MEEG 467 Exam Format:
Short answer 20-30 questions/small calculations/diagrams (40%)
Exam is cumulative.
Time will be three hours. Know how to do problems COLD as time will be an issue.
Expected study time: 12-14 hours concentrated.
Problems: Answer four of five problems, nominally 15 points each, total (60%)
Step 1: Study the midterm. Some questions may magically reappear with a few numbers
switched! All material from the first part of the course is fair game. Study exam prep
questions from midterm.
Sample Questions –
Chapter 5, example 5.8 and homeworks.
 Know CI concepts and be able to calculate efficiencies. Look closely at
homeworks and book.
Chapter 9, Turbocharging and supercharging
 Name and describe basic types of superchargers
 Discuss advantages of each
 Difference between Turbocharging and supercharging
 Know how to calculate pressure ratios, density ratios, effects of intercoolers and
efficiencies. All info from spreadsheet is fair game
 Know how to pick an appropriate turbocharger
Chapter 11 – Engine Modeling
 Know how to calculate position and acceleration numerically
 Any formulas used in the spreadsheet are fair game
 Understand shaking moments and relationships between weights and lengths with
respect to dynamics.
 Understand the Weibe function
 Understand how pressures, dynamic forces and torques are calculated
 Know why total work is path dependant
 Understand how and where energy is lost, even when heat transfer is ignored
 You should be able to derive each formula used in the spreadsheet
 Look at the PowerPoint presentation and understand concepts
Chapter 7 –2 Stroke Engines
 Know concepts and timing diagrams.
 Understand mechanics and flows.
 See powerpoint and your notes for important areas. Read book.
Turbocharging
A 3.0 ltr. Engine is being developed.
 Boost is to be limited to 1.0 bars,,
Max RPM is 7200.
 o , Overall arbitrary efficiency will be 30%
Vf; Volumetric Efficiency is 90%
Standard atmospheric conditions are as follows:
 Tamb = 17C ; Pamb = 101 kPa = 1.0 bar
 Ratio of Specific Heats () 1.4; A/F mixture (by wt) 14.7
 Compressor Efficiency c = 65%
 Calorific value for fuel is 44MJ/kg. Rair=287 J/kgK,
At maximum RPM:
a) What is the pressure ratio (r)? (1)
b) What is the IDEAL temperature after the compressor? (1)
c) What is the ACTUAL temperature after the compressor? (2)
d) What is the density ratio? (1)
e) What is the airflow (m3/sec) at through the intake manifold (1)
(hint: same as no boost)?
f) What is the airflow (m3/sec) at the turbocharger inlet? (2)
g) What are the MASS flows per second of air and fuel (kg/min)? (2)
h) How much power is produced at 7500 RPM (1 HP = 747.5 W) (1)
Add an intercooler with 90% efficiency and 1 psi pressure drop
i) What is the temperature after the intercooler? (2)
j) What is the total pressure after the intercooler, in BARS? (1)
k) What is the intercooled density ratio? (1)
l) What is the airflow (m3/sec) at the turbocharger inlet? (2)
m) What are the MASS flows per MINUTE of air and fuel (kg/min)? (2)
n) How much intercooled power is produced at 7500 RPM (1 HP = 747.5 W) (1)
Engine Dynamics
A single cylinder engine is designed with a bore of 100mm and a stroke of 60mm.
Rod length is 150mm. Rod weight is 1000g and piston weight is 500g.
The center of gravity of the rod is 50 mm from the big end. The engine rotates counter clockwise and )
degrees is TDC.
At a crank angle of 45 degrees:
a)
Draw the configuration with the origin at the crank main bearing and the X-axis aligned with the
centerline of the cylinder bore.
b) What is the position of the rod bearing (X&Y coordinates in mm)
c) What is the position of the piston pin?
d) What is the position of the Rod CG?
e) What is the rod angle?
