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PROCEEDINGS
Computation
Seminar
AUGUST
1951
EDITED BY IBM APPLIED SCIENCE DEPARTMENT
CUTHBERT c. HURD, Director
INTERNATIONAL BUSINESS MACHINES CORPORATION
NEW YORK + NEW YORK
Copyright 1951
International Business Machines Corporation
590 Madison Avenue, New York 22, N. Y.
Form 22-8705-0
P R I N TED N THE U NIT E D S TAT E S o F AMERICA
FORE WORD
A COMPUTATION SEMINAR, sponsored by the International Business
.I1. Machines Corporation, was held in the IBM Department of
Education, Endicott, New York, from August 13 to August 17, 1951.
Participating in this Seminar were ninety research engineers and scien-
tists representing computing facilities which employ IBM Card-
Programmed Electronic Calculators. The discussion centered on the
mathematical and computational aspects of a variety of important
problems which have been solved on the Card-Programmed Elec-
tronic Calculator. The formal papers of the Seminar and a digest of
the ensuing discussion are published in this volume. In addition,
informal papers were presented at several valuable supplementary
sessions. Dr. W. J. Ec"kert presided at a session on Training of Personnel
for Computing Laboratories at which Mr. Murray Lesser, Mr. Walter
Ramshaw and Professor Frank Verzuh led the discussion. Mr. P. M.
Thompson presided at a session on the Organization of a Computing
Installation at which Mr. W. D. Bell, Dr. H. R. J. Grosch, and Mr.
J. D. Madden gave short papers. Mr. E. B. Gardner presided at a
session in which there was widespread discussion of the subject of
Data Reduction. More generally, all participants in the Seminar con-
tributed generously in discussions. The International Business Ma-
chines Corporation wishes to express its appreciation to all who
participated in this Seminar.
CONTENTS
Application of the IBM Card-Programmed Electronic Calculator to
Engineering Procedures at The Glenn L. Martin Company - WARREN B. KOCH . . . . . . . 13
Reduction of Six-Component Wind Tunnel Data Using the IBM
Card-Programmed Electronic Calculator, Model II - MURRAY L. LESSER. 17
IBM Card-Programmed Electronic Calculator Operations -HARLEY E. TILLITT
Using a Type 402-417 BB and 604-2 MARTHA KENYON
BRUCE OLDFIELD. 27
The Combomat -JOHN D. MADDEN 33
The IBM Type 604 Electronic Calculating Punch
As a Miniature Card-Programmed Electronic Calculator -PAUL T. NIMS. 37
General-Purpose Floating Point Control Panels for -NORMAN A. PATTON
the IBM Card-Programmed Electronic Calculator KATHLEEN BERGER
L. RICHARD TURNER . 48
Catapult Takeoff Analysis -JOHN R. LOWE 65
Computation of Loan Amortization Schedules on
the IBM Card-Programmed Electronic Calculator -CHARLES H. GUSHEE . . . . . . 72
Techniques for Handling Graphical Data on
the IBM Card-Programmed Electronic Calculator - WILLIAM D. BELL . . . . . . . 77
Calculation of the Flow Properties in an
Arbitrary Two-Dimensional Cascade -JOHN T. HORNER . . . . . . . 81
Automatic Calculation of the Roots of Complex
Polynomial Equations Using the IBM
Card-Programmed Electronic Calculator -JOHN GALLISHAW, JR. . 87
A Recursion Relation for Computing Least Square
Polynomials over Moving-Arcs -GEORGE R. TRIMBLE, JR. 93
Numerical Solution of Second-Order Non-Linear
Simultaneous Differential Equations -HENRY S. WOLANSKI. . . . . . 98
Matrix Inversion and Solution of Simultaneous Linear
Algebraic Equations with the IBM Type 604
Electronic Calculating Punch -GEORGE W. PETRIE, III. . . . . 105
The Determination of Eigenvectors and Eigenvalues
of Symmetric Matrices -EVERETT C. YOWELL. . . '" . 112
An Application of the IBM Card-Programmed Electronic
Calculator to Analysis of Airplane Maneuvering
Horizontal Tail Loads -LOGAN T. WATERMAN 120
Fifth-Order Aberration in an Optical System -RUTH K. ANDERSON. 130
Theory of Elastic Vibrations of
Helicopter Fuselages -PETER F. LEONE . . . . . . . . 132
Machine Procedure for Computation of Elastic
Vibrations of Helicopter Fuselages - WILLIAM P. HEISING . . . . . . 146
PART Ie I PAN TS
ANDERSON, RUTH K., Mathematician ECKERT , WALLACE J., Director
National Bureau of Standards Department of Pure Science, Watson Scientific Computing Laboratory
