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How Spark Ignition Systems work
....more than you wanted to know....
This is article ALSO contains, revised, the now deleted old article:  ignitionsystems
Copyright, 2014, R. Fleischer

The purpose of a spark ignition system is to provide an electric spark at a spark plug electrode gap located inside the combustion chamber.  This spark must occur in the correct relationship to piston travel and rpm.  On some vehicles, but NOT on BMW Airheads,... control is also in relation to throttle position or intake manifold vacuum or pressure.  The electric spark ignites the fuel-air mixture in the combustion chamber by its heat (not exactly correct) and the ion function of that spark, particularly just before the spark occurs. Once the voltage exceeds the dielectric strength of the spark plug gap, the ionized gas becomes a conductor and allows current to flow across the gap. In the stock BMW Airhead motorcycle ignition system, there is one spark plug per cylinder; both cylinders have an ignition spark at the same time, but only one cylinder is under compression pressure, the other has a 'wasted spark'.  

The higher the pressure in the combustion chamber at the time of ignition, the higher the voltage needed to jump the spark plug electrode gap.  If you were to try to test for a possibly faulty ignition coil, the standard gap of a spark plug located outside of the cylinder is NOT a good need a MUCH wider gap; or, a type of apparatus that puts a spark plug into a pressurized (typically from the shop air compressor) container...and has a high pressure safety window to look through.   This type of tester tests spark plugs & an advanced type also tests coils.  It is called a Bomb Tester.  I don't know the history of why those two words were used.   It takes less voltage to jump sharp/pointed metal parts, and the less gas/air pressure around the gap the less the voltage required.  It is not easy, without experience, to test coil output.  I keep cleaned old spark plugs for EXternal-to-the-cylinder testing, with the ground electrode almost totally removed, and thus the gap is quite wide.

How 4 stroke cycle gasoline engine basic ignition systems operate:
The following is a SIMPLIFIED explanation, although lengthy.  Following these explanations, I will get into the BMW Airhead system more deeply.  I will also provide a more nerdy and detailed explanation.

The earliest ignition systems (that had much similarity to today's) were in the days of quite early automobiles. At around the same time that magneto's were in use, there were also wooden boxes containing some iron metal rods or other iron shapes, with wire turns wrapped on them in two windings, one with a very large number of turns, the other with far fewer turns.  Spring loaded electrical contacts were arranged such that a storage battery fed electricity into the lesser-turns coil of wire wound on the iron core that caused magnetism to be developed in the core. One end of the iron core was in close proximity to a thin metal reed to which two contact points were affixed.  The magnetism, when great enough, pulled the reed away from its normally closed position, usually to a second contact point, interrupting the current flow.  This repeated over and over, rather fast. The "vibrating contacts" opened and closed, similar to a very old fashioned electric vibrating door bell.  Since the vibrating contact opened and closed the circuit rapidly, the low-turns coil winding (called the PRIMARY winding) was interrupted from current flow quickly and often. Each time the contact closed, the coil charged up magnetically, and each time the contact opened, the coil transformed that stored energy into high voltage in the SECONDARY winding   by the process called TRANSFORMER action.  Those many extra turns on the secondary winding 'transformed' the lower voltage of the battery to a few thousand volts or more, and this was applied to a spark plug. In many, if not most very early cars, that high voltage was applied continuously to one spark plug. Thus the spark was essentially continuous at that spark plug.  This was primarily done on one and two cylinder engines.  Engines with more cylinders USUALLY had a circularly rotating switch called a DISTRIBUTOR, usually mechanically driven from the camshaft, that selected the particular cylinder's spark plug to be energized.

The biggest problems with the vibrating contact system were:
1.  The high voltage output is relatively constantly flowing, and it is hard to 'time' the initialization of the combustion event, even if one had the rotating contact distributor. This was not a big problem with very low output engines with very low rpm and compression ratios.    A typical vibrating contact wooden box coil of the type described is still easily purchased brand-new; for Ford Model T cars.  
2.  The current input was fairly low to keep the points from deteriorating fast.

Later systems used one or two breaker points sets, typically located within the distributor, with a capacitor ("condenser") to reduce points wear and 'condition' the electrical waveform to better work with what was universally now called the Ignition Coil.  NO vibrating contacts were used.  The points are adjustable for gap and for ignition timing, thus the spark can be made to occur at a precise position of the engine piston(s).   This system is generally called a Kettering Ignition, and is capable of high performance, and is still in wide use today, the points having been eliminated in favor of electronics.

"Condenser" is an old name for a CAPACITOR.  BMW Airhead motorcycles had points and condenser on all models up to and including 1980.  Inside the condenser are two very long pieces of super-thin aluminum foil, and a means of insulating these two pieces of aluminum foil from each other, and the long pieces and insulation are all wound together at the same time into a tubular shape; with one connection to one piece of foil, one connection to the other piece.  A capacitor/condenser has the ability to store an electrical charge directly.  A battery does NOT, in case you were wondering about that...a battery stores potential electrical energy as a potential CHEMICAL reaction; and when the battery is called upon to deliver electricity, THEN the chemical reaction begins.  The condenser (capacitor) stores excess electrons on one of the long strip pieces of aluminum, with regards to the other piece.  A capacitor takes TIME to fully charge from any applied voltage, and the faster it is charged, the more current flows into the condenser during that period of time.  The purpose of the capacitor is TWO-FOLD.  (1) It greatly improves the quality of the spark and charging/discharging waveform, by making sure that nearly every bit of the energy stored in the coil is transform...the primary coil magnetic the secondary high voltage winding...just how it does this is rather complicated; (2) the capacitor greatly reduces the erosion of the points by dampening the spark at the points as they open.

Here I will add a more explicit explanation:
When the points CLOSE, power from the + side of the battery travels through the coil(s) primary windings, through the points, to ground (ground is the - side of the battery). The flow of electricity causes a substantial magnetic field, after a very short period of 'charging time', in the ignition coil metal core.  The points cam shape insures that the charging time (points closed time) is very much larger than the points opening time, for any RPM.