Assume the acceleration of the CG is (–6000,-4000) m/s2 and the acceleration of the piston pin is (6020, 0) m/s2 (this occurs as 5079 RPM). IGNORE ANGULAR MOMENTUM
Draw a free body diagram of the rod
f) Calculate the rod bearing and piston pin forces due to the acceleration of the rod center of gravity.
Hint: Sum moments about rod bearing and ignore mass of piston here.
g) Calculate the force at the piston pin due to the acceleration of the piston
h) Calculate the force along the centerline of the rod due to the piston acceleration
i) Calculate the force at the rod bearing due to piston acceleration
j) Calculate the total forces on the rod bearing in the X&Y Directions (Hint – draw a diagram here to
keep signs straight!)
k) Calculate the instantaneous torque on the crankshaft from these forces.
POWER A direct injection engine has a swept volume of 2.5 liters, full load performance is
shown below. Calorific Value is 44MJ/kg. Ambient temperature is 17C and pressure is 101Kpa.
Rair=287 J/kgK,
a)
b)
c)
d)
e)
f)
g)
h)
i)
What is the maximum power output (in KW and HP, 1 HP = 747.5 W)? (3)
What is the volume air flow at this output(m3/sec)? (2)
What is the mass air flow at this output (g/sec)? (2)
What is the fuel flow rate (kg/sec) (2)
What is the gravenometric AFR? (2)
What is the BMEP at Max Power? (2)
What is the BMEP at max TORQUE (2)
What is the maximum overall (brake) efficiency?
How much power and torque are made there?
Ideal Air Otto Cycle
An engine is designed with a compression ratio of 10:1 and has total volume of 500 CC per cylinder.
Temperature at beginning of compression is 50C and pressure is atmospheric at 100 kPa Assume ideal
gas behavior
Gravonometric A/F Mixture is 15:1 (by weight)
Calorific value for fuel is 44MJ/kg.
Rair=287 J/kgK,
Heat Capacity products and reactants is the same, C v= 950 J/kgK
Cp=1330 J/kgK
Both compression and expansion are reversible isentropic adiabatic with:
 pv = constant
Tv -1=const
 = 1.4
a)
b)
c)
d)
e)
f)
g)
h)
i)
j)
k)
l)
m)
n)
Draw the PV diagram for an Ideal Air standard Otto Cycle (SI engine). Label states as 1-2-3-4.
Label heat flows, axes
What is the mass of air in the cylinder?
What is the mass of fuel in the cylinder?
How much heat is released by combustion?
What is the temperature after compression (state 2)?
What is the temperature after combustion (state 3)?
What is the temperature after expansion (state 4)?
What is the pressure after compression (state 2)?
What is the pressure after combustion (state 3)?
What is the pressure after expansion (state 4)?
How much heat must be released to return to the initial state?
What is the Otto efficiency? (Hint you can calculate three ways to check numbers)
What is the total work for this cycle?
Calculate work by integration of compression and expansion strokes
Engine and cycles:
A single cylinder high performance DEISEL engine has a
Vs (swept volume) of 500cc
Compression ratio of 22:1
Rated for max power is at 4000 RPM.
Indicated efficiency is 55% of the corresponding ideal air Otto cycle. Mechanical efficiency is
85% and volumetric efficiency is 90%.
Gravimetric air fuel mixture is 13:1 and
Calorific value of fuel is 54MJ/kg.
Air is inducted at 100kPa and 20C.
Ratio of specific heats is 1.4
Rair = 287 J/kgK
Cp=1330 J/kgK Cv= 950 J/kgK
Calculate:
a)
b)
c)
d)
e)
f)
g)
h)
i)
j)
k)
l)
m)
n)
o)
p)
q)
r)
s)
t)
u)
v)
w)
Otto Efficiency
Arbitrary overall efficiency
Specific Fuel Consumption (sfc)
Air Volume flow rate
Air Mass flow rate (kg/s)
Fuel mass flow rate (kg/s)
Brake Power Output (kW)
BMEP (kPa)
Draw the PV diagram for an Ideal Air Deisel Otto Cycle (SI engine
What is the combustion chamber volume?