Washington, D. C. IBM Corporation, New York, New York
ARNOLD, KENNETH j., Assistant Professor of Mathematics Ev ANS, GEORGE W., II, Associate Mathematician
University of Wisconsin Argonne National Laboratory
Madison, Wisconsin Chicago, Illinois
AROIAN, LEO A., Chief, Computation Group FEIGENBAUM, DAVID, Associate Research Engineer
Research and Development Laboratories Cornell Aeronautical Laboratory
Hughes Aircraft Company, Culver City, California Buffalo, New York
BAUGH, HAROLD W., Electronic Scientist FERBER, BENJAMIN, Senior Research Engineer
Computer Branch, U. S. Naval Air Missile Test Center Consolidated Vultee Aircraft Corporation
Point Mugu, California San Diego, California
BELL, WILLIAM D., Vice-President FUHRMEISTER, PAUL F., Aeronautical Research Scientist
Telecomputing Corporation National Advisory Committee for Aeronautics
Burbank, California Langley Field, Virginia
BERKOWITZ, RAYMOND S., Associate GALLISHAW, JOHN, JR., Tabulating Methods Specialist
Moore School of Electrical Engineering Chance Vought Aircraft
University of Pennsylvania, Philadelphia, Pennsylvania Dallas, Texas
BRINKLEY, STUART R., JR., Head GARDNER, EARL B., Chief
Mathematical and Theoretical Physics Section Automatic Computing Unit, Data Reduction Branch'
U. S. Bureau of Mines, Pittsburgh, Pennsylvania Holloman Air Force Base, New Mexico
BROOKS, JACK E., Principal Stress Analyst GROSCH, H. R. j., Head
Republic A viation Corporation Technical Computing Bureau, IBM Corporation
Farmingdale, New York Washington, D. C.
BROOKSHIRE, JACK W., Tabulating Research Specialist GROSH, LOUIS E., JR., Associate
North American Aviation, Incorporated Statistical Laboratory, Purdue University
Los Angeles, California West Lafayette, Indiana
BROWN, DONALD M., Supervisor GROSS, GEORGE L., Research Engineer
Mathematical Services Group, Willow Run Research Center Grumman Aircraft Engineering Corporation
University of Michigan, Ann Arbor, Michigan Bethpage, Long Island, New York
CARTER, DAVID S., Research Associate GUSHEE, CHARLES H., President
Forrestal Research Center, Princeton University Financial Publishing Company
Princeton, New Jersey Boston, Massachusetts
CHEYDLEUR, BENJAMIN F., Chief HAMMING, RICHARD W., Research Mathematician
Applied Mathematics Laboratory Bell Telephone Laboratories
U. S. Naval Ordnance Laboratory, Silver Spring, Maryland Murray Hill, New Jersey
CONANT, GEORGE H., JR., Mathematician HARP, WILLIAM M., Section Head
The Perkin-Elmer Corporation Refining Technical Service Division
Cambridge, Massachusetts Humble Oil and Refining Company, Baytown, Texas
COZZONE, FRANK P., Manager HEISING, WILLIAM P., Mathematician
Mathematical Analysis Department Technical Computing Bureau, IBM Corporation
Lockheed Aircraft Corporation, Burbank, California New York, New York
DEUTSCH, MURRAY L., Physicist HERGET, PAUL, Director
Research and Development Laboratory University of Cincinnati Observatory
Socony-Vacuum Oil Company, Paulsboro, New Jersey Cincinnati, Ohio
DEVRIES, JOHN A., Senior Stress Analyst HILL, W. HENRY, Coordinator of Naval Aviation Stati.rtics
Propeller Division, Curtiss-Wright Corporation Office of Chief of Naval Operations
Caldwell, New Jersey Washington, D. C.
DUGGAN, JOHN M., Mathematician HOELZER, HELMUT, Chief, Computation Center
A. V. Roe, Canada, Limited Ordnance Guided Missile Center
Malton, Ontario Redstone Arsenal, Huntsville, Alabama
HORNER, JOHN T., Senior Project Engineer PORTER, RANDALL E., Research Engineer
Allison Division, General Motors Corporation Boeing Airplane Company
Indianapolis, Indiana Seattle, Washington
HURD, CUTHBERT C., Director RACHFORD, HENRY H., JR., Research Engineer
Applied Science Department, IBM Corporation Humble Oil and Refining Company
New York, New York Houston, Texas
JACKSON, IRWIN E., JR., Marine Engineer RAMSHAW, WALTER A., Analytical Engineer
Bureau of Ships, U. S. Navy Department United Aircraft Corporation
Washington, D. C. East Hartford, Connecticut
JACOBSON, ARVID W., Associate Professor of Afathematics RIDGWAY, ANDRESS 0., Mathematician
Wayne University U. S. Navy Hydrographic Office
Detroit, Michigan Washington, D. C.
