2. Geometric parameter of reciprocating engine
The performance of the internal combustion
engine is characterized with several geometric
and thermodynamic parameters
The following geometric parameters are of
particular interest: bore(B), connecting rod length
(l), crank radius (a), stroke (S) and crank angle
(ө)
For any single cylinder, the cranks shaft,
connecting rod, piston, and head assembly can be
represented by the mechanism shown to the left
2
3. Geometric parameter of reciprocating engine
The top dead center TDC of an engine refers to
the crankshaft being in a position such that ө=00.
The volume at TDC is minimum and is often called
the clearance volume Vc
The bottom dead center (BDC) refers to the
crankshaft being at ө=1800, the volume at BDC
is maximum and often denoted by VT
The difference between the VT and Vc is the
displacement volume Vd
3
4. Geometric parameter of reciprocating engine
Engine Capacity (Ve)
Where n- is number of cylinders
Vd - cylinder swept volume
Displacement Rate
Stroke VS
Bore
VS VS VS
TDC
BDC
( )
=
×
=
4
2
B
nS
n
V
V d
e
π
For 4-Stroke Engine
5. Geometrical Properties of Reciprocating Engines
Compression ratio r,
o r = 8 to 12 for SI engines and
o r = 12 to 24 for CI engines;
Ratio of Cylinder bore to piston Stroke:
B/S = 0.8 to 1.2 for small- and medium-size engines,
about 0.5 for large slow-speed CI engines;
5
6. Geometrical Properties of Reciprocating Engines
Ratio of Connecting rod length to crank radius:
R = 3 to 4 for small- and medium-size engines,
increasing to 5 to 9 for large slow-speed CI
engines.
The stroke and crank radius are related by
a
l
R =
6
7. The cylinder volume V at any crank position
The volume of the cylinder can be determined as
function of crank angle ( ), from the compression
ratio, the stroke, bore and connecting rod length.
At TDC the crank shaft is at crank angle of 0o.
(Clearance volume, Vc)
At BDC the crank angle is at 180 o. (Maximum
cylinder volume, VT )
θ
7
8. The cylinder volume V at any crank position
Displacement volume = (Maximum -
minimum) cylinder volume
The displacement volume can also be
represented as a function of the bore and
stroke
At a given crank angle the volume is given by:
)
(
4
2
θ
π
x
B
V
V C +
=
θ
8
9. The cylinder volume V at any crank position
Again using geometry, a relationship for x(ө) can
be developed:
The compression ratio becomes
Solving for Vc results in:
( )
+
−
−
+
= θ
θ
θ cos
sin
)
( 2
1
2
2
2
a
a
l
l
a
x
θ
9
10. The cylinder volume V at any crank position
The cylinder volume at any crank angle becomes:
Since, a=S/2 and setting, , gives:
( )
+
−
−
+
+
−
= θ
θ
π
cos
sin
4
1
2
1
2
2
2
2
a
a
l
l
a
B
r
V
V D
+
−
−
+
+
−
= θ
θ
π
cos
sin
1
4
1
2
1
2
2
2
a
l
a
l
a
B
r
V
V D
a
l
R =
( )
−
−
−
+
+
−
= 2
1
2
2
sin
cos
1
2
1
θ
θ R
R
V
r
V
V D
D
Non-dimensional form of the above
equation becomes,
.
( )
−
−
−
+
+
−
= 2
1
2
2
sin
cos
1
2
1
1
1
θ
θ R
R
r
V
V
D
θ
10
11. The cylinder volume V at any crank position
11
−
−
+
−
−
−
= θ
θ 2
2
sin
2
2
1
2
cos
1
1
V
S
l
S
l
r
r
VD
a
V
D
V
TDC
V
BDC
B
l
θ
If crank angle is measured from BDC in CCW
direction
θ
12. The cylinder volume V at any crank position
The cylinder volume at any crank angle becomes:
Since, a=S/2 and setting, , gives:
( )
+
−
−
+
+
−
= θ
θ
π
cos
sin
4
1
2
1
2
2
2
2
a
a
l
l
a
B
r
V
V D
+
−
−
+
+
−
= θ
θ
π
cos
sin
1
4
1
2
1
2
2
2
a
l
a
l
a
B
r
V
V D
a
l
R =
( )
−
−
−
+
+
−
= 2
1
2
2
sin
cos
1
2
1
θ
θ R
R
V
r
V
V D
D
Non-dimensional form of the above
equation becomes,
.
