My related essay on Baker Electric car technology is here: Technology of Baker Electric Car
My related photo essay on the recently closed Wells Auto Museum is here: Tribute to the Wells Auto Museum
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Overview
      Owen Magnetic
Owen Magnetic -- Baker goes high power and high tech in 1916
      Entz double machine
     Slip rings
     Owen Magnetic wiring diagram
     Patent 1,207,732 controller
     What is the hp rating of these machines?
     How high is brush current? How high is the voltage?
     Owen Magnetic links
         Video of Owen Magnetic started and driven
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Appendix -- How the Entz/Owen Magnetic electromagnetic transmission really works,
                                    a circuit model and mathematical analysis
  *** Overview of how Entz transmission works
         Introduction
         How does it work?
         Entz patent search
         Basic structure of Entz's double machine
      * Entz proposes three ways to change speed
         Entz patent 732,062 Power Transmission and Control, filed 1898
         Entz patent 1,164,588, Self Propelled Vehicle, filed 1908
         Entz patent 1,207,732, Motor Vehicle Control, filed 1915
         How does changing EMF ratios change the gearing?
    ** Circuit model of Entz double machine
  *** Gearing equation of Entz transmission derived from double machine circuit model
    ** Details of the model
    ** Field weakening in the gears
         Machine hp rating considerations
         Online reference --- Review of an Owen Magnetic car and 'explanation' of how it works

Overview
        The Baker electric car years of 1900 to 1915 spanned the range when individual electric cars were popular. Because 1,000 lbs of batteries could only deliver 2-3 kw for 2-3 hours, the hp rating of these cars was low (2-4 hp) and their range was limited. Prior to 1900 was the era of commercial electric vehicles: taxis and trucks, many made by Electric Vehicle Company of Hartford Conn, which sold cars under the brand name Columbia. After 1915 there was a short lived period of a few high power, high performance electric drive cars where the battery was replaced by a combustion engine coupled to a dynamo. While this increased the available power by x10 to x20, and solved the range problem too, it produced an expensive and heavy car. The most notable of these high power, electric drive cars was the Owen Magnetic, which had a unique electromagnetic transmission designed by Justus Entz. Walter Baker of Baker Electric acquired the patent rights to Entz drive train in 1912 and guided the Owen Magnetic into production in 1915 where it survived until 1922.

        The Owen Magnetic is an interesting car mostly because of its amazing electromagnetic transmission, which having no gears needed no clutching to shift, and so made driving a high power car easy. It's sometimes called an early hybrid car, but it's not really a hybrid, it has no reserve source of peak energy. Finding no decent description of how its transmission worked, as a retired motor control engineer I set out to understand it. This essay on the Owen Magnetic includes my circuit model and mathematical analysis of its easy shifting electromagnetic transmission.

Owen Magnetic
        Leno owns one of the dozen or so surviving Owen Magnetics, and he describes his 1916 Owen Magnetic as having no mechanical connection of the combustion engine to the wheels (correct). Electric motors provide all the torque to the wheels in this car. It is a USA version of the much earlier European high power electrics with a dynamo powered by a large powerful combustion engine, but the Owen Magnetic had a unique twist. It's dynamo and electric motor formed a double machine that functioned also as an electromagnetic transmission allowing the driver to easily shift gears. The dynamo/electric motor were combined into a single housing that bolted to the combustion engine.

        As I researched this car, curiously the story doubled back to the Baker Electric on which I was working. Walter Baker held some of the key patents used in the Owen Magnetic. While the first Owen Magnetics of 1915 were manufactured in Manhattan (factory on 5th Ave!) in 1916 production was moved to Cleveland and for a couple of years the newly merged Baker and Rauch and Lang electric car company also made the Owen Magnetic.

        As the photo (below) shows the Owen Magnetic was a large car. Curiously for a 1916 car (electric starter was invented in 1912) this combustion engine car clearly has a crank. The Entz 1915 patent shows the crank too (in a figure), but does not discuss it, indicating that it is probably not needed for routine starting, and it fact a video of the Owen Magnetic being started shows the crank is not used. After looking at Entz's patents, I suspect the crank was a fall back needed only if your battery died.

        The Entz's patent on which the Owen Magnetic is based (1,207,732) included an electric starting mode where the dynamo, powered by the car's headlight battery, was used to start the engine. Running current into the dynamo armature and field coils in series operates it as a motor generating a torque between its two coils, but mechanically the dynamo in the Owen Magnetic is an odd beast since both coils are connected to shafts that can rotate. So either the engine crankshaft turned over pretty easily or maybe the driver was advised to apply the brakes while starting the engine to get a good crank and to keep the car from moving. Rereading the key Entz patent it hints that the brake needed to be applied while starting, saying if not applied the car could go backward,. Backward because the dynamo series field winding is reversed in the controller starting position causing a reversal in the direction of the torque. The Baker Electric schematic shows the Baker Electrics also used a reversal of the series field winding of its motor to put the car into reverse.

Owen Magnetic -- Baker goes high power and high tech in 1916
        The Owen Magnetic car, which began production in 1915 under license from Walter Baker, was a high power electric car where the battery was replaced by a combustion engine/generator, but it was most notable for having an electromagnetic transmission. The only car ever to include such a transmission. A manual shift transmission that made driving easy because it shifted without clutching or gear synchronizing.

        Baker Electric car technology seems to have changed little over the 15 years or so of Baker Electric's existence so it came as a huge shock when deep into writing an essay on Baker technology I stumbled onto a high tech, high power electric car that Baker manufactured for a two or three years beginning in 1916. This car was the Owen Magnetic (cool name). In 1912 Walter Baker had bought up the patents on an electromagnetic transmission from its inventor, Justin B. Entz, and he licensed Raymond and Ralph Owen of New York to design the high power Owen Magnetic car with Entz's electromagnetic transmission. Entz's electromagnetic transmission was a tricky double machine that, like the Prius hybrid transmission, featured a power splitter and two parallel power/torque paths. The prototype Own Magnetic car was shown in an auto show in 1914 and began limited production (250 cars) in NYT in 2015. Baker soon absorbed R. M. Owen and moved production of the Owen Magnetic to the newly merged Baker & Rauch and Lang factory in Cleveland.

        The picture below shows the Own Magnetic was a large, impressive and expensive car. Many references note that Enrico Caruso owned one, and now Jay Leno has one too.

        On a quick look it appeared that the Owen Magnetic was similar to the earlier Mercedes and Porsche high power electrics where a high hp gasoline engine/dynamo (generator) replaced the battery, but a deeper look shows the Owen Magnetic was much more high tech. It employed a very tricky, very advanced, double machine that was the work of master motor designer, Justus B. Entz, former chief electrician of the Edison Machine Works, who had worked on the concept for nearly twenty years.

Entz double machine
        A straight forward replacement of the battery in an electric car would employ a generator driven by a combustion engine. The voltage (fixed or variable) from the engine/dynamo would be only electrically coupled to an electric motor that would power the car. In other words there would be two separate rotating shafts, that of the engine/dynamo and of the electric motor, with only an electrical connection between them.

        But the Owen Magnetic is from a control perspective a very different machine. Its generator (armature) and electric motor (armature) are mounted on the same shaft, so they always turn at the same speed, and critically the coupling between the generator and motor is both mechanical (torque) and electrical. From a control perspective this is a highly complex, double machine, and nothing I have seen online explains how it really works. To understand it the patents of Entz would need to be dug out and studied. (which I did) And as the diagram (below) shows, mechanically this integrated double machine 'transmission' of the Owen Magnetic was quite complex.

