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1. Performance and Operating
Characteristics of IC Engine
1

2. Geometric parameter of reciprocating engine
Theperformanceoftheinternalcombustion
engineischaracterizedwithseveralgeometric
andthermodynamicparameters

Thefollowinggeometricparametersareof
particularinterest:bore(B),connectingrodlength
(l),crankradius(a),stroke(S)andcrankangle
(ө)
Foranysinglecylinder,thecranksshaft,
connectingrod,piston,andheadassemblycanbe
representedbythemechanismshowntotheleft
2

3. Geometric parameter of reciprocating engine
ThetopdeadcenterTDCofanenginerefersto
thecrankshaftbeinginapositionsuchthatө=0
0
.
ThevolumeatTDCisminimumandisoftencalled
theclearancevolumeV
c

Thebottomdeadcenter(BDC)referstothe
crankshaftbeingatө=180
0
,thevolumeatBDC
ismaximumandoftendenotedbyV
T
ThedifferencebetweentheV
TandV
cisthe
displacementvolumeV
d
3

4. Geometric parameter of reciprocating engine
Engine Capacity (V
e)
Where n-is number of cylinders
V
d-cylinder swept volume
Displacement Rate
Stroke V
S
Bore
V
S V
S V
S
TDC
BDC( )








=×=
4
2
B
nSnVV
de
π
For 4-Stroke Engine

5. Geometrical Properties of Reciprocating Engines
Compression ratio r,
or = 8 to 12 for SI engines and
or = 12 to 24 for CI engines;
Ratio of Cylinder bore to piston Stroke:
B/S=0.8to1.2forsmall-andmedium-size engines,
about0.5forlargeslow-speedCIengines;
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.
Thestrokeandcrankradiusarerelatedby
a
l
R=
6

7. The cylinder volume V at any crank position
Thevolumeofthecylindercanbedetermineda s
functionofcrankangle(),fromthecompression
ratio,thestroke,boreandconnectingrodlength.
AtTDCthecrankshaftisatcrankangleof0
o
.
(Clearancevolume,V
c)
AtBDCthecrankangleisat180
o
.(Maximum
cylindervolume,V
T)
θ
7

8. The cylinder volume V at any crank position
Displacement volume = (Maximum -
minimum) cylinder volume
Thedisplacementvolumecanalsobe
representedasafunctionoftheboreand
stroke
Atagivencrankanglethevolumeisgivenby:
)(
4
2
θ
πx
B
VV
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 V
cresults in:
( )




+−−+=
θθθcossin)(
2
1
222
aallax
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:
( )










+−−++
−
=
θθ
πcossin
41
2
1
222
2
aalla
B
r
V
V
D




















+








−






−++
−
=
θθ
πcossin1
41
2
1
2
2
2
a
l
a
l
a
B
r
V
V
D
a
l
R=
( )




−−−++
−
=
2
1
22
sincos1
21θθRR
V
r
V
V
DD
Non-dimensionalformoftheabove
equationbecomes,
.
( )




−−−++
−
=
2
1
22
sincos1
2
1
1
1θθRR
rV
V
D
θ
10

11. The cylinder volume V at any crank position
11
















−





−





+




−
−





−
=
θ
θ
2
2
sin
2
2
1
2
cos1
1
V
S
l
S
l
r
r
V
D
a
V
D
V
TDC
V
BDC
B
l
θ
IfcrankangleismeasuredfromBDCinCCW
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:
( )










+−−++
−
=
θθ
πcossin
41
2
1
222
2
aalla
B
r
V
V
D




















+








−






−++
−
=
θθ
πcossin1
41
2
1
2
2
2
a
l
a
l
a
B
r
V
V
D
a
l
R=
( )




−−−++
−
=
2
1
22
sincos1
21θθRR
V
r
V
V
DD
Non-dimensionalformoftheabove
equationbecomes,
.
( )




−−−++
−
=
2
1
22
sincos1
2
1
1
1θθRR
rV
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 angleV
disp Pr Crank angle V
disp 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
Theperformanceoftheenginedependsoninter-relationshipbetween
powerdeveloped,speedandthespecificfuelconsumptionateach
operatingconditionwithintheusefulrangeofspeedandload.
PERFORMANCE
OF ENGINE
POWER
13

14. Engine performance
Internalcombustionengineshouldgenerallyoperatewithinauseful
rangeofspeed.
Someenginesaremadetorunatfixedspeedbymeansofaspeed
governorwhichisitsratedspeed

Ateachspeedwithintheusefulrange,thepoweroutputvariesandithas
amaximumusablevalue.
Thespecificfuelconsumptionvarieswithloadandspeed
14

15. Engine performance definition
AbsoluteRatedPower:Thehighestpowerwhichtheenginecould
developatsealevelwithnoarbitrarylimitationonspeed,fuel-airratio
orthrottleopening
Maximumratedpower:Thehighestpoweranengineisallowedto
developforshortperiodsofoperation.

