AC vs DC Power
Tesla's Induction Motor
& Sprague's dc Trolley Motor
                 created 7/06
                    revised 3/17/17
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      DC & AC power compete
      AC distribution advantage
      AC has a motor problem
      Tesla dazzles
      How to get AC induction motor into use
      No one really understands how the induction motor works
      Induction motor dynamics are figured out
      How come it took almost a century to understand the induction motor?
      Tesla's development of the induction motor
 ** Induction motor -- Tesla patent 382,279
 ** My induction motor patents

         Links to Tesla's online papers and articles
         How induction motors generate torque -- a tutorial
         Switched variable reluctance motors -- a tutorial
         Comparison motor sketches
         Reading US patents online

Westinghouse/Tesla Gallery
         Tesla engineering overview
         Huge tesla coil sparks at Colorado lab
         Westinghouse AC generators at 1893 exposition
       Westinghouse Niagra AC generators

Frank Sprague's self-regulating DC trolley motor
       Frank Sprague
       'Self-regulated' DC motor
       Richmond's 1887 trolley system and central power station
       DC shunt motor
       Trolley truck design
       Sprague's motor patents

More on incandescent light bulbs

        The AC induction motor, the world's most common motor, was invented by the engineering genius, Nikola Tesla, about 120 years ago. It was the first practical AC motor, and it helped AC power replace DC power. How it worked was so hard to understand that it took almost a century before it was really understood. I worked on induction motors for a few years starting in the late 1970's, and I played a role in helping to figure out how it worked and how to better control it.

DC & AC power compete
        The first electric lights and electric motors in the US were run on DC (direct current). Edison was a leader in developing DC power. In 1882 his company built the first large DC power plant, Pearl Street Station, in lower Manhattan. By 1887 there were 121 Edison DC power plants in the US.

        There is another form of electricity called AC (alternating current). In 1886 George Westinghouse, who had grown rich from his invention of the air brake, started Westinghouse Corp to compete with Edison in the building of power plants, but Westinghouse was going to build AC power plants. Many of the early key AC patents came from one man, an independent engineer recently arrived in the US from Serbia by way of Paris, named Nikola Tesla. Westinghouse's AC technology was largely build on the ideas and patents he purchased from Nikola Tesla.

DC distribution problem
          Most of the early power plants generated DC, but DC has a huge problem. You cannot economically sent it more than a mile or so from the plant. So those 121 DC power plants created just 121 little electric islands each about 1 mile in radius. Here on a map of lower Manhattan is the area served by the Pearl Street Station (courtesy of IEEE museum).

        With any type of electricity the voltage seen by the customer is (slightly) lower than the voltage generated at the plant. The voltage loss in the distribution wiring is due to Ohms Law, which is voltage (in wire)  = current (in wire) x resistance (of wire). The longer the wire the higher its resistance. Thicker wire has lower resistance, but as it gets thicker it get more expensive and heavier.

        The voltage drop in the wiring of the system must be kept to a few percent of the voltage, otherwise houses near the plant will have a much higher voltage than houses far away. What's wrong with this? Well, a lot. Lighting was the first major residential use of electricity. The brightness of incandescent bulbs is incredible sensitive to voltage. Houses near the plant with high voltage would have bulbs too bright with a short lifetime, while houses far from the plant with low voltage would have bulbs that are too dim.

An interesting aside on light bulbs --- Edison was not alone in working on the development of a practical incandescent light bulb. Other inventors at about the same time had working prototype light bulbs in their labs and were getting good lifetime. But Edison from the beginning recognized that it was not enough for the bulb filament to last a long time while burning bright. It was also necessary for the resistance of the filament to be high and controlled. (See 'More on incandescent light bulbs' below)

        In the lab the resistance of a bulb's filament doesn't matter. If the filament of a 50 watt bulb has, say, 2 ohm resistance, then just apply 10 volts. The bulb will draw 5 A = 10 V/2 ohm and dissipate 50 watts (5 A x 10 V = 50 W).   In contrast Edison only tested high resistance filaments for his light bulbs. He planned to run them on about 100V, the highest voltage he considered safe, generated by a central power station. In a 100V system a 50 watt bulb needs to have a 200 ohm resistance so it will run at its designed 50 watt power. {100V/200 ohm = 0.5A and 0.5A x 100V = 50 watts}. Low resistance filaments need so much current that the voltage drops in the wiring between the central power plant and the house would be excessive.

Trivia --- Edison, who was a telegrapher, nicknamed his first two children dot and dash.

Nature of power
        Power is the product of current & voltage (P = I x V).  A 100 KW dynamo (size of Edison's 'Jumbo' dynamo) can be designed to put out 1,000 A at 100V or 100 A at 1,000 V. In both cases the machine weighs the same and requires the same amount of coal to run it. The difference is only in how the machine is wound. The 1,000 V dynamo is wound with x10 the turns of the 100 V machine, but the wire is smaller with only 1/10th the cross sectional area, so the windings of both dynamos fit in the same volume and dissipate the same heat.

Circumventing Ohm's Law
            Let's see how far we can send the power from our two 100 KW dynamos. Edison considered voltages above 100 V too dangerous for users so his 100 KW dynamo was wound for 100V at 1,000 A. We know the practical limit of his 100 V systems was about 1 mile.

        Let's assume for the moment we had an efficient  'magic box'  that could down-convert 1,000 V (@ n A) to 100 V (@ 10n A). We could then distribute our power at 1,000 V and put our magic box near the customer to give him a safe 100 V.

        To keep things simple, suppose the distribution system for our 1,000 V dynamo uses the same wire as the 100 V dynamo. How far can we send the power at 1,000 V?  Can we send the power 10 miles, or 10 times as far?  No, surprisingly we can send the power 100 miles, or 100 times as far! It's the per cent loss of voltage, or the ratio of  voltage drop in the distribution wiring to the voltage, that's important. The 1,000 V dynamo relative to the 100 V dynamo has ten times the voltage and one tenth the current, so the distance you can send power while maintaining voltage regulation goes up as the square of the voltage.

Aside --- Edison avoids a big generator mistake
        I stumbled upon an essay of J. B. Calvert, who makes an interesting point about Edison's jumbo dynamo. In generator design a key issue is how to set its resistance. At the time it was known that batteries delivered maximum power when load resistance matched the battery resistance. This became enshrined as the (sort of magical) 'Maximum Power Transfer Theorem'. (I remember learning about this theorem a century later in engineering school.) Following this rule Siemens and Gramme in the 1870's wound their early generators to have a fairly high resistance. The result was the generators were less than 50% efficient and ran hot as a bastard.
        Calvert says, "When Edison was designing his lighting system in 1880, the received wisdom was to make the armature (generator) resistance equal to the resistance of the load. Siemens and Gramme initially committed the error of making the armature resistance too high, because of a misinterpretation of the conditions for maximum power transfer. Either he, or Upton, his mathematical advisor, saw that this was quite incorrect. The Z dynamos and the Jumbos were made with very low armature resistance, and at one step he obtained efficiencies of 90%. He was ridiculed in the technical press by American "experts" who proved conclusively that he could not have done what he in fact did." (
        What had been misunderstood was that the 'Maximum Power Transfer Theorem's' matched load condition applies when you are adjusting the load resistance, like with a battery. When you are adjusting the source resistance, for example in a generator by choosing how much copper to use, the principle is "maximum power transfer occurs for zero internal resistance", so you aim for as low a generator resistance was possible.
AC distribution advantage
        AC has a huge, overwhelming advantage over DC in power distribution, because a 'magic' voltage changing box existed for AC. There is no equivalent for DC.  The voltage changing box is called a transformer. In simple terms it is just two copper windings, with different number of turns, wound on a steel loop. In an AC system distribution is at high voltage and each neighborhood has its own local (often up a pole) small step-down transformer.

        Of course, the area a plant can serve goes as the square of the distance the power can be sent, so the potential area an AC plant can serve goes up (approximately) as the 4th power of the voltage increase. This gives AC an astounding advantage over DC. An AC plant can (potentially) serve 10,000 sq miles for every sq mile a DC plant serves!

    Caveat --- The previous arguments for distance and area advantages of AC over DC somewhat overstate the case for AC because wire not only has resistance it also has inductance. Inductance is a magnetic effect that causes a voltage to appear across a wire whenever the current is changing, and in AC (unlike DC) the current is changing all the time. In fact the voltage regulation of AC depends more on the inductance of the wire than its resistance, but (luckily) transformers reduce both the resistive and inductive voltage losses in the distribution wiring by the square of the increase in voltage.

AC has a motor problem
        But in the early days AC had its own big disadvantage. Electricity was used mostly for three things: lighting, heating, and motors. AC works just as well as DC for lighting and heating. The DC motor had been invented early and worked well (think street cars). The big problem with AC in the early days was there was no practical AC motor. So while AC had a huge advantage in distribution and many AC power plants got built, the lack of a good AC motor was a serious problem with AC power.

Tesla dazzles
        Tesla on arriving in the US briefly worked for Edison, but soon left to start his own small company developing AC technology. By 1887 Tesla and a few associates had built working prototypes of a complete multi-phase AC power distribution system with step-up and step-down transformers and for the first time anywhere a practical AC motor. They filed 14 patents to protect it all. A professor from Columbia and the head of the new electrical engineering group IEEE came to his lab in Manhattan. They studied and tested his motors, measured the efficiency, measured the fast response, and were amazed at the excellent performance, and all done without commutators. They encouraged Tesla to give a paper and motor demonstration at an upcoming IEEE meeting because at that time he was almost unknown in the engineering community. After that meeting, the engineering community began to see him as the genius (at age 31) he was. Westinghouse soon bought the rights to use Tesla's AC  technology and patents, and Tesla began to worked closely with the Westinghouse company to get his AC technology into production.

Nikola Tesla age 38 in 1894
(6 ft 4 in, born 1856, died 1943, age 87)

        You can read more about the AC/DC battle and development of the induction motor in these two books. The Jonnes book is by far the better book. It is more than twice the length of the McNichol book. Jonnes is an historian, but she had some technical help with the writing and the engineering basics are covered. McNichol covers the PR and personalities, but has little on the engineering.

