RESEARCH INC. - HAZARDOUS LOCATION SPECIALISTS
MINIMUM SPARK IGNITION ENERGIES--- A MATHEMATICAL MODEL
To show mathematical models of spark ignition curves. These curves are normally derived through rigorous
testing using a cadmium wheel in conjunction with tungsten wires (also known as the spark ignition tester).
If one is to examine the graphs derived through this testing, (the graphs can be seen in CSA or IEC standards 60079-11) will
see a rather nonlinear curve, or at least one that does not seem to have a correlating function
in the mathematical world.
If we were to examine the values for the minimum ignition energy required in joules has stated in the book
“combustion” by Irvin Glassman, appendix G. "minimum spark ignition energies and quenching distances"- table
1, we would easily see that there is direct useful data correlating ignition energy in joules to specific gases.
taking this data and plugging it into the common formula for energy in a capacitance spark (as follows)
E=1/2 C(vg- vf)squared
Where E is the electrical energy obtained in joules, C is the capacitance of the condenser in farads, vg is a voltage
on the condenser just before the spark occurs squared, vf is the voltage at the instance the spark ceases-squared.
(if we assume that Vf is equal to 0, we will have the worst-case scenario in that the capacitor will have discharged
all its energy in a theoretical time span of 0)
By plotting these values, directly against the "capacitance circuits ignition voltage in methane"-figure 1, we can
see that the corresponding curves much more linear and already contains a large built-in safety factor. as would
normally be expected.
What should be noted here is the fact that in the original CSA capacitance curves, we see that, as the voltage is
decreased, the slope of the curve becomes increasingly high - this results in an inordinate amount of capacitance
that may be allowed within the lower range. - This can be explained largely due to the fact of the test apparatus
itself, As the cadmium wheel turns it is not allowing for full discharge of the capacitor, the faster the wheel turns,
the less difference between v1 and v2 .The corollary being , that the higher the capacitance, the slower the
requirement for the wheel to turn, or the greater the value that is required for v2-v1, since the tungsten wires
contain some resistance, this would explain the limitations of the graph when large values of capacitance are
Using a similar mathematical approach curves can be derived for the inductances and resistance. The curves can
also be made to be gas specific, taking the values from table 1. in Glassman’s book
the formulas however are different, for inductance :
E=1/2 L(Ig- If)squared