How Spark Ignition Systems work
....more than you wanted to know....
This is article ALSO contains, revised, the now deleted old article: ignitionsystems
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 test...you 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:
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 used...to transform...the primary coil magnetic energy....to 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):
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.
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: http://bmwmotorcycletech.info/ignition.htm
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.
BE SURE TO READ ARTICLE 29, IT HAS A LOT MORE ABOUT POINTS....AND IGNITION.
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: http://bmwmotorcycletech.info/Ignition.htm for more information. If you need wiring information for an old Accel, see my REFERENCES article. http://bmwmotorcycletech.info/references.htm
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 problems....so 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 website....as is information on how to properly repair a broken tip on the camshaft.
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.
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 damaged....as 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 points.....it 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.
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 Accel....to see info in References.
©Copyright, 2014, R. Fleischer
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Last check/edit: Wednesday, November 30, 2016