# Re: Spark gap resistance

```Barry and all,

The "big Fleming book" is most likely "The Principles of Electric Wave
Telegraphy and Telephony" by John Ambrose Fleming, Longmans, Green and
Co.

I do have a beat-up reading copy of the 1910 2nd edition, which is 906
pages in length. The section you've provided above is part of a section
entitled "The Resistance of an Oscillatory Spark", and it references
work done by professor A. Slaby. Unfortunately, I presently don't have a
scanner available, so I'll attempt to summarize some of the findings in
the text. Dr. Slaby found that the resistance of a sparkgap rises
parabolically with sparklength for small lengths, but afterwards
increases linearly. He also found that increasing the capacity of the
oscillating RLC circuit [and thus the current] decreased the spark
resistance per mm. Estimating off a graph he measured the following:

400 pF   1222 pF
Spark R  Spark R
Spark Length    (Ohms)   (Ohms)
1 mm        0.25    ~0.01   (~Values are estimated from graph)
2 mm        0.9     ~0.15
3 mm        2.3     ~0.25
4 mm        5.0     ~0.8
5 mm        7.0     ~2.0

For all breakrates with the same spark voltage small sparklengths have
higher conductivity per unit of length than long ones, thus pointing to
the advantage of using a number of small gaps in series instead of one
long one. [Interestingly, J. Zenneck, below, found quite the opposite
situation!]

In addition, Dr. Slaby tried various metal balls (10 mm diameter) to
determine the effect on spark resistance, determining that tin, silver,
cadmium, zinc, brass, and copper balls gave lowest resistance, while
lead, aluminum, magnesium, and iron resulted in significantly higher
spark resistance.

Dr. J. Zenneck [" Wireless Telegraphy", 1st ed., McGraw-Hill, 1915,
443pp] had previously demonstrated that when an oscillatory circuit
contains a sparkgap, simple exponential decay does not hold, and instead
the waveform decays linearly - this was in 1904 by the way(!),
reflecting the fact that the actual spark resistance increases as the
amplitude of the tank current decreases. However, most experimenters of
the time assumed that the spark resistance was constant, and computed an
"effective" spark resistance by measuring a mean value of the rate at
which the oscillations decreased - called the decrement. The decrement
of an exponential curve is the ratio of amplitudes at the beginning (A1)
and the end (A2) of a cycle, or d = A1/A2. The logarithmic decrement is
the natural log of this: ln(d) = ln(A1/A2), and the amplitude of the
oscillatory envelope would be:

A = Ao*e^(-d/T)*t
where T = period for 1 cycle of oscillation
e = 2.718281828

For an RLC circuit with only Joule losses [i.e., no radiation or energy
transfer to the secondary], it can be shown that d = Pi*R*(Sqrt(C/L) and
the behavior is exponential.

The more important case (for us at least) is that solved by Zenneck for
the linear decrement often observed when a sparkgap is inserted into a
low-loss RLC circuit. Where the sparkgap is the predominant source of
energy loss, the decrement actually reflects the _difference_ in
amplitude between cycles (A1 - A2) instead of their ratios as in the
exponential case above. For this case, energy loss is NOT proportional
to the tank current squared. Zenneck solved this case and defined an
average (but still non-linear) "gap resistance" as the "average"
resistance that, if substituted for the gap, would absorb the same
amount of energy as is actually absorbed by the sparkgap during the
entire oscillation series. For this to occur, the gap voltage is assumed
to remain essentially constant during all the time the gap is
conducting.

Zenneck found that the "equivalent" gap resistance, when the gap was the
predominant source of energy loss, was inversely proportional to the
current (more current means lower Rg), directly proportional to the
squareroot of the inductance (more inductance means higher Rg), and
inversely proportional to the squareroot of the tank capacitance (more
capacitance means less Rg). Zenneck then shows some curves which
indicate that gap resistance also tends to linearly increase with
increasing gap length. Finally, Zenneck also states that multiple gaps
tend to, overall, have a higher decrement than single gaps up to 80 kV.

Seems like we've "rediscovered" much of what these earlier pioneers
already knew - and they didn't have the oscilloscopes, computers, and
simulation tools that we now take for granted... my hat's off to them!!
:^)

-- Bert --

Tesla List wrote:
>
> Original Poster: "B2" <bensonbd-at-erols-dot-com>
>
> Hi All,
>  This is a quote from *Fleming's big book:
>
> "Measurements of oscillatory spark resistance have also been made by G.
Rempp.
> Rempp employed the Bjerknes resonance method above described, the secondary
> circuit (details in book, which I don't have) being very loosely coupled with
> the primary circuit containing the spark gap.  He employed rather small
> capacities, 270 to 6080 mmfds (270 pF to 6080 pF), and long spark gaps, 0
to 5
> cms (0 to 2 inches roughly).  His chief result is that as the spark length
> increases from zero the spark resistance falls to a minimum, which occurs at
> about 3 mm. (0.118" or 1/8", 2.75 Ohm, 273 pF) for small capacities and 6 mm.
> (0.236" or 1/4", 0.5 Ohm, 6080pF?) for large capacities, and that after
this is
> reached the spark resistance increases with spark length very rapidly for
small
> capacities, but much more slowly for larger capacities.  He found, as others
> have done, that beyond a certain capacity the spark resistance ceases to
> diminish with increase of capacity."
>
> G. Rempp, Ann. der Physik, 1905, vol. 17, p. 627, or Science Abstracts, 1905,
> vol. 8, A., p. 606.
>
> *Don't know the name of the book.  Some kind of anthology (Bert do you have a
> live copy of this book?).

```