        Empires of Light --- Edison, Tesla, Westinghouse, and the Race to Electrify the World by Jill Jonnes, 2003
        AC/DC: The Savage Tale of the First Standards War by Tom McNichol, 2006

        Here's my Amazon review where I savaged McNichol's book (found helpful by 21 of 21 readers)

Title: Too short, omits most technical stuff, October 7, 2006 By  Donald E. Fulton
        AC/DC, subtitled The Savage Tale of the First Standards War, is a quick read that does a pretty good job telling the PR and human side of the AC/DC story, but skimps badly on technical issues related to the AC/DC battle. This book is less than half the length of the much better book on the same topic, Empires of Light --- Edison, Tesla, Westinghouse, and the Race to Electrify the World, by Jill Jonnes (2003).
        McNichols has two chapters on the bizarre electrocutions of animals and prisoners with details of every voltage used and electrode placement. But on a key technical point, getting Tesla's induction motor to actually work outside the laboratory, McNichols says next to nothing. The fact is that even though Westinghouse had bought the patent rights to Tesla's AC induction motor, Tesla's AC motor would not run on Westinghouse's early AC power. In the lab Tesla was running his motor on a polyphase AC generator that he had designed. McNichol says (page 83), "Tesla moved to Pittsburgh ... adapting the Tesla motor to the Westinghouse system". McNichols has got it backwards.

        Tesla in Pittsburgh probably did teach Westinghouse's engineers about his AC induction motor, but the important point historically and relevant to today is that Tesla worked to get Westinghouse to redesign his power plants and distribution systems so that the AC induction motor would start and run well. This required lowering the AC frequency from 133 hz to 60 hz and changing from single phase to three phase power. The latter meaning the distribution wiring had to change, going from two wires to three wires.

        The reason that Tesla's induction motor needed three phase AC is that it worked by establishing a smoothly rotating magnetic field that dragged the shorted rotor around with it. You can't do this with single phase AC power. The frequency change (133 hz to 60 hz) was because an induction motor is essentially controlled by the frequency of AC power and 133 hz caused the motor to run too fast and (very likely) not start well.

        On the most important technical issue in the AC/DC battle, how far power could be sent, McNichols makes no attempt to explain how AC can be sent further than DC. The key is the way transformers work. While AC does not flow as easily in wire as DC due to inductance, this disadvantage is more than overcome by the fact that effective length of the wiring can be reduced by the square of the voltage increase. For example, distributing AC at 3,000 V vs 100V for DC makes the wire length look shorter by a factor of 30 squared, which is 900! This is a huge advantage for AC.

        Jonnes records that in 1888 after Mark Twain saw drawings and an article about  Westinghouse's Tesla machine he wrote in his diary that it was going to revolutionize the electrical field and be the most valuable patent since the telephone.

Tesla invents an AC motor
        Tesla apparently spend several years in the mid 1880 thinking about and experimenting with AC motors. In 1887 Tesla had a working prototype of a AC motor with shorted windings on the rotor that ran as he said in his patent, "nearly synchronous with the rotation of the poles of the field". This was Tesla's most important invention, the AC induction motor. He filed for a patent on it on Nov 30, 1887 and the patent issued May 1, 1888 (US patent 382,279).

Variable reluctance AC motor
        When Tesla replaced the wound rotor with an asymmetrical steel rotor (no windings), it also rotated and worked as a motor, but this time it rotated synchronously. He filed for a patent on this motor too, a few weeks before the induction motor, and the patent issued on the same day as the induction motor patent. This 2nd AC motor is known as a variable reluctance synchronous motor. However, it has a problem, it doesn't start well (very low starting torque), so for this reason it is not widely used.
        The AC induction motor is potentially more reliable than a DC motor because it has no brushes. Brushes in a DC motor are sliding contacts that bring power to the part of the motor that rotates (rotor). Brushes wear out and need to be replaced regularly. AC induction motors have no brushes or wearing contacts. Power is brought to the rotor via induction, the mechanism used to transfer power in transformers.

        The AC induction motor was a major breakthrough because it meant that AC power plants could not only provide power for lights and heat, but for motion too. However, AC motors have a limitation that DC motors don't. It's relatively easy to vary the speed of a DC motor either by changing the (low power) field winding current or the input voltage. This made DC motors well suited for early traction vehicles (trolleys and trains) where with a few relays the speed of the vehicle could be stepped up.

        In contrast (prior to the days of modern electronic motor control) there was no easy way to vary the speed of an AC motor. The reason is the speed is set by the frequency of the distribution voltage. Excited with 60 hz the rotor will spin at 60 rotations/sec (3,600 rpm) (approx), or some integer submultiples like 1,800, 1,200, or 900 rpm depending on how the motor is wound. Essentially an AC motor is a fixed speed on/off motor, but that doesn't mean it can't be very useful, think refrigerator and garbage disposal, and in factories running a conveyer belt line.

How to get AC induction motor into use
        But, but ... even after the induction motor was 'invented' and practical prototypes were running in the laboratory,  there were two huge hurdles to getting it into use. The problems were related to the AC frequency and phases:

Frequency problem
        Early Westinghouse AC power plants, built before Westinghouse bought the rights to Tesla's induction motor, ran at a frequency of 133 hz. Tesla complained to Westinghouse that this was too high a frequency for his motor. The speed of an induction motor, and how powerfully it starts, depend mostly on the line frequency. With such a high line frequency his motor would not start well and it would run too fast.  Tesla pushed for the line frequency to be lowered to 60 hz, but Westinghouse resisted. His technology was based at 133 hz and lowering the frequency was a big deal. It would make the transformers and generators bigger, and the generators would  need to run at a different speed.
Phase problem
        The prototype induction motors that Tesla had built all ran on multi-phase AC power obtained from special generators that he built. Tesla's use of multi-phase AC was one of the keys to his induction motor design.  With multi-phase AC he found he could generate a smoothly rotating magnetic field inside the motor that in effect dragged the rotor around with it.

        With single phase AC you get two counter rotating magnetic fields, one clockwise the other counterclockwise. During start these two counter rotating fields pretty much cancel each other out with the result that the motor will not reliably start. Very likely the reason why others before Tesla had been unable to get an AC motor to work was that they had used single phase AC.

        The early Westinghouse AC power plants put out only single phase AC. Tesla told Westinghouse that had to change, his motor needed multi-phase AC to work well. Westinghouse was distributing his one phase AC over two wires, but multi-phase AC power needs (at least) three wires, so Westinghouse was also going to have to change all the distribution wiring.

        In principle multi-phase AC for the motor could be two phase AC power, where the phases of the AC differ by 90 degrees, or it could be three phase AC power where the phases differ by 120 degrees. The AC motor can be designed to run well on either, and Tesla knew this. He generally drew two phase versions of his prototype AC  motors, probably because two phase is easier to explain, but he occasionally showed a three phase variant in his patents. When the AC power standard was chosen, it was three phase. This is because three phase power can be distributed on three wires, whereas it takes four wires for two phase power.

        I know it seems strange that adding one more phase decreases the number of wires. The reason this works is that when three equal currents at 0, 120 and 240 degrees are added the result is zero. (This can be seen by doing a vector addition.) This cancellation provided by three phase AC means that the earth can (in effect) be used as a return path for all three phases, sort of a '4th wire' if you will, for the small unbalance current that results from imperfect cancellation.

        All modern induction motors run, except for small ones, run on three phase AC power. Small induction motors, like in your refrigerator, use a trick to internally synthesize a second phase, which is needed only briefly for starting, allowing the motors to be run off the one phase 120 VAC or 240 VAC, which is used in the USA for residential power.

         So to get the AC induction motor off the ground meant Westinghouse in advance would need to make big changes to the design of his AC power plants and the AC distribution systems, changing the frequency, number of wires and phases. The AC motor doesn't really care about the voltage. The reason is that's easy to wind a motor to run on 100 V, 120 V, or 240 V  or whatever is available. When it comes to the AC induction motor, it's the frequency and number of phases that matter.

AC is complex
        In general AC is a lot more difficult to understand and work with than DC. One of the reasons I am sure that Edison worked only with DC was that he didn't understand AC. It took decades after Faraday discovered the principle of induction to figure out how to properly design transformers. Induction motors are sort of like rotating transformers but with the serious complication that the real objective is torque.

How do AC induction motors work?
        I am sure another major complication in getting induction motors off the ground was that it was difficult for most everyone to understand how his induction motors worked. Physically the motors were simple and easy to use, but in some sense they seem to operate as if my magic. Even today it's very hard to think about how the rotor and stator fields rotate and how the torque is generated. Starting is extra complicated. Tesla apparently had a very good intuitive/visual understanding of its operation. But to design motors you need not just a qualitative understanding, you need to be able to calculate everything, size, torque, turns, gaps, heating. Motor design is a tradeoff of many parameters and consequently quite complex.

        Tesla was obviously good at doing the calculations required to build practical motors. Even his first prototype motors when evaluated by outside professors were found to work well and run efficiently.  Later Tesla was heavily involved in designing the turbines and distribution system of  the first big hydro powered power plant at Niagara Falls.

Induction motors hit the market
        Eventually Westinghouse made the changes to his AC plants and distribution systems that Tesla wanted.  Induction motors soon became a common motor and for most of the 20th century it has been the world's most common motor, the workhouse of industry.

        Let's jump to the 1970's. During this decade a major area of research in factory automation was figuring out how to put motors under computer control. The faster the motor could respond  to a requested change in torque, speed, or position the better. Faster motor response meant shorter industrial cycles times and more product output per hour. The generic name for motors with fast response time is servo motors.

        In the 1970's an induction motor's speed could be varied using a box of electronics, called a volt/hz drive, that varied the voltage and frequency to the motor, but the change in motor speed using this method was slow. The goal of induction motor control research was to make the response faster, more precise, to make an induction motor into a servo motor. In the 1970's this problem was worked on at many companies and universities. GE at its Schenectady NY research laboratory had whole stable of Phd's working on this problem.

Baffled by the rotor time constant
        For several years all attempts at getting servo-like performance from the induction motor failed.  A step of torque (really a fast ramp) would be requested, but the motor, if it made the torque step at all, would then 'ring' the torque for a half second or so. No one could figure out how to stop the ringing.

        All conductors have resistance (R) and inductance (L). Inductance is a measure of the energy of the magnetic field created by the current flowing in the conductor. The ratio of L/R has the units of time and forms a natural time constant that is a measure of how fast  the current and magnetic field of the conductor can change. The rotor of an induction motor has embedded in it a conducting loop of copper in which current flows round and around. It was known that the 'ringing' seen in the induction motor matched the rotor time constant, so it was pretty clear the rotor time constant was in some way causing the ringing.  The rotor time constant of the typical induction motors is about 0.1 to 0.3 seconds.