( )
−
−
−
+
+
−
= 2
1
2
2
sin
cos
1
2
1
1
1
θ
θ R
R
r
V
V
D
θ
12
Full throttle operation chemically correct mixture (Y=12.5)
Fuel C8H18 Speed 4000rpm
Tm 300k P1 1atm
Friction and heat transfer neglected Fuel vaporization neglect
Crank angle Vdisp Pr Crank angle Vdisp Pr
(deg) (cc) (bar) (cc) (bar)
360 636.6 1
0 636.6 1 375 629.8 1
15 629.8 1 390 609.4 1
30 609.4 1.1 405 575.3 1
45 575.3 1.2 420 528.1 1
60 528.1 1.3 435 469 1
75 469 1.5 450 400.4 1
90 400.4 1.9 465 326.4 1
105 326.4 2.5 480 252.8 1
120 252.8 3.6 495 186 1
135 186 5.6 510 132.5 1
150 132.5 9 525 98 1
165 98 13.7 540 86 1
180 86 16.5 540 86 1
180 86 98.2 555 98 1
195 98 81.9 570 132.5 1
210 132.5 53.6 585 186 1
225 186 33.4 600 252.8 1
240 252.8 21.7 615 326.5 1
255 326.5 15.2 630 400.4 1
270 400.4 11.4 645 469 1
285 469 9.1 660 528.1 1
300 528.1 7.7 675 575.3 1
315 575.3 6.9 690 609.4 1
330 609.4 6.3 705 629.8 1
345 629.8 6 720 636.6 1
360 636.6 6
0
20
40
60
80
100
120
0 100 200 300 400 500 600 700
volume (cc)
pressure
(bar)
13. Engine Performance Parameters
The performance of the engine depends on inter-relationship between
power developed, speed and the specific fuel consumption at each
operating condition within the useful range of speed and load.
PERFORMANCE
OF ENGINE
POWER
13
14. Engine performance
Internal combustion engine should generally operate within a useful
range of speed.
Some engines are made to run at fixed speed by means of a speed
governor which is its rated speed
At each speed within the useful range, the power output varies and it has
a maximum usable value.
The specific fuel consumption varies with load and speed
14
15. Engine performance definition
Absolute Rated Power: The highest power which the engine could
develop at sea level with no arbitrary limitation on speed, fuel-air ratio
or throttle opening
Maximum rated power: The highest power an engine is allowed to
develop for short periods of operation.
Normal rated power: The highest power an engine is allowed to
develop in continuous operation.
Rated speed: The crankshaft rotational speed at which rated power is
developed
15
16. Engine Performance Parameters
The performance an engine is judged by quantifying its
efficiencies
Five important engine efficiencies are
Indicated thermal efficiency (ηith) Indicated Power
Brake thermal efficiency (ηbth) Brake Power
Mechanical efficiency (ηm)
Volumetric efficiency (ηv)
Relative efficiency or Efficiency ratio (ηrel)
16
17. Engine Performance Parameters
Other Engine performance Parameters
Mean effective pressure (MEP or Pm)
Mean piston speed (sp)
Specific power output (Ps)
Specific fuel consumption (sfc)
Inlet-valve Mach Index (Z)
Fuel-air or air-fuel ratio (F/A or AI F)
Calorific value of the fuel (CV)
17
18. The Energy Flow
The energy flow through the engine is expressed in 3
distinct terms
Indicated Power
Brake Power
Friction Power
18
21. Indicated work
The Engine cycle on a P-V coordinates, is often called an indicator
diagram.
The indicated work per cycle Wc,i is obtained by integrating around the
curve to obtain the area enclosed on the diagram
∫
= PdV
W i
c,
21
22. Gross Indicated Work
The upper loop of the engine cycle of the indicator diagram, the
compression and power strokes, where output work is generated is
called the gross indicated work.
