7.1 Define swept volume of an internal combustion engine - NSC Mechanical Technology Automotive - Question 7 - 2023 - Paper 1

1. Removing shims between the cylinder block and cylinder head to decrease the volume of the combustion chamber.

2. Fitting a thinner cylinder head gasket to reduce clearance volume.

3. Skimming metal from the cylinder head to lower the volume above the piston.

To calculate the swept volume (SV), we use the formula:

$SV = \frac{\pi D^2}{4} \times L$

Where:

• $D$ is the bore diameter (90 mm = 0.09 m)
• $L$ is the stroke length (100 mm = 0.1 m)

Substituting the values:

$SV = \frac{\pi (0.09)^2}{4} \times 0.1 = 0.63617 \, cm^3$

The original clearance volume (CV) can be calculated using the formula:

$CV = \frac{SV}{CR - 1}$

Where:

• $CR$ is the compression ratio (10.5)

Substituting the values:

$CV = \frac{0.63617}{10.5 - 1} = 0.06697 \, cm^3$

Using the new compression ratio, we first find the new swept volume:

$SV = CV \times (CR - 1)$

Substituting for the new compression ratio 11:

$SV = 0.06697 \times (11 - 1) = 0.6697 \, cm^3$

Now, using the formula for SV:

$SV = \frac{\pi D^2}{4} \times L$

We rearrange this to find D:

$D = \sqrt{\frac{(SV \times 4)}{\pi \times L}}$

Now substituting the values:

$D = \sqrt{\frac{(0.6697 \times 4)}{\pi \times 0.1}} = 0.09234 \, m = 92.34 \, mm$

The indicated power (IP) can be calculated using the formula:

$IP = P \times A \times n \times N$

Where:

• $P$ = Mean effective pressure (900 kPa = 900 x 10³ Pa)
• $A$ = Area of the bore in square meters
• $n$ = Number of cycles per revolution (2 for a two-stroke engine)
• $N$ = Number of power strokes per second.

Calculating area:

$A = \frac{\pi D^2}{4} = \frac{\pi (0.084)^2}{4} = 5.542 \times 10^{-3} \, m^2$

And the number of power strokes:

$N = \frac{2000}{60} \times 1 = 33.33 \, strokes/second$

Finally,

$IP = (900 \times 10^3)(5.542 \times 10^{-3})(2)(33.33) = 28.59 \, kW$

The brake power (BP) can be calculated using the formula:

$BP = \frac{2 \pi n T}{60}$

Where:

• $T$ is torque which is calculated as: $T = \text{Force} \times \text{radius}$
• $Force = 25 \times 10 = 250$ N.
• Brake arm length = 0.4 m.

Now substituting:

$T = 250 \times 0.4 = 100 \, Nm$

Then,

$BP = \frac{2 \pi (2000/60)(100)}{1} = 20.94 \, kW$

Mechanical efficiency can be calculated as:

$\eta = \frac{BP}{IP} \times 100$

Substituting the values:

$\eta = \frac{20.94}{28.59} \times 100 = 73.24\%$