7.1 Define the term compression ratio of an engine - NSC Mechanical Technology Automotive - Question 7 - 2019 - Paper 1

The swept volume (SV) of an engine can be calculated using the formula:

SV = rac{ ext{π}}{4} imes D^2 imes L

Where:

• D is the bore diameter (84 mm or 0.084 m)
• L is the stroke length (90 mm or 0.090 m)

Substituting the values:

SV = rac{ ext{π}}{4} imes (0.084)^2 imes 0.090 = 0.00049776 ext{ m}^3

Converting to cm³:

$SV = 497.76 ext{ cm}^3$

To find the original clearance volume (CV), we can use the formula relating the compression ratio (CR), swept volume (SV), and clearance volume (CV):

CR = rac{SV + CV}{CV}

Given: CR = 8.5 and SV = 497.76 cm³,

Rearranging the formula:

CV = rac{SV}{CR - 1}

Substituting the values:

CV = rac{497.76}{8.5 - 1} = 66.50 ext{ cm}^3

To find the new bore diameter (D) when the compression ratio is increased to 9.5:1, we keep the clearance volume the same:

Using the formula:

CR = rac{SV + CV}{CV}

We have:

• CV = 66.50 cm³
• New CR = 9.5
• The swept volume SV remains the same (497.76 cm³).

Rearranging and solving for D:

D^2 = rac{4 imes SV imes (CR - 1)}{ ext{π} imes L}

Substituting:

D = rac{ ext{√}(4 imes 497.76 imes (9.5 - 1))}{ ext{π} imes 90} ext{mm}

This simplifies to approximately 89.4 mm.

Torque (T) can be calculated using the formula:

$T = ext{Force} imes ext{radius}$

Where:

• Force = Balance reading × g = 125 kg × 10 = 1250 N
• radius = Brake arm length = 300 mm = 0.3 m.

So,

$T = 1250 imes 0.3 = 375 ext{ Nm}$

Indicated Power (IP) can be calculated using the formula:

$IP = ext{P} imes ext{L} imes A imes N imes n$

Where:

• P = Mean effective pressure = 950 kPa = 950000 Pa
• L = Stroke length in meters = 140 mm = 0.14 m
• A = Area of piston = A = rac{ ext{π} imes D^2}{4}
• N = Crankshaft revolutions per minute = 2400 r/min, converted to power strokes per second = 2400 / 60 = 40 power strokes/s
• n = number of cylinders = 4.

Calculate A:

ightarrow ext{Convert to } cm^2$$ Plugging the values: $$IP = 950000 imes 0.14 imes 11.31 imes 10^{-3} imes 40 ightarrow $$ giving approximately 120.34 kW.

Brake Power (BP) can be calculated using the formula:

$BP = 2 imes ext{π} imes N imes T$

Substituting the known values:

$BP = 2 imes ext{π} imes 40 imes 375$

Calculating this gives approximately 94.25 kW.

Mechanical Efficiency (ME) can be calculated using the formula:

ext{ME} = rac{BP}{IP} imes 100 ext{%}

Substituting the values:

ightarrow $$ gives approximately 78.32%.