employee Taxable Wage
Reports, W-2 For.m Information (to the best of the author's knowledge
there are no W-2 forms that will fit the basic 1620 typewriter), Sick
Leave and Vacation Tally Reports and a number of others. With slight
if any at all modification the distribution programs may be used to
handle other distributions unrelated to the payroll.
These programs have supplied their developers with up-tothe-minute information on the financial status of all their projects information which in the past was delinquent and incomplete. It is
the authors' belief that such programs as these presented in this
paper although not money making will provide a user with invaluable
service.
VI.

APPEND IX

Included in the appendix to this paper is a general flow
chart of both program packages and input-output samples of their most
important phas~s.
The back side of the
the packages. In the register
represents the horizontal sums
grand total is obtained twice;
horizontal sums.

time sheet is not used in either of
of payroll deductions the last colwnn
of the other columns. Note that the
one from the vertical and once from the

Two projects of the labor distribution report are shown on
same page. Actually they would appear each on a separate sheet
the carriage being controlled by the program. Totals of the project
SUlllllary are obtained at the end but are not shown in the sample.
The
project status at the bottom shows a sub-total and a total. The
developer of the programs wanted to divide the projects into two groups
each having a subtotal. The subtotal shown is that of the second group
of pro jects •
t~

o

13

The bi-weekly Labor Cost Breakdown report shows a partial
listing of project No. 61151:' There are only 16 of the 20 activities
shown. The number acress the top indica,te the employee numbers. Had
there been more than eight employees a second or even more sheets would
have been needed. In such a case the column headed ACC would indicate
the accumulative totals to that sheet. The last display shows a partial
Accumulative Labor Cost Breakdown report. The numbers 15 - 21 across
the top indicate the'activity numbers. There are actually two more
sheets to this report for activities 1 - 7 and 8 - 14. Note that activity
21 is the sum of the first 20 activities.

~\

~;

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'I"

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2-

I#-

GENERAL FLOW CHART
-

o

PAYROLL -

lidding
Time
SlJeets

MaclJil7~ 70~

of Hour,$ and EX,CJenses
~K

-·-'L-.-/---II

I.--

Expense
5heets

L3olonce ;riflJ fhi~ ~,a!'
lIoars O'~ £.xp~/'}se s

I
Totdls

ChecK
Labor f)istribufiol7
Oofa 7dpe

Dofa

70

PreporQTiol7

Program
Ad./'vsfed Poy

Rare..s ?Ope

LaborCotjf
Ol:J fnol./tlol1
Proql'?:1m
Pac~of1e

Payroll
001'0 hpe

Payroll
Chec.ks

Payroll

Regisler

Program

Program

Poyroll A1Q.s/~r

Tape
tlpdo/~d 'pqyro//
MO.5f~r 7Ope. Use

it? Pay- /Jed. Re9.

·0

t:JaIa/Jc~ OJeds
-~

fo

...--

Pdyr()/I £e?isler

Payroll
Checks

GENERAL FLOW CHART
-

Lfl80R.

COST DISTR./I3UTION

0

Lobor '/)i6fr:
~-~

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.

/Jato Sorf.

~----'

Ad./v~f~d Pay Rofe.s ?Ope

Program

Lahor Di.5lrib. Dafa ?Ope

j

Pro.leef
Masfer ?ape
Sorfed Labor

Oi6frlo"f/on

Oofa 7bpe.
Labor CO.$f
fJreak.(8/JI'eeJ) Opfiol'Jd/
.Program

Labor COst
Olslribuflon
f7roqrCln7

8reak.
,ee,oorf

(8iJl'~

LaborCosf

Breakdown Tope
t/pdafe ProJect
A1asler lOpe

_-..1..---__
Acfillify
LaborCosf
Bred/:::. .(Ac~UIJ)

A1a~f~r

lOpes

Prog/?::J/77

LoborCOsI

P,sfn'b"

Oi.slr;buT:

SU/7Jl17Qry

t/pdofed Acf/I//ty
Mosf~r

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Prqjed
.5faftls

t

~ f}%nce

•
I
Report- 701015 ,.J

70 Payroll Reg is fer
~7

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a

'ERDMAN
-

LOCATION.

DAILY TIME

/

HOURS
W

--

8

3

8

/3

LOCATION;

R~esfe;; /\I. Y NAMEJoha

--

T

-

F

TOTAL

PROJECT

HOURS

NO.

!

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TITLE:

WEEK ENDINGI

OPER.

J. ../oh/JS -# 1

Protl:smon

/1-22-~3

!

-

T

M

S

DAILY TIME REPORT

I

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--OPER.
DAILY

ERDMAN 8 ANTHONY

I

REPORT

John ../. John s ~11
TITLE: fl.
1'1.
'/0 'S/nQI?

WEEK ENDING:

S

A'NTHO NY

NAME:

Roc/;e.sler; Il/. Y.

NO.

o
DAILY HOURS

NO.

S

.3

8

M

S

T

TOTAL
T

W

PROJECT
NO.

HOURS

F

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8

8

8

Z

-

8

2214.

I

8

8

24- 22/4.

I

24

2214. J

12

10

1114.

13

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4

8

8

220/.

8

//14.

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Employee( JSitr1tire

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1 HEREBY CERTIFY that the ti"" reported above is a true and comp.et.
fA myll~.lr
period.

I liz I

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I'

----

11

...

!

I HEREBY CERTIFY 'that the time report.d above ia a true cmd complet.
lng
p.rlod.

sto(U'

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Empoye, ;511 no(0/"
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(J\TTACH RECEIPl"S WHEN ~BTAlNABL~ }'Olt ALL ITEMS)

==ii:=:;=='~=~~=;==;==~=::::::~==T=====\ii;=1 ====:.~~=. A~~

[~T

===:'

(Please print)
statement of

K'£NETfI

Date

Itjtl;/63

/p.zj&3

-

Brief statement of itinerary, etc.,
showing nature of expense items listed
Day in columns right

~i

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Jab //l~?eCfiOI?

~1/5/.

JOb

/PI/51,

1115jlPch'oJ?

===:
Mileage

II
11M!

II
r

and
Transp.

Lodg-

4.DO

6.50

ing

....-:

Other

Meals (Itemize) .

7,50

~y

ToW

/8.00
4.f)O

4.00

I

__..--~
;./

=

S I

11.1:

-#:'7

ff~

JII/, !3ROWN

Man~ Address
~=

I~_~===Y_!

W

II

T

=====:::~

F

-==

-===

====

--=-:

t

I

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S
l\{

IpJfo3
I~D#3

T

w

Job //J.5jJecfi olJ
. 5VfJj'it'f's

4.00

60/5/.

I

22-14.

il ,

Zoo

3.00

Z,2B

2.28

/,2.tJO 0,50 10.50 2#2/3

8QB

\I

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T

-

F
~iEREBY CERTIFY that this 1s a true and
c:)mple!c st.atement of authorized expenses
incurred by me in connection with company
b-:.lDineSSl for thls p1lY'rC!'9 period.

J

Employee

•

keMdlt

(J).

