**EXPLOSION
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

analyzed.

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

(If there are any
errors or omissions, or you would like to make a comment, please feel free to
contact me at the home page)

(c) Explosion Research Ltd. all rights reserved

.