No one really understands how the induction motor works
        The failure to tame the rotor time constant was indicative of the fact that no one, not even the experts, 'really' understood how the induction motor worked. At least they didn't understand it dynamically. The induction motor, while complicated, had long been written up in the motor text books, and the text books were accurate as long as things didn't change too fast. Think how remarkable this is. The world's most common motor and almost a century since its invention, and no one really understands how it works!

         One of the difficulties in understanding the induction motor is that it is not a linear device; it often operates with partial saturation in its iron. This non linearity in the motor frustrated the efforts of the mathematically oriented researchers to understand the motor by writing out its equations. They had some limited success. Their equations would be valid for small signal changes about an operating point, so in those limited regions the desired fast, clean torque step was obtained, but in the general case the torque response remained contaminated by the dreaded rotor time constant ring.

Induction motor dynamics are figured out
        Here is where my work comes in.... I solved the ring problem. Yes, I did, the patent record confirms it. I contributed to improved understanding of the induction motor dynamically, and my contribution laid the groundwork for the standard ('vector') induction motor controller of today. I worked on induction motors first at Draper Laboratory (formerly MIT Instrumentation Laboratory), which was a large, mostly government funded research and development laboratory in Cambridge MA. They filed for a patent on my induction motor breakthrough in 1980 with me as sole inventor, and in 1982 the patent was granted. (US patent 4,348,627).

       A work of genius? Hardly, I just put in the final piece of the puzzle if you will. Here is the full story (as I remember it) ...

         Draper Lab specialized in guidance system development for US missiles working under contract to the US defense dept. Guidance systems are full of motors nearly all of which are controlled by state of the art, price is no object, control systems. So many engineers at Draper knew a lot about motor control and that included me. I was motor control/circuit designer at Draper for 15 years. As it turned out, however, none of the motors in our guidance systems were induction motors, so we started off our work on induction motors from a state of profound ignorance, which is sometimes a good thing.

          In the late 1970 there was interest at the Lab in getting some commercial work as guidance system work was winding down. Around that time General Motors was looking for partners to help with the development of motor controls for electric cars. Those two developments prompted two small teams at Draper to start working on induction motor controls. The two teams competed furiously as we thought hard about the induction motor in totally different ways. For months there were internal engineering memos written by both teams almost every week arguing the latest ideas about the motor's control. I wrote nearly all the memos for our team, which consisted for the most part of just me (full time) and my boss, Bill Curtiss (part time).

         I remember how the break through happened. I was in the quiet Draper library reading a colleague's draft MIT's Master Thesis on induction motors (work unrelated to Curtiss's and my work) when it suddenly occurred to me that maybe the phase of the motor currents were not being properly controlled, i.e. there was a missing phase term in the equations. I sketched what I thought the phase term should be (surprise, it is related to the rotor time constant) and we plugged it into a computer induction motor model which we already had that displayed the torque ringing. When the phase term was added, the ringing completely disappeared. So within an hour it was pretty clear that I had guessed right, we had found the key to getting servo like performance from an induction motor!

         After the break through, I soon wrote up a draft patent application describing how current should be controlled for servo-like performance. With the title Induction Motor Controller with Rapid Torque Response the patent application was filed in March 1980 and in Sept 1982 the patent issued (US patent 4,348,627).  Two years later, having left Draper Lab with other Draper people to form a new start up company doing cutting edge work in motor control (IMEC Corp), Robert Comstock and I used our recently won understanding of induction motors to make one of the first induction motor controllers. We developed, prototyped, and patented a complete high performance induction servo controller in 1982. (US Patent 4,484,126, filed 1982, issued 1984). I presented a paper at an engineering conference showing our new model of the induction motor. Machine Design, a well known engineering magazine, picked up the conference paper and republished it in their magazine as a feature article.

         Quite a while after our 'breakthrough' we found we were not first. Although we did not know it at the time, a Japanese professor (Nabae) had figured out that the phase term was missing a year or two earlier. We had never heard of his paper and apparently he did not at the time file a US patent application so our patent remained solid.

        Nabae had in fact done a terrific piece of work. His paper was difficult to read so I think a lot of people missed its significance at first. In fact when the IEEE selected a few dozen motor control papers to be collected and reprinted in an IEEE motor control paperback book, Nabae's paper was omitted!  In only seven pages he put out a new accurate model for the induction motor, including its non-linear flux saturation, then he proceeded to invert the motor model generating the optimum model for a rapid response induction motor controller. A superb paper.

        Something similar happened with the invention/discovery of the theory of electron/photon interaction called QED (Quantum Electro Dynamics). Feynman (at CalTech) and Schwinger (at Harvard) had 'clearly' invented QED in the USA in the 1940's after the war. Except later it was discovered that Tomonaga in Japan had published essentially the same theory five years earlier during the war (1943).  Tomonaga, Feynman, and Schwinger shared the 1965 Nobel prize for physics for the development of QED.
How come it took almost a century to understand the induction motor?
        I already mentioned how the (conventional) mathematical approach had been stymied by the non-linear flux saturation of the motor. Nabae circumvented this problem by not trying to write equations. He stuck closely to the motor physics generating a new block diagram that cleanly incorporated the flux non-linearity and could be inverted.

         But I think there was a more subtle problem that interfered with understanding the induction motor. For years I had heard of a classic MIT motor text book called Electric Machinery by Fitzgerald & Kingsley originally published in 1952 with the 6th edition published 40 years later. I searched out this book in the MIT library to look at its treatment of induction motors. There was a section on (supposedly) induction motor dynamics, but it had little to say. It was clear the authors, like everyone else, had no real understanding of induction motor dynamics.

        While looking through Fitzgerald & Kingsley I noticed something interesting. Induction motors had their own separate section of the book and its title page had just one phase on it  "Asynchronous Motors". That's wrong!! Generations of students had been taught that induction motors were asynchronous motors. Asynchronous motors are motors that are phase insensitive. No wonder the phase term was missing from the models! Everyone 'knew'  from the text books that induction motors were phase insensitive, so why put in a phase term.  Our Draper team had not studied induction motors in school, we were too ignorant to know induction motors were supposed to be phase insensitive.

        The full story is that the text books were right of course for the static and quasi-static operation that they analyzed. In this time domain induction motors are asynchronous and phase insensitive. But when response times of less than a second, less than the rotor time constant, are considered, the induction motor behaves like a synchronous motor and that means its currents need to be controlled in phase as they are in a synchronous motor.

Tesla's development of the induction motor
        A story or mystique has grown up about how Tesla conceived of, and visualized, a possible AC motor many years before he actually built a prototype. Who knows how much truth there is to this, but a hard record does exist in the form of Tesla's patent filings.

        Tesla received 111 patents. The reference at the link below is very useful as an index into his patents. It includes all of Tesla's patents, and they are sorted by subject and filing dates. Filing dates usually give a pretty good indication of when ideas are conceived making them much more useful than issue dates, which most patent indexes list. Unfortunately as is common with patents, the patent title often tells you little about the invention of the patent. Patent titles tend to be very general, and it is common for many patents to have virtually the same name. Tesla's patent attorney was really bad in this regard titling 15 of his motor patents with exactly the same name: "Electro-magnetic motor"! And sometimes patent titles are just plain misleading. For example, the famous Bell telephone invention is contained within a patent titled 'Improvement in Telegraphy'.
                  excellent index to Tesla's 111 patents, searchable text and image pdf formats,
                                                                                                           listed by file date (with small image of first page)
       MIT Tesla bio site that links to all of Tesla's patents listed alphabetically and
                                                                                                           by grant date, but not file date

         So to trace Tesla's path toward the induction motor required looking at a lot of Tesla patents. This tends to be a slow process because the figures in older patents (at least to modern eyes) are particularly unclear, requiring that the text be scanned to decode the figures and to see what is claimed. Another complication is that you often see Tesla filing two (or more) patents on the same day. Likely this is on advice of his patent attorney to satisfy the patent office rule that a patent application can only have one invention in it.

Online nonsense
        When it comes to Tesla's induction motor patent, you find a fair amount of confusion and nonsense online. It is common to see references to Tesla's 'first' or 'second' induction motor patents. Baloney. People are labeling an earlier (Oct 12, 1887) AC motor developed and patented by Tesla as his 'first' induction motor. The Oct 12, 1887 filings do not show an induction motor. The rotor is wrong, it has no coils. The induction motor filing come six weeks later on Nov 30, 1887, when a new rotor with shorted coils is substituted. It is this Nov 30, 1887 filing, issued as patent 382,279, that is Tesla's induction motor patent. (A second filing on Nov  30, 1887, which issues as patent 381,969, is another synchronous AC motor unrelated to the induction motor.)

Synchronous motor
        The patent record shows Tesla in 1885 - 1887 working on generators (dynamos). In the configuration of his Oct 12, 1887 filings he shows a two phase AC motor with its stator wiring connected to a two phase generator. This configuration produces a smoothly rotating magnetic field inside the motor that tracks the angle of the generator. This was a key step in the development of an AC motor, and may very well have been what Tesla visualized.

       Below is the key figure from the synchronous motor patent 381,968 (filed Oct 12, 1887). The same figure is in patent 382,280 filed on the same day. Motor is on the left powered by a two phase AC generator on right. The rotor, which has no coils, rotates at exactly the frequency of the spinning stator magnetic field. The rotor disc material (D) is soft iron, and note it is not radially symmetric. This is important. The magnetic field that goes across the torrid diameter will rotate the disk to the angle where the magnetic field is strongest, because that puts the system in a minimum energy state. If the magnetic field starts to rotate, it will pull the rotor along with it, rotating it not only at the same frequency, but also at (approx) the same phase as the magnetic field.

Two phase synchronous motor  --- Tesla patent 381,968 filed Oct 12, 1887

        This type of AC motor is not an induction motor. It is a synchronous, variable reluctance motor, and like most synchronous motors it has a huge weakness. It's virtually useless for doing work, because it doesn't reliably self-start, something Tesla surely knew, but did not mention in his patents. The only way to reliable start it is to kick it, or to slowly bring up the generator frequency from zero. The latter Tesla could do in the lab because it was running from his own generator.