For idealized operation:
What is the mass of air in the cylinder?
What is the mass of fuel in the cylinder?
How much heat is released by combustion?
What is the temperature after compression (state 2)?
What is the temperature after combustion (state 3)?
What is the temperature after expansion (state 4)?
What is the pressure after compression (state 2)?
What is the pressure after combustion (state 3)?
What is the pressure after expansion (state 4)?
How much heat must be released to return to the initial state?
What is the temperature in the final state (state 5)?
What is the Otto efficiency? (Hint you can calculate three ways to check numbers)
What is the total work for this cycle?
An engine is being developed as follows:
2.5 ltr SI four Cylinder, 100mm bore. Rev limit will be 7,000 RPM. The normally aspirated version is
planned to make 155 Hp at 6800 RPM with a Volumetric Efficiency of 95% and mechanical efficiency of
85%. A/F ratio will be 14.7:1 with 44MJ/kg CV. Ratio of specific heats is standard (1.4) and pressures and
temp are 25C and 1 bar (101Kpa). Indicated (Arbitrary overall) efficiency is 60% of the otto cycle. Cv =
950MJ/kgK. R=287J/kgK
The turbocharged version will make 300 HP and run 8:1 compression ratio and is expected to have the
same efficiencies. The engine will develop no boost under 2500 RPM, rise linearly to 80% max boost at
3500 RPM and reach full boost at 4,000 RPM. Boost will trail off from 100% to 90% from 6500 to 7000
RPM. Assume average compressor efficiency of 70% as a first cut.
a)
What compression ratio is needed for the NA engine to make this power? Perform all calculations
by hand and show all work INCLUDING:
i.
Convert HP to kW and calculate desired work per cycle
ii.
Calculate mass of air and fuel per cycle
iii.
Calculate the required otto efficiency to make this power
iv.
Calculate all pressures and temperatures for the ideal air standard otto cycle, heat flows,
otto efficiency.
(hint see exam question problem 3 and work backwards)
Make up an excel spreadsheet with the same calculations.
b) The goal is to make 300 HP at 6,500 RPM. Do calculations by hand and then generate an Excel
spreadsheet to allow for multiple RPM and boost calculations. First assume 1.0 bar boost and
6500 RPM
i.
Calculate T1 & T2s
ii.
Calculate T2
iii.
Calculate the density ratio
iv.
Calculate air flow per minute (CFM, LB/Min and kg/sec)
v.
Calculate fuel flow per minute (kg/sec)
vi.
Calculate power in kW and Horsepower.
c) Add a column to your spreadsheet and increase/decrease boost until 300HP is attained. Report
i..vi above
d) Calculate power and torque for BOTH NA and Turbocharged and graph the results (RPM as the X
axis). On a separate axis graph boost.
e) Comment on the need for a waste gate.
f) Select an appropriate turbocharger from the Turbonetics page, print out the compressor map, and
graph results.
g) Add intercoolers to both of the engines above. Assume a 1psi pressure drop and 80% efficiency.
h) Calculate density ratio and resulting power.
i) What happens at low RPM (zero boost)?
j) What effect will this have on Lag?
Combustion chamber design
1) What is the maximum valve area to cylinder bore area for each of the following (show diagrams)
(6)
a) 2V Hemi –w- 30 degree valve angle.
b) 2V Wedge
c) 4V flat
d) 4V Pent Roof, 30 degree valve angle (show diagram and estimate)
2) Draw the layout for valves in a 5V engine without rockers using only lifters and two cams. Show
spark plug and cams and indicate which valves are intake and which are exhaust (3)
3) What are the four considerations of a well-designed combustion chamber? (4)
4) For a 4” bore 2V hemi with equally sized valves inclined at 30 degrees, draw a planar diagram and
label all dimensions used in the following (6):
a) If the valves touch the cylinder wall and each other, what are their diameters?
b) The radius of curvature of the combustion chamber?
c) The volume of the combustion chamber (assume inner surface of valves follows arc)
5) Besides valve size, what advantages do hemi heads have over wedge-heads (3)?
