Early Analog Computer Concepts and Developments

As noted in footnote 2, the initial purpose of Project Wizard was to develop a defensive guided missile system in 1946. But with the 1947 scale back, the research at the U. of M. in 1947 specified the use of DC amplifiers as the basis of a general purpose analog computer.⁸ Note: These DC amplifiers became known as “operational amplifiers” or, more popularly as “op amps” and are still called that today.

Simultaneously with the Army Air Force’s Project Wizard, the U.S. Navy launched its own program to develop guided missiles which it named Project Cyclone. The Navy selected Reeves Instrument Company⁹ in 1946, for “development of a guided missile simulator and the operation of a simulation laboratory [for] research and development on guided missile simulation” and “development and construction of a rapid and precise automatic analog computer suitable for detailed simulation of guided missiles”. The contract’s Task Order II on June 12, 1947, required Reeves to provide “a simulation laboratory, the Project Cyclone Laboratory, which was to be operated by the Reeves Analysis and Computer Group.” Reeves built the lab’s original Reeves Electronic Analog Computers (REACs) in 1947, and a new computing lab of REACs was contracted under Task Order III in 1949. “The guided missile simulator of Task Order II was completed in early 1949 [with a] satisfactory demonstration in February 1949 of the guided missile simulator solving a three-dimensional guided missile problem”.

A commercial version of REAC soon followed, with more than 60 installed by 1950. Why is this important in this document? The Aerospace Dept. of the U. of M. bought a REAC in 1951 to add to its growing analog computer capability.

A research group called Project RAND began within the Douglas Aircraft Company during WW II. On May 14, 1948, Project RAND separated from the Douglas Aircraft Company and became an independent, nonprofit organization. The new entity was chartered in the state of California to “further and promote scientific, educational, and charitable purposes for the public welfare and security of the United States.” Shortly after becoming independent, Project RAND acquired an early model REAC and almost immediately made a number of significant improvements to it, many of which were quickly absorbed by the tiny postwar analog computing industry. Chief among these improvements was a new design for the DC op amp.

In 1949, Prof. L. L. (Larry) Rauch joined the U.of M., Aerospace Dept. from Princeton. In 1950, Prof. Rauch instituted a program of replacing the amplifiers built earlier at the U. of M. with the RAND amplifier design.

One of the problems associated with the DC amplifiers built at the U. of M., starting in 1947, and other such amplifiers, was drift over time in the amplifier output voltage. Rebalancing the amplifiers regularly was a time-consuming necessity. A method for eliminating this drift, called chopper stabilization, was worked out by RCA, and Leeds and Northrup and a patent for this invention was filed in 1949. This was a major step forward in the usefulness of the DC op amp.

Analog computer applications work at the U. of M. began with solving simple, linear, ordinary differential equation models which had time as the only independent variable. This work then progressed to solving a bending beam equation. This equation is a fourth order partial differential equation which has both time and space coordinates as independent variables. The space variable partial differentials were discretized to produce a set of coupled difference/differential equations with time as the only independent variable that had to be solved subject to a set of boundary conditions.

What was the purpose of looking at this example? Well, the wing of an aircraft could be thought of as a bending beam, free at each end, with a pilot controlled fuselage in the center that could insert forces and moments on the beam at that point. This was the subject of several research efforts and reports in the 1948 to1950 period as part of the Project Wizard program.

ADI’s Change From Analog to Digital Computing in 1975

From June 1975 until September, 1992, ADI was a wholly owned subsidiary of a Dutch conglomerate called the Internatio Muller Group (IM) of Rotterdam, The Netherlands. A brief history of ADI in this period is presented in Appendix F. This was a very interesting period for ADI, one in which the Company replaced its analog computer products with high speed, special purpose, digital simulation products. The first of these was called the AD 10. It was also a period of significant growth in size and profitability for the Company.

This change in direction to digital technology opened a whole new area of research for Bob Howe, particularly when ADI began developing a Numerical Integration Processor for the AD 10 around 1977. ADI needed to supply some fixed step-size, numerical integration routines for use with this new processor. The literature provided a number of possibilities. The question was which ones were viable candidates in terms of complexity, computational time required, accuracy, numerical stability, etc.