h1!!-o/

~~~~~.-----------------------

r?

------

0

----~-

-

---

0..

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~j

l

ERDMAN AND ANTHONY, CONSULTING ENGINEERS

---'1 i2 2/63-------------------- PAYROLL MASJER.J'APE- - - - - - - - - -- ---- - --- -- - - - - - - --- - - -- - - -

--1

----------~-~----------------------------------------------------------------------------~
~

)

kmpL

Pay

- ____4 ___A:.- - - --- - - - - - -- --- - --\
KENETH W. BROWN.
7705.92 174.00 1064.21 164.2~~L29
I
94 1 33 46
1 .00
5. 50 • 60 "
i
i

------------------------------------------------------------------------------------------,
______ 3__ 3.!~SQ_~__ _.. Q9 ___ .!1l1l __ ~... ~___ ...,oj_1_.l29j_.OO_____._O.0_j52_.J 0_. ___ 2J __.61 ____ .______________ J
l

MARY BENSON

126 34 9929

.00

•

.00.60

6909.45 174.00

813.16

108.81

515.68

____999 ___ .1009_ 0___ -,.00 ___ .. .0.0 ___ ... .0.0___ ...o.o_!)_____ .. DD__ __ ....0.0_______0.0__. __ ....00__________________ .:

.2 _________________ .. _________________________________ - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

1' _________________________________________________ ______________________________________ .__
~

~

,,/9

TARtE OF

o

ADDRESSF~

The addresses shown in the table represent the address or the left most position
of each Tariab1e.
Em'RY
NUMB.

MAN

REG.

M.

NUMB.

1

19830

HOORS
18530

HOURS
17230

2

19820

18520

3

19810

4

PERS.
EIP.

ENTRY

MAN

REG.

NUMB.

NUMB.

mRS •

OVT.
HOUJG

EXP.

17010

15nO

15930 • 23

19610

HOURS
18110

17220

15920

24

19600

18300

17000

15700

18510

17210

15910

25

19590

18290

16990

15690

19800

18500

17200

15900

26

19580

18280

16980

15680

5

19790

18490

1n90

15890

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__________________________ EBQ~A~_AMQ_A~I~ONY,-CONSULIING_ENGJNEERS _______________________ ~
i
_ _~REG.H

OVT.H

REG..P

OVT.P

GROSS

EWJ

FICA

SWT

DED

EXP

NET. __

i

-JOHN-J:-JOHNS---11858~-------------4443~75-----------------------------------------------1

____ 1 ___ 80 .00_10.00 __ 180 .00---33. 7S--213 .. 1S---1 .. 1S __ 38 .. ~8 ___ 5.29---- 25.60- - - __ .• 00_--136.63--.,

~

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80 !O_.28 .083.1 L ... 10 .01._ . 6.34_225.12_ I

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_________________________________________ --______________________________________________ J
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11 _________________________________________________________________________________________ _
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ERDMAN AND ANTHONY

223

,/

CONSULTING ENGINEERS

,/'

ROCHESTER, N. Y.

DATE

[i1-;~9/63

*4

CHECK No·118

•
:

:

EAST AVE.

BRANCH

~

•I

~

136.63

/"
Or,c/C/~L

Y.

1:022 3 111 00

/
DOLL.. r(S .CENTS

/j,ef'llr

TO GENESEE VALLEY UNION TRUST CO.
ROCHESTER. N.

t?~~//

1•

JOHN J. JOHNS
PAYROLL ACCOUNT

II

,6~CI

58

/"-//0>-

PAY
TO THE
ORDER

OF

//

~81:

5

~0"'8 ~8b

S/6/V'/J r(/£E.5
3 111 :iii'

-0
(.ri
STATEMENT OF EARNINGS AND DEDUCTIONS

REGULAR
HRS.

OVERTIME
HRS.

80.00 10.00
FED. TAX

F.I.C.A.

38.48

7.75

REGULAR
PAY

RATE

OVERTIME
PAY

2.250 180 .00
STATE

TAX

5.29

HOSP.

INS.

33.75

BONDS

.00

GROSS
PAY

EXPENSES

213.75

SAVINGS

PENSION

.00 25.00

.00

.00
N.Y.DISA.

.60

MISC.

.00

NET

PAY

136.63

YEAR·TO-DATE TOTALS
PER. END. DATE

11/22/63

GROSS PAY

FED. TAX

4443.75

799.88

F.I.C.A.

161.20

STATE

TAX

PENSION

100.58

~
.........

CJ

(j

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- - - - - - - - - - -

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_________ ._ . . _ _ _ _ _---=-PRQJECT

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PROJECT ...NQ.

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---.---.-------, ---- ERDMAN AND ANTHONY; CONSULT I NG- ENG'! NEERS----·--·-·

10/11/63

LABOR

2203.

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",00

• 00

538.20

.. 00

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0

13

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0

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ERDMAN AND ANTHONY

CONSULTING ENGINEERS

---------------------------------~----~---------------------------------------------_.----

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SPIRE
(System for Personnel Information REtrieval)

Prepared by:
G. J. Reed
Albuquerque Division
ACF Industries, Inc.
December 9, 1963

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INTRODUCTION
The management of ACF Industries, Incorporated real ized that manual methods for
accessing personnel information were inadequate both with respect to speed and
accuracy. Many requests for summarized information either could not be answered
or became a costly venture in man hours alone. As an attempt to remedy th is problem, a punched card system was designed to hold personnel information in coded
form. Th is card system proved inadequate in speed, type and amount of information
stored, and updating capabil ity. With th is system as a background, SPI RE was
developed.
SPIRE is an acronym for "System for Personnel Information REtrieval. II Th is system
was designed for and implemented on a magnetic tape 60K IBM 1620 and has been
operational since February, 1963. Since that date, no revisions have been necessary in the type or format of the information.

11.

CONTENT
The informat ion content of SPI RE was spec ifica Ily designed for ACF's use. Personnel
information was carefully analyzed and organized to determine what information had
been recorded by the previous system and what part of this information had been useful. By categorizing the useful information, it was possible to devise coding techniques
wh ich mad~ each item unique in the system and thus recoverable.
The information in SPIRE is broken into the following five categories:
1.

Personal - name, date of birth, se,x, date of hire, marital status, socia1 security
number, etc.

2.

Previous Experience v ision, etc.

3.

ACF Experience - complete file on all pertinent happenings at ACF with the
employees status (job title, grade, salary, department, etc.) recorded at the
time of the action.

4.

Education - includes all completed levels of education and the extent, ma jor,
minor, and univ.ersity, if applicable, 'for each level.

5.

Mil itary Experience - contains the same information as the previous experience
category with the branch of service added.

,

job code, position title, time on job, extent of super-

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To obta in th is information in coded form for all employees, superv isors interviewed
their subordinates and coded their education and experience backgrounds. The ACF
experience involved so much detail that it was necessary to code each part of the
employee's experience using the permanent personnel records. As new employees are
h ired, the ir backgrounds are coded and added to the master file.

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.

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III.

APPLICATIONS
Although SPIRE was developed as a general purpose information system that could be
used for the generation of virtually any report involving personnel information, one
appl ication appears to be the most notable, that of in-plant recruiting. Prior to the
development of SPIRE, to fill a vacant position from within required the personnel in
Salary Administration to have an intimate knowledge of the background of all salaried
personnel. Th is, of course, became a virtually impossible task as the number of employees increased. Qual ified people could easily have been overlooked, and the
preparation of readable resumes for the managers became a monumental task. SPI RE
now assures that no qual ified individual is overlooked and automatically prepares
the ir resumes Th is resume, as printed, contains virtually no coded information, thus
providing management with a concise, complete, easily read and understood document
on any salaried employee

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Of course, qual ification is a matter of definition. A professional analyst takes the
vacant position and determines the background necessary to qual ify an individual. The
analyst specifies acceptable work experience and the minimum years of experience in
related fields. He also specifies the acceptable areas of education and the minimum
acceptable level. From the years of experience and the education level spec ified, a
minimum number of "points" are computed by the system which will qual ify on individual
for the vacant position. Individuals may accrue the necessary points in any combination
of related experience and education. Thus, if an individual had a masters degree in an
appl icable field and only a bachelors was required, he could qual ify for the position
with less experience than that specified The equating of education and experience
used in the SPIRE system is based on the ACF position rating plan. The analyst also
spec ifies the acceptabl e sal ary grades for the search. Th is keeps sen ior men from "dropping out" for junior jobs for which they would be qualified. In addition to the preciseness with wh ich th is search for qual ified employees is conducted i a considerable savings
in both time and money exists.
0

The normal time to complete a search for any given position varies between six and
eight minutes. This same job accomplished by manual methods would take about six
man hours.
Another appl ication which has saved a considerable number of man days is the generation of the quarterly Merit Rev iew Report. Th is report is by department and contains
pertinent .information concerning past salary increases for all employees who are to be
reviewed during the next quarter . The normal time to complete th is run is about 15
to 20 minutes as opposed to approximately 32 man hours
0

Other current appl ications of SPIRE include: creation of summary reports on salary
increases for any time period, skills inventories, projections for salary budgeting,
preparation of data for salary surveys, current salary status reports, salary distribution
studies, and the generation of resumes for specific purposes.

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COMPUTER TECHNIQUES
SPIRE is centered about a master information tape. The information stored on this tape
is first punched into cards. Each card contains all the pertinent information about a
single happen ing in the employees past. Every card entering the system is identified
by the category number and the employee IS permanent number. The remainder of the
card contains identifying codes for the data as well as alphameric descriptions.
The master tape is blocked by employee. All the information about any employee forms
a single tape record. Within th is record the information is held in card images sorted
by category and date where appl icable. Th is means that the maximum number of records
to be read or bypassed will be the number of employees in the system. The employeels
current salary grade is carried as part of the first card image so that for many appl icatioris
a decision can be made as to whether or not a particular record is of interest to the search
before actually performing a resume scan. This is particularly useful in the recruitment
appl ication.
The accuracy of the information contained in the master file is, of course, quite critical.
To provide this accuracy, a great deal of time and effort has been placed in the program
used to update the file. A total of 47 different errors are uniquely detectable in the updating data. This program allows total resume replacement or deleting, individual card
replacement or deletion with in any resume, and the addition of any new information to
any given resume.
In general the customary way the master file is used in supplying information, other than
complete resumes, is to scan the master tape and write a summary tape of the requ ired
information. The information on th is summary tape may then be sorted or interrogated
in any prescribed manner. Several of these codes that prepare summary tapes have been
written In the ma jority of spec ial requests, one or more of these summary tapes can
provide the necessary data. In these instances it is usually possible to write a program
using ACF's magnetic tape FORCOM system which will interrogate the summary tape
and prepare the necessary report. This provides a quick, economical way to satisfy
demands made on the system.
0

V.

CONCLUSIONS
SPIRE has proved a complete and useful system. It has resulted in large cost savings
and has been well accepted by management. Th is acceptance is born out by the constant increase in requests for information from th is system. To date there has been no
request that could not be satisfied because the data had not been included in the system.

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SPIRE was designed specifically for ACFls needs by ACF personnel and, as such, it may
or may not be appl icable to any other organization. Th is system is operational and in
fact is far exceeding the original expectations in speed and versatil ity.

103

• •••• ACF PRIVATE ••••• ACF PRIVATE ••••• ACF PRIVATE •••• ACF PRIVATE ••••• ACF PRIVATE .••••• ACF PRIVATE ••••• ACF PRIVATE

SECTY-STENO 4N HS GRAD PLUS SHORT SPECIALIZED TRNG 1-3YRS EXPR

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PERM. NO.

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A COMPUTER PROGRAM FOR THE CALCULATION
OF PRIME IMPLICANTS FROM A
LIST OF BOOLEAN MINTERMS

THOMAS R. HOFFMAN

UNION COLLEGE
SCHENECTADY, NEW YORK

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A Computer Program for the Calculation of

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Prime Implicants from a List of Boolean Minterms

I

Introduction
Boolean algebra has proven to be a most useful tool in the logical
design of digital circuits.

In general, the method employed involves

four phases:
1- definition of the problem (verbal statements)

2- translation of verbal statements into Boolean equations
3- simplification of the equations
4- implementation of the simplified equations
Step 3 - Boolean simplification - can be done in a number of ways.
·1

method is attributed to Quine..

One

The program to be discussed here enables

the 1620 computer to simplify Boolean functions in a manner very similar
to that proposed by Quine, obtaining as a result all the prime implicants
of the original function.
II

The Quine Method

2

To simplify a Boolean function by the Quine method, it is necessary
to express the function as a sum of minterms.

The N-letter minterms are

then systematically compared with each other two at a time, and all pairs
differing in the state of only one letter are combined according to the
identity:
XA+XA=X
where A represents the letter eliminated and X is all other letters in
the minterms involved.
After all possible comparisons have been made, there is in general
a list of terms having N-I letters.

If any minterm

all during this process, it is a prime implicant.

did not combine at

Minterms are checked

as they are found to combine, to facilitate spotting of "non-combiners".
Comparisons continue among the N-I letter terms, with the restriction
that only terms containing the same letters can possibly combine.

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The

N-l letter terms fall in as many as N different sets, and further combination
is possible only within these sets.

Successful combination of N-I letter terms produces N-2 letter terms.
Again, uncombinable terms are prime implicants.
This process is continued until no further combinations are possible.
Uncombinable terms at any level are prime implicants.

The Quine method

then goes on to select the simplest set of prime implicants that is
logically equivalent to the original function.

This last phase is not

handled by the program to be discussed - its output is simply a list of
all prime implicants.
The reader is referred to Reference 2 for a much more detailed
description of the Quine method, along with numerous examples.
III The Program - General
The program to be discussed was written by Mr. H. Huhta of the General
Electric Co. as part of his M.S. thesis project at Union College.

The

required inputs are:
1: KV - the number of variables (cannot exceed 9)
2: KN

the number of minterms in the function (cannot exceed 60)

3: the list of minterms, coded in octal form (see IV A)
The resulting outputs are the prime implicants, coded as described in IV D.
The FORTRAN-O language was used.

The following paragraphs point up

various aspects of the program organization.

A detailed example is included,

together with Veitch diagram verification of its correctness.
The Union 1620 has only 20 K memory.
program may not fit.

If both KV and KN are large, the

To insure the ability of the machine to cope with any

9-variable problem, a second program was written to perform a single level
of reduction.

Thus the output, with 9-1etter minterms, would be 8-letter

terms which would then be reentered to produce 7-letter- terms, etc.

The

second program will not be discussed further in this paper.
The first program has been shown to handle an 8-variable, 24-minterm
problem successfully.

The exact limits are not yet known.

IV Program Details
(A) Input Coding
Input minterms are coded as fixed-point octal numbers.
octal~digit

Each

specifies the state (i.e. - complemented or not) of three

variables, hence three octal places will suffice for a 9-variable

IO~

o

, \"j""(jmj""')iifli"' 'MY' """,i",mi,"ijmii"j

"

o

problem.

For example the 5-letter minterm ABC D E would be entered

as 25, using the conventional scheme of representing an uncomp1emented
letter by 1 and a complemented letter by 0 - but converting to octal (25)
rather than decimal (21).
(B) Comblnabi1ity
Terms at any level are combinable if:
1- they contain the same letters
2- all letters but one are in the same state
Satisfaction of requirement 2 is detected by a two-step process.

First,

terms must differ in only one octal place, and second, the differing
octal digits must differ in only one binary place.

The fact that the

second of these steps can be carried out at the octal level follows
directly from the relationship between the binary and octal number
systems.

A table L (I) contains the necessary information.

This

43-entry table relates Reference Octal Digit M· and Compared Octal Digit
N.

It is addressed by the number N + SM, and contents of each address

is either 4,2,1 or 0 - to indicate the weight of the differing binary
place.

0 means: "These two occa1 digits do !!2!. differ in just one

binary place, hence they are not combinable."
Terms at any level in the process are always arranged in ascending
order prior to comparison.

Thus if M is larger than

N,

it means that

the terms being compared differ in at least one other octal position hence they do not combine.

The entries for all cases of M) N are there-

fore 0 in the table.
(C) Set Identification
As mentioned in II, comparisons at all levels beyond the minterm
level take place only

within~.

The program must therefore generate

a set identification number ( SIN) to identify each combined pair.
The SIN increment generated by any particular comparison is simply
the octal weight of the letter eliminated.

As terms pregress through

successive levels, an up-to-date SIN is maintained by cumulative
addition of the weight of each eliminated variable.

o

(D) Example - to determine the prime imp1icants of the function:

ItO

j',

(1) List minterms in ascending order in octal systemm3 .... 0003
m
4

-+

0004

m5

~

0005

m7 .-. 0007
m9 .... 0011
m
lO

~

0012

m ~0014
12
m
13

-+ 0015

(4 digits are shown, because this is the way FORTRAN 0 represents
fixed point numbers internally.

Leading O's need not be typed.)

(2) Investigate all possible combinations.

Start with 3, and compare

each term with all higher-numbered ones.
ex:

3

= 011

differences.~

three binary

not combinable

4 = 100
3
5
3

7

t

= 011
= 101

two binary differences, .not combinable

= 011
= 111

combinable; the most significant binary place
is the one that combines

The decision as to whether or not a pair of octal digits is combinable
is made by referring to the table L (I), as discussed in IV-B.

In the

3-7 comparison just described, the most significant place is the one
that combines, so address 22 (7 + 5 X 3

= 22)

of the table contains the

number 4 - the octal weight of the eliminated variable.
the SIN of the combined term.

4 now becomes

It is attached in the 5th place of the

lower-valued of the two combined minterms, and the result stored to
await processing at the next level (5 places are now possible because
the combined term is given a floating point FORTRAN name).
This process continues until all possible combinations are tried.
Minterms involved in one or more comparisons are tagged by putting a
9 in the 4th (most significant) place.

If any minterms have not entered

into any comparisons when the processing of level N is complete, they
are printed out.

They are prime implicants.

III

o

"!"'''i'iI''

'-WWWRZU

•
The complete level 4 results appear below:

o

Initial
