# Oral-History:Sakae Yamamura

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== About Sakae Yamamura == | == About Sakae Yamamura == | ||

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+ | [[Image:Sakae Yamamura 3539.jpg|thumb|left|Sakae Yamamura]] | ||

Sakae Yamamura is an electrical engineer best known for his work on magnetic field driving of electrical arc, his work on analytical theory of the linear induction motor and its applications to magnetic levitation, his development of spiral vector theory, and his work on numerically controlled machine tools. He received his bachelor's degree in engineering from the University of Tokyo and became a lecturer at the University of Tokyo immediately upon graduation. During World War II, Yamamura served in the Japanese Navy, repairing ships at the Kure shipyard and working on the acoustic torpedo project. After the war he taught at the University of Tokyo until the occupation forces sent him to Michigan State University in 1950 where he wrote his M.S. thesis on electrical circuit transformation; he received his Ph.D. from Ohio State University, for a thesis on the transient analysis of induction motors. After receiving his doctoral degree from Ohio State, Yamamura went back to Japan and wrote another thesis on electric arc discharge to receive a Japanese Doctor of Engineering degree. He is retired from his position at the University of Tokyo but continues to work as a senior advisor for a wide range of professional and public organizations. | Sakae Yamamura is an electrical engineer best known for his work on magnetic field driving of electrical arc, his work on analytical theory of the linear induction motor and its applications to magnetic levitation, his development of spiral vector theory, and his work on numerically controlled machine tools. He received his bachelor's degree in engineering from the University of Tokyo and became a lecturer at the University of Tokyo immediately upon graduation. During World War II, Yamamura served in the Japanese Navy, repairing ships at the Kure shipyard and working on the acoustic torpedo project. After the war he taught at the University of Tokyo until the occupation forces sent him to Michigan State University in 1950 where he wrote his M.S. thesis on electrical circuit transformation; he received his Ph.D. from Ohio State University, for a thesis on the transient analysis of induction motors. After receiving his doctoral degree from Ohio State, Yamamura went back to Japan and wrote another thesis on electric arc discharge to receive a Japanese Doctor of Engineering degree. He is retired from his position at the University of Tokyo but continues to work as a senior advisor for a wide range of professional and public organizations. | ||

− | The interview begins with Yamamura describing the projects for which he is best known: magnetic field driving of electrical arcs, linear induction motor analysis and applications, spiral vector theory, and numerically controlled machine tools. He also mentions the various books he has published on these topics and the book he hopes to write on spiral vector theory. Midway through the interview Yamamura describes his early education, his bachelors' degree work at the University of Tokyo, his wartime experiences and his study in the United States. He then discusses his activities with CRIEPI and his affiliations with a range of professional and public organizations. The interview concludes with his discussion of his IEEE activities, including his Life Fellowship and his receipt of the IEEE Nikola Tesla Medal; he also mentions his work for the IEC and his hopes for applying spiral vector theory to the unification of electrical circuit theories. | + | The interview begins with Yamamura describing the projects for which he is best known: magnetic field driving of electrical arcs, linear induction motor analysis and applications, spiral vector theory, and numerically controlled machine tools. He also mentions the various books he has published on these topics and the book he hopes to write on spiral vector theory. Midway through the interview Yamamura describes his early education, his bachelors' degree work at the University of Tokyo, his wartime experiences and his study in the United States. He then discusses his activities with CRIEPI and his affiliations with a range of professional and public organizations. The interview concludes with his discussion of his [[IEEE History|IEEE]] activities, including his Life Fellowship and his receipt of the IEEE Nikola Tesla Medal; he also mentions his work for the IEC and his hopes for applying spiral vector theory to the unification of electrical circuit theories. |

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== About the Interview == | == About the Interview == | ||

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SAKAE YAMAMURA: An Interview Conducted by William Aspray, Center for the History of Electrical Engineering, May 25, 1994 | SAKAE YAMAMURA: An Interview Conducted by William Aspray, Center for the History of Electrical Engineering, May 25, 1994 | ||

− | Interview # 210 Sponsored by Center for the History of Electrical Engineering, The Institute of Electrical and Electronics Engineers, Inc. | + | Interview # 210 Sponsored by Center for the History of Electrical Engineering, The Institute of Electrical and Electronics Engineers, Inc. |

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== Copyright Statement == | == Copyright Statement == | ||

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This manuscript is being made available for research purposes only. All literary rights in the manuscript, including the right to publish, are reserved to the IEEE History Center. No part of the manuscript may be quoted for publication without the written permission of the Director of IEEE History Center. | This manuscript is being made available for research purposes only. All literary rights in the manuscript, including the right to publish, are reserved to the IEEE History Center. No part of the manuscript may be quoted for publication without the written permission of the Director of IEEE History Center. | ||

− | Request for permission to quote for publication should be addressed to the IEEE History Center Oral History Program | + | Request for permission to quote for publication should be addressed to the IEEE History Center Oral History Program, 39 Union Street, New Brunswick, NJ 08901-8538 USA. It should include identification of the specific passages to be quoted, anticipated use of the passages, and identification of the user. |

It is recommended that this oral history be cited as follows: | It is recommended that this oral history be cited as follows: | ||

− | Sakae Yamamura, an oral history conducted in 1994 by William Aspray, IEEE History Center | + | Sakae Yamamura, an oral history conducted in 1994 by William Aspray, IEEE History Center, New Brunswick, NJ, USA. |

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== Interview == | == Interview == | ||

− | Interview: Sakae Yamamura | + | Interview: Sakae Yamamura |

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+ | Interviewer: William Aspray | ||

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+ | Date: May 25, 1994 | ||

[Note: Dr. Yuzo Takahashi: of the Tokyo University of Agriculture & Technology was also present at the interview.] | [Note: Dr. Yuzo Takahashi: of the Tokyo University of Agriculture & Technology was also present at the interview.] | ||

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'''Yamamura:''' | '''Yamamura:''' | ||

