THE PRESENT PAPER is intended to describe some important problems being solved by the IBlYI in-stallation in the engineering department of the Beech Aircraft Corporation. Emphasis is placed .on the various types of jobs processed by the IBM group for our engi-neering and sales departments. Consistent with the stated objective of the Forum, particular emphasis is placed on problems which arise frequently in structural engineering.
It is hoped that the ideas contained herein will help stimu-late discussi.on and thereby foster a mutual exchange of ideas.
INTRODUC1.'ION
At the present time the computing installation in Beech's Engineering Department includes one each of the follow-ing International Business :Machines:
Type 601 Multiplier
Type 513 Reproducing Punch Type 080 Sorter
Type 405 Accounting Machine Type 552Interpreter
Type 031 Alphabetic Key Punch
The need for such an installation was envisioned during the war as a practical solution to some problems arising from critical manpower shortages. It was considered that the IBM group would function in the following ways:
1. Accammodate certain types .of periodic and inter-mittent wark-loads of our engineering department.
2. Alleviate shortages and losses toO the armed forces of skilled technical personnel.
3. Help relieve engineering personnel of routine calcu-lations, thereby providing time far more important duties.
To date our IBM group has handled a cansiderable amount of w.ork relating to airplane weight cantrol, struc-tural analyses, sales research, time-labor studies, field service engineering, library records, and other engineering problems. Some of these projects are discussed herein.
Consistent with the stated area of discussion, however,
54
particular emphasis will be placed on technical prablems of aircraft engineering.
"VEIGHT CONTROL PROBLEMS
Of impartance is the current usage.of machine methods in weight contral calculations. In much of this type of work the machines are required to shoulder intermittent, heavy work-loads, and have demonstrated appreciable sav-ings in time and labor. In a general sense, our weight con-trol graup determines the c.onditions of weight and balance of the variaus Beech airplanes. In particular, this group investigates the weights and center of gravity locations of campasite airplanes far various loading canditions. Such informati.on usually is obtained by cansidering the weights and centroid lacatians of all fixed and movable items of mass in the airplane. Punched card methods are readily adapted to handle the large volumes of weight and bal-ance calculations associated with this type .of wark.
SALES RESEARCH PROBLEMS
Our computing installation was used recently in a sales research pr.ogram ta determine potential markets far Beech praducts. This pragram was essentially a statistical survey .of numeraus parameters relating to sales patentials in various geographical areas. The labar entailed in the mathematical manipulatian of these parameters was con-siderable. However, many basic operations were repeated, and therefore adapted to punched card meth.ods of solu-tion. The machines relieved the sales research group of many haurs of "donkey wark."
STRUCTURAL PROBLEMS
Weare set up to handle the fallawing structural engi-neering problems by machine methads:
Three-dimensional flutter analyses .of aircraft structures.
Harmonic analysis.
SQlution of linear simultaneous equations.
Solution of complex matrix equations.
Computation of section properties of aircraft structures.
For each of th~se problems we have provided our IBM group with a master deck .of precoded cards, wiring dia-grams, and a set of written instructions. The master decks are considered as permanent equipment, that is, they are not processed in the solution of a particular problem. For specific problems, the master decks are reproduced to obtain working decks of cards which are prQcessed in accordance with the written instructions. The instruction sheets we use at Beech avoid, wherever possible, reference to technical significances of the steps being performed.
This divorcing of engineering aspects of a problem from the required machine operatiQns enables the IB:M operator to concentrate mainly on manipulation of the cards.
Flutter
The punched card method of flutter analysis we use is based on the theory given in ACTR No. 4798.1 Standard procedures have been set up for the following basic flutter modes:
1. Fixed surface bending vs. fixed surface torsiQn vs.
rotation of control surface (with or without geared
tab). .
2. Fixed surface bending vs. fixed surface torsion vs.
airplane roll or vertical translation.
3. Fixed surface bending vs. fixed surface torsion vs.
rotation .of control surface (with or without geared tab) vs. airplane roll or vertical translation.
These flutter modes are solved entirely by the machines, except that a few manual operations are required during the final stages of solution.
Usually, flutter analyses are conducted to determine the critical flutter speeds and frequencies and the associated values of damping coefficients. In SQme cases, additional information such as mode shapes and amplitude ratios of the component degrees of freedom also may be required.
The problem of determining these items may be resolved into the two rather distinct phases of formulating and solving the stability determinant. We formulate the de-terminant by straightforward operations on matrices, then solve the determinant by trial-and-error iteration. Some discussion on these important steps is considered desirable.
For any mode of flutter, the stability determinant is composed of complex elements. The numerical value of each element may be determined by evaluating and sum-ming up certain aerodynamical and mechanical integrals.
Careful study has shown that:
1. Each of these integrals may be expreSsed as a sum-mation of products of finite quantities. This would be equivalent to considering that the wing is divided into a finite number .of chordwise strips.
2. Multiplication and summation of these products may be accomplished readily using methods of matrix algebra.
3. The llumerical value of each element of any stability determinant may be expressed as the product of four matrices.
On the basis of these observations, we form stability de-terminants entirely by machine·methQds.