6) What advantages does a wedge head have over a hemi 2V (3)?
Weibe Function: Combustion begins at  = 10 degrees BTDC and is 99% done at 30
degrees ATDC. a=5, m=2 Ignore all delays.
   0 
(show work) Weibe  x( )  1  exp( a 

  b 
Compression ratio is 13:1
m 1
)
Displacement is 500cc, Vf = 100%
AFR is 14.7:1 and assume all fuel burns
a.
b.
c.
d.
e.
f.
g.
Draw the weibe function
How much total air is inducted per cycle
How much fuel (in kg) is burned per cycle
What percentage of the fuel is burned up to TDC? (2)
How much fuel is burned between TDC and 5 degrees ATDC? (2)
Draw a graph of fuel burned vs.  and properly label axes (2)
State the pressure, volume and temperature at 5 degrees ATDC for both
the unfired and fired states.
A large diesel engine inducts 3 KG of air per cycle per cylinder. It is slow revving and
has a compression ratio of 26:1. It’s volumetric efficiency is 104% at 1.0 bar (101kPa)
and 27C, R=287J.kgK, CV=44 MJ/kg; Cv=950 J/kgK Cp = 1.33 KJ/kgK for reactants and
products and the ratio of specific heats is 1.4. Assume an ideal cycle with the following:
a) What is the swept volume in LITERS? (1)
b) Draw a PV diagram and label pressures and volumes as well as  (P1V1 though P4V4)
(2)
c) What is the size of the combustion chamber? (1)
d) What is the volume V1 (1)
e) What is the temp, pressure, volume (T2, V2, P2) after compression assuming
reversible
adiabatic isentropic? (2)
f)
Assuming a AFR of 18:1, how much heat is released during combustion? (2)
g) What is the temp, pressure and volume after combustion (T3, P3, V3) assuming only
85% of the heat is retained due to poor insulation? (3) DO NOT USE PV=mRT since
you do not know R of the products!
h) What is the load ratio ? (2)
i)
What is the Diesel cycle efficiency? (1)
Cam and float, An engine uses an overhead cam and rockers.
Weights are as follows:
Camshaft 1200g
rocker 112.5g Ratio 1.5:1, Radius of Gyration: 25mm
springs 120g,
valve 125g
retainer/keepers 35g.
rv=50.8mm
A cam is designed using modified trapezoidal rise and fall with 300 degrees crank
duration and 0.35” lift.
The free height of the valve spring is 1.6”, the installed height 1.51”, and coil bind occurs
at 1.00”. Spring pressure at coil bind is 300 lbs.
a) What is the effective valve train mass in grams and lbs (hint use 1 lb = 0.450 kg)?
b) What are the spring rate and the preload?
c) If single rise and single return profiles are used back to back, what is the cam
duration angle () in cam degrees of EACH profile?
d) Using a modified trapezoidal profile, where is valve float most likely to occur and
why?
e) What are the displacement and the spring force at this point?
f) At what crankshaft RPM does float occur at this point?
g) What spring rate is needed to allow for 8000 RPM?
h) What percentage effect do each of the following have on the RPM at which float
occurs show work (2 each)
Duration is increased by 20%
Valve train effective mass is reduced by 10%
What effect does a 10% increase in lift have on RPM limit?