        But with AC power from a central power station, the frequency is fixed. For all practical purposes a large synchronous motor of this type will not start when it is switched onto the line. So regardless of how much work a motor can do when it's at speed, if it won't start (without a kick), it's basically useless. (I have hands on experience with starting synchronous motors, because I worked on and patented (patent 4,455,513) a method to start synchronous PM motors.)

        A synchronous motor with a dedicated generator might find practical use in remote or 'off grid' areas. Here the generator and motor would be connected together all the time and the speed control provided by the generator prime mover. This system's approach, which Tesla favored, is in a way a work around for the inherent starting problem of the synchronous motor.

        However, the operation of this synchronous motor was probably very revealing to Tesla. The motor rotor tracking the generator and staying in sync with it would have provided Tesla a nice visual indication that his mult-phase generator connected to his mult-phase motor was generating a smoothly rotating magnetic field.

Motor drawings
        Tesla in his patent figures drew his motors two ways: idealized and realistic. The motor structure in the figure (above) is an idealized structure. Tesla drew the motor as just a simple torrid with four windings (plus rotor) when he wanted to illustrate the principle of his motor's operation. Real motors, however,  were build quite differently, with coils wound around what are called 'teeth'. Tesla would sometime include the real world 'tooth' structure in his patents too, as shown in the induction figure of patent 382,279 (below).

        DC motors were made by many companies in 1887 and were quite advanced. Electric trolley service had begun in 1886. Hence I suspect that the realistic winding drawings that Tesla included in his patents didn't require any real engineering on his part, that these winding details were pretty much the state of the art of motor winding at the time. The engineering of the induction motor was all in the rotor and characterization and understanding of the resulting motor.

        In its toroidal form the way to think about the magnetic fields is this: The magnetic field generated from each of the pair of series winding (180 degrees apart physically) are in opposite directions, i.e. clockwise and counterclockwise. The result is that in the region where the two opposite fields oppose the fields are forced to jump across the torrid (through the rotor if there is one). The two pairs of windings are in what is called 'spatial quadrature' meaning they generate fields that jump the diameter of the torrid separated by 90 degrees. In effect one phase makes a component of the magnetic field that goes up/down while the other phase makes a component of the magnetic field that goes right/left.

        The trick to making a smoothly rotating magnetic field in the center region of the torrid is to modulate the strength of the currents in the two phases, one as sine and the other as cosine, and this is what his two phase generator does. The reason this works depends on the trigonometric identity below:

[sin(angle)]^2 + [cos(angle)]^2 = 1

The second sin/cos term comes from the physical arrangement of the motor. As the rotor turns, the magnetic coupling between the stator and rotor physically varies by sin(rotor angle) for one winding and cos(rotor angle) for the other winding. The trigonometric identity tells us that if we balance the amplitude of the currents in the two windings the torque pulsations from one winding exactly cancels the torque pulsations from the other winding, so the rotor feels only a steady torque and rotation is smooth.

        In the same filing (381,968) Tesla includes a three phase version of his variable reluctance synchronous motor shown in a realistic configuration.

Three phase variable reluctance motor --- Tesla patent 381,968 filed Oct 12, 1887

Induction motor -- Tesla patent 382,279
        Six weeks later on Nov 30, 1887 Tesla files a patent application showing a slightly different configuration. The only change from the configuration of Oct 12, 1887 is that Tesla has changed the rotor of the motor. The new rotor is now radially symmetrical and has two coils on it that are shorted. This simple change dramatically changes the way the motor works. It now starts pretty well when switched onto the rotating generator, and it can put out a lot of torque. In short it's a practical, robust AC motor (now known as an induction motor).

        It works on a different principle than the synchronous motor. The motor rotor no longer rotates in step with the generator rotor. The motor rotor rotates slightly slower than the generator, and slightly slower than the stator magnetic field. In modern terminology the rotor continually 'slips'. Sitting on the motor rotor you would see a slowly rotating magnetic field cutting through the shorted turns on the rotor at the difference frequency between the rotating stator magnetic field and the rotor speed. Trying to put a changing magnetic flux though a shorted coil causes the coil to respond (via induction) with a current of its own that bucks the external field. It is the interaction of the induced rotor currents with the stator magnetic field via Lorentz force law (F=I x B) that produces the rotor rotation and motor torque. This type of motor is known as an induction motor.

        It's clear from the text of the patent that Tesla had a good understanding of the basic character of this motor. He noted that, "When these motors are not loaded, the rotation of the armature is nearly synchronous with the rotation of the poles of the field", and when the motor is loaded, "the (rotor) speed tends to diminish and the current in the (shorted rotor) coils are augmented, so that the rotary effect (torque) is increased proportionately". And he added, the motor shows a "remarkably powerful tendency to rotation", which is his way of saying the motor starts well.

        Below is the realistic figure of the induction motor from Tesla's induction motor patent 382,279 (filed Nov 30, 1887). C and C prime is the two phase stator winding making a smoothly rotating magnetic field across the rotor. E and E prime are shorted coils (in quadrature) on the rotor.

Two phase induction motor  --- Tesla patent 382,279 filed Nov 30, 1887

Rotor detail of induction motor  --- Tesla patent 382,279 filed Nov 30, 1887
(E and E prime are copper shorting plates around D iron armature)

        Above is detail of the induction motor rotor from the Nov 30, 1887 filing. Tesla understood that for the motor to work well the low frequency (slip frequency) AC field cutting the rotor had to create a large current. This meant the rotor coil impedance needed to be low, meaning low resistance and low inductance. This Tesla achieved by putting only one turn on the rotor (low L) and instead of using wire he used copper plate (low R). This is pretty much the way it is done today. It's hard to see on the figure above, but the (one of the two) shorted copper plate loops is the narrow, continuous crosshatch 'E prime' around the outside of the rotor. Inside this is a soft iron magnetic material.

Comparison of AC and DC motors
        One of the major elements in the competition between AC and DC central power stations to electrically power america was that with DC power you not only had lighting and heating, but also power for (DC) motors. There was no comparable motor for AC systems until Tesla's induction motor. There is no significant difference in the efficiency of AC and DC motors, and if the AC motor is of the induction type, both types of motors have good starting torque, though the DC motor probably has a little edge here. However, in some important ways the AC and DC motor are very different beasts, are suited for different applications, so let's compare:

DC motors
        DC motors are inherently variable speed motors. The speed of a DC motor depends on the applied voltage, vary the voltage and the motor speed changes. But there is a second way to change the speed of a DC motor without changing the voltage, just change the field current of the motor. The field winding is a relatively low power winding that sets the level of magnetic field of the stator. This flexibility in speed made the DC motor the workhorse of traction applications widely used in trains and early electric cars.
AC motors
        AC motors are (essentially) fixed speed motors, at least when operated from a central AC power station. This is because the speed of an AC motor depends on the frequency of the source not the voltage. Hence an AC motor is most useful for single speed on/off type applications, think of the induction motor in your refrigerator and garbage disposal. (There is a way with multiple winding to get some limited variation in speed in AC motors.) This motor in the early days was not suitable for traction applications.
My induction motor patents
        Below are two images from my breakthrough induction motor controller patent (filed 1980) that solved the 'ring' problem. This was a concept patent verified by computer simulation. The first image is a blowup of the key configuration, and the second image shows the same configuration in context on the first page of the patent. Patent 4,348,627  "Induction motor controller with rapid torque response", issued 1982.

Solution to the 'ring' problem of induction motor controllers (from Fulton patent 4,348,627, filed Mar 24, 1980)

Step of torque
        Prior to this time researchers at GE had 'ringy' induction controllers. In GE controllers when a step of torque was desired, the current amplitude and slip frequency were stepped, consistent with the classic textbook models of induction motors. The configuration (above) from my patent solves the ring problem. In my configuration when a step of torque is desired, the current amplitude, slip frequency and phase are stepped.

        The input at left (marked Slip Command) is also the torque command. Notice the oscillator has two sets of three phase outputs that are combined to form the current commands to the motor. The lower set has fixed amplitude and can be thought of as the setting the motor flux current. The upper set is time shifted 90 degrees, and scaled in amplitude by the torque command, and can be thought of as setting the motor torque current. The net result is that commanded torque currents are always in time quadrature with the flux currents. Steps in torque command result in some step in phase as well as stepping the amplitude and slip frequency in the classic manner.

Why does this work?
        This works because the rotor of an induction motor can be though of as (sort of) a PM (permanent magnet) that slowly 'slips' around the rotor. For times less than the rotor time constant (less than a second or so) the PM is locked to the rotor physically. This means that for times less than the rotor time constant an induction motor is a synchronous motor! And like any synchronous motor the torque currents have to be phase controlled relative to the rotor.

        A little later (in 1982) a fully functioning hardware/software induction motor controller was built, based on the induction controller configuration of my patent 4,348,627, and it worked as expected. I did the motor modeling and designed the hardware and Bob Comstock implemented the controller architecture in code. Below is the first page of the Fulton, Comstock patent on our 1982 induction motor controller. Patent 4,484,126 "Induction motor controller", issued 1984.



Links to Tesla's oneline papers and articles
        Dozens of Teslas papers and articles are oneline, below has links to many dozens.

How induction motors generate torque -- a tutorial (update 7/12)
        I gave a talk to local HS physics students in spring 2012 about how motors work. In coming up with a simple way to explain to them how torque is generated in DC motors, I learned something myself, and it applies to induction motors too.

Lorentz view
       Start with the lorentz law (F = I x B). In physics text books a straight wire carrying I is shown in a uniform external magnetic field B. Since F results from the product of two vectors, it points perpendicular to both I and B. The Lorentz viewpoint (below) is looking into the axis of the motor, so rotor currents are seen to flow in/out and the stator magnetic field cuts horizontally across the rotor.

Induction axial rotor currents
        This view can be applied to the rotor currents of both a small wound rotor DC motor and an induction motor. In both these motors the rotor conductors run axially, so rotor currents run down one side of the rotor, loop around (shorted at the ends), and flow back up the other side. The stator makes a magnetic field that cuts (say) horizontally across the rotor. The cross production action of the F=I x B lorentz law then produces a force UPWARD on the conductors on one side of the rotor and a force DOWNWARD (because sign of I is reversed) on the the other side, in other words, a torque. The interpretation of the lorentz law here is that motor torque is the product of the ROTOR current x STATOR magnetic B field (or vice versa for a PM motor). This is a very general motor relationship.