Owen Magnetic double machine  'transmission',
two machines mounted on same shaft inside a single housing.
Shows crossectional area of the two machines to be exactly the same.
(source -- http://www.hemmings.com/hmn/stories/2011/07/01/hmn_feature23.html)

        The Fountainhead Antique Auto Museum of Fairbanks Alaska owns an Owen Magnetic. They say on their site that 974 were made from 1915 to 1921 and about a dozen are known to survive. They have this simplified diagram (too simplified) of how the Owen double machine worked,.

        Note in the simplified diagram above there is a (possible) clue here as to how the double machine works. The field supply of the dynamo (left) is shown here as a rotating PM magnet. If it was a PM (permanent magnet), that's important. The dynamo field winding is connected to the combustion engine drive shaft, which means it rotates so there is no easy way to supply electricity to it, but a PM fits right in because it makes a magnetic field without requiring wires or power. However, one limitation of a PM field supply is that the strength of the magnetic field is fixed, so that means the back EMF (induced voltage) in the dynamo armature is proportional to the speed of the combustion engine, or in this case the speed of the combustion engine minus the speed of the drive shaft, because once the car starts to move both are rotating. I told you this would be complicated. (This relationship come directly from maxwell's equations that shows the voltage is the derivative of the magnetic field.) The action of the engine when the Owen is accelerating from a dead stop is described this way: engine speed accelerates and then levels off while the car continues to accelerate. (This last sentence is not true, or is at best misleading, and it faked me out for a while. See the Nethercutt video showing the Owen being accelerated.)

        If we put these clues together, one guess is that the initially during an acceleration from a dead stop the engine speed quickly rises to produce the battery voltage (24V) in the dynamo armature winding, and then as the car accelerates the engine speeds up too so as to hold the dynamo output voltage at 24V. From the DC motor's perspective there is a 24V power source available, a combination of a battery and the dynamo DC output voltage, so a conventional switched resistance controller could be used to drive the DC motor. This seemed neat until I worked some numbers. 24V is too low for a high power motor drive, it makes the current far too high. Say the current is 100A, then electrical power levels are dinky, about the same as the classic Baker electric car, just a tiny fraction of the power the large combustion engine can produce [24V x 100A = 2,400 watts or 3.2 hp]. So what gives? Is power from the combustion engine also passing via torque within the dynamo to the drive shaft? (This paragraph is wrong, wrong! Here I was just starting to think about how it might work and was mislead by the previous paragraph, and I had not yet read the patents. As I was beginning to suspect, later confirmed by the patents, the battery is not part of the drive train, used only for starting the car and the headlights.)

        However, to further confuse things I found this (listed by a poster only as from Dykes). This is a more realistic sketch and appears to show the field assembly of the dynamo not as a PM, but a wound coil field (wires are even shown coming out). The associated text says this field assembly is bolted to the combustion engine crank shaft (in place of a flywheel), so it is rotating. So where does the current come from to power this field? There could potentially be another (3rd) machine on the shaft (nope), a PM generator to generate the low power needed for the field, but it doesn't show up in any diagrams I have seen.

Slip rings
       The solution might be slip rings! (yup) When I blow up the cross section  (above), I see the dotted structure in the center is labelled 'collecting rings', and there are two of them. This may be the answer. With two slip rings the battery could provide (relatively low) power needed to put DC current into the dynamo's field windings, and it opens up new control options, because now by inserting resistors the strength of the dynamo field winding could be made adjustable. (update --- Yup, slip rings are right, but they are high current slip rings because Entz's patent makes it clear that his machines are series connected, i.e. the armature and field windings are in series.)

Owen rotating, adjustable machine #1 (dynamos) field assembly

        While I haven't worked through the details (or yet read any patents), one thought is that for the dynamo machine to directly torque its armature (and drive shaft) the dynamo armature windings (via brushes) would be shorted. (correct in top gear) This is interesting (if it works!). It would be the DC version of an induction motor. There would be a 'slip' frequency, the word 'slip' does appear in some of the associated text, meaning the motor crank shaft would be turning just slightly faster than the drive shaft. A high current would be induced in a shorted dynamo armature winding that would oppose (and load) the combustion engine. But as usual I see a  problem. The current can't be too high in the dynamo armature, because this current has to exit the armature via brushes, and the size of the brushes limits how high the current can be. It may still work, but unlike an AC induction motor where the armature is wound with a single (very high current) turn, this DC variant of an induction motor would need a lot of turns on its armature winding to keep the brush current down. The result of this is likely to be that the inductance of the armature will make the 'slip' high, resulting in sort of a soft, springy connection between crank shaft speed and drive shaft speed.

Owen Magnetic wiring diagram
        I found a wiring diagram of a 1917 Owens and this gives more clues, but unfortunately in this wiring diagram the windings of the two machines are not broken out.

        In the upper right corner we see an old friend, a switched resistance controller used in nearly all the (classic) electric cars, so this is probably how the DC motor is controlled. The range on the embedded amp meters is shown as 150A max, so our guess of 100A for the operating current (initially) looks reasonable. Here the battery voltage is a little higher at 34V, but that's still less than 5 hp. However, it might be that current is higher, an ammeter shunt can be designed to divide the current with only a fraction going to the meter, still operation at such a low voltage would make the current to be handled by the controller very high. Unfortunately the windings of the dynamo and motor (within the box left marked 'Electric Transmission') are not detailed. A basic system would need just six contacts: 2 for dynamo armature (via brushes) output, 2 for motor armature (via brushes) input and 2 for motor field winding, but the figure shows ten contacts, six of which are hooked to the switched resistance controller.

Patent 1,207,732 controller
        Compare the Owen controller in upper right corner (above) to the controller in Entz's 1915 patent, 1,207,732 (below). They are not exactly the same, but they are very close. Note especially the unusual shape of the terminals to the resistor taps, which below are on the right and above are on the left. Also resistors (13, 14) for field weakening are nearly identical in both figures. This is a (very) strong clue that the Owen Magnetic transmission and controller are probably based on the Entz's patent 1,207,732, filed 1915.

Controller figure from Entz Motor Vehicle Control patent, # 1,207,732, filed 1915.
-- resistor 14 weakens field of machine #1 (dynamo) in 1st gear
-- multi-tapped resistor 13 weakens field of  machine #2 (motor) in higher gears

        A technical description (here) of the Owen transmission says: "On high-speed position the motor plays no part in the transmission of power, but is used as a charging generator for the storage battery, which is used for cranking the engine and the electric lights." This may be the solution to the power problem. The implication is that the so-called dynamo in some modes works as a motor, and it may very well be that much of the power from combustion engine is not passed electrically via the motor, but is passed mechanically, i.e. the dynamo is directly torquing the shaft [Power = torque x speed]. (yup) This Owens architecture has some similarity to the the (continuous) transmissions in some modern hybrids, which adjust gear ratio by adjusting power/torque in two parallel paths. One path is mechanically direct from the dynamo to the drive shaft. The dynamo is operated such that it puts a load on the combustion engine and the resulting current in the dynamo (armature) winding torques the drive shaft, so via [P = torque x speed] power is passed mechanically to the wheels of the car. The other path operates the dynamo to bleed electrical power from its brushes, out to the controller and back to the motor, which then also torques the drive shaft.

How high is brush current? How high is the voltage?
       A related potential problem I see is brush current. Some references hint the voltage fed from the dynamo to the motor is quite low (24V) to match the battery and to allow battery recharge. The problem is even if the brush current is as high as 100A, this is power flow to the motor of only 2.4 kw, which is less than the 3.5 hp of the dinky Baker electric car.