− | Let me see. This book, ''Theory of Linear Induction Motors'', was published in 1972. Before the publication I worked on this project for at least ten years. On the linear induction motor, the air gap of the motor is open at both ends. There is discontinuity of the electromagnetic field at both the entrance and the exit. It was therefore difficult to solve Maxwell's equations for this air gap. It's not closed like the rotating machine. So I tried to solve Maxwell's equations and obtained a three-dimensional solution: X component, Y component, and Z component. I gave the three-dimensional solution. For obtaining the X component I used the Laplace transformation. For obtaining the Y component, I used the ordinary differential equation method. For obtaining the Z factor, I used a Fourier transformation. The analytical solution for obtaining this result was rather lengthy and complicated, and finally I obtained this and calculated the field distribution in the X direction. This is then the exit, and this is the distribution of the magnetic field in the Z direction. The thrust of the motor is rather difficult to calculate. But I could calculate rather accurately to obtain this thrust. If we don't have edge effect and end effect, we would get this torque shown by the broken line, but actually we got this thrust. Parameters are the number of poles. If the number of poles is small, the torque is reduced significantly. This means that in order to remove adverse effect from the end effect and edge effect, we need to use a larger number of poles. That was my conclusion. | + | Let me see. This book, ''Theory of Linear Induction Motors'', was published in 1972. Before the publication I worked on this project for at least ten years. On the linear induction motor, the air gap of the motor is open at both ends. There is discontinuity of the electromagnetic field at both the entrance and the exit. It was therefore difficult to solve [[Maxwell's Equations|Maxwell's equations]] for this air gap. It's not closed like the rotating machine. So I tried to solve Maxwell's equations and obtained a three-dimensional solution: X component, Y component, and Z component. I gave the three-dimensional solution. For obtaining the X component I used the Laplace transformation. For obtaining the Y component, I used the ordinary differential equation method. For obtaining the Z factor, I used a Fourier transformation. The analytical solution for obtaining this result was rather lengthy and complicated, and finally I obtained this and calculated the field distribution in the X direction. This is then the exit, and this is the distribution of the magnetic field in the Z direction. The thrust of the motor is rather difficult to calculate. But I could calculate rather accurately to obtain this thrust. If we don't have edge effect and end effect, we would get this torque shown by the broken line, but actually we got this thrust. Parameters are the number of poles. If the number of poles is small, the torque is reduced significantly. This means that in order to remove adverse effect from the end effect and edge effect, we need to use a larger number of poles. That was my conclusion. |

'''Aspray:''' | '''Aspray:''' | ||

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'''Aspray:''' | '''Aspray:''' | ||

− | I would like to ask a question about the possible practical use of this in the following way. When people like Oliver Heaviside were developing mathematical approaches to electrical phenomena, and when Steinmetz at GE was doing this, one of the problems they had was that although their mathematical techniques were very powerful, it was hard to get practicing engineers to use them. Do you anticipate there will be any problems in this case? Is your mathematics easy enough for the practical engineer to be able to use? | + | I would like to ask a question about the possible practical use of this in the following way. When people like [[Oliver Heaviside|Oliver Heaviside]] were developing mathematical approaches to electrical phenomena, and when [[Charles Proteus Steinmetz|Steinmetz]] at [[General Electric (GE)|GE]] was doing this, one of the problems they had was that although their mathematical techniques were very powerful, it was hard to get practicing engineers to use them. Do you anticipate there will be any problems in this case? Is your mathematics easy enough for the practical engineer to be able to use? |

'''Yamamura:''' | '''Yamamura:''' | ||

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'''Aspray:''' | '''Aspray:''' | ||

− | + | [To Takahashi] Now, in your university, do you think that this would be used? In teaching? | |

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'''Takahashi:''' | '''Takahashi:''' | ||

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'''Yamamura:''' | '''Yamamura:''' | ||

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+ | <flashmp3>210 - yamamura - clip 1.mp3</flashmp3> | ||

Let me see. One is missing. Ah, yes. Maybe analysis of the magnetic levitation. The Japan railway is working on magnetically levitated trains that reach the speed of 500 kilometers per hour, or something like that. This system is using superconducting magnets for both levitation and for driving trains, for producing lift force and thrust force. But when I was in the university, I thought that the normal conducting magnet might be cheaper and safer, so I worked on the levitation magnet using normal temperature magnets. Ordinary electromagnets. We needed four magnets, at the corner of the car or tracks. At many places in the world, analysis or experimentation of the magnetic levitation using normal conducting magnets is underway. We worked on the analysis of the magnetic levitation of vehicles, using normal conducting magnets. This is the pulling force, not the repulsive force, which comes from the superconducting magnet. The repulsive force gives a natural stable point without controlling it. But if we use attracting force of the normal conductive magnets, then there is no stable point. | Let me see. One is missing. Ah, yes. Maybe analysis of the magnetic levitation. The Japan railway is working on magnetically levitated trains that reach the speed of 500 kilometers per hour, or something like that. This system is using superconducting magnets for both levitation and for driving trains, for producing lift force and thrust force. But when I was in the university, I thought that the normal conducting magnet might be cheaper and safer, so I worked on the levitation magnet using normal temperature magnets. Ordinary electromagnets. We needed four magnets, at the corner of the car or tracks. At many places in the world, analysis or experimentation of the magnetic levitation using normal conducting magnets is underway. We worked on the analysis of the magnetic levitation of vehicles, using normal conducting magnets. This is the pulling force, not the repulsive force, which comes from the superconducting magnet. The repulsive force gives a natural stable point without controlling it. But if we use attracting force of the normal conductive magnets, then there is no stable point. | ||

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'''Aspray:''' | '''Aspray:''' | ||

− | When you were growing up, did you have hobbies that showed your science and engineering interests, such as building radios and machines? | + | When you were growing up, did you have hobbies that showed your science and engineering interests, such as building [[Radio|radios]] and machines? |

'''Yamamura:''' | '''Yamamura:''' | ||

− | Yes. My elder brother and I built a ham radio, and I myself built a movie machine. So I think that my hobbies were rather oriented toward science. I went to the third Asada high school, located in Kyoto. At that time, the high schools were very small in number. The entrance examination to a high school was more difficult than the entrance examination to university. The number of graduates from high school and the number of graduates from universities, national universities at least, were about the same. At this high school I thought that the students were very well selected, so the level of teaching at the high school was amazingly high. I learned English, German, mathematics, and so on. At the high school level, our specialty was already decided. I chose the science course. The teaching of mathematics, physics, and so on was at very high level. The teaching of foreign languages was also very high. I studied German for three years. I could read and write German better than English, although I studied English in my middle school — and also at high school — for seven years. And so, after learning German for three years at my high school, I could read German much better than English, so at the entrance examination to the University of Tokyo, I chose German, and fortunately I passed. | + | Yes. My elder brother and I built a [[Amateur Radio|ham radio]], and I myself built a movie machine. So I think that my hobbies were rather oriented toward science. I went to the third Asada high school, located in Kyoto. At that time, the high schools were very small in number. The entrance examination to a high school was more difficult than the entrance examination to university. The number of graduates from high school and the number of graduates from universities, national universities at least, were about the same. At this high school I thought that the students were very well selected, so the level of teaching at the high school was amazingly high. I learned English, German, mathematics, and so on. At the high school level, our specialty was already decided. I chose the science course. The teaching of mathematics, physics, and so on was at very high level. The teaching of foreign languages was also very high. I studied German for three years. I could read and write German better than English, although I studied English in my middle school — and also at high school — for seven years. And so, after learning German for three years at my high school, I could read German much better than English, so at the entrance examination to the University of Tokyo, I chose German, and fortunately I passed. |