Rotor circuit model
       The circuit model of an induction rotor is [R + Lw + Voltage source], where the rotor Voltage source is d(stator flux)/dt as seen from the ROTOR. The stator flux in an induction motor is usually run constant, so that means the AMPLITUDE of the voltage in the rotor model is proportional to slip frequency. The rotor is designed to be very low impedance shorted loop, i.e. R is made very low. It's a single shorted turn with large conductors. The inductance is also designed to be small, because in the operating slip region of the motor we want the impedance to be dominated by R (Lw < R). Once the slip frequency hits the R/L frequency not only does the current stop rising, but it shifts in angle such that less and less torque is generated.

Torque proportional to slip
       Note this viewpoint explains why the torque of an induction motor is proportional to slip. As the slip frequency increases, the amplitude of the d(flux)/dt voltage source in the rotor model linearly rises, which since it is loaded by the resistance of the rotor means the amplitude of the rotor current rises linearly with slip, and from lorentz (F=I x B) so does the (rotational) force on the rotor conductors.

        Thus the objective in an induction motor is to make CURRENT on the rotor to interact with the stator magnetic field, and it is desirable to do it with minimum R (for lowest copper loss) and with the SMALLEST possible d(flux)/dt voltage induced in the rotor, because this means minimum slip, the motor operating closer to synchronous speed. Higher rotor R just means higher rotor loss for the same torque. (Because most induction motors are line operated and have to start with slip of 100% there tons of literature on rotor resistance. It is used shape the Torque vs Speed curve to get good starting. Generally all this rotor resistance stuff can be ignored for an inverter controlled induction motor.)

Switched variable reluctance motors -- a tutorial (update 7/12)
        The concept of a variable reluctance motor has been around since at least 1877 when Tesla built one and patented it. However, they were rarely seen commercially in the following 100+ years, except as low speed stepper motors. When I recently learned that variable reluctance motors have become successful in at least a few consumer products, like Dyson portable vacuum (@ 104 krmp!) and Dyson hand blowdrier (@ 84 krmp), I did a little googling to see what control strategies were out there for variable reluctance motors. One good starting point is the app notes of IC firms that make controllers for motors. I found the same basic inverter structure in an TI variable reluctance app note and Wikipedia ('Switched reluctance motors'). Here's what I have learned, a mini-tutorial on variable reluctance motors, if you will.

        Here's what Wikipedia calls the "most common", smoothest torque, best starting inverter for a variable reluctance motor. One and two winding versions are possible too, but with less control, more ripple torque, and poorer starting.

(source --- Wikipedia 'Switched Reluctance Motor')

    Just like a piece of iron is attracted equally strongly to the N or S pole of a motor, reluctance torque is not sensitive to the polarity of the magnetic field. This is important, it drives the inverter architecture. Unlike PM or induction (or most) motors you can't reverse the polarity of the torque by reversing the direction of the current. This is probably why you don't see the standard inverter used with variable reluctance motor. The torque polarity can be reversed, but to do it requires moving the current to a different coil relative to the location of the rotor.

        What I generally find in researching reluctance motors control is the motor windings (1, 2, or 3) are brought out separately to the inverter where each winding is driven by a half H bridge. (See fig from Wikipedia article above). A half H bridge here is two IGBTs in diagonal corners and two diodes in the other two corners. With this arrangement the winding can be switched to the bus to ramp up the current and be shorted to allow the current to continue to flow. A one or two winding variable reluctance motor is generally shown with each of its coils also driven by a half H bridge, as in the figure above.

     While the semiconductor counts are the same (or not much different) from a standard inverter (six IGBTs and six diodes for three windings) the problem here is that they are not wired together the same. This configuration is available commercially, but with far less selection than with the standard inverter where each IGBT has an anti-parallel diode.

Number of motor phases
      Number of phases are related to ripple torque and starting. With three (or more) phases the the torque can be made smoother and starting will be reliable. While one phase can run the motor, it won't be able to start a motor that stops at the wrong place (zero torque position). Not quite sure where the starting limitation is with two phases, but it's claimed to not be as reliable starting as three phases.

Synchronous commutation
       A variable reluctance motor is a synchronous motor. To know which winding to power you MUST know the location of the rotor. Reading the marketing hype on the Dyson site their 2nd generation vacuum motor seems to be Hall commutated with PMs on the rotor. They mention the hall sensors are on the PC board, which might work if the PC board wraps around the neck of the motor. (Their 100 krmp motor is very small, only about two inches in dia.)

EMF and sensorless control
        Since a variable reluctance motor is run by switching currents on/off in it's various windings, it is not continuously fluxed, thus I doubt that there is much to see in the way of back EMF in an unpowered winding. My guess is that sensorless control of this motor is difficult (maybe not possible), therefore it needs a commutating sensor if it is to run closed loop.

        Like other synchronous motors you can run a variable reluctance motor open loop. This is the rotating energy well concept. Use only a fraction of the available flux and accept that if the the speed profile is not carefully chosen the motor may 'drop out of sync'. Variable motors run like this are called stepper motors and are very common in industrial machines. (I myself designed a stepper controller.) PM stepper motors are often designed with many poles and to have strong detent torques at many (equally spaced) angles around the circumference. This allows them to hold these positions without being powered, a useful feature that machine design often exploits.

      Torque control is complicated in this motor. On a plot of inductance vs angle (for a coil) torque polarity will be positive at angles where the slope is positive (i.e. inductance increasing with angle) and negative where the slope is negative (i.e. inductance decreasing with angle). Even when the flux is not saturated the torque depends on the current amplitude squared (air gap energy density goes as H^2), and it gets worse because apparently a lot of these motors run with magnetic saturation. But various solutions (or work arounds) to this have over the years been found using look up tables in the controller memory to shape the current waveforms.

Speed range
        There are a lot of combinations of rotor and stator shapes (saliency) that can be usefully combined to make a variable reluctance motor. Small, low speed variable reluctance motors that are run open loop are common in machines and are called stepper motors. Dyson has shown that variable reluctance motors with a rotor angle sensor used for commutation can successfully be run to very high speeds (100,000 rpm for a 2 inch motor powering a small vacuum cleaner).

TI Reluctance controller

Wikipedia -- switched reluctance motor

Comparison motor sketches (update 10/10)
        I have sketched up three basic types of motors to illustrate their principle of operation. All sketches are looking in toward the axis of the motor. The outside of the motor is the stator built with with copper coils and iron. Stator currents are varied such that the stator magnetic field (indicated by N and S poles) smoothly rotates (here shown rotating counter-clockwise as indicated by the arrows) and is of constant strength. The rotating part of the motor in the center, called (surprise!) the rotor, is basically 'dragged around' by the stator magnetic field.

PM motor
        Three types of motors are shown in the sketches. The first sketch just shows the rotating stator magnetic field with no rotor. Top center, a PM magnet is embedded in the rotor. The PM poles seek out the opposite stator magnetic poles, so as the stator magnetic field rotates the rotor is dragged along with it. This is the PM motor.

Variable reluctance motor
        Top right, a bar of steel (or any ferromagnetic material) is embedded in the rotor. Just as a bar of steel is pulled toward the poles of a horseshoe magnet, here the steel bar want to align at the angle where the stator magnetic field is strongest, so as the stator magnetic field rotates the rotor is dragged along with it. This type of motor is called a variable reluctance motor.

Induction motor
       The bottom sketch are all the same motor at different times. Here the rotor has its own coils of wire, but there is no electrical path to the rotor coils, i.e. no slip rings or brushes. This is an induction motor. In an induction motor the rotor rotates slightly slower (0.1% to 3%) than the stator magnetic field. The arrow on the rotor can be thought of a painted arrow on the rotor. In the left sketch the rotor painted arrow (happens to be) aligned with the stator magnetic magnetic field, but as we go right in time we see that the rotor painted arrow begins to lag the stator field and as time goes on it lags more and more, since it is rotating slightly slower. If say the stator magnetic field is rotating 30 rev/sec (as it would in a 60 hz powered 1,750 rmp motor), then the rotor (under heavy load) would typically be rotating about 29 rev/sec, about 3% slower. The small difference (1 rev/sec) in rotation rates of the (physical) rotor and stator magnetic field is called induction motor's slip frequency.

        If you visualize yourself sitting on the rotor spinning at 29 rev/sec, you would see the 30 rev/sec magnetic field from the stator rotating at only 1 rev/sec, at the motor's slip frequency. This low frequency (but high amplitude) magnetic field 'seen by' the rotor coils induces (Of course, the reason why it's called an induction motor!) currents in the rotor coils. As seen from the outside, the magnetic field of the rotor (N/S rotor poles) now rotates at exactly the speed of the stator magnetic field (30 rev/sec), 29 rev/sec coming from the rotor physical rotation and an additive 1 rev/sec coming from the rotor magnet field slowly varying (relative to the physical rotor). So in the sketches I show the S/N of the rotor magnetic field remaining aligned with the N/S of the stator magnetic field even though the physical rotor is rotating slightly slower than the stator magnetic field.

PM motor, variable reluctance motor and induction motor comparison
PM motor and variable reluctance motor rotate 'in sync' with stator magnetic field
Induction motor 'slips', i.e. it rotates slightly slower than stator magnetic field
(Commutation angle shown at 0 degrees for simpicity)

         Note, in the sketches above I show the S/N poles of the rotor aligned directly opposite with N/S poles of the stator field. While it illustrates the principle of operation, it is not exactly how the magnetic fields align in real motors. If the rotor is allowed to rotate freely relative to the stator magnetic field and the motor is unloaded, then the rotor will align approximately as shown in the sketches, because this is where the torque approaches zero. But we don't want the rotor 'feeling' a low torque, we want it to feel a high torque (for a given stator current).

Commutation circuit
        The solution is to add to the motor controller a circuit, called the commutation circuit, that forces the rotor and stator magnetic fields (in the case of PM motors and variable reluctance motors) to always be in quadrature, i.e. 90 degrees apart (electrical). This is done by sensing the rotor angle and steering the stator current into the correct windings, such that the stator magnetic field always leads the rotor by 90 degrees. In a quadrature alignment the outer parts of the rotor feel the strongest push and pull from the stator magnetic field, so the motor develops the most torque for the least current and the least heat.

