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Aftermarket Alternators
Installation, Capability, Performance

Copyright, 2014, R. Fleischer

Note:  Read 15-A and 15-B, first!!!



Discussion:  (much of this discussion is pertinent to ALL charging systems!!):

Measuring or specifying output in watts is not as simple as it may seem.   The
simple part is that watts is equal to voltage multiplied by amperes; often shown as  P = VI. 

Unless the output wattage of the alternator system is specified at a practical usable rated
, it is possible for the output voltage to sag from a large load (big headlamp, driving
lights, heated clothing, whatever).  The output current (and even wattage) could possibly
be high, yet the voltage is too low for a full battery charge.   If the output voltage was too
low to keep the battery fully charged; yet the current availability was high, it is possible for
false wattage advertising.
By false I mean that while the wattage may be high, it cannot be used properly because the
battery MUST HAVE enough voltage, or it is not fully charged. 
What is really important is
the real output with a "reasonable & usable" charging voltage at the battery, that keeps the
battery well charged....and high enough of a charge to have LONG BATTERY LIFE.  You
also want a reasonable fast recharging, after such as starting, or being for a while at a
traffic signal, etc.

If the voltage is too high, the battery could deteriorate from too much voltage being
applied, which also means too much current, which means wattage (HEAT) being MADE
by all that electricity flowing INTO the battery.  The battery could overheat & warp; or use
water too fast, or if a sealed type it might have enough internal pressure to open the
safety valve (VRLA types and other sealed batteries).

You want the battery to recharge quickly after starting the bike or perhaps from long
periods of waiting at stop lights... and then riding off.   If the battery terminal voltage
falls to 12.7 (or below) whilst on the highway, that is not enough voltage to truly maintain
the battery at a full charge.  In fact, if the battery terminal is below about 12.5, the battery
is being drained!  

You also need a higher charging voltage than 12.7, to enable the battery, due to
inefficiencies in the battery chemistry itself, to REACH FULLY charged.  It becomes
more critical when doing stop and go riding in, for example, city traffic.   At the time
you stop where you are going, be it work or home or other, you want the battery to
be fully charged...or very close to that.

There are three basic reasons for an aftermarket system; (1) you need more watts; &
(2) you want more reliability, perhaps; & (3) you'd like the additional watts to be
available at idle RPM, or, not much above it.  That is helpful for stop and go riding in
big city traffic.

An aftermarket system usually should not only have MORE TOTAL REAL WATTS
available, but the system should properly maintain the battery under typical operating
circumstances.  This includes idling for periods of time in stop and go traffic.  Even
if the voltage sags 'some' at a stop light, the alternator desirably should be capable of
fast recharging.

The system should be capable of handling all the electrical items likely to be in use at
the same time for reasonable periods of time.  Idle rpm output, or slightly above idle
rpm output, should be sufficient for normal use, as this is one of the complaints about
the stock system, in stop and go commuting use.

NOTE that the idle rpm of Airhead motorcycles should not be set below 900 rpm, no
matter what you read elsewhere's, and no matter what alternator, stock or otherwise. 
I highly recommend a target of 1000 to 1050 rpm for idle rpm, after a full engine warm-up
(5 miles or 6 minutes perhaps) at the normal altitude and temperature you ride in.    
This rpm was selected by me for a variety of factors, including carburetor performance
& synchronization.

I did a careful installation & testing to evaluate the practicality of the ORIGINAL
 permanent magnet alternator system.  A known perfect battery was used.
The system used light electrical loading & was allowed to fully charge the battery
according to the system voltage regulation (14.24 in this conversion instance).  Then
the battery was loaded moderately for a while until a known value of battery DEcrease
in voltage was noted.  At this point the output was measured by starting the engine
(which additionally slightly drained the battery), & then I used, quickly, various rpm
during immediate measurements.  That is a simplification of the various tests I did.  
My method for testing other alternators, whether aftermarket or stock, is the same,
although the voltage noted above might be different, depending on if a fixed setting, or
if it was adjustable...and if so, if I adjusted it.

