Engineering Mathematics: Power of Engines

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This article discusses the calculation of engine power, brake horsepower, engine piston displacement, compression ratio, thermal efficiency, and engine speed for a single cylinder four-stroke engine in mechanical engineering.

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ENGINEERING MATHEMATICS: POWER OF ENGINES
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Introduction
Engineering mathematics is a vital subject to mechanical engineering. One of the
applications of engineering mathematics in mechanical engineering is the calculation of engine
power, brake horsepower, engine piston displacement, compression ration, thermal efficiency,
and engine speed. One of the reasons for calculating the power of an engine is to understand
speed, fuel efficiency, and the power of the engine. In this paper, the engine power, brake
horsepower, engine piston displacement, compression ratio, thermal efficiency, and the engine
speed for a single cylinder four-stroke engine will be calculated, interpreted, and discussed.
Analysis
Engine displacement as one of the factors that determine the power and the size of an engine is
derived by combining the volume of all cylinder in an engine and multiplying it with the number
of cylinders.
The general volume of a cylinder is given as π* radiu2 * height
Using the same criteria of the volume of a cylinder, the volume of the cylinder in an engine is
derived. However, the following assumptions are made.
Assumption
i) Radius = 1
2 bore
ii) Height is the stroke length
The volume of the engine cylinder = π* ( Bore
2 )2
* stroke length
= π* ( B
2 )
2
* S
= π
4 * ( B )2 * S
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Engineering Mathematics 3
But displacement = volume * number of cylinders
Displacement = π
4 * ( B ) 2 * S*C
Solution
Indicated Horsepower
Firstly, the indicated horsepower is calculated for a single cylinder four-stroke engine. The
formula to calculate the indicated horse power is given as below:
Indicated horsepower = PLAN
330002
Where:
P is the indicated mean effective pressure measured lbs /inch2
L is the length of stroke in feet/meter
A is the area of cross-section of cylinder measured in cm2
inch2
N is the number of revolutions per minute
For a single cylinder four-stroke engine, the mean effective pressure, length of stroke, and the
area of cross-section of the cylinder are given as below.
Mean effective pressure, P = 10 lbs/ inch2
Length of stroke, L = 4.19 = 0.13 feet
Area of cross-section of cylinder, A = π r2 = bore2 * 3.142
But the bore = 4.6 cm = 1.8 inch
Thus
A = bore2 * 3.142 = 1.82 * 3.142 = 10.17 inch2
The number of revolutions per minute, N = 1100 rev/ min
Substituting the number of
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Engineering Mathematics 4
Therefore, the Indicated horsepower = PLAN
330002
= 700.1310.171100
330002
= 1.54
Thus
ihp = 1.54
Brake Horse Power
The bore ratios formula will be utilized in this section to calculate the brake horsepower
Bore ratio formula (bhp) = D2N
2.5
Where:
D is the diameter of a cylinder in inches
N is the number of cylinders.
In this case scenario for single cylinder four-stroke engine;
N= 1
D = 1.8 inches
bhp = D2N
2.5 = 1.821
2.5 = 1.29
Displacement, D
D = π
4 * B2 * S * C
Where:
D is displacement
π is equivalent to 3.14
B is the bore

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S is the stroke
C is the number of cylinders
Since
π=3.14
B= 10.17
S = L = 0.13
C= 1
Then
D = π
4 * 10.172 * 0.13 * 1 = 10.56 cc
Compression Ratio
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Engineering Mathematics 6
Compression ratio, CR = volume at BDC
Volume at TDC
CR = volume at BDC
Volume at TDC = ( π
4 B2S )+V c
V c
CR = ( π
4 10.1720.131)+1
1
=10.56
Engine Speed
Engine speed is measured in piston per up and down movement of the piston in a crankshaft
(Langston, 2018).
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Engineering Mathematics 7
Engine speed = piston speed = stroke * revolutions per minute
6
= 0.13 * 1100
6 = 23.833 ft/min
Interpretation
The car has a high compression ratio (CR=10.56); therefore, the engine has good thermal
efficiency. Engines with high compression ratio extract more mechanical energy from mass of
air-fuel mixture than engines with low compression ratio (Machinery's handbook pocket
companion 2001). In real life examples, a diesel engine is fuel efficient than a petrol engine of
the same fuel capacity.
The value of engine displacement is one of the many factors that indicate the output
power of an engine. The modern-day engines come in 4, 6, and 8 pistons. The higher the
displacement value of an engine, the powerful and bigger the engine size (Borgnakke, Sonntag,
Van Wylen, and Sonntag, 2009).In this case scenario, the displacement of a single cylinder four-
stroke engine is 10.56 cubic centimeter. The calculated displacement for a single cylinder four-
stroke engine is relatively high; thus, the power and size of the engine are high. The piston speed
in feet per minute is approximately 23.833 ft/min. Therefore, the piston speed is relatively low
for a single cylinder four-stroke engine.
Discussion
Even though engine displacement in cubic centimeter is interpreted as the power and size
of an engine, there are other factors which influence the power of an engine. Such factors include
compression ratio, turbochargers, type of induction system, and supercharges. As Morin (2009)
quotes that engines with high compression ratio are more powerful than engines with low

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compression ration because they extract more mechanical energy from the mass of the air-fuel
mixture. Lastly, the piston speed is relatively low for a single cylinder four-stroke engine.
Reference List
Borgnakke, C., Sonntag, R., Van Wylen, G. and Sonntag, R. (2009). Fundamentals of
thermodynamics. Hoboken, NJ: Wiley.
Langston, L. (2018). A Useful Equation for Gas Turbine Design. Mechanical Engineering,
140(03), p.S52.
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Engineering Mathematics 9
Machinery's handbook pocket companion. (2001). Choice Reviews Online, 38(08), pp.38-4485-
38-4485.
Morin, D. (2009). Introduction to Classical Mechanics. New Delhi: Cambridge University Press
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