Reading US patents online
(update 8/08) Google patent search
        Google has a new patent search in beta. Unlike the patent office you can search for old patents without knowing the patent number. You can use inventor names, dates (filing or issued), words in patent, etc. These options are accessed via the Google advanced patent search screen. You can download the whole patent in pdf format, or you can jump directly to the patent at the US patent office site. The latter is useful as I find it a lot easier to read the patent online at the US patent office site using their magnify feature than trying to navigate around pdf documents.

        However, the Google patent search is not without its problems. I did a few trials searching with different criteria, and lot of patents seemed to be missing. Workaround: search several ways. Another problem seems to be the poor quality text from the patent office on some old patents is defeating the text reading algorithms. Even the titles of some 1870's patents I pulled up were full of gross spelling errors.
US patent office web site
        All US patents back to 1790 are available on the US patent office web site and can be read and printed out free. To look at an induction motor patent select 'patent number search', enter the patent number (say, 382,280), then click 'images' for each page. Here is a link to the patent search page on the US patent office web site.

         There is a little problem in looking at patents at the US patent office site. All patent page 'images' are in an unusual .tiff format that needs a special viewer. If you poke around on the US patent office web site, they will point you to an appropriate .tiff free viewer. Here is the .tiff viewer download link (from the patent office web site) for the viewer I use. My recommendation is choose the 3rd option (alternatiff-1_8_1.exe), which installs a plug-in for your browser. Once the viewer is installed your browser will automatically open patent page images, and you will be able to print patents a page at a time.

        On a new PC after I installed Alternatiff I found I could view patent (image) pages, but I couldn't  print them.  Poking around on the Alternatiff web site I found why I couldn't print. No toolbar (with print icon) at the top of the patent page image means that Alternatiff, even though it may be installed, is not running. In my PC Quicktime was opening the patent .tiff images because it was default tiff file handler.

        Here is the print fix (assuming Quicktime is the problem): Go to Control Panel and double click Quicktime icon. Go to browser tab, Mime Setting, and expand Still Images files, and uncheck TIFF image. Click OK's, then restart computer.

Westinghouse/Tesla Gallery

Tesla engineering overview
        PBS Tesla bio 1 hr video consistent with the Tesla bio book I read ('Tesla' by Bernard Carlson) make it clear that Tesla made only one major contribution to engineering, the development of the AC induction motor. I've read and commented above on Tesla's first AC motor patents which are the patents that attracted Westinghouse. The video pointed out that in the year or so that Tesla worked with Westinghouse engineers at Pittsburgh on the motor and AC distribution system resulted in 18 patents. These patents might be worth reading.

        He also pioneered a totally new new field in his many experiments with high frequency/high voltage using a resonant step up coil he developed called now the Tesla coil. It's a wonderful toy still shown in science museums, and Tesla gave wildly popular demonstrations with it showing that it could light tubes he filled with gas and no wires. But Tesla engineering sense failed him here, no practical product ever came out of this.

        He followed this up with an even more off the wall project where for years he worked to build a large scale tesla coil demo in Colorado followed by a larger prototype on Long Island to (unbelievably) power the whole world by pumping power into the earth! He somehow convinced himself in Colorado he could send power/communications long distance, but apparently only did very short range tests, trusting it verified his mathematics modelling. A terrible engineering/experimental mistake. And there is no indication that he took into account 50 years worth of tests the telegraph people had done on the earth, where they never figured out how to model the earth. The physics commenter in the video is the head of MIT physics dept, and he thinks Tesla made a terrible mistake here. He thinks it was never going to work. Maybe he said the Long Island monster tesla coil might have have been able to send signals a mile.

        Below are Images captured from Nov 2016 PBS 1 hr Tesla bio video.

Huge tesla coil sparks at Colorado lab

Spectacular Tesla coil photo (probably a multiple exposure)
(probably taken at Tesla's large development lab in Colorado)
Westinghouse AC generators at 1893 exposition

Westinghouse AC generators used to power the 1893 Chicago Columbia Exposition
Westinghouse Niagra AC generators

Westinghouse Niagra AC generators
Frank J. Sprague's self-regulating DC traction motor for trolleys

Frank J. Sprague
        From a recent PBS special ('Race Underground') on the building of the subway in Boston I learned about an interesting early motor designer who I had never heard of Frank J. Sprague. In many ways he was the DC equivalent of Tesla, both clever designers who came up with new and very useful electric motors. They were both doing their early pioneering work in the 1880s, Sprague a few years ahead of Tesla. Sprague, a former Edison engineer, provided the dc motor that Edison recommended to customers of his DC power stations.

PBS's American Experience -- Race Underground
       (53 min)

Frank J. Sprague (1857 - 1934) is famous for several major 'inventions':

            1) first practical electric trolley system, which incorporated several major advances:
                     a) improved dc motor with a flat speed vs load characteristic ('self regulating'), meaning it would run at about the same speed
                            regardless of the number of passengers in the car and (very likely) did not have a current surge when starting from zero speed.
                     b) 'three point mount' of the trolley motor (now standard) that allowed the motor to move up/down but still be powered.
                     c) power  to the car provided by a single overhead high voltage wire that the car picks up with a rolling contact, the rails and earth
                            providing the return path to the power station.
            2) train controls  --- developed the car-to-car controls to allow multiple self powered cars to be configured into a train that operates as
                           a single unit. Used by all subways trains. The book 'Race Underground' says both Sprague and GE were working on this idea,
                           but Sprague beat out GE. A year later GE bought the rights to it from Sprague..
            3) electrification of elevators

Frank J. Sprague
(source --- scn capture from PBS subway video jan 2017)

Sprague family
       As a working EE engineer, the Sprague name was familiar to me because Sprague was one of the major manufacturers of capacitors in the USA (now sold by Vishay). Turns out this company was founded and run by Frank Sprague's son, Robert Sprague (1926 - 1987). There was also during my working years a smaller Sprague electronics company based in MA. Peter Sprague, Frank Sprague's grandson, was CEO of National Semiconductor for 30 years (1965 - 1995).
        Frank Sprague focused on adopting the DC motor to the demanding job of powering trolleys replacing the horses which for years had pulled the cars on rails. The first public transport vehicle in cities had been the omnibus (Wikipedia calls it the 'horsebus'), which was a big carriage with wooden wheels pulled over city streets by horses. Since most of the streets were unpaved the ride was terrible and slow. In the 1860s when steel became available rails were laid down and not only was the ride remarkable better and faster, but Wikipedia says the same horse could pull from x3 to x10 times more people. The PBS shows says that Boston in the 1880s had the largest public transport system in the world, larger than New York of London, with about 7,000 horses.

        Sprague, who came to be known as the father of traction motors, customized his DC motor in several ways to make it suitable for trolley operation, but Sprague did much more. Sprague had some capital and was CEO of his own company and with a team of about a dozen engineers he hired, he designed and built the first large electric trolley system (40 cars and 12 miles of track), which meant building the cars, the overhead wires, the tracks and the central powerhouse to run all the cars.

'Self-regulated' DC motor
        My real interest in digging into Frank Sprague was to understand his new dc motor. He had come up with this motor design soon after leaving Edison about 1883. Trolling through the catalogue of the 1884 Philadelphia Electrical Exposition I came across Sprague's entry (below). Biographies indicate this motor became a good seller after the exposition, and provided him with cash flow to work on the trolley problem for the next 2-3 years. Edison recommended to his customers of his DC power plants (famous Edison Pearl Station in Manhattan was opened in 1882) that the best DC motor was a Sprague dc motor.

        Note his catalogue entry shows the big selling point of his motor is its flat speed vs current (load) characteristic. However, there also seems to be a (potential) drawback. He says the motor can be started "gradually with load on". Now either this means the torque at zero and low speed is particularly weak, or perhaps he just means that the normal high surge of current (and torque) when most motors start from zero speed is missing. Upon thinking about it I suspect the latter is the case.

frank sprague dc motor entry in 1884 philadelphia electrical exposition catalogue
Sprague's entry in the 1884 Philadelphia Electrical Exposition catalogue

Is Sprague's Self-regulated' DC motor novel?
        Digging into Sprague's 'self regulated' motor there appears to be less novelty here than I expected. Maybe this is just the perspective of 130 years! In terms of motor characteristics what is wanted for a trolley is a speed vs load curve that is quite flat. A choice of several flux levels with the car controller allows the car's speed to be controlled, and with a flat speed vs load characteristic the car would accelerate about the same regardless of the number of passengers or the grade.

        There are three basic types of DC motors: series wound, shunt wound and compound wound (combination of series and shunt). These three DC motor types are really just three different ways of configuring the two coils of the motor. Turns out the shunt motor is pretty much what is wanted for the trolley. Sprague calls his motor in his early trolley patents a 'shunt motor'. It's often called a 'constant speed' motor. I see data that some (modern) dc shunt motors have only a 5% variation in speed from no load to full load. A shunt motor  will still slow down a little under heavy load, but its speed vs load curve can be tweaked up (flattened) by running some of the armature current into the field winding in a reverse sense such that it lowers the flux at heavy load which increases the speed.

        I have no knowledge of how the DC motor developed, but looking at the big dc generators of the early 1880s you can see a lot of sophistication. On the other hand the first central DC power station, Pearl St Station in NYC, went online in 1882, so it's only in that time frame that customers could begin to apply dc motor to a range of applications.

        I think it very unlikely that Sprague 'invented' the shunt DC motor or was the first to use it. For example, Sprague uses the term 'shunt motor' in his early motor patents as though this would be known to someone skilled in the motor art of the time. So I think what he did was to (correctly) adopt the shunt motor for applications where holding speed was desired. Then he came up with a clever way to sell it, calling it a 'self-regulated' DC motor. This descriptive phrase nicely described how his shunt motors inherently held speed even if the torque varied or the input voltage varied.

       Sprague's first motor patents of 1883 (filed) feature the self-regulation, but it is not easy to see what in practice exactly he did, because basically he sketched out every variation he could think of for varying the flux of the motor by switching between taps on his motor field windings.. I also came on a contemporaneous article that varying the motor field using the armature current had been explored by other researchers a couple of years, before Sprague. Thinking about it, this does indicate that this tweaking of the motor field to to get the response you wanted from the motor was new, and of course, Sprague began commercializing it right away, selling motors beginning in 1884.