Level 4

Final
Level 4

Transferred
to Level 3

Combination of min terms

0003

9003

40003

0003 and 0007

0004

9004

10004

0004 and 0005

0005

9005

100004

0004 and 0014

0007

9007

20005

0005 and 0007

0011

9011

100005

0005 and 0015

0012

0012

40011

0011 and 0015

0014
0015

9014
10014
0014 and 0015
9015
At this point, 0012 (minterm ten) is outputted - it is a prime

implicant.

Output coding will be discussed in paragraph (3)

Processing of level 3 starts by arranging the transferred terms
into sets having identical S I Nls, and putting the terms in each
set into ascending order.

10004~

SIN

The result is:

=1

10014--'
20005

S I N- 2

40003} S I N
40011

=4

10000')- SIN = 10
100005
Digit-by-digit comparisons are now made within each set, just as
before.

Since the S I Nls of two terms being compared are the same,

comparison need be made only of the four least significant digits.
(The SIN is actually dropped before comparison, by returning to use
of fixed-point variables.)
The terms with SIN

=1

combine, since they differ only in the

second least significant octal place, and 0 and 1 combine (Table L (I»
to eliminate the variable of weight 1.

o

The new SIN is therefore 10

(generated at level 3) + 1 (generated at level 4) = 11.
transferred is therefore 110004.

The term

Note that the SIN increment of 10

indicates that the variable eliminated had weight eight.

__

~"

••_~".;.;" ..•• ~:•.• ::.. -:. .o-

f,
f

There is only one term having S I N
at the conclusion of level 3 processing.
with SIN

=4

= 2,

hence 20005 is outputted

Similarily, the two terms

do not combine, hence both 40003 and 40011 are outputted.

0
.

All three of these terms are prime implicants.
The terms with SIN = 10 combine, since 4 and 5 combine to
eliminate the variable of weight 1.

The new SIN would be 11, and

the transferred term 110004 - identical to that derived from the
SIN

=1

set.

The program avoids this duplication by a means that

will be discussed in paragraph 6.
Since only one term was transferred to level 2, it is of course
a prime implicant.

The problem is now complete, except for the

decoding of the computer output.

There are five prime imp1icants,

so far identified as follows:
At level 4: minterm 00012 (note that the SIN of all minterms
is 0)
At level 3: terms 20005
40003
40011
At level 2: term 110004
(3) Output Format
Three fixed point numbers are printed out for each prime
implicant.

They are:

1- the minterm from which the P.l. was derived;
2- the final SIN, to tell which letters have been
eliminated;
3- the level, to tell how many letters will appear in
the P.l. (this is a check on the others; it contains
no new information)
If two P.I. 's come from the same set, the SIN and the level
will be printed only once.

.

.,
(4) Output Decoding

o

The output format of (3) can be translated to literal form as
follows (using the first prime implicant to illustrate):
1- write letters for variables: ABC D
2- translate octal minterm to binary:
3- translate SIN to binary:

12
0

-+ 1010
~

0000

Now each 0 in binary SIN indicates a letter present in the prime
implicant (in this case, all four).

The binary minterm now indicates

complemented variables by 0, true variables by 1.
is therefore
notation.

- ABC D,

The prime implicant

which is minterm ten, in the usual decimal

The output level -4- verifies the fact that the term should

contain four letters, which it does.

Similarly, the other prime

imp1icants decode as follows:

ABC D
010
o0 1

5

2

3

o0

3
4

3

1

010

11

100

4

010

3

010

4

11

100

2

~t
~J-+
~~
~~

ABD

AC D

AC D

BC

(5) Check of Results

The solution of this problem by Veitch diagram is shown below.
It is readily verified that the computer solution is correct.
Prime imp1icants: ABC D (m

A

I ..
J '3

I

o

•
I

If

IS

,t

I,.
c.

I

•
7

3

I

t-

O

,

)

B C (m4 + mS + m12 + m13)

I 'I

Is

10

A B D (m

A C D (m

D

S
3

A C D (m
9

+ ID7)
+m )
7

+ m13 )

r

:>1
I
I

(6) Elimination of Duplication
It is inherent in the Quine system that identical combined
terms will arise from different series of comparisons.

For

example, a term A C could arise by eliminating B from ABC and
ABC, or by eliminating D from A C D and A C D.

The program

eliminates such duplication at all levels by the following
procedure:
When a combinable pair is found, the 9ld SIN and the weight
of the variable just eliminated are compared.

The term is

transferred to the next level of comparison only if the old
SIN is less than the weight of the variable just eliminated.
For example, in the problem just illustrated, the two terms
with SIN

=1

combined to eliminate the variable of weight 10

(decimal eight).

Since 1 <10, the term was transferred.

Later on, the two terms with SIN

= 10

combined to eliminate

the variable of weight 1 (which would have produced the same
term).

This term was not transferred because 10) 1.

References
(1) "The Problem of Simplifying Truth Functions" by W.V. Quine
(American mathematical monthly, p. 521, 1952)
(2) "Logical Design of Digital Computers" by M. Phister·
(Wiley, 1958)

(p. 68-75)

/y/pm~

/f. A'# ~

Thomas R•.Hoffman
Prof. of Elect. Eng.
Union Co lIe ge

o

•

o

CR I T ICAL SPEED. STRE SS, AND

[3El~\R

ItJG

REACTION CALCULATIONS FOR A GENERAL
SHAFT US I tJG NUt1ER I CAL INTEGRA T I Ot~

8Y RALPH B. BATES

COtJTENTS
SUMMARY------------------------------------PAGE

2

INTRODUCTION-------------------------------PAGE

3

T~~ EOR '( -------------------·------------------P AG E

3

NUMERICAL INTEGRATION----------------------PAGE

6

t~ETHOD-------------------------------------PAGE

8

REt1ARKS------------------------------------PAGE 12
REFERENCES---------------------------------PAGE 15

116

...

,.

ii' h·W·jfb······tj"··ij'·,······¥·· ·ff·¥t-Ef ·W·T§··5 '·T -'p"rrn'rp 1t'""feTFPI2M?'TllirUg-prJ'yr' "W"U"j-j'j
f

n

...

_.

'wwwnw

•
StlOlAlY

o

Critical apeed,atre •• ea, and bearing reaction. can be calculated on a
digital computer for a general cwo bearing .haft, which caD have each
bearing located anywhere on the ahaft, any number of croe •••ctions,
variable loading, and any length.
B•• ide. elLminatlng the tediou. labor of the calculations, the computer
provide. flexibility. A number of calculations may be rapidly made to
opttmiae design or to check out application variations on a standard deaign.

Bae18 of the Calculations
In ganeral, the critical speed calculation i8 baaed on "yleigh'. method
using the following formula

where Hc i. the first critical speed. rpm
W. is the load at the I po.ition excluding external loads without
ma•• , such as belt pull, pounds.
Ys i. the Itatic deflection of the load at the a poeition due to
the loads W. with the loads reversed between bearings.
The .tatic deflectiona ud bending moMnt. are found by u.aing the same
principlea o~ mechanica which are the baai, of graphical determination
of be. . deflectiona. Numerical integration ia u•• d to relate load, .hear.
bending moment, alope. and deflection. Thi. integration, althouah numerical) gives exact areas &8 lODl a. the loads and momenta of tnertia
are con.tant over the incrementa of ahaft length.
The bearing rea-ctlons are found by taking momenta about each beariug
equal to zero in accordance with statics.

.cr•••• and combined
shear .tre•• are calculated according to tne usual equatlona of strength
of material ••

The ahaft bending tenaile stre.l, tor.ional shear

Method
The method i. illustrated in detail by an example calculation. Briefly,
it con.iata of dividing the shaft into increment. of length, determining
the 10a4 aDO abaft momenta of inertia in each increment anel the cOliputer
calculate. critical speed, .tr••••• and bearing reactions. If there ia
only .haft weight in a number of increment., the O.D. and I.D. of the ahaft
are sufficient input data and the computer will calculate the load and
momenta of inertia.

o

Other Factors in Critical Spe.d
There are other factors affecting critical speed, such as, .bear deflection,
gyroscopic effects, bearing length, and bearing flexibility. Bearing support
and oil film deflection may be accounted for by adding the bearing deflection
to the deflections used in calculating critical speed.

JI7

Page

Z

Critical .peed. .tr••••• , ad baar1ng,~ r ••ct1en. for a leD.ral .haft MY
be calculated on a d1altal computer by utilizing numerical tDtegratloa.
The '''.1'.1 .haft baa each of two b••rin&' located anywhere on tbe .haft,
any nu.ber of cro•••action., and any numb.r of load••

rf--"'\.

~)

Be.ide. altainatina th. tedi0U8 labor of the calcalatlona, the ~t.r
It allow. the calculation of • number of variatiaa.
in order to opt~l.e dea1gn or evaluate application variatton. of .taadard

offer. flexibility.

de·Lan••
THIqIlY

Ipi'lIb '. l . .rpKetho •... (4) ud

(1)1

byleip'. energy method may be ueed to determine lova.t natural fr. .uency
of a 'Yltam. The _tbod eoa.i.t. of
a configuration for the .yat.
which vill approximate the max~ amplitude of the fUDdamental mode 01" lowe.t Datwal frequency. • ...4 on thi. conftl.atloD. the aaaxiaum potential

"'.iDa

energy 18 calculated at maximua dl.placement (zero velocity) ad "uatad to

the ..x~ kinetic eaerlY at the .y.t. . . .ul11b~lum po.it1oD (max~UD veloTbl. r.latlen.blp may then be lolved for the lowe.t natural frequency.
city).

The dynamic deflection curve at max~ .lspl.c.... t fer lateral dl.,laceaeat
of • b... may be ...... 4 to be very cl••• to the .tatic dafleetloa curve.
When the confiaurat1ea due to .tatic lo.41a" .f • be. . with lta CNn low 1a
ue.d for calculattRa the fundamental fr ..~cy by "yletab l . . .tbod. the freqUeRCY 1a wLthto the accuracy ....treG fer ... t . . . iD.e~tD.~cal~ul.tlon••

SiDee lAyle1ah'. method conailta ....ati.1ty of ....t1n& inertia for c•• of
the rotatinl _ •••• to the re.torina forc •• of the ahaft. 'at.nal forcea
which do not have " 8 . auch .. belt p.ll t . . . . t Ht be i.acladed. a&yle1&h
foad that the .yetem vibrate. 1D a IMDQeI' wblch make. tbe freq.mcy a a1DiIaua.
Tnia _ _, that tile inertia forc •••f the ...... aut act i.a 4irectl.a ca.aing
max~ defleetton..
ID. two b.ar1D& abaft the .tatic load. between the b••riD,.... t be rever.ed te produce lI&Xiaaa deflection and millllaua f't'eq\18llcy.

I.&yl.ip·. methed 1. tile work clone on the
be. . 1n moviog ita load. from the equilibrium po.1t~ to the 4yQaalc dafl.eti_ curve .t .aiJDua deflect1oa. ('rbi. i •••• u.4 the .ame .. the .tatlc

The potential eoerlY iAvolved 1a

_flection cutve without. external loada and with loa" raver.ed between
be.rial·.)
'£hue l

, .1.

• 1/2

~

Iw.y.1

The uxiaum velocity of the weigbt W. wlth amplituda ,. in har1aonle motion
1. pya • Bence. the max~ kinetic en.ray of tbe .,.tem i.

~.I.
1.

•

..L ~ tv. (p1s)21

o

2,'"

Humber. in parenth•• 1A cteatpate refer_c•• at .ct of papel'.
'age 3

II~

-------------------~--~---------

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

-----

.----~~-~

The .ymhol. in the previoua equation. are:

0

'.1.

1, potential energy.

W.

18 the load at the • poattion,

Ys

i. the deflection of tbe load at the a position.

It.!.

ie the kinetic energy.

g

is the acceleration of gravity.

p

ia the natural circular frequency.

8

• 1,2,3,---.

The la. of conservation of enerey require. that the potential energy ....1
the kinetic enerlY in tmclamped .yatema. Solv1Da fen: p2 giv•• the fol1ow1aa
re.ult:

1: IW.~sl

~lw.y.21

The flr.t critical speed of a abaft may be conaldered to occur when the
circular frequency (&) of shaft rotation e,Wil. tba natural frequency of
lateral vib~ation of the rotors (considered aa a beam). The rotatina abaft
1. deflected by the ...11 unbalance force. in the rotating .y.t... wbieh
cannot be elia1a.ated entirely 111 actual roto.... Th••• exciting lerce. have
a frequency 1n a lateral plane equal to the eircular frequency of rotation.
When the exciting forces have the same frequency as the natural frequency
of lateral vibrat1on, r.~anc. occur•• whlch uaually caua•• UDde.tr ••bl.
exc•• aive vibration of the macbine. Thua2
W

2

Henee:

•

187.7

IV,Y11+IW2YaJ+lv,Yl l+ ••
IW1)11' IW2yz2!+ 1·'Y3"

where

1a the fir.t critical .peed, rpa.
i. the load at the • poaitioa _clGd1n& external 1••d.
without mae., 8uch . . belt p.ll.~, pouDda.

Ys

1. the .tatic defl.ettoa of the load at the I po.lt~
(W.> with the l ••da 'l"ner.ed between tu bearl.... 1Ilcbu.

Deflection
The It.tic defl.etl~

of the abaft .y.t. . may be deter.iDed by utl1lataa
the prlncipl •• of . .chanic. which ar. the bull of araphlcal det.rainatiOD
of beam deflectl. . . . .beND in riaure 1.(13). (10), and (3).

o

B'Artpl ...ctlona
The b••ring r.actions are foun4 by taktng moment• •bout each beartna .,..1
to aero in accordance with atatics.

'f ~

Page 4

...

Simply Support.Jtd Beam

1!11111!'l

l1B the lO3.d per un1t length-

v

r. 1s the bea.r1ng reaction at the left and

,',-

converted to loa.d per un1 t lengt.h.

r z 1s the beari'llg react10n at the right end
oonverted to load per un! t length.
If

)

Loa.d D1asram

r.l

1s the load per un1 t length including
the be~r1ng react1ons.

l

V

V 1s the shear.
V•

Sw dx

:: Area. under the

W

ourve; and

~ :: W

~

--1f-dx

~ .. x

M Moment Diagram

M=SV dx+externa.1 moments; and

E

Shear Dla.gr8.!ll

L b

M 1s the bending moment.

1-1

'- x

fx = V

= Area under the V aurve

1- Mext
( Mo st shafts have zero external bending '!loments.)'

.

-..f t--dx

• x

is the modulus of elc.sli1city.

Ia 1s ·the moment of 1nertin of the beaa
cross-sectional area ~.,n th respect to
the axis in the neutral plane.

.

D.x

~~4x

-,-,--~------------------------------:-..:.:.:---

-&

is the area under the (!~/EI~) curve.

S + Cs·

S(M/EI a)

dx =e-;

ruld.~:~
SZ
1&:1.S 1s the slope and as 1s the
consta.nt.

5=&-Os;

S

dS - ~(M
({X-If;

and.

-u

1nte~rat1on

b

is the area under the & curve.

,.+0,.::

SS dx ~S(e--CI)

dx=~-Osx;

1=~'-CsX-Oy ; and ~#-.4L..c,;

ax u

l' 1s the

derlectlorl~

and 0., is

80

t.~e

1

a.ni

~,.e!-OB

~.&
ax

consts.nt.

'·0'
.

FIGURE 1 - BASIS OF 3-RAPHICAL DETER·!INAT10N OF DEFLECTIONS

Pa.ge 5

..

~

)

F

'ttMIU

o

.he_

The .baft badiq teuil• • tre•• , tor.loaal .bur .tr. . . . . . cOllb1Ded
.tr••• are ealculatett aecordlnl to the uaual equation. of .tt_8tb of
JUterlal. (13).

Sba

•

K.; I

Su

•

T.

~I

Where all value. are at .ectlon • of the .baftl
1. beDding teD.il • • tr •••• p.l

to the outer .haft .urlac. d1yf.da. by
the IIIOIII8Ilt of iIlertia .f the ero•••eetlollal area
with r •• peet to radial axl.,

1. the rad1u.

Ln.-'.

1. the .baft tor.lonel

u

the torque in the

lu..r

laut,

.tre•• , pa1
lD. - lhe.

ta tbe radlua to tbe outer ahaft .urface divided by

the aoaeot of tnertla of the crol.

..cti~

With r ..pect to the Icmgltud1Dal &Xu, in.

ar.a

1. tile .haft aaxiaum cOllblae4 abe. . . tre•• , p.i

'.ur8

The iDtearatlona .bowD in
1 ...y be ,...for.d by ll.-rical . .an.
with & COIIIputft. lhauical 1ntear&tloD teebDi,• • IDA)' be approxiute,
(8) and (IS). Iowever, tbi. numerical 1ntearattoD 1. exact if tbe load
and the IIIOIMIlt of inertia are COD.tant OYC the lncre.ent of x, ( a x)
.ad the follow1na formul.. are u.ed.

Zaylol'"

r....l.

(8)

rr.. calculua Tayler'. fermala with rema1nder fo11""
f'Ca) (x • .) + • • • • + f (a> ,.
( ) (x • .)Il· + I (~\
x ·f()
. + --r!t
i
Ix _ .)" + 1

f( )

1.

Ia

ria_e 2

•.• Yz

a.

1f x • b tbea (x - a>.

•

~

n+

!

_4 11 x • c thee (x • .) • 6. x

+ ~~
Ax i. the f.acr_t of l ..... th aloq the be_•
• 1. the .tatioo liDe 111 tAe center of II x.
Sub.cript I de.1in.taa the value at the 'tation lin••
Sub.cript • • ·Yz. de.ignatea the value at the left of Ax.
Sublcript • + 'I" cIe.1.pate. the value at the right of Ax.

rIGta! 2
I~J

' •• 6

-- - --

-

-

.-------~---~---

Shear formulas
Vi

•

dV

•

di,

v • (constant over

A x).

ws;

V"

-

0

C

l ... \,

,;

Bending Moment Formulas
M'

•

dM

+ y~.

Hs

•

dX

M't

V;

Ms .. Y2,.

-

+

V8

•

V'

r::I

_

w

•

Y2,. (l::t. x) + .L w. ( A x)

2

2_

Slope ForlUu.laa
dS.

M

~

and since S

i-C.;

•

BIz

where EI

9'

Z8

is constant over

6

dS

•

~

4

a

x

.2i
•
dx

-

Deflection Formulas
~
ds

•

d~

di'"'"

S

S + Ca

•

c.(3)
eJ

•

y

and since

9

a

ft
•

i

$

S - c.

therefore

x - Cy

~'

!I.
•
dx
•

!.i
dx

- C

•

•

S·

i

,(S)

V

0·0

BIz.

JJ. '"

Page '1

Ii

1

o

Therefore, the only .rror introduced in the integration 1. due to the approximation which i. necessary to keep the loading and moment of inertia constant
over the increment of x, ( l1 x).
If desired, the amount of error can be
determined by approximating the load with higb value. and the moment of tnertia with low value. for one calculation. A second calculation i. then
made by approximating the load with low value. and the moment of inertia
witb high valu... The total etTOr will be lea8 than the difference between
result. of the two calculation.. The error may be reduced by maktng further
calculation. with amaller increments of x. Th1a 1. not require' for moat
engineering calculations with the u.ual .afety factor ••

a.-

The calculation method 1s i1lu.trated by uaing the ahaft ~ in ,1gure 3a.
This is a compre •• or rotor mounted on a stepped sbaft with two bearing..
cause the loads need to be regarded differently, the calculation. are done ln
two parts.
Example Caleu1.tion .' Part 1
Firat, the bearing reactions and'.tr ..... are determine. incluciin& external
load. without maaa and with load. in their normal, direction (cIowmIard) ae
tabulated 10 Table 1.
The input data for 'art 1 of the calculation. i. de.cribed belowl
Colum

Description

Sll!!bol

bx

The~

increment of length.

•

Statioa numbers of bearing location••

1

•

Station l10e number ira the center of l1 x.

2

J.s

Load per unit l.oatil includina external 10ao
without mus in noraa! dlrect1oD.. Coneentrated
load. BlUst be distributed over the lncremeat6x.
Actual .haft and rotor load. are more often distributed than concentrated.

9

C/l~a

Se. Page 6.

11

s••

Page 6.

12

s••

Page 6.

The calculation. made for Part 1 are de.crlbed below!

o

ColWDll

Sl!!ol

3

"'2

4

De.crlRtton
/

MomenU about ba.ulng 2 station Une aa follow.
1Il2 •
.£ 8 (s(of bearing 2) • a) calculated at

.ach station line, lb/tn x atation number.
/
Momenta about bearing 1 .tatioo 11ne aa follovl:
1111 • 1s [.(of bearing 1) - . ]
calculated
at each station line., 1b/in x station number.
PageS

1

2

3

4

5

6

9

8

7

10

a. Rotors

0
-100

is

r-r-~~--;r=*=*=M=-_=_*,==-=.~,~~=*~-----.~~--,-r-.

!
I:

1

-x

I

b. Loads, Part 1

LJ

-200

500

!
:
'-~"

.

I
,
.

,

, ;

-1,000

r'

5,000
2,500
0

'x

Sh.ear. Part 1

-500

se

I '

,-'--

0

V

.

I

;

'~.~.t---_.....--

fj
:\

·

~- .~

.

I·

•.

:

4---~------

..

.

I

_------+--

- : - - '-

x

d.Comblned Shear Stress, Part 1
1

0

I

-.,_--.i-_-I- - - - ;- - + - -.....-/~=-~~~"""'"""_.-"""'-;--

I---=--'
__
-"-"
....

"-.

-5,000

f·r

-10,000

..'"
,)8

",",,-//

.~,.,..

~

I

X

'

'

.

:

e. SendiDg Moment, Part 1

o
-~OOl

t . . Deflection,

P[\rt 2

o

FIGURE 3 - B:{A.7·!PLE CALCULATION DIAGRA.!-1:S
Pa.ge

9

Sol,.

0

•

5

,..1

"ac~lRt1on

........ n"t1oft I, lba/lD

"1

~l

II ~
It w) 'S!f~ liM}
• at ll.... lq 1 •• at --iDi

• •

11

leal't.q reactt. 1, lbl.

1'2

"'~1q

~2

+

•

7
8

• 1'1 (

~

x)

z::.(ate_G!!!""
,ytM U.~
LDa 2 •• at --Iai 1)

1.U'iIIa I'MCtiaD 2, IN.

W,

LeU

aZ.

1'2 ( 6 x)

,.1' UDit l_tla iacl"iDa be_tna I'uctt..i
L• ...pt

. , b--iDa 1, w. •

w, •

aM at burial Z,
6

1

react1ea 2, lba/ia

&2

w. ·

1

2)

'. +'1,
II. + 'II.

. . . . . . . ' . . 7.

X.

_

i.

+ ~1

i.

+ 1"2

........ 6 • • 7.
..... 6 . . 7.

10

Sb.

see ,,,. 6

13

Sta

s.. .... 6

14

SCI

S..

'a,8 6

a

iI'lIl! Calc!I!S"BI • lIES

i....

S.cad J tile c~ltieal .,... :La .. tenlMd .-:1-.4" utuaal 1. . . vitlMtut . . .
uti With the 1.... bettle_ b• •
reYer••a
talMtlate4 (Q ~abl. 2.
lot. the .hr1ak. fit of the
ntel' ad tIw . . , l l q Ilub MY be e.-

t.,.....) ..

COIIpI'.".

l1de"l. to tacr.... the abaft dl... ~ wh.a calealatiaa ••1tical _peed, (14).
!be tap., ••ta for .art 2 of the

St1-

-

o

11"&
b.x

c.lc.l.t~

1a delcrlbed bel. . :

blttl,S",
!b. 1.cr....t

.r

1...,11"

•

•

Statioa .WIIb.r. of b__ 1q locatiou •

1

•

StatloG liM . . . .r. 10 tbe .entel' of

2

1.

II x.

Load pel' _It leqtll uclu.1a1 atenal 10'"
v1tbeut • •'. _ _ u-ace4 10... _ t be 41••
tr1butecl over the :Lncr-.at A x. Actual abaft
. 4 I'otor 10." .... _tte .ftaa cU.. ~lb.ted than

eone_teat.d.

12

IX.

1I,w. at at_tieD

I.

S. . . . . . 5 •

••.,.10

The calc"latiolUl .... for Put 2 u. "acriNd Ml...
Ctl,..

S_l

3

~

4

~

S. .

•

r1

See hl't 1.

•

Jr

S.. Part 1.

S

".

,"SlpS1ft

C'

s.. , .. t 1.

2

,

,

,

~7

Puc 1.

I

S_ 'art 1. !he loe1.. _
of --iDa rMCtlMaa
.., be que.tl_ed .laGe c.u, .........1 1"-

JIIMrI..

.1dane .....
it .., .. . . . . that
tIM iDelua1ea. . , beu1q wuctlou 1a .......,.
1» _ _ tIM' iatepoat1oa , •
'eet al-.
the l-.tJa .f tbe abaft.

f ... ....

6

LNd, . .ludLaa a.Canal lea_ at .tatia . . . .
., lb.. V. • 1. ( A x) •

7

s.. , ....

8

See ..... 6 aftd 7.

10

I.

S.. . . . . . S,6_47.

+ 'II.

b.

11

6 ael 7.

s.......

12

S, 6, aM 7.
See ' . l l. .taa.

Deflect£on.

11
14

,w.t, ,

Ab.elute value .f 001_ 6 ·x ..1.. 12 at

'•.,.2,

Abaol"te

.tatloa I.

"al_ of _1.- 13 x .001_ 12

atatia '.

'irat Crf.~lCa1
" ' • Sea .... 3.