        But the magnetic transmission in the Owen is hooked up to a large combustion engine, 38 hp in one reference, and it has to pass that power, otherwise there is no advantage in putting such a large engine in the car. In electrical terms 38 hp is roughly 30 kw, which can be achieved by [300V x 100A, or 200V x 150A, or 100V x 300A, or 50V x 600A]. So a big question is, 'How high a current could the brushes and windings of the machines handle?' The only way to keep the current down to 100A would be to let the voltage rise to 300, obviously far, far higher than the battery voltage. (The voltage here being the sum of the internal EMF of the dynamo and the voltage across its brushes.) Note even in so-called 'lockup' of top gear, where the dynamo brushes are shorted, the brushes still have to handle the dynamo winding current of 100A and 300V has to internally drop across the dynamo winding @ 30 kw. Maybe these machines are just so big that high brush and winding currents and high voltages are no problem. I see no mention of this a potential problem in the patents.

Owen Magnetic links
        Below is about as good a technical writeup on the Own Magnetic transmission as can be found. However, like all the descriptions I have seen online of how the Owen Magnetic transmission (supposedly) works, it really doesn't describe how it works! Sure it functionally says which machine is torquing in the various gears, but why that causes the speed ratio to vary is never explained.

        I set out to solve this problem and in the Appendix can be found my circuit model and the gearing equation derived from it. My analysis shows the gearing ratio is a function of the ratios of the kt's (field scaling constants) of the two machines. This is consistent with Entz's patent for the Owen Magnetic where his various speeds are all achieved by various field weakening of the two machines.

         http://www.edisontechcenter.org/ElectricCars.html#owen

        It says at start 100% of the torque comes from the motor. (I think this is wrong.) Presumably as the speed of the car rises the fraction of the combustion engine traction power (or maybe it's fraction of torque) diverted through the electrical/motor pathway gets smaller and smaller, the gearing ratio walking down, until at some speed it hits one and this is 'lock up'. In 'lock up' the motor ideally has has no current and provides no torque, all the torque to drive the car would be coming from the dynamo machine. This makes some sense.

        At (true) lockup all the traction power has to come mechanically through the dynamo (slip speed is zero), so the conclusion I come to is these electrical machines must be quite large. If it takes say 20 hp for the car to cruise at its max speed, then the dynamo must be rated at 20 hp, because it has to pass all this power since the motor is providing no torque. And likely the dynamo (and by extension the motor too) has to have a transient rating equal to the combustion engine power rating for use during the peak of the acceleration curve. Maybe this is why the cost and weight of the car is so high.

        Somewhere in this structure there must be a low power control input allowing the driver on his steering wheel to adjust the power split. I have seen no detailed description of how the Owen Magnetic is driven. Is the driver controlling both the combustion engine speed, or is he just controlling the car's torque/speed with the split variable and the combustion engine speed adjust automatically. (Ans I think is both when the car is accelerated, and at speed just the throttle.) One brief description I found seem to imply the latter. (However, this conflicts with what I find in Entz patents. From the driver's perspective the Entz magnetic transmission would work pretty much like a modern manual transmission, so the Owen could probably be accelerated like a modern car using the throttle and controller lever for gear shifting.)

        An efficiency number for the transmission of 93% is throw out without giving the conditions. Presumably this is the most efficient number and would probably be for so-called 'lock up'. I think this is a believable number for 'lock up'. A modern motor can pass high power like this with a loss of only 1%-2%, but electric machines a century ago were far less efficient.
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         The link below is a history of Rauch and Lang that includes material on the Owen Magnetic, which the recently merged Baker and Rauch and Lang began to manufacture in 1916. According to this source the drive train for the Owen Magnetic was made in the former Baker plant and its coachwork in the former Rauch and Lang plant both located in Cleveland, Ohio.

         http://www.coachbuilt.com/bui/b/baker_raulang/baker_raulang.htm
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Video of Owen Magnetic started and driven
        Here's a very interesting 30 min Vimeo video from the Nethercutt Museum, Sylmar CA. They have a huge collection of old cars (240 cars, free admission, Sylmar CA is 20 miles north of Hollywood). The video includes a drive in a 1914 Rauch and Lang electric followed by a drive in a 1921 Owen Magnetic.

http://www.bing.com/videos/search?q=Vintage%20electric%20cars&qs=n&form=QBVR&pq=vintage%20electric%20cars&sc=8-21&sp=-1&sk=#view=detail&mid=AB1666A26FDBE905444CAB1666A26FDBE905444C

        Curator says, "Owen Magnetic is controlled by one lever on steering column", so this tells us where controller lever is located. Yikes not only does this museum have a restored Owen Magnetic they have a cut away chassis of the Owen with a view into the transmission! This gives some perspective as to the size of the magnetics. Video taken inside the Owen shows it being started and driven. The car has a crank, but we see it started electrically by selecting start on the controller. "Controller speeds control the magnetism and we control the speed with the accelerator on floor." Curator says while driving Owen in top gear "it will do probably 65 mph easily". As he accelerated he goes through 5 forward gears: 1,2,3,4, high gear. The comments of the curator very accurate, except (to please host) he starts off by describing the Owen Magnetic as a 'hybrid" (it's not), but soon corrects saying the car is more about the "Entz transmission" making the car easy to control than being a hybrid.

Owen Magnetic images from video:

Introduction
        Almost exactly 100 years ago (1915) the Owen Magnetic car with its wonderful and unusual electromagnetic transmission came onto the market. This efficient, gearless transmission was totally unique in the history of cars. With no gears no clutching was required, so this transmission made a high power car of the day easier to drive as it allowed allowed manual shifting through multiple gears just by moving a lever on the steering column. In the days before electronics it was built from just two DC machines, a few resistors and a switch controller that reconfigured the wiring to change the gearing ratio. After reading the key patents of its designer, Justus B. Entz, making a circuit model and doing some mathematical analysis, I now have a good understanding of the basic concepts on which the Entz transmission is built.

*** Overview of how Entz transmission works
        Several sites on the web purport to explain how the Entz transmission works, but the one's I've found do little more than say which of the two machines is providing the most torque, and this explains nothing. My purpose in this appendix is to provide a real explanation of how the Entz transmission works by using a circuit model, a derived gearing equation, and mathematical analysis. But before diving into the details an overview is useful.

        Entz starts with an unusual DC machine. His first machine has two independent shafts each connected to a winding, meaning both windings can rotate. Unlike standard DC motor/dynamos, which have two 'ports', this machine has three. Power fed into one shaft from the engine and can split with some (or all) of it coming out the second shaft to the drive shaft as mechanical work [torque x speed], and the balance coming out of the brushes as electrical power [i x v]. In top gear with the brushes shorted no electrical power comes out, so all the engine power coming in comes out as mechanical work to the drive shaft. In top gear machine #1 alone powers the car providing 100% of the running torque.

        To double the torque Entz adds a second machine, similar in size and windings to the first machine, that he powered from voltage tapped off a break in the series connection of the windings of the first machine (see sketch below). This second machine is a standard DC motor with a single shaft that runs through the armature and sticks out both sides. Connecting its single shaft to the first machine on one side and to the drive shaft on the other side allows this second machine to add torque to the drive shaft (or not). According to Entz's patent the double torque configuration is 2nd gear. By field weakening machine #2 with a tapped resistor switched across its field winding he reduces its torque in steps providing intermediate total torque levels for gears 3, 4, 5.

        Here's my sketch of the two machines in Entz's transmission showing how they are physically and (functionally) electrically connected. The three top windings all rotate at the speed of the shaft that ends at the winding [armature and field of machine #1] or passes through the winding [armature of machine #2]. Only the bottom winding [field of machine #2] does not rotate.