        The key Sprague patent on his self regulated motor seems to be his patent 295,454, filed 1883, issued 1884 (also patent 315,180). Decoding this patent is a challenge because it includes a huge number of variations, and I am not familiar with the conventions of dc motors from the 1880s. However, Sprague in later patents does talk about the perfect winding configuration where he sets certain winding ratios to achieve the flattening he wants.

        The simplest of the many configurations in this patent (295,454) is fig 4 below. For trolley use C and C (prime) would represent the overhead (450V) power line. At this point I don't understand the rotor wiring. It looks like there are two rotor circuits each with their own set of brushes? (Note the brush assembly in the picture below of the 1884 prototype Sprague motor picture does appear to show two sets of brushes.)  The left one is shown connected directly to the power line, and the rotor winding right may be cross connected with the field winding. The other variations in the patent seem to be to the right side only. (Even on blow up, the patent figures are not carefully drawn, so it is a guessing game as to where wires connect and how the field coils are wound and tapped. There's also a frustrating disconnect between the text and figures with text symbols missing from the figures.)  On the other hand maybe the patent image below is for a single winding, with the overview at left and detail at right. Confused.

Frank Sprague's dc motor patent 295,454 (issued 1884), figure 4
(source --

        For a lot of applications like trolleys (and elevators too) it is very desirable if a speed can be selected and the speed will hold over a large torque variation. In other words a vehicle runs at pretty much the same (selected) speed whether or not the car is lightly loaded or fully loaded. A normal DC motor with a fixed field current and a fixed voltage applied to the amature will run slower as the load is increased. This is due to IR voltage drop across the armature resistance causing the internal EMF to drop as current (load) goes up. I found one reference that said in words what Sprague had done and I sketched out out a simple motor model based on that, so I am pretty sure I know what Sprague did. He ran the armature current through a few turns of heavy wire on the field coils such that the field is weakened when armature current flows, and a weakened field causes the motor to run faster. In this way he compensated for the IR drop in the armature which was what caused the motor to slow down under heavy load. Sprague had worked for Edison for a year and Edison knew of Sprague's motor and liked it. In 1885 the Edison Electric Light company strongly recommended the motor to customers connected to its DC power stations.

    "In 1885, the Edison Electric Light Company officially endorsed Sprague's motor in a circular sent to its local companies. "A practical motor has been a want seriously felt in our system," it read. "The Sprague motor is believed to meet . . . all the exigencies of the case, and the Edison Electric Light Company feels it can safely recommend it to all its licensees as the only practical and economic motor existing today." (
Side tapped field coils
       Sprague did not use teeth in his motors (at least his early demo motors). Pictures show the field was set with a two pairs of huge coils extending to the side. To my eyes the motor magnetic design is rather unusual looking, but for all I know this was common at the time (yup, see bottom right). It is a basic straight forward magnetic design, the magnetic flux forming the motor field being the sum of flux from the right and left pair of coils. As Sprague's patents show for speed steps in his controller he tapped the coil at many places giving him a range of field currents (from the fixed DC voltage powering the car). This was much more efficient than the resistive control used later in electric cars. The extra iron required for the field path may have been an advantage thermally in helping to dissipate heat from the rotor, obviously good cooling was important for a trolley.

(left) Large coils on the side are field coils (early 1884 Sprague prototype motor)
(source --
(right) Competitors dc motors shown at Phil Exposition 1884.
(source --- 1884 Philadelphia Electrical Exposition catalogue)

        The PBS video has these images of sprague motors. With the rotary switch in front these look like some sort of demo set up. The motor at right has no covering so the field winding is visible. The left winding, which would normally be there, is missing here. Note each field coil produces a magnetic flux that loops around passing through the amature in the center. The 'field' of the motor is the sum of the right and left field fluxes. (what is going on with the flaring of the edge of the rotor I have no idea). Unfortunately the brushes are not clearly shown in this end view. The Sprague patent suggests that in the trolley production motor the  field coils are horizontal with each side having two coils in series. This give more options to tap and configure the field windings which is the heart of Sprague's self regulating control method.

Sprague demo motors
(source --- scn capture from PBS subway video jan 2017)

Field windings
       I made a little sketch below to show how in principle the field windings in a DC motor can be placed to the side (as can be seen in the Sprague demo motors above) or wound on teeth inside the cylindrical steel stator of the motor, which is how the motors in the trucks of the Sprague trolleys look.  The equation that predicts the flux in a flux circuit are very similar to ohms law which predicts a current given a voltage source and resistor. Here the driving force, replacing the voltage source, is NI [field current x N (number of turns)], the resistance is replaced by what is called the reluctance of the air gaps, and the predicted result is the flux, which is (B x area).

How a DC motor makes torque
        The objective of the field windings and the associated steel path on which it is wound it to create a magnetic field (labelled 'B' in the sketches) that runs downward through the rotor jumping two small stator/rotor air gaps. Conductors in the rotor winding (not shown) loop axially (in/out of the paper). When the interaction of the rotor current near the top of the rotor and the magnetic field B produces a force pointing to the left, at the same time a corresponding force pointing to the right is occurring near the bottom of the rotor because the looping rotor current here also interacting with B is flowing in the opposite direction. These two opposite forces generated near the edge of the rotor create a twisting action or torque that causes the rotor to rotate. The addition of a sliding contacts, called a commutator, in the rotor circuit insures that the direction of the rotor currents relative to the B field stays about the same, and that results in a steady torque in one direction.

my little sketch showing that in principle the field windings can be placed either to the side
or (in the modern sense) wound on teeth that project out from the stator steel.
In both cases the NI of the field windings drives a flux (B x area) around a closed steel path
jumping two rotor/stator air gaps. 

Sprung motor mount
       The PBS video makes a big point that another of Sprague's key motor inventions for the trolley was a new motor mount. Since the tracks in early days were laid often on unpaved roads, it was very desirable to allow each wheel to move up/down while still remaining being powered by the motor. This was accomplished by how the motor was sprung and geared down to the wheel. References call this a 'three point motor mount' and say it has been standard on trolleys ever since.

Sealed motor case
       To keep out the rain and mud each motor (with its brush assembly) was enclosed in a steel case. All of Sprague's motor had a distinctive shape due to the field coils sticking out to the sides.

Startup surge
       The natural tendency of a dc motor (or almost any motor) is to draw a big surge in current when starting from zero speed because the back EMF is zero. This is very undesirable in a trolley for several reasons. One, a current surge is also a torque surge so every time the trolley starts it will jerk. Two, the stability of the voltage of the track cable will be improved and the load on the central power station will be less if the motor can be configured to avoid a current surge when starting from zero speed. Three, since trolleys start and stop all the time a current surge on every start probably is a non-neglible contribution to the heating of the motor.
Trolley truck design
        The PBS video implies that the trucks below were used in the Richmond trolleys, but they may just be representative of Sprague's early truck designs. The graphic below is a nicely done animation showing how the wheels move up/down as an irregular surface glides by. The pictures combined with the graphic make it clear that the wheel is powered by the large ring of teeth either on its inner surface or connected to it, the wheel teeth meshing with a much higher speed small gear most likely mounted on the motor shaft. My memory is that it is a 12:1 fixed speed step down. The lower picture shows the truck symmetrical right/left, the motor must have a double shaft driving a right/left pair of wheels on the truck. The contract (and the PBS video) specified that each car have two motors, so each car must have two motors each  driving a pair of wheels.

Animation of Sprague's three point motor mount (showing motor moving up/down)
Outside travler wheels, which ride in a specaial track, must have been a design tool, as they are not present on the production cars.
(source --- scn capture from PBS subway video jan 2017)

sketch of Sprague's tolley truck
This sketch includes travler wheels (left) riding on a special track.
(source --- scn capture from PBS subway video jan 2017)

        In the two images below of Sprague's truck we can see that the all four wheels are driven by two double shafted motors via step down gears. It's not clear from this viewpoint how the motors are mounted.


(source --- scn capture from PBS subway video jan 2017)

Richmond cars lined up
These cars have the first generation cable pickup

Richmond's 1887 trolley system and central power station
        While the motor was a key element in an electric trolley system, there was another equally important aspect. How to power the cars? Sprague's answer here was a high voltage wire (about 18 ft above the ground) mounted over the center of the tracks. A small wheel at the end of a sprung pole from the car pushed on the wire, bringing 450 VDC into the car to the motors. Sprague used the grounded steel rails as the return path. For safety and reliability at regular intervals the steel rails were connected to large grounding plates (with pipes) as was the central power stating itself.

        For his Richmond system (1887) with 40 cars (80 motors) he built a 375 hp (278 kw) central station. This was accomplished using multiple units in parallel that apparently he could buy off the shelf: three 125 hp (92.5 kw) engines (probably steam engines powered by coal), each powering two 40 kw generators. So to power the contact wire he had six generators in parallel (sort of) each rated 450 VDC, 89A (total 450V @ 533A). To keep the voltage drop down in the 12 mile cable the multiple generators were attached to the operating line at connected at various points to the cable.

three 125 hp (92.5 kw) (steam) engines each powering two 40 kw dynamos.
contact wire voltage spec: 450 VDC.
trolley motors spec: 7.5 hp (12.4A @ 450 VDC)
(scn capture of power section of the Richmond specification from PBS video)

        The hp rating of the car motors in Richmond is unclear from the PBS video commentary, but the Richmond specification is briefly shown in the video and I captured from it the power specification (see above). It is a little unclear, but it looks like the motors are each rated at 7.5 hp (5.59 kw, 12.4A @ 450V) which per trolley is 15 hp (24.8A @ 450V) . (Wikipedia's article on the Richmond trolley says each car had two 7.5 hp motors, however the book Race Underground says the motors were 7 hp.)  As the story goes when one of the cars were first tested on a steep Richmond hill it climbed the hill, but doing so burned out the motor. Sprague then quickly either changed the gearing (or went to a larger motor or both). Looking at the number of cars Richmond was able to run simultaneously and with two motors per car (specified in the contract), my guess is the cars had two 7.5 hp motors (yup), and that Sprague during testing had lowered the gearing increasing the torque and decreasing the maximum speed of the trolleys.

        I can find no information on the trolley braking. Obviously this was a concern in Richmond with its steep hills as the passengers had to fell comfortable that the trolley was not going to roll backwards going up and would remain under control going down. I read that at some point Sprague solved the problem of using the motors as brakes, but slowing a car down this way is tricky. Motors inherently work backward as dynamos, but I think it very unlikely that engines in the power house could absorb and significant reverse current. This was my business. Modern motor controllers do this using the simple strategy that when the DC bus voltage pumps up, a resistor is switched in across the bus. In this way the extracted mechanical energy as the trolley slows down is dumped as heat in the resistor.

