INTERNAL COMBUSTION ENGINES
By: Dennis Ballou and Barbara McCord
This paper presents the essential design features of the spark ignition (SI), piston-cylinder engine. 1: Referring to Figure 1
S - Stroke
s - Distance between crank and
wrist pin axes
， - Crank angle
B - Bore
r – Connecting rod
a – Crankshaft offset
V – Clearance volume c
V – Displacement volume d
TDC – Top dead center
BDC – Bottom dead center
Figure 1: Piston and Cylinder Geometry of
Top Dead Center (TDC) - Maximum travel of piston toward cylinder head. The cylinder volume at TDC
is called the clearance volume.
Bottom Dead Center (BDC) - Minimum travel of piston toward crankshaft.
Bore (B) - Cylinder diameter (piston diameter = cylinder diameter - clearance).
Stroke (S) - Distance between TDC and BDC.
Displacement (V) - volume of cylinder between TDC and BDC. d
1 Reference 1., p. 36.
2 The Four-Stroke, Air Standard Ideal Otto Cycle
3 Referring to Figure 2:
First stroke, Process 6-1 (Induction).
The piston travels from TDC to BDC with the intake valve open and the exhaust valve closed (some valve overlap occurs near the ends of strokes to accommodate the finite time required for valve operation). The temperature of the incoming air is increased 25-35 ~C over the surrounding air as the air passes through the hot intake manifold.
Second Stroke, Process 1-2 (Compression).
At BDC the intake valve closes. The piston travels to TDC compressing the cylinder contents at constant entropy. Just before TDC, the spark plug fires initiating combustion.
Combustion, Process 2-3.
This process is modeled at constant volume even though combustion requires a finite time in a real engine (cylinder is moving). Peak cycle temperature and pressure occur at state 3.
Third Stroke, Process 3-4 (Expansion or power stroke).
With all valves closed, the piston travels from TDC to BDC. The process is modeled at constant entropy.
Exhaust Blowdown, Process 4-5.
Near the end of the power stroke, the exhaust valve is opened. The resulting pressure differential forces cylinder gases out dropping the pressure to that of the exhaust manifold. The process is modeled at constant volume.
Figure 2: Ideal air-Standard Otto Cycle
Fourth Stroke, Process 5-6.
With the exhaust valve open, the piston travels from BDC to TDC expelling most of the remaining exhaust gases.
Note: The four strokes require two complete
revolutions of the crankshaft.
2 Id., pp. 25 and 72. 3 Id., p. 73.
Process 6-1. wPvv，？;；61016？
Process 1-2. q，0 wuu，？;；12？1212？
QQmQ，，(w，0Process 2-3. qquu，，？;；23？infLHVc23？2332？in
Q， Where: lower heating value of the fuel LHV
(，combustion efficiency - the fraction of fuel actually burned. c4Its usual range is 0.95-0.98.
AF = air/fuel ratio QAFuu(，？？1;；;；LHVc32
Note: This expression assumes that the cylinder contents are air (e.g. 15 lb of air plus one lb of
fuel per lb of fuel).
q，0Process 3-4. wuu，？;；34？3434？
Process 4-5. quu，？;；4554？
Process 5-6. wPvv，？;；56065？
wqnetout，？qq(，，？1Thermal efficiency. ww，inoutt?netij？qqijij,?inin;；
Ideal Thermal Efficiency - Cold Air Standard
If we express differences in internal energy as differences in temperature multiplied by a constant
specific heat (cold air standard), the ideal thermal efficiency becomes:
We can use the following relationships for the isentropic processes occurring between states 1-2 and 3-4 for
the cold air standard (constant properties).
k？1k？1????TvTv1234，， and ?，?，TvTv(?2143(?
4 Id., p. 59.
Substituting these expressions into the equation for ideal thermal efficiency above results in an expression for ideal efficiency in terms of the compression ratio; thus:
，v/v，N4/3where r=compression ratio 12
5Modern spark ignition engines have compression ratios of 8-11. Compression ratio is limited primarily by
the tendency of the fuel to detonate resulting in the condition called knock. Otherwise, the ratio should be as high as practicable if good efficiency is the primary goal.
6Figure 3 shows that the efficiency rises steeply with compression ratio up to about r= 4 and then tapers c off somewhat while continuing to rise.