At the very instant the points start to open, the charging circuit is opened, and the coils magnetic field collapses, made more speedy and in a way more powerful (it makes some of the DC act like AC) by the CONDENSER, which is often wrongly thought of as just something to help reduce the electrical arcing at the points. The condenser does, greatly, reduce sparking/arcing at the points, because when the magnetic field collapses in the coil, it cause a reverse-current, at substantial voltage, to be across the points. But, the condenser is short-circuited when the points are closed, and the core is charging. The condenser takes a teeny bit of time to charge up as the points are just barely opening, so the condenser acts like a short circuit at that instant in time. The electrical charge direction in the coil reverses, and then tries to charge up the condenser. This all happens in an extremely short period of time....thousandths of a second. The condenser ensures that the coil secondary winding develops a very large voltage, of a waveform that is 'decaying oscillatory'. It is that large voltage that is applied to the spark plug. The spark jumps across the spark plug gap, and also eliminates a potential problem: If the spark plug wires were not connected to a spark plug, but just open/hanging, voltages in the coil WILL reach extremely high values, MANY tens of thousands of volts, and the coil windings insulation would likely be damaged. The type of ignition, coil, condenser, & points, is called a Kettering ignition. It, by a sort of trickery as outlined, lets a D.C. circuit act like a bastardized form of A.C., and A.C. can be 'transformed'. The coil is the transformer, transforming the battery voltage to 20,000 volts or more; sometimes a LOT more... in actual operation.  The transformation, for the nerdy here, is a waveform that is a decaying oscillation type, usually portrayed in text books as a decaying amplitude sine-wave.

The circuit is simple, reliable, and in the Airheads, it is perfectly adequate for over 7000 rpm (coil output drops with rpm, and the number of cylinders...that is, the number of sparks per second required).

The current and voltage at the points causes the points to deteriorate, slowly, over many miles. The best quality points have a thin precious metal or tough metal coating, such as tungsten, which helps with the erosion, but the coil, condenser, & points systems, are not perfect. The points not only arc electrically, but that electrical arc tends to cause wear in what is called tit and valley (mountain/valley if being Politically Correct), so one side of the points has a tit, the other side a matching valley, and slightly irregular in shape and fit. When that gets extreme enough, the points don't work all that well, and filing the points, even if carefully done, only lasts a moderate amount of miles....but, in truth, can be done over and over...usually. Timing needs to be checked too. Generally speaking, points gap and timing needs to be done every 5,000 miles, and at that time the cam, and felt (felt piece is part of the points assemblies before 1979) needs some slight lubrication. The lubrication is to help ensure that the insulating rubbing block on the points does not wear fast from lack of minute amount of lubrication.

Amplifiers and Boosters (preliminary):
As noted, points deterioration, and that tits and valley thing too is a wear area. The other major wear area is the rubbing block. If not abused, the spring will hold up for the points assembly lifetime. Abuse is opening the points way too wide with your fingers.

An amplifier/booster is a transistorized circuit, that uses the prime characteristics of a transistor, which is that of a current amplifier.  The transistor (of whatever type), acts as the switch, in place of the points, which are used to trigger the amplifier. The amplifier/booster is designed so a small voltage and small current is applied to the points, and the points opening and closing triggers the transistor, which, as a switch, controls the coil(s) primary current from the battery.

Thus, the points can last MUCH longer than they might, otherwise, without the amplifier/booster. It is important to continue checking points gap, timing, and for the slight lubrication of the points cam (and felt), at 5000 mile intervals. For the 1979-1980 canister points ignition, the same holds true, except that there is no felt.

The most popular amplifier/booster is the one from Dyna.  There are other sources, and even kits to assemble your own.  It is quite possible to use a modified kit to handle the higher currents demanded by lower primary ohms coils. You will find the kits information, etc., near the top of:

Note that all of the most popular Electronics Ignitions work exactly the same BASIC way as the outlined points system, but they use some form of electronics trigger, and electronics, to power the coil(s).  They usually do not need a condenser, and use semiconductors to perform the condenser function.

Magnetos, Kettering, Diesels, CDI, Electronic triggering, ATU cam, Dwell:

Magnetos are simply a permanent magnet method of using mechanical rotational energy, instead of a battery, to produce the high voltage for the spark plug. Magneto's are usually equipped with a set of points (contact points plate), and a condenser, and the energy transfer from the small number of turns coil in the contacts plate circuit primary circuit, to the secondary many turns winding, is done at the moment the points open, which is set to coincide with a particular high energy alignment of the iron core stator...  in relationship to the rotating magnet (actually at the switching point of magnetic poles, but that is a nerdy point here).  Magneto output tends to rise with rpm (as opposed to coil ignition which has output lowering with higher rpm).  Since the exact time the spark occurs can be controlled by positioning the points, same as with the points and coil ignitions, timing on magnetos can be just as precise.  Many early BMW motorcycles (before late 1969) used a magneto system.  A very big advantage is that NO battery is needed.  Magneto ignition was quite popular for a push or kick-started motor, and is used in many motors, from lawn equipment and motorcycles to aircraft piston engines. 

If the motorcycle had LIGHTS, some other electrical source method is needed, either as part of the magneto system, or from an alternator, or generator.......and usually, not always, with a battery.  It is NOT a necessity to have a battery, the lights can be run on alternating current from a specialized magneto or alternator.   This was even done with generators occasionally.  Some versions of older popular scooters (Vespa, for instance), had minimal lighting systems, run on A.C. from a separate coil in the magneto system.  There are some modern dirt bikes that use A.C. for lighting.

Magneto's are difficult to keep down in size when you need quite high energy sparks (such as with lean-running engines or engines with quite high compression ratios, or both).  Magnetos have rotating mass and inertia which may be a factor for engine or camshaft design, since they are typically attached to the crankshaft or camshaft.   Magneto's have some other problems, that is why they are not used much now on modern designs. They do have increasing voltage as they rotate faster, but that means lower output when you are kick-starting the engine....and if anything is slightly marginal, the engine may not start; or not easily.  Some older race engines used them, but most race engines now use sophisticated electronic ignition.  Magnetos, or some form of them, ARE still used in many small engines, especially in things like home garden equipment.  Some small motorcycle and scooter engines may still use them.  Magnetos are also used with piston engines in aircraft...most have TWO such magnetos, allowing firing of two plugs per cylinder, for safety redundancy and higher combustion efficiency.

Later BMW's from the end of 1969 (/5 and later models), up through 1980, had coil ignition with a points contacts assembly being driven off the camshaft.  Points contacts are nothing more than a rotating switch. There is a condenser, electrically connected across the points. This system of contact points, condenser, and coil (or two coils on some airheads), all being driven by a battery, was invented by, and still named for Mr. Kettering.   It is a goodly improvement on the vibrating contacts coil mentioned earlier.   Note that the magneto, with its condenser, is basically a Kettering system too!

