Question

A spark ignition engine is idling at 500 rpm. If the average flame speed is 10 \(m\cdot s^{-1}\) and the flame front must travel 50 mm from the spark plug to consume 85 % of the fuel-air mixture, how much spark advance is needed if 85 % of the fuel is to be consumed before the crankshaft reaches 10\(^\circ\) after HDC?

• A. 16.5\(^\circ\)
• B. 15\(^\circ\)
• C. 6.5\(^\circ\)
• D. 5\(^\circ\)

Hint:

To avoid confusion, write the equation:
\[ \text{Combustion Start (Spark Advance)} = \text{Combustion Duration (deg)} - \text{End Crank Angle (deg after TDC)} \] Here: \(15^\circ - 10^\circ = 5^\circ\) before TDC.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Spark advance determines how early the spark fires relative to the piston reaching the Top Dead Center (TDC/HDC) to allow the flame front enough time to burn the fuel.

Step 2: Key Formula or Approach:
1. Calculate the burn time \(t\) using:
\[ t = \frac{\text{Distance}}{\text{Flame Speed}} \] 2. Determine the crankshaft rotational speed in degrees per second (\(\omega\)):
\[ \omega = N \left(\frac{\text{rev}}{\text{min}}\right) \times \frac{1 \text{ min}}{60 \text{ s}} \times \frac{360^\circ}{1 \text{ rev}} \] 3. Find the crankshaft rotation angle (\(\Delta\theta\)) swept during the burn time:
\[ \Delta\theta = \omega \times t \]

Step 3: Detailed Explanation:
1. Calculate the burn time \(t\) for the flame to travel \(50\text{ mm}\) (\(0.05\text{ m}\)):
\[ t = \frac{0.05\text{ m}}{10\text{ m}\cdot\text{s}^{-1}} = 0.005\text{ s} \] 2. Convert the engine speed of \(500\text{ rpm}\) to degrees per second:
\[ \omega = \frac{500}{60} \times 360^\circ/\text{s} = 3000^\circ/\text{s} \] 3. Calculate the angle turned by the crankshaft during this burn time:
\[ \Delta\theta = 3000^\circ/\text{s} \times 0.005\text{ s} = 15^\circ \] 4. The combustion process must be \(85\%\) complete by \(10^\circ\) after HDC.
Since the total angle needed is \(15^\circ\), ignition must begin:
\[ \theta_{\text{start}} = 10^\circ \text{ (after HDC)} - 15^\circ = -5^\circ \text{ (which is } 5^\circ \text{ before HDC)} \] Thus, a spark advance of \(5^\circ\) before HDC is required.

Step 4: Final Answer:
The correct option is 4, which corresponds to 5\(^\circ\).