Spring pressure increased by 10% (increases preload by same ratio)
***** SHOW ALL WORK AND UNITS! ********
A direct injection four cylinder engine has a swept volume of 2 liters, full load
performance is shown below. Calorific Value is 44MJ/kg. Ambient temperature
is 17C and pressure is 101Kpa. Rair=287 J/kgK,
j) At what RPM is maximum power made? (1)
USE THIS RPM FOR ALL CALCULATIONS!
k) What is the maximum power output (in KW and HP, 1 HP = 747.5 W)? (3)
l) What is the volume air flow at this output(m3/sec)? (2)
m) What is the mass air flow at this output (g/sec)? (2)
n) What is the fuel flow rate (kg/sec) (2)
o) What is the gravenometric AFR? (2)
p) What is the BMEP at Max Power? (2)
q) What is the BMEP at max TORQUE (2)
r) What is the maximum overall (brake) efficiency? (2)
s) How power and torque are made there? (2)
***** SHOW ALL WORK AND UNITS! ********
A 2.5 ltr. Engine is being developed.
 Boost is to be limited to 0.8 bars
 Max RPM is 7800.
 o , Overall arbitrary efficiency will be 30%
 Vf; Volumetric Efficiency is 105%
Standard atmospheric conditions are as follows:
 Tamb = 27C ; Pamb = 100 kPa = 1.0 bar
 Ratio of Specific Heats () 1.4; A/F mixture (by wt) 14.7
 Compressor Efficiency c = 65%
 Calorific value for fuel is 44MJ/kg. Rair=287 J/kgK,
At maximum RPM:
a) What is the pressure ratio (r)? (1)
b) What is the IDEAL temperature after the compressor? (1)
c) What is the ACTUAL temperature after the compressor? (2)
d) What is the density ratio? (1)
e) What is the airflow (m3/sec) at through the intake manifold (1)
(hint: same as no boost)?
f) What is the airflow (m3/sec) at the turbocharger inlet? (2)
g) What are the MASS flows per second of air and fuel (kg/min)? (2)
h) How much power is produced at 7800 RPM (1 HP = 747.5 W) (1)
Add an intercooler with 90% efficiency and 1 psi pressure drop
i) What is the temperature after the intercooler? (2)
j) What is the total pressure after the intercooler, in BARS? (1)
k) What is the intercooled density ratio? (1)
l) What is the airflow (m3/sec) at the turbocharger inlet? (2)
m) What are the MASS flows per MINUTE of air and fuel (kg/min)? (2)
n) How much intercooled power is produced at 7800 RPM (1 HP = 747.5 W) (1)
A single cylinder engine is designed with a bore of 100mm and a stroke of 100mm.
Rod length is 200mm. Rod weight is 700g and piston weight is 300g.
The center of gravity of the rod is 50 mm from center of the big end. The engine
rotates clockwise and 0 degrees is TDC.
At a crank angle of 30 degrees ATDC:
l) Draw the configuration with the origin at the crank main bearing and the X-axis
aligned with the centerline of the cylinder bore.
m) What is the position of the rod bearing (X&Y coordinates in mm)
n) What is the position of the piston pin?
o) What is the position of the Rod CG? (hint – use similar triangles)
p) What is the rod angle w.r.t. the X axis?
Assume the acceleration of the CG is (–3000,-2700) m/s2 and the acceleration of the
piston pin is (-3200, 0) m/s2 (this occurs as 2585 RPM). IGNORE ANGULAR
MOMENTUM
q) Draw a free body diagram of the rod
r) Calculate the rod bearing and piston pin forces due to the acceleration of the rod
center of gravity. Hint: Sum moments about rod bearing and ignore mass of
piston here.
s) Calculate the force at the piston pin due to the acceleration of the piston
t) Calculate the force along the centerline of the rod due to the piston acceleration
u) Calculate the force at the rod bearing due to piston acceleration
v) Calculate the total forces on the rod bearing in the X&Y Directions (Hint – draw a
diagram here to keep signs straight!)
w) Calculate the instantaneous torque on the crankshaft from these forces.
 RT
ideal gas: PV=mRT or as a rate equation Pv  m
otto  1 
 sc 
1
rv
 1
ma
ma  me
tr 
ma
mi
1
sfc 
CV * overall
d 
   0 
Weibe  x ( )  1  exp( a 

  b 
mi
Vs  ambient
nch 
ma
Vs  ambient
m 1
)