The charging characteristics of batteries of different types varies rather a considerable
amount.   For MOST types of lead-acid batteries, if one applies a voltage of about
12.8, constantly
, eventually...and this could take a LONG LONG TIME... the battery would 
reach nearly full charge and then require very little current, from the charger or system,
to maintain that stabilized voltage.  For most batteries, 12.8 volts at room temperature
is very close to a full charge (but not what is called a higher 'surface charge', which is
unimportant here).    If the applied voltage is raised, within reason (not exceeding a
maximum value, often nearly 15 volts), the battery will reach the new applied voltage &
then the charging current needed to maintain that voltage will be higher than at a lower
voltage...that is, the charging current needed will be progressively higher for a stabilized
higher voltage.  Some battery types are quicker to convert chemically to a full charge. 
I deem this characteristic relatively UNimportant.

Batteries vary rather WIDELY as to the current needed from the voltage source for any
one specific voltage.   Generally speaking, a typical 'flooded' type of battery of motorcycle
size (I will use the larger motorcycle size, about 28AH, as illustration), will need about 2
or 3 amperes to maintain about 14.1 volts AT the battery TERMINALS.   Some Gel and
AGM type batteries are quite different.   This 2-3 amperes has NOTHING to do with
what the rest of the motorcycle will require for ignition, lights, etc.

A battery requires more voltage to maintain its full charge at lower temperatures.
For the regulator at room temperature, the bike's system will try to keep the battery
at a high floating charge level, perhaps around 14.2 volts (this could be 13.8-14.7,
depending on VR and other things), when the rpm is high enough, assuming
enough alternator output capability.  As temperature drops, the VR output should
increase SLIGHTLY, and vice-versa.  A tenth or two tenths of a volt is typical, with
maybe another tenth if the temperature is near freezing or somewhat below.
BMW's original VR settings for the stock bikes is ~13.8 volts.  I have always felt that BMW
was WRONG in selecting 13.8 volts but I understand why; which has to do with water use
from the flooded batteries, and some minor other things.  The Authorities (Police) VR
is set higher than even the EnDuraLast, however....nearly 14.5, depending on
Most voltage regulators have a voltage versus temperature effect, purposely
built-in. This is because the voltage needed to maintain any given charge percentage on
a lead-acid battery will vary with temperature, AND, the chemical conversion works faster
with a slightly higher charging supply voltage, if the battery is COLD.  The COLDER the
battery, the more voltage is needed from the system.  The voltage regulator, ideally, is
mounted in the same airflow as the battery.  Generally, only a few tenths of a volt is the
temperature compensation, from perhaps 120F down to perhaps 20F.....the typical
range of temperatures seen by the battery and VR.  Some wider temperatures are
seen sometimes, and one can add a few tenths of a volt if going lower, subtract a few if
going higher.  Motorcyclists rarely ride where battery temperature will exceed 140F
(typically from engine heat blown over the battery).  Some ride when the thermometer
is below freezing.  As the battery temperature falls towards freezing and below, the battery
has a much more difficult time (it is, at its core, a chemical reaction device) producing the
current needed to start the engine...which has higher friction due to cold and thick oil and
decreased clearances from metal shrinkage; THUS the starter motor is going to pull a lot
more battery current.  The chemical conversion in the battery, to produce electricity, ALSO
gets more sluggish, and this is not only in battery delivery of electricity, but in re-charging,
hence the higher charging voltage.  So, in cold weather, everything is being much harder
on the electrical system.

At the time I am updating this article, on December 26nd, 2015, I have still be unable to
arrange the testing of the latest EnDuraLast alternator, nor, the latest Omega, therefore
testing results are for the original models.

The STOCK Bosch Alternators:

BMW has used several versions of the 'stock' Bosch alternator in its various
Airhead motorcycles.  The highest output was 280 watts rated, used in the /6
and well into the eighties.   The lowest output was 238 watts rated, on the
last of the Airheads (but it began charging somewhat lower in rpm).
The following is TRUE ACTUAL USABLE OUTPUT of the stock 280
watt Bosch alternator, using 3.7 or 2.8 ohm later model rotor; known good
connections, wiring, battery, switch, etc.
NOTE that you can REALLY expect to get VERY close to the RATED
output from Bosch Alternators.  This is NOT necessarily so, with the
aftermarket ones.  You will be able to see that, later in this article.


Output, amperes







Approximately the point of equilibrium with the stock system drain of lights and ignition



see above.  5+ amperes is available for charging after considering the ignition, basic lamps, etc.