KELLY, ROBERT G., Mathematician ROSE, ARTHUR, Associate Professor of Chemical Engineering
Applied Physics Laboratory, Johns Hopkins University The Pennsylvania State College
Silver Spring, Maryland State College, Pennsylvania
KENNEDY, ERNEST C., Senior Research Engineer SCHLIESER, WALTER C., JR., Computing Supervisor
Ordnance Aerophysics Laboratory, Consolidated Vultee Douglas Aircraft Company, Inc.
Aircraft Corporation, Daingerfield, Texas EI Segundo, California
KOCH, WARREN B., Senior Mathematician SCHUTZBERGER, HENRY, Supervisor
The Glenn L. Martin Company Test Data Division, Sandia Corporation
Baltimore,Maryland Albuquerque, New Mexico
LEONE, PETER F. SELLS, BERT E., Turbine Engineer
Piasecki Helicopter Corporation General Electric Company
Morton, Pennsylvania Boston, Massachusetts
LESSER, MURRAY L., Methods-Coordination Engineer SHELDON, JOHN W., Head
Theoretical Aerodynamics Department Technical Computing Bureau, IBM Corporation
Northrop Aircraft, Inc., Hawthorne, California New York, New York
LOWE, JOHN R., Computing Engineer SHIPMAN, JEROME S., Mathematician
Douglas Aircraft Company, Inc. Laboratory for Electronics, Incorporated
Santa Monica, California Boston, Massachusetts
MACINTYRE, NEIL W., Administrative Assistant SMITH, CHARLES V. L., Head
Mutual Life Insurance Company of New York Computer Branch, Office of Naval Research
New York, New York Washington, D. C.
MADDEN, JOHN D., Assistant Mathematician SMITH, ROBERT W., JR., Mathematician
The RAND Corporation U. S. Bureau of Mines
Santa Monica, California Pittsburgh, Pennsylvania
MAGINNISS, FRANK j., Application Engineer SOWERS, NELSON E., Mathematical Data Analyst
Analytical Division, General Electric Company Army Field Forces Board 4
Schenectady, New York Fort Bliss, Texas
MCPHERSON, JOHN C., Vice-President THOMAS, L. H., Senior Staff Member
IBM Corporation Watson Scientific Computing Laboratory, IBM Corporation
New York, New York New York, New York
NIMS, PAUL T., Staff Engineer-Research Tf{OMPSON, PHILIP M., Head
Engineering Division, Chrysler Corporation Computing Laboratory, Hanford Works, General Electric Company
Detroit, Michigan Richland, Washington
PATTON, NORMAN A., Aeronautical Research Scientist TILLITT, HARLEY E.
Lewis Flight Propulsion Laboratory U. S. Naval Ordnance Test Station, Inyokern
National Advisory Committee for Aeronautics, Cleveland, Ohio China Lake, California
PETRIE, GEORGEW., III, Mathematician TRIMBLE, GEORGE R., JR., Mathematician
Applied Science Department, IBM Corporation Ordnance Ballistic Research Laboratory
Washington, D. C. Aberdeen Proving Ground, Maryland
VERZUH, FRANK M., Director of Statistical Services WEST, GEORGE P., Aeronautical Research Scientist
Massachusetts Institute of Technology Ames Aeronautical Laboratory
Cambridge, Massachusetts National Advisory Committee for Aeronautics
Moffett Field, California
VIALL, JOHN, Supervisor
IBM Computing Installation, Douglas Aircraft Company, Inc.
Long Beach, California
WHITE, J. HUNTER, JR., Mathematician
Applied Science Department, IBM Corporation
New York, New York
VON HOLDT, RICHARD, Staff Member
University of California; Los Alamos Scientific Laboratory
Los Alamos, New Mex:co WHITE, LAWRENCE L., Mathematician
IBM Unit, U. S. Air Force Flight Research Laboratory
Dayton, Ohio
WADDELL, WILLIAM L., Group Engineer
Computation Analysis, Northrop Aircraft, Inc.