        To get higher torque for 1st gear Entz removes the field weakening from the second machine and switches in a (single) field weakening resistor across the first machine, my guess is a 3:1 field reduction. A weaker field in the first machine forces the generated voltage down and the current up. This is a key 'trick'. A higher current from the first machine into the second machine increases second machine's torque by the square of the current (likely tripling it using the motor's 300% overload rating). Combined with the torque from the first machine, which remains unchanged since its field is weakened, the total torque on the drive shaft is now twice as high as 2nd gear and four times as high as top gear. This gives the transmission a 4:1 range and provides a good, high torque first gear for the car.

        The Owen/Entz transmission has four basic configurations that it uses for its six forward gears (seven gears in the key Entz patent). Let's look at these four configurations:

        1) Top gear (6th gear in car) --- Ratio 1:1 (nom), drive shaft speed runs at approx the same speed as engine crankshaft speed, sometimes called 'lockup' but in reality there is a small slip (frequency) between them (80 rpm in one reference) since no electromagnetic machine is 100% efficient. In top gear the car runs only on machine #1, which is mechanically configured in an usual way with the field winding spun by the engine and the armature attached to the drive shaft.

        2) 5th to 3rd gear (in car) --- Ratio 1:(1+ to 2-), two machines are active with machine #2 running at a fraction of torque of machine #1. The armature of machine #2 is also connected to the drive shaft and powered by electrical power tapped off machine #1. In 5th gear a small increase in torque is provided by switching in machine #2 heavily field weakened, then as gearing drops to 4th and 3rd, field weakening of machine #2 is relaxed in steps to increase its torque.

        3) 2nd gear --- Ratio 1:2, two machines are active and torque equally, neither field weakened. Since the two machines are similar and operate at the same current, the torque in 2nd gear is double the torque in top gear. Conservation of energy insures that doubling the torque halves the available speed. From a circuit point of view speed drops in half because the EMF induced in machine #1 by the engine speed is balanced by two counterEMF in series from the drive shaft speed.

        4) 1st gear --- Ratio 1:4, two machines are active and with machine #2 running at three times the torque of machine #1. ('Three' times is my guess since there are no numbers in the Entz patent.) Field weakening machine #1 reduces its ability to generate voltage (counterEMF) causing its electoral power to machine #2 to shift to lower voltage and higher current. Current higher by x1.73 to machine #2 triples its torque (both machines are series connected), likely using the machine's 300% overload rating, while the torque of machine #1 remains constant. The result is 1st gear with twice the total torque of 2nd gear and four times the total torque of top gear giving the transmission a torque/speed ratio of 4:1. Conservation of energy insures an inverse relationship between torque and speed in all gears.

        No transmission is true in most modern pure electric cars of today. The prototype of the first Tesla Roadster, a high performance electric car, started out with a two speed transmission, but it proved unreliable and improvements in motor control and in the motors themselves allowed it to be removed. Top speeds substantially in excess of 100 mph are now accommodated by running the motors up to very high speeds, 16,000 rpm in a Tesla Model S.

        After nearly 20 years of thinking and patenting several iterations, Justus Entz came up with a practical way to change gearing in the Own Magnetic car without mechanical gears. Entz called it his magnetic transmission. Actually Entz's invention was much more than a transmission. Entz managed to combine in his double machine control of the car's speed/torque along with the three power functions needed by a large electric car

                    a) Dynamo --- mechanical to electrical conversion of the engine power
                    b) Motor --- torquing of the wheels
                    c) Transmission --- different gearings between the engine speed and wheel speed

For example, his first machine, which he called 'dynamo', not only had a dynamo function (loading the engine), but in top gear functioned as the electric motor of the car fully powering the wheels while in lower gears functioned as part of the transmission efficiently providing partial wheel torque at a lower drive shaft speed than the engine speed.

How does it work?
        I looked and looked online for an analysis of how Entz's tricky double-machine electromagnetic transmission worked, but could find little other than a physical descriptions and unsupported statements about which machine was torquing in which mode. A Univ of Maine student had written a booklet on it in 1916, but it is not available online even from the Univ of Maine. I'm a retired motor control engineer, and this double machine intrigued me, so I determined to figure it out.

        It was quickly apparent that Entz transmission's basic architecture bears at least some resemblance to the continuously variable transmission in the Prius hybrid (and most hybrids on the market today) in that his first stage splits the power from the engine creating two parallel path for power/torque flow to the wheels (see below). My initial guess was the Entz transmission, like the Prius transmission, adjusted the gear ratio by changing ratio of power/torque of the two paths. However, decoding exactly how Entz's double machine (dynamo + motor) accomplished this was not so obvious. This thing was magnetically complex and unlike anything I had ever seen, and it took me some time to get a handle on what he was doing.

Entz patent search
       After searching the web and coming up with very little, I began searching Justus B. Entz's patents. This guy had a lot of patents issued over about fifty years (1888 to 1940) on all aspects of electric cars (and train controls too), not just the magnetic transmission, but on many aspects of a car including mechanical clutches and storage batteries. One references said he had over 70 patents, my search engines pulled up 30-40 patents. Only a few of his many patents detailed his magnetic transmission variations, so it was a slow process, opening patent after patent to look at the figures. In his early 20's Entz had been a motor/dynamo designer working for Edison, and Edison's papers at Rudgers have records of Entz licensing to Edison in 1890 his patents on his designs for the traditional one dollar. By 1898 Entz, now working for a company that was making electrical taxies had come up with the basic structure of his double machine for control of an electric car. Over the next 25 years, even as late at the early 1920s when the Own Magnetic and virtually all electric cars were dead, he continued to tweak it, but the basic structure from 1898 remained the core.

        The three key USA Entz patents for the magnetic transmission seem to be:

            732,062       filed:  1898           Power Transmission and Control             patent granted: 1903
         1,164,588       filed:  1908           Self Propelled Vehicle                             patent granted: 1915
         1,207,732       filed:  1915           Motor Vehicle Control                             patent granted: 1916

        The text of these patents contain long descriptions of the operation of the two magnetic machines in terms of counterEMF, but no control equations and no actual numbers (no resistances, amps, volts or watts). Most helpfully, however, each of these patents contains a figure showing the interconnect of the field and armature windings for both machines, along with associated resistances and/or batteries, for each of the forward gears (reverse gears too). A study of these figures reveals how the 'kv's of the two machines are adjusted (qualitatively) in each of the speeds, and critically the 'kv' adjustment is done differently in each of the patents.

Basic structure of Entz's double machine
        Entz used two DC machines connected between the engine and drive shaft (wheels). While the patents didn't specify the relative size of the two machines in later commercial implementations, very likely the Owen Magnetic, the two machines in cross-section drawings are shown to be same size. The first machine to which the crankshaft of the engine was connected Entz generally called the 'dynamo', but this name is misleading as it functioned also as a motor. The unusual thing about the first machine is that its field supply (field magnets) is connected to the crankshaft of the combustion engine and rotates at engine speed (say 1,000 to 3,000 RPM). As the field of this machine is set up by an electromagnet, slip rings are required to bring the field winding out so it can be excited (and controlled). The armature of this first machine is mounted on the drive shaft, and its armature circuit (via brushes) is accessible externally. Also mounted on the drive shaft is the armature of a second machine that Entz generally called the "motor". Its field winding is fixed to the frame of the car in a normal manner. Electrically the armatures of the two machines were wired in series, meaning the current from the first machine armature via its brushes is fed into the second machine via its brushes. This is a very unusual structure and initially I had no idea how to think about it or model it.