Normalratedpower:Thehighestpoweranengineisallowedto
developincontinuousoperation.
Ratedspeed: Thecrankshaftrotationalspeedatwhichratedpoweris
developed
15

16. Engine Performance Parameters
Theperformanceanengineisjudgedbyquantifyingits
efficiencies
Five important engine efficiencies are
Indicated thermal efficiency (η
ith) Indicated Power
Brake thermal efficiency(η
bth) Brake Power
Mechanical efficiency (η
m)
Volumetric efficiency (η
v)
Relative efficiency or Efficiency ratio (η
rel)
16

17. Engine Performance Parameters
Other Engine performance Parameters
Mean effective pressure (MEP or P
m)
Mean piston speed (s
p)
Specific power output (P
s)
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

19. The Energy Flow
Expansion Force

20. The Energy Flow

21. Indicated work
TheEnginecycleonaP-Vcoordinates,isoftencalledanindicator
diagram.
Theindicatedworkpercycle W
c,i
isobtainedbyintegratingaroundthe
curvetoobtaintheareaenclosedonthediagram
∫
=PdVW
ic,
21

22. Gross Indicated Work
Theupperloopoftheenginecycleoftheindicatordiagram,the
compressionandpowerstrokes,whereoutputworkisgeneratedis
calledthegrossindicatedwork.
CAW
igc
+=
,
22

23. Pump work
Thelowerloop,whichincludestheintakeandexhaustiscalledPumpwork
andabsorbsworkfromtheengine.

Wide-Open Throttle (WOT) Engine operated with throttle valve fully open
when maximum power and/or speed is desired.
Pumpigcinetc
pumpWWW CBW
−=
+=
,,
Net indicated work is
23

24. Indicated Work at Part Throttle
AtWOTthepressureattheintakevalveisjustbelowatmospheric
pressure,howeveratpartthrottlethepressureismuchlowerthan
atmospheric
Thereforeatpartthrottlethe
pumpwork(areaB+C)can
besignificantcomparedto
grossindicatedwork(area
A+C)
24

25. Indicated Work with Supercharging/Turbocharged
Engineswithsuperchargersorturbochargerscanhaveintake
pressuresgreaterthantheexhaustpressure,givingapositivepump
work
( )( ) BAreaAAreaW
net +=
Superchargesincreasethenet
indicatedworkbutisaparasitic
loadsincetheyaredrivenbythe
crankshaft
25

26. Work during engine cycle
26

27. Indicated Power (ip) or (P
i)
Gross indicated work

28. p = imep (N/m
2
)
A (m
2
)
F= P.A (N)
L (m)
F (N)
Work(W)=F.L(Nm)
Time (t) = 60 / (N
e/k) (s)
Indicated power (P
i)
cylinder= W/t = F.L .N
e/(k*60) (W)
(P
i)
cylinder= (imep.A.L.N) / (n
R. 60)
(P
i)
engine = imep. (A.L.n) N) / (n
R. 60)
(P
i)
engine= [imep. V
e. 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
Theindicatedpowerperenginecanalsobegivenintermsof
indicatedworkpercycle:
where N–crankshaft speed in rev/s
n
R -number of crank revolutions per cycle
= 2 for 4-stroke= 1 for 2-stroke
R
i
in
NW
n
P
××
=
29

30. Indicated, brake and frictional power
Thetermbrakepower,P
b,isusedtospecifythatthepowerismeasured
attheoutputshaft,thisistheusablepowerdeliveredbytheengineto
theload.
Partofthegrossindicatedworkpercycleorpowerisusedtoexpel
exhaustgasesandinductfreshcharge.