Hawthorne, California WITT, EDWARD C., Mathematician
K-25 Plant, Carbide and Carbon Chemicals Corporation
Oak Ridge, Tennessee
WALKER, JOHN H., Mathematician
U. S. Naval Proving Ground
Dahlgren, Virginia WOLANSKI, HENRY S., Aerophysics Engineer
Consolidated Vultee Aircraft Corporation
WATERMAN, LOGAN T., Chief of Flutter and Vibrations Fort Worth, Texas
Fairchild Aircraft Division
Fairchild Engine and Airplane Corporation, Hagerstown, Maryland
YOWELL, EVERETT C., Mathematician
Institute for Numerical Analysis
WELMERS, EVERETT T., Chief of Dynamics N adonal Bureau of Standards
Bell Aircraft Corporation, Niagara Falls, New York Los Angeles, California
Application of the IBM
Card-Programmed Electronic Calculator to Engineering
Procedures at The Glenn L. Martin Company
WARREN B. KOCH
The Glenn L. Martin Company
THE PUR P 0 S E of this paper is to describe the most Jordan method resulting in a unit diagonal matrix. Since
important engineering problems that have been adapted the floating decimal setup is used, no attempt has been
for processing on the IBM Card-Programmed Electronic made to select the largest terms as divisors; rather, these
Calculator at The Glenn L. Martin Company. However, operator coefficients are selected down the main diagonal.
before starting upon any such discourse, it is advisable to The solution is substituted back into the original equations
consider first the tools of operation-in this case, the type and, when necessary, the errors thus resulting are operated
of control panels that are in use. upon to obtain corrections to the original results.
I t has been found necessary to design only two control
panels for the CPC, the operations available from one or Flutter Analysis
the other proving adequate to cover all needs up to the
The only type of flutter analysis which has been thus far
present time. They are a floating decimal type with seven-
investigated is that of determining the critical flutter speed
digit capacity and a fixed decimal with six-digit capacity.
of any aircraft; that is, the speed at which the damping
Of course, it would always be advantageous to program
of the structure is attained. This job is laborious in that it
jobs on a floating decimal setup, but because of the addi-
involves the expansion of a number of determinants of
tional complications involved in wiring such a control panel,
order equal to the number of degrees of freedom for which
fewer operations are available than on a fixed decimal
design. the aircraft is designed. The Dynamics Department has lim-
ited the size of these determinants to fourth order through
The operations programmed on the floating decimal con-
various simplifying assumptions, but a setup is now being
trol panel include only addition, subtraction, multiplication,
evolved which will handle sixth order determinants on the
division, and square root, while the fixed decimal control
CPC. The result of an expansion of one of these determi-
panel allows for all these operations in addition to that of
nants is a polynomial with complex coefficients of degree
substitution of an argument into a polynomial of at most
equal to the order of the determinant.
the fourth degree. This latter operation works in conjunc-
A method has been devised of applying the CPC to the
tion with a selection which makes it possible to select any
solution of any polynomial with coefficients either properly
one of a number of polynomials, depending upon the magni-
complex or real. Because of the limitations of storage, the
tude of the argument used. This type of operation is par-
system has been designed for polynomials of degree no
ticularly valuable when it is necessary to approximate
more than eight. The mathematical technique involved is
graphical data with polynomials, and different equations
Newton's method. Up to the present time, no difficulty has
must be used over certain ranges of the curve.
been realized in obtaining any roots-in fact, the number of
iterations required to obtain six-digit accuracy in the root
FLOATING DECIMAL JOBS usually has been less than twenty.
Simultaneous Linear Algebraic Equations
Vibration Frequency Analysis
We shall now consider the more or less routine jobs that
have been adapted for the floating decimal control panel. A method has been developed in the Dynamics Depart-
The first of these is the solution of simultaneous linear alge- ment for determining the natural vibration frequencies of a
braic equations. The method used is essentially the Gauss- beam for either bending vibrations alone or coupled bend-
13
14 COMPUTATION
ing-torsion vibrations. The calculation is initiated by first FIX:eD D:eCIMAL JOBS
dividing the beam into sections with discrete masses con-
Simultaneous Ordinary Differential Equations
centrated at each station and then describing these stations
by series of matrices. a The most important use of the fixed decimal control
The matrices are written with the frequency factor, K, as panel, and in fact of the CPC itself, has been in the solution
a variable. Then, by simply multiplying the proper coeffi- of simultaneous ordinary differential equations. This prob-
cients by any value of K, the problem may be processed for lem has become one of frequent occurrence with the en-
any particular frequency. The routine is simply one of trial trance into the guided missile field and its attendant prob-
and error, where a value of K is substituted, and the asso- lems of automatic control and trajectory computations. Of
ciated matrices of successive beam stations are continually course, this problem occurs within other problems but, by
premultiplied until a final matrix equation is obtained re- far, the preponderance of work done on the CPC at The
lating the boundary conditions on both ends of the vibrating Glenn L. Martin Company has been concerned with trajec-
beam. The imbalance of any chosen end condition is plotted tory calculations.