Entz proposes three ways to change speed
        The patents disclose that the basic way of changing the speed of the drive shaft, i.e. the 'gearing' of the transmission, is to change the ratio of the counterEMFs of the two armatures. Over the years in three different patents Entz shows three ways to do this as detailed below. Entz was associated with Electric Vehicle Company, in 1907 he was a VP,  that in the 1890s manufactured electric taxis and an early electric car (Columbia). A detailed history of the Electric Vehicle Company hints that they may have built prototype cars based on Entz's patents of 1898 and 1908. This is consistent with at least his 1908 patent, which looks like it is describing a real car because it includes lots of detail drawings of the drive train components. To show his thinking I will describe his three key transmission patents in the order in which they were filed. It is his last transmission patent, filed 1915, that is the basis for the Owen Magnetic transmission and controller.

Entz patent 732,062 Power Transmission and Control, filed 1898
        His first transmission patent of 1898 (filing date) adjusts the armature EMFs by inserting storage battery(s) in series with the armature windings, so the batteries are carrying the full armature current. The same batteries also exit the fields of the machines at a fixed level. This is high impedance field winding that does not draw much current from the battery. He shows five forward gears (1st to 5th). The lowest gear (1st gear) inserts two batteries in series, 2nd gear one battery, 3rd gear no battery, 4th gear one battery flipped in polarity and 5th gear two batteries in series flipped in polarity.

        While in a later patent he claims to have had great success with this approach, it's clear to me (and I guess later to him) it was not usable in a commercial electric car. The reason is that in 1st and 2nd gear the (high) armature is charging the batteries and worse while cruising along in 4th and 5th gear the batteries are continually discharging. Clearly having batteries whose state of charge or discharge depends on the type of driving being done is not going to work for a practical car. The 1898 approach may have been useful as a proof of principle, but clearly some other way was needed  to change the machines EMFs if this transmission architecture was to be practical.

Entz patent 1,164,588, Self Propelled Vehicle, filed 1908
        In a patent of 1908, ten years after the first transmission patent and seven years before the introduction of the Owen Magnetic car, Entz discloses a new way to adjust the EMFs without using storage batteries. His second machine (C, motor) now has two windings on its armature, which at lower speeds he connects in series and at higher speeds connects in parallel. Also he is using a small battery, which he calls an 'exciter' battery, and switched resistances to changes the field strength of the first machine (dynamo). Now both machines are series connected, the high current of the armature exciting the field. He combines the split motor windings with various levels of field weakenings of the dynamo.

        While I don't believe he mentions it in his patent, clearly having two windings on the motor armature, to allow the motor EMF to be changed by a factor of two (by configuring the armature windings in series or parallel), complicates the design of the second machine because two sets of brushes are needed instead of one. In his next transmission patent (below) the split winding of the motor is gone.

Entz patent 1,207,732, Motor Vehicle Control, filed 1915
       In a patent filed in 1915, just about the time of the introduction of the Owen Magnetic, Entz discloses yet anther way adjusting the EMFs. Gone is the complication of a dual winding on the second machine, both machines now have a single armature winding (via a single pair of brushes). Also gone is the exciter battery (N) used to help excite the fields. Here Entz has added a couple of more forward speeds, including 'lockup' at top speed. The important point is that adjustments of the EMFs (via adjustment of kvs (kts)) are now done almost entirely by use of resistive bleeds across the field windings of the both machines, which remain series connected.

        Notice at all speeds (except 7th) the armatures of both machines are wired in series; they run at same current. Since [torque =  kt x amps], the torque contributions from the two machines to the drive shaft is thus proportional to their respective kts. The kt of the first machine ('dynamo') cannot be set to zero otherwise there would be no dynamo action, i.e. no electrical output to drive the second machine, hence it is not correct (as some references state) that all the car's starting torque in 1st speed comes from the motor, both machines contribute torque when the car is accelerated from rest.

        A resistor switched across the field winding of a DC machine lowers the current in the field winding by resistive divider action. A weaker field means a lower EMF (due to lower 'kv') for the same speed and means a lower torque (due to lower 'kt') for the same current. Resistive field weakening was widely used in electrical trains of the time for speed control.

        So which approach is used in the actual Own Magnetic car, that of 1908 or 1915?  Don't know for sure, but I suspect strongly it is the latter since it's cleaner and reflects nearly 20 years of thinking about the problem by Entz. Another hint it is 1915 is that the controller shorting pattern shown in an Owen Magnetic wiring diagram looks an awfully lot like the controller Entz included in his 1915 patent.

        Entz has many other patents where he tweaks the transmission structure, but his objectives in these patents was to improve or simplify other vehicle modes like starting, battery charging, etc. In particular Entz struggled to find a way to electrically reverse the speed/torque of his double machine architecture. The crosssection figure of the double machine (above), which is likely from the Owen Magnetic car, shows that by the time of the car's design he had not succeeded, since it includes reversing gears. Below is a figure from Entz's 1,207,732 showing the battery charging and engine starting modes of the controller.

How does changing EMF ratios change the gearing?
        How does changing EMF ratios change the gearing? This is the 64 dollar question. When I first started to write this, I didn't have a simple intuitive explanation, but I knew the equation that fell out of my double machine model showed that changing the ratio of kvs of the two machines changed the gearing. One key, of course, is to remember that changing 'kv' to change EMF means 'kt' is also changed, because 'kv' and 'kt' are the same constant just expressed in different units. A high 'kv' not only increases the EMF for a given speed, but it also increases the torque for a given current. Since the armatures are nearly always wired in series, they run at the same current. Thus they contribute torque in proportion to their individual kvs (kts), the machine with higher 'kt' making the largest contribution to the torque on the drive shaft.

Parallel paths
       A key idea of Entz magnetic transmission is there are two parallel torque/power paths from the engine to the drive shaft with different and adjustable torque constants ('kt'). The torque on the drive shaft is the sum of the torque from the dynamo and motor. Via switching in/out of field weakening resistors,  and potentially other means, 'kt' (torque/amp) of both machines is adjustable to create the multiple 'gears' for the car. The equation (derived below) shows it is the ratio of the kts of the two machines, i.e. [kt dynamo/(kt dynamo + kt motor)], that scales the engine speed to the drive shaft speed. To obtain a large step down in speed, and corresponding increase in torque, for 1st gear to start the car from rest the kt of the motor has to be set much larger than the kt of the dynamo (maybe x3 higher?), so that means motor does produce the bulk of the torque in 1st gear.

** Somewhat intuitive way to explain how it works
        Upon rereading this essay I saw another way to look at what Entz is doing. By adding a second machine on the drive shaft and powering it efficiently from electrical power tapped off the dynamo, he can boost the torque applied to the drive shaft. The key here is that the torque boost is accomplished by this architecture in an efficient manner. Motors even at the time were quite efficient. There is no big power loss resistor added. So if in 1st gear torque can be boosted in an efficient manner, basic physics [power = torque x speed] says speed must drop. Thus it's a transmission, the more the torque is boosted, the lower must be the rotation speed because power cannot just materialize out of thin air. Maybe not entirely intuitive, but familiar to anyone who has studied mechanics in freshman physics, the same inverse relation between force and speed pops up again and again in levers and pulleys.

Cruising in top gear
       In the limit at top speed (7th gear in the patent, 6th gear in the car) the motor can be shut down altogether so all the power from the engine comes out of the dynamo mechanically. In other words cruising along in the Owen Magnetic's top gear means the first machine (so-called 'dynamo') is alone powering the car. From power considerations this must mean in top gear the drive shaft speed is nearly the same as the engine speed (1,000 to 3,000 rpm nominal), and as engine speed is varied the speed of the car is varied, meaning it functions like a manual transmission in a modern car.