Ie • 187. 7 ,W' }Ii

•

£,. .~~

_atarat.at!_ of Y'
It ... ahewD

<'aa.

' 'OIl b.
5) that
y

Since

u

:It

b·

•

tbe c:llatan¢e a101&1

C~c
•
y

tu __ =

x • • (A x)

Let '. • the atatiDG number at befttBC 1
sb • the .tatioa Dumoer at beartDa 2
, • the ~ .t b. .ciDa 1

••

~b

the

•

~. at beari.q

2

Since the deflection y • 0 at bear1n& 1 an. bearina 2 than

~a

• C.s a < A x) + Cy and

bb •

Cas b ( A x)

'~b

+ Cy

••• u

ct'

Solytaa thea. two a ..ut1OD1 fO'l' C. aad C, aDd ••batitutlq iDto tb. . . . .t1.a
for y thell

' •• S••

o

Thla 18 the . _
15

•

(abb • •

I.

cS b ) -

(gb·

s.,>

I

.1

bI - ~•

(~b -~.)

-

( • b- .

I.

s,)Ax
)4x

( ••

lleace y i. the cU.ff. . .ce 1D value Dew.. tb8 value of b. ad the .t..alallt liD.
'1 which 10" throvah each beuina . . .hIND 1n rtpre It.

rlCUll 4

.AUS
U.e of • CO!p!tec
Beeauae of the ted£OYa laboc 10901••• 18 th... laner.1 abaft calcu1.tlODe, the
uee of • cOliputer 1a ......U')'. The input data for: the co.put.r coaputat1eD.a
differ_ al1sbtly fn. that -..cr1bed iD the . . , 1 . , whicb i.11_tI"'tec1 the .thod.
The 1Dput dat. to the c.,utu ia •• follow I

o

1.

ldentific.tion

2.

A. x.

3.

• ...iD. location at.tlOD DWIb....

4.

bten.1 10ade vlttaout .... and loc.tion Itation number••

5.

Ior. .,..,.r tran8lDltted with .tart and end atat101l numb•••

6.

rpm

7.

Modulua of elalticlty.

J~ 1

'ace

12

In additi011 either of the
8.

l.i1_iDa,

Load. .xcl.dIDS Ihaft _lpt

aDd extera.l 10•••

vlt~

"

.....

I.

Shaft O.D. witb .cut ad ...
atatieD aUllb.I.

10.

Shaft 1.D. vitia .tut _cI ...
atatlora .u.b....

Le... excl_iaa utenal 1....
wf.thMac _ I ••

10!
11!

z,.
C. wbleh 18 liZ ahaft O.D.

't ..

Val• • •uch .1 5.
4 10 vIllell .., be the .... f • • 8 . . . . . of .tat1ou ...
e.. ter to put iDto tIM COIIputer . . . '1a&1. val_ f ... ltart .ucla a.ber to
end It.CiAm 0\18)_. 1xten&1 1..... 4, • • ptat 1Dto tbe COIIpUt. . . ..,...tel1 eo
that they . .y be _e4 COl: ule.la's... lia11w to • • c 1 of the .....1. ad .
excluded fro. calc.l.' ...... 1la111a to , . . t 2 of the .....
If tM 'baft baa
an \IOuual .eeel. 110 that e, 1a aad 1. camaot 1M c.lcuate4 froa abaft 0.1 • •
1.1. tile" 8; ,~ 10~ ad 11· ar. the f.Dfut uta of that It.tieD laItucI of 8, ,
_41 18.

1..

The caleulatl... . . . by tM coaplItn' an aWl_ to tbN. 1D tU .....1. acept
to .laaft "labt), I''.., CI Ip.. I . . . llu •• calculat•• , .... Itn,ut
data S, 6, 7. 8 . 4 ,. !be COIIpUUI' uti. . aldlel' laput ••ta 4 + 8 + ~ 1. (..... to
,Daft wt) 01' 1aput clata 4 + 8' AI J.. ill caleu1etlou aWI_ to , ..t 1. ID
ca1culatloD' ....11&1' to 'ut 2, the .....tc .... 1ft,.t uta 8 +1, (. . to Daft
wt) 01" input data 8', with the 1."SH-" beRt.aaa ""....H, .. 1. ••

...1,('''.

~lvgt.'.

!be

p~lnclpal

1.
2.

.....tae•••f th••• leGeral abaft calculatteDa awe lilted

be~1

.,,1,

to any two beartna ahaft witll each beRtaa
l ..aced aaytIbere 011 the .uft wlth • ., v_iul. cre•• aactlaa
ael loadiq aM with .., l-atla.

fte calc:ulatl.a

..UIlcluy ...aitl• • •a .valutad 18 the u1 ••1atloG. by ..._
the fUlt lHCI at
1 ael -lal un cleflectiAtnat ucla

be-1a&.

.t.,....

3.

De.ip• .., b• .,tia1sed by al••lattal • Daber of • • latleraa by
Cllllputer _41 ••1ectiq the Mat.

4.

Vulatwa. ill ltaadad d•• ll1l ••\IOb . . . D. . . .r of belt ,..J..1I, ..,
b. cIa••ked by Mkia& a ...... • , aalovlaciGu by cOIIpU".

Mcveey
'l'he accUZ'acy of the caln1&tioDa an affected by tbe f~11ow1D& J

1.

lavina the 1. . . . . . taut ovel' tM i.Der.-nt of lalllth (Ax).

2.

1&9101 the ahaft cn••••oti_ ...-u of la.rtia COG.tant
ta. increment of l-.th ( A x) •

3.

...aumiD.g the atatic deflection curve 1a· the dyJaam1c def,.cit1oa 18

O'N'I'

caleulattna eritical apeed.

'.ae 13

o

0·'·

.,..d.

4.

CODe.ntr.ttas the l.ad 1n the tDcreaent of lenlth 1D calculattDs

s.

U.ing Rayl-lIbr-'. _tbed to calcualate critical .peed.

critical

I,

Tbe error d_ to 1 ad 2 precedf.q .., be evaluated .. lDcl1catect _ ' ' ' . 8.

n. en..

clue to 4 .., be rdaiai. .cI by Uk"" _11 1acr_t. .f

!be error. due to 3 _d 5 .., be raduced
ud... the iaanla f . . . . . : - , (4)
V

•a

~

•

11

Y

.1 11

(

c1

,

iii~

i_til ( 6. .) •

OJ ..eo.lo\ll.t .... tM cl'ltlo&1 ....4

1...
2

V••

-aa

Ax

calculattDa • lecoad critLeal ..... value

.02 • 187.7 £,-,2'12'
1:"1 '

.:1

Sub.cript 1 r.feca to va1uea 1. the flr.t calou1atlea ..d luhacw1ft 2

~.f....

ee

val... ill the ••cond calcutatin.

Icl liDee tU Ida.tlc --ayla •
itaetl. of .... whil. potatial __., la • fuaotioD .f the _ .. Cia foI'oe.

lIota that -.1 11 ...eI ill tile calculacieD of

ttW: 'HCD'

a.

l! Crit&ctl . .

I" ...

!hue are OeMI' factor. affeot1q c.. ltloal .,...
heaI: de'lecCia. (3)
eel (5). &y1'. .coplo .ffeete, (2). (3). act (6). __ lq 1_tIl (3) . . . . -'laa
f1albil1C7 (3). ---iDa ...port _cI .11 fila flulblllC)' "y, be u,*-ced , .
by ad4taa the beal'1Di 4ef1eotioa to Cba 1. to ~ calculat~ .f c~ltlca1 .p..d.

o
.... 11t

1.

ADder.au, R. A. "'laual Vlbratlo1l8 of UraifOl'll ..... Accord1la& to tbe
Tt.• •Make !heory". Jetil'. Ap,l. llech, v. 20. A. 4.
(Dec. 1953)

2.

Bert, Chari•• V.....f1ectlou :La

Ste,,..

SUfte·.
24, 1960 ". 121-131.

.~

IMhLp, ...",

3.

Cburcb, A. B. "Celltrlbaa1 ..... _41lANa'." . . . . I.kt
J.... Wiley.
1t44. pp. 291·296

4.

Church, A. B. !!J.cha'"l

"'t

1957, pp.

5.

Cw1e, Al_der

'lI.t..,.
•..
.20 •

York, .,.. Vl1e)' & _ ,

t • • Tabular Ketlled f_ Calc,datiDa Defleocw.. ef Step,..
ad Tap.ed Shaft.". !If!b1ae I!.ya
t. 1916)

eheuko, S. and D, H. YoUlll. V1b!:.t12M Ir'bl~ 1n haW...m,
3rd edt J Nev Y.rk: D. Van ... tr_COIIpany, 1934;,. 40.

15.

tJaaar, Eric C. "Numerical IDtearatiOl1 Sillp11fiea CorIplex .... ip".
Product 1y1n..... W (Harc.b 16 J ~9S9) I pp. 50 .. 54,

S.

lr,
1

13 ()

'aa.

1S
1

1',1

.

.

TABLE 1 .. EXAHlLE CALCULA'rION • PAllt 1
(InclUding external loads without maaa and wlth normal direction of loacla)

o

Ax •
1

3
m
2

2

• 1.
'/In

1..2
1.S

2.0

..... ,

,;

-70

I

1.

inches • Bearing No 1 at

I 4

-,.'t·;,· :.. '

-490

I

144 r864

2,5

t

i

I

.20

-4

l..Q.

f

3.51

(

j

~

-4 ,-16

~

4.51

I

)
f

J

5,0

I

-4

~
!

5.51
6,0

6.5

i

I

I

~

7,01

-4

.-

-2

0

I

t
1
t

!

l~
i

~

j,

I

9.0

iI

10,0

I

I
I

I

i

t

.~

i

!

i

I

i

480

I

-4

i
!

I
f

Ij

I
I
I

,

464

-70401

()

0

1-41361 0.16
•

3100

t

I

365,2'6300

~

2781.6300

,

~

j
91

I 0.40

-112 i

\

I.

I

i 26300

0.20 fS260 5260
;

11 126300

0.40

J 0.20

+----+". -.~-I

1

L-

r 1 • + 346 I/ln. r 2 •• 94 I/in.
R, • 1384 lb. &2. -376 lb ••

13 /

t.

5260

I ! !
i
l
f
!!
!

I

I

t

it

__.L. . . . ___ . .J.. _. . _._.L___.. . ---~. -_l
* ..

10.20 15260' 5260
t
}

II

l
I

~ -28

i

I

t

1120 1122

1

1

!

i 0.40

f

10 • 08

r

i
Is
l

i

0.08 1120 1128
1
f
I
1
'i

I

~

-672

)

I

.}-2280 ,i 0.16
·352

0.08 \1120 11132

I

I

1

~ -228

L

I

I

f

I,
I!
; !
I
\
I
10 •51
I
(
!
0 I
0 1
I
·.···----r-.·-·\---t·.--·.·--t--.---.- . -.. --.-...-i-----+--t;._-376:

0.,08 1110 1138

t
661 126300

I

-2

L

1175 26300

1

-5088!

J.

-14

0.08 1110 1130

/-61661 0.16 I 9-86126300

-

I

f

730126300

I

-96

56
+84

0.20 5260 5261

563 26300

I

I

l

!

TotAL -252; .1~84

in-lb,

I

448 I -137-61

·+10

1

Su
1Il-. P_1..l p.l

I

I

'-7348 0.16

I

I

1

I
+28

r:

S
CI

I

i

j

-14

14

13

I

-8721 -6288

64

I

1'.1

-2832

I

9.5 I

~:'

1-4552 0.16

J

~.

'. +8

-2 '1 +2

Sba

_l~

I

I

I

I

I

•

i

i

I

8.5

12 •

-1408, 0.40

496

i

1+12

11
T

I

-560

-280

~

I

342

-140

I
I•

i

~

I'

i!

!l

~

7• 5 t

I

i

~ -4

t

~

H.

!

0

I

-856

i +8

i

8.0

Ii

I -4
j

i

1-4

0

Ii

i+4
,i

!

I

0

t

J

-4 t -8

i
l
i

1-12

j

10

9

......s..-

iI

II

~

~

i.!1

I

-70
1

!-288 1~144

It -4

8

in -lbr;. . \n;Jl.;s.·

I

J

~

I

I
I

l
i

7

Bearing No 2 at • •

I

".

c:o

.+~a.

Illn

!!. ..

8 •

K.+ y&

V

w.
0

,

6

5

lilt
111'0 }'lln
I

iQ.

0.5

!t

Page 16

1-I .__.<_

TABU 2 - IXAMJ'LI CAJ.ClJLATlmi - .AaT 2

(Ixcluding external loads witbout .... and with lo.de rev.r ••d between bearing_)

2

1
•

!

1.

v.
Illn

'/ln

I

,

Ilin

'lln

,

in-lb.

o

0.5

-210

-490

-70

1.5
-864

I

-20

-16

12

I-144 I -5761
I
,-856
I
-4
-4! -16l

-288

4

330 r

t

t

I

t

-4

f

-81

I

-17 -1154

3240 3740

1

-75

-560

1000
-2832

3650

2320

-677

-12

I

38

9

-519

0

o

0

-966

105

17-

2

-1497

126

20

3

-2086

89

14

1

108

-2726

1

o

0

108

-3318

-99

8

l

-4030

-200

28

56

-5717'

-6288
360

4

I

16 1

!

I

-108 1
-2

I 464

-5312

t

1-208871

t

16

360

1
I

48.0

I

-3424

f
-260671

-1472

-8
64

-28832

-352

-8

-112

.56

-32525

360

o

10.5

I

360

56

-14

1

I

16

4

13937
-

360

I

i

4

-7136

!

9.5
84

-235

~

448

..

I

10

-202

360

-16

~

! I

1

28

I

-872

Q!

8

10.0 -14

,

0

f

i

496

:1

o

t

i

4

!

1000
-280

r

8

-28°1

-70

1I

la.2.

rad ..

I

00

!Jl

D.I

o

-32567

. . . .---1--- .--'-'+----t----4---.+----+---.--+-----I----+----+---.......-----I---1336
-424

totAt~288

7015

----,--~--~--.--~--~----~._ _- - _ L_ __ _

1"1 • 334 111n • r
He •

187.7

613V~,

--106 Ilin
~

IJ~

I

I,~,

Page 17

I
!

,

•

o~

.

......

CRITICAL SPEED. STRESS. AND 8EARING REACTION

C

_ _ _._ .•._". __ , .... "." .............

~N·_···

CA~CULATIONS

........_ ..... ..

FOR A GENERAL SHAFT USING NUMERICAL INTEGRATION

C

c

**********

C

PROGRAM DOES NOT INCLUDE A TRACE ROUTINE
... ---.-....
...-.. -- ..
.......-.------...----.-._. __ .,..-NO SWITCH SETTINGS

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

C

.

-~.

-"~

*****

C

~.- ----~-

PART A-1

*****

**** DIMENSION STATEMENT

C

DIMENSION A(102).b(102).C(lQ2)
C

**** INITIALIZE ARRAYS AND SUMS LOCATIONS

50

DO 51 K=1.102
A(K)=O.O

- - - - - .. _. __._ •. _...._.. _--_._--_..._.. _.....---_._ ... -_

..

B(K)=O.O
....

--.--..-. -"

51

._ ....- ..

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

ClK)=O.O
SUMA=O.O

--------_.._-_.._.__ __._--_.._._.• ---_. __ ......... ---_.._-_.
.

SUM8=O.O

- - - - - - -.. _---_.._ SUMCcO.O
..

.........-.. "'~------------------

C
...

--_...

--

c** READ IN EXTERNAL LOADS

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

-----

._-------.._-_ ........ _....

,lOt W1 ,lIt W.?' I 2. W3 , I 3 , W4 , 14

K=I1+1

A(K)=W1,

K=I2+1
A(K)=w2

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

........

...

K=I3+1

A(K)=W3

K= 14.+ 1
A(K)=W4

o

IF (10)60,60,100

c

**** READ NO.1 INPUT DATA

100 READ
PUN CH ,IS I ZE,. I CAL, I TYP ,M , S 1 , S 2 ,H P t RPM, DX

133

C

**** CALCULATE .IORQUE •• T•••THE TURNING MOMENT
T=63025. *HP IRP.r~
M=M+l
51=51+1.
52=52 +1.

C

**** READ =2 INPUT DATA

110 READ
J=J+l
L=L+l
A(l)=O.O
IF (OD) 114.114.115
C

**** TO DET.IF IX.W ARE GIVEN

115 IF
C

4
4
t

4

(W)111,111.11~

**** CALCULATE SHAFT WEIGHT W=PI/4(OD**2-ID**2)*0.285*DX
•

__ • •

w"O.

_.

..__

_

•

". _."._

~~

.~_."

¥ _ _ ." .. _ _ _ _ _

~,_

.. _..._ •• _

".

_

IIi W=O.7853982*(OD**2-XID**2)*O.285*DX

112 IF (XIX)l13,113,120
C
C

**** CALCULATE THE MOMENT OF INERTIA OF THE CROSS SECTIONAL AREA.IX
WITH RESPECT TO THE RADIAL AXIS--IX=(OD**4-ID**4)*PI/64
....
. _---

,

.

t

113 XIX=(OD**4-XID**4)*0.049087385

C
C

4

**** CALCULATE THE MOMENT OF INERTIA OF THE CROSS SECTIONAL AREA,IP

1

WITH RESPECT TO THE LONGITUDINAL AXIS--IX=IY,SO IP=IX*IY=2*lX
XIP=2.*XIX

C
C

**** CALCULATE C/IX(S),THE RADIUS TO THE

OUTE~

SHAFT SURFACE DIVIDED

BY THE MOMENT OF INERTIA OF THE CROSS SECTIONAL AREA W.R.TO

c
120 CDIX=(OD/2.)/XIX
I

C

**** CALCULATE C/IP(S),THE RADIUS TO THE OTHER SHAFT SURFACE DIVIDED

C

BY THE MOMENT Of INERTIA OF THE CROSS SECTIONAL AREA W.R. TO

C

THE LONGITUDINAL AXIS.IN**-3

1,

f

I

CDIP=(OD/2.)/XIP
GO TO 116
C
C

**** CALCULATE LS(ACK)+LS)=LOAD PER INCREMENT INCLUDING EXTERNAL
LOADS WITHOUT MASS IN NORMAL DIRECTION. CONCENTRATED LOADS MUST

l311

o

c

aE DISTRIbUTED OVER THE INCREMENT DELTA X. ACTUAL SHAFT AND

C

ROTOR LUADS ARE MORE OFTEN JISTRI8UTED THAN CONCENTRATED

C

****

DIR~CTION

OF LOAD, DOWN = -

114 CJIX=O.O
CDIP=O.O
116 DO 130 I=J,L
PUNCH,CDIX,OO,CuIP,XID
A(I)=-(A(I)+w)
C

**** CALCULATE M2 (B(J»=MOMENTS ABOUT BEARING 2 STATION LINE

C

M2=LS*«5 OF dEARING 2)-S)---WHERE S=STATION NO. SO THAT M2 IS

C

CALCULATED AT EACH STATION LINE.
S=I
8(I)=A(I)*(S2-S)

C

**** CALCULATE M1 (C(J»)=MOMENTS ABOUT BEARING 1 STATION LINE

C

M1=LS*«S OF BEARING l)-S)---WHERE S=STATION NO. SO THAT M1 IS

C

CALCULATED AT EACH STATION LINE
C(I)=A(I)*(S1-S)
SUiY\C=SUMC+C ( I )
SUMb=SUMd+t:)(I)

130 SUMA=SUMA+A(I)
If (L-M)110,140,140

140 I=S1
A(I)=A(I)+SUMd/(Sl-S2)
SUMA=SUMA+SUM8/(Sl-S2)
1=52
A(I)=A(I)+SUMC/(S2-S1)
SUMA=SUMA+SUMC/(S2-S1)
C

**** PUNCH OUTPUT DATA---S,W,M2,M1
DO 150 I=1,M

0,",:,

S1=1-1

,,'.

150 PUNCH,S1,A(I),d(I),C(I)
C

**** PUNCH TOTALS OF M2,M1,W

GO TO 50
END
*****

C
C

PART A-2

****

**** DIMENSION STATEMENT
DIMENSION A(102),P(102),XC102)

C

**** INITIALIZE ARRAYS AND SUMS LOCATIONS

100 DO 101 K=1,102
P(K)=u.O
101 X(K)=O.O
SUMV=O.O
SUMD=O.O
SUME=O.O
READ

,ISIZE,ICAL,ITYP,M

READ

,Sl,S2,HP,RPM

READ

,UX

PUNCH,ISIZE,ICAL,ITYP,M,Sl,S2,HP.RPM,DX
C

**** STORE C/IX

IN X( I ) ARRAY

C

**** STORE ClIP

IN PC I ) ARRAY

M=f'.1+ 1
DO 102 I=1,M
READ

,CDIX,OD,CDIP,XID

X(!)=CDIX
102 PCI)=CDIP
DO 103 I=l,M
103 READ
READ

,S,A(I}

,Z,ZU

,T,SUMd,SUMC,SUMA

5=0.0
V1=O.O
D1=0.0
DO 120 I=l,M
C

**** CALCULATE SHEAR A STATION (S+1/2}---V(S+1/2}=V(S-1/Z)+WS*DX
V2=Vl+A(I)*DX

C

**** CALCULATE bENDING MOMENT AT STATION (5+1/2)----

o

•

---M(S+1/2)=M(S-1/2)+V(S-1/2)*OX+1/2*WS*OX**2

(

D2=D1+0.5*DX*(V1+V2)

o

(

**** (ALCULATE dENDING MOMENT AT STATION (S)---- M(S)=E(I)
---MCS)=M(S-1/2)+1/2*VCS-1/2)*OX+1/6*WS*UX**2

(

(

**** (ALCULATE bEN0ING

STRESS,PSI---SBS=MS*C/IX

T~NSILE

S8=E1*X(I)

104 SB=-SB

c

****

CALCULAT~

SH~FT

TORSIONAL SHEAR STRESS,PSI---ST5=T*C/IP

105 ST=T*P(I)
C

****

THE ShAFT MAX.

(OMDIN~D

SHEAR

STR~SS,PSl---

---S(5=(ST**2+(5dS/2)**2)**.5

(

(

CALCJLAT~

**** PUNCH OUTPUT

DATA---V~5+1/2),M(S+1/2),MS,C/IX,SBS,T,C/IP,STS,SC

5=1-1
IF (X(I»110,110.111
110 Q=O.
111 PUNCH, S, £1 ,x ( I ) ,S6 ,Q, P ( I ) ,S T ,SC
Q=T
5=5+.5
PUNCH,S,V2,D2
V1=V2
120 D1=D2
GO TO 100
END
C

REARRANGE THE OUTPUT DATA OF 62-001SA1,2 INTO TABLE
D I ME NS ION A ( 1 02 ) , 0 ( 1 0 2 ) ,C ( 1 02 ) , T ( 1 u 2 ), V( 1 02 ) ,D ( 1 0 2 )

100 READ,ISIZE,ICAL,ITYP,M

o

READ,Sl,S2,rlP,RPM
READ,DX
PUNCH,15IZ[,lCAL,ITYP,M,Sl,S2,HP,RPM,DX
K=M+l

137

C

****

R~Au,C/IX,OJ,C/IP.lu

•

00 110 I=l.K
110

READ,Rl.R2,R3,R~

C

**** READ S,wS,M2,M1
DO 120 I=ltK

READ,S ,R1,R2,R3
PUNCH,S ,R1.R2,R3
S=S+.5
120 PUNCH.S
S=S-s
READ,R4.5UMd.SUMC,SUMA
PUNCH,S ,SUMA,SUMb,SUMC
R L=SUrvtBI ( S 1-52

)

R2=$UMC/(S2-S1)

READ,Sl.S2,HP.RPM
READ,DX
C

****

A(I)=C/IP,o(I)=STS,C(I)=SCS

DO 130 I=l,K
READ,Sl,5M,CDIX,SB

READ,5, V( I ) ,D ( I )
130 PUNCH,Sl,SM,CDIX,Sb
DO 131 1=1tK
S=1
5=S-.5
131 PUNCH,S,V(I),D(I)
S=S-s
PUNCH.S.R1,R2
DO

140 I=l,K

GO TO

o

100

eND

I'

&Z

»

C

o

*****

C

*****

PART B-1

**** DIMENSION STATEMENT
DIMENSION A(10Z),X(lU2),Y(102)

C

**** INITIALIZE WuRING AREAS

90

DO 91 1=1,102
A(I)=O.O
X(I)=O.O

91

Y(I)=O.O
Vl=O.O
Dl=O.O
Fl=O.O
Gl=O.O
SUMb=0.
SUMC=O.

C

**** READ INPUT DATA NO.1
READ
PUNCH,I5IZE,ICAL,ITYP,M,Sl,S2,rlP,RPM,DX

C

**** READ C/IX «(vIX)
M=M+l
Sl=Sl+l.
52=52+1.
DO 101 I=l,M

READ

,X(I),Ou,CP,CX

IF (X(I»101,101,100
100 X(I)=(OD/2.)/X(I)

101 CONTINUE
C

**** READ STATION,LS,M2,Ml
DO

105 I=l,M

READ

o

S=S+l.
C

**** CALCULATE LS=LOAO PER INCREMENT EXCLUDING
MASS AND wITH

C

~ITHOUT

C

CONCENTRATED

LOA~S

LOAO~

MUST

d~

REVERbED

EXT~RNAL

d~TwtEN

LOADS

bEARINGS.

DISTRIo0Tt0 OVLR THE INCREMENT DX.

C

ACTUAL ShAFT

C

CONCt:NTRATEO.

AN~

RuTOR

LOAD~ ARE I~OR£

•

0FTiN OlSTRIoUT£D THAN

IF (5-52)102,104,104

o

102 IF (S-51)104,104,103
103 A(l)=-A(I)
b=-8
C=-C
104 SUMB=SUMb+b
PuNCH,I ,A( I)
105 SuMC=SUMC+C
READ,T,tj,C,SA
K=51
b=A(K)-B/(S1-52)
A(K)=B+SUMB/(Sl-S2)
PUNCH,K,A(K)
K=S2
C=A(K)-C/(S2-S1)
A(K)=C+5UMC/(S2-S1)
PUNCH,K,A(K)
DO 170 K=l,M
C

**** CALCULATE SrlEAR AT STATION (S+1/2)---V(S+1/2)=V(S-1/2)+WS*DX
V2=V1+A(K)*DX

C

**** CALCULATt:

C

0EN01~~

MOMENT AT STATION (5+112)---

---M(S+1/2)=M(S-1/2)+V(S-1/2)*OX+I/Z*WS*DX**Z
D2=Dl+O.5*DX*(Vl+Vl)

C

**** CALCULATE THt AREA UNDER THE (M/EIZ) CURVE AT STATION (S+1/2)--

C

--F(S+1/2)=F(S-1/2)+(2M(S-1/2+1/2V(S-1/2)+M(S+1/2»*DX 1(3*EIX)
IF (X(K»110,110,120

110 F2=Fl

o

G2=G1+F1*DX
Y(K)=G1+.5*DX*F1
GO TO 130
120 F2=Fl+(2.*Dl+0.5*Vl+D2)*DX/(3.*X(K)*30.E06)

l'io

C

****

THe AREA UNDER THE F CURVE AT STATION (S+1/2)---

G(S+1/Z)=G(S-1/2)+DX*(FCS-I/Z)+(12M(S-1/2)+DX(3V(S-1/2)

C

o

CALCULAT~

+V(S+112) »*DX/24EI)

" C

G2=Gl+DX*(Fl+(12.*Dl+DX*C3.*Vl+V2»*DX/(24.*X(K)*30.0E06»
C

**** CALCULATE THc AREA UNDER THE F CURVE AT STATION S---

C

---G =G(S-1/2)+1/2DX(F1+CM(S-1/2)+1/48*DX(7VCS-l/2)+V(S+1/2)
Y(K)=Gl+.5*DX*(Fl+(Dl+.02083333*DX*{7.*Vl+V2»*DX/C4.*X(K)*30.E06»

C

****CALCULATE DEFLECTION AT STATION S---GS1=Gl.G=GS2

130 PUNCH,Vl,V2,Dl,D2,Fl,F2,G1tG2,Y(K)
V1=V2
D1=D2
F1=F2
G1=G2
170 CONTINUE
K=S1
G1=Y(K)
A(K)=B
K=S2
G2=Y(K)
A(K)=C
C

**** CALCULATE ASS. SUM OF WS*YS--WS=WS*DX
SUMP=O.O
SUMK.=O.O
DO 240 K=l,M
S=K
Y(K)=Y(K)-Gl-(G2-Gl)*(S-S1)/(S2-S1)
SUMP=SUMP+(ACK)*0X)*YCK)
SUMK=SUMK+CACK)*DX)*Y(K)*Y(K)
PUNCH,SUMP,SUMK,Y(K)

o

IF (SUMP)210,220,220
210 SUMP=-Surv1p

220 IF (SUMK)23C,24Q,240
230

SUMK=-SU~1K

___

\

..

!t.

•

••••

ff

•• ~

".l:

~_'i-!_l!._=-: __ ""'--""

-

..

Q

..

--------------... - •.. - - . - - - -

240 CONTINUE
C

**** CALCULATE THE FIRST

~RITICAL

NC=187.7*(SUM OF WY/SUM OF WY**2)**.5

C

XNC=187.7*(SUMP/SUMK)**.5
C

SPEED,RPM

****

PUNCH JUTPUT--YS AND NC

Rl=SUMB/(Sl-SZ)
R2=SUMC/(S2-S1)
PUNCH,Rl,R2,XNC
DO 250 I=l,M
K=I-l
250 PUNCH,K,Y(I)
GO TO 90
END

o

THREE DIMENSIONAL SURFACE FIT
M-151

December 9, 1963
D. G. Kitzinger

/43

c

•

o
TABLE OF CONTENTS
Page

............................

2

ANAL YS IS· .... • • ... • • .. • • • .. • • • . . . . . . . . . . . .

2

FIGURE 1 .••.••..•...••.....••••••..........

3

SURFACE FITTING TECHNIQUE·.·············

5

FIGURE 2 ...•...•.•.•..••.•.••.........•....

6

TRANSFORMATION OF VARIABLES..... ..•....

6

I NTRODUCTI ON

....................................
....................................

8

I NPUT PARAMETERS ......... · • .. • . • . . • . . . . . ..

10

I NPUT TECH NIQUE .................•...•....

12

TABLE 3 ......................................

13

SAMPLE PROBLEM ......•.•.........•.....•.•

14

TABLE 4 ..................•....... • ... • ... • ..

14

TABLE 5· ............... • .......... • .. · • . . . ..

15

TABLE 6· . . . . . . . . . . . . . . . . . . . . . . . . . . . . • . . . . . ..

16

FLOW CHART ...............................

16

TABLE 1
TABLE 2

o

7

.•

"

... "
,,~'

INTRODUCTION
An ever present problem in engineering is the need to represent the three dimensional array
of data by a mathematical equation. Many physical quantities can be described only in
three-space. Com.puter storage limitations prevent table look-up of a large number of these
quantities, expecially if their range of values is extensive. M-1Sl uses nth order multiple
interpolation together with extensive transformation of variables to describe most three
dimensional functions. The method used has the advantage of separating the three dimensional
characteristics of the array into components described in two dimensions, hence easy to define by the user. Since many functions (exponentials, sinusoidals, etc.) are not best described
by the polynomials used in interpolation, the first approximation to the function might be sadly
deficient. Better successive approximations to the function can be easily made using the
appropriate output option accompanied by transformation of variables. An error analysis
assists the programmer in choosing the best fit of a function, and in the case of second and
th ird order interpolation, the best fit is selected from a number of possible fits.

ANALYSIS
Let us represent a three dimensional array by x = f [Y(y), Z(zll, where Y(y) and Z(z) are
polynomials in y and z, respectively. Let us I imit the order of these polynom ials to nand
m so that

Y(y) =a +ay+···+ay

o

1

n

n

.+b z
m

n

L

=

a.y

i=0

m

(1 )

i

I

m

L

=

(2) •

i= 0

At the ith value of y,
m

Z. =
I

b .. z i

E

i=0

II

Define:
n

x = f(Y, Z.)
I

=

L
i=O

n

m

L L
i = 0 i= 0

b .. z iy i

(3) •

II

m

Then, c. =
I

L

(4) •

i= 0

-2-

Note that x is a smooth function of y and z with (n + 1)(m + 1) coefficients and hence requiring the same number of known members of the array. In general, an (n + l)(m + 1) order
matrix would have to be solved to obtain values for the unknown coefficients.
Referring to equations (3) and (4), note that both a. and x vary in the same way with changes
I

in z. Thus, by studying the behavior of x with changing z, the behavior of a. with changing
I

z is also known.

By holding y constant, a. is a function of z alone. If values of a. are
I

I

known at each of (m + 1) values of z, the b .. values in equation (4) are defined by the
I'
appropriate matrix solution. If z is held constant at z. and if (n + 1) values for x = g(y, Z4)
I
I
are known, (n + 1) a •. coefficients are determined. Define a restriction that allows easy
II
.
determination of the a .. and b .. coefficients: y takes on, at most, (n + 1) values; z takes on,
II
II
at most, (m + 1) values; and the value of x is defined for all allowed values of y and z. At