Bob Howe’s Second Book

Bob Howe was involved in ADI’s decision to switch from analog to digital technology for supplying real time, hardware-in-the-loop, computational power. His research interests quickly turned to investigating and analyzing various aspects of this new technology approach. Eventually some of ADI’s customers began asking Bob to write a book based on this research work. He wrote eleven chapters covering a variety of pertinent topics. These chapters are available on ADI’s web site, adi.com. To find them, go to the web site and follow the path Resources > Technical Documents > Book “Dynamics of Real Time Simulation” (currently on the bottom of page 3).

In the Introduction to this book Bob states:

“Computational methods in real-time simulation and control are in general not well understood by scientists and engineers, even when they have had extensive experience in non-real-time simulation. In particular, many of the methods used to control dynamic errors and stability in traditional simulation are just not applicable in the real-time case. A vast array of simulation and control tools and other technology have been developed over the past decades that help abstract the complexity of real-time. However, without a deep understanding of the first principles nature of this technology the real-time engineer can fall into many traps. This book is made available to help anyone strengthen their knowledge of the dynamics of real-time and help us all develop better solutions as the world of complex systems becomes increasingly complex.”

Unfortunately, Bob was not able to complete the book. He started on a twelfth chapter, but he was unable to finish it. We will never know whether that would have been the last one or not. Nonetheless, the eleven chapters that are available are a significant contribution to the knowledge of real time digital simulation.

Appendix A – Mechanical Analog Computers and Their Electronic Descendants

Mechanical Analog Computers

The concept of a mechanical analog computer or mechanical differential analyzer is virtually unknown today. However, decades before electronic devices of any kind were even dreamed of, people had applications for which they needed a solution.

The history of mechanical analog devices goes back at least to Vitruvius (1st century BC), who described the use of a wheel for measuring arc length along a curve, the most simple integral in space. Many other elementary analog devices were described before the modern period: Differential gears used for adding or subtracting two variables. are usually ascribed to Leonardo da Vinci: and Leibniz is credited for the idea late in the seventeenth century of a similar-triangles device for equation solving or root solving.¹⁸

In the 1800s governments in various parts of the US were granting homesteads and surveying was a very important occupation. Surveyors need to determine the area of a piece of land with an irregular boundary, such as a river, that can be depicted as a two-dimensional, closed figure on a piece of paper. From a mathematical standpoint, determination of this area requires an integration process. A device for determining this area is called a planimeter.

The following paper provides documentation of work beginning in 1814 and proceeding to the work of Hannibal Ford relative to the development of mechanical analog computer capabilities. It has lots of colorful illustrations to help the reader understand the concepts.

Cones, Disks, Wheels and Spheres for Area and Integration

http://www.rechnerlexikon.de/files/drehae2011.pdf

This paper begins as follows:

“Abstract

The very first planimeter, invented in 1814 by Johann Martin Hermann in Bavaria, used a cone wheel gear as an integrating mechanism for area measurements. The same principle was implemented in high precision instruments with up to 18 integrators initiated by Vannevar Bush¹⁹ for evaluating differential equations in higher physics.

This article presents the history of these instruments and their inventors. It illustrates the rise of a simple kinematic principle from measuring devices to mechanical supercomputers.

1 The First Generation: Cones, Disks and Wheels

It was in the first half of the 19th century when efforts for tax equality and the rise of cadastral authorities in Europe led to an urgent need for devices that could simplify the calculation of areas of real estate.

The first apparatuses were simple analog devices which assisted the calculating clerk in taking the measurements and sometimes multiplying two quantities. These instruments were either only approximating the area or they were restricted in the type of region they could handle.

The simplest devices are so called harp planimeters. Harp planimeters divide the area to be measured into narrow stripes of equal width (much like the strings of a harp). The sum of the lengths of the stripes multiplied by their width gives an approximation for the demanded area.

The first device for calculating the area within a closed curve, was the integrator of B.H. Hermann in 1814. Hermann’s integrator was essentially a wheel pressed against a disk. An early application of such integrators was the integration of force over distance to measure work. Another application was a planimeter to measure the area within a closed curve. In fact. the chief impetus behind the early integrator inventions of the nineteenth century was to get an improved planimeter. James Clerk Maxwell described a ball type of integrating device while he was an undergraduate: it was incorporated in a planimeter design. In about 1863. James Thomson’ conceived an equivalent integrator in which a ball rotates between the disk and a cylinder.