C
A
W ig
c +
=
,
22
23. Pump work
The lower loop, which includes the intake and exhaust is called Pump work
and absorbs work from the engine.
Wide-Open Throttle (WOT) Engine operated with throttle valve fully open
when maximum power and/or speed is desired.
Pump
ig
c
inet
c
pump
W
W
W
C
B
W
−
=
+
=
,
,
Net indicated work is
23
24. Indicated Work at Part Throttle
At WOT the pressure at the intake valve is just below atmospheric
pressure, however at part throttle the pressure is much lower than
atmospheric
Therefore at part throttle the
pump work (area B+C) can
be significant compared to
gross indicated work (area
A+C)
24
25. Indicated Work with Supercharging/Turbocharged
Engines with superchargers or turbochargers can have intake
pressures greater than the exhaust pressure, giving a positive pump
work
( ) ( )
B
Area
A
Area
Wnet +
=
Supercharges increase the net
indicated work but is a parasitic
load since they are driven by the
crankshaft
25
28. p = imep (N/m2)
A (m2)
F= P.A (N)
L (m)
F (N)
Work (W) = F.L (N m)
Time (t) = 60 / (Ne /k) (s)
Indicated power (Pi) cylinder = W/t = F.L .Ne/(k*60) (W)
(Pi) cylinder = (imep.A.L.N) / (n R . 60)
(Pi) engine = imep. (A.L.n) N) / (n R . 60)
(Pi) engine = [imep. Ve . N)/ (n R . 60)] (W)
a
b
c
n R = 2 (four stroke)
n R = 1 (two stoke)
n = number of cylinder
29. Indicated, brake and frictional power
The indicated power per engine can also be given in terms of
indicated work per cycle :
where N–crankshaft speed in rev/s
nR - number of crank revolutions per cycle
= 2 for 4-stroke
= 1 for 2-stroke
R
i
i
n
N
W
n
P
×
×
=
29
30. Indicated, brake and frictional power
The term brake power, Pb, is used to specify that the power is measured
at the output shaft, this is the usable power delivered by the engine to
the load.
Part of the gross indicated work per cycle or power is used to expel
exhaust gases and induct fresh charge.
An additional portion is used to overcome the friction of the bearings,
pistons, and other mechanical components of the engine, and to drive
the engine accessories.
30
31. Power flows in an engine
The power flow through the engine is expressed in 3
distinct terms
Indicated Power
Brake Power
Friction Power
31
f
b
ig P
P
P +
=
g
32. Mechanical Efficiency
The ratio of the brake (or useful) power delivered by the engine to
the indicated power is called the mechanical efficiency.
Mechanical efficiency depends on throttle position as well as engine
design and engine speed.
Typical values for a modern automotive engine at wide open or full
throttle are 90 percent at speeds below about 30 to 40 rev/s (1800
to 2400 rev/min), decreasing to 75 percent at maximum rated
speed.
ig
f
ig
b
m
P
P
P
P
−
=
= 1
η
32
33. Power Speed Curve
Where:
Pig = indicated power
Pb= brake power
Pf = friction power
33
f
b
ig P
P
P +
=
ig
f
ig
b
m
P
P
P
P
−
=
= 1
η
34. Mean effective pressure (mep)
MEP is a fictitious pressure that, if acted on the piston during the entire
power stroke, would produce the same amount of net work as that
produced during the actual cycle
Mean effective pressure (mep) is the work done per unit displacement
volume.
mep = W/VD
The net work during the intake and exhaust strokes is:
Wp, net = (Pi-Pe)
34
35. Mean effective pressure
The work per displacement volume required to pump the working fluid
into and out of the engine during the intake and exhaust strokes is
termed as the pumping work ( WP) and the mean effective pressure is
called pumping mean effective pressure (PMEP)
WP, net/VD =pmep= (Pi-Pe)
The indicated mean effective pressure (imep) is defined as the work per
unit displacement volume done by the gas during the compression and
expansion stroke.