There are other types of ignition methods: Diesel motors may use glowing coils of wire.  There is a type of ignition for gasoline motors called CDI which stands for Capacitor Discharge Ignition.  That type typically produces a VERY high voltage, and the TIME from when the voltage starts to rise, until the spark occurs, can be ULTRA SHORT.  It can be so very short that this type of ignition can actually fire spark plugs that are moderately fouled (potentially partially shorted). It does that by the voltage rising so fast that the spark occurs before the carbon-path, contaminants, etc., can fully conduct (there is a lot more to that, which I won't get into here).   That very fast 'risetime' CDI ignition may have a drawback, its SPARK DURATION is almost always EXTREMELY short.   It takes a reasonable amount of spark DURATION to properly ignite a fuel-air mixture, particularly when running lean. However, some CDI ignitions also are very powerful, with a short high current spark, which will usually work with any type of engine.

As a general rule, the higher the ENERGY in the spark, the better the ignition of combustion.  It is the energy of the spark, that can also be called the HEAT of the spark, and is measured in Joules, that is important, at least in so far as having at least what is needed, and then some extra, all for ensuring good ignition of the gas-fuel mixture.  However, at least a good ionization of the gas mixture at the spark plug gap is needed, and then high energy level of the spark itself will ensure good ignition.

The camshaft(s) of most 4-stroke-cycle engines rotates at half the crankshaft speed.  Airheads have the end of the valves-operating camshaft mechanically driving opening and closing switches, called POINTS, on all models up through 1980. There are two lobes on the cam called the points cam, that is at the forward end of the valves camshaft, whether located on the camshaft tip area in the ATU in pre-1979 models, or in a canister on 1979-1980 models.  Each of the two lobes will open and close the points for ONE camshaft revolution (which is once every two crankshaft turns). 

The 1981 and later BMW motorcycles ignition design eliminates the points in favor of an electronic triggering device, the two lobes now being a butterfly-looking piece of metal that rotates past a sensor, called a Hall element, a transistor that is magnetically sensitive. 

The amount of TIME, expressed in rotational degrees per coil charging event rotation, that battery current flows into the coil, is called DWELL.  A NOMINAL 78, 110, and 120 (of crankshaft rotation) has been used on BMW Airhead motorcycles for POINTS models.   The value depends on the model/type of automatic timing device cam, and the points gap has an effect on it.   104 is the value used IN THE CANISTER electronics models;....and is a bit of nerdy information, since it is not very important except to the engineers who designed it.  The longer the dwell time, the more heat is developed in the COIL...and, for the 1981+ models, the more heat that is developed in the ignition MODULE, located under the fuel tank.

A reasonably long dwell time is required for battery current flow to fully magnetize the coil(s) core.  That time is more critical as rpm rises quite high as the number of sparks per unit of time is also increasing.  If the DWELL period is too long, the coil(s) might overheat.  Too short, and the high voltage output will suffer at high rpm.   On a practical basis, the ignition systems in BMW motorcycles are FULLY adequate for ANY RPM the BMW motor can reach, primarily because the number of sparks per second is small, compared to engines with many more cylinders. 

Here is yet another explanation of how the ignition system works in a mechanical points and condenser ignition.  This article on ignition theory contains variously-said explanations to be sure you fully understand the theory.

The ignition coil consists of an iron core (actually multiple thin special magnetic iron pieces or small diameter rods, for technical reasons) that contains TWO separate windings. One winding, called the PRIMARY, has a modest amount of turns of a relatively thick and insulated wire as it will be handling a large current flow (several to numerous amperes). The push-on male spade terminals on your Airhead's single tower coil are connected to the respective two ends of this "primary" winding. Well insulated from this winding there is another winding. This separate high voltage winding, called the Secondary, consists of thousands of turns of a thin and also insulated wire.  This wire is thin because otherwise the many turns would not fit into the case.  Thin is OK, since this winding operates with low current, but high voltage. 

For the single tower coil, one end of the secondary winding connects to the 'tower' on the coil, into which the lead to the spark plug is pushed, and the other end of this high voltage coil winding is connected to one of the low voltage winding terminals, to act as a ground return path (not the case/ground, as is sometimes assumed).  The twin tower coil has the secondary two wires connected only to the two towers.

1. Battery voltage through the ignition switch is applied to one primary winding terminal on a coil. The coil is rated at 6 volts for that coil primary, so that coil is series connected to a second coil, and the second coil's primary winding terminal connects to the ignition points insulated contact. For 1981 and later Airheads, the twin tower coil replaces these two coils.  On your Airhead, single tower coil push-on terminals are usually marked 1 and 15, and maybe + and -.   These terminals are marked so that the connection to the battery is made such that the high voltage output is negative, which adds to the negative electrons given off by a spark plug center electrode (when it is red-hot)...and so this also helps with making the spark occur slightly more easily.   With TWO separate coils, the coil primaries are connected in series in such a way that BOTH spark plugs always receive the negative voltage.   LATER IN THIS ARTICLE I WILL EXPLAIN MORE ABOUT THE NEGATIVE-GOING ELECTRICITY AND TWIN OUTPUT COILS.

2. The other points contact is mechanically and electrically connected to the metal plate of the points contact assembly which connects to the engine metal structure, and thereby this completes the circuit to the battery negative terminal, through the engine case.

3. During engine operation the points are closed for a much longer period of time of rotation, compared to the time the points are open. This is what is meant by "dwell angle, or dwell time", as a portion of rotation. For Airheads, we actually mean the ratio for any of the two lobes on the points cam.  Dwell angle is used by some folks in setting points gap. YOU do NOT need to do that, it is hardly critical, and using the points GAP setting is quite good enough, and is the one I prefer and use.  It is far more important that the points gap be reasonable, than the dwell be some particular amount, for a non-full-out-racing-HIGH-rpm Airhead.  There are drawbacks to trying to obtain 'proper' dwell angle, if the points are too narrow.

4. Nerdy: With the battery connected and the points suddenly closed, current flow does NOT instantaneously rise to maximum like it would with the coil of wire removed from the iron core and just stretched straight out.  Magnetic theory is quite involved and not easy to understand. I will simplify it greatly here.  Instead of instantaneously, the current starts flowing at a low level, and the current increases smoothly on a specific mathematical 'curve', and if the battery is connected long enough, the current reaches the value calculated by Ohms law (that is, the maximum current is from the applied voltage divided by the resistance of the coil(s) in ohms).