Most of these instruments were cumbersome to operate and none of them could handle arbitrarily shaped areas.

Hermann’s construction dates back to 1814, but since he abstained from publishing it, his invention did not receive closer attention at that time. The prototype of Hermann’s planimeter was disposed as scrap metal, and the inventor’s manuscripts were forgotten for about 40 years.”

This document goes on from here to describe numerous mechanical devices for handling specific applications. By the early 1900s military applications, particularly for naval ship guns, began to get more attention, albeit slowly. By the 1930s the complexity of a mechanical integrator developed for naval gun control by Hannibal Ford is shown in Figure 8, page 25 of the Ben Clymer paper.

The most important use of mechanical analog computers in the 1930s and through 1945 was for US Navy gunnery fire control systems on ships.

A number of educational institutes in the US and elsewhere developed general purpose mechanical analog computers for various studies and demonstration purposes. However, these units were expensive to build, time-consuming to program and slow in operation. As the last paragraph in the paper presented above states:

“Finally, the 18 integrator machine from 1940 marks the culmination as well as the end of the evolution of a simple kinematic principle. The unavoidable destiny of all these differential analyzers was the same as for the very first integrating planimeter of Hermann: It is now scrap metal, dismantled and, if lucky, on show in a museum.”

Electronic Analog Computers

In about 1940 the market for general purpose tools for performing mathematical operations was quite small. Mechanical desk calculators served acceptably for all but the largest problems, such as gun fire control and exterior ballistics.²⁰ When Thornton C. Fry wrote a survey article about the extent of the use of mathematics in industry, he had little to report outside the telephone and aircraft industries. One could not then imagine the explosion of electrical and electronic technologies that would eventually result in a flood of computers available at modest cost.

Two reasons for the lack of effort to develop electrical analog computers for the Navy until the early 1940s was concern that electronic (vacuum tube) systems couldn’t withstand the rugged environment of life at sea²¹ and that the required parts (resistors, potentiometers, and capacitors) lacked sufficient precision for fire control. The second of these reasons changed rapidly once the Navy decided to invest in the development of the electronic analog computer approach to gun control. While it is very unlikely that any of the details of the electronic gun control units were known for a number of years after the end of WW II for security reasons, the availability of high quality electronic components was a definite benefit for the commercial development of electronic analog computers that occurred at the U. of M. and elsewhere in the years after the war.

DC (direct current) amplifiers had been used since the post-World War I days of radio. They were highly developed in the 1930s by Bell Telephone Laboratories (BTL), which used them for signal amplification in telephony. They were used by George Philbrick at Foxboro, as early as 1937 or 1938, for simulation of linear processes and control systems. Developments of amplifiers for use in simulation were also made by John Ragazzini et al., at Columbia University in about 1940. In fact, the design of the amplifiers constructed at the U. of M. in 1947 was published in an article by Ragazzini et al., in: “Proc. IRE, vol. 35, no. 5, pp. 444-452, May 1947”.

Mechanical analog computer world evolved in two directions in the 1940s, branching into developments in AC analog computers and DC analog computers. AC analog computers were based on AC amplifiers. These amplifiers amplified AC (alternating current) signals but had no DC link between the input signal and the output signal. DC analog computers, on the other hand, incorporated DC amplifiers which did have a DC path connecting amplifier input to amplifier output.

DC Analog Developments

BTL devoted itself to the development of DC vacuum tube amplifiers for use in analog computers for fire control after about June 1940. In November 1940, Western Electric (a member of the Bell Telephone companies) received a contract to develop a model of a DC analog gun director, the T-10. It was to use the BTL-developed DC analog technology. The model was tested successfully in December 1941. The success of the T-10 led to a contract to build the production version, the M-9 Gun Director. It was delivered in December 1942, and it was placed in service in early 1943 for land-based applications. It was used during the V-1 “buzz bomb” attack on London to control the fire of 90-mm guns located along the English coast. During the month of August it shot down 90 percent of the buzz bombs that arrived, and in its best week it shot down 89 of the 91 that arrived. The M-9 was aided by radar and proximity fuzes. A British version of the M-9 (the T-24 directing 4.5 inch AA guns) had its prototype completed by May 1942.