MAXIMUM available, battery at 13.5 v, and rising.  This is 270 watts.  Very slightly more will be available as the voltage rises a wee bit more.



watts = voltage multiplied by amperes

NOTE that the stock alternator produces what Bosch specified.  Note also that
the voltage is a decent value, & above the minimum needed by the battery,
to maintain a FULL CHARGE, even at maximum output.

The "ORIGINAL" first generation "400" Omega Alternator,
as sold by Motorrad Elektrik:
Note that there are two sources for the GENUINE  "Omega" Alternators, mfr by
Jeff Lee of Emerald Island...products of high quality.
Those sources are Motorrad Elektrik and Beemershop.

The tests on the original Omega were not as extensively done as on the temperature, oscilloscope, stress gauges, hot/cold differences,
etc.  Still, what follows for the early Omega is probably what YOU can actually
expect of it.

Testing was with a known accurate ammeter with short heavy gauge leads, connected in
series with the Omega diode board output.   The battery was drained somewhat to begin
with (on purpose); and, a digital voltmeter was placed across the battery terminals.  
Readings were taken well before the battery was charged, with heated grips, accessory
lights, and headlight... all turned on.   Readings were repeated with lights off, & also with the
battery fully charged.   The "set point" of the VR appeared to be close to 13.8 volts. I
consider that somewhat too low for best battery life and system performance, but it does
extend intervals between adding water on flooded type batteries.

The chart below is a summary, & where you see two instances of a higher rpm with lower
voltage, that was due to battery charge condition at the instant of measurement, & small
deviations from expectations, due to, I think, heating, etc.


Voltage at battery

Output in amperes


1550 11.70 2 23.4
1700 12.5 5 62.5
1750 11.83 8 95.6
1750  tst 1 12.5 5 62.5
2200  tst 2 12.8 12.5 160
4000  tst 1 12.64 28 354
4000  tst 2 13.5 20 270
5000 13.2 31.5 415.8









 You would need ~2400 rpm to enable the output of the stock 280 Bosch at 2100.  THUS, you can
rightly assume that this alternator is not any better for constant stop and go in town, unless you
have a bit of distance between stops....wild guess would be a half mile or more.   But, this
alternator DOES produce considerably more wattage than the stock 280 Bosch, out on the road.

NOTE CAREFULLY, the two 1750 & the two 4000 rpm tests. Note how the wattage varies
with the voltage.  I specifically loaded the system in order to get these readings.   What
especially interests ME, Mr. Nerd, is that at 1750 rpm, a heavy load that dragged the
system to 12.5 volts produced 95.6 watts, but the voltage was too low to fully charge the
battery.  Compare carefully to the two 4000 rpm tests....and to my extensive comments
early-on in this article.

You can see that the battery would be MARGINALLY CHARGED at 4000 rpm if 28
amperes of load was used.   This resulted in 354 watts.   If the load was DEcreased, the
voltage rose to 13.5 volts.  That is STILL not enough floating voltage...I'd prefer to see
14 volts or even a bit more.    Increasing rpm beyond 5000 did not yield increased output.

To be FAIR about all these things,
I note that this alternator WILL keep the battery charged
more than enough to enable you to use WELL OVER the maximum wattage that the Bosch

Output might be better for the battery if the VR was set higher. The voltage regulator
was NOT the adjustable type on this tested bike.   The battery was also not new.
   The ammeter & its
leads & connections add a small series resistance; this would have the effect of moving the output
higher up in rpm (although slight).   This also applies to the Bosch and EnDuraLast during tests.  
While voltage multiplied by amperes is how one converts to watts, it is entirely possible, under some
circumstances, for a battery not 100% charged, to have a lesser or greater current input at a
particular terminal voltage....and as such, the USABLE system wattage is a bit difficult to interpret
to the layperson.   

It is interesting to compare figures with the stock Bosch system.   While it is possible that there are
some anomalies present that I did not go into, especially noted is that the stock Bosch-equipped
bike I tested had perfect electrical connections, etc.....
still, the Omega output was low at low
rpm, but it rapidly overcame the stock system as rpm into the cruising area was attained. 

It is important for those with considerable need for more wattage, to understand that the
output of the Omega is ultimately HIGHER than the EnDuraLast.....but that the EnDuraLast
has much higher output at truly low rpm, thusly, is PROBABLY better for COMMUTERS,
especially if their electrical needs are modest.

The weight of the Omega is nearly identical with the stock Bosch; differences are so small as to be
of no concern.

