# Spark plug discharged energy analysis

To estimate the actual electric energy consumed of spark plug in the cylinder, the resistance of the ignition system was considered.

The equivalent circuit of spark plug used in the analysis is shown in Fig.

The total resistance of the equivalent circuit is expressed using Eq. (1).

The total discharge power PTOTAL was defined using Eq. (2).

The in-cylinder discharged power PIN was defined using Eq. (3).

In the equivalent circuit, PTOTAL is equivalent to the inductive energy of the ignition coils, and PIN is equivalent to the electric power consumed at the spark channel between the plug gap.

Eq. (4) indicates the energy transfer ratio of in-cylinder spark plug discharged energy to the inductive energy of the ignition coils.

(1)

${R}_{\mathit{TOTAL}}={R}_{\mathit{GAP}}+{R}_{\mathit{PC}}+{R}_{\mathit{IP}}$

(2)

${P}_{\mathit{TOTAL}}={R}_{\mathit{TOTAL}}{I}^{2}$

(3)

${P}_{\mathit{IN}}={R}_{\mathit{GAP}}{I}^{2}$

(4)

$\eta =\frac{{P}_{\mathit{IN}}}{{P}_{\mathit{TOTAL}}}=\frac{{R}_{\mathit{GAP}}}{{R}_{\mathit{TOTAL}}}=\frac{{R}_{\mathit{GAP}}}{{R}_{\mathit{GAP}}+{R}_{\mathit{PC}}+{R}_{\mathit{IP}}}$

Here, RGAP, RPC, RIP are the resistance of spark channel, plug cord, and ignition plug, respectively.

In the discharged energy analysis, the resistance of spark channel RGAP was estimated using Eq. (5). The in-cylinder discharged energy EIN was estimated from Eq. (6) using the time-resolved discharge waveform.

（5）

${R}_{\mathit{GAP}}=\frac{V}{I}–{R}_{\mathit{PC}}–{R}_{\mathit{IP}}$

（6）

${E}_{\mathit{IN}}=\int {R}_{\mathit{GAP}}{I}^{2}dt$