against K and the process repeated for a new value of K A stepwise method is used to solve the equations with
until a K is found which gives no imbalance. The K result- values of the dependent variables at the beginning of each
ing in this balance condition determines the vibrating fre- step determined by quadratic extrapolation from previous
quency desired. The machine calculations begin after the information. These extrapolated values are then improved
matrices have been written and cover the substitution of the upon later by a single iteration and the difference between
K values, the matrix multiplication, and the determination extrapolated and iterated values compared. This error is
of the imbalance between end conditions. used to determine the maximum allowable interval into
which the independent variable may be divided and also
Transfer Functions serves as a check on the machine calculations.
There is almost no limit on the number of equations (or
Quite extensive use of the CPC has been made in the dependent variables) that may be handled simultaneously,
formulation and evaluation of transfer functions in the in- and there is no problem in taking care of complicated non-
vestigation of dynamic stability of guided missiles. The linearities in the coefficients.
transfer function of any component is essentially its equa- Recently, a trajectory has been calculated at The Glenn
tion of motion expressed in differential operator form as L. Martin Company in which three distinct rectangular co-
the ratio of the input to the output. The closed loop stability ordinate systems, each in three dimensions, were handled
characteristics can be determined from the so-called Nyquist simultaneously. It was necessary to write a set of 76 equa-
diagram obtained from the evaluation of the transfer func- tions to describe the system completely. Of these, about
tion. For a sinusoidal input, the phase anJ amplitude of the one-third were differential equations, and the rest were
output are plotted in the complex plane as a function of either simply definition or angular resolution equations. Of
frequency. The stability is determined as a function of the course, it was impossible to store all values of the dependent
encirclements of the - 1 point on the real axis. variables; so it became necessary to summary punch many
For the airframe itself, any transfer function (such as a of them and reload them into the machine at various times
function of elevator, roll as a function of aileron, etc.) is in the following interval. This was done by prepunching
completely determined by the flight condition and aero- decks of summary cards with operation instructions and
dynamic properties as determined in a wind tunnel. A CPC then merely running the deck of program cards through the
p~ocedure has been set up to accept this type of data in 402 once, replacing the pertinent cards with newly punched
order to formulate any transfer function describing the summary cards and continuing this process until a com-
missile dynamics. The transfer functions of other compo- plete trajectory was calculated. Under this system, it was
nents (servos, amplifiers, valves, etc.) are determined by possible to go through one complete cycle of processing
either analysis or test. about 400 cards through the accounting machine, reloading
Given the transfer functions of n consecutive components the new summary cards and starting to process again in five
in a control system-call them Ai, where i = 1, ... , n- minutes. A complete solution required approximately 80
another procedure on the CPC obtains the response as a machine hours and described 13 seconds of flight time.
function of frequency of not only each component Ai but Manually, this job would have taken some 3,000 hours.
also of the products Al X A 2 , Al X A2 X As, . . . ,
Al X A2 X ... X An. Analysis of a Cabin Conditioning System,
aThe method of developing these matrices has been fully described During the course of a recent investigation of the per-
in an article in the October, 1947, issue of the Journal of the Aero- formance of a cabin air conditioning and pressurization
nautical Sciences by W. P. Targoff entitled "The Associated Mat-
rices of Bending and Coupled Bending-Torsion Vibrations." system, an analytical method for studying this problem was
SEMINAR 15
devised. This method, although applied to just this one sys- a. Tare and interference, which is the influence ex-
tem, should have extended application, and it can be tied in erted on the model by the supports and support
exceedingly well with CPC methods. This is so because the fairings.
system is basically one of trial and error, where each trial b. Alignment, or inclination of the wind stream to
involves a lengthy calculation on a small amount of data. the balance system.
