Engine Performance parameters and Numerical and Theory

1. Chapter 6
Characteristics of motor
vehicle engine
1

2. 1. Engine performance
2. Examples
Content
2

3. James Watts Solution

4. Power and torque
• Engine performance is specified in both in terms of power and engine
torque - which is more important?
– Wheel torque = engine torque x gear ratio tells you whether you can
climb the hill
– Gear ratio in transmission typically 3:1 or 4:1 in 1st gear, 1:1 in
highest gear; gear ratio in differential typically 3:1
– Power tells you how fast you can climb the hill
– Torque can be increased by transmission (e.g. 2:1 gear ratio ideally
multiplies torque by 2)
P (in horsepower) 
N (revolutions per minute, RPM) x Torque (in foot pounds)
5252
– Power tells how fast you can accelerate or how fast you can climb a
hill, but power to torque ratio ~ N tells you what gear ratios you'll need
to do the job

7. ANALYSIS OF ENGINE PERFORMANCE

9. ۲
Cylinder Swept Volume (Vc):
where:
Vc= cylinder swept volume [cm3 (cc) or L]
Ac = cylinder area [cm2 or cm2/100]
dc = cylinder diameter [cm or cm/10]
L = stroke length (the distance between the TDC and
BDC) [cm or cm/10]
BDC = Bottom Dead Center
TDC = Top Dead Center
The units of cylinder swept volume is measured in (cm3, cubic
centimeter (cc), or liter).

10. Ratio between cylinder diameter to stroke ratio

11. Piston
Position

12. Compression Ratio (r):
where:
r = compression ratio
Vs = cylinder swept volume (combustion chamber volume) [cc,
L, or m3] it is design parameter
Vc = cylinder volume [cc, L, or m3] it is design paramete
* Increase the compression ratio increase engine power
- r (gasoline engine) = 7:12, the upper limit is engine pre ignition
- r (diesel engine) = 10:18, the upper limit is the stresses on
٥engine parts

13. ٦
Engine Volumetric Efficiency (hv):
where: ηV = volumetric efficiency
Vair = volume of air taken into cylinder [cc, L, or m3]
Vc = cylinder swept volume [cc, L, or m3]
* Increase the engine volumetric efficiency increase engine
power
- Engine of normal aspiration has a volumetric efficiency of
80% to 90%
- Engine volumetric efficiency can be increased by using:
(turbo and supper charger can increase the volumetric
efficiency by 50%)

14. Compression
W<0
Power
W>0
Intake
W>0
Exhaust
W<0
WA > 0
WB < 0
The definition of BMEP is: the average (mean) pressure which,
if imposed on the pistons uniformly from the top to the bottom
of each power stroke, would produce the measured (brake)
power output.
Mean Effective Pressure:

15. Mean effective pressure is the ratio of work done (W)
during the working stroke(s) of a cycle to the stroke
volume or swept volume (Vs) of the cylinder. It is
denoted by ‘pm‘ and its unit is N/m2.
Brake mean effective pressure (BMEP) - Mean effective
pressure calculated from measured brake torque. Brake Mean
Effective Pressure (bmep) is, calculated by putting the
measured dynamometer torque into the above equation.
Gross indicated mean effective pressure (IMEPg) - Mean
effective pressure calculated from in-cylinder pressure over
compression and expansion portion of engine cycle (360° in a
four-stroke, 180° in a two-stroke).
۹

16. Therefore Indicated mean effective pressure
(imep):
is a hypothetical pressure which if acting
on the engine piston during the working
stroke would results in the indicated work
of the engine. This means it is the height
of a rectangle having the same length and
area as the cycle plotted on a p- v
diagram.
۱۰

17. ۸

18. ۱۲

19. ۱۳

20. ۱٤

21. ENGINE PERFORMANCE
The basic performance parameters of internal combustion engine (I.C.E) may be
summarized as follows:
1. Indicated power (i.p.):
Figure (1): indicator diagram of SI engine
۱٥

22. ۱٦
Engine Indicated Torque (Ti):
where:
Ti = engine indicated torque [Nm]
imep = indicated mean effective pressure [N/m2]
Ac = cylinder area [m2]
L = stroke length [m]
z = 1 (for 2 stroke engines), 2 (for 4 stroke engines)
n = number of cylinders
θ = crank shaft angle [1/s]

23. ۱۷
Engine Indicated Power (Pi):