Power rating of the magnetics
        There is little doubt that in top gear all the torque applied to the drive shaft must be generated by the first machine (dynamo). So my first thought is an Owen with a 38 hp engine needed electrical machines rated at 38 hp too. But clearly this is wrong. First, it would make the double machine of the Owen Magnetic far too large, something like 78 hp or x22 higher than the 3.5 hp of a Baker electric motor! And it does not look anywhere near that large in a museum cutaway. Like most cars the high hp of the combustion engine is used transiently for acceleration. The power the engine puts out on average (on level ground) is just the power required to overcome wind resistance and rolling resistance. These old cars did not go that fast, in the Nethercutt museum drive the driver says the Owen could maybe do 60 mph,  so the continuous power the machines have to handle is far less than the 38 hp of the engine.

'kv' and 'kt' are the same parameter
        Entz's patents always speak of counterEMF. The EMF scaling constant is normally labelled 'kv' as in [EMF = kv x speed], but a related motor parameter is the (scaling) torque constant, 'kt' as in [Torque = kt x current]. It might appear that kv and kt are totally different parameters, but in fact they are the same parameter just expressed in different units. This can be proven by equating the electrical power into EMF in a motor model [power = amps x EMF] to the output power in mechanical terms [power = torque x speed]. Substitute [EMF = 'kv' x speed] and [torque = 'kt' x amps] and you find 'speed' and 'amps' cancel leaving 'kt' = 'kv'.

        So for starting the car from rest, where high torque is needed, in the Entz transmission this is obtained by configuring the motor to have a higher kv, best thought of as a higher kt, than the dynamo, while at the same time the dynamo kv (and kt) may be reduced (but not to zero). Since the same armature current flows in both machines these adjustments to their kts, cause the bulk of the torque at start to come from the motor. Under constraints of fixed power a general relationship exists between power and torque [Power = Torque x Speed], which is that drive shaft torque and speed must be inversely related. As speed of the drive shaft is driven down the available torque must go up, or perhaps more intuitively, as the torque applied to the drive shaft is boosted its rotation speed must drop.

        Articles that claim at start 100% of the torque comes from the motor are wrong, and similarly at high speed the transmission does not really lock up. Articles that say this are also wrong (or oversimplifying). The dynamic range of the Entz transmission is wide enough that in one gear the torque from the motor can be totally eliminated. This is done by switching in a short across dynamo electrical outputs, which effectively removes the motor from the circuit (see top speeds in the patent filings of 1908 and 1915).

        It is impossible to fully kill the torque from the dynamo at start for the following reason. The current in the motor armature is flowing in the dynamo armature too so the only way to kill torque from the dynamo would be to kill its kt. It might seen that this could be done by opening its rotating field winding which is brought outside via slip rings, but then there is no load on the engine, so this doesn't work. I do know Entz does not show opening or fully shorting the dynamo field winding in any of his patents, and there is probably a reason for this (it doesn't work!), but in 1915 he does show field weakening the dynamo field to an (unknown) extent. So at start with both armatures carrying the same high current, and with kt of the dynamo potentially reduced but likely not killed, the dynamo must be contributing some torque at start.

*** Circuit model of Entz double machine
        Entz's transmission is all about controlling the car's speed and the speed ratio of the transmission's six 'gears', yet Entz's transmission patents contain not a single equation or any quantitative information. Nor does he include any circuit models. I think this is (partly) understandable because prior to the days of electronics what circuit theory could do was limited. However, I know from studying multiplex telegraph patents, which preceded this work by decades, that circuit theory was in use at the time. However, Entz does explain in long sentences and in considerable detail his view of how the transmission works. And his perspective focuses on the EMF of the motors, which is understandable because these were DC motor that in the days before electronics were driven by voltages.

        One of the advantages of a circuit model is that it explains (at least to a circuit designer!) much more clearly and concisely than a long wordy description how a circuit works. A further advantage, and a big advantage it is here, is that with a model in hand (by inspection) an equation can be written for the gearing, the  drive shaft speed as a function of the engine speed. An equation can also be written for the current, and this gives the torque from the machines as [torque = 'kt' x current], where 'kt' is really 'kv' (EMF constant) just written in different units. Given that these machines are controlled by voltages, the natural model to adopt for a winding is a [back EMF + resistor], where the back EMF (or shorthand EMF) is a voltage source equal to the speed of rotation of the magnetic field times a scaling constant, usually called 'kv'. 'kv' is in fact an independent variable, which since it is proportional to the strength of the motor field, is subject to manipulation and Entz in his third transmission patent exploits this for control of the transmission.

        My circuit model of the Entz/Owen Magnetic (double machine) electromagnetic transmission is below, and by inspection it leads to a formula for the gearing ratio (wsh/wen) that is a function of the ratio of the kv (kt) of the two machines.

*** Gearing equation of Entz transmission derived from double machine circuit model
        My circuit model notes (above) have the gearing equation in terms of kv, and its alternate form in terms of kt is below.
 

        Simplifying a little by ignoring the voltage drop across the winding resistances, by inspection an equation can be written from the model; the left voltage source ((kv1 x engine speed), which models power in from the engine, must equal the sum of the other two voltage sources, which model mechanical power delivered to the drive shaft by the dynamo and the motor. Since both of these armatures are mounted on the same shaft, both of these voltage sources are proportional to drive shaft speed, but being separate machines they have the own individual scaling constants dependent of the strength of their respective fields. Solving this equation for drive shaft speed as a function of engine speed we get the equation in the figure above. This is the key equation of the Entz transmission and shows that it is the ratio of field strength of the two machines that controls the gearing of the transmission. The field strength of the two machines, of course, can be manipulated with switched in resistors (field weakening resistors) thus providing a mechanism for the transmission to be 'shifted'.

        The expression in brackets in the equation is the gearing, the ratio between drive shaft speed and engine speed. It can be seen that the car's speed is theoretically adjustable by varying either the speed of the engine or the scaling constants (kv or kt) of the magnetic fields of the dynamo and motor, or both. But in a car it makes sense to set up the bracket expression for each of the car's 'gears', which is what Entz does, and use the engine throttle for most speed control. This, of course, is just how a car of today with a manual transmission is accelerated. (update --- In a video of an Owen Magnetic at Nethercutt Museum being driven this is just what the museum curator says as he accelerates the Own up through the gears.)

        The voltage model in the figure (above) is a good fit for the first machine (dynamo) because an input voltage source can be written as the (known) speed of the engine scaled by kv1 of the dynamo. This power flows out of twoFs of the dynamo both of can easily be modelled as voltages too. The back EMF voltage source of the dynamo times current represents mechanical power  [torque x speed] delivered directly as torque to the drive shaft. Note both of the voltage sources in the dynamo, power in from the engine rotation and mechanical power out to the drive shaft rotation, being in the same machine have the same the scaling voltage constant (kv1). The other power flow out of the dynamo is electrical, current times a measurable voltage between the dynamo brushes to the motor armature. The motor voltage is modelled in the standard way as its [back EMF + R x i]. The motor being a different machine with its own field winding has its own voltage scaling constant (kv2). This is important.

        This resulting voltage model of the double machine with the two armature windings in series is very simple, just three voltage sources plus winding resistances, which since all are in series reduces to a nearly trivial net voltage across a resistor. The sum of the voltage sources divided by the total resistance yields the current, and the current via the individual kts of the motor and dynamo yield the toque (and power) each is delivering to the drive shaft. Neat...

** Details of the model
       Ok, we have a formula for gearing, but for a more complete understanding of the Entz transmission we need to look in detail at the current, voltage, torque and power of the model components in different gears. This is also an important check of the model I derived. If the model is right, everything will be consistent, but if it wrong, we will likely find inconsistencies.