=== University of Tokyo === | === University of Tokyo === | ||

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'''Aspray:''' | '''Aspray:''' | ||

− | President of IEEJ, also. | + | President of [[Institute of Electrical Engineers of Japan (IEEJ) History|IEEJ]], also. |

'''Yamamura:''' | '''Yamamura:''' | ||

− | Yes. I am an honorary member of IEEJ and a life fellow of IEEE also. | + | Yes. I am an honorary member of [[Institute of Electrical Engineers of Japan (IEEJ) History|IEEJ]] and a life fellow of IEEE also. |

'''Aspray:''' | '''Aspray:''' | ||

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Yes. I received the Nikola Tesla Award from IEEE. I am very proud of it. The citation was for linear motor analysis, and my work in that field. | Yes. I received the Nikola Tesla Award from IEEE. I am very proud of it. The citation was for linear motor analysis, and my work in that field. | ||

− | + | [[Category:People and organizations|Yamamura]] [[Category:Universities|Yamamura]] [[Category:Engineers|Yamamura]] [[Category:Inventors|Yamamura]] [[Category:Business, management & industry|Yamamura]] [[Category:International collaboration|Yamamura]] [[Category:Manufacturing industries|Yamamura]] [[Category:Culture and society|Yamamura]] [[Category:Defense & security|Yamamura]] [[Category:World War II|Yamamura]] [[Category:International affairs & development|Yamamura]] [[Category:International affairs & development|Yamamura]] [[Category:International affairs & development|Yamamura]] [[Category:Engineering profession|Yamamura]] [[Category:Engineering education|Yamamura]] [[Category:Training|Yamamura]] [[Category:Professional societies|Yamamura]] [[Category:IEEE|Yamamura]] [[Category:Awards & fellow activities|Yamamura]] [[Category:Engineered materials & dielectrics|Yamamura]] [[Category:Arc discharges|Yamamura]] [[Category:Components, circuits, devices & systems|Yamamura]] [[Category:Circuit types|Yamamura]] [[Category:Automation|Yamamura]] [[Category:Control design & engineering|Yamamura]] [[Category:Control equipment|Yamamura]] [[Category:Fields, waves & electromagnetics|Yamamura]] [[Category:Electromagnetic fields|Yamamura]] [[Category:Electromagnetic induction|Yamamura]] [[Category:Standardization|Yamamura]] [[Category:News|Yamamura]] | |

− | [[Category: | + |

## Revision as of 17:51, 9 May 2014

## About Sakae Yamamura

Sakae Yamamura is an electrical engineer best known for his work on magnetic field driving of electrical arc, his work on analytical theory of the linear induction motor and its applications to magnetic levitation, his development of spiral vector theory, and his work on numerically controlled machine tools. He received his bachelor's degree in engineering from the University of Tokyo and became a lecturer at the University of Tokyo immediately upon graduation. During World War II, Yamamura served in the Japanese Navy, repairing ships at the Kure shipyard and working on the acoustic torpedo project. After the war he taught at the University of Tokyo until the occupation forces sent him to Michigan State University in 1950 where he wrote his M.S. thesis on electrical circuit transformation; he received his Ph.D. from Ohio State University, for a thesis on the transient analysis of induction motors. After receiving his doctoral degree from Ohio State, Yamamura went back to Japan and wrote another thesis on electric arc discharge to receive a Japanese Doctor of Engineering degree. He is retired from his position at the University of Tokyo but continues to work as a senior advisor for a wide range of professional and public organizations.

The interview begins with Yamamura describing the projects for which he is best known: magnetic field driving of electrical arcs, linear induction motor analysis and applications, spiral vector theory, and numerically controlled machine tools. He also mentions the various books he has published on these topics and the book he hopes to write on spiral vector theory. Midway through the interview Yamamura describes his early education, his bachelors' degree work at the University of Tokyo, his wartime experiences and his study in the United States. He then discusses his activities with CRIEPI and his affiliations with a range of professional and public organizations. The interview concludes with his discussion of his IEEE activities, including his Life Fellowship and his receipt of the IEEE Nikola Tesla Medal; he also mentions his work for the IEC and his hopes for applying spiral vector theory to the unification of electrical circuit theories.

## About the Interview

SAKAE YAMAMURA: An Interview Conducted by William Aspray, Center for the History of Electrical Engineering, May 25, 1994

Interview # 210 Sponsored by Center for the History of Electrical Engineering, The Institute of Electrical and Electronics Engineers, Inc.

## Copyright Statement

This manuscript is being made available for research purposes only. All literary rights in the manuscript, including the right to publish, are reserved to the IEEE History Center. No part of the manuscript may be quoted for publication without the written permission of the Director of IEEE History Center.

Request for permission to quote for publication should be addressed to the IEEE History Center Oral History Program, 39 Union Street, New Brunswick, NJ 08901-8538 USA. It should include identification of the specific passages to be quoted, anticipated use of the passages, and identification of the user.

It is recommended that this oral history be cited as follows:

Sakae Yamamura, an oral history conducted in 1994 by William Aspray, IEEE History Center, New Brunswick, NJ, USA.

## Interview

Interview: Sakae Yamamura

Interviewer: William Aspray

Date: May 25, 1994

[Note: Dr. Yuzo Takahashi: of the Tokyo University of Agriculture & Technology was also present at the interview.]

### Magnetic Field Driving of Electrical Arcs

**Yamamura:**

I taught at the University of Tokyo more than thirty-five years. I taught machinery and automatic control theory. I'm retired, but I'm still working here as a senior advisor. I worked on many research projects. I published many papers and books concerning the research projects on which I worked. I think that three or four of them might be interesting to you. Right after graduation from the University of Tokyo, I worked on magnetic field driving of electric arc. [Using projector] The electromagnetic force is applied to electric arc here, and it moves this way. At a certain atmospheric pressure, the arc cannot be extinguished by the magnetic field. If the atmospheric pressure is reduced further, then the arc moves in the opposite way, opposite to the direction of the electro-magnetic force (Coulon force). I found this phenomenon: if the switch is open the arc stands there, immobile for a short time, before being driven by the electromagnetic force. This is the atmospheric pressure. This is the speed of the arc. As the pressure is reduced, driven speed begins to decrease, and finally the speed becomes zero. It's here that the arc cannot be driven. Right after the switch was opened the arc stayed at the point where the arc was initiated. I found this phenomena, and I published it in the *Journal of Applied Physics* (Physical Society of USA) right after the war.