The Mark 8 Fire Control Computer was also developed by BTL during World War II. It was initially requested by the USN Bureau of Ordnance as an alternative to the widely used Ford Instruments Mark I Fire Control Computer, in case supplies of the Mk I were interrupted or were unable to be manufactured in the required numbers. The Mk 8 computer used all electric methods of computation, in contrast to the Mk 1, which performed most computations via mechanical devices. The Mk 8 was found to be more accurate than the Mk 1 and substantially faster in reaching a fire control solution, but by the time it was developed and tested in 1944, supplies of the Mk 1 were found to be sufficient in quantity. The USN extensively tested the Mk 8 and may have incorporated some of its technology into the post war Ford Instruments Mk1A computer. The Mk 8 technology was similar to that used in the M9 gun data computer used by the US Army for coast defense fire control and in the SCR-584 radar system computer.

AC Analog Developments

The principles of AC (alternating current) electrical analog circuits had been known since Steinmetz in the 1880s. Currents entering a node were known to add. The charge on a capacitor was known to be the time integral of the current that had flowed through it. It was known that a servo-driven potentiometer could be “tapped” to yield a function or a product of two variables. This technology was not developed, however, until BTL found application for it in a developmental gun director early in World War II.

The BTL project was to develop an AC analog gun director, the T-15. It was funded in November 1941, and the model was completed a year later and tested in December 1942. The T-15 was never put into production: it was, however, used for research with targets flying trajectories that were not straight lines, i.e., an anti aircraft application. The T-15 led to a proposal to the Navy, in February 1942, to construct an AC analog version of the Ford Instrument Company’s Computer Mark 1²². A contract was awarded in September 1942 for development of this “Mark 8 Computer.” Although it proved to be faster than the Computer Mark 1 in completing the initial transient of acquiring and locking onto a target, the Mark 8 Computer was never produced. It had one other feature worth noting: a special electrical integrator that was developed for it.

From 1945 to 1950 the Dynamic Analysis and Control Laboratory at MIT developed an AC analog computer, using 400-cycle AC components in a guided missile flight simulator. This was an activity within Project Meteor. The flight table was mounted on four concentric gimbals so driven as to avoid gimbal lock under all conditions.

While these were interesting applications of the AC amplifier, this type of analog computer did not survive long term. In fact, the work described in the section above entitled “Evaluation of the Computer Section of Flight Training Simulators” and the related material in Appendix C below likely had a lot to do with the demise of the AC amplifier based analog computer.

Appendix C – Evaluation of the Computer Section of Flight Training Simulators

Two aircraft examples were used for this study: The F-86D fighter and the B 47 bomber. The most difficult area for accurate simulation was the longitudinal or pitch motion. The reason this mode was problematic was that the transient that occurs following a pilot commanded change in altitude consists of two distinct parts: A fast, short term response followed by a slower response called phugoid motion.

The study involved two separate aspects pursued in parallel:

• • The first was to identify pertinent simulator manufacturers, locations of the subject simulators for each selected manufacturer, pilots trained on each of these selected simulators, and the aircraft manufacturers of each of the two selected aircraft. Visits were made and data was collected as detailed in the project’s interim and final reports. All the simulator computer sections studied in this project were based on the AC version of an electronic amplifier.²⁴
• • The second aspect of this project involved expanding the analog computer capability of the Aero. Dept. beyond what was available in the REAC, and other recently built equipment. The goal was to be able to simulate a complete 6 degree of freedom, nonlinear equations of motion model of an aircraft. This meant adding both amplifiers and servo multipliers. Once this expansion was completed, Elmer Gilbert programmed the equations for the longitudinal characteristics of each of the two aircraft mentioned above. This was the area of most difficulty for accurate simulation. His report included strip chart recordings to document the results for a variety of different training simulator situations.

The AC amplifier version used in all the computer simulator sections in this project could not reproduce the fast, pitch mode transient, but Elmer Gilbert’s simulation did. The dynamic performance of these AC amplifiers was definitely inferior to that of the enlarged, DC amplifier based system that the U. of M. now had. Elmer Gilbert’s report provided the evidence needed to make the case against the existing AC amplifier based systems reviewed.