        In the table below top gear is taken as the baseline with 'shaft speed' and 'Torque total' assigned a normalized value of 1. It is critical if the Entz is be a real transmission that the load on the engine not vary as the transmission is shifted through it gears. For gears where max speed is lowered by '(1/n)', the (total) torque applied to the drive shaft must increase by 'n' to keep power out of the transmission constant [P = T x speed], and this is just what we find. Table below shows 1st gear has three times the torque of top gear at 1/3rd the speed. The second table shows deepening the dynamo field weakening widens the dynamic range of the transmission
 

Deeper dynamo field weakening
        1st gear in table above is for (my assumed) 2:1 split in the field current of the dynamo (meaning 1/2 of the current flows in the field winding). The pattern of the 1st gear results in table 1 make it relatively easy to extend it for deeper levels of dynamo field weakening (3:1 and 4:1 splits), which widen the range of the transmission driving 1st gear torque higher and corresponding max shaft speed lower. A study of these two tables reveals a lot about how field weakening works in Entz's double machine. And it provides good insights on how the transmission really works, meaning how it is able to increase the torque at lower gear ratios. Notice Tmot (motor torque) tracks the dynamo field weakening current split, for example a 3:1 current split in dynamo field weakening increases the motor torque x3 (relative to 2nd gear where there is no field weakening).
 

** Field weakening in the gears
        From Entz key patent (#1,207,732) for the Owen Magnetic, 'Motor Vehicle Control' filed 1915, the patent figure (below) shows the double machine wiring in the seven forward gears and how field weakening resistors 13 and 14 are employed.

        Starting in top gear as the gearing drops field weakening in the motor becomes lighter and the torque of the motor increases until at 2nd gear, where there is no field weakening in the motor or dynamo, the torque of the motor has increased to the level of the dynamo the current remaining constant. In other words in 2nd gear by connecting a second machine on the drive shaft and powering it from electrical power tapped off the dynamo doubles the drive shaft torque (halves max speed) because both machines operated identically at the same current and field strength.

        To get higher levels of torque for a 1st gear Entz shifts to field weakening the dynamo. This shifts the electrical power from the dynamo to higher current and lower voltage. It's current in a motor that makes torque, and the numbers in the table show the torque of the motor tracks the field current split going up to 2 for 2:1, 3 for 3:1, 4 for 4:1; the current rising as the square root of the motor torque. But the cost of the higher 1st gear torque is higher current in the brushes, slip rings and heating in the windings of both machines, which goes as the square of the current. The limit as to how far this can be pushed is probably the saturation of the magnetics in the motor. The Baker electric motor had a 300% overload rating, meaning for short periods of time the torque could be tripled, so the table above probably covers the practical range.  My guess is the 3:1 split is most likely for dynamo field weakening because it works well with a motor having a 300% torque overload rating.

        The reason the motor torque increases as the square of the current is that the motor is series connected, i.e. the field winding is in series with the armature. [Torque = kt2 x current] and the table shows both terms increases with deeper dynamo field weakening, so for example a sqrt{3} increase in current produces a sqrt{3} increase in the motor field strength resulting in a tripling of the motor torque.

        The situation in the dynamo is different. If motor current rises, say by sqrt{3}, the dynamo armature current rises too because the armatures of the two machines are in series, but whereas the motor field increases by sqrt{3}, the dynamo field decreases by sqrt{3}. The reason is that 3:1 dynamo field weakening is switched in so only 1/3rd of the (increased) armature current flows in the dynamo field winding. The result is that with current increasing by sqrt{3} and the dynamo field decreasing by sqrt{3}, the torque from the dynamo remains unchanged. Hence the effect of switching in 3:1 field weakening of the dynamo when going from [gear 2 => gear 1] is to double the total torque on the drive shaft [To + To => To + 3To]. This is x4 the torque in top gear giving the Entz transmission a 4:1 toque/speed range.

Field weakening lowers the dynamo impedance
        So how does dynamo field weakening increase drive shaft torque above the 2nd gear level? The numbers in the table tells that by field weakening the dynamo what's happening is that the impedance of the dynamo is being lowered, i.e. deeper field weakening of the dynamo for the same power level results in lower voltage and higher current. It's current that makes torque, so higher current can increases the motor torque, probably utilizing a 300% overload rating in 1st gear. The motor torque increases as the square of the current so it only takes a 173% current increase to triple its torque. The same higher current flows in the dynamo, but the numbers in the table tell us its torque remains constant since a x1.73 higher armature current is being scaled by a x(1/1.73) kt lower field strength.

        So this is how the Entz transmission 'multiplies' torque in 1st gear. Field weakening the dynamo lowers its counterEMF and increases current. The series connected motor (sans any field weakening) fed with higher current and lower voltage increases its torque as the square of the current, probably utilizing the motor's 300% overload range.
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Assumptions
        To proceed we need to make some assumptions, because a lot of things are not fully spelled out in the patents or online.  Here are my assumptions, which I think are both reasonable and simple.

                1) Assume two machines wound the same (same # of turns in coils). There is no hard reason for this to be true even if the machines have the same cross-section, but it leads to the simplest analysis and from a manufacturing point of view it is preferred.

                2) Shaft speed in each gear is obviously variable, so shaft speed in the table is the upper limit for the gear.

                3) Each machine has its field winding in series with its armature winding (stated in patent), so its kv (kt) goes as current corrected for any field weakening.

                4) How much field weakening? In gears where field weakening is employed patent 1,207,732 (nor any other Entz patent) gives no hint as by how much, but it does show in 1st gear machine #1 (dynamo) field is weakened, and 3-6 gear machine #2 (motor) field is weakened. In both cases I am going to pick a field weakening resistor with the same resistance of the (series) field winding. This splits the current in half making the field current half the armature current.

Calculations
       These assumptions allow the calculations to proceed. First step finding the current in 1st gear. Since the dynamo engine voltage is known (kv1 x engine speed), the current is set to keep the loading on the engine (input power) in 1st gear to be the same as in other gears. This turns out to be the current increasing by sqrt{2} because voltage is down by 1/sqrt{2} [P = 1.414 amps x .707 volts].  In 1st gear only half the current flows in the dynamo field winding so even with current up (to 1.414) engine voltage and kv1 are down 50% (to .707). Next with the kvs (kts) now specified the gearing equation can be used to calculate the max shaft speed relative to engine speed [.333 = kv1/(kv1 +kv2) =.707/(.707 + 1.414)].

        In 2nd gear there is no field weakening and with assumption #1 we can proceed with the calculation. In gear 3-6 kv2 is half that of 2nd gear due to switched in field weakening resistor. 7th gear (top gear, lock up) is fully defined in the patent as the motor is shorted out and no field weakening is employed across the dynamo, so is the baseline. All the results are summarized in the table above.

Results
        Good news is that everything looks consistent, so model and gearing formula are probably right.
                     [Veng =  Vdyn + Vmot],  [Peng = Pdyn + Pmot],  [Ttotal = Tdyn + Tmot],  [shaft speed (max) = kv1/(kv1 + kv2) x engine speed]

         The trickiest calculation was figuring out 1st speed. I tried parsing the dynamo field weakening factor of 2 into an increase in current by sqrt{2}= 1.414 and a reduction in voltage of the engine source of 1/sqrt{2}= .707. This seemed to work as it kept the loading of the engine constant and all the other 1st gear numbers came out consistent, so this is probably right.

Discussion
         In online descriptions of the Owen Magnetic it is generally understood that in lower gears with lower (max) speed the motor torque rises. Some references saying all the torque is coming from the motor in 1st gear, but my results show this is wrong. I have never seen any mention online that the torque from the dynamo stays the same in all gears.