Anadditionalportionisusedtoovercomethefrictionofthebearings,
pistons,andothermechanicalcomponentsoftheengine,andtodrive
theengineaccessories.
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
fbig
PPP +=
g

32. Mechanical Efficiency
Theratioofthebrake(oruseful)powerdeliveredbytheengineto
theindicatedpoweriscalledthemechanicalefficiency.
Mechanicalefficiencydependsonthrottlepositionaswellasengine
designandenginespeed.
Typicalvaluesforamodernautomotiveengineatwideopenorfull
throttleare90percentatspeedsbelowabout30to40rev/s(1800
to2400rev/min),decreasingto75percentatmaximumrated
speed.
ig
f
ig
b
mP
P
P
P
−== 1
η
32

33. Power Speed Curve
Where:
P
ig= indicated power
P
b= brake power
P
f= friction power
33
fbigPPP +=
ig
f
ig
b
mP
P
P
P
−== 1
η

34. Mean effective pressure (mep)
MEPisafictitiouspressurethat,ifactedonthepistonduringtheentire
powerstroke,wouldproducethesameamountofnetworkasthat
producedduringtheactualcycle
Meaneffectivepressure(mep)istheworkdoneperunitdisplacement
volume.
mep=W/V
D

Thenetworkduringtheintakeandexhauststrokesis:
W
p,net=(P
i-P
e)
34

35. Mean effective pressure
Theworkperdisplacementvolumerequiredtopumptheworkingfluid
intoandoutoftheengineduringtheintakeandexhauststrokesis
termedasthepumpingwork(W
P)andthemeaneffectivepressureis
calledpumpingmeaneffectivepressure(PMEP)
W
P,net/V
D=pmep=(P
i-P
e)
Theindicatedmeaneffectivepressure(imep)isdefinedastheworkper
unitdisplacementvolumedonebythegasduringthecompressionand
expansionstroke.
imep=W
i/V
D
Thenetindicatedmeaneffectivepressureforthewholecycle,
imep
net=imep-pmep
35

36. Mean effective pressure
mep = W/V
D
n
Ris the number of crank revolutions for each power stroke per
cylinder
N
nP
W
R
i×
=
NV
nP
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:
)()(
106)(
)(
3
4
2
rpmNmV
nkWP
mNmep
D
R
×
×××
=
)(
)(2
)(
3
2
mV
nNmT
mNmep
D
R
×
=π
)()(
106)(
)(
3
4
2
rpmNmV
nkWP
mNimep
D
Ri
×
×××
=
[]W
NmTrpmN
P
60
)()(2 ×
=
π
37

38. )()(
10
6)(
)(
3
4
2
rpmNmV
nkWP
mNbmep
D
Rb
×
×××
=
38
Brake mean effective pressure

39. Engine Torque T
e-Torque and crankshaft angle
Workisalsoaccomplishedwhenthe
torqueisappliedthroughanangle.

Distance
Where:
θrxy=
θθTFrxyFW ===.
()π2TW
revolutionper
=
()ωπTtTtWP === 2
60
2N
π
ω
=
39

40. Engine Brake Torque T
e
Brake mean effective pressure can also be expressed in terms of
torque
Where:
N= Engine speed (rpm)
V
D= engine Displacement capacity (m
3
)
n
R= 2, for 4-stroke engines
1, for 2-stroke engines
()()
()kW
rpmNNmTTN
TP
ee
eb
955060
2 ×
=
×
=×=
π
ω
)(
).(2
)(
3
2
mV
nmNT
mNbmep
D
Re
×
=π
R
D
e
n
mVmNbmep
mNT
×
×
=π2
)()(
).(
32
40

41. Engine Torque T
e
oThereisadirectrelationship
betweenBMEPandtorqueoutput.
oThetorquecurvewithenginerpmis
identicaltothebmepcurve,with
differentvalues.
41

42. 42
Thereisamaximuminthebrakepowerversus
enginespeedcalledtheratedbrakepower
(RBP).
Athigherspeedsbrakepowerdecreasesas
frictionpowerbecomessignificantcompared
totheindicatedpower
Thereisamaximuminthetorqueversus
speedcalledmaximumbraketorque
(MBT).
Braketorquedropsoff:
•atlowerspeedsdotoheatlosses
•athigherspeedsitbecomesmoredifficult
toingestafullchargeofair.
Max brake torque
1 kW = 1.341 hp
Rated brake power
Power and Torque versus Engine Speed at WOT
figb
PPP −=

43. Mean Piston Speed
Animportantcharacteristicspeedisthemeanpistonspeed
Where:Sisthestrokeand
Nistherotationalspeedofthecrankshaft.
Resistancetogasflowintotheengineorstressesduetotheinertia
ofthemovingpistonlimitthemaximummeanpistonspeedto
withintherange8to15m/s.
pS
pS
NSSp2=
43

44. Specific Power
Specificpoweroutputofanengineisdefinedasthepower
outputperunitpistonarea.
Itisameasureoftheenginedesigner’ssuccessinusingthe
availablepistonarearegardlessofcylindersize.
P
b
A
P
SPpowerspecific =,
)1012(
,
5
××
×
=
R
p
n
Sbmep
SPpowerspecific
44
)()(
10
6)(
)(
3
4
2
rpmNmV
nkWP
mNbmep
D
Rb
×
×××
=