particular Z.I
I
n

(5),

x.(y, z.) = a i + a 1iY + . . • + an iY
O
I
I

wh ich is a form that allows solution for (n + 1) values of a .. , when the (n + 1) values of y
are used.
.
II

x

X m+ l=a O,

m+ 1+a 1, m+ 1Y
.

+.. ·+a

n,m+1

y

n

I

/

/

I
/

/

/
/
I

/
/
~

____

/

~/~

zl

/

/
__ ________________
__________________________ z
~/

z2

~/

z

m+1

FIGURE 1

-3-

t

III

.Choose the (m + 1) values of z successively, then an array of a.(z.} values results:
I
I
i = 0, 1, 2, . . . , ni i = 0, 1, 2, . . . , m. Fit the (m + 1) values of a. by
I '

a.(z} = boo + b .z + . . . + b .z
1I
I
I
ml

m

(6),

with the result that the b .. coefficients in equation (3) are evaluated. EquQtion (3) defines
II
a function of y and z that passes through (n + l)(m + 1) data points. Furthermore, the function
of y and z is smooth, and if planes parallel to the y or z axis and perpendicular to the y z
plane are chosen, they intersect the x = g(y, z} surface in I ines described by polynom ials
of order nand m, respectively. For practical purposes, nand m may be selected by choosing
their values dependent on the study of the z = constant plane intersections and the y =
constant plane intersections with the surface x = g(y, z}. Note that experimental data are
often determined most easily by holding all variables constant except one. This procedure
guarantees compl iance with the restrictions imposed regarding values of x at each combi nation
of allowable y and z.
The usefulness of the assumed fit given by equation (3) is I imited when the surface to be fit is
best described using exponential, trigonometric, fractional exponent and hyperbolic functions.
AI though it is true that most usefu I eng ineering functions can be described by infinite series
approximated by the form given in equation (3), it would be better to use the appropriate
functional transformation directlf" For instance, assume that a surface is known to be of the
form x = f(y) = [sin(7y+3)]la +a y ]. Let xl = f(Yl)andx = f(Y2) and define
o 1
2
g(y) = sin(7y + 3), x; = x /g(y), x = xig(y) and, in general, Xl . = x/g(y). Then fit
1
Xl = a + a y by a first order polynomial using x; and x as data points.
O
1

2

2

Having determined the values of a and a l' x is defined by xlg(y). The expression for x is
O
valid not only at Yl and Y2' but over the entire region in which g(y) is a suitable transformation. It should be noted that the data points xl and x could have been fitted by
2
x = a + aly without considering g(y). However, only the two data points and the points
O
1
where (7y + 3) = sin- (l) w~ld be satisfied by x = a '+ 0l Y'
O
Theoretically, provided the matrix solution is exact, the polynomial fit given by equation (3)
shou Id fit exactly the (n + l){m + 1) primary data points. If the function to be described is of
the form x = g (y )

c

n

m

i=O

L
j=O

L

b .. z iy i, a study of the primary data points will not give
II

information concern ing the su itabil ity of g(y) as the appropriate transformation of variables, .
since all primary data points are fitted, independent of the form of g{y). Hence, secondary
data points not used in the determination of the b .. coefficients must be studied to arrive at
II
g{y). M-151 allows secondary data points for either arpitrary y or z, but not both arbitrary.
Either y or z must be an lIaliowed li value, in the sense that defines primary data points. The
other coordinate, z or y respectively, may be arbitrary.

J47

-4-

To help decrease the importance of the user in deciding on allowed values of y and z for
primary data points, over-definition of the problem is allowed in the cases of second and
th ird order fitting. As many as seven allowed values may be chosen and the program wi II
use all combinations of seven points taken three and four at a time, respectively for second
and th ird order fits.
.

SURFACE FITTING TECHNIQUE

1.

Select the dependent variable, x

2.

Plot famil ies of curves
a.
y = constant pi otted on the x y plane
b.
z = constant plotted on the xy plane

n

3.

m

b.z i
i=O
j=O I
on the xz and xy planes, respectively. If there is uncertainty concerning the best
value of nand m, all possible values should be. used in separate cases, using the
average error and maximum error features of the code to decide between cases. It
is not crucial that the very best case be used, if transformation of variables can be
used to force a best fit. For instance, x = sin(7y + 3) is fit best in certain regions
Assume nand m for .fitting y and z such that x =

L

ajyi and x =

L

2

by x =

L

a.yi without transformation of variables, but with transformation of
I

i =0
variables x/sin(7y

+ 3) = x' = 1 is fit exactly by a zero order fit: x'

= aO =

1.

In the interest of developing a technique independent of curve fitting experience, it

2

L

a.yi, provided that the region of definition will remain
I
i = 0
small. However, any curve fitting experience at the user's disposal should be used
is better to use x =

0

4.

To effect more accurate fits, use the output option in which transformed data is output ready for further transformations. Th is option prints the transformed values of x
(for example, x/g{y) is printed if the transformation is Xl. = x/g{y) and x is printed
if there is no transformation), the fit of the transformed variable, the difference including sign between Xl and its fit, and the ratio xi/(fit of x'). Referring to figure 2:
x = f(y), the fit of x = g(y), and h(y) = x - {fit of x)o

-5-

g(y)

x
/

/'

lZJ
/

f(y)

/

I

l1J

I

o

primary points

El

secondary points
fit of points, g(y)
function to be fit, f(y)
y

FIGURE 2

The transformation that effects an exact solution is f(y) = h(y) + g(y). Since h(y)
can be approximated by a sinusoidal with appropriate ampl itude and period, the
sinusoidal transformation is made on all data points using the program to make the
change: Xl = x - h(y). Upon rerunning this case with the transformation included,
the printout will include Xl, the fit of Xl, Xl - fit of Xl, and the ratio xl/(fit of Xl).
Once again, hl(y) = Xl - fit of Xl = fl(y) - gl(y). To determine our fit, Xl =
hl(y) + gl(y) and x = Xl + h(y) = h(y) + h'(y) + gl(y). Correspondingly, 'the ratio
x/(fit of x) may be used by plotting th is ratio and describing it just as h (y) was described. Code capabil ity allows as many as ten transformations to be made. It is
necessary, in order to ach ieve an improvement in the fit, that the transformation
of variables be such that the original data points will not be seriously sh ifted by the
transformation. As an example, consider the translation without distortion of the
fit of the array to more closely approximate secondary data points in the array. If
this translation is fit once again, the fit of the translated array will be parallel to the
original fit with no improvement over the original fit in regard to secondary data points
in the array.

TRANSFORMATION OF VARIABLES

o

The util ity of transformation of variables was demonstrated in the section on surface fitting
technique. Basically, there are two types of transformations available in this code: functional transformations that deal with the man ipulation of complete generated functions of x,
y and Zj and transformations of individual variables x, y and Z to form the functions used
in functional transformation. Functional transformations available are I isted in Table 1
and transformation of variables are I isted in Table 2.

-6-

T

TABLE 1
~-(

-~.

FUNCTIONAL TRANSFORMATIONS

=

NMODE = 1

NMODE

None

None

2

f(x)

f(x)

3

xg(y)

xh(z)

4

x + g(y)

x + h(z)

5

x/g(y}

x/h(z)

6

x[g(y) + k(y)]

x[h(z) + I (z)]

7

x/[g(y) + k(y)]

x/[h(z) + I(z)]

8

xg(y)h (z)

x/[g(y) h (z)]

9

x [ 9 (y) + h (z)]

x/[g(y) + h(z)]

xg(y)/h(z)

xh(z)/g(y)

NVT

10

ISo

2

-7-

•

TABLE 2
TRANSFORMATION OF VARIABLES
Let v take on the value x, y or z. v shall be transformed.

TRANSFORMATION

INVERSE TRANSFORMATION

None

NT :::
None

NT ::: 2
0+ be

cv + d

NT ::: 3
0+ bv

c

NT ::: 4
a

sin-1 ( (a + b sin ~CV + d) - a] ) _ d

+ b sin (cv + d)

NT ::: 5

c

In [(a +

b~ dv) -

a]

d In c

NT ::: 6

exp ([a + b In b(cV + d)J - a) - d
c

a + b In (cv + d)

lSI

-8-

(Table 2, Continued)

([a + b I\{v + d)] - a)

NT = 7

- d

c

a+bln (v+d)
c

NT = 8
c
a+bln v+d

- d

ce

a +

b
(v + c)

~

a+

d

.

NT = 10

(In

[11 + ([a+bSinh{~V-l:d)J - a )2(2

+ [a + b

sinh{~v + d)] -a

cos- 1 ( [a + b

NT = 11
a + b cos(cv + d)

] _ d)!

co~{cv + d)].-

a ) _d

c

tan (la + b tan- ~ (cv + d)J - a ) _ d

NT = 12
a + b tan -1 (cv + d)

c

= 13

( ± In

[I -

a + b cosh(cv + d)

+ [a + b
with the restriction i-hat (cv + d)

~

b

- c

-a

(v + c)d

a + b sinh (cv + d)

NT

lid

b

NT = 9

1 + ( [a + b

cosh~cv + d)l - a

c~sh (cv + d ~l a ) 211/2
] _d

Y

> 1.

/s~

-9-

•

Cl

I NPUT PARAMETERS
AT, BT, CT, DT - These are the coefficients a, b, c, and d defined in Table 2. Referring
to Table 1, these coefficients apply to each single function transformation, but apply
only to g(y) if NMODE = 1 or h(z) if NMODE = 2, when a transformation is used
that involves two d ist inct changes of variables. (An examp Ie is NVT = 6 and
NMODE = 1 from Table 1, where g(y) and k(y) are distinct changes of variables
having distinct characteristic coefficients.)
AT2, BT2, CT2, DT2 - These are the coefficients a, b, c, and d defined in Table 2. Referring to Table 2, these coefficients apply only when a two function transformation is
used. When NMODE = 1, only k(y) or h(z) is described; and when NMODE = 2,
only I (z) or g(y) is described.
DC -

x values defined as primary (see analysis). Values of x are allowed only for (YC, ZC)
coordinate pairs. To fill input cards, nonvalid values of DC are set equal to 1.OOOE-9.
The order in wh ich DC values are placed on cards is defined by the order in wh ich ZC
values are read. YC is held constant for any DC input card.

DY -

x values defined as secondary (see analysis). Arbitrary values of z are allowed for
each YC value. To fill input cards, nonvalid values of DY are set equal to 1.000E-9o
The order in wh ich DY values are placed on cards is defined by the order in wh ich Z
values are read. YC is held constant for any DY card and packets of DY and Z cards
are read in the same order as YC values were read.

DZ -

x values defined as secondary (see analysis). Arbitrary values of yare allowed for
each ZC value. To fill input cards, nonvalid values of DZ are set equal to 1.OOOE-9.
The order in which DZ values are placed on cards is defined by the order in which Y
values are read. ZC is held constant for any DZ card and packets of DZ and Y cards
are read in the same order as ZC values were read.

KO -

output selector: KO = 1 - only the b .. coefficients are printed; KO = 2 - b .. coli
II
efficients, x, y, z, fit of x, x - (fit of x), average per centage error, and maximum
per centage error are printed; KO = 3 - same as KO = 2 with the addition of the
transformed x = x I, fit of x I, Xl - (fit of x I), and xl/(fit of x I} printed. Table 3 shows
a fourth order function fitted with a first order approximation using K 0 = 1, 2, and 30

MO -

order -of polynomial Z defined in equation (2), where MO = m. MO may be as
large as ten, but calculational error is such that it is suggested that MO be kept less
than seven.

MC -(MO + 1) except for second and third order fits where MC may be as large os seven.
There ,are MC values of ZC. MC ~ 12

c

NC -

(NO + 1) except for second and th ird order fits where NC may be as large as seven.
There are NC values of YC. NC~ 12

153

-10-

T

NC2 - the number of secondary values of x to be read in for each valu'e of YC. There are
NC2 arbitrary z values. NC2 is::; 18.
NC3 - the number of secondary values of x to be read in for each value of ZC. There are
NC3 arbitrary y values. NC3 is ~ 18.
NE -

operator that governs the type of error analysis us~ to distingu ish between possible
fits when there are multiple fits allowed. Consequently, NE is useful only for second
and th ird order fits where over-definition is possible (see analysis).
NE

TYPE FIT
numerical average

2

product

3

numerical average X product

4

/.
average2maximum
error

5

product with minimum error stripped out

6

average with maximum stripped out

7

product with maximum stripped out

8

product with maximum and min imum stripped out

NIv\ODE - an operator, together with NVT, that is used to define transformations in Table 1 .
NO - order of polynomial Y defined in equation (1), where NO = n. NO may be as large
as ten, but calculational error is such that it is suggested that NO be kept less than
seven.

NPASS - number of transformations allowed sequencially. Referring to the section on techniques, NPASS takes on the value 2 if x" transformations are made
0

NT - defined in Table 2 and treated similar to coefficients AT( BT, CT and DTo
NT2 - defined in the same way as NT but treated sim ilar to coefficients AT2, BT2, CT2 and
DT2.
NVT - an operator, together with NMODE, that is used to define transformations in Table 1.
Y - an arbitrary value of y which, together with a ZC, defines a secondary point, x.
YC -

the value of y used to define primary data points in the DC array and secondary data
points in the DY array.

154

-11-

;e' .

, __

oC

o

Z - an arbitrary value of z which, together with a YC, defines a secondary point, x.
ZC - the value of z used to define primary data points in the DC array and secondary data
points in the DZ array.

INPUT TECHNIQUE
Cards 3 and 4 below are read in repetitively in packages consisting of one card 3 followed by
one card 4 prov ided MC ~ 6 or by two card 4s when MC > 6. NC of these packages are read
in. Card 5 is repeated MC times. Cards 6, 7 and 8 form a package that is read in NC times.
If NC2 = 0, cards seven and eight are not included in the package. If 0 < NC2 ~ 6, just one
card 7 and card 8 follow NC2. If 6 < NC2 ~ 12, the sequence is 6, 7, 8, 7, 8. If 12 < NC2 ~ 18,
the sequence is 6,7,8,7,8,7,8. Cards 9, 10and 11 form a package that is read in MC times.
This package is handled the same as the 6, 7 and 8 package. Cards 13, 14, 15 and 16 fo"rm a package that is read in NPASS times. If NVT (I) < 6, cards 14 and 15 are omitted.

55 symbol comments card

55H

2

NO, MO, NC, MC, NE, KO

614

3

YC(I)

EO.4

4

DC(I,J), DC(I, J + 1), DC(I, J + 2), DC(I, J+ 3),
DC(I, J + 4), DC(I, J + 5)

6E8.4

5

ZC(J)

EB.4

6

NC2

14

7

DY(I, J), DY(I, J + 1), DY(I, J + 2), DY(I, J + 3),
DY(I, J + 4), DY(I, J + 5)

6EO.4

()

Z(I, J), Z(I, J + 1), Z(I, J + 2), Z(I, J + 3), Z(I, J + 4),
Z(I,J+5)

6E8.4

NC3

14

10

DZ(J, I), DZ(J +1,1), DZ(J + 2,1), DZ(J + 3,1),
DZ(J+4,1), DZ(J+5,1)

6E8.4

11

Y(J, I), Y(J + 1, I), Y(J + 2, I), Y(J + 3, I), Y(J + 4, I),
Y(J+5,1)

6E8.4

12

NPASS

14

13

NVT(I), NMODE(I), NT(I)

314

14

NT2(1 )

14

15

AT2(1), BT2(1), CT2(1), DT2(1)

4E8.4

16

AT(I), BT(I), CT(I), DT(I)

4EB.4

()

9

0

Format

Description

Card

166

-12-

KO

XIHk£E OINENSIONAl SURFACf FIT caUE, "-151
"-151 DEMONSTRATION

PRO~lEN.

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POwER

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FIT CODE.

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~'I

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TABLE

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• UtlOnOf·Ol

'rJ 6

3

(,

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'-/

-13-

o

SAMPLE PROBLEM
I

A practical problem involving the fit of hydrogen thermal conductivity as a function of
temperature and pressure was met with success using M-151. The technique of regression
analysis proved unwieldy in solving the same problem; lack of success be ing attributed to
inexperience in picking suitable form for the fit plusthe inherent I imitations of regression
analysis, such as inaccuracies resulting from the need to solve for large numbers of coefficients simultaneously. Some of the data points used are presented in Table 4. Referring
to the section on Surface Fitting,Je,chnique, thermal conductivity was made the independent variable, pressure = y a~d femper(]t~Je= i:. Th'e'families:of curves were not plotted
since it was decided to choose many combinations of n andm and study the. resulting error
analysis. : Table.5 presents input us~dwhen n =:= m = 4. Step 4 in the,technique section
was not used extensively since good results were ach ieved with the 4 x 4 order fit. Because
of the vot0meofoutput wi-th the 4 x 4'case, only the error 'analysis w;ilJ:be, presented together with th~, ~rrors fro"", other case,s in Table 6. Table 3 presents examples of output
available.'
, ,.

TABLE 4
THERMAL CONDUCTIVITY OF HYDROGEN
6
(X10 )

;.

~
50

.

TEMPERATURE, OR
.'

,

.'

2700

3100

3500'

3900

4300

~82f1

'.9425

1<094

1.31'2

1.687 .', 2.166

,

~

100

.8211

.9352

1.073

200

'.82 t'1

:927"1

1 .04,1

1.262
1.571
1.212: . ', 1.451 '

4600

14800

5000

'2.626

3.230

,.

,

",.

1. 947 '

2.301

2.760

J .721

1,.965

2.273

,

"

I/)

0..

...

300

L..

:>

I/)
I/)

Q)
L..

0..

.821,1
"

Q)

.9264

1.047

';

1.203
i

1.430
!

1.682

::8211

.9250

1,.043 " 1.194: "

1.409

:1 .643.;',

500 ,,' ;.0211

.9237

1.0~9

1 .184, ,

1.3Sa <

J..604,

400

1.907

2 191

l~850

2" 109

.793
"'1~:: 678

2.026

1.627

10789

v

',:

--,

700

.'ri2 1"1

~. 9210

1'~ 031

1. 166: "

1.34$'

""1.526'

1000

.8211

.9204

1.029

1 . 159

1.327

1.491

>"J

,

1.862

c
-14-

T

TABLE 5

M-151
4

50.
.8211
100.
.8211
300.
.8211
500.
.8211
1000.
.8211
2700.
3500.
4300.
4800.
5000.

DEHONSTRATIONPROBLEM, ORDER=4X4
4

5

5

2

3

1.094

1.687

2.626

3.23

1.OOOE-9

1.073

1.571

2.301

2. 76

l.OOOE-9

1.047

1..43

1.907

2. 191

1.000E-9

1 .039

1.388

1.793

2.026

1.000E-9

1.029

1.327

1.621

1.789

1.000E-9

1.014
3300.

1. 19
3700.

1.471
4100.

(t

2.38
700.

2.909
4900.

1 .0
3300.

1 • 158
3700.

1.396
4100.

2. 112
4700.

2.510
49QC.

.9838
.3300.

1 • 119

3700.

1.304
4100.

1.788
4700.

2.041
4900.

.9789
3300.

1.107
3700.

1.276
4100.

1.694
4700.

1.903
4900.

.895"4

.9127

3000.
0
0

3300.

1.09
3700.

1.237
4100.

1.556
4700.

1.704
4900.

6

.9091
3000.
6
.9047

3000.
6

.8992
3000.
6

.8974
3000.
6

0

0
0
0

-15-

0

' do.

TABLE 6
ERROR ANALYSIS
Order (n x m)

Maximum

Average % Error

%

1x 1

12.22

36.31

1x 2

7.755

18.20

2x2

8.681

18.82

2x3

2.645

13.25

3x2

9.439

21.38

3x3

2.653

9.839

4x4

.04456

.3445

5x5

.07827

.7006

6x6

2.201

38.67

7x7

51.29

1211.

FLOW

Error

CHART

START
LOAD

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MAX IlVfUlvl LIKELIHOOD RESOLUTION OF TWO

()

MIXED NORMAL DISTRIBU'rrONS

Reimut Wette
Biomathematics Unit, Division of Hesearch,
The University of Texas M.D. Anderson Hospitat and
Tumor Institute, Houston, Texas

Abstract:
Samptes exhibiting particutar deviations from an assumed normat
distribution can, in certain situations, be interpreted on the
assumption that the parent distribution consists of two normatty
distributed subpoputations, with different means and/or variances,
and mixed in a finite proportion. The statisticat probtem is, then,
to estimate the respective parameters. In the generat case, where
no simptifying assumptions (e.g. equatity of variances) can be
made, five parameters have to be estimated, viz. two means, two
variances (or standard deviations), and the proportion of mixture.
The author's estimation method of choice was the maximum tiketihood scoring system. The derived estimator is of the iterative type,
and modified insofar as the information matrix is estimated as the
dyadic square of the score vector. Numericat execution of this
iterative estimation procedure requires initiat estimates of the
five parameters; these are, at present, obtained

~anuatty

from a

normit graph of the data. A generatized distance from origin of the
score vector (i.e. the quadratic form of the estimated variancecovariance matrix) is used as a criterion to exit from the iteration
cyctes.
rr'he pro cedure was programmed for the

IJ3~\1 1 620

(with 1 311) in

FOR1 HAN II-D. The main program consists of two parts: 1.- Routines
1

for controt transfer set-up, standard form data input or transfer
to either of two optionat non-standard data input subprograms.
2.- The resoLution procedure proper, routines for optionat intermediate and other output ~~lnd transfer to two optiona t subprograms.

/ bJ.

The program ?rovides, at present, the fottowing I/O (punched cards)
and test opt ions (under parameter card contro t) :
Data input:

(1) Ungrouped or grouped data not exceeding
200 variates or ctasseso
(2) Grouping of ungrouped raw dataJ ctass interval. and grouping range computed from initial.
estimates.

(3) Grouping of fixed-interval. vatued ungrouped
data.
Output and test options:
(1) Output of grouped data frequency diStribution.
(2) Output of expected frequency and cumutative
frequency distribution together with observed
distribution (grouped data onty).
(3) Chi-squared test for normatity against skewness
and kurtosis (cumutant test), with programmed
bypass of resotution peocedure when not
significant.

(4) Intermediate iteration output of estimated
information and variance-covariance matrix,
parameter estimates and corrections, and
convergence criterion.
Input options 2 and 3 and output options 2 and 3 are subprograms
catted as LOCALs on a 40k machine. A data traiter card controts