24. ۱۸
where:
imep = is the indicated mean effective pressure
[N/m2],
Ac = cylinder area [m2],
L = stroke length [m],
n = number of cylinders,
N = engine speed [rpm],
z = 1 (for 2 stroke engines), 2 (for 4 stroke engines),
Vc = cylinder swept volume [m3],
Ve = engine swept volume [m3],
Ti = engine indicated torque [Nm], and
ω = engine angular speed [1/s]

25. ۱۹
Engine Mechanical Efficiency (ηm):
where:
m = mechanical efficiency
Pb = engine brake power [kW]
Pi = engine indicated power [kW]
Pf = engine friction power [kW]

26. ۲۰
Engine Specific Fuel Consumption (SFC):
where:
SFC = specific fuel consumption
[(kg/h)/kW, kg/(3600 s x kW=kJ/s), kg/(3600
kJ)]
FC= fuel consumption [kg/h]
Pb = brake power [kW]

27. ۲۱
Engine Thermal Efficiency (η𝑡ℎ):

28. 5. Brake mean effective pressure (bmep) and brake thermal
efficiency:
The bmep (Pb) may be thought of as that mean effective pressure acting on the
pistons which would give the measured b.p., i.e.
b.p. = bmep AL x active cycles/ min
The overall efficiency of the engine is given by the brake thermal efficiency, 𝜼𝑩𝑻
i.e.
where 𝒎̇ 𝒇 is the mass of fuel consumed per unit time, and 𝑸𝒏𝒆𝒕is the lower
calorific value of the fuel.
۲۲

29. 7. Indicated thermal efficiency (η𝑰𝑻):
It is defined in a similar way to (η𝑩𝑻)
۲۳

30. Example-1: A four cylinder
car engine has bore and stroke
= 79 mm and 77 mm
respectively.
What is the capacity of the
engine in cc?
Solution: Capacity in cc =
n.(π/4) d squar . S
Here, n= number of cylinders
d= bore diameter in cm
S= stroke length in cm,
Therefore, Engine Capacity in
cc = 4 x (π/4) x (7.9)2 x (7.7)
= 1۲
5٤
09 ≈ 1500 cc Ans.

31. ۲٥
Example-2 If the same engine (Ex-2) (i.e., four-
stroke, 2 liters) as above produces 76 kW at 5400
rpm, Find its bmep.

32. ۲٦
Example-3: A 4-Cylinder, 2-stroke IC engine has the
following particulars: engine speed = 3000 rpm, bore
= 120 mm, crank radius = 60 mm, mechanical
efficiency = 90% and the engine develops 75 bhp.
Calculate the swept volume and mean effective
pressure (MEP).

33. ۲۷

34. ۲۸

38. Indicated Work
Given the cylinder pressure data over the operating
cycle of the engine one can calculate the work done
by the gas on the piston.
The indicated work per cycle is W =  pdV
Compression
W<0
Power
W>0
Intake
W>0
Exhaust
W<0
WA > 0
WB < 0

39. Pi = Wi N / nR w/units: (kJ/cycle) (rev/s) / (rev/cycle)
where N – crankshaft speed in rev/s
nR – number of crank revolutions per cycle
= 2 for 4-stroke
= 1 for 2-stroke
Power can be increased by increasing:
• the engine size, Vd
• compression ratio, rc
• engine speed, N
Indicated Power

40. Cycle Performance Parameters
Net Work Transfer :
=  pd(mv)
Wnet
This is work done by working fluid on the piston, also called as
Indicated Work.
Indicative Performance:
=  pd(mv)
f
m CV
ind
η

54. Engine Torque and Power
Torque is measured using a dynamometer.
Load cell
Force F
Stator
Rotor
b
N
The torque exerted by the engine is: T = F b with units: J
The power P delivered by the engine turning at a speed N and
absorbed by the dynamometer is:
P =  T = (2πN) T w/units: (rad/rev)(rev/s)(J) = Watt
Note:  is the shaft angular velocity with units: rad/s

58. Mechanical Efficiency
Some of the power generated in the cylinder is used
to overcome engine friction. The friction power is
used to describe these losses:
Pf = Pi - Pb
Friction power can be measured by motoring the engine.
The mechanical efficiency is defined as:
m = Pb / Pi = 1- (Pf / Pi )
Mechanical efficiency depends on throttle position, engine
design, and engine speed. Typical values for car engines
at WOT are 90% @2000 RPM and 75% @ max speed.

