Charging time voltage using sphere gap

[haversin]

   I blew up the small 2 nF salt water cap I was using for making Lichtenberg figures while doing some sphere gap voltage tests. The cap flashed over a few times at 1.5 cm sphere gap setting (45 kV) and then held strong. I increased the gap to 2.0 cm (57 kV)  expecting another flash over but instead I heard a muffled bang and the cap would no longer charge. An autopsy revealed a small crack in the plastic bottle under the outer Alum foil.
   I then made a 5.5 nF cap from a large Costco plastic pretzel container with Alum foil on both inside and out. This cap charges up to 57 kV with no problems. Here is the voltage testing setup:

The sphere gap is in parallel with the cap and the VDG charges the cap until either sphere gap breaks down or the cap breaks down. The white cross pipe holding the upper shank and sphere is a 100 k water resistor to limit current through the sphere gap.

Here's a small python script to calculate sphere gap breakdown voltage:

Code: [Select]

from math import *
p0, t0 = 760., 20.
# p is atmospheric pressure in mm Hg, t is temperature in deg C.
p, t = 29.98*25.4, (66. - 32.)/1.8
# r is sphere radius in cm, d is sphere gap in cm.
r, d = 4.8/2.,1.2
delta = p/p0*(273. + t0)/(273. + t)
# vb is breakdown voltage in kV.
vb = 27.2*delta*r*4.*(1. + 0.54/sqrt(delta*r))*d/r/(d/r + 1. + sqrt((d/r + 1.)**2 + 8.))
print 'vb = ',vb,' kV'The equations are from here:
https://www.hindawi.com/journals/aee/2014/980913/

   I want to make some Lichtenberg figures at 50 kV but I first must test how accurate the charging time method is in determining discharge voltage. My VDG charging current is down to 3.9 uA due to an old belt, it's 6 uA with a new one but I refuse to replace it until it completely falls apart. These very low charging currents limit the way voltage on the cap can be measured.

 To test the accuracy of using charging time to determine voltage I used the above setup and did the following:
     1) Measure time between sphere gap sparks (T1) for a sphere gap distance of 1.2 cm without the 5.5 nF cap in the test circuit.
     2) Measure time between sphere gap sparks (T2) for the same gap size with the 5.5 nF cap in the test circuit.
Now assuming that:
    a) the measured VDG short circuit current is the same as cap charging current and is constant.
    b) The cap completely discharges during a sphere gap breakdown.

Then the calculated voltage:

V = I(T2-T1)/C       where I is the charging current (3.9 uA) and C is the cap value (5.5 nF)  equation 1

can be compared to the sphere gap breakdown voltage calculated from the python script with
sphere diameter(4.8 cm), gap size(1.2 cm), temperature (66 deg F) and atmospheric pressure (29.98 inHg).

T1 was measured to be 0.45 sec. from 73 sphere gap sparks occurring in 32.9 seconds.

T2 was measured to be 51.55, 50.15 and 51.00 seconds from three trials of  ten sparks each occurring in 515.5 , 501.5, and 510. seconds.

From equation 1 this gives cap voltages of 36.2 kV,  35.2 kV and 35.8 kV.
From the python script the sphere gap breakdown voltage is 37.6 kV

I was surprised that the charge time voltages were lower than the sphere gap breakdown voltage because there must be some leakage current at the higher voltages. However because the two different methods of calculating voltage agree within 7 % gives some confidence to the charge time method for determining cap voltage. The sphere gap breakdown voltage calculation was tested with a NST and variac and agreed to the resolution of the variac dial but the arc would really eat up the sphere metal plating so I need to come up with a better way of testing this.


Curious about the flash over vs puncture of plastic bottles I did some 30 sec exposures in the dark of  a few different plastic bottles filled with salt water and no outer Alum foil. The bottles were put on a grounded pie tin and the inner salt water was connected to the VDG.
The first photo show a puncture breakdown on the middle left side of the bottle. This surprised me because the bottle only flashed over once before this occurred.


The rest of the photos show flash overs