exit to MONeAL or return "Linkage to part 1 of the main progra.m.
Maximum core storage used is 35,604 cores (Monitor I, modif. 2,
att-in-core subroutines), program package (2 main/"Link, 4 subprograms)
disk storage is 435 sectors. Interation cycte running time is about

2.7 seconds per point (variate or frequency ctass).
Convergence in this iterative estimation procedure de,ends on
the goodness of the initial estimates, on sampte size and structure.
Experience gather'ed so far indicates that convereence, if attainabte,
is comparativety fast (tess than 10 iterations). Convergence coutd
not be attained in a few instances of

s~att

and itt-behaved samptes,

of size around 20 and l.ess, from \v11ich rel.ia"bl.e initiat estimates
coul.d not be obtained.
I

I b'3

1:

o

The author gratefu1ty acknow1edees the extensive assistance of
Mr. Lawrence E. :rewton, Jr., in ~rop:rammine and testing different
versions of the method in the Computer Science Laboratory of the
hl~D. Anderson Hospital" and Tumor Institute.

Note: Methoc1ol"ogical" and
e1sewhere.

proEramminr~

deta.i 1.s wi 1.1. be pub1.ished

o

EVALUATION

or

TWO METHODS

or

FINDING SIGNIFICANT

CONTRIBUTORS IN MULTIPLE REGRESSION ANALYSIS
1/

Mo Jo Garber and Richard H. Hill-

With the advent of computers in recent years tremendous strides have been
made in the ability to reduce to manageable numbers vast accumulations of data.
In evaluation of experimental results the major emphasis is now on punching and
proofing the observed values with the assurance that a generalized computer
program is probably on the shelf ready for use.

In the majority of cases this

is true, but thoughts and concepts have expanded along with the increase in
ability to do arithmetic quickly and accurately.

We are, of course, now find-

ing problems even large scale computers cannot solve in a reasonable period of
time.
One such problem is mUltiple regression involving many independent variabIes.

A number of years ago the first of approximately 60 such problems was

handed to the senior author o

One phase of the experiment dealt with growth in

a greenhouse of citrus seedlings in 102 nonfumigated old citrus soils.
of 35 measurements was made on each.

A total

These included chemical, physical, and

biological properties of the soil, plant composition, and relative growthe
Locating statistically the best single contributor and the best set of 33 of the
34 independent variables is relatively a trivial operation.

The best single

contributor is the variable with the highest coefficient of determination

(r~oy)e
~

The best set of 33 (or ndl) contributors is easily found by entering all n vari=

~
I
I

I

ables into the regression equation, and deleting the variable with the smallest

1/

University of California, Riverside, and Informatics, Inc.

2

absolute partial correlation

(Ir·.

.

YXj • x.;x
•

.J

=,,.,~

k

I ') ~
'

Mre Hill (then at the University

of California. Los Angeles> wrote the MISLE program for the 709
The best set of

two~

0

the best set of n ... 2 9 and all best sets between these

extremes present a very different problem.

The best set of two will not neces-

sarily contain the best single contributorS) and the best set of 1'1-2 could contain
the variable not included in the best set of n-10
analysis all best sets should be calculated.
problem.

For a statistically efficient

But this presents a formidable

For example. the final regression equation for the above problem con-

tained 10 independent variables.

Finding the best set of 10 among 34 variables

can be quite a chorel! even for a computer.

is 34!/(lO!24!) or 131,128,14011

The number of sets to be evaluated

Assuming that a computer can solve these at the

rate of one per second, over 36,424 hours are required for finding the best set
of 10.
A number of questions immediately come to mind:
(1)

Is the best set of 10 significantly better than the one
selected by this procedure?

(2)

How does the best set of 10 compare statistically with
the best set of lIt or any other best set?

(3)

As the correlation coefficients are statisticsf) and not
parameters, is the additional labor worth doing?

After some soul searching it was decided that initially the following threephase procedure would be used:
(1)

MISLE Program (presently UCRBL

0052~

1620 Library File No. 6.0.37)

All independent variables are entered into the regression equation, the
inverse matrix af sums of squares and cross products being calculated in the
process.

2
All b./e
.. are calculated, where bo is the partial regression coef1

11

1

ficient of y on the ith independent variable, and e i i is the major diagonal

1

166

l~
I:)

-.----~----

~-

---

--------

1'1

3

o
element for that variable in the inverse matrixo

As Fisher (1) has shown

b~/cii is

the variance (equivalent to a sum of squares with one degree of freedom) which
would drop into the error sum of squares of y if the variable were deleted.
2
The variable with the smallest b /c is deleted. and the remaining n-l
independent variables are entered into the regression equation.

This procedure

is continued until only one variable remains.
An example of such analysis is illustrated in Table 1 in terms of the squares
of partial correlation coefficients.

Note that. in general. the simple correlation

coefficients, the squares of which are shown in the second line of the table, do
not reflect in any way the magnitudes of the squares of the partial correlation
coefficients as variables are deleted.
The leftmost 10 variables were found to be statistically significant contributors (0.05 level of probability), and it should be noted that four of these showed
nonsignificant simple correlation with the dependent variable.

The magnitude of

R2 was 0.5387.
Variable 34 has the largest simple correlation.
other variables its contribution is relatively small.

Yet. in combination with
On the other hand. Variable 31

which was not significantly directly associated with the dependent variable is relatively a large contributor in the presence of other variables.
(2)

Stepwise Regression (UCRBL 0018, 1620 Library File No. 6.0.031, a
modification of the BIMD 9 developed at UCLA by the Biostatistics
group)

Here the procedure is to begin with the variable most highly correlated with y co
From the remaining variables the one with the highest (absolute) partial correlation
is selected for entry (assuming that it meets the F criterion), and the magnitudes
of the two contributions are evaluated.

Either both are retained or one is deleted

/ b7

..

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

.. ----""

~,--,

..

---

-------

-----------

4

(a parameter card entered with the data contains the minimum F value required to
enter a variable into the regression equation and the minimum F value required for
retention of a variable)

0

This process of entering, evaluat ing. and deleting var i-

abIes continues until the criteria can no longer be met.
For the problem being considered here nine variables were found to be
2
statistically' significant contributors (R = .5205) when grouped, Eight of these
variables were also selected, by the HISLE program.
(3)

MISLE Runs
(a)

The eleven variables selected by either or both of the above

programs were fed into the computer for another HISLE evaluation.

Ten of the vari-

abIes were found to be significant contributors, and the first variable of the
eleven to be deleted was the one unique to the Program IB run.

There was thus no

significant gain.
(b)

It was then decided to make another run, this time including

the eleven above and certain additional variables,
(~

Examination of the F values

1) led to the choice of the two variables last deleted by Program 52 and the

succeeding three which would have been entered by Program lB.

Two of these were

common to both runs.
Of the fourteen variables entered for the final run 10 were found to be significant.

Seven of these were among the variables found significant by both

programs, two common, but in the noncritical area, and the tenth being a signifi-cant contributor found by Program lB.

The magnitude of R2 was .5433.

The 10 variables statistically significant in this run were the ones coneluded to be real contributors (paper by Martin, Harding, and Garber (2»
The four curves are shown in Figure I.

t.

The curve of multiple R2 calculated

by Program 52 (labeled 521) is almost smooth. running essentially horizontally

o

5

until approximately six varidbles have been deleted o
steep as addit lonal variables are deletedo

The drop off becomes quite

It should be noted that the last remain=

lng variable is not the one most: highly correlated with yo

The la'tter Sl Variable 349

was dropped after the 26th run.
The curve of mUltiple R2 calculated by Program 18 begins by entering
Variable 34 then rising in a somewhat oscillatory manner to essentially ma.tch
the 521 curve after 9 variables have been entered o
The short spur labeled 521Ia is the graphic result of the MISLE run with
11 variables&

The short section·of curve (52I1b) exhibits a sharper break than either of
the first two.
The remaining two curves in the figure are from the 521 rune.

The curve of

2

"Cumulated b /e" shows the addition to the residual sum of squares (all variables
initially entered into the regression equation) as variables are deleted..

The

curve of "Residual Mean Squares" falls off from its initial value i then rises

t)

Recalling that the residual mean square is the quotient of the residual sum of
squares by the residual degrees of freedom it is seen in this example that in the
initial phases of variable deletion the denominator is increasing relatively more
rapidly than the numeratoro.

Only after approximately half the number of variables

has been deleted does the curve begin to rise o
A summary of the evaluation of 55 experiments· is given in Table 20
left side of the table the r criterion was set at 1 00
0

0

For the

For the right side of the

table the 0 05 level of probability was the criterion o
41

In eight of the 55 experiments Program

U

programs.,

No~

18 was the better of the two

In four experiments Program NO e 52 gave better results o

In one experI-

ment each of the programs provided information both significant and unique u

•
6

In one experiment. the order of entering variables indicated the advisability
of a third run.

The outcome was the set of four variables selected by both programs.

For the remaining 41 experiments both programs gave the same results in the
initial runs.

The third run was unnecessary.

In summary, there is no clear cut indication of the superiority of one method
over the other.

For our purposes at Riverside we will continue to evaluate large

problems by both the deletion and the stepwise methods.

LITERATURE CITED

1.

Fisher, Sir R. A.
10th Editione

2.

(1948).

Statistical Methods for Research Workers.

Hafner Publishing Company.

Martin, J, P., R.. Bo Harding, anq M, J. Garber.

(196l).

Re'lation of Soil

Properties and Plant Composition to Growth of Citrus Seedlings in 100
Nonfumigated and Fumigated Old Citrus Soils.

17D-

Soil Science 91(5):317-323.

'0

...............

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2
LEGEND
8
5
4
6
7
3
1. Variable number (Variables were deleted from right to left)
6
7
6
2
(Two decimal digits)
5
2. SiJap Ie rYXi

Table 1.

3.

2
Multiple Ry.ijk--- (Four decimal digits)

4.

2
Partial ryi.jk---

(Two decimal digits)

Computer re.ults (34 independent variables, 102 sets of
observation.).

Table 20

No. of
Indep.
Var.
34
32

32
31
31
30

-

- ..J

>U

Degrees
of
Freedom

Summary of evaluation of 55 experLments.

No. of Variables No. of
Selected by
Var. in
Common
0018
0052

101
44
44
44
44

12

44

7
4

2

7
9

5
4

12
3

10

9
6
4

5

8
3
2
2

6

3

2

1

29
9

44
15

31
31
10

44
44

3

2

6

2

6

72
72

5
1

2

2

33

101

6

6

4

32

44

4

5

4

4

Final Selection
No. of Variables
No. Unigue to
No. of
No.
Unique to
0018
0052
Variables Common
0052
0018
10
2

9

9
6
4

8
3

3

3-

3
1

6
2

1
3
1

3

2

3

2

6

2
2

1
1
2

2
2

2

2

5

3

1

4

4

2

2

7

3
1
3
2

1
2
2
5
1
1

1
2
1
3
2
2
3
1

2

3
4

2
2

2
1

1

SU1IID&ry of 41 additional experLments:
No. of independent variables: 6 to 32
No. of degrees of freedom:
24 to 152
No. of significant contributors selected in common by 0052 and 0018:

0 to 5

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U. S. ARMY ENGINEER DISTRICT, WALLA WALLA
WALLA WALLA t WASHINGTON

AN INTEGRATED SPS EARTHWORK
SYSTEM FOR THE IBM 1620

A Paper Presented at the IBi-1 1620 Users Group

Western Region Conference at Tempe, Arizona
12 December 1963

o

Prepared by
Cecil L. Ashley
ADP Coordinator, NPW
November 1963

t.

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rid! S"HM"{bHi4¥"j"'-'" i!I'iier--"Uffi8P?T'"'%WtpW"" um'M'w
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CONTENTS
Page
ABSTRACT •
PART I

PART II

PART III -

...... .. . .........

• • • • • •

ii

• • • • • • • • • • • • • • •

1

Terrain • • • • • • • • • • • • • • • • • • •
Variety of Criteria • • • • • • • • • • • • •

1

APPROACH TO

. .. ... . . .....

2

Acquiring Data
••••••••••••• • •
Data Translation and Preparation • • • • • • •

2
2

INTEGRATED PROCESSING

4

GENERAL PROBLEM

PROBLm~

. .... .......

Alignment and Realignment • • • • • • • •
Template Generation ••• • • • • • • • •
Quantity Computation • • • • • • • • • • •
Design for Contract
• • • • • • • •
Special Options • • • • • • • • • • • • •
Pay Quantities Computation • • • • • • • •
PART IV
PART V

4
4
4
4
5
5

... ..... . .... .. . ...
ABSTRACTS OF PROGRAMS . . . . .
• • • • •

7

1.
2.
3.

7
8
9

5.

6.
7.
8.
9.
10.
11.
12.
13.

o

• •
• •
• •

RESULTS

4.

FIGURE 1 -

• •
• •
• •

1

HORIZONTAL ALIGNMENT • • • • • • • • • ••
GEOMETRIC COMPUTATIONS • • • • • • • • ••
EARTHWORK DATA CHECK • • • • • • • • • ••
PROFILE GRADE AND TEMPLATE GENERATION ••
SLOPE SELECTION - TEMPLATE GENERATION ••
EARTHWORK QUANTITY CO~~PUTATIONS •• • ••
EARTHWORK LINE SHIFT
••••••••••
EARTHWORK TEMPLATE SHIFT • • • • • • • ••
EARTHWORK ALIGNMENT OFFSET • • • • • • ••
EARTHWORK DATA PLOT REDUCTION • • • • ••
CENTERLINE DATA PLOT REDUCTION • • • • ••
STATIOn INTERVAL QUANTITY SUMMARY • • • •
PLANE COORDINATE CONVERSION PHOTOGRAMMETRY LEAST SQUARES METHOD ••

SYSTEI-1 FLOW CHARTS • • • • • • • • • • • •
PREPARATION OF X-SECTION CARDS
COMPUTATION OF CUT AND FILL QUANTITIES

i

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6

9
9
10
10
10
11
11
11
11
11
12

.--~-----

- ...- - --

--~~~

_...... .. , '

o
ABSTRACT

The purpose of this paper is to review the group of roadway design
programs being utilized and developed by the Uo S. Army Engineer Division,
North Pacific, in cooperation with State Highway Departments of Washington,
Oregon, a.nd California, U. S. Bureau of Public Roads, Uo S. Forest Service
and IBM.
Programs discussed include horizontal and vertical control, data check,
template design, alignment offset, quantity computation and several related
utility programs, all of which are coded in SPS and make up an integrated
system which is convenient as well as fast. The specific use of these
programs by the Corps of Engineers is in conjunction with relocation of
highways, railroads, county roads and municipalities involved in the
design and construction of large multi-purpose hydroelectric projects.
The "System" of programs has been developed through a combination
of initial development, modification of others' programs and adoption of
others' programs with no modification. Coordination of programming
efforts is accomplished largely through facilities of HEEP.
The abstracts of programs at the end of this paper are brief and
general in nature. Writeups are complete but not necessarily in compliance
with USERS GROUP Standards. Interested parties should address inquiries
to:
Division Engineer
Uo S. Army Engineer Division, North Pacific
210 Custom House
Portland 9, Oregon

o
ii

o

PART I
GENERAL PROBLEM
Terrain.
The nature of the earthwork problems being encountered
by the Walla Walla District may not be entirely unique, but they are
certainly extreme at times. The Columbia and Snake Rivers have both
cut deeply into Miocene basalt flows that form the regional bedrock.
For 45 miles above the John Day Lock and Dam project, the Columbia River
flows in a relatively deep valley with precipitous walls rising to a
height of 3,000 feet above the general land surface on the north side,
and up to 1,000 feet on the south side. The canyon walls consist of a
series of stepped basalt cliffs interposed with steep talus slopes and
terminating at the top in relatively flat plateau areas. Because of
the constricted nature of the canyon, there is very little choice for ,
the alignments; however, where the alignment is benched into the basalt
edges, a minor shift in alignment can mean a major difference in cost
because of the rock excavation and high fills which may occur.
Because of the type and shape of the terrain, alignment is quite
critical and many trial alignments may be required in order to arrive
at what is considered an optimum one.
Variety of Criteria.
Another feature that requires considerable
attention is the number of agencies to be dealt with. In one project
area there may be up to three State Highway Commissions, four railroads,
and a dozen counties involved; all of which have from minor to major
differences in criteria. This condition is emphasized when two railroads and a highway are aligned adjacently and there is hardly room
for one of them in the canyon. Something has to move up the hill.
The John Day Lock and Dam presents a good example of the magnitude
of the work being done in the North Pacific Division. This will be
a concrete gravity structure with an ultimate installation of 2,700,000
Kl1 produced by twenty 135 ,ago KWT units driven by Kaplan turbines
measuring 305 inches throat'diameter. The total excavation for the
project will be approximately 80,000,000 cubic yards, half of which
will be hard rock. This total excavation figure is exceeded only by
Owyhee, Fort Randall, Fort Peck, and Garrison project; all of which
are earth or rockfill dams. As far as we know, the 40,000,000 cubic
yards of hard rock excavation will comprise a world record.

c

The relocation at this project involves 80 miles of SP&S Railroad,
57 miles of UP Railroad, 40 miles of Washington State Highway, 32 miles
of Oregon Interstate Highway, and the town of Arlington with a population
of 633, 1960 census.
When the alignments involved are required to be revised up to 8
or 10 times in order to reach a compromise with economics .and the
agencies concerned, the workload approaches staggering proportions.
1

..
PART II
APPROACH TO PROBLEM
Acquiring Data.
In order to plan and design such a project and
its accompanying relocation work, surface data must be translated
into punched cards representing ground cross sections along the alignment centerline.
First. of course, an approximate alignment must be determined On
paper. The horizontal alignment and geometric computation programs
are utilized at this stage for horizontal control. Survey parties then
either "flag" that alignment in the field, or establish control points.
Helicopters are utilized to transport the party members to inaccessible
locations. Aerial photographers are then hired to "fly" the line and
the resulting film is converted to glass plates. Sufficient area is
covered to enable the designer to shift the alignment or position several
roadway alignments such as railroad mainline and shoofly. and highway
and detour.
Data Translation and Preparation.
With the pictures taken and plates
made, the next problem is to translate these to punched cards which are
input media to the computer. This is accomplished by one of two ways,
with emphasis on minimum manual work. For planning and design stages,
if contour maps are available, alignments may be laid out on them and
cross section cards punched by means of the Benson-Lehner Digital Scale.
If contour maps are unavailable. or if for other reasons. it is desirable
to do so. the cross section cards are prepared on a WILD A-7 Autograph
Stereo Plotter connected to an IBM 026 Key Punch through a WILD EK-5.
A hard copy is prepared concurrently on an electric typewriter. An
optional feature of this system permits printing out on typewriter the
X, Y. and Z coordinates at points selected.
For initial phases. cross sections are taken covering sufficient
area to allow for alignment shifts and multiple alignments.
Once the cross section cards are punched. they are checked for
"detectable bulls"by means of a computer pass using the "Data Check"
program which senses such errors as overhangs, double or no centerline.
excessive horizontal or vertical difference between rod readings, etc.
as may be logically determined.
At this stage, cross sections can be plotted by the Benson-Lehner
Electroplotter. To many designers, cross sections are considered
obsolete but the terrain and materials with which we have to contend
make cross sections desirable and often necessary.
Another means by which segments of cross sections are sometimes
prepared is the Benson-Lehner Oscar Trace Record Reader. This machine

2

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c