If one had 3 ohms of total primary resistance, & 14 volts was available, the current could reach 4.7 amperes, this is 65 watts needed from the battery and alternator.  NOTE, however, that this drain is NOT continuous, remember the points opening and close and their dwell period!   Thus, the AVERAGE drain is lower.   The AVERAGE drain also varies with engine rpm.   BMW has also used two coils of ~3/4 ohm (1981-1984, twin-coils-models, electronic ignition).  This means that theoretically the current flow could reach over 9 amperes.  BMW has also had single two-tower coils of ~1.25 ohm, giving 11 amperes of drain.  The very last of Airheads production used a HALF OHM primary winding on the SINGLE TWIN TOWER COIL.  A rather high amount of current could flow, 28 amperes, ....but this is NOT continuous...we have that dwell angle thing to thank for that.  Still, a fair amount of heat is generated, one of the causes for early plastic-bodied coils to crack and fail, and for modules to overheat if the heat sink paste was not in good condition.

Without getting into the nerdy mathematics of the shape of the charging curve (if one was to plot the current input to the coil over TIME), and without getting into the theory even deeper otherwise...suffice it to say that the coil is likely going to reach peak current in perhaps 15 milliseconds.  For 99.9% of you that is totally nerdy & unneeded information.

If too many sparks are required by too high an rpm, the coil charging time is INsufficient to fully charge the coil magnetically & the ignition coil voltage, & thus energy output for the spark plugs, will be lower, and lowering, as rpm rises, until at some high rpm the voltage is insufficient & intermittent spark plug firing occurs.  This results in misfiring, wasted fuel, & if severe enough, will be very noticeable to the rider.  In the stock BMW Airhead motorcycles, the rpm that CAN be reached under normal use is insufficient to require fancy super-sophisticated ignitions systems.  BMW upgraded the ignition for 1979 and again in 1981.  This was done first to improve timing consistency and improve output somewhat, and, for 1981 was done to produce higher voltage & higher energy sparks required for the leaner running engines.   Note that the Airheads, even at 7500 rpm, hardly stress the ignition system, because there are only 2 cylinders.  If there was 6 or more cylinders, the ignition would not be OK at that rpm.

5.  Earlier in this article I stated that the MAGNETOS used on pre-1970 models had low output during cranking.  The OPPOSITE is true for coil ignition.  Thus, coil ignition can give a good high energy spark for easier starting, and the excellent spark enables higher engine tuning for increased power.  A properly designed magneto system can certainly produce enough output for good starting in nearly all circumstances; this is easily seen by anyone with experience with BMW's /2 era engines.

  Some have asked about making measurements at the points to 'static time' the Airhead engine.  Static timing means to set timing without the engine actually running. This is acceptable to initiate timing at something close to the correct value.   The correct method, or final method, is to time the engine at maximum advance.  That means at high enough rpm that the automatic timing unit is no longer      advancing the ignition point if the rpm is further raised. For static timing you can use an ohmmeter or a voltmeter, or a piece of the very thin 'cigarette' rolling paper. If you use an ohmmeter, leave the ignition off or you might burn out the meter.  Either type meter is connected across the points.

The engine is VERY slowly rotated by hand, so as to see the exact place the following happens.  Noting the flywheel-marked "S" timing point (which can be thought of as for Static timing, but really is not exactly the same thing), the ohmmeter indication should suddenly increase (more ohms).   If using a voltmeter, turn on the ignition, and the timing point is when the voltage rises suddenly from zero to approximately battery voltage. If using cigarette rolling paper, which is extremely thin, the timing point is when the cigarette paper can just barely be pulled through without grabbing. You must rotate the engine in the normal direction VERY SLOWLY, degree by degree, when finding the exact Static timing point.  Many will put the transmission into top gear and 'bump' the rear wheel to very slowly get the engine to nearly the S timing mark, and then VERY slowly bump the wheel and note the flywheel indication where the points JUST BARELY open, as shown on a meter, or where you can JUST pull the cigarette paper out without tearing it. 

***DO NOT try to measure anything via a meter, for the canister ignition, 1981 and MAY injure the ignition, even with power off.  BMW has a very special test instrument to allow static timing of the electronic ignition, but YOU DO NOT NEED IT.  I recommend putting a pencil mark on the canister and the engine case, opposite each other, so that when removing a canister, it can be returned to the same marks upon re-installation, which will be plenty close enough for starting the engine.  CONTRARY to some books, you can NOT put the canister 180 out of phase, as the locating-driven-tang is OFFSET.

Remember that capacitor/condenser used on POINTS models?   During the relatively long time the points were closed (compared to being open), and the coil charging up in magnetic energy, that capacitor is SHORTED by the points. At the instant the points separate the tiniest amount, the coil 'tries' to charge the capacitor (how is WAY beyond even this nerdiness). Since it takes TIME for the electrons to move to the capacitor, the coil really "sees" ..INITIALLY....mostly a dead short at the capacitor, said dead short slowly rising to less and less of a short, as the coil dumps energy into the capacitor and the capacitor 'charges up'.  The dumping process reverses the magnetic field and current flow directions in the coil, allowing a transforming effect from primary to secondary.  While this process will occur withOUT a condenser, the efficiency would suffer. The capacitor has other effects.  Due to the slow charging inherent in a capacitor, the capacitor greatly reduces the spark at the points, that means it limits points damage by the spark at the points.  An additional effect is to improve the duration of the high voltage spark.

This is a complex process, and actually the current reverses numerous times as it dies down, and is shortened when the spark occurs at the spark plug. We call it a decaying or damped waveform, as seen on an oscilloscope...a type of TV-like device that will display the electrical waveform.  The points contact winding (primary winding) also sees an increase in voltage, although much lower in value, perhaps a couple hundred volts at most.  Voltage and current relationships, especially with TIME, in a ignition coil, are not constant as the cam points open and close.  This makes the process difficult to properly understand unless you are an electrical engineer or understand calculus.

This same thing happens in the electronic ignition models, which do not need a condenser.

A good way for YOU to think of the condenser's function in the points models is that it helps with POINTS reducing the spark arcing at the POINTS; and, that another function is to augment the rapid collapse of the magnetic field.  Capacitors (condensers) have an electrical value called capacitance.  The value was selected by Bosch/BMW for a compromise between protecting the points from arcing, and characteristics of the voltage and current that develop in the spark....and the spark waveform duration. 