As previously mentioned, we solve the flutter determi-nant by trial-and-error iteration. It has been determined that this process will converge at a practicaJ rate, since the preponderant elements usually lie on the principal diagonal.
In most cases the iteration stabilizes satisfactorily in two or three trials. However, in some cases fQur or more trials may be required. In general the iteration process is carried out in the following way:
1. First a trial value of w is substituted in all but one of the elements along tli.e principal diagonal.
2. The determinant is reduced to the third order, if necessary, then expanded to obtain a linear equatiQn in one unknown.
Practically all of the labor of solving the stability determi-nant is done by the machines. However, some manual operations are required to estimate initial trial values of (J) and calculate flutter speeds, frequencies and damping co-efficients at the final stage of solution.
Estimates of the time required for the solution of a three-degrees-of-freedom flutter mode by manual methods as compared with our punched card method, based on the assumption that five values of (v/bw) are investigated f.or each mode, are as follows:
56
Wave/orm. Analysis
Complex periodic waveforms frequently occur on vibra-tion records of structural investigavibra-tions such as flight test-ing, fatigue testing and vibration tests of power plant installations. It is impossible to analyze many of these waveforms by ordinary inspection methods. However, any complex periodic wave may be represented by the super-position of a number of simple .sine and cosine waves. It might also be mentioned that aperiodic curves, continuous in a finite interval, also can be represented by assuming that the given curve represents a single cycle of variation.
The problem of waveform analysis is primarily that of determining the amplitudes and frequencies of the sine and cosine components present in the synthesized wave.
At any point along the reference axis, the ordinate of a composite waveform is equal to the sum of the ordinates of the component harmonics.
At Beech, we have expanded the Fourier series to obtain the general equations corresponding to five, eleven, twenty-three and forty-seven harmonics. Particular solutions may be obtained by substituting into these expansions the nu- ' merical values of the ordinates of a given curve.
We have transferred the trigono.metric. constants of these expansions into. a master deck of 4704 coded cards.
Solution of a, specific problem may be obtained by punch-ing into a workpunch-ing deck (reproduction of the master deck) the measured values of the ordinates. The cards are then pro.cessed in accordance with standard instructions. Solu-tion is accomplished almost entirely by th~ machines; some divisions and extractions of square roots must be per-formed manually.
A comparison of time required by manual and punched card techniques for waveform analysis is of interest.
Numberof Corresponding Est. llf allual Est. Machine
Ordinates Number of Time_
Time-to Curve Harmonics Hour{ Hours, matrix equation, on the left side, contains a square matrix of constant coefficients postmultiplied by a column matrix of the unknowns. The right-hand side of the equation has only one column matrix of constants. The square matrix
S C I E N T I F I C COMPUTATION
of coefficients is operated on by rows and by columns until all terms below the principal diagonal are zeros and each term along the diagonal is unity. During operations on rows, the· column matrix on the right side of the equation is also modified. It is clear that the value of the nth un-known is immediately given on completion of these opera-tions. The value of the nth unknown then is employed in a back-tracking process to determine the (11-1) th un-known, and so on.
It has been determined that time saved by machine methods over manual methods increases appreciably with increasing numbers of equations and unknowns. This may be seen from the following comparisOli:
Number 0/
Equations and Unknowns
ApproJ;imate TI~me for Soluti011i-7ManHouys
IBM IBM
by Decimals by Powers Manual 10 equations by the Kimballmethod.2 It is particularly useful ,in performing the basic operations of matrix algebra on matrices with complex elements. The method is also useful in manipulating matrices with variable elements when the solutions are approximately known or when the prepon-derant elements lie along the principal diagonal. This latter feature is a reasonable guarantee that trial-and-error iter-ation will converge at a practical rate.
Other Projects
At the present time we are investigating the feasibility of solving the following structural problems by punched card methods:
1. Spanwise airload distribution for monoplane wings.
2. Natural torsional frequencies of crank..,systems using Holzer's technique.
3. Natural uncoupled frequencies of beams using Sto-dola's iteration procedure.
4. Analysis of shear lag in aircraft structures.
TIME ASPECTS
The time estimates previously given for several struc-tural problems were based on actual performances. They were determined by solving given problems manually and by machine. Now the approximate average rates of, our machines are as follows:
Multiplier-15 cards per minute Reproducer-lOO cards per minute Sorter-450 cards per minute
Accounting Machine-' 80 cards per minute (detail print) 150 cards per minute (group print) Interpreter-60 cards per minute
Processing time for most problems can definitely be im-proved through usage of faster calculating punches. We probably will consider faster machines when the need for more rapid processing becomes manifest.
RECOMMENDA'tIONS
Usually, punched card procedures can be adapted to a given engineering problem in a number of ways. From time and labor standpoints some procedures will be more efficient than others. Among other factors, a determination of the optimum procedure depends on a knowledge of the full capabilities of the machines available for our use. For this knowledge we rely to an appreciable extent on the Wichita staff of International Business Machines Corpo-ration. We have always found them highly cooperative.
However, in some cases they were unable to provide us with enough information on specialized capabilities of the machines, particularly our Type 601 Multiplier.