uses fathometer graphs as input and produces punched cards in the
same format produced by the Digital Scale or WILD A-7. This method is
useful where the toe of proposed fill slopes extend below present water
surfaces and in navigation channel and powerhouse excavation applications.
A program is currently being developed by the Walla Walla District which
will update cross section data cards by extending on either side. by
inserting additional readings or replacing corrected readings.

c
3

- - - . - -••- ...- - - - - -.••. ,... --

········ ....

".~_.,c,c=_

..... __

PART III

INTEGRATED PROCESSING
Alignment and Realignment.
With the cross section cards prepared
and checked, the question arises, "Has the alignment been revised
during the process of preparing the data cards?" If so, the new
alignment computation data is combined with the original or previous
alignment data and processed through the Earthwork Offset Alignment
Reference program which computes the offset and skew angle between
the two alignments and new stationing. If the skew angle is not too
great and the original cross section cards cover sufficient distance,
the output cards of this computer pass serve as header cards which
are combined with the cross section cards and processed through the
Earthwork Alignment Shift program to compute new cross section cards
referenced to the new alignment centerline.
Template Generation.
Roadway templates to be used for computing
cut and fill quantities can be prepared on the computer at this stage
through what is at present a two-pass process. The first pass
establishes profile grade and the coordinates of the basic roadway
points reflecting superelevation for horizontal curves. This basic
roadway consists of two to four planes defined by from three to five
points.
The second pass completes the templates by adding ditches where
required, and slope readings. This pass also serves as an additional
data check by indicating slopes that will not catch, etc. The complexity
of road design involving berms on fill slopes for embankment protection,
and benches on cut slopes for rock fall protection or due to material
classification change, has prompted a recent modification to this program
which enables the designer to specify these features on the terminal
slopes of the template. Templates can be produced with either slope
readings or catch point coordinates at extremities.
Quantity Computation.
For computing quantities, the cross section
and template cards are merged and processed through the Earthwork
Quantity Computation program. The output of the pass provides cut and
fill areas. accumulated cut and fill quantities and mass ordinate.
This program also has optional features for dredging and levee applications. in which case. directed slopes and outside catch points are
used. It will also make quantity adjustments for curvature correction.
Design for Contract.
Listings of this output are provided the
designer who then determines if and where alignment needs to be
revised vertically or horizontally. This is repeated usually for
various segments of the line, then when the alignment is satisfactory,
the complete line is recomputed for quantities.

4

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Special Options.
If two alignments are adjacent and the embankments sometime overlap, the Stage Development program is used to
combine the cross section and template cards to produce new cross
section cards which can then be line-shifted and used to compute
berms for riprap which is to be computed separately from basic
quantities.
The answer cards from the quantity run can be processed through
the Station Interval Quantity summary to produce listings of quantity
summations at selected intervals.
Cross section and template cards are processed through the
Earthwork Data Plot Reduction program to replace template slope
readings with catch point coordinates and reference all vertical
coordinates to a common elevation so the cross sections and templates
can be plotted.
Pay Quantities Computation.
During and after construction when
pay quantities are to be computed, the line is re-flown and "asbuilt" templates prepared. These cards differ from the previously
mentioned templates in that they do not have slope readings but
extend from catch point to catch point. These templates are merged
with cross section cards of the final alignment and pay quantities
are computed through the Earthwork Quantity Computation program.
The "as-built" template cards are point-plotted over the "asdesigned" cross sections and used to check for over- or under-built
conditions.

',,·,
0.
"

5

PART IV

RESULTS
Opinions of the users of these programs are varied. so in order
to avoid giving an overly optimistic view, this example was taken
from the most "conservative" user. Sixty miles of railroad alignment
on the Little Goose Lock and Dam project was processed through eight
aligrunents before arriving at the final choice. By thoroughly
analyzing the first seven alignments. five million yards of rock
excavation were saved between the seventh and eighth alignments. If
hand methods had been used, there would not have been time for more
than four "shotgun" alignments and the savings resulting from computer
utilization would not have been possible.
The cost involved in design stages may be equal to or even
greater than that incurred by "shotgun" manual methods, but this
includes increased analyzation of alignments, making possible savings
such as cited in the example. Even greater savings are being realized
with a computer on-site in the Walla Walla District so that even more
alignment trials can be made in certain areas where the alignment is
most problematical.
One installation has combined template design and quantity computation programs enabling them to obtain quantities in one pass without
producing intermediate templates. This version also incorporates
line shifting as an integral part of the single pass. It requires
a different format of data cards than that being used by our District
and 60 K. The type of processing usually encountered in the Walla Walla
District require some insertion of hand-prepared templates before the
final pass, so we have not seriously considered their degree of
combination. The two passes of template design might be combined to
advantage, providing header card storage did not become too restricted.

6

J31

o
PART V

ABSTRACTS OF PROGRAMS

1. HORIZONTAL ALIGNMENT
This program computes horizontal
alignment from the following basic input alignment data:
a.

Beginning station and coordinates (RP)

b.

Coordinates of PI's

c.

Degree or radius of curves

d.

Spiral lengths (highways) or chord lengths and number

(UPRR)
Output information includes:
a.

Bearing and length of course between PI's

b.

Stations and coordinates of all curve points

c.

Deflection angle

d.

Degree. length and radius of circular curves

e.

Deflection angle (DE). x and y. u and v of spirals

(~)

and semi-tangents

Curve definition can be by arc or chord. Distances are rounded
to nearest .01 foot. coordinates are carried to nearest .001 foot.

"I
'"
7

2. GEOMETRIC COMPUTATION
The present geometric program
combines the features of several related programs which were used on
the IBM 650. The following types of computations can be performed
singly or in combination in one machine pass.
a.

Survey traverse using bearings with azimuth or deflection

b.

Compass or transit rule traverse adjustment.

I

c.

Areas bounded by traverses which may contain circular

f

angles.

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segments.

i

d. In a traverse between known points, a combination of two
unknowns (bearings, 2 distances or a distance and a bearing) may be
solved for and stored for recall in subsequent problems in same pass
with interdependency of geometric figures.

I

e. Location of points on tangents, circular curves, spirals
or offset spirals and intersections of any two of these.
f. The intersection of tangents or circular curves with
spirals or offset spirals.
g.
to another.

Convert selected coordinates from anyone plane system

The ability to store data pertaining to any course for use in
problems which follow makes it possible for the engineer to begin
with a minimum of data and to solve complex office and field layout
problems in one pass on the computer.
Problems are arranged in logical sequence to develop intermediate
answers as would be done by "people-computers" following traditional
methods.
A closed traverse can be adjusted in one problem, for instance,
and an adjusted loop can be run from it to close on any point for
which coordinates are known or have been computed. Two alignments can
be intersected and the bearing and distance to land corners or other
references readily determined. The area of gusset plates can be
determined and a host of other geometric problems can be solved. As
a matter of fact, some users say"it can do anything~"

o
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3.

EARTHWORK DATA CHECK

This program checks earthwork input data in format used by
U. S. Army Engineer Division, North Pacific, and its various Districts.
Errors which would result in erroneous results or machine halts are
detected and error messages typed or punched identifying the station
and specifying the type of error detected.

4.

PROFILE GRADE AND TEMPLATE GENERATION

This program converted from Washington State Highway Department's
Five-Point Profile Grade Program. produces the following results:
a. Generates basic roadbed templates for input to Slope
Selection - Template Generation Program.
b. Produces pavement elevation cards supplying elevation of
five points at each station to .01 foot accuracy.
c.

Computes profile grade at selected or incremental stations.

d. Reproduces templates inserting new profile grade elevation
in the reference elevation field.
e.

Punches· a summary of vertical control data at end of each

run.

5.

SLOPE SELECTION - TEMPLATE GENERATION

This program requires ground line cross section cards plus
the template cards produced by the Profile Grade Program as basic data.
Other input consists of slope specification cards and bench-berm data
cards. Three fill slopes and four cut slopes may be specified for
appropriate depths of fill or cut. Ditches can be specified with V
or flat bottom with depth and slope optional. Terminal slopes may
include bench (cut) or berm (fill).
The templates produced may include catch points. or the
terminal rod readings may be replaced with slope readings in the form
xxx.xx horizontal to 1 foot vertical.
These templates when collated with ground line cross section
cards are the input to the Earthwork Quantity Computation Program.

o
9

•

6.

EARTHWORK QUANTITY COMPUTATIONS

a. The purpose of this program is to compute quantities of
earthwork to be excavated and placed on a given Job. The program is
patterned after the I~~ 650 Cut and Fill Program (H-84l) as modified
by Bureau of Public Roads, Vancouver, Washington. The computations
are performed in the conventional manner by taking the original ground
topography and the design of the completed section, as specified by
the engineer, and computing the cut and fill end areas. These are
then used to compute the volumes between sections by the Average-EndArea method. This program will apply a volume correction due to
curvature if desired. Swelling or compaction can be applied to either
the cut or the fill and these quantities are accumulated throughout
a project to produce a mass-ordinate. The total accumulated quantities
of unadjusted cut and fill are also available for each section.

'-

b. As a by-product of these computations, some design information is available at each section to aid the engineer in his appraisal
of the design that has just been computed. These include the cut or
fill at the pivot point, at the toe of both the right and left slope,
and at centerline. Also, the rod and distance to the catch point of
the template slope and the original ground line, if these were not
part of the input data.

7.

EARTHWORK LINE SHIFT,

The purpose of this program is to shift topog card data
(type "0") to a new or offset centerline. This enables the engineer
the choice of running multiple trial alignments while using the original
topog data but shifting the topog data to coincide with the alignment.
The program can also be used for station adjustment and for the reverse
line shifting of topog data. It is desirable in some phases of earthwork to shift the topog data from the original line to an offset line,
generate templates at the offset line, stage the ground line, and then
shift the staged ground back to the original line. By proper program
control in the Job Control Card, the original line shift headers (used
to shift original topog to an offset line) and the staged ground at
the offset line can be used to shift the staged ground back to the
original line.

8.

EARTHWORK TEMPLATE SHIFT

This program is designed to take the Type "1" templates that
were prepared or generated at an 'offset centerline and punch new templates
having original centerline stationing and shot distances referenced to
the original centerline. The new Type ttl" templates can then be collated
with the original terrain cards (Type "0") and a plotter deck is obtained
which has the original centerline as a base for plotting of both terrain

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10
Ii,

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I:

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data and Type "1" templates. Use of this program will facilitate
plotting operations when more than one roadway section is planned and
is to be plotted on the same cross section of terrain.

9.

EARTHWORK ALIGHMENT OFFSET

This program is designed to compute offset distances. skevT
angles, and centerline station coordinates of a base line and an
offset line. Output also includes line shift headers which enables
the Earthwork Line Shift Program to produce a new set of ground line
cards referenced to the offset line.
10.

EARTH\'/ORK DATA PLOT REDUCTION

This program reproduces ground line and template cards adding
plotter signs where necessary and references both type of cards to a
common reference elevation. It will also provide demand origin offset
codes and insert blank cards where necessary.
11.

CENTEHLINE DA'rA PLOT REDUCTION

This program compiles station numbers and centerline elevations
of ground line cross sections or template cards in a format for plotting
of centerline profile.
12.

STATION IUTERVAL QUAnTITY Sill1l·1ARY

The purpose of this program is to produce a summary of quantities
of earthwork to be excavated and/or placed on a given job. Two types
of summary options are available: Station or Interval. The listings
are used by the engineer for design analyses and as tabulated quantity
listings for plan and profile drawings for design memorandums and/or
contract drawings.
13.

PLANE COORDInATE CONVERSION - PHOTOGRAMMETRY LEAST SQUARES r-1ETHOD

The purpose of this program is primarily to convert the machine
coordinates of a universal stereo-plotter to a local coordinate system.
applying the least squares method of conversion (Helmert).
This conversion is mathematically expressed as follows:

o

x

=p

+ k X cos a - k Y sin a

y

=q

+ k Y cos a + k X sin a

The quantities p and q are ground coordinates of the origin of -the
machine coordinate system, a is the angle of rotation between the two
systems, and k is the distance scale factor.
11

PREPARATION OF X-SECTION CARDS

PUNCH X-SECTION
CARDS VIA WILD
A-7 AUTOGRAPH
STEREO PLOTTER

COMPUTATION OF CUT AND FILL QUANTITIES

A

PROCESS THROUGH
PROFILE GRADE
PROGRAM TO
COMPUTE BASIC
ROADBED
PROCESS THROUGH
ALIGNMENT SHIFT
TO PRODUCE NEW
X-SECTION CARDS

PROCESS THROUGH
......._ _ _ _ _-L:SLOPE SELECTION
OGRAM TO COMPLETE TEMPLATES
MERGE X-SECTION &
TEMPLATE CARDS-INSERT
HAND PREPARED
TEMPlATES IF ANY

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REVISE HORIZONTAL
AND/OR VERTICAL !....io----t--=;:~T~7__j.-...J
ALIGNMENT

12

;;37

FIG. 1

c

HYDRO SYSTEM DAILY OPERATION
ANALYSIS PROGRAM

CHARLES R. HEBBLE
U.S. ARMY ENGINEER DISTRICT, WALLA WALLA
WALLA WALLA, WASHINGTON

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HYDRO SYSTEM DAILY OPERATION ANALYSIS PROGRAM
by
Charles R. Hebble

11

INTRODUCTION
The computer program described in this paper, along with certain
fixed input data, constitutes a detailed mathematical model of a system
of hydroelectric projects. It is a general program applicable to any
river system .3.nd scheme of development. Natural lake and channel storage
may be synthesized in addition to reservoir storage and backwater effects.
The program is capable of accurately simulating the hour-by-hour power
loading and water regulation of a hydro system.
Through use of the program it is possible to determine the operating
characteristics of planned future projects for various-sized power
installations. Backwater encroachment on upstream reservoirs, pondage
requirements, and the effects of peaking discharges on downstream river
stages and reservoirs may be evaluated.
The program may also be used to compare alternative distributions
of system load among an existing group of hydraulically and electrically
integrated projects. It is thus possible, through a trial and error
approach, to determine optimum load distribution.
The pxngram has been used in investigating existing system development, along with future planned developments of the lower Columbi~ and
lower Snake Rivers. Here a series of run-of-river projects, below
Grand Coulee Dam, will develop almost all of the available head (see
Figures 1 and 2). It is anticipated the program will be used to analyse
future operating problems in regards to power loading and water regulation.
DESCRIPTION OF EQUIPMENT
Two versions of the program exist: one for an IBM 1620 having a
40,000 digit memory with an" IBM 1622 Card READ-PUNCH for input-output;
the other for an IBM 1920 System (combined IBM 1620/1401) having a
60,000 digit memory in the IEM 1620 and 4,000 digits in the IBM 1401.
This latter system has both an IBM 1402 Card READ-PUNCH and an IBM 1403
on-line printer for input-output. Both systems have the following
optional features required for program execution: Transfer Numeric
Strip, Transfer Numeric Fill, Move Flag, and Indirect Addressing.

o

1/

Civil Engineer, Automatic Data Processing Section
U. S. Army Engineer District, Walla Walla

Peripheral equipment required is as follows: card keypunch, card
verifier, and card sorter. In addition, for the system with the IBM
1622, a card tabulating machine with a special wired panel is required.
ANALYSIS AND METHOD OF SOLUTION
General. - The program is intended for the detailed hour-by-hour
analysis of hydro system operations; basic input to the program and
output from the program is hourly. However, periods greater or less
than one hour may be used. There is no limit to the number of realtime operating intervals which can be simulated by the computer. The
program continues to run as long as there are input data in-the READ
hopper. Ordinarily, however, real-time periods of more than a week
are not analyzed because of the excessive length of the computer runs
for all but the smallest systems. As a rough estimate, the program
requires two minutes to compute one day's output for each hydro project
in the system. The number of reaches and projects that can be analyzed
in a given system is dependent on the computer storage capacity. The
program instructions require approximately 25,000 digits of memory. A
rule-of-thumb estimate for a given hydro system, including open river
reaches, is 1,000 digits of memory for each hydro station. Variation
of memory requirement is due to optional lengths of tables used to
define system parameters.
Program Operating Modes. - Discharges from the various hydro projects
are specified, either directly or indirectly as input to the program for
each real-time period. Four operating modes exist for this purpose:
(1) station power loading given; (2) system power load plus generation
allocation (breakpoint) settings given; (3) total project discharge
given; and (4) project forebay elevations specified. Any of the foregoing, in combination with other fixed and variable data, determines the
individual project discharges. Different projects may be operated
under different operating modes at the same time, and the operating mode
of any project may be changed at any time.
Variable Input. - Each hydro station obtains operating data for
each real-time period from coded variable input cards. Variable input
data include project power loads (or discharges), system loads with
project breakpoint settings for load-frequency control, local inflow,
optional spill, and number of generating units synchronized on the line
and available. These data may be varied as desired during the course
of a run.
~ration Sequence. - The program begins with the upstream project
of the series and proceeds downstream, routing flows through each open
channel reach or reservoir. Local inflow between projects is added to
the routed flows. The outflow from the projects is computed as the sum

2

c
of power discharge, spill, and average fixed release. (The average
