# Re: [TCML] Spark gap loss

```Hi everyone,

indeed very interesting reading. The paper quotes an
equation by Mesyats, i.e. equation 33 on page 67, which looks like
the best fit to the experimental data and can be rewritten as:

R(t) = p*d^2 / (a*E(t)),

where R is the resistance of the gap (as a function of time), p the pressure,
d the gap spacing, E(t) the energy deposited in the arc up to time t
and a some constant.

This can be written as

R(t)/d = p/(a*E(t)/d),

which relates the resistance per unit length to the energy deposited in the
arc per unit length, which makes the equation more sensible in terms
of its interpretation. This result, though, does not take into account,
that for longer lasting arcs energy will be conducted or radiated away.

The effect of this can be seen in the paper, when after a few us time the
arc resistance will increase again, even though there is still energy fed
into the arc. For longer lasting arcs, such as in a TC the energy lost
due to heat conduction, radiation etc. will have to be accounted for.

I think a reasonable assumption would be, that the heat loss speed
is proportional to the energy in the arc. That implies, that after some
time the energy in the arc becomes proportional to the power fed in, i.e.

R = p*d^2 / (b*P),

where b is some constant and P the power, i.e. R*I^2,
where I is the arc current. We find thus:

R = p*d^2 / (b*R*I^2) or equivalently

R^2 * I^2 = p*d^2 / b

The left side is the gap voltage squared, i.e.

V^2 = p*d^2 / b or

V = d * sqrt (p/b)

This means, that the gap voltage is independent of the current.
This agrees with Berts measurement, where he found a
gap resistance inversely proportional to the current, i.e. R*I constant.
This also agrees with Garys data, where he found a linear voltage
decay in a tank due to gap losses.

Garys measurement results are reminiscent of DRSSTC primary
current rampups, but the other way around. In Garys experiment,
he observed a constant voltage loss for every cycle, while in
a DRSSTC there is a constant voltage gain for every cycle.
A DRSSTC with its phase reversed by 180 degrees works like
a spark gap with constant voltage drop.

Specifically this means, that for every cycle of primary voltage, the
primary cap looses 4 times the gap voltage. Decreasing the gap
spacing would reduce that voltage, but that can't be done, since the
gap shouldn't fire to early. Gap spacing is chosen according to the
primary voltage one wants to achieve.

All together this implies, that the percentage of voltage lost in every cycle
is more or less independent on the choice of max primary voltage.
A pressurized gap helps, though. If you, e.g. double the pressure,
the gap spacing can be reduced by a factor of 2. From the equation

V = d * sqrt (p/b)

halving d and doubling p would reduce the gap voltage by a factor of
sqrt(2).

Another option to decrease losses would be reducing the number of
cycles the coil runs. This number of cycles for complete power transfer
from primary to secondary is determind by the coupling. A larger coupling
would be an advantage, but as every coiler knows, racing sparks put
a limit to this.

Udo

```
----- Original Message ----- From: "Bert Hickman" <bert@xxxxxxxxxxxxxxxxxxxxx>
```To: "Tesla Coil Mailing List" <tesla@xxxxxxxxxx>
Sent: Wednesday, November 15, 2017 7:56 PM
Subject: Re: [TCML] Spark gap loss

```
```Hi Steve,

Thanks for the link - very interesting paper.

```
I really didn't address your question of energy loss or efficiency in my earlier post. IN the late 1990's I did a series of experiments on my static spark gap coil. These were designed to measure energy losses during primary-secondary energy transfers.
```
```
As you are aware, a full energy transfer from Pri -> Sec (or vice versa) for a SG coil typically takes 2.5 to 4 RF cycles to complete. By setting the coupling coefficient (k) to one of the "magic" values (such as 0.133, 0.153, 0.18, or 0.22), complete Pri -> Sec or Sec -> Pri energy transfers can be done within an integral number of RF half-cycles. Using a magic value avoids stranding some energy in either the primary or secondary, simplifying primary V or I measurements and resulting energy calculations.
```
k:     RF cycles:   RF Half-cycles (N):
0.133    4               8
0.153    3.5             7
0.18     3               6
0.22     2.5             5

```
My test coil was set up with a k of 0.18. During testing, I purposely reduced the bang size so that the secondary did NOT break out to prevent streamer losses from introducing errors.
```
```
Spark gap coils never "ideally" quench at the first primary notch (single Pri -> Sec) energy transfer), especially when the secondary is prevented from breaking out. So, after all the system energy has been transferred to the secondary, the gap continues to conduct, and energy in the ringing secondary now transfer "backwards", ringing up the primary tank circuit. After another "N" RF half-cycles, all remaining system energy now resides back in the primary circuit. By comparing the initial peak voltage in the primary circuit versus the peak voltage (or current) returned to the primary circuit after a full Pri -> Sec -> Pri energy transfer, I was able to calculate the total energy lost during a round-trip cycle. A wideband current transformer could used to measure primary current to make similar energy calculations.
```
```
For my coil, the portion of system energy lost when making a primary to secondary energy transfer (from ALL causes) was about 15%. Most of the losses likely came from the spark gaps, since my system used a series vacuum gap with 8-12 static gaps. Because of the large number of gaps, my losses may be higher than for a typical rotary gap. If you have a HV divider or wideband CT to measure primary capacitor voltage or tank circuit current and an oscilloscope, you can duplicate these measurements for your system.
```
```
Although my coil transferred 85% of primary bang energy to the secondary, a well designed SG coil with fewer gaps might hit 90%, perhaps more...
```
Bert

Steve White wrote:
```
I was reading a thesis that studied spark gap losses recently. Although the test apparatus (electrode material, diameter, and gap spacing) does not match exactly what you would find in a typical tesla coil, I found the results very interesting. The closest to the tesla coil scenario was the following from the paper.
```
1. Electrode material: copper-tungsten
2. Electrode diameter: 2.5 cm
3. Gap spacing: 1.4 cm
4. Trigger voltage: ~30K volts
5. Trigger energy: ~1K joule
6. Air at 1 atmosphere

```
The test results at these conditions measured an energy loss of about 7%. If I extrapolate these results to my 4800 watt coil, I am losing about 336 watts in the rotary spark gap. This is less than I imagined since I have always been lead to believe that the spark gap was very lossy.
```
Does anyone else have any other data which shows the loss caused by a spark gap?
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