We recommend that local IBM offices be provided with up-to-date information on the full computing capabilities of the machines in their region. It may be possible to estab-lish, on a current basis, the flow of such information from the various IBM research laboratories and computing centers to branch offices. This would help people like our-selves to realize the maximum potential utility of IBM installations and avoid needless duplication of effort.
REFERENCES
1. B. SMILG and L. S. WASSERMAN, "Application of Three-Dimen-sional Flutter Theory to Aircraft Structures,"Materiel Divi-sion, Air Corps, ACTR 4798 (1942). number of years. It was very easy for two or three people to keep in touch with each other. Within the last two or three years, there has been such a sudden cloudburst that to have people everywhere supplied at the right time with the right information is a little difficult. Steps are' being taken; IBM has now, among other things, special repre-sentatives in the Sales Department who understand what you are trying to accomplish. They know what is available in IBM, and they are at your call.
With respect to the local manager, he also has a very tough assignment when you ask him for methods ,of doing things he has never heard of. That gap has to be bridged, and I am sure it will be in a very short time.
There is still another way which is open at the moment, and that is to call on us at the Watson Laboratory or write us a letter. Weare always glad to hear from you. I think in-formation fro111 your laboratory to our installations, but could pick up ideas from us to be passed on. Such repre-sentatives would be very valuable.
Dr. Eckert: That is the intention. The difficulty is to get the right man, get him trained in a very difficult field, and get him to you.
Dr. Kortz: Why not send Dr. Grosch?
J.\:lr. Schroedel: 1\ir. Kimball, Dr. Grosch, and I par-ticipated in a rather successful experiment along those lines recently. Lectures were given at the Cornell Aero-nautical Laboratory in Buffalo, and people from other computing groups in the vicinity also attended. We learned a good deal from the meeting. But there are fifty or sixty installations in various parts of the country, and it is not easy for all of us to visit every locality and work with you long enough to really make a contribution. We hope to have more technically trained representatives in the Sales Department as time goes on.
Mr. Bisch: Several points, which could stand some com-ment and emphasis, were picked out of the very interest-ing talks of our aircraft representatives, Messrs. Ferber, Bell and Kintas. Instead of taking one point at a time, it seems more constructive and brief to present all my com-ments as a whole.
Many engineering organizations are looking today for powerful means of calculation. What the Engineering De-partment of North' American did four years ago was to look to IBM for the main answer to this need, after a general survey of the field. Fast progress was desired, and to this end production methods were used in the crea-tion and the development of our Engineering Seccrea-tion of accounting machines.
Such methods call mainly for extensive specialization and perfect coordination. To be concrete, we select the structures section, although the following would be true for the aerodynamics section as well.
An engineer with a long acquaintance with problems of structures, company policy, and organization methods was asked to select the problems and among their various solu-tions those which result in speed and efficient use of the IBM machines. This engineer familiarized himself with the various functions of the IBM equipment and the pat-tern of calculation most suitable for it, but he made no attempt to learn how to operate it. As a result, he was able to increase the contribution of the machines and he promptly reached the conclusion that for a given standard problem, the machines can do everything from the punch-ing of the initial data to the final report printpunch-ing. It is
58
important to remark that he was the only engineer in direct contact with the accounting machine section.
On the other hand, an IBM operator with several years of experience and a mathematical knowledge equivalent to a master's degree was assigned to program for the ma-chines the problems offered by the structural engineer, to propose profitable changes in the mathematical processes, to suggest further use of the equipment, and to select the selected as supervisor of this group. This group is an inde-pendent section of the main accounting section with its own machines, and it derives many obvious advantages such as readily available service for the machines and the incidental facilities of a large. installation, by not being separate from the main IBM body. The two men at its head, the mathematician and the supervisor, form a per-fect team for the dual purposes of large volume and con-tinuous improvement.
The Engineering Section is therefore made of two parts:
the engineering part and the accounting machine part, through which a perfect coordination is possible by a one-man contact. It is now opportune to detail further the duties and achievements of each component.
The engineering part, which is also assigned to seek new technical and experimental solutions of aircraft engi-neering problems, to write reports on the algebraic and tabular solutions of problems and to conduct experimental work, keeps an accounting of the approximate number of arithmetical operations required by every job sent to the IBM section. This number is easily arrived at for standard problems, using simple algebraic formulas. On the other hand, an extensive survey has shown that an engineer can perform an average of one hundred arithmetical opera-tions for each remunerated hour. As shown by two years of coverage, an IBl\1 operator performs on the average of one thousand such operations per hour; therefore his speed is ten times greater.
Finally, last year's operations show an average of seven thousand engineer-hours per month performed by an IBM Section of four operators, which would cost a minimum of twenty-one thousand dollars per month, if performed by engineers, against an over-all cost of six thousand dol-lars by the IBM group, thus effecting a saving of fifteen thousand dollars per month. This approximate saving of seventy-five per cent which was evidenced at the very be-ginning was the real selling point to our management.
However, the engineering management has become con-scious of other less tangible although equally important advantages. They are:
SCIENTIFIC COMPUTATION Unprecedented dependability from the point of view
of time and accuracy.
of time and accuracy.