**Aspray:**

Had other people noticed the phenomena that you explained it, or were you the first to notice the phenomena as well as explain it?

**Yamamura:**

I was the first man to notice this phenomenon. At first it was difficult to me to explain it to people. It was concerned with circuit breaker operation, so it has some practical meaning. At greater heights than Mount Fuji, electricity goes in the opposite direction.

**Aspray:**

Can you say a few more words about the practical importance of this?

**Yamamura:**

Yes. If circuit breakers are located at a very high altitude, the arc may go in the wrong direction. Then the capacity of the circuit breaker will deteriorate. The arc of the circuit breaker is driven into the extinguishing chamber under the normal atmospheric pressure. But at high altitude, say 3000 meters high, the arc goes in the opposite direction. I found this phenomena when I was very young, about fifty years ago.

### Analytical Theory of Linear Induction Motor

**Yamamura:**

The next thing I would like to explain is the analytical theory of the linear induction motor. The application of the linear induction motor just started when I got interested in the analysis of the linear induction motor.

**Aspray:**

About what year was that?

**Yamamura:**

Let me see. This book, *Theory of Linear Induction Motors*, was published in 1972. Before the publication I worked on this project for at least ten years. On the linear induction motor, the air gap of the motor is open at both ends. There is discontinuity of the electromagnetic field at both the entrance and the exit. It was therefore difficult to solve Maxwell's equations for this air gap. It's not closed like the rotating machine. So I tried to solve Maxwell's equations and obtained a three-dimensional solution: X component, Y component, and Z component. I gave the three-dimensional solution. For obtaining the X component I used the Laplace transformation. For obtaining the Y component, I used the ordinary differential equation method. For obtaining the Z factor, I used a Fourier transformation. The analytical solution for obtaining this result was rather lengthy and complicated, and finally I obtained this and calculated the field distribution in the X direction. This is then the exit, and this is the distribution of the magnetic field in the Z direction. The thrust of the motor is rather difficult to calculate. But I could calculate rather accurately to obtain this thrust. If we don't have edge effect and end effect, we would get this torque shown by the broken line, but actually we got this thrust. Parameters are the number of poles. If the number of poles is small, the torque is reduced significantly. This means that in order to remove adverse effect from the end effect and edge effect, we need to use a larger number of poles. That was my conclusion.

**Aspray:**

There are applications of this work, aren't there?

**Yamamura:**

Yes. Originally, we planned to construct magnetically levitated trains, but the practical applications of the magnetically levitated train are very few at present. They are taking into consideration this phenomenon. In industrial applications, in a factory, for example, in the clean room for manufacturing semiconductor devices, they are carrying parts and product by this magnetically levitated cart. It is very necessary to use a contact-less cart, in order to avoid dust.

**Aspray:**

So the people who were working on the design of the motors for the magnetically levitated trains were doing so in an empirical way without the advantage of having a theoretical understanding?

**Yamamura:**

Yes, I think so.

**Aspray:**

And this provides the understanding for doing that work?

**Yamamura:**

Yes. If the speed is not so high, then this effect isn't so large. For example, I visited France, where the train was levitated not by magnetic levitation, but by air cushion levitation. This train was driven by a linear induction motor, and it had only two poles. The performance was terribly low. That was before my theory was developed, and I think they are now using more poles, at least six, for higher speed.

**Aspray:**

As I understand it, the trains that are being designed for use in Japan might be going five hundred kilometers per hour?

**Yamamura:**

They are hoping.

**Aspray:**

And in that situation, is that fast enough that this is a real concern?

**Yamamura:**

Oh yes. Japan Railway is working on the development of linear motor trains, but now they are using superconducting magnets for levitation, and these superconducting magnets also are used for driving, so the motor is now a synchronous motor rather than an induction motor.

### Spiral Vector Theory

**Yamamura:**

The next project I would like to talk about is the spiral vector theory. [Shows overhead] The spiral vector is an exponential time function with a complex index. It can express steady state DC and AC, and transient state DC and AC. It is a universal way of expressing state variables in electrical engineering. The spiral vector can be written like this: a current will be expressed by this spiral vector. As time goes on, it depicts a spiral in the complex plane. If lambda is zero, this describes a circle. I call it a circular vector. It corresponds to the steady-state alternating current, sine or cosine. If the omega becomes zero, this is attenuating DC. If both omega and lambda are zero, this corresponds to steady state DC. So, in electrical engineering, most state variables can be expressed by the spiral vector.

**Aspray:**

It's a generalization, in a sense, of previous methods for doing this?

**Yamamura:**

Yes, you are right. At present we are using circular vector, which is a complex, for steady-state analysis of alternating current, and we are using real-value expressions for the transient state. So the two theories, the steady state theory and the transient state theory are separated by the two different expressions of state variables. It is very strange to me. It is causing a great amount of inconvenience, difficulties, and awkwardness in the analysis and computer simulation at present. I am trying to unify these conventional theories, and it works very well. I am now trying to unify electric circuit theory. It gives much convenience in the compatibility of state variables, and it makes computer simulation much easier in the amount of time needed to do the simulation. I wrote a book on this subject entitled, *Spiral Vector Theory of Electrical Circuits and Machines*. It is working very well.

**Aspray:**

Has this caught on in other places? Are other people using this spiral vector theory?

**Yamamura:**

Yes, they have just begun to use the spiral vector method. I will give you some examples. [Showing some material.] These lines read, "six spiral vector theorems were established" They are the fundamental theorems for using spiral vector methods in electrical circuit analysis. The next item is number two, "Spiral Vector Theory of Electric Circuits." It unifies the conventional circuit theories, which are derived due to the different expressions of state variables, as I just told you. They are using different expressions for state variables, for steady state and transient state. It's very funny to me. It had been so for about one hundred years, from the beginning of the century up to now.

**Aspray:**

A historical accident, I think.

**Yamamura:**

Yes. At present, I think spiral theory has removed inconveniences and awkwardness of the conventional theories, and saves time in computer simulations. The next line is, "all kinds of general solutions of such equations are spiral vectors, which are natural modes of circuit behaviors. General solution of any circuit equations is spiral vectors." I read this paper at the monthly meeting of the Japan Academy, explaining the six theorems for using spiral vector theory method in the electrical circuit analysis. There are a few very famous mathematicians among the members of the Academy. I am a member of the Academy also. These famous mathematicians praised the method, so I was very glad.