The main thing for you to know is that the primary winding has a lot of magnetism charged-up, the points or module opens electrically, the secondary winding develops a VERY high voltage, which we hope goes to a spark plug that now has a spark jumping its spark-gap.    IF you pulled the spark plug cap off the spark plug (a VERY BAD thing to do), the secondary voltage can rise up much higher than the insulation inside the coil safely allows.  Also, the voltage at the condenser and points can rise up rather high too, and also be damaged.   Thus, if you pull the spark plug cap off it can damage the condenser and coil components (the damage may not show up right away).  For the electronic ignition models, the damage can be $$ EXTENSIVE, and also MIGHT not show up for some time...damage can be to, besides the coil(s), the Hall triggering device inside the canister, and the module.   Back in the days of the BMW magneto engines, no damage to the system would occur if a spark plug cap was removed, as there was a safety spark gap built into the magneto.

8.  A bit nerdy:  If the capacitor fails by OPENING, not only is the spark vastly less powerful, but the ignition timing changes quite a will retard due to the much slower rise in the waveform.  Typically the motor may misfire or otherwise run VERY BADLY, if at all. Thus, the combination of the capacitor (condenser) characteristics and the ignition coil characteristics, has a substantial effect on the ignition system operation.  The condenser capacitance value is not critical, but it must be there, not open, not shorted.  If shorted, you will not be able to start the bike, because there are no sparks. 

HINT!    Be sure the capacitor is at fault before replacing it.  It is NOT UNCOMMON to see a crushed wire from the points cavity, caused by someone not replacing the alloy outer cover carefully into the grommet (or, the grommet not installed carefully); or, new points were wrongly installed, such as with a wrong screw height, causing a short circuit....etc.

The coil primary winding (and effects of the magnetically-coupled secondary) is in series with the condenser when the points are just barely opening.  This open circuit causes, in electrical engineering speak, a "Series Connection Resonant Circuit".  This is responsible for the damped waveform and spark generation.  The circuit has a "Low-Q factor", so the value of the condenser (in microfarads) is NOT CRITICAL.   A very broad range of frequency is accommodated by this low-Q circuit, in RPM or sparks per second or minute.     Q stands for Quality, but that is VERY confusing to those who do not understand the formulas behind it.  It is NOT what you may think it is! Want to know what Q is?  Try a search engine.

9.  In a Kettering system as described, the high voltage output of the coil has a rather complex type of waveform, but it is ALSO definitely polarized. That is why the two spade terminals on the two separate coils system should be connected to the correct wires. They are marked + and -, or 15 and 1, or both. By convention and standardization, terminal 1 is ground or negative, and terminal 15 is power, or positive.   While the coil might well fire the spark plugs if coil primaries are connected backwards, the effective energy of the spark could be reduced.   The effect MIGHT be noticed at high rpm & large throttle amounts... or if the ignition system was not quite good over-all. Misfiring & stumbling can occur, depending on the severity. 

BMW uses standardized character markings for electrical items, together with standardized wiring color codes.  There is an article on this website that discusses wire colors, terminal numbers, functions, and more:

If your airhead uses two coils & single plug ignition, these are 6 volt coils with primary windings connected in series, and all the foregoing descriptions still apply. If you have a dual-output 12 volt single coil, as on R80ST, GS, and many later Airheads, including all from 1985,  there is a difference in operation regarding the internal coil connections and the output polarity.  MOST Dual-tower coils have just one secondary winding, the ends of which are connected to the respective towers.  In this type of coil, if you were to use an ohmmeter (with coil disconnected from the bike wiring) on the coil, you would find an infinite resistance between either tower and the coil case or either tower to any primary terminal.   This type of coil IN USE always has one tower as negative output, the other as positive output.  With such a coil IN THE AIRHEADS, as both cylinders are not under compression stroke at the same time, the spark jumps the non-compression stroke spark plug easily, & since the other spark plug's cylinder is under compression, it takes more voltage to jump the gap, but it works out OK, as there is plenty of voltage.  Yes, the two cylinders' sparks are not perfectly always the same, due to the coil output to one of the cylinders always being negative, the other positive. 

For those of you with dual plug ignition conversions, the normal setup is that there are TWO 6 volt (or proper primary coil resistance) dual tower output coils, with the primaries connected in series.  There is usually no polarity markings on these coils.    You want the strongest spark under conditions of high compression pressure in the combustion chamber as the mixture is ignited by the spark plugs, THUS IT IS BEST if EACH ONE of the two-tower ignition coils connects to both both cylinders. The other coil is obviously similarly connected.   It makes no difference if one coil connects to a top and bottom spark plug on left and right cylinder; same for other....or; if one coil connects to top plugs, the other connects to bottom plugs.  To explain this just a bit more, ONE cylinder will NOT be at compression pressure at the time of the spark, so the spark WILL jump THAT spark plug quite a bit easier. Higher the pressure in the cylinder under compression, the harder for the spark to jump.  

10.  In BMW Airhead models after 1980, the points and condenser functions are replaced by a shaped metal vane and semiconductor parts located in the canister & in the ignition module.  The module is 'triggered' on and off by the proximity of the specially shaped rotating metal vane in the canister.   The sort-of butterfly-shaped plate passes by a semiconductor part that is magnetically sensitive, & is called a Hall Sensor and the sensor is built into a specialized type of transistor that provides initial amplification of a very tiny output from the sensor. The electrical signal is then applied to an electronic amplifying circuit, which does a lot of other things besides amplification.  It is located inside and is part of the module under the fuel tank. Hall devices are sensitive to stray magnetic & electric fields & electrical spikes on wires connected to it. That is A VERY STRONG REASON the spark plug wires must NOT be disconnected if the engine is running (or not) with the ignition key ON.  The Hall device is damaged by stray electric currents. The spark plug caps must always be provided a grounding method through the spark plugs or a shorting wire.  The spark plug caps MUST be of the 5000 ohm type; the early Airhead 1000 ohm caps are NOT OK!    The system WILL be damaged & the damage might not show up immediately, if you have a spark plug cap off, or the caps are 1000 ohms or are defective.   Do not use resistor spark plugs, they add to cap resistance & lower the spark intensity/energy value.  Do not use resistor plugs with no-resistance caps, you cannot depend on the next person knowing that; AND, in SOME resistor type spark plugs, the resistor is NOT really a resistor, rather, it is a tiny coil, & MIGHT NOT work with the electronic ignition very well. The over-all system is reliable & requires no regular maintenance, the exception being checking the timing at the maximum timing point ("Z") every 10Kmi or so & cleaning & re-applying heat conducting grease to the module under the tank every few years (except riveted versions).   I suggest one drop of oil every year or so on the outrigger bearing, even though the bearing material is supposedly sintered and lifetime lubricated.  