The system contains essentially a primary compressor,
secondary compressor turbine unit, two heat exchangers, a c. Effect of the constraint of the wind tunnel walls.
water separator, two combustion heaters and fans, and vari- d. Buoyancy, which is the effect of fore and aft pres-
ous ducts, valves, and control mechanisms. The primary sure gradients in the tunnel.
problem is the establishment of criteria for determining an All of the data required to apply these corrections are
unique set of operating points for the various components. determined by exacting wind tunnel testing, and the correc-
The only parameter known is the primary compressor im- tions applied in equation form to the aerodynamic coeffi-
peller speed. All other compressor variables are unknown; cients.
furthermore, the performances of the secondary compressor These corrected coefficients lie in a wind axis coordinate
and turbine are dependent on each other, and the perform- system with the origin at the point of attachment between
ances of this entire unit and the primary compressor unit model and support. The coefficients are finally transferred
are dependent on each other. Therefore. the performance of to two other coordinate systems: (1) the wind axes with
the entire system cannot be predicted by any straightfor- origin at the center of gravity of the model, and (2) the
ward method of calculation, and a trial-and-error system stability axes.
must be adopted.
The method most frequently used in this type of problem
is to assume several values of each of the independent vari- Aeroelastic Influences on Control Surface Effectiveness
ables, and calculate the performance until the values chosen
satisfy the equilibrium criteria. However, because of the The aeroelastic problem is concerned with the loss of
wide variations of the conditions of flight, and because of effectiveness of comrol surfaces, including ailerons, flaps
the customary use of various automatic limiting devices and elevators, because of the elastic deformations of wing
which arbitrarily change the functional configuration, it is fuselage and tail. The deformations are brought about by
felt that this simple trial-and-error method is unsatisfactory. both the twisting and bending of these various parts, which
Rather, several values of two arbitrarily chosen variables are due to angle of attack and deflection of the control
are assumed in a systematic relationship so that existing surfaces.
trends become apparent. In addition, if the various assumed Twisting is brought about by the fact that the chordwise
operating points bracket (or nearly bracket) the actual centers of pressure of loads which are due to control surface
operating point, this point can be established with accept- deflections and angle of attack are not located at the elastic
able accuracy. axis, thus producing powerful torques which tend to twist
The CPC is particularly suited to this procedure, since a the wing or tail surface and change the effective angle of
few points may be computed rapidly and then any desired attack. This twisting, in turn, produces loads which further
re-trials may be run by simply changing a few load cards. influence the elastic deformation of the wing or tail.
The problem is one of iteration since, to begm with, the
final spanwise twist distribution cannot be predicted accu-
Wind Tunnel Data Reduction rately. A twist distribution must be assumed, the torques
which are due to this twist and basic loads must be com-
Until recently, all wind tunnel data reductions have been
puted, and a new twist distribution is determined from
calculated on the IBlV[ Type 604 Electronic Calculating
these torques. \Vith this new twist distribution, the problem
Punch. It has been found that the CPC can be adequately
is started anew, and the same steps are carried out to find a
adapted to this calculation with a resultant time saving of
third twist distribution, and so forth, until the solutions
60% over the 604.
converge to a final twist distribution.
All computations, with the exception of the correction of
Once the nature of the twist curve is determined, the
forces and moments for residual balance readings, are per-
problem becomes simple and straightforward. Now the load
formed on the CPC. This initial correction is obtained more
distributions, caused both by the basic load moments and
conveniently on the 604. The remaining calculations in-
the moments resulting from the twist distribution loads, are
clude:
computed accurately by the \N eissinger method.
1. Converting the force and moment data to coefficient This entire computation procedure is programmed by
form. approximately two thousand cards, of which half are used
2. Correcting these coefficients for: as many times as necessary (usually three) in the iteration
16 COMPUTATION
procedure. There are only about two hundred cards con- Also I was wondering if you have done any investigating
taining data that must be changed for different configura- so that, instead of having to predict the next stop, you use
tions, and these are specially coded so that they may be a much simpler form of numerical analysis and just take
changed readily between jobs. This system, which takes your intervals a little closer together.
about four hours per configuration, has replaced a proce- Mr. Koch: No matter how small the intervals are made,
dure that usually required three weeks to complete by hand- we always have to predict.
computing methods.