        My guess is Sprague put a large (tapped) resistor bank under the car and trolley operator manually switched in several resistance values across the armature winding going downhill. To hold the car on the upside of the hill, say while it was stopped picking up passengers, it would only be necessary to short the armature terminals. To keep the motor functioning while braking or holding the overhead contact voltage would be used to power the motor field windings in the usual manner and which will produce across the armature terminals an EMF proportional to the motor speed.

      Short Wikipedia page on the Richmond system  gives the overhead voltage (450 VDC), car's motors hp rating (two 7.5 hp), weight and # if passengers for largest cars (6,900 lb, 40  seats, 100  passengers), and running speed 7.5 mph (15 mph max). The number of passengers seems high. A specification in the video describes a standard nine bench car.

DC shunt motor
        The basic shunt DC motor is shown below. The armature can be modelled as a voltage source in series with a resistor. The voltage source is the back EMF voltage source, proportional to speed scaled by the flux of the motor. The resistor is the resistance of the armature winding which for good motor efficiency is designed to be low.

        References emphasize that a shunt motor has a relatively flat torque vs speed curve. However, the shunt motor has another interesting and useful feature, which at first appears counterintuitive, the speed does not depend on the applied voltage! If say the input voltage is doubled, then the flux is doubled (assuming the motor iron remains in its linear region), so without changing speed the back EMF is doubled to match the doubled input voltage.

        So how then do you change the speed of the motor? By changing the motor flux using a series of taps of the field coils, which is just what you find in Frank Sprague's trolley patents.

The shunt wound DC motor falls under the category of self excited DC motors,
where the field windings are shunted to, or are connected in parallel to the armature winding of the motor.
The input voltage is applied across both the armature and the field winding,
the field winding of course is wound with many turns of high resistance wire, so the field current is small.
(In the image right the two large coils on the right & left side determine the field magnetic flux
that crosses the two rotor/stator air gaps and returns around the outside steel ring.)
(source --
(source --

        -- A very important and interesting fact about the dc shunt motor, is in its ability to self regulate its speed on application of load to the shaft of the rotor terminals. This essentially means that on switching the motor running condition from no load to loaded, surprisingly there is no considerable change in speed of running, as would be expected in the absence of any speed regulating modifications from outside. (

        -- DC shunt motor has 20% speed variation no load to full load and this can be made flatter by a compound winding in reverse polarity (DC motor thesi)

Notice how flat the Shunt motor speed vs current (load) curve is
(source --
Line surge
        So what happens with the trolley starts up and the 450 VDC is suddenly switched across the motor? Will there be a current surge? Yup. Is there anything Sprague could do with his extra flux windings to eliminate it? I don't think so. You might think that having 1st gear be a very low speed, would minimize the time of the surge, but the problem with this is a motor based on it's magnetic design can only produce so much flux and trying to force it higher just causes the magnetic material (iron) to saturate.

        When the motor is switched across the line, the motor for all practical purposes is fluxed instantaneously. The Back EMF, while scaled by a large number, is still proportional to motor speed, so the current will not drop to the sustained level until the motor comes up to the 1st gear speed. References speak of the trolley starting smoothly, but some of this is probably hot air because intrinsically as the car accelerated there would be a series of jerks as the field windings are switched, but a skilled motorman could probably help smooth out the acceleration by timing the switching.

Line surge limited by inductance?
        However, thinking about it I can see in a trolley there's another factor that (might) limit the size of the surge current spike, the inductance of the distribution system. I don't know if Sprague used capacitors on his high voltage wire to limit voltage excursion, but I suspect not to make the system simple and robust. I know from my lab work that the inductance 'rule of thumb' for a straight piece of wire is 1 uh/meter. Scaling this up (probably not strictly valid) approx 1.5 mh/mile, or 5 mh for three miles of wire. The rise of current across the wiring inductor would be di/dt = 450V/5 mh = (4.5 x 10^2)/(5 x 10^-3) = 0,9 x 10^5 amp/sec = 90,000 A/sec. Unfortunately this is not very helpful. If it took say the trolley 0.1 sec to come up to its first gear speed, the current could rise through the distribution wiring in that time to 9,000 A. Looking beyond the distribution wiring we would see the output inductance of the generators.

        One good reference is a trolley museum in East Haven CT (Shore Line Trolley Museum) where a lot of Sprague material ended up. Sprague had grown up in centrsl MA just north of where the museum is. The passenger terminal of the museum is called Sprague. Apparently Frank Sprague's widow turned over the material she had to the New York Public Library in the 30's (accessible via rare book collection), and the material the Shore Line Trolley got came from Frank Sprague's son.

Sprague's motor patents
        A google search for 'new york public library 'frank sprague" collection' produces several hits. So Sprgue's papers at the library may be searchable online. Here are a list of his 1884/5 patents:

                    295,454         motor                        details motor winding to achieve self regulation
                    315,180         motor                        more winding details
                    315,181         motor + gen              more winding details
                    315,183         train method
                    315,668         motor
                    317,235         electric railroad       shown in video
                    321,147         motor
More on incandescent light bulbs
        Oliver Sacks in his book Uncle Tungsten (his uncle manufactured tungsten light bulbs) adds some interesting perspective to incandescent bulbs. You need really high filament temperatures to produce a lot of light and whiter light. Ideal would be filament temperature close to the sun's surface temperature (5,500C), but this is not practical. For one thing the highest melting temperature of all elements (don't know about alloys) is carbon, which sublimates at 3,600C.

        But how to make a filament out of what is essentially soot? Not easy, but Edison did it using the trick of starting with an organic material (bamboo or cotton thread) and then heating it to carbonize it. Carbon filament bulbs are run in a vacuum. They dominated the market for about thirty years (1882 to 1912). Edison managed to get about 1,200 hours out of his carbon bulbs, partly by running them pretty cool (and red). Carbon filament bulbs are still made today for ornamental lighting.

                             Edison 1889 carbon filament         triple loop carbon filament bulb (modern reproduction)
                    Dr. Hugo Hicks collection                  70w power (light output eq to 25W tungsten)

        Uncle tungsten argued what you really wanted for a filament was metal with a high melting temperature (> 3,000C), since most metals can be drawn into strong thin wires. Only three such metals were known: osmium (#76, melts 3,000C), tantalum (#73, melts 3,000C), and tungsten (#74, melts 3,400C). A few early bulbs (1897) were made from osmium, but osmium was not only extremely rare (& expensive), but couldn't be drawn into thin wire. Tantalum bulbs were "all the rage" until the first world war, but because the resistance of tantalum is low, the filament needed to be a long and spidery (see below, this one is a classic).

tantalum filament bulb (1907 - 1910) (vacuum)
showing details of long spider filament needed for high for resistance
source: kilokat's antique light bulb site

        Wikipedia shows tungsten has an even lower resistance than tantalum (about 2.5 times lower!), so the spidery problem should be worse. However, in pictures of antique tungsten bulbs the spider doesn't look all that bad. Don't know why, maybe the tungsten was alloyed or maybe it was drawn into finer wire. More serious, says Sacks, was that some of it vaporized and quickly coated the inside of the glass darkening it. The darkening problem was reduced by replacing the vacuum with an inert gas (argon). Sacks says this works because the gas molecules exert some sort of back pressure on the filament (reducing its vaporization?).

Early tungsten lamp (100W, 125V, operated here at 30V)
(13 supports for filament spider)

        When the first spidery tungsten filaments were run in argon gas, another problem was revealed: heat loss. Without a vacuum more heat flowed from the spidery filament out to the glass. One fix was to run the gas pressure low, and another fix was to tightly coil the tungsten filament wire and place it in the center as far from the glass as possible. (According to the Virtual Science Museum the wire in a standard 15W bulb tungsten filament (before being coiled) is 3/4th of meter long!)

        Kilokat's antique light bulb site huge collection shows tungsten bulbs came in three types. Very early (circa 1907) tungsten bulb filaments (described by Kilokat as sintered or pressed) were spidery and operated in vacuum. Tungsten bulbs circa 1915 have drawn tungsten filaments (spidery, but less spidery than the picture of the tantalum filament above), and these are also all operated in vacuum. Later tungsten bulbs (circa 1920's, some as early as 1915) have coiled tungsten filaments, and these all operate in gas. Kilokat just specs "gas filled", but Sacks, supported by Wikipedia (Argon), indicates that the gas is argon, which makes sense, because argon is a nobel gas and makes up almost 1% of the earth's atmosphere. (As best as I can figure out, (it's hard to find specs) modern incandescent light bulbs all have coiled tungsten filaments operated in argon.)
         Halogen bulbs have tungsten filaments run in an inert gas (argon?) doped with iodine or bromine (halogens). The halogen gases react with the tungsten causing vaporized tungsten to redeposit on the filament. As a consequence, halogen bulb tungsten filaments are typically run hotter producing more visible light and whiter light.

        I see quite a few 100+ year old carbon filament lamps that still work. This says the vacuum, both the glass and the wire-to-glass seal (for feed wires), is still good after over a century. Amazing. I read the early bulbs uses platinum feed wires, because platinum didn't corrode, the glass adhered well to it and its thermal expansion matched the glass. In 1911 a special (& cheaper) low expansion alloy was developed for feed wires called the Dumet seal. Wikipedia ( 'Glass to metal' seal) says, Dumet-wire is a copper wire with a core of an iron-nickel alloy with a low coefficient of thermal expansion.

Double coiled tungsten filament
        Not only does double coiling (coil within a coil) put a lot of wire and surface area in a small volume (away from the glass), but the long length of small dia wire is necessary to raise the resistance of the tungsten metal high enough so that tungsten bulbs can be run off normal line voltages.

        From the coiling and fine wire size I knew the resistance of tungsten had to be pretty low, but I had never compared it with copper, so I did. It is low, it is about x3 higher than copper, which has the lowest resistance of any common material.

Tungsten filament
Close up view clearly shows coiling, one of the tricks of tungten filaments.
The looped filament of this bulb has a coil within a coil (double coil).
(I scanned this from the tungsten page of a book on the elements. It gave no details of the bulb.)