The first recommendation in the final report was that the Air Force should not allow AC amplifiers to be used in any future training simulators bought by the Air Force. Relative to the second point raised above, the recommendation was that in every future simulator procurement the selected vendor would be required to:

• • Obtain or already have the pertinent flight test data for the aircraft type and model from its manufacturer; and
• • Demonstrate that the simulator’s response to certain specified pilot commands was within a certain range – say 25% – of the behavior shown in the flight test data for each such command.

Appendix E – ADI’s Historical Competitors

In its first few years, ADI developed a series of small to medium size analog computers that were probably sold to academic institutions and certain research groups such as the AC Sparkplug Division of General Motors. At the same time, companies that would be significant competitors to ADI in the 1960s were both bigger than ADI and further ahead in developing their analog computer products.

• • Reeves Instruments – founded sometime before 1945 – had sold 60 commercial REACs by 1950;
• • Beckman Instruments— founded in the 1930s to manufacture lab instruments – manufactured the EASE (Electronic Analog and Simulation Equipment) from 1953 to at least 1965;
• • Goodyear Aircraft — GEDA – (Goodyear Electronic Differential Analyzer) started dev. in 1948 to support in house missile work. Shipped 1st sys in 1949? Gen 3 started shipping in 1953 – exit ???;
• • Electronic Associates, Inc. (EAI)- founded in 1945 – began shipping analog computers in 1952;
• • Astrodata Comcor – couldn’t find any historical information – was a significant competitor in the 1960s

In the 1960s the three major suppliers of analog computers in terms of numbers of systems sold were: ADI, Comcor and EAI with EAI being the leader. By 1975 the age of the analog computer was essentially over.

Appendix G – Excerpt from Bob Howe’s Prepared Obituary

“In 1952 he developed the first tabletop analog computer specifically for simulation in laboratory courses, as well as an analog computer developed and delivered to the US Navy for the study of underwater sound propagation. In 1953 he became deeply involved in flight simulation training with a USAF (i.e., US Air Force) research contract from the Wright Air Development Center. In 1954 he started and served as first chairman of the Midwestern Simulation Council, and in 1957 became the first president of the national parent Simulation Councils Inc. Also, as a consultant for Link Aviation in 1957, he developed simplified math models used in flight simulators for the DC-8, Boeing 707 and Convair 880 aircraft, the first US jet transports. As a side note, the aero department expertise in analog computers and real-time simulation led in 1957 to the founding by Bob and three of his colleagues, of Applied Dynamics Incorporated. This well known Ann Arbor company developed and marketed analog computers, emphasizing their application to real-time simulation with Bob as chairman of the board for the first twelve years of company existence in addition to his appointment at the University of Michigan. The company continues today as Applied Dynamics International, marketing real-time simulations using digital hardware and software. From 1963-68, Bob served as chairman of the University of Michigan interdepartmental graduate program Information and Control Engineering, and from 1968-82 as chairman of the Aerospace Engineering Department. His many honors include the 1983 AIAA (i.e., US Institute of Aeronautics and Astronautics) deFlorez Training Award for Flight Simulation, the 1978 Award for Meritorious Civilian Service while a member from 1971-79 of the USAF Scientific Advisory Board, and the Society for Computer Simulation International Technical Award, 1978. Bob’s significant additional committee memberships included the NASA Advisory Council Space Systems and Technology Committee (1978-81), Chairman of the Ad Hoc NASA Subcommittee on Shuttle Launched Entry Research Vehicles (1978-81), and Chairman of the Research Advisory Panel, USAF Human Resources Laboratory, Operational Training Division (1979-82). During the last decade of his teaching and research activity in the University of Michigan Department of Aerospace Engineering, Bob participated in flight simulation research jointly with the Psychology Department. Bob officially retired in 1991 as a professor emeritus. During his 41 year career at the University of Michigan he published over 100 technical papers as well as a book on analog computers, and served as chairman of a large number of PhD student committees. In 1947, Bob married Joan (Jo) Craig, whom he met during his last year at Oberlin College. He is survived by Jo, three of his four children and five grandchildren.”