Brian et al,

Well, you caught me with a simplification that I made.  Actually, the spark 
voltage (at the coil) on an oscilloscope looks roughly like what you 
described; a decaying sinusoid.  However, I think that you may have 
broadened the study beyond the actual spark.

The first peak has a rapid rise determined by your formula where the 
capacitance is the point capacitor in a Kettering ignition, and just stray 
capacitance in either capacitor discharge ignition (CDI) or inductive 
discharge ignition (IDI).  Indeed, the inductance is from the coil.  (This 
makes for a fast rise time in electronic ignitions and may create radio 
interference problems.  Various types of spark plug wires are used to slow 
this rise time at the plug to reduce this problem.)

The top of the first peak is limited by the striking of the spark.  The 
duration of the spark is the length of the top of this truncated first 
sinusoidal cycle.  Note that it is the only time in this picture that a 
spark is present.

The remaining decaying sinusoidal cycles are as you described, with the 
resistance mostly in inductor losses and radiated energy in the form of 
radio waves.

My original time constant simplification deals only with the top of that 
first peak when the spark is struck.  The stray capacitance it tiny for an 
IDI and thus can be ignored during the spark, leaving only the inductance 
which describes the energy source, and the spark resistance which describes 
the energy sink to consider.  In other words L/R.

In the CDI case the coil acts as a pulse transformer and the inductance of 
the coil can be ignored pretty much for the duration of the pulse (but 
certainly not the decay).  Since it is only the pulse that we're interested 
in, and the capacitor describes the energy source, I think R*C roughly 
describes the time constant of the spark.

Now I admit that the spark itself is not a linear resistance.  However, my 
point is only that for energy supplied by an inductor versus a capacitor 
the duration of the actual spark has opposite relationships.

If I am correct, bigger gaps are better for CDI, smaller for IDI.  My 60's 
measurements confirmed this.  However, good science requires replication, 
and I was hoping that someone on this list could do that for all our 
benefit.

BTW, both CDI and IDI don't wear points electrically.  In modern instances, 
both also eliminate points in favor of electronic pickups.

I am still curious about what "modern" computer controlled cars use for 
their ignitions.  My shop manuals only show black boxes.

Mike