45. Specific Fuel Consumption (sfc)
sfcshowshowmuchfuelisconsumedbyanenginetodoacertainamount
ofwork.
Specific fuel consumption represents the massor 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) isfuel 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

=
)(
)/(
)/(
kWP
sgm
Jmgsfc
f

=
)(
)/(
)./(
kWP
hgm
hkWgsfc
f

=
b
f
P
m
bsfc

=
Pi
m
isfc
f

=
46

47. Brake Specific Fuel Consumption vsEngine Size
Brakespecificfuelconsumptiongenerallydecreaseswith
enginesize,beingbest(lowest)forverylargeengines.
Onereasonforthisisless
heatlossduetothehigher
volumetosurfacearearatio
ofthecombustionchamberin
largeengines.
Alsolargeenginesoperate
atlowerspeedswhich
reducefrictionlosses.
47

48. Brake Specific Fuel Consumption vsEngine Speed
Brakespecificfuelconsumptiondecreasesasenginespeed
increases,reachesaminimum,andthenincreasesathigh
speeds.
Fuelconsumptionincreasesat
highspeedsbecauseofgreater
frictionlosses.
Atlowenginespeed,thelonger
timepercycleallowsmoreheat
lossandfuelconsumptiongoes
up.
48

49. Engine Thermal Efficiencies
Thetimeforcombustioninthecylinderisveryshortsonotallthefuel
maybeconsumedorlocaltemperaturesmaynotfavorcombustion

Asmallfractionofthefuelmaynotreactandexitswiththeexhaust
gas
The combustion efficiency is defined as:
Where Q
in = heat added by combustion per cycle
m
f = mass of fuel added to cylinder per cycleQ
HV= heating value of the fuel (chemical energy per unit mass)
HVf
in
C
Qm
Q
inputheatltheoretica
inputheatactual
==
η
49

50. Energy flow
50

51. Indicated thermal efficiency ( η
ith)
Indicated thermal efficiency (η
ith)
istheratioofenergyintheindicatedpower,P
i,tothe
inputfuelenergyinappropriateunits
CHVf
i
in
ii
ithQm
P
Q
P
cycleperinputheatofrate
Pη
η
===
Indicatedthermalefficienciesaretypically50%to60%
andbrakethermalefficienciesareusuallyabout30%
51

52. Brake Thermal Efficiency(η
bth)
Is the ratio of energy in the brake power P
bto the input
fuel energy in appropriate units
CHVf
b
in
bb
bthQm
P
Q
P
cycleperinputheatofrate
Pη
η
===
52

53. Thermal efficiency
CHV
bthQbsfcηη
1
=
P
m
sfc
f

=
CHV
ith
Qisfcη
η
1
=
or
From specific fuel consumption
53
CHVf
i
in
ii
ithQm
P
Q
P
cycleperinputheatofrate
Pη
η
===

54. Fuel conversion efficiency
Fuel conversion efficiency is defined as:
Thus thermal efficiency may be defined as:
C
f
t
η
η
η
=
HVHVfHVf
C
f
QsfcQm
P
Qm
W
cycleperinputHeatTheortical
cycleperWork 1
====

η
54

55. Air-Fuel Ratio and Fuel-Air Ratio
Therelativeproportionsofthefuelandairintheengine
cylinderareveryimportantfromthestandpointof
combustionandtheefficiencyoftheengine.

Air-Fuelratio(AF)orFuel-Airratio(FA)areusedto
describethemixtureratioofthecharge.
55

56. Air-Fuel Ratio and Fuel-Air Ratio
ForSIenginehydrocarbonfuel:
IdealorStoichiometricAFisabout15:1(14.7:1)
Combustionpossibleintherangeof6:1to25:1
ForCIenginehydrocarbonfuel:
IdealorStoichiometricAFisalsoabout15(14.7:1)
Combustionpossibleintherangeof18:1to70:1

57. Fuel-Air (F/A)or Air-Fuel Ratio (A/F)
IntheSIenginethefuel-airratiopracticallyremainsaconstant
overawiderangeofoperation.
InCIenginesatagivenspeedtheairflowdoesnotvarywith
load;itisthefuelflowthatvariesdirectlywithload.
Therefore,thetermfuel-airratioisgenerallyusedinsteadof
air-fuelratio.