A condition can occur where the automatic advance parts tend to stick, often from a tiny amount of a part swelling or varnish contaminants or hardened lubricant...then the canister must be disassembled for repair.  Typically this shows up as a very increased idle rpm with the engine fully warmed-up.    Since this is not the only thing that can cause high rpm after warmup, including mis-adjustment of the carburetor's idle mixture and leaking intake hoses, information on how to determine if the canister is at fault, is on this website in the  article.   Some dislike the repair process and prefer to install an Emerald Island ignition canister and module (also called the Omega ignition), ETC.

11. No matter which, points or electronics, some means must be available on all gasoline engines (other than ancient antique engines and such as lawn equipment, etc.) to change the timing of the spark in relation to the piston stroke, as the rpm increases. Needed is a retarded spark to enable starting and proper lower rpm performance; and, a considerably increased ignition advance is needed at higher rpm.  As rpm increases, there is less TIME for the ignited mixture flame to completely burn, so the spark must occur EARLIER in the process.   Common usage has EARLIER meaning ADVANCED, LATER meaning RETARDED.   You need a method of adjustment to compensate for points mechanical wear, chain and sprocket wear, etc.

BMW uses a mechanical advance device in all its Airheads models; and used them before the Airheads. This mechanical device, often called an ATU, for Automatic Timing Unit, is simply a pair of shaped metal weights with calibrated springs attached, that move from an at-rest position to further & further outward, due to centripetal forces as rpm's increase, up to their preset stops, which occurs at ~2000 or ~3000 RPM (crankshaft speed), depending on ATU version.   The moving weights are mechanically linked to the rotating points cam (or butterfly trigger metal in the electronics models). By carefully designing the weights for shape and weight, and strength of the springs, the factory is able to give the optimum...or nearly so...'advance curve' that the proper timing occurs at the rpm found best by dynamometer and road tests. It is not perfect, especially since no device is added such as the automotive type of vacuum advance/retard, which can be designed to compensate for throttle amount, which is somewhat allied to effective cylinder pressures.   On a practical basis, BMW's system works fine.  More extensive details on the advance units are posted/discussed elsewhere's on this site.

This mechanical device, the Automatic Timing Unit (ATU), is part of the IGNITION cam assembly that is free to move upon, & the assembly as a whole is driven by the valves controlling camshaft in the engine. That engine valves camshaft is chain driven by the crankshaft.  As the chain stretches & chain sprockets & automatic chain tensioner wear, the valve & ignition timing will change, so the ignition timing relationship to the crankshaft position needs to be reset even on the electronic model, although the amount of change is very slow, and generally seen only after large mileages; much increased mileages than with the points models, where these larger timing changes occur as the points rubbing block & points wear. 

When the chain, sprockets & guides are worn to the very sloppy chain movement point, the timing will be affected quite adversely as you move the throttle more open & as you back off the throttle.  There will also be more instability. This is usually seen with an ignition-driven strobe light focused on the timing window of the engine case (near the oil dipstick). Reasons for the split (dual) stroboscopic ignition image usually seen is due to sloppiness in the ignition timing from these various causes, made worse by the valves camshaft NOT being a smooth load on the engine, so the chain & all associated parts in the timing chest, all see an irregular loading.

NERDY NOTE:  As these parts wear, the valves timing by the camshaft, in relation to the crankshaft position and thus the piston, will change and you will get a decrease in power from that, which you cannot 'adjust-out' by adjusting the ignition.  The valves operating camshaft will be more and more RETARDED, versus the crankshaft, as the miles accumulate, also reducing power.

On POINTS models, points wear from electrical spark erosion, but especially the points insulating rubbing block wears.  It helps to keep the points cam SLIGHTLY greased, & even so, the rubbing block driving the points will wear and the points will slowly close-up.  The closing-up of the points also changes the ignition timing!   Points should be checked at 5000 mile intervals.  Points life can be extended CONSIDERABLY by using a Points Amplifier & keeping the POINTS cam SLIGHTLY greased.  See  Commonly, folks to forget to lubricate the cam, and only the faintest lubrication is needed, and these same folks forget to check the points gap, & when the gap becomes approximately non-existent, the bike will not start, or not properly.

12. Points also have problems with the points not following the points cam at extremely high rpm's...and also, being mechanical devices on a driven angle, tend to rattle around & vibrate a bit, which affects timing stability.  These are some of the reasons BMW went to a special coupling arrangement in the canister points models, which was produced only in 1979 and 1980, just before the 1981 change to full electronic ignition; which also uses that new type of mechanical joining/driving method, called an Oldham Coupling.

Points have advantages: They are exceptionally simple, & can almost always be 'fixed' by the side of the road.  They also can be fitted with a simple booster, or points amplifier, which GREATLY reduces the current through the points, hence they can have a very much longer life than they normally would otherwise;......and maintenance is also reduced....but, do keep that cam slightly greased, the felt too if you have one (points canisters do not).... & check gap and then timing at 5000 mile intervals, at which time you are going to check the valves clearances, etc., anyway.



Points amplifiers, sometimes call points boosters, are made by a number of manufacturer's.  They will GREATLY increase points life.   Numerous makers.  Accel and Dyna were two of the popular brands.  The DYNA is still being produced; as are some kit types, etc.    SEE: for more information.  If you need wiring information for an old Accel, see my REFERENCES article.

These are, at their simplest, one or more transistors, some resistors and maybe some diodes, and maybe a capacitor or two, and little else.  The main power transistor is a type that will handle maybe 4 or more amperes and acts as a current amplifiying switch, triggered by the points.  Since a common transistor is, at its heart, a current amplifier, then the current that used to be in the points, can now be greatly lessened.  Some use different transistors, or in combination, but the idea is the same.  Thus, the points, as far as erosion and wear from electrical sparking is concerned, is greatly reduced.  Points life is not infinite, as the points rubbing block will wear (greatly lessened by use of a very thin layer of quality high temperature moderate viscosity grease on the points cam and its associated felt if you have that).  There is a very slow deterioration of the points spring tension, and other wearing things, but these are small effects, very long term effects.  If the points current that drives the amplifier is too small, there is likely to be insufficient electricity to keep the points clean enough electrically, especially if there is any faint oil vapor contamination.   If the amplifier fails, one can always, and rather simply, go back to the stock points triggering, just by moving around a couple or three wires.  Points amplifiers are not required, but some prefer them... I think them worthwhile.