**Aspray:**

It's very elegant from a mathematical point of view.

**Yamamura:**

It's not high-class mathematics at all, but the electric circuit theory was in a rather strange shape, at least to me, so I wanted to change it.

**Aspray:**

I would like to ask a question about the possible practical use of this in the following way. When people like Oliver Heaviside were developing mathematical approaches to electrical phenomena, and when Steinmetz at GE was doing this, one of the problems they had was that although their mathematical techniques were very powerful, it was hard to get practicing engineers to use them. Do you anticipate there will be any problems in this case? Is your mathematics easy enough for the practical engineer to be able to use?

**Yamamura:**

Yes, I think so. As I told you, electrical circuit theories were divided into two parts, the steady-state theory, and the transient state theory. The state variable expressions are different in these two theories. In order to unify, they are using the Heaviside operation method or Laplace's transformation method in order to get the universal solution from such equations. But I don't think that Heaviside's method is mathematically accurate. I mean it's mathematically sound, Heaviside's method, as an operation, but mathematically Laplace's transformation is correct, and Heaviside's transformation is a little different from the mathematically rigid Laplace transformation. But the Laplace transformation is only our method to solve the differential equation, not the electric circuits theory at all. Introducing Laplace transformations so early in the electrical circuit theory it gives difficulty to beginners to understand Laplace transformation. It's high-class mathematics. We should get rid of the Laplace transformation at such early stages of learning electrical engineering. If we use the spiral vector method, it is not necessary to resort to the Laplace transformation at such an early stage of learning. Then we can stay with the ordinary way of solving differential equations. The general solution has a particular solution plus steady state solution.

**Aspray:**

Plus the general solution.

**Yamamura:**

Plus the complementary solution (transient solution). That's enough. And this general transient part is a spiral vector. Even the steady states a spiral vector. All naturally come out as spiral vectors, so we should use them.

### Uses and Teaching of Spiral Vector Theory

**Aspray:**

[To Takahashi] Now, in your university, do you think that this would be used? In teaching?

**Takahashi:**

I cannot answer that. I must learn the method myself before I could answer.

**Yamamura:**

[To Takahashi] Yes, please. Please read this! Now I am thinking of writing another book. It's title may be, *Spiral Vectors, the Fundamentals of Electrical Circuits Based on Spiral Vector Methods*.

**Aspray:**

This would be used as a textbook?

**Yamamura:**

Yes. For beginners. I would remove the Laplace transformation or Heaviside transformation. It's not necessary. Just one method of solving differential equations, that's all. At first I applied the spiral vector method to analyze induction motors, three-phase induction motors. [Showing an overhead] Please look at number three: "Spiral Vector Theory of Rotating Machines." It discusses phase segregation. Phase segregation means that in a three-phase machine only one phase is sufficient. The other phases are the same. The only difference is a phase difference of one hundred and twenty degrees. So at least for steady state we use phase segregation. We use state variables of one phase. That is sufficient to describe the whole machine of three phases. But the spiral vector does this to the transient state. That is very important. At present they are using two-axis theory. There are two phases, and in order to use two-axis theory, we need complicated variable transformations. But in the spiral vector method, there is no need. We don't need to transform state variables at all. We use the original state variables expressed in the spiral vector. Solution of the circuit equation gives spiral vectors, so we should use it them without variable transformation. Just as we have done for about one century, only for steady state, but now we can use the phase segregation — only one phase is sufficient to analyze this three-phase machine completely. No variable transformation is necessary. This is very important.

If the operation of the three-phase machine is not symmetrical, or as many people say, "it is not balanced." (I don't like "balanced," you know. We should say "symmetric.") If the operation is not symmetrical, we can apply the symmetry component method, but this method, invented by Mr. Fortescue in the United States, has been applied only to steady-state analysis. But the spiral vector method makes the symmetric components method applicable to three-phase operation. This is another very important merit of the new method. Next we have control of an induction motor, which has made the induction motor much superior to the DC motor. In control applications, DC motors have been used for many years, but now AC motors are replacing DC motors. In this transition from DC to AC control motors, I think the spiral vector method gives very good analysis, very good computer simulation. The next is the spiral vector method of salient pole synchronous machine including [inaudible] DC motor. The serial pole synchronous machine is very difficult to analyze. The Park's equations and two-reaction theory have been used for about one quarter of the century. They are rather complicated. They are based on the d,q- axis theory: Two-phase theory instead of three phase theory — but still the theory is complicated because of the many kinds of variable transformations.

Next: "Large power system analysis with computer simulation." By the spiral vector method these can be made much easier, much simpler, I hope, than the conventional method, such as two-reactions theories, and Park's equations. Power systems are very large. Thousands of generators are connected. They are operating in synchronism. When a new phenomenon happens, for example a lightning strike and so on, the stability of the whole system is disturbed. Analyses of such kinds are not easy under the present method, and I am hoping that the spiral vector method will give a better way, or a simpler way, of solving this large power system. The analysis of the salient pole system becomes simpler by using the spiral vector method. At present, very close to one hundred percent of all power is generated by synchronous machines, and they are all salient pole machines. The inductances of the machine change more or less as the rotors rotates. So the synchronous machine is a complicated machine that is difficult to analyze. I think the present conventional methods are causing much waste of time, much difficulty in analysis. The big power outage that occurred in Tokyo was because of the lack of adequate analysis. [Showing another overhead]. I'm not going to be mathematical with this, but the idea is here on the spiral vector expression.

The spiral vector expression can cover almost all state variables that appear in here, except pulses. The power can also be expressed by spiral vectors. This is the real component of the power, and this imaginary part gives the reactive component of the power. If we use real-value expressions, it is difficult to find this point. These are general circuit equations. A (P) and B (P) are polynomials of P, and the terminal voltage V is given by this. This is the circular vector that corresponds to steady- state AC. This terminal voltage is steady-state sine wave. Then the general solution of this equation is given thus by. These are general and particular steady-state solutions, given by replacing P with JW. This is a conventional common method of solving steady-state solutions. At this point most teachers and students are having trouble understanding why P can be replaced with JW (omega) in order to get the steady-state solution. I looked at many papers and books. The writers are having trouble explaining why P can be replaced with JW (omega). But, if we use spiral vectors, P becomes JW (omega) immediately, because the P is only an exponential function, so immediately we get JW (omega) here and here. Naturally, and mathematically, it is clear that P becomes JW (omega). This is a very difficult point to explain to beginners, why P can be replaced by JW (omega). And another point, general transient solutions in this circuitry are all spiral vectors. So we should use them. That's my theory.