59. There is a maximum in the brake power
versus engine speed called the rated
brake power.
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

64. BC
L
TC
l
VC
s
a
θ
B




+ 1/ 2
2
cosθ
= sinθ
2
π 
1

 (
(l / a)2
− sin θ)
S p
Sp
Average and instantaneous piston speeds are:
dt
=
ds
S
S p = 2LN
p
Where N is the rotational speed of the crank
shaft in units revolutions per second
s = acosθ+ (
l2
− a2
sin2
θ)
1/ 2
Average piston speed for a standard auto engine
is ~15 m/s. Ultimately limited by material strength.
Therefore engines with large strokes run at lower
speeds those with small strokes can run
at higher speeds.
Mean and Instantaneous Piston Speeds

65. Indicated Mean Effective Pressure (IMEP)
imep is a fictitious constant pressure that would produce the same
work per cycle if it acted on the piston during the power stroke.
imep = Wi / Vd = (Pi nR) / (Vd N)
so Pi = imep Vd N / nR = imep Ap Up / (2 nR)
imep does not depend on engine speed, just like torque.
imep is a better parameter than torque to compare engines for design and
output because it is independent of engine speed, N, and engine size, Vd.
Brake mean effective pressure (bmep) is defined as:
2π
nR
T =
bmepVd
bmep =
Wb =
2πT nR
Vd Vd
→

66. Maximum BMEP
• The maximum bmep is obtained at WOT at a particular engine speed
• Closing the throttle decreases the bmep
• For a given displacement, a higher maximum bmep means more torque
• For a given torque, a higher maximum bmep means smaller engine
•Higher maximum bmep means higher stresses and temperatures in the
engine hence shorter engine life, or bulkier engine.
• For the same bmep 2-strokes have almost twice the power of 4-stroke
=
2πT nR
Vd Vd
bmep =
Wb

67. Specific Fuel Consumption
• For transportation vehicles fuel economy is generally given as
mpg, or liters/100 km.
• In engine testing the fuel consumption is measured in terms of
the fuel mass flow rate.
• The specific fuel consumption, sfc, is a measure of how efficiently
the fuel supplied to the engine is used to produce power,
.
bsfc = mf / Pb
.
isfc = mf / Pi (w/units: g/kW-hr)
• Clearly a low value for sfc is desirable since at a given power
level less fuel will be consumed

68. Brake Specific Fuel Consumption vs Size
•BSFC decreases with engine size due to reduced heat losses
from gas to cylinder wall.
cylinder volume r
π
r2L
•Note: cylinder surface to volume ratio increases with bore diameter.
cylinder surface area = 2π
rL  1

69. Brake Specific Fuel Consumption vs Speed
• At high speeds the bsfc increases due to increased friction
• At lower speeds the bsfc increases due to increased time for heat
losses from the gas to the cylinder and piston wall
• Bsfc increases with compression ratio due to higher thermal efficiency
• There is a minimum in the bsfc versus engine speed curve

70. Performance Maps
Performance map is used to display the bsfc over the engines full load
and speed range. Using a dynamometer to measure the torque and fuel
mass flow rate you can calculate:
bmep = 2 T nR / Vd Pb = 2 N T
Constant bsfc contours from a
two-liter four cylinder SI engine
bmep@WOT
.
bsfc = mf / Pb

71. Combustion Efficiency
• The time for combustion in the cylinder is very short so
not all the fuel may be consumed or local temperatures
may not support combustion
• A small fraction of the fuel may not react and exits with the
exhaust gas. The combustion efficiency is defined as
actual heat input divided by theoretical heat input:
. .
Where
c = Qin/ (mf QHV) = Qin / (mf QHV)
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)

72. Thermal Efficiency
t = work per cycle / heat input per cycle
t = W / Qin = W / (c mf QHV)
or in terms of rates…
t = power out/rate of heat input
. .
t = P/Qin = P/(c mf QHV)
• Thermal efficiencies can be given in terms of brake or indicated values
• Indicated thermal efficiencies are typically 50% to 60% and brake
thermal efficiencies are usually about 30%

73. Arbitrary Efficiency
(aka fuel conversion efficiency)
Note: ηfis very similar to ηt,the difference is that ηttakes into
account only the actual fuel combusted in the engine.
.
Recall that sfc = mf / Pb
Thus f = 1 / (sfc QHV)
.
f = Wb / (mf QHV) = Pb / (mf QHV)

