# Re: [TCML] Subject: Overheated Secondary

```Hi Phil,

```
VA is simply transformer ratings. It would be ideal to use actual wall plug power measurements. But since I use this in a design program, VA is as close as I can get beforehand. For all practical purposes, it won't vary enough to make a significant impact on spark length.
```
```
The equation is simply a refinement of John Freua's spark length equation, 1.7 x sqrt(W). This equation specifically states that spark length changes with input power. What you don't see in that equation is that it is based on 120 bps and on whatever losses were occurring in John's test systems, and it's been a good ballpark for years. I wanted to factor in various cap sizes, various bps, cap charge time, cap voltage, and input power into the equation.
```
Here are detailed ingredients to the following equation:
-----------------------------------------------------------------------
Spark Length (inches) = sqrt(VA) + (sqrt(eJ x BPS x 1.263) x .75)
Where:
VA = volt amps = transformer ratings
BPS = breaks per second.
eJ = effective cap energy in joules = 0.5 x C(tank) x eVp^2
eVp = effective cap peak voltage = x_vp*(1-pow(2.7182818,(-rsg_fr/rsg_t1))).
x_vp = transformer peak output voltage.
rsg_fr = rotary gap firing rate (1/bps).
rsg_t1 = time for cap to charge to one time constant.
The .75 is a conservative loss factor (inserted at the bang energy portion).
-----------------------------------------------------------------------

```
You won't see a major change in spark length, but you will see variations with time and energy. Here are some comparisons to the JF equation and I think you'll find this equation is very conservative (if anything):
```
In all cases = 12kV rating, 60Hz, 120V input
```
I will show mA increase for various cap sizes through 120bps, 240bps, 480bps. BTW, if the table is messed up in formatting, here is what it looked like before I sent it.
```http://www.classictesla.com/temp/Spark%20Length.txt

Take care,
Bart

Cap     BPS     mA      Bart    JF
-------------------------------------
0.01uF	120	30	28.7"	32.3"
0.01uF	120	60	37.7"	45.6"
0.01uF	120	90	43.9"	55.9"
0.01uF	120	120	49.0"	64.5"
0.01uF	120	300	71.1"	102"

0.03uF	120	30	28.6"	32.3"
0.03uF	120	60	41.2"	45.6"
0.03uF	120	90	49.7"	55.9"
0.03uF	120	120	55.9"	64.5"
0.03uF	120	300	79.2"	102"

0.05uF	120	30	27.4"	32.3"
0.05uF	120	60	40.8"	45.6"
0.05uF	120	90	50.5"	55.9"
0.05uF	120	120	58.0"	64.5"
0.05uF	120	300	84.4"	102"

Cap	BPS	mA	Bart	JF
-------------------------------------
0.01uF	240	30	29.1"	32.3"
0.01uF	240	60	40.6"	45.6"
0.01uF	240	90	47.8"	55.9"
0.01uF	240	120	53.4"	64.5"
0.01uF	240	300	75.7"	102"

0.03uF	240	30	26.9"	32.3"
0.03uF	240	60	40.4"	45.6"
0.03uF	240	90	50.4"	55.9"
0.03uF	240	120	58.3"	64.5"
0.03uF	240	300	86.3"	102"

0.05uF	240	30	25.6"	32.3"
0.05uF	240	60	38.8"	45.6"
0.05uF	240	90	49.1"	55.9"
0.05uF	240	120	57.8"	64.5"
0.05uF	240	300	90.7"	102"

Cap	BPS	mA	Bart	JF
-------------------------------------
0.01uF	480	30	28.0"	32.3"
0.01uF	480	60	41.2"	45.6"
0.01uF	480	90	50.4"	55.9"
0.01uF	480	120	57.3"	64.5"
0.01uF	480	300	82.0"	102"

0.03uF	480	30	25.1"	32.3"
0.03uF	480	60	38.1"	45.6"
0.03uF	480	90	48.4"	55.9"
0.03uF	480	120	57.2"	64.5"
0.03uF	480	300	91.6"	102"

0.05uF	480	30	23.9"	32.3"
0.05uF	480	60	36.2"	45.6"
0.05uF	480	90	46.2"	55.9"
0.05uF	480	120	54.8"	64.5"
0.05uF	480	300	92.1"	102"

FIFTYGUY@xxxxxxx wrote:
```
```Is this "VA" the nominal open-circuit voltage times the nominal
short-circuit current of the power supply?
If so, why would this matter (past a certain point with a SRSG, or past
```
another point with a RSG)? If I plug my primary into the local overhead power
```line, neither the bang energy nor the BPS will be any different than if I
```
use, say, a PT. And even then, once we get a big enough power supply that is
```1:1 "resonant" with the primary cap, how much more gain is to be had?
But from your equation, using a power supply with 100 times a
```
"reasonable" VA rating would always yield a significant *multiplication* of spark
```length.

-Phil LaBudde
Center for the Advanced Study of Ballistic Improbabilities
```
```
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