58. Fuel-Air (F/A)or Air-Fuel Ratio (A/F)
Amixturethatcontainsjustenoughairforcompletecombustionofall
thefuelinthemixtureiscalledachemicallycorrectorstoichiometric
fuel-airratio.
Amixturehavingmorefuelthanthatinachemicallycorrectmixtureis
termedasrichmixtureand
amixturethatcontainslessfuel(orexcessair)iscalledaleanmixture.
Theratioofactualfuel-airratiotostoichiometricfuel-airratioiscalled
equivalenceratioandisdenotedby
Φ=1 Stoichiometric
Φ>1 RichMixture
Φ<1 LeanMixture








−
−
=
ratioairfueltricStoichiome
ratioAirfuelActual
φ

59. Equivalent ratio & Relative A/F ratio

60. Volumetric efficiency CI ( )
Thevolumetricefficiencyisusedtomeasuretheeffectivenessofan
engine'sinductionprocess.
Volumetricefficiencyisusuallyusedwithfour-strokecycleengines
whichhaveadistinctinductionprocess.

Itisdefinedasthevolumeflowrateofairintotheintakesystem
dividedbytherateatwhichvolumeisdisplacedbythepiston:
Where:m
aisthemassofairinductedintothecylinderpercycle.
NV
m
V
m
Dia
a
Dia
a
V
,,
2
ρρ
η

==
V
η
60

61. Volumetric Efficiency SI (η
v)
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
dia,
a
vρ
η
fm+
=
•
61

62. Volumetric efficiency
Typicalvaluesofvolumetricefficiencyforanengineatwide-open
throttle(WOT)areintherange75%to90%,goingdownto
muchlowervaluesasthethrottleisclosed.
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 (η
v)
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

64. Volumetric Efficiency
ntDisplacemeEngine
EnginetheEnteringAir
η
V
=
64

65. Engine Specific Weight and Specific Volume
Engineweightandbulkvolumeforagivenratedpowerare
importantinmanyapplications.Twoparametersusefulfor
comparingtheseattributesformoneenginetoanotherare:
Theseparametersindicatetheeffectivenesswithwhichtheengine
designerhasusedtheenginematerialsandpackagedtheengine
components.
powerrated
Weightengine
WeightSpecific =
powerrated
volumeengine
volumeSpecific =
65

66. Calorific Value (CV)
Calorificvalueofafuelisthethermalenergyreleasedperunit
quantityofthefuelwhenthefuelisburnedcompletelyandthe
productsofcombustionarecooledbacktotheinitialtemperature
ofthecombustiblemixture
Othertermsusedforthecalorificvalueareheatingvalueand
heatofCombustion.
Whentheproductsofcombustionarecooledto25°Cpractically
allthewatervapourresultingfromthecombustionprocessis
condensed.

67. Calorific Value (CV)
WhenH
2Oisinproductsiscondensedtoliquidadditionalheatis
realizedandthetotalheatliberatediscalledHigherCalorificValue
(HCV)
whenH
2Ointheproductsisinthevaporformheatisnotremoved
thiscalorificvalueiscallediscalledLowercalorificValues(LCV)
L.C.V.=H.C.V.–(MassofH
2O*2454.1)inkJ

68. Engine Performance Curves
1.I
mep
2.B
mepand 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
Dynamometersareusedtomeasuretorqueandpowerovertheengine
operatingrangesofspeedandload.
Dynamometersusevariousmethodstoabsorbtheenergyoutputofthe
engine,allofwhicheventuallyendsupasheat.
Somedynamometersabsorbenergyinamechanicalfrictionbrake,
hydraulicfluidandmagneticfield

70. Dynamometer vs. Engine Setup
TheEngineisclampedonatestbedandtheshaftisconnectedtothe
dynamometerrotor.

Therotoriscoupledelectromagnetically,hydraulicallyorby
mechanicalfrictiontoastator
Thetorqueexertedonthestatorwiththerotorturningismeasured
bybalancingthestatorwithweights,springsorpneumaticmeans.
Load cell
Force F
Stator
Rotor
b
N

71. Brake Torque and Power
Workisdefinedastheproductofaforceandthedistancethroughwhich
thepointofapplicationoftheforcemoves
Whenthedriveshaftoftheengineturnsthroughonerevolution,any
pointontheperipheryoftherigidlyattachedrotermovesthrougha
distanceofequalto
Duringthismovementafrictionforce,f,isactingonthestator.
Thefrictionforce,f,isthusactingthroughthedistance and
producingawork

72. Brake Torque and Power
Work during one revolution = Distance * f
= *f
Thetorque,r*f,producedbythedriveshaftisopposedbyaturning
momentequaltotheproductofthelengthofthemomentarmband
theforceFmeasuredbythescale
T=r*f=F*b
Workduringonerevolution= Fb
Power=Work/Time=FbN/60