Step-by-step spark advance calculation:

• Engine rotational speed: \(N = 500\text{ rpm}\). - Angular speed in degrees per second: \[ \omega = \frac{500 \times 360^\circ}{60} = 3000^\circ/\text{s} \]
• Time for flame to travel 50 mm:
  \[ t = \frac{\text{Distance}}{\text{Flame Speed}} = \frac{0.050\text{ m}}{10\text{ m/s}} = 0.005\text{ seconds} \]
• Crank angle rotated during flame travel:
  \[ \Delta \theta = \omega \times t = 3000^\circ/\text{s} \times 0.005\text{ s} = 15^\circ \]
• Spark timing calculation:
  • Burning must finish at \(10^\circ\) After Top Dead Centre (ATDC). - Therefore, the spark must be initiated \(15^\circ\) prior to \(10^\circ\) ATDC: \[ \text{Spark Timing} = 10^\circ \text{ ATDC} - 15^\circ = -5^\circ = 5^\circ \text{ Before Top Dead Centre (BTDC)} \]

Calculation of pitch line velocity:

• Pitch circle diameter (\(D\)) of the pinion\lt /strong\gt : \[ D = m \times T = 7\text{ mm} \times 21 = 147\text{ mm} = 0.147\text{ m} \]
• Rotational speed: \(N = 600\text{ rpm}\). 3. \lt strong\gt Pitch line velocity (\(v\))\lt /strong\gt : \[ v = \frac{\pi D N}{60} = \frac{\pi \times 0.147 \times 600}{60} = \pi \times 0.147 \times 10 = 1.47 \pi \approx 4.618\text{ m/s} \approx 4.62\text{ m/s} \]