The 'new' higher powered '450 watt' Omega:
This unit has a 81 mm rotor (instead of the original Omega's 76 mm) and a larger stator to match.
When tests are run on a 450 system they will be posted here.

SAME, for the EnDuraLast similar to the Omega.

The EnDuraLast Alternator
(the original, with the PERMANENT MAGNET ROTOR):

The weight of all removed stock Bosch components:  diode board, stator, rotor, housing, regulator,
some wiring, etc., is 87 ounces; all the EnDuraLast items as installed will weigh almost exactly the
same.   For the Omega, as noted above, weight is also about the same as the stock Bosch.

Leakage current:  under 1.5 MICROamperes, worst conditions.

Rotor diametrical clearance to stator:  0.006-0.008".  This can vary some with the components,
as well as the exact fitment of the inner timing chest to the engine casting, which is adjusted
slightly during a timing chain or other similar R/R job.
Rotor runout, axial: negligible.
Rotor lateral runout (side to side):  0.00075" maximum.

EnDuraLast Rectifier/Regulator:  In a normal system in a motorcycle, the regulator is USUALLY
mounted in an area that allows some engine heat (comparable to battery temperature in a modest
way), to influence it.  In most modern cars the the regulator is usually PART OF the alternator ITSELF,
and thus as the alternator warms up, the regulating voltage DEcreases slightly, on purpose, to match
battery temperature characteristics.   This is not necessarily so on this conversion; depending on
where the regulator is mounted, and HOW (it generates heat internally).  However, from my testing
results, the EnDuraLast RR unit is OK over a normal temperature range, and I do NOT
consider its location to be of importance, EXCEPT that it should be kept away from areas
of high heat, to extend its life.  This means to NOT mount it to engine metal parts.

Note that there have been reports of RR unit failures when high levels of alternator output
are consistently-continually used. Best that it be mounted where relatively cool air is on it.


The EnDuraLast voltage regulator is supposedly internally fixed at about 14-14.26, and hence a small
amount more of the EnDuraLast output is used to keep the battery charged, once charged, than with
the stock voltage regulator setup, this is truly a minor thing. A very good thing is that voltage,
which is high enough to very nicely keep a full floating charge on the battery, during
most uses....and anything over about 1500 to 1600 rpm is QUITE adequate to supply the
stock motorcycle, or, with one with an added headlamp.  That means that an RPM that
is much lower than cruising RPM is going to produce plenty of wattage. 

ACTUAL results for the EnDuraLast (but, see information much further downwards
about later tests on a different bike and different type of installation).

RPM Current, Voltage Watts
900 6 amperes  
1000 7.5 amperes, 13.12 volts 98.3
1000 8 amperes  
1200 12.5 amperes, 13.39 volts 167.4
1500 15 amperes  
1600 16 amperes  
1900 18 amperes, 14.24 volts 256.3
2050 20 amperes, 12.81 volts 256.2


26.5 amperes, 12.8 volts 339.2

Did you notice that the output voltage seriously sags above 1900 rpm?  Still, it
does not sag so much that the battery is discharging.   For the more nerdy
reading this, the voltage on the battery would be a bit over 14, which is very
good, IF the drain I put on the system had been lower.  It may be very important
for you to understand some details about the BIG differences in output watts &
voltage, between the Bosch and Omega-type, and the EnDuraLast.
I was UNable to obtain more watts, no matter the rpm.   This is a
characteristic of permanent magnet alternators.  Another characteristic
is larger voltage sag percentages [compared to the Bosch & Omega...
basically any WOUND ROTOR types] as you reach top output levels.

Note that for the otherwise stock motorcycle, & no additional electrical
loads, the EnDuraLast alternator will maintain a reasonable charge at
about 1100 rpm.  This means that keeping the battery charged during
stop and go big-city-type-commuting is no longer an considerable
  THIS is where the EnDuraLast is really good.

Re-said, differently:
The EnDuraLast has more usable wattage output at very low rpm, compared
to the stock Bosch, or the 400 Omega.  However, the Omega has higher
absolute maximum output wattage. Note also that the voltages at high
watts output is not actually all that much different, and sometimes worse,
than the stock 280 watt Bosch. Compare very carefully!  The advantage
of the EnDuraLast is at low rpm....and, it does NOT give any huge amount
more wattage at its maximum output, compared to the stock Bosch.