74. Volumetric Efficiency
• Due to the short cycle time and flow restrictions less than ideal
amount of air enters the cylinder.
• The effectiveness of an engine to induct air into the cylinders is
measured by the volumetric efficiency which is the ratio of actual
air inducted divided by the theoretical air inducted:
.
v = ma / (a Vd) = nR ma / (a Vd N)
where a is the density of air at atmospheric conditions Po, To for an
ideal gas ρa =Po / RaTo and Ra = 0.287 kJ/kg-K (at standard conditions
a= 1.181 kg/m3)
• Typical values for WOT are in the range 75%-90%, and lower when
the throttle is closed

75. Air-Fuel Ratio
• For combustion to take place, the proper ratio of air and fuel
must be present in the cylinder.
•The air-fuel ratio is defined as
. .
AF = ma / mf = ma / mf
• The ideal AF is about 15:1, with homogenous
combustion possible in the range of 6 to 19.
• For a SI engine the AF is in the range of 12 to 18 depending
on the operating conditions.
• For a CI engine, where the mixture is highly non-homogeneous
and the AF is in the range of 18 to 70.

76. I.C. Engine Test Rig

77. Specific Fuel Consumption
PX
XSFC =
mf
 XSFC – specific fuel consumption (kg/kWh).
 X must always be specified when reporting these
values (i.e., I for indicated)
Fuel consumption of an engine reported in L/h or kg/h because
these values ignore engine power. A better measure of fuel
consumption is,

78. Specific Fuel Consumption Variations
• ISFC – indicated specific fuel consumption
• BSFC - brake specific fuel consumption
• PSFC – PTO specific fuel consumption
• DSFC – drawbar specific fuel consumption

79. Indicative Mean Effective Pressure:
vmax − vmin
 pdv
IMEP =
Actual Fuel-Air Ratio :
mair,act
mfuel
=
 
 A act
 F 
Stoichiometric Fuel- Air Ratio :
mair,sto
mfuel
=
 
 A sto
 F 
Parameters for Performance Diagnosis
Fuel Air Equivalence Ratio:
 
 A sto
 F 
 
 F 
φ=  A act

80. Optimizing Engine Performance
• Engines are most efficient at or near peak load.
• Efficiency drops with a reduction in torque load.
• At zero brake torque, all fuel energy is expended in engine
friction.
• Lower rated engine speeds provide lower BSFC, and at the
same time reduce torque reserve – design compromise.
• Heavy engines for a given capacity….. More inertial losses…
• Compromise – Necessary Evil …..
• Any alternate to overcome this fact…..
• Develop an idea to Change natural behaviour…..

93. Given,
Displacement Volume = 3 l =0.003 metre cube
Number of Cylinder = V6=6
Stroke = 4 Stroke
RPM =3600
Compression ratio =9.5
Length of Connecting Rod =16.6 cm
Square Engine B=S

100. (Cp/Cv=k=1.35)
Do an Otto cycle analysis (state 1 to 4) by
a. Obtaining the temperature and pressure from state 1 to 4.
b. Describing what occurs in each process.
c. Determining the heat and work outflow in each process.

102. Given,
No. of Cylinder = 4
Four Stroke Otto Cycle
Wide Open Throttle at = 3000 rpm
Compression Ration = 8.6:1
Mechanical Efficiency = 86%
Stroke to Bore Ratio =1.025
AF ratio =15
Heating value = 44300 kJ/kg
Combustion efficiency = 100%
At the start of compression stroke 1-2:
P1= 100 kPa
T1= 60 C
Exhaust residual = 4%
Do Complete Thermodynamics analysis of Engine:
(Cp/Cv=k=1.35)

103. ??
(Cp/Cv=k=1.35)

104. (Cp/Cv=k=1.35)

107. (Cp/Cv=k=1.35)

108. Total mass of gas in cylinder = mass of air + mass of Fuel + mass of exhaust residual
So,
Total mass of air = 0.00074 kg
Now,
Mass of exhaust(mex) = 4% of 0.00074 = 4 x 0.00074/100 = 0.0000296=0.000030 kg
As air fuel ratio is 15:1= (16 ratios)
Mass of air(ma) = (15/16) x (100-4)% of 0.00074 = 0.000666 kg
Mass of fuel (mf) = (1/16) x (100-4)% of 0.00074 = 0.000044 kg