13.   In the pre-1979 models, the cavity in the engine that the points are located in must have its cavity surround rubber O-ring and also the rubber grommet (that the wire passes through) all intact, to help prevent moisture and atmospheric contaminants from entering the points area.  DO NOT use an evaporating grease on the cam.  Special greases are made by such as Bosch; there are two types, one for the points cam, and one for the inside of the ATU, although many greases could substitute.

14.   In all stock systems all coils fire at the same time, although one cylinder is not on the firing stroke (BMW calls this a 'wasted spark').

15. There are other types of ignition systems for 4 stroke engines, one popular high performance type is called a 'capacitor discharge ignition'.  If carefully designed, the spark can occur so fast that it will fire somewhat fouled spark plugs. This type of ignition is NOT needed on our BMW Airheads, and can actually have drawbacks, due to their complexity AND that the spark duration is so short that in some instances the mixture MIGHT not be ignited properly, as the engine, and spark plug type, is not designed for CDI ignition.  There can be problems with electrical interference with Hall elements too. There are other types of electronics ignition conversions for the BMW Airheads, including some mounted to the alternator so as to be driven mechanically by the crankshaft, which eliminates the chain, chain guides and tensioner, etc.

Several ignition types eliminate the points (including versions of the Dyna and Boyer), some have built-in advance (Boyer, for example), and there are crankshaft triggered types. None of these help all that much as far as actual spark plug firing on a stock or dual-plugged engine, and are only slightly more helpful for a moderately modified engine. However, they can eliminate or reduce points long as they do not fail.  Some have characteristics that do NOT match the Airhead engine.  Another advantage, with some, like the Boyer, is that a broken cam nose tip is no longer a serious repair with precise repair techniques needed.  Thus, the Boyer is used for where the cam tip was broken by those who over-tightened the ATU nut (pre-1979).  Information on the Boyer is on this is information on how to properly repair a broken tip on the camshaft.

ALL Airhead Ignition Systems can be damaged if the spark plug wires are removed from the spark plug with the engine running...or the engine is being cranked or other wise operated.... if the spark plug wires/caps are not grounded properly.

Damage may not show up for some time. The damage can occur to points or electronic ignition. Hall devices, the module, or the coil(s), or any combination can be damaged. The system may be damaged if the spark plug caps are not the correct ~5000 ohm types on the 1981+ models.   1000 ohm caps CAN be used on 1980 and earlier models, you do not have to use 5000 Ω on the points models. Even with the points models, the coils can be internally damaged from lifting the spark plug caps without grounding the inner contact in them. 

****If you see otherwise in some literature, the LITERATURE IS WRONG! ****

Totally Nerdy Section. This is a rambling, highly technical section, for the intensely curious!

A spark plug can be thought of as a capacitor.   A capacitor is two plates, separated by an insulator.  The ground leg of the spark plug and the central electrode can be thought of as a very tiny value capacitor, the "insulator" being the ceramic plus the air and some water vapor and a bit of exhaust gases that were not completely removed during the previous exhaust stroke.   In the spark plug electrode GAP, the high voltage coming from the ignition coil creates an electrostatic field in the "gap insulation".  That electrostatic field rises very rapidly in intensity as the voltage is applied.  When the forces applied to the molecules in the gap reach the required level, electrons are ripped loose from the outer shells of the atoms, creating atoms with a net positive charge.   This is called IONIZATION.  

Once an ionization path is created from one electrode to another, current will flow.  This current, flowing through the resistance of the gap, creates the heat that starts the combustion process.   The sudden flow of current, combined with that tiny capacitance (and other small capacitances in the ignition system)....create high-frequency oscillations that want to radiate from the spark gap.   This gap and spark plug is electrically wired to the rest of the ignition system, and to the whole bike, actually, via the grounding of the case; not to mention every wire, etc.  Some radiation is through the air, like a radio signal from a transmitting antenna; other radiation is conductive on the wires.   These oscillations/radiations cover a very broad band of frequencies.  It is these that cause radio frequency interference from the ignition system.  The electrical 'noise' radiates back towards the ignition coil, and the rest of the electrical system and radiates from the motorcycle and can cause problems with such as radios, nearby TV's run off antennas, cause confusion with your bike's electronic tachometer, bike's engine control computer, etc.  

When such radiation gets into the bike's WIRING, it can cause what is called Standing Waves.  These can, under some circumstances, reach very high voltages.  The coil could be well as the electronic module, Hall device in the canister....and on points models even the points capacitor/condenser.   The effects noted above are NOT the only way such 'radiations of energy' are found around the motorcycle, and IN the wiring of the bike.  The collapsing of the magnetic field in the coil as the spark event is initiated (or, just the points or module electrically opening and causing the high voltage generation to begin) is coupled back to the primary coil, which in itself produces a back-voltage.   This back voltage is very complex, and DOES get into the motorcycle's wiring system, through many paths, including the power wire from battery to ignition coil, the tachometer wire connection to the coil, and many other wiring connection details.  If a spark plug cap is lifted and high voltage initiated in a coil, the radiated and conducted electrical field can be VERY HIGH, and VERY DAMAGING.

One of the lines of defense is the spark plug itself.  In cars and trucks, a resistor is mounted inside the spark plug.  Since the spark plug has capacitance TO GROUND besides the gap capacitance mentioned earlier, the electrical noise will find it easier to go to ground, rather than back through that resistor towards the ignition coil, via the ignition wire.  The CURRENT is much lower in the spark too....and current flow is associated with magnetic field strength, while voltage is associated more with electrical field strength.    These field strengths interact, all over the bike.

In CARS/TRUCKS, the wire from the plug to the coil is also usually a resistor...relatively evenly distributed along the high voltage wire's length.  Typically this wire has a core of a Aramide fiber (like used in tires) covered in a somewhat conductive graphite mixture.  Typically the wire resistance is about 5,000 ohms per FOOT.  This wire is a fairly poor radiator of spark energy, from several effects, not just the lowering of current....all of which are just what is needed.   The wire is sometimes called Suppressor Wire.  These act as a plate of a capacitor, while the engine block acts as the other plate.  yes, true, even though widely separated in distance.   So, the resistor wire is not only a poor antenna, but it is a capacitor that shunts off the high frequency noise to ground, rather than allow it to travel through the car/truck.  Some very modern cars are using even more sophisticated methods of Radio Frequency Interference (RFI) reduction, possibly due to the very sensitive nature of the computers, etc., in newer cars, and in some instances to produce very high performance ignition, with possibly each cylinder's ignition being adjustable by computer, at high speeds.     Most of these cars have one coil mounted AT EACH spark plug. 