You see, if voltage V is a spiral vector, it's not steady, but minus lambda plus JW (omega) t. This is AC voltage attenuating. Then we get the spiral vector, not a circular vector, but one that shrinks or expands. I applied the spiral vector method to the analysis of the induction motor, and I called it the field acceleration method control. In the steady state, the speed torque characteristic carnes of the induction motor become completely straight lines. Just like DC motors. Or I should say in reality much better than DC motors. Completely straight. This is perfect for control motors. Up to now, only DC motors could have this kind of straight torque-speed characteristic. For over a century, DC motors were used as control motors for high-speed elevators, for escalators, for high-speed trains and so on. But now we replace DC motors with induction motors. If the motor is switched on to the power supply, then a transient occurs in torque like this and in the current. This kind of response is not good. But if we use FAM control, the torque response is instantaneous. Torque command and torque response are exactly the same. No transient. We can remove transient completely if we use the FAM control. In this method, exciting current is kept constant. Exciting current of the induction motor is given before command currents. A very small current, 2 or 3% of the rated current, is given from the beginning. Then the torque components of the three-phase current are given suddenly, and we get this response. I worked on synchronous motor analysis and put the results in a book. I think that the ST theory of the synchronous machine will compete with the two- axis theory and Park's equations, which have been used about three quarters of one century. I am hoping that it might be able to exceed these.

**Aspray:**

Is your method being taught in any university right now?

**Yamamura:**

I don't know. There are some professors studying, reading my papers and books, and there is at some universities graduate students are writing technical papers on spiral vector theory. Graduate students are working on the application of my theory to rotating machines, mostly, synchronous generators, the analysis of power systems and so on.

**Aspray:**

It's a long process before it filters down to the regular course of study for, say, the undergraduate electrical engineer. It starts with the graduate students and works its way down typically.

**Yamamura:**

I think it is going that way now.

### Magnetic Levitation

**Aspray:**

When you first started you said there were four things you wanted to talk to us about, and if I have counted correctly I have heard three so far.

**Yamamura:**

Let me see. One is missing. Ah, yes. Maybe analysis of the magnetic levitation. The Japan railway is working on magnetically levitated trains that reach the speed of 500 kilometers per hour, or something like that. This system is using superconducting magnets for both levitation and for driving trains, for producing lift force and thrust force. But when I was in the university, I thought that the normal conducting magnet might be cheaper and safer, so I worked on the levitation magnet using normal temperature magnets. Ordinary electromagnets. We needed four magnets, at the corner of the car or tracks. At many places in the world, analysis or experimentation of the magnetic levitation using normal conducting magnets is underway. We worked on the analysis of the magnetic levitation of vehicles, using normal conducting magnets. This is the pulling force, not the repulsive force, which comes from the superconducting magnet. The repulsive force gives a natural stable point without controlling it. But if we use attracting force of the normal conductive magnets, then there is no stable point.

At my laboratory at the University of Tokyo, we investigated and analyzed the controller of the magnetic levitation that uses the normal conducting magnet. There are many such programs in the world. There are many magnets, at least four, at each corner of the vehicle. The information from the four magnets is fed to a central computer, and the control theory is rather complicated. Not only is the control itself complicated, but the analysis of it is also complicated. We tried to separate the control of the magnet. We succeeded in deriving independent control of the four magnets. The response of the independent control is very close to the centralized control, which puts all the information from the four magnets in the centralized computer. We calculated the response and found that our independent response was as good as the very complicated central computer control of all the magnets. We then built a small-scale magnetically levitated vehicle, and it ran. It was very good, very stable. We did such work on magnetic levitation.

**Aspray:**

Would there be any problems of going beyond that to use it commercially?

**Yamamura:**

No. You see, this kind of small-scale magnetically levitated carts is used in some clean rooms for manufacture of semiconductor devices, in order to remove dust from the air.

### Numerical Control of Machine Tools

**Aspray:**

Another area that I read about in your materials was about your work on numerical control. Could you tell me about that?

**Yamamura:**

Yes. Maybe it was more than thirty years ago, when numerical control of machine tools and robots began. At that time all control motors were DC motors. I worked with a company named Fanuc. Fanuc used to be the biggest manufacturer of robots in the world.

**Takahashi:**

It's a sister company of Fujitsu.

**Yamamura:**

Yes, now it's a sister company, but then it was completely a part of Fujitsu.

**Aspray:**

Yes, the company is well known in the United States.

**Yamamura:**

They asked me to give advice on their development of robots, for example for the first milling machines for die presses in the automobile industry.

**Takahashi:**

For example, to make the body of the car symmetrical.

**Yamamura:**

Yes, to make the body — the die presses.

**Aspray:**

Yes, that's the word in English.

**Yamamura:**

This milling machine was numerically controlled for machining three-dimensional die presses with a large and complicated shape, for example part of the car body. There was no control program for driving three-dimensional numerically controlled milling machines. Our laboratory developed a program for it, and a pressed part was manufactured successfully with the program. It was the first numerically controlled machine tool in Japan. I got an award for it. We tried to reduce the torque ripple of driving motors. First it was DC motors. Fanuc wanted to reduce the torque ripple — less than 1% at first. Then the torque ratio was 0.5%. Now it is very low. In order to get the very good machining finish, the torque ripple must be very small. We worked on such a project.

**Aspray:**

Would you be willing to tell me something about your career? Biographical information?

**Yamamura:**

Yes.

### Family Background and Childhood

**Aspray:**

Could we quickly go through from the very beginning of your life?

**Yamamura:**

I had four brothers. I was the second son. My elder brother was a professor at the University of Osaka.

**Aspray:**

In what field?

**Yamamura:**

Electrical engineering also. The third child died during the war. He was a navy officer, and the fourth is still living. He is a civil engineer. He built many dams for electric power generation. So I think our brothers are...

**Takahashi:**

Science oriented.

**Yamamura:**

Science oriented, yes. My father graduated from the University of Tokyo also, but he attended the faculty of law. My father graduated from the University, and my daughter graduated from the University of Tokyo. She is married and is now a professor at Waseda University in chemistry. She graduated from Tokyo University, but in the faculty of science. No woman was admitted to the staff of the faculty, so she went to a private university, Waseda University. She's a professor now, and she is doing very well. She got a very good prize from the Japan Society of Chemistry just recently, so I am very glad. Her son passed the entrance examination to the University of Tokyo. So in my family tree, four generations have entered the University of Tokyo. We are happy about it. The University of Tokyo is very difficult to enter: the entrance examination is very severe.

**Aspray:**

When you were growing up, did you have hobbies that showed your science and engineering interests, such as building radios and machines?