imep = Wi /VD
The net indicated mean effective pressure for the whole cycle,
imep net = imep-pmep
35
36. Mean effective pressure
mep = W/VD
nR is the number of crank revolutions for each power stroke per
cylinder
N
n
P
W R
i
×
= N
V
n
P
mep
D
R
×
×
=
36
37. Indicated and brake Mean effective Pressure
For SI unit
Mean effective pressure can also be expressed in terms of
torque
Indicated power gives indicated mean effective pressure:
)
(
)
(
10
6
)
(
)
( 3
4
2
rpm
N
m
V
n
kW
P
m
N
mep
D
R
×
×
×
×
=
)
(
)
(
2
)
( 3
2
m
V
n
Nm
T
m
N
mep
D
R
×
=
π
)
(
)
(
10
6
)
(
)
( 3
4
2
rpm
N
m
V
n
kW
P
m
N
imep
D
R
i
×
×
×
×
=
[ ]
W
Nm
T
rpm
N
P
60
)
(
)
(
2 ×
=
π
37
39. Engine Torque Te-Torque and crankshaft angle
Work is also accomplished when the
torque is applied through an angle.
Distance
Where:
θ
r
xy =
θ
θ T
Fr
xy
F
W =
=
= .
( )
π
2
T
W revolution
per =
( ) ω
π T
t
T
t
W
P =
=
= 2
60
2 N
π
ω =
39
40. Engine Brake Torque Te
Brake mean effective pressure can also be expressed in terms of
torque
Where:
N = Engine speed (rpm)
VD = engine Displacement capacity (m3)
n R = 2, for 4-stroke engines
1, for 2-stroke engines
( ) ( ) ( )
kW
rpm
N
Nm
T
T
N
T
P e
e
e
b
9550
60
2 ×
=
×
=
×
=
π
ω
)
(
)
.
(
2
)
( 3
2
m
V
n
m
N
T
m
N
bmep
D
R
e ×
=
π
R
D
e
n
m
V
m
N
bmep
m
N
T
×
×
=
π
2
)
(
)
(
)
.
(
3
2
40
41. Engine Torque Te
o There is a direct relationship
between BMEP and torque output.
o The torque curve with engine rpm is
identical to the bmep curve, with
different values.
41
42. 42
There is a maximum in the brake power versus
engine speed called the rated brake power
(RBP).
At higher speeds brake power decreases as
friction power becomes significant compared
to the indicated power
There is a maximum in the torque versus
speed called maximum brake torque
(MBT).
Brake torque drops off:
• at lower speeds do to heat losses
• at higher speeds it becomes more difficult
to ingest a full charge of air.
Max brake torque
1 kW = 1.341 hp
Rated brake power
Power and Torque versus Engine Speed at WOT
f
ig
b P
P
P −
=
43. Mean Piston Speed
An important characteristic speed is the mean piston speed
Where: S is the stroke and
N is the rotational speed of the crankshaft.
Resistance to gas flow into the engine or stresses due to the inertia
of the moving piston limit the maximum mean piston speed to
within the range 8 to 15 m/s.
p
S
p
S
N
S
S p 2
=
43
44. Specific Power
Specific power output of an engine is defined as the power
output per unit piston area.
It is a measure of the engine designer’s success in using the
available piston area regardless of cylinder size.
P
b
A
P
SP
power
specific =
,
)
10
12
(
, 5
×
×
×
=
R
p
n
S
bmep
SP
power
specific
44
)
(
)
(
10
6
)
(
)
( 3
4
2
rpm
N
m
V
n
kW
P
m
N
bmep
D
R
b
×
×
×
×
=
45. Specific Fuel Consumption (sfc)
sfc shows how much fuel is consumed by an engine to do a certain amount
of work.
Specific fuel consumption represents the mass or volume of fuel an engine
consumes per hour while it produces 1 kW of power.
It depends on
Engine size
Operation load
Engine design
Specific fuel consumption is given in kilograms of fuel per
kilowatt-hour.
45
46. Specific fuel consumption and efficiency
Specific fuel consumption (sfc) is fuel flow rate per unit power output.
It measures how efficiently an engine is using the fuel supplied to
produce work:
Brake power gives brake specific fuel consumption:
Indicated power gives indicated specific fuel consumption:
P
m
sfc
f
= )
(
)
/
(
)
/
(
kW
P
s
g
m
J
mg
sfc
f
=
)
(
)
/
(
)
.