There are cars that have very special leads from the coil, or distributor, to the spark plug.  There may be a ferrite rod in the middle of the spark plug wire, and a spring coil, the combination of which 'chokes out' RFI.  The spring coil design and the ferrite (concentrates magnetic fields) are critically designed.  The parts are frequency sensitive.     Did you know that Stealth Airplanes have been made covered in ferrite?  

The use of these methods is effective, and avoids the expense and problems of fully shielding the ignition components.....which is the approach used in piston engine airplanes, where the shielding needs to be 100%.    There is usually, in cars, an additional bypass capacitor, of substantial capacitance, on the battery power lead to the coil(s).   This shunts to ground any RFI that might get that far.     Fully shielding the ignition has been done, and partially on BMW Police (Authorities) motorcycles.  A fully shielded ignition can have problems at high rpm, as the capacitance has bad effects on the spark, if said capacitance is high enough, and IT IS for metal-covered ignition wires. Full shielding also allows coils to heat up more.  That happened on the /5 Police bikes, and the fix was to reduce the DWELL of the was found to NOT reduce performance, so that DWELL change became permanent for the civilian bikes....until later dwell angles were used.

Your Airhead motorcycle ignition does NOT use resistance wire nor resistor spark plugs.  Some K-bikes came with radios, or they were a factory option, for which  BMW changed to resistor spark plugs and continued the resistor spark plug caps.  If you do not have a radio in your K bike, you can use standard non-resistor spark plugs, but ONLY if you have resistor caps (5000 ohm).  The K75 was a special case, it had a GAP in the ignition high voltage cables.  Not going to get into the reasoning here.  Just know that the gap can prevent proper ohmmeter readings.

The output of the Ignition Coil is very much effected not only by the number of turns of wire on both primary and secondary, the type of iron core, and many other small details, but also the CAPACITANCE in the secondary windings.   While one can substitute coils that are not the same as the original type's specifications, and the ignition system may seem to work OK, it may be marginal.  The ignition system was designed as a total system, and if you make changes, they can have results that are found out about immediately, or not until much later. 

The theory behind the Kettering ignition is hardly as simple as it appears.  MANY of the finer details were not even known by Kettering and his group.

How to determine the polarity of the ignition coil output (assuming it is unmarked):

This can be done with a high voltage probe and an oscilloscope, or a special type of sensor placed on the high voltage spark plug wire.    Since almost none of you have these things, I have a simple procedure for you.

Warning!   Do NOT do the following procedure, unless you really do have a need, understand the following COMPLETELY, and follow safe practices.  YOU COULD RECEIVE A SEVERE ELECTRIC SHOCK IF YOU DO NOT!   You could also damage your ignition system if the procedure is done improperly.


Cap here means the original existing spark plug cap AND its insulated wire to the ignition coil. The spoke piece is inserted into the cap in place of the spark plug threaded top.  NOTE that I captured the sketch of the spark plug off the Internet, so here it is shown with a snap top style, while the Airheads use the THREADED top style.

This procedure is BEST done by not touching anything, that is, fashioning a method to hold the items in place at the proper distance between them.  If you use gloves, be SURE they are very well electrically insulated.  AGAIN...the BEST thing is to NOT touch anything!   I will outline THAT method!

1.  Remove the spark plug resistor cap from the spark plug.  Insert a piece of threaded spoke into the spark plug cap.  The idea is to have the ignition output, THROUGH THE CAP RESISTANCE, available for making a spark gap. Sharpen the end of the spoke piece a bit.

2.  Set things up so that the spoke piece slightly sharpened end is at 3/8" from the spark plug threaded top.  You must be absolutely certain that the distance is not too great, as you MUST be able to have the spark jump from the spoke to the spark plug top. You do NOT want the high voltage generated without a spark happening, as it could damage the ignition system.   Make this setup so that the spark plug cable, cap, and spoke piece, are all sturdy and will not move out of position.  This is very important to protect the ignition system.  I suggest small pieces of dry wood, and using clamping or whatever you have available. 

3.  Sharpen a standard graphite pencil...yes, an old-fashioned wood & graphite center pencil.  A nice longish point is best.

4.  Fashion a method to hold the sharpened pencil tip graphite core between the spark plug top and the high voltage wire.  The pencil graphite core must not touch either.  The pencil must NOT lay or be close to the metal of the engine. Suspending the pencil vertically using a piece of thin string works OK, or using tape, etc.   Take time to do this properly.

5.  In a darkened area, turn on the ignition.  Crank the engine or otherwise cause the ignition system to fire.  The spark between the spoke & plug top threads must be such that the spark
sprays between pencil & plug top, & NOT between pencil & spoke piece.  If the spark sprays between pencil graphite core and spoke piece, then  the polarity is wrong.  Correct polarity in this test means the electricity is negative.

04/15/2003:  MAJOR revision.  Combine ignitiontheory.htm and ignitionsystems.htm, and major editing.
11/28/2006:  add paragraph explaining points amplifiers
01/07/2009:  revise entire article for clarity
10/03/2009:  Again revise for more clarity, and more technical details this time too.
01/25/2010:  add Nerdy section
01/28/2010:  expand a bit on CDI
06/13 /2011:  Revise for clarity
10/05/2012:  Add language button, update Google Ad-Sense code; improve clarity in a number of places.
11/28/2012:  Add QR code, inadvertently left off the above revision.
02/12/2012:  Revise entire article for better clarity, and remove a FEW extraneous things.
02/16/2013:  Clarity; expand info on condenser, resonant circuit, and other details.
03/09/2014:  Revise entire article for clarity, and adding more nerdy comments, clarify existing ones, etc.
09/15/2014:  Revise to improve clarity even more.  A few technical changes, fix typos, etc. NO serious changes to technical details.  Change order in which certain paragraphs/sections appear.
03/19/2015:  Add section on polarity determination, and some changes in rest of article to direct to that area.
11/08/2015:  Clarity improvements
03/05/2016:  Update meta-codes, layout.
07/30/2016:  Update metacodes and scripts.  Improve explanations. Add sketch.  Improve layout and fonts.
11/30/2016:  Add a note to info on see info in References.

Copyright, 2014, R. Fleischer

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Last check/edit: Monday, January 15, 2018