**Yamamura:**

Yes. My elder brother and I built a ham radio, and I myself built a movie machine. So I think that my hobbies were rather oriented toward science. I went to the third Asada high school, located in Kyoto. At that time, the high schools were very small in number. The entrance examination to a high school was more difficult than the entrance examination to university. The number of graduates from high school and the number of graduates from universities, national universities at least, were about the same. At this high school I thought that the students were very well selected, so the level of teaching at the high school was amazingly high. I learned English, German, mathematics, and so on. At the high school level, our specialty was already decided. I chose the science course. The teaching of mathematics, physics, and so on was at very high level. The teaching of foreign languages was also very high. I studied German for three years. I could read and write German better than English, although I studied English in my middle school — and also at high school — for seven years. And so, after learning German for three years at my high school, I could read German much better than English, so at the entrance examination to the University of Tokyo, I chose German, and fortunately I passed.

### University of Tokyo

**Aspray:**

I can understand why you chose the University of Tokyo. Why did you choose the engineering curriculum?

**Yamamura:**

At the high school in Kyoto, when my school attendance was coming near the end of the three years, I couldn't decide which subject to take. I chose two subjects, physics in the science faculty and electrical engineering in the engineering faculty. I couldn't decide for some time, but finally I chose electrical engineering. At that time even at the entrance examination, each department accepted students. So the entrance examination in each of them was independent.

**Aspray:**

What effect did the war have on your career?

**Yamamura:**

In education? In school I followed the normal course. I graduated from the University of Tokyo in 1941, when the war broke out. I graduated in the spring of that year, so the school curriculum was not disturbed in my case.

**Aspray:**

But what happened to you?

**Yamamura:**

After graduation, I was nominated to be a lecturer at the University of Tokyo immediately, without going into the graduate school. At that time very few students entered graduate school. Luckily I was nominated to be a lecturer and got some salary.

### Acoustic Torpedo

**Aspray:**

What were your duties as a lecturer?

**Yamamura:**

In my first year as lecturer I gave some lectures on electric circuits and taught laboratory work. The war already was going, in China at least, so almost all males had to go into military service. I left the university that fall. I went into the Japanese navy. I stayed in Kure, which was the biggest navy shipyard.

**Takahashi:**

Located next to Hiroshima.

**Yamamura:**

Yes, next to Hiroshima. I stayed there for four years. I didn't go out of Kurei at all. I stayed there and repaired ships. I also worked on a new weapon, the acoustic torpedo, automatically controlled torpedo. For two years, I was the head of the project for the development of the acoustic torpedo. I did it, we tested it, and finally it was successfully driven toward a target, a running small boat, radiating hydraulic noises. The torpedo had microphones. The torpedo was controlled by the noise. We did experiments, but fortunately we didn't use it at all. But experimentally it was successful. I started to measure the noise of the torpedo. I measured the noise from torpedoes at different speeds. There is a critical speed of torpedoes. Beyond that the noise was terribly large. That speed was 26.5 knots. So the speed of the torpedo was a little less than this, 26 knots. Then the torpedo was very quiet, and we could catch…

**Aspray:**

The sound from the propellers of the target ship.

**Yamamura:**

Target sound, yes. The speed of the torpedo was not fast, but it was fast enough for an ordinary ship, not a warship. After the American occupation force came, I was called to the headquarters of General MacArthur and asked to explain the torpedo project. I explained all that I had in memory, and that's all. But I asked whether the United States Navy was working on such projects.

**Aspray:**

But they said no?

**Yamamura:**

But they said no. The atomic bomb and the proximity fuse, and so on.

**Aspray:**

When the war was over, what did you do?

### Michigan State and Ohio State Universities

**Yamamura:**

I went back to the University of Tokyo. I became assistant professor. In 1950, luckily I was accepted as a student to the United States. The occupation force sent us.

**Aspray:**

This was to Michigan State?

**Yamamura:**

Yes.

**Aspray:**

Why did the occupation forces want you to go?

**Yamamura:**

About 450 young people went to the United States. I think it was a part of the occupation.

**Aspray:**

Rebuilding the country?

**Yamamura:**

Yes. I was very grateful to study in the United States for three years. I was assigned to Michigan State by headquarters. We had no choice.

**Aspray:**

How did you find Michigan State?

**Yamamura:**

It is a good university. Over there, I got a master's degree. I wrote a master's thesis on electrical circuit transformation using matrices. Luckily I could write the thesis within one year, so I went to Ohio State.

**Aspray:**

Was that also assigned, or did you choose that?

**Yamamura:**

Oh no. I could get an assistantship at Ohio State, so I was working part-time. Also within two years I could write a doctoral thesis, fortunately.

**Aspray:**

What was the subject of your doctoral dissertation?

**Yamamura:**

Transient analysis of the induction motor.

**Aspray:**

Then you came back to Japan?

**Yamamura:**

Yes, to the University of Tokyo again.

**Aspray:**

I see that you took another degree in Japan.

**Yamamura:**

Yes.

**Aspray:**

Why was that?

**Yamamura:**

It's rather complicated. In Japan the foreign doctorates are not used so much. It was required to get a Japanese doctorate to become a full professor. So I was asked to get an engineering doctorate in Japan. So I put a paper together in one year. It was on electric arc discharge.

**Aspray:**

You were able to get your degrees very rapidly in the United States. It usually takes Americans much longer to do that.

**Yamamura:**

Yes, I know that.

**Aspray:**

How were you able to do this?

**Yamamura:**

It was rather busy. I studied during the summer vacation time, and since I was a little older than the average students, I think my knowledge was a little better.

**Aspray:**

You applied yourself more?

**Yamamura:**

Yes. I did. I had some ideas for my degree.

**Aspray:**

Your work was of a theoretical character in your master's and Ph.D.?

**Yamamura:**

Yes. I thought that the analytical work could be shorter in time. Research work takes some time, so I chose analytical work. I didn't do any experimental work.

### Mathematics and Theory

**Aspray:**

The things that you have shown us today...many of them have had a mathematical or theoretical character to them. Would you say that runs through your whole career?

**Yamamura:**

At my high school I was praised in mathematics by a professor. This professor, Doctor Akizuki, later became very famous at the University of Kyoto. Later he became one of the number one mathematicians. This professor gave us homework, and he asked me to give an answer on the blackboard. He asked me to explain the solution of the homework. He praised my way of solving the problem. I used the non-rectangular coordinates. Then the solution became very simple. This professor praised my way of solving this homework. I remember this. So at the end of the study year he asked me, "Which subject did you choose to study at the university?" I told him that I chose electrical engineering. "You chose engineering, not science," he said.

**Aspray:**

He was disappointed?