Figure 3: Thermal Efficiency as a Function of Compression Ratio for SI Engines
The output of any heat engine is work. The work is done by pressurized gas moving a piston. It is given by:
WPdV，wPdv， or ))
Two other definitions of work are useful in describing and comparing internal combustion engines. Indicated work is that obtained by measuring cylinder pressure and plotting it against volume to obtain the actual cycle representation (the so-called indicator card). Integration of the resulting closed curve gives the indicated work. Brake work is that obtained by measuring shaft torque and converting to power. The difference between indicated work and brake (or shaft) work represents losses due to mechanical friction and parasitic loads on the engine (such as the air conditioning compressor, oil pump, alternator, etc). Brake
work and indicated work are related by:
wb , where η is the mechanical efficiency of the engine. ，mwi(m
5 Id., p. 41. 6 Id., p. 77.
Mean Effective Pressure
The mean effective pressure is an artificial pressure which when multiplied by the displacement gives the
work. It is useful in comparing performance of different engines; thus:
Indicated mean effective pressure (imep) and brake mean effective pressure (bmep) are:
wbbmep， vd7Typical values of bmep:
Naturally aspirated SI engines 850-1050 kPa (120-150 psi)
Naturally aspirated CI engines 700-900 kPa (100-130 psi)
Turbocharged CI engines 1000-1200 kPa (145-175 psi)
Specific Fuel Consumption
Brake specific fuel consumption (bsfc) and indicated specific fuel consumption (isfc) are defined by:
8Bsfc as a function of engine speed is shown below:
Figure 2-12, Pulkrabek, p57
Figure 4: Brake Specific Fuel Consumption as a Function of Engine Speed
7 Id., p50. 8 Id., p57.
For a given displacement volume, the longer the stroke the smaller the bore and combustion chamber surface area thus resulting in less heat energy loss. The longer stroke, however, means higher piston speeds and thus higher friction.
Bore sizes of engines range from 0.5m to 0.5 cm (20-.02 in). See Table 1 below.
The bore-to-stroke ratio (B/S) of most modern automobile engines is very nearly unity (B/S = 1 implies a square engine). Some are slightly over square (B/S >1); others are under square (B/S <1). To keep height to a minimum, the engine should be designed over square. B/S for small engines is usually in the range 0.8-1.2.
9 Table 1 – Typical Engine Operating Parameters
PARAMETERS Model Airplane Automobile Large Stationary
Two-Stroke Cycle Four-Stroke Cycle Two-Stroke Cycle
2.00 9.42 50.0 BORE (cm)
2.04 9.89 161 STROKE (cm)
0.0066 0.69 316 DISPLACEMENT/cyl (L)
13,000 5200 125 SPEED (RPM)
0.72 35 311 POWER/cyl (kW)
8.84 17.1 6.71 AVERAGE PISTON
109 50.7 0.98 POWER/DISPLACEMENT
503 1170 472 BMEP (kPa)
The Air-Fuel ratio (AF) is the ratio of the cylinder air mass (or mass rate) to the fuel mass (or mass rate). The ideal (stoichiometric) AF for gasoline is very close to 15. The normal range for AF in gasoline automobile engines is 12-18. Combustion can occur in the range 6-19.
Fuel-Air Ratio and Equivalence Ratio
The Fuel-Air ratio is the reciprocal of the Air-Fuel ratio. The Equivalence ratio is the actual fuel-air ，;；
ratio divided by the ideal fuel-air ratio.
An equivalence ratio less than one is said to be lean; greater than one, rich.
9 Id., p. 37.
Inlet Air Density
Air entering the cylinder will depart from the standard sea level ambient condition (14.7 psia, 537 ~R)
because of pressure drops in the manifold, air cleaner, etc. and some pre-heating. Furthermore, the fuel
vapor at maximum power will reduce inlet-air density by about 2 %. For preliminary design, assume a
pressure drop of 4 % and a temperature increase of 10 % of the Fahrenheit value.
Torque and Brake Horsepower
We can derive a formula for torque and brake horsepower using the geometry of a prony brake. A 10 schematic diagram of a prony brake is shown below.
Figure 5: Adaptation of Prony Brake for Power Measurement
A friction band is tightened around the flywheel (radius, r) of the engine. A friction force, f, acting at distance r, therefore opposes engine rotation. The moment thus produced is balanced by a force F acting
with a moment arm R . The shaft torque is thus:
The work during a single revolution is and the engine power is equal to work per revolution times the 2；；
Caution!!!! Be very careful with units to ensure consistency.
10 Reference 3., p 4-8.
Volumetric efficiency is defined as the ratio of the actual air mass drawn into the engine during one cycle to that corresponding to atmospheric conditions. Thus:
m，where: actual mass of air in a
m， steady-state air flow in a
：， air density at atmospheric conditions a
V， displacement d
engine speed N，
n， revolutions per cycle
Typical values of volumetric efficiency are in the range 75-90%.
11Mean Piston Speed
Piston speed is limited by inertia stresses and requirements for reliability and durability and is chosen by reference to previous experience with similar engines. Where maximum fuel economy is desired, select a piston speed from the range 1000-1200 ft/min (5-6 m/s). To keep engine size to a minimum, the highest practical rated speed should be used. For automobile engines, high rated speeds can be used because 12maximum engine speed is seldom used. Taylor advises that 3