Dr. Grosch: I would like to suggest the possibility of
DISCUSSION increasing rather than decreasing the interval, for this
reason: The steps of l\fr. Koch's procedure take him about
Mr. Von H oldt: At Los Alamos we punch out eight dif-
five minutes; so this looks like something of the order of
ferent numbers and put the instructions in 1 to 10 auto-
1,000 steps he has to go through in his 80 hours. But sup-
matically. They are in the instruction deck and go into the
pose we could decrease the number of steps tenfold by tak-
summary punched card; so it is not necessary to have pre-
ing the interval ten times as large, at the expense of having
punched cards.
to store more data for the extrapolation. For instance, if
Dr. Brown: When you mentioned the 80 hours of run-
you have nine space intervals you might have to store four
ning time on the machine, Mr. Koch, how did that compare
or five extra orders of differences for each one of those nine,
with the number of hours it would have taken by hand
i.e., 36; and that might mean punching out twenty or thirty
operations?
extra summary cards, which will take up ten or twenty
Mr. Koch: It would have taken 3,000 hours.
per cent extra time per step. But if you have reduced the
Mr. Lowe: If I understood you correctly, you extrapolate
number of steps tenfold, you still have a gain of eightfold
in your trajectory programming with some quadratic ex-
in your time of running, and cut down from 80 hours to
trapolations involving a prior point. Is that correct, or do
ten hours.
you use two prior points?
It is true that the programming will be more complex,
Mr. Koch: We use two prior points.
and it is also true that every time you get a discontinuity
Dr. Yowell: I am very much interested in some of the
you are going to have more trouble in getting past. But I
systems you say you have handled with more than eight
think you are more likely to get more results out of your
differential equations at a time, where you have had to
machine by increasing the interval than by decreasing it.
punch out the results from one step to the next and put
them back in again. Has it been necessary to punch more Dr. Thomas: I would like to warn people that while what
than two cards with the same values on them? Dr. Grosch has said is likely to be very true for computa-
Mr. Koch: Yes, it has. Occasionally we have had to tions which are carried to great accuracy, like astronomical
punch the same value in a number of different cards to be computations, it is not at all likely to be true for calculations
used at different places in the calculation. which do not have to be carried to such great accuracy, like
Mr. Lesser: \\lith regard to summary punching multiple trajectory problems. If you are only going to something
cards from the same set of data, the technique that we used like a tenth of a per cent to start with, then the optimum
was to bring out the 12-impulse from the digit-emitter in interval for simple formulas is not going to be very greatly
the summary punch back through the summary punch X increased by using more complicated formulas.
control wires to the accounting machine through a latch If, however, you wanted to carry the same calculation to
selector on the accounting machine, and then back through twice as many decimal places, you would probably do very
a second summary punch X control wire to pick up punch much better by using more complicated formulas than by
selectors. On additional summary punch cycles, the punch using shorter intervals. But for calculations which are only
selectors caused the data to be gang punched from the lower of relatively low accuracy, from the astronomical point of
brushes back to the punch magnets as many times as we view, the very complicated formulas with many differences
desired. really do not pay.
Reduction of Six-Component Wind Tunnel Data
Using the IBM Card-Programmed Electronic Calculator.}
Model [[*
MURRAY L. LESSER
Northrop Aircraft, Inc.
T EST D A T A taken during a wind tunnel program on 1. DATA REDUCTION FORMULAS
a scale model of a Northrop airplane, conducted in the ten- The test data are recorded, from a strain gage balance
foot pressure tunnel at Wright-Patterson Air Force Base, system located in the sting mount, in the form of readings
were reduced to coefficient form using the IBM Card-Pro- on a Brown self-balancing potentiometer. In order to elimi-
grammed Electronic Calculator, Model II. Six-component nate tares and effects of battery voltage variation, a "zero"
test dataa for each test point were key-punched into a single reading for each strain gage is subtracted from the particu-
IBM card (average key punch time was approximately 75 lar reading before the point is recorded on the key-punch
test points per hour). The data cards were machine collated form (Figure 1). The recorded values, as entered on the
into a prepared program deck, and the results were com- form, are the net strain gage readings divided by 100. The
puted and printed in coefficient form for both stability and six-component data are recorded from the balance system
wind axes (simultaneously) in one pass through the calcu- in the form of forward and rear normal force gage readings,
lator at a rate of three test points per minute. Because of nl and n2, respectively; chord force reading, c; forward and
the nature of the balance system and the small size of the rear side force readings, Sl and S2; and a rolling moment
model relative to the tunnel, corrections were not required reading, r. The associated loads are obtained from the fol-
for tares or wall effects. lowing calibration data:
The programming and wiring of the CPC for this com-
putation are discussed in more than usual detail as an illus- Nl = 316.0 nl
(lb.)
N2 80.0n2 (lb.)
trative example of the flexibility available in the CPC
Model I1. b This flexibility allows parallel-serial operation
C' = 31.7 c (lb.)