**Yamamura:**

Yes. I felt that. He was very young at that time. Later he became a professor at the University of Kyoto. He died, but he was a very famous mathematician.

**Aspray:**

As part of the training of electrical engineering at the undergraduate level at Tokyo, were there courses in mathematics that you had to take as part of the curriculum?

**Yamamura:**

Yes. At the University of Tokyo, we took differential equations theory and also the theory of dynamics. This was not engineering itself, but mathematics and dynamics are very useful.

**Aspray:**

I am sorry that I don't know the Japanese educational system. Does one have an option of taking additional courses? If you were interested in mathematics as an electrical engineering student, could you take extra courses in mathematics?

**Yamamura:**

There are some recommended subjects, but we could choose any subject.

**Aspray:**

If the Japanese system is like the American system, so much is required of the engineering student that there is not much time left in one's course of study to take extra courses. You might have a little time, but not a lot.

**Yamamura:**

You're right, yes. The standard courses are too many already. So actually, freedom is very limited.

### CRIEPI and IERE

**Aspray:**

Do you want to take a couple of minutes to tell me about CRIEPI?

**Yamamura:**

Yes. The central office is located in the center of Tokyo. We have about eight hundred people. The annual budget, I think, is thirty million yen. I think the system is very similar to the EPRI in the United States.

**Aspray:**

Yes.

**Yamamura:**

In size and budget also. We are doing about the same work, I think. We have very good relations. We exchange people, and we exchange research results. One difference is that CRIEPI can get money from all electric power companies, which are ten in number. So all power companies give us money without difficulty. They give us 0.2% of their total sale of electric power, which is about 30 billion yen. But in the United States EPRI had to collect money from all the power companies, which is about 3500 companies. They are having rather a hard time, unfortunately. We don't have a hard time getting money. This is a big difference.

**Aspray:**

Could you talk about your own role with CRIEPI?

**Yamamura:**

Until last year I was one of the vice-presidents. Last year I retired. But now I am a senior advisor and come here every day. My duties are not so many. I am in charge of foreign liaison.

**Aspray:**

When you were vice-president, what were your duties?

**Yamamura:**

Foreign affairs were my biggest duty, but on special research projects I gave advice, and I am still giving advice on large power systems analysis and the theoretical analysis of large power systems.

**Takahashi:**

Maybe I should explain something about IERE? As an advanced industry country we have a union for the utility industries. He was in charge of it.

**Yamamura:**

Yes, IERE. That stands for International Electrical Research Exchange. It was established twenty-five years ago, and CREPI proposed to establish this organization. Only industrial countries such as the United States, Canada, eight European countries, and Japan, are the members. They get together and exchange opinions. They talk about the strategies of research projects. The people are top managers of research projects of electric power companies. We exchange information and results of our research projects. I am in charge of this. Last month the twentieth annual meeting was held in Japan. I was chairman.

**Takahashi:**

It was held in Nagoya.

**Aspray:**

It sounds like a very useful organization.

**Yamamura:**

I think so. Yes. This year was the twenty-fifth anniversary of its establishment, and the twentieth general meeting.

### IEEJ, IEEE and Other Societies

**Aspray:**

Can you tell me about some of the other professional activities you have been involved with? I know you were active in IEE Japan.

**Yamamura:**

I was a member of quite a few government and non-governmental committees. For example I was a member of — I don't know the English expression for this — the Electric Governmental Power Generation Development Adjustment Committee. The chairman was the prime minister, and I think six members were the ministers of MITI, Agriculture, and so on. I was one of them. In this committee, the final approvals were made on initiation of power plant building and all power plants projects must be cleared by this committee. So it was a very high-level committee. I had always felt that high-level committees do nothing — just a formality. But two years ago, Hitachi, the big manufacturer, thanked me for obtaining an order for two rotary condensers. I said, "I had nothing to do with it!" I didn't remember anything. Then later a man from Toshiba also thanked me for receiving two big rotary condensers. So I thought I might be connected with these orders. Finally I sorted it out. I made some proposal in this high level committee, and Tokyo Electric Power Company invited me to go to inspect the new re-built rotary condenser. Before this happened, the Tokyo area had a rather big power stoppage. A wide area within Tokyo didn't get electricity for four hours or so. It was reported at this committee. So I reported that a static condenser was not sufficient. I recommended a rotary condenser. But as I told you, I forgot it completely. So sometimes this kind of high-level committee is useful I thought! [Laughter] I am a member of other high-policy making committees within government and outside government. I am in the government-industry policy committee in the MITI, Ministry of International Trade and Industry. I was a member of the Transportation Policy Committee, and so on. I was chairman of the Superconducting Application Committee of the Ministry of International Trade and Industry, and so on.

**Aspray:**

President of IEEJ, also.

**Yamamura:**

Yes. I am an honorary member of IEEJ and a life fellow of IEEE also.

**Aspray:**

And the Japan Academy.

**Yamamura:**

Oh yes. I am proud of it. I am very pleased. The number of members in the Japan Academy is rather small: one hundred and thirty at present and only two electrical scientists, very few. I am very glad. It is our duty to read papers sometimes; this theory, for example.

**Aspray:**

Oh, so this paper was to the Academy?

**Yamamura:**

Yes, and top-level scientists praised this paper, so I was so glad. Top mathematicians.

**Aspray:**

Are there any other things you would like to talk about during the interview?

**Yamamura:**

Yes. I started to work on the spiral vectors theory about fifteen years ago, and I applied it to the induction motor in the past, and I applied it to synchronous generators. Some people started to apply it to large power system analysis. Now I am trying to apply it to the unification of electrical circuit theories. I feel that some explanation or some advertisement is still necessary for this theory to be known by more people. I also want to write on the application of spiral vector method to circuit analysis. As I told you, to me at least, the present state of analysis of electrical circuit is not in good shape at all.

### Nikola Tesla Medal

**Takahashi:**

Please say something about the Nikola Tesla Medal, and also your activities in connection with the IEC.

**Yamamura:**

I used to work as chairman of the International Electrical Commission, the IEC. I attended the technical committee meetings of IEC many times in the field of electrical machinery, transformer units in the Transformer Committee, the Rotating Machinery Committee, meetings on household appliances such as washing machines and refrigerators. So I spent much time in standardization, internationally or domestically here also. I like standardization work. I spent much time at it. But that is not my specialty, not at all. I don't have any special knowledge in manufacturing household appliances. I was a user of household appliances and interested in standardization.

**Takahashi:**

And how about the Nikola Tesla medal?

**Yamamura:**

Yes. I received the Nikola Tesla Award from IEEE. I am very proud of it. The citation was for linear motor analysis, and my work in that field.