/
(
kW
P
h
g
m
h
kW
g
sfc
f
=
b
f
P
m
bsfc
=
Pi
m
isfc
f
=
46
47. Brake Specific Fuel Consumption vs Engine Size
Brake specific fuel consumption generally decreases with
engine size, being best (lowest) for very large engines.
One reason for this is less
heat loss due to the higher
volume to surface area ratio
of the combustion chamber in
large engines.
Also large engines operate
at lower speeds which
reduce friction losses.
47
48. Brake Specific Fuel Consumption vs Engine Speed
Brake specific fuel consumption decreases as engine speed
increases, reaches a minimum, and then increases at high
speeds.
Fuel consumption increases at
high speeds because of greater
friction losses.
At low engine speed, the longer
time per cycle allows more heat
loss and fuel consumption goes
up.
48
49. Engine Thermal Efficiencies
The time for combustion in the cylinder is very short so not all the fuel
may be consumed or local temperatures may not favor combustion
A small fraction of the fuel may not react and exits with the exhaust
gas
The combustion efficiency is defined as:
Where Qin = heat added by combustion per cycle
mf = mass of fuel added to cylinder per cycle
QHV= heating value of the fuel (chemical energy per unit mass)
HV
f
in
C
Q
m
Q
input
heat
l
theoretica
input
heat
actual
=
=
η
49
51. Indicated thermal efficiency (ηith)
Indicated thermal efficiency (ηith)
is the ratio of energy in the indicated power, Pi, to the
input fuel energy in appropriate units
C
HV
f
i
in
i
i
ith
Q
m
P
Q
P
cycle
per
input
heat
of
rate
P
η
η
=
=
=
Indicated thermal efficiencies are typically 50% to 60%
and brake thermal efficiencies are usually about 30%
51
52. Brake Thermal Efficiency(ηbth)
Is the ratio of energy in the brake power Pb to the input
fuel energy in appropriate units
C
HV
f
b
in
b
b
bth
Q
m
P
Q
P
cycle
per
input
heat
of
rate
P
η
η
=
=
=
52
54. Fuel conversion efficiency
Fuel conversion efficiency is defined as:
Thus thermal efficiency may be defined as:
C
f
t
η
η
η =
HV
HV
f
HV
f
C
f
Q
sfc
Q
m
P
Q
m
W
cycle
per
input
Heat
Theortical
cycle
per
Work 1
=
=
=
=
η
54
55. Air-Fuel Ratio and Fuel-Air Ratio
The relative proportions of the fuel and air in the engine
cylinder are very important from the standpoint of
combustion and the efficiency of the engine.
Air-Fuel ratio (AF) or Fuel-Air ratio (FA) are used to
describe the mixture ratio of the charge.
55
56. Air-Fuel Ratio and Fuel-Air Ratio
For SI engine hydrocarbon fuel:
Ideal or Stoichiometric AF is about 15:1 (14.7:1)
Combustion possible in the range of 6:1 to 25:1
For CI engine hydrocarbon fuel:
Ideal or Stoichiometric AF is also about 15 (14.7:1)
Combustion possible in the range of 18:1 to 70:1
57. Fuel-Air (F/A) or Air-Fuel Ratio (A/F)
In the SI engine the fuel-air ratio practically remains a constant
over a wide range of operation.
In CI engines at a given speed the air flow does not vary with
load; it is the fuel flow that varies directly with load.
Therefore, the term fuel-air ratio is generally used instead of
air-fuel ratio.
58. Fuel-Air (F/A) or Air-Fuel Ratio (A/F)
A mixture that contains just enough air for complete combustion of all
the fuel in the mixture is called a chemically correct or stoichiometric
fuel-air ratio.
A mixture having more fuel than that in a chemically correct mixture is
termed as rich mixture and
a mixture that contains less fuel (or excess air) is called a lean mixture.
The ratio of actual fuel-air ratio to stoichiometric fuel-air ratio is called
equivalence ratio and is denoted by
Φ=1 Stoichiometric
Φ>1 Rich Mixture
Φ<1 Lean Mixture
−
−
=
ratio
air
fuel
tric
Stoichiome
ratio
Air
fuel
Actual
φ
60. Volumetric efficiency CI ( )
The volumetric efficiency is used to measure the effectiveness of an
engine's induction process.