fixed release, which must remain constant throughout the run, includes
losses due to lockage, leakage, and useage.) The entire process is
repeated for successive IS-minute computation (routing) periods.
Project and desired reach answers are obtained upon completion of the
fourth routing period. The variable data for the next hour is then read
in and the entire process repeated. Routing and output intervals may
be varied by a special job definition routine. The routing interval
may be different for different projects or river reaches but must be
a multiple of the basic routing interval. The computer program has
two fundamental parts. One is the method of simulating a hydro-power
station, the other is the flow routing procedure. Each part will be
considered separately and in some detail.
Hydro-Power Station Simulation. - Each generating station synthesized in the program is represented by individual unit characteristics
as illustrated in Figure 3. This is in contrast to the method used in
other power programs for coarser increments of time which consider only
generating station characteristics as a whole. Such programs assume
some operating efficiency between best efficiency and, say, full-gate
efficiency. This assumption, while adequate for studies having a basic
time period of day, week, or month, during which there are many swings
in 'station power loadings, are inadequate for the detailed hourly computations required in the study of peaking operations. The number of
generating units synchronized on the line may be specified as variable
input or may be automatically selected by the program. The program has
the ability to automatically add units as required to meet the load up
to the maximum number available. When a power load in excess of the
maximum capability of the installation is specified, generation will
automatically be adjusted to equal plant capability as limited by head.
The output is coded to indicate this alteration by the computer program.
Under automatic selection of units the program computes the number
of units for best efficiency operation. The total station load (or
discharge) is divided by the unit best-efficiency loading (or discharge)
for the particular head existing on the station to determine the desired
number of units. Fractional numbers of units are truncated; thus unit
loadings are at or higher than the best efficiency point. The number of
units selected is limited to the maximum available.
The program automatically causes all excess water above maximum
pool elevation to be spilled. This is termed "mandatory" spill. Power
discharge, fixed release, optional spill and mandatory spill are summed
to arrive at the total project discharge. The alarm section of the output is coded calling attention to such mandatory spill.

o

Should a project attempt to draft below its m1n~um pool elevation
as a result of releases exceeding inflow; the power discharge and hence,
3

generation is automatically reduced to prevent the overdraft,
irrespective of the power demand or discharge called for by the input
data. Here again the alarm section of the output is coded.
The computation of power, discharge, head, etc. are accomplished
by means of table look-up and interpolation. For existing projects,
unit performance tables may be prepared from observed data. In the
case of planned projects, the basic data must first be computed. A
separate computer program has been developed which can quickly compute
performance characteristics. The program is based on the turbine
performance characteristics of a unit machine, i.e., a machine runner
diameter of-one foot operating under a net head of one foot. These
data are summarized in a unit performance hill in which power output
is plotted against the peripheral speed coefficient. It is thus
possible to quickly evaluate the performance of different sized units
and units having different characteristics.
Centra lized Load- Frequency Control. - A feature of the program is
a provision for simulating centralized control of the station power
loadings in a manner similar to that of centralized load-frequency
control equipment. Such equipment is presently installed at the major
Federal hydro stations on the Columbia River. The power loadings of
these projects are centrally controlled from the system load dispatcher's
office in Portland, Oregon.
When the load-frequency control feature of the program is used,
participating settings for each of the hydro stations are then included
as input data and a single system load rather than individual station
loadings are specified. The system load is apportioned among the hydro
stations in accordance with station participation values. Other than
this, the program operates in the same manner as when individual loadings
are prescribed for the several hydro stations.
This centralized, automatic dispatching of power loadings affords
the opportunity for efficient coordinated system operation of the Federal
projects. Use of the load-frequency control feature of the computer
program will allow planning· studies and scheduling of power operations
in conjunction with the equipment, in addition to it~ other uses. It is
envisioned that ultimately the load dispatching of these hydro stations
will be directly and automatically controlled by computer. The present
program could well serve as a basis for such a future program.
Flow Routing. - The total discharge from a project (power discharge,
spill, and fixed release) is routed downstream by a method of flow routing
known as incremental storage routing. This approach consists of subdividing reservoirs or river channels into incremental reaches. Each
incremental reach is represented in the program by two tables: one giving

4

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the relationship between storage and elevation for the particular reach;
the other giving the relationship between discharge and elevat.ion. By
proper selection of routing interval and choice of the number of reaches,
actual hydraulic conditions may be accurately approximated. The discharge
from any reach is computed as a function of the reach elevation, or where
backwater effects must be considered, as a function of the next downstream reach as well. The change in storage content of the incremental
reservoirs is related to the difference between inflow and outflow.
The combined effect of the storage-elevation and discharge-elevation
relationships mentioned in the preceding paragraph causes a time constant
to be introduced into the routing. This is known a'S "time of storage"
and is defined as the change in storage per unit change in discharge.
Ts

~ S/ ~ Z

Il

Q/ Il Z

where,
Ts = time of storage
S
storage volume
Q = discharge rate
Z = elevation
Dimensionally, using the units adopted for program use,
Ts (min) =

~
~

S (kc fs-min)/ ~ Z (feet)
Q(kcfs)/ ~ Z(feet)

The routing procedure used in the program does not explicitly consider
time of storage; however, the routing interval used in the program must
be shorter than the minimum time of storage for any given reach. Failure
to observe this criterion will result in oscillations of the reach elevation and discharge. These oscillations tend to increase in amplitude
until the range of tables is exceeded. A reservoir which is encroached
upon by backwater from a downstream reservoir may have an extremely short
time of storage.
The time-of-storage concept may be visualized by assuming a constant
rate of increase in inflow to an incremental reservoir. Outflow from the
reservoir will eventually reach an equilibrium condition where it is
increasing at the same rate as the inflow; at this time, the outflow
hydrograph will be displaced from the inflow hydrograph by the time of
storage. Figure 4 illustrates a discharge hydrograph routed through six
identical incremental reservoirs. Storage-elevation and dischargeelevation curves are shown on this same sheet.

c

5

Overlapping reservoirs are normally subdivided into two reaches:
a forebay reach and a tailwater reach for the next upstream project.
The sum of the storages of the individual reaches must equal the actual
reservoir storage.
In subdividing open channel reaches into incremental reaches, no
definite rules can be given for the number of increments. In general,
the greater the number of reaches, the greater the translation of the
discharge hydrograph with minimum attenuation. Discharge hydrographs
can be modified, to a lesser degree, by choice of routing interval.
Here again, selection of routing interval beyond that required to prevent oscillation, is subject to rules established for particular problem
definition.
For river systems where all tailwater reaches have extremely short
times of storages, an alternate routing method is available. This
method permits use of relatively long routing intervals, up to the answer
output .interval if desired. In effect it considers the time of storage
to be zero. Tailwater elevation is first determined as a function of
inflow (and next downstream reach elevation if necessary); the storage
corresponding to the new tailwater elevation is then computed as is the
change in storage during the routing interval; this change in storage
is converted to an average rate of flow during the routing interval and
added (or subtracted) to tailwater inflow to arrive at the outflow.
The algebraic sum added to the inflow is dependent on change of tailwater
elevation during the routing period, i.e., a rising tailwater will cause
outflow to be less than inflow with the opposite occurring on a declining
tailwater condition.
The flow and storage-routing procedure used in the program has a
sound theoretical basis which permits analysis of future reservoirs as
well as existing reservoirs and river reaches. The computation of
discharge, elevation, storage content, etc. are accomplished by means
of table look-up and interpolation. Volume-elevation relationships for
open river reaches and reservoirs are generally obtained from survey
data. Water surface profiles are computed for various forebay elevations
and rates of flow by independent means. (Here again separate computer
programs are available for determining water surface profiles, and
volume relationship, in reservoirs or open channel reaches.) From these
profiles, the discbarge-elevation-volume relationships are derived.

PROGRAM OUTPUT
Output Data. - Program output consists of the following data for
each project:
Date and time
project name

Abb~eviated

6

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St··· . "tiff -..¥j,iiNIIij'i"'wbcwJ["lW·\·l·\!!!·-

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End-of-period forebay elevation
End-of-period tai1water elevation
Average head
Forebay storage content
Storage change during period
Local inflow
Routed inflow
Power discharge
Spill
Total discharge
Generation
Nu~ber of units operating
Alarm codes
Operating mode number
Project number
O~tput may be obtained for selected reaches, in addition to project
data, at users option. Reach output consists of the following data:

Date and time
Abbreviated reach name
End-of-period elevation
End-of-period total discharge
Reach number
The 1920 System program output consists of both on-line printing
and punched cards. The same data are given by both forms of output.
Choice of output mode is optional with user. The 1620 System output is
punched cards. The 1920 System uses an auxiliary listing program to list
the punched cards for each project or optional reach and system Summary
Cards.
Output data consists of ~roject Cards, selected Reach Cards and
Summary Cards containing end-of-period system generation totals and
system potential energy remaining in storage. The sequence of the
punched card output and on-line printout is as follows: An initial
SUImnary Card gives potential energy in the system based on starting
profile data. This is followed by data for each hydro project and for
optional selected reaches for the initial time period. A Smnnary Card
concludes the data for the initial time period. Project, Reach and
Summary data are then punched out for the next subsequent output interval.
Output intervals may be varied by spec:ia1 control. In the absence of
special control, the output interval is one hour. Sample output formats
of a typical study are shown on Figure 5 for the IBM 1620 System and on
Figure 6 for the IBM 1920 System.
7

ACKNOWLEDGEMENTS

The original program was developed under the direction of
Mr. C. E. Hildebrand, Water Control Branch, U. S. Army Engineer
Division, North Pacific, Portland, Oregon. Michael A. C. Mann,
Consulting Engineer, assisted in the analysis and programmed the
basic program and supplementary routines for the IBM 650. The
author wishes to acknowledge the work of Mr. Lyle A. Dunstan of
H. Zinder and Associates, who programmed the present version. This
work was financed by the U. S. Bureau of Reclamation and the program
used by them in their planning studies. Additional logic, and
program refinement was accomplished as a joint effort by U. S. Army
Engineer Division, North Pacific and Walla Walla District, Corps of
Engineers. The assistance of C. E. Hildebrand and Robert D. Moffitt
of the U. S. Army Engineer Division, North Pacific in accomplishing
the latte~ and in the preparation of this paper is great fully
acknowledged.
Requests for program details should be directed to: Division
Engineer, U. S. Army Engineer Division, North Pacific, 210 Custom
House, Portland, Oregon, 97209.

8

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CANADA
UNITED

STATES
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ROCK ISLAND

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LEGEND
)

Existing

projects

~

Authorized projects

-...

SCALE IN MILES

25

0

25

50
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EXISTING AND FUTURE PROJECTS OF THE LOWER COLUMBIA AND SNAKE RIVERS
Fig. 1

ELEV ATION I N FEET ABOVE M. S. L.

8

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OUTER END OF JETTY

BONNEVILLE
EL. 74

<
m

THE DALLES
_ _III EL. 160

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DAY ~

EL. 265

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CHINA
GARDENS
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EL. 910
=~ ASOTIN
EL. 842.5
_ _LOWER GRANIT
EL. 735

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8

\ 100

1..;1

LITTLE GOOSE
'1"
EL. 638
i
~.......

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LOWER
MONUMENTAL
EL. 540
~_. ICE HARBOR
EL. 440
"':., BEN FRANKLI N
I
EL. 385
I
PRIEST RAPIDS
EL. 486.5
~-..WANAPUM

EL. 570
~_ ROCK ISLAND
EL. 606.5
~~ ROCKY REACH
EL. 707
~-=T

WELLS
: EL. 775

550

CHIEF
JOSEPH
EL. 946

----1

GRAND
COULEE
. .
600 . . .

00

8

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ELEVATION IN FEET ABOVE M. S. L.
i.:

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25~------~------~--------~----------------

20

....'"u

FULL-GATE LIMIT

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BEST EFF.
LOADING
5

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10

20

30

40

50

60

GENERA TOR OUTPUT, megawatts

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GENERATING UNIT CHARACTERISTICS

F!.a. 3

INFLOW
150
III

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24

12

TIME, hours

DISCHARGE , K cfs
10_O_ _
410 0r---_ _ _-'T

Q)
Q)

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200·

300

400

400
~

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~

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390

0

380

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_ _ _---L_ _ _ _- ' -_ _ _........
20

30

STORAGE, M cfs - min,
INCREMENTAL RESERVOIR ROUTING EXAMPLE WITH STORAGE ELEVATION AND DISCHARGE - ELEVATION CURVES
fig. 4

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DATE-TIME

il

~
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oil

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15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
15
·15
15

1
1
1
1
1
1

i

i
1
1
1
1
1
1

1
1
1
1

1
1

1
1
1
1

85
85
85
85
85
85
85
85
85
85
85
85
85
85
85
85
85
85
85
85
85
8S
85
85

100
200
300
.. 00
500
600
700
800
900
1000
1100
120C
1300
1400
1500
1600
1700
1800
1900
2000
2100
22CO
23CO
2400

PROJ
GCl
GCl
GCl
GCl
Gel
GCl
Gel
GCl
Gel.
GCl
Gel
GCl
Gel
Gel
Gel
Gel
Gel
Gel
GCl
Gel
Gel
Gel

Gel
Gel

FORE8AY TAllWATER
FF.ET
FEET
1262.08
1262.16
1262.24
1262.33
1262.40
1262.44
1262.41
1262.32
1262.20
1262.09
1261.97
1261.86
1261.76
1261.68
1261.61
1261.53
1261.41
1261.29
1261.18
1261.07
1260.99
1260.96
1260.97
1261.02

945.41
944.47
944.05
943.89
944.48
945.99
950.20
953.79
955.99
957.01
957.57

304.1
304.7
305.4
305.7
305.1
304.1
303.5
303.3
303.7
305.1
307.9
311.1

04.0~2

05.485
06.991
08.497
09.765
10.496
09.903
08.301
06.310
04.295
02.268
00.233
198.556
197.192
195.930
194.470

192.41+8
190.1+13
188.371
186.491
185.117
184.555
18 ... 797·
185.524

7415.34
22866.42

,

315.3
317.1
317.9
318.2
318.0
317.0
314.4
310.6
307.4
305.7
304.7

957.89 301+.2
957.38
956.50
955.83
955.84
956.91
957.52
957.85
957.72
956.69
954.43
951.15
947 ••6

30281.97
,Ii

AVG FORE8AY STOR
HEAD SlOR
CHANGE

760.474

1.313
1,"23
1.506
1.506
1.268
731
594-

lOCAL
INFLOW

ROUTED

INFLOW
'7~7'O

1.9912.0152.0262.0351.6771.3641.2621.460";
2.0222.0342.042·1.8801.37..-·
562242
728

'6.700
36.650
36.650
36.620
36.650
36.620
·'6.650
36.650
36.620
36,650
36.620
36.650
36.650
36.620
36.650
36.620
36.650
36.650
36.620
S6.650
36.620
36.650
36.650

17.223-

880.510

1.602-

POWER
DISCH

SPIll
DISCH

TOTAL
DISCH

5.740
2.050

GEM MO.
MW UNITS C

6.240
2.550
500
500
6.190
19.100
50.870
75.090
84,430
84.990
85.280
85.470
76.880
69.390
66.920
71.690
85.150
85,470
85.660
81.740
69.630
50.110
30.840
19.190

,.690
1•• 600
50.370

74.590
.'.930
.4.490
84.780
84.970
76~3'0

68.890
66 ... 20
71.190
'''.650
.... 970
85.160
81.240
69.130
49.610
30.340
18.690

133
45
133
439
1.197
1.749
1.94~

1.944
1.944
1.944
1,749
1.580
1.527
1.638
1.944
1.944
1,944
1.853
1.~80

1.139
704
439

2.0 2
1.0 2
2
2
2.0 2
4.0 2
13.0 2
20.0 2
22.7 2
23.0 2
23.0 2
23.0 2
21.0 2
1e.5 2
le.o 2
19.0 2
23.0 2
23.0 2
23.0 2
22.0 2
19.0 2
13.0 Z
8.0 2
5.0 2

29,513
1.281,880

1,293.880

346.2

'11
.

;!

~

•

va

........

~,

l>-I~' ,"'"

...

I

,

:

,-,,' ~- ,.;.
11

~i

<

".'

t~~;~~ -'<-~

.

~ .. ~ ~•

f

,

DR. JOHN MANfOn:s
COMPUTER TECHNOLOGY DEPT.
PURDUE UNIVERSITY
CALUMET CAMPUS

HYDRO SYSTIM DAILY OPERATION ANALYSIS
U. S. ARMY ENGINEER DIVISION, NOIT" 'AClfIC

C.-l UN1T.S IFI

.

HAMMOND. IN 46323 PAGE
<' . - .

4

• ...

GRAND COULEE
ELtV. ~ND PERIOD
FOttEISA., TAIL"'"
FEET
FElT

DATE AND TIMt.
1~
1~

15
1~
l~

l'
I)
15

lS

15
1,
15
1~
1~
1~

1")
1,
IS
1)
1,
1~

15
I')
1~

01
01
01
01
01
01
Ol
01
01
01
01
01
01
01
01
01
01
01
01
01
01
01
01
01

85
85
85
85
85
85
85
85
85
85
8S
85
85
85
85
85
85
85
85
85
85
85
85
85

0100 1262.08
0200 12e»l.16
0300 1262.21t
0400 1262.33
0,00 12b2.40
0600 12bl.44
0100 12u2.41
0800 1262 •.Jl
0900 12~1.20
1000 - 12~2.09
1100 1261.91
1200 1261.86
1300 12b1.1b
1400 1261.68
1500 1261.61
1600 126'1.53
1100 1261.41
1800 1261.29
1900 12bl.18
2000 1261.01
2100 1260.99
2200 12b(,.96
2300 12bO.91
2400 12bl.02

945.41

91t4.ltl
941t.()'
91t3.89
91t4.48
94'.99
950.20
9.,3.19
955.99
951.01
951.51
951.89
951.38
9S6.!iO
955.83

955.81t
956.91
951.~2

951.85
951.12

956.b9
954.43
951.15
941.86

AVG.
HEAD
FEEl

FOREeAY
STORAGE
CFS-DYS

DELT'
STORAGE
CFS-DYS

315.30
311.19

204.062

1,311

205,lt85

1.1t23

311.91t

206,991

318.21

208.1t91

1.506
1.506
1,268
131
5941,6021,9912.0152.0262,035-

318.02 209,165
311.05 210.496
314.43 209,903
310.61 208,301
J01.45 206,310
30S.13 .201t,295
304.19 202,268
304.21 200,2)')
JOIt.13 198.556
301t.l1 191,192
J05.43 195,9)0
305.14 194.410
305.18 192,448
301t.19 190,1t13
303.,8 . 188.111
303.33 186,491
303. lit 185,111
305.11 184,555
)01.96 184.191
)11.19 185,524

1,b111,3641,2621,4602,0222.0)42,042- .
1,8801.314562242
121

••••••••• INFLON ••••••••
TOTAL
ROUIEO
LOCAL
CFS
CFS
CfS
0
0
0
0
0
0
0
.0
0
0

°

0
0
0
0
0
0
0
0
0
0
0
0
0

31,150
36.100
16.650
36,6,0
36,620
36,650
36.620
36,650
)6,650
36,620
36,650
36,620
36.6,0
16.650
16.620
16.650
36,620
36,650
36.6,0
36.620
)6,650
36,620
36,6§0
36.650

31,150
36,100
36.650
36,650
36,620
36,650
36,620
36.650
36.650
)6,~20

36.650
36,620
36,650
16,650
36.620
16,650
36,620
)6,650
36,650
36,620
)6,650
36,620
36,650
36,650

••••••• DISCHARGE •••••••
TOTAL
POWER
SPILL
CFS
CFS
CFS
5.140
2,050
0
0
5.690
18,600
50,310
14,590
83.930
81t,lt90
84,180
84,910
16.380
68,890
66,,.20
11,190
84.650
84,910
85,160
81.240
69,130
49.610
30,340
18,690

0
0
.0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0

6,240
2,550
500
500
6,190
19,100
50,810
15.090
84,430
84,990
85,280
85.410
16,880
69,390
66,920
11,690
85,150
85,410
85,660
81,140
69.630
50,110
30,840
1~,190

AVERAGES

1Zbl.l,

952.,11

308.'11

198,353

133
itS
0
0
133
439
1.191
1.149
1.944
1.944
1,944
1, 9it~
1,149
1,)80
1,521
1,638
1,944
1.944
1,944
1,853
1,580
1,139
101t
439

AVERAGE
NUMBER
UNITS
2.0
1.0
0.0
0.0
2.0
4.0
13.0
20.0
22.1
23.0
23.0
l3.0
~1.0

18.5
18.0
19.0
23.0
23.0
23.0
22.0
19.0
13.0
8.0
5.0

OP,
CD

•
22

2
2
1.
1

it
I
~

"

1

2
l..

,
1
1
2
2

2

2
1

2
2
2

29,513

11,223-

TOTALS

AVG.
GEN.
MW

0

36,690

36,.90

53,410

0

53,910

1.23C

11t.4

;2

1
.0\

•

F~
l,!

)

\)
/

,

i



---

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