The EnDuraLast is better for in-city stop and go, than the stock or Omega
alternators.   The Omega is better for maximum output, and for maintaining
the preferred higher battery voltage AT such a higher output....a DUAL benefit.

It was noted that the Regulator set point for the EnDuralast that was tested, at
84F, was  14.48-14.50 volts, which is higher than expected, and more to my
liking than the Omega.
  Since the set-point is slightly affected by where the regulator
is mounted;... due to LEAD LENGTHS between stator and regulator this voltage may be
a bit different, if you have your regulator mounted next to the battery (which is a good
place, and was my suggestion to the developers). MY installation was to have the
regulator mounted in the R100RT fairing air inlet area...where I could control
air flow, etc, for my testing.  I suggested to John Rayski, that his literature
reflect my findings.  He did so, with SOME of my findings.

1981 & later BMW airhead motorcycles; & earlier models with aftermarket electronic
ignitions, are somewhat sensitive to electrical noise in the battery supply. That is ONE
reason, of several, that the original MECHANICAL VR was changed to an electronic
type in 1981.  Some electronics, including diodes and a RR regulating transistor, can
CREATE high-frequency spiking type of electrical noise.   Thus, tests with an dual-trace
type of oscilloscope were going to be run on the system; one trace monitoring the battery,
and one trace monitoring the ignition pulses. 

Somewhat nerdy:
As you have seen, the EnDuraLast did not do what its advertisements seemed to say,
regarding output, performance curve, etc. advertised specifications, certainly NOT in a
meaningful and USABLE manner.  Considering that my EnDuraLast was provided to
me for FREE, and for me to KEEP; in return for my comments, technical advice, etc,
all this from the manufacturer of the system; rest assured that my negativity in some
areas certainly DOES reflect my independent thought.
My results did not duplicate
the specifications/information on output performance.  I did try to improve the
installation (one of what I promised to John Rayski). 
I made some minor changes,
eliminating some quite small voltage drops... that helped some.  I have thought
about these things at some length.
   I have an IDEA of what may be PART of the
problem... & this is theoretical:
   The stator output is via TWO wires, with NO grounding reference. That is, the
output is single phase, which is much less efficient than the 3-phase
of the other alternator systems in this article.  Because the output is
just TWO wires, this has to be so.  The EnDuralast Rectifier/Regulator unit
COULD, and probably does, have a circuit that involves a type of multiple-diode
rectifier called a "Bridge Rectifier".  That can be done with special transistors
acting like controlling diodes (and, hence, act as regulators); or, by power diodes.
Makes no real difference as to what type.  I did not test the output of the RR unit
for type of waveform for determining the type of rectification.
 For my own
curiosity, I should have....although the end result would mean nothing for
performance....that is fixed by the inherent design.
While a half-wave rectifier could be used, I am 90% sure THAT is not the design....
because that is illogical, as output would greatly suffer; and, the extra parts for the
bridge-type are cheap.    This discussion of rectifier types is really nerdy here.
What is still nerdy, but actually of some importance, is this:
A property of a two-wire source to any type of rectifier, is that the IMPEDANCE
(nearly the same thing as resistance) of the STATOR, and connecting wires from
that stator, can be MUCH higher, with little deleterious effect, than the same
increase in EFFECTIVE output resistance.   THUS, the STATOR wires....the
EnDuraLast YELLOW wires...can have more resistance in them and still get decent
output; but, the RED wires output, and the CASE ground output, will need heavy
gauge wires, and negligible voltage drop in connectors and connections.
electrical reasons are not easy to explain to someone without serious knowledge
of impedance/resistance and magnetic coil characteristics.

NOT nerdy:
I WAS able to get a modest improvement (about 1.3 amperes, nearly 18 watts) by
simply repairing just the bullet connectors of the RED wires, as furnished by the
manufacturer, EuroMoto Electrics. This was reported to the manufacturer, so that
the KIT could be upgraded/improved.  I think that FURTHER improvement would be mounting the RR unit next to the battery due to the very short
output-side wires then possible.  As such, my recommendations to the makers of
the EnDuraLast was to mount their RR assembly next to the battery, which would
be a decent heat sink also.  At the time, I had not tested this idea, but I have, since,
and there IS a small improvement.  Additionally, the mounting of the RR was placed
onto the frame downtube on the left side of the battery area, which exposes it to
cooler air....this will lengthen its life.   SEE NEXT SECTION!