Volumetric efficiency is usually used with four-stroke cycle engines
which have a distinct induction process.
It is defined as the volume flow rate of air into the intake system
divided by the rate at which volume is displaced by the piston:
Where: ma is the mass of air inducted into the cylinder per cycle.
N
V
m
V
m
D
i
a
a
D
i
a
a
V
,
,
2
ρ
ρ
η
=
=
V
η
60
61. Volumetric Efficiency SI (ηv)
Where number of intake strokes per
minutes
n=N/2 for 4-S Engines
n= N for 2-S Engines
N= speed of engine in rpm
N
V
)
m
(
2
d
i
a,
a
v
ρ
η f
m
+
=
•
61
62. Volumetric efficiency
Typical values of volumetric efficiency for an engine at wide-open
throttle (WOT) are in the range 75% to 90%, going down to
much lower values as the throttle is closed.
Can be measured:
At the inlet port
Intake of the engine
Any suitable location in the intake manifold
If measured at the intake of the engine, it is also called the
overall volumetric efficiency.
62
63. Volumetric Efficiency (ηv)
Volumetric efficiency depends upon
throttle opening and engine speed
induction and exhaust system layout,
port size and
valve timing and opening duration.
High volumetric efficiency increases engine power.
Volumetric Efficiency can be greater than one where Super charger
or turbocharger fitted
Turbo charging is capable of increasing volumetric efficiency up to 50%.
63
65. Engine Specific Weight and Specific Volume
Engine weight and bulk volume for a given rated power are
important in many applications. Two parameters useful for
comparing these attributes form one engine to another are:
These parameters indicate the effectiveness with which the engine
designer has used the engine materials and packaged the engine
components.
power
rated
Weight
engine
Weight
Specific =
power
rated
volume
engine
volume
Specific =
65
66. Calorific Value (CV)
Calorific value of a fuel is the thermal energy released per unit
quantity of the fuel when the fuel is burned completely and the
products of combustion are cooled back to the initial temperature
of the combustible mixture
Other terms used for the calorific value are heating value and
heat of Combustion.
When the products of combustion are cooled to 25 °C practically
all the water vapour resulting from the combustion process is
condensed.
67. Calorific Value (CV)
When H2O is in products is condensed to liquid additional heat is
realized and the total heat liberated is called Higher Calorific Value
(HCV)
when H2O in the products is in the vapor form heat is not removed
this calorific value is called is called Lower calorific Values (LCV)
L.C.V. = H.C.V. –(Mass of H2O * 2454.1 ) in kJ
68. Engine Performance Curves
1. Imep
2. Bmep and torque
3. Indicated power
4. Brake power
5. Indicated thermal efficiency
6. Brake thermal efficiency
7. Specific fuel consumption
69. Brake Torque and Power measurement
Dynamometers are used to measure torque and power over the engine
operating ranges of speed and load.
Dynamometers use various methods to absorb the energy output of the
engine, all of which eventually ends up as heat.
Some dynamometers absorb energy in a mechanical friction brake,
hydraulic fluid and magnetic field
70. Dynamometer vs. Engine Setup
The Engine is clamped on a test bed and the shaft is connected to the
dynamometer rotor.
The rotor is coupled electromagnetically, hydraulically or by
mechanical friction to a stator
The torque exerted on the stator with the rotor turning is measured
by balancing the stator with weights, springs or pneumatic means.
Load cell
Force F
Stator
Rotor
b
N
71. Brake Torque and Power
Work is defined as the product of a force and the distance through which
the point of application of the force moves
When the drive shaft of the engine turns through one revolution, any
point on the periphery of the rigidly attached roter moves through a
distance of equal to
During this movement a friction force, f, is acting on the stator.
The friction force, f, is thus acting through the distance and
producing a work
72. Brake Torque and Power
Work during one revolution = Distance * f
= * f
The torque , r*f , produced by the drive shaft is opposed by a turning
moment equal to the product of the length of the moment arm b and
the force F measured by the scale
T = r*f = F*b
Work during one revolution = Fb
Power = Work/Time = Fb N/60