        In top gear the object is to come as closely as possible to 'locking up' the drive shaft to the motor engine speed, in other words a gearing of approx 1:1. The gearing equation shows this requires kv2 (motor) be zero. This is easily achieved by shorting the output of the brushes in top gear (as shown in patent) which keeps current out of the motor so it can produce no torque. With no electric power bled out all the power coming in from the engine goes out as mechanically (P = Tdyn x speed), except for some heat loses in the winding. Therefore in top gear the first machine, the so-called dynamo, from one perspective is effectively functioning as the electric motor that fully powers the car. From another perspective it functions as a magnetic clutch.

        In practice there can be no (hard) lockup because not all the power that comes in mechanically from the engine to the dynamo can go out mechanically (torque x speed) to the drive shaft, because some input power is lost as heat in the dynamo winding resistance (i^2 R). This explains why in tests of an Owen Magnetic car cruising in top gear it was found that drive shaft tended to run about 80 rpm slower than engine speed. Since engine speed is reportedly 1,000 to 3,000 rpm, 80 rpm slip reflects a thermal power loss in the first machine of 2.7% of the engine power at 3,000 rpm, rising to 8% at 1,000 rpm. In the table (above) the transmission is idealized to have no resistive losses.

      In top gear all the torque applied to the drive shaft has to be generated by the dynamo. I think there is little doubt of that. However, while driving in top gear nearly all the power from the engine passes through the dynamo to the drive shaft with just a small 'slip' loss providing the power for the ohmic heating in the windings. While in top gear the dynamo is torquing as hard as if it were a motor, so with corresponding ohmic heat loss in it windings, it should, however, run somewhat cooler that if it was configured as a standard motor. This is because a second major heat loss term in motors is in the steel due to the magnetic field in it continually reversing. While in a motor the reversing frequency depends on the motor speed, here it depends on the difference between the shaft speed and the crankshaft speed. This magnetic loss term is highly frequency dependent, so with such a small slip frequency during cruise the magnetic loss will be negligible. This might lower the heat loss of the dynamo by 20% - 30% compared to a normal motor rating.

        A clue to the power rating of the dynamo, i.e. the power the dynamo needs to pass when the car is cruising at high speed, comes from rule of thumb for hp needed to overcome wind resistance of modern cars: 5 hp @ 40 mph, 10 hp @ 50 mph. Clearly early cars were not aerodynamic like modern cars and their tires may have had higher rolling resistance, but on the other hand they probably didn't spend much time at high speed because roads weren't good and their braking left a lot to be desired. I can believe that the machines in the Entz transmission might have been rated at 10-13 hp (continuous) and that excursions to higher hp were transient (for passing and acceleration). 10-13 hp size would be consistent with the pictures I see. This, combined with reduced magnetic losses when used as a 'magnetic clutch', may be the answer. It may be this simple.
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Useful Owen Magnetic references
        In looking for information on how the Owen Magnetic drive and how it worked I came across two useful references.  In a video made at Nethercutt Museum in CA the curator of the museum is shown driving and shifting an Owen Magnetic. He accurately says what the gear shift lever is doing is adjusting the magnetic fields in the machines. In the second reference (below) the author writes about driving an Owen Magnetic and provides some useful data and perspective.

http://www.bing.com/videos/search?q=Vintage%20electric%20cars&qs=n&form=QBVR&pq=vintage%20electric%20cars&sc=8-21&sp=-1&sk=#view=detail&mid=AB1666A26FDBE905444CAB1666A26FDBE905444C

         http://uniquecarsandparts.com/lost_marques_owen_magnetic.htm

        "Except for its transmission system (a very big exception) the car is a conventional member of the highest class of petrol propelled vehicles. The engine is large - 38 hp - and the car itself is big. On the road it has all the characteristics that one expects to find in a car which is both luxurious and expensive. Instead of the ordinary clutch, the flywheel carries, on an extension of its flange, a set of electro-magnets. On the end of the propeller shaft and between these magnets is mounted an armature, and just behind this armature is situated a second. Obviously, if either of these armatures be compelled to revolve the propeller shaft revolves with them, or, conversely, whenever the car is moving along the road these two armatures are also revolving. Around the first armature, the field magnets on the flywheel revolve whenever the engine is turning. Around the second armature is placed a second set of field magnets, which are bolted rigidly to a casing, and cannot revolve under any circumstances.

         Assume that the engine is started and that the car is stationary, the magnets of the first of the two electrical units mentioned are now revolving round their armature, which is, of course, stationary. The result is the generation of current, the unit forming an ordinary electric dynamo. But, besides generating current, the two units of the primary motor, or dynamo, are exercising a mutual drag, and there is a tendency for the rotating magnets to pull the armature round with them. (These are DC machines. It is more straightforward to say that current in the first machine torques its armature (drive shaft) and can do mechanical work on it.)

          Now suppose it is desired to start the car. The controlling switch is put in such a position that the current generated by what may be termed the slipping between rotating magnets and the armature is directed to the secondary motor. As soon as the magnets of this unit are energized, the armature is made to revolve, so that there are two forces at work, both tending to turn the propeller shaft and so propel the car. The first is the magnetic drag between the two units of the first motor. The second is the ordinary electric motor action in the secondary motor. The practical effect of putting the switch into the number one position of the quadrant on the steering wheel is that the car will almost imperceptibly move forward.' (In other words at start both the dynamo and motor are torquing, which is right, however what is missing here is that in 1st gear it is the motor that provides the bulk of the torque.)

         The speed control quadrant was calibrated to show a 'charging' position, in which the engine could be run while the car was at a standstill to top up the 24 volt starting and lighting batteries; a 'starting' position, in which current from these batteries was used to spin the engine via the primary motor; 'neutral' and six speeds forward, in which the current supplied -to the secondary motor was progressively reduced, until, in 'high', the rotating magnets and their armature were magnetically locked together and no current was passing to the secondary unit. In fact, as there was no mechanical connection between magnets and armature, there was a perceptible amount of slip between them. (The description here is not accurate. According to the patent it is not the current to the motor that is reduced, because except for top gear the armatures of the two machines are in series so they run at the same current, it is the field strength of the two machines that are adjusted to change gears.)

        ** Oddly enough, tests showed that whether the engine was turning at 1,000 or 3,000 rpm, there was always a difference of 80 rpm between flywheel speed and armature speed.  (This is a useful piece of data that is easily explained. This small slip of 80 rpm (few percent) in top gear is needed to supply resistive losses in the dynamo winding. In other words not all the power that comes in from the engine can go out as mechanical work to the drive shaft, because some is lost as heat, and this requires some 'slip' between the engine speed and drive shaft speed.)

        'When the car is on the road, there is a delightful absence of that sense of friction that is always more or less present in the transmission system of an ordinary car'. Another advantage was that the car could coast once it had gathered sufficient momentum, or was running downhill, with consequent fuel economies. If the car was put into 'neutral' while coasting, the motors were converted into a powerful electromagnetic brake, which became ineffective below 15 mph, so that it could never cause the wheels to lock and skid." (Where exactly this regenerative braking power goes is not clear. Into the engine?)

More surviving Own Magnetics

Here's an unrestored Owen Magnetic that recently turned up. What a difference!

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Prius hybrid 'power splitter'
        Here is my Prius power splitter diagram from my 2009 essay 'Hybrid and Electric Car Technology'. By varying power flow in its parallel paths a continuous transmission results. Something similar happens in the Entz transmission where the dynamo is also a power splitter with power from the engine exiting mechanically (as torque x speed) directly to the drive shaft and electrically (as voltage between brushes x current) that is fed to 2nd machine. Like the Prius Entz varied the power flows in his two parallel paths and as a result was able to change the gearing of his transmission.