In June, 2015, I tested a permanent magnet EnDuraLast alternator in a 1995 R100RT,
MY OWN!    Installation was of the 'new method', of the type I had recommended; with
some mounting improvements too, & the RR unit was mounted on the left rear frame
member next to the battery.  I made sure all connections, etc., were solid and proper,
before I load tested the Odyssey battery (yes, an Odyssey, which is a not recommend
type for the EnDuraLast), and then ran the battery down a few ampere-hours more,
before doing tests.  These were simple tests, with a digital voltmeter at the battery;
and an ammeter in series with the RR unit's output by replacing the fuse with jumpers,
which were nearly a foot long overall, and not of heavy enough gauge, to give absolute
maximum possible performance values but adequate for older installations, with some
years on them, etc..  These are, then, real-world representative numbers; what YOU might
really expect.  If large gauge wires were used, or a clamp-on/over meter, and a more
discharged battery, particularly if not an Odyssey, I believe the output would have been
slightly higher.
8 amperes output at 900 rpm
10 amperes output at 1000 rpm (and, 12.42 volts)
13 amperes output at 1200 rpm
17 amperes output at 1500 rpm
17.5 amperes output at 1600 rpm
18 amperes output at 1900 rpm
21 amperes output at 2050 rpm
I did a further test as the battery began to recharge, but still was not fully charged.
That test was at 2500 rpm, and I got 19 amperes at 13.95 volts (265 watts)....and,
after several minutes, noted the RR unit was getting fairly hot. This was with NO
forced air cooling.  I did not try for an absolute maximum wattage output, which
would have required discharging the battery again, and this time more considerably.

You should compare these figures with the chart ones, well above.
The results reinforce my statements, condensed here, that the EnDuraLast is
the alternator to use if you are doing stop and go city-commuting; but NOT the
alternator to purchase if you really need lots more maximum wattage.

Note:  The permanent magnet rotor in the EnDuraLast alternator has fan blades
at the forward end.  Due to the fan proximity to the cover, ETC., the fan makes a
small amount of whirring noise during operation, that varies with engine RPM.
This has been remarked upon now and then, but is not annoying, unless you
have 'just' noticed it.


1.  The stock 238 to 280 watt Bosch systems are adequate for most Airhead riders.   If
driving lights, heated grips, and other accessories are contemplated, the stock alternator
will be marginal or negative on electricity generation.   It depends on how much additional
load is being actually used, for how long, and what the average rpm is, peak rpm, and idle
time.   Very difficult to make a definitive statement, as riders differ in how they ride and
use the engine.  If you want some estimates for the type of loads and your usage, I can do
that for you, upon request to the Airheads LIST on the Internet.

2.  For CITY COMMUTERS with reasonable to modestly high electrical loads who do a lot
of very short distance stop and go, you might consider the EnDuraLast over the 400 Omega.  
For those with similar electrical loads, or higher, but who do mostly open highway riding,
the Omega will produce the additional electricity that might be needed.  There is no question
that the EnDuraLast Permanent Magnet unit is considerably better for in-town short distance
stop and go riding.

 I may modify recommendations after testing the 450 Omega and other alternators.

 The Omega definitely has the best maximum output.  This means the Omega would be
better for those with very large electrical loads but who are not necessarily city commuters. 
I may modify this paragraph after I test the 450 Omega.


Reliability is improved, if one has a /5, by using a later, better ventilated, front metal engine cover.

Reliability is improved, if one has a RS or RT, with NON-louvred front fiberglass cover, by installing
a louvred one, or by making slots in the solid fiberglass cover.

rev:  01/27/2008...checked for clarity
02/06/2009:  mention of the Omega 450
09/16/2009:  update article for clarity, numerous places
05/07/2011:  Clarifications for comprehension, entire article
09/17/2012:  Minor updates. QR code added; Google ad layout changed.
2013:            Remove language button, due to problems on some browsers.
10/22/2014:  Minor updates, nothing substantial....but I did include some commentary about
                    real-world usage, at equilibrium and slightly above, that I had not emphasized previously.
06/16/2015:  Addendum
12/26/2015:  Increase font size.  Update meta-codes.  Justify left for everything.  Clarify a few things.


Copyright, 2014, R. Fleischer

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