Sl 44.2 Sl (lb.) (1)
of the calculator where a small number of digits will carry
S2 22.9 S2 (lb.)
the required information. With few exceptions, the compu-
R = 446.0r (in.-lb. )
tations required are elementary, and no originality is
claimed for the manner in which they are accomplished. In addition to the chord force determined directly from
It should be pointed out that the machine time for an the reading of c, it was found during the calibration tests
equivalent computation on the CPC Model I would have that there existed interaction effects on c because of the
been approximately twice as long. Also, it would have been other loads. Hence, the net chord force, in pounds, is given
necessary to split the key-punched data for one test point by the folio wing expression:
into two cards, thus increasing the possibility of error C = C' + 0.0116 Nl + 0.0050 N2 + 0.011 Sl
through operator mishandling as well as increasing the + 0.022 R + 0.888 tf! . (2)
key-punch time. The value of tf! used above is the preset value, tf!u, cor-
aData key-punched into the card consisted of the six wind tunnel rected for deflection in the mounting system due to air-
strain gage readings, the uncorrected angles of attack and yaw, the loads. Calibration tests provided the following correction
tunnel dynamic pressure, and an identifying run number.
bIt should be noted that the discussion on machine operation (Sec- *The terms Model I and Model II are used in this paper as simplified
tion II) assumes a speaking knowledge of IBM computing tech- CPC designations for the Type 402-417BB, 604-3, and the Type
niques on the part of the reader; in particular, familiarity with the 402-417AA, 604-2, respectively; the terms Model I and Model II
concepts of the CPC Model I is implied. do not refer to actual machine types.-Editor's note.
17
18 COMPUTATION
10- FOOT WIND TUNNEL TEST DATA
I 56 1016 2C 21 2f~6 3C 31 3536 4C 41 4546 5051 55
q RUN NO. 0( It' nl n2 C 51 52 r
L i L I
I
L L L : L L L
L L L L L L I
L I
L
I
L L I
I
L L L I
I L I
I
L L
L L I
I
1- L L L L L
L L I L L L L L L
L L I
I
L L L L L L
I
L L_ I
I
L L L L L L
I
L L I
L L L L L L
L L I
L ! L L L L L
i I
L L I
I
L L L L L L
L L I
I- L L L L L
L L L L L L L L
I
L L L L L i L L L
1- L L I L L L L L
i I
I
L L L L I L L L L
:
L L L L L ! L L L
L 1
L L L L L L L
L : L L L L L L L
I
L L L L L L L L
i
L L L L L L L L
1- L L L L L L : L
:
L L L L L L L L
L L L L L L L L
!
NOTE: DECIMAL POINT IN EACH QUANTITY LOCAT.ED BY VERTICAL DOTTE 0 . LINE. IF QUANTITY IS NEGATIVE. PLACE "X"
IN BOX IN UPPER RIGHT CORNER. FI LL ALL SPACES TO RIGHT OF LEAST SIGNIFICANT FIGU.RE WfTH ZEROS.
FIGURE 1. TEST DATA FORM
expressions for the angle of attack, ~, and the angle of yaw, A. Stability Axes
""in degrees: (4)
~ = ~u + 0.0016N + f(N Lift == Ls = (N1 +N2 ) cos~ - Csin~ (lb.)
2 1)
Drag == Ds = Ccos~+ (N1 +N2 ) sin~ (lb.)
feNd = 0.0022 N1 (for N1 > 0) Side force == Y s = S1 + S2 (lb.)
= 0.0032 N1 (for N1 < 0) (3)
Pitching moment == Ms = -0.169 Nl - 9.581 N2 (in.-Ib.)
t/t = t/tu + 0.0028 S1 + 0.0020 S2. Yawing moment == ns = (-1.134 S1 - 10.546 S2) cos ~
- R sin ~ (in.-Ib.)
From the geometry of the model and balance system, and
the conventional definitions of the aerodynamic forces and Rolling moment == ls = (-1.134 S1 - 10.546 S2) sin ~
moments, the following' expressions are derived: + R cos ~ (in.-Ib.)
SEMINAR 19
B. Wind Axes capacity of seven digits plus sign. The unused digits are not
wired to the entry or exit chains.) The use of 12 counter
Lift == Lw = Ls groups was also suggested by the fact that there are twelve
Drag== D w = D s cos tf; + Y s sin if; items (exclusive of run number) to compute and print for
Side force == Y w = Y s cos tf; - Dssintf; (5) each point: ex, tf;, CL , Cn, and two values each of CD, Cy , CM,
Pitching moment == M w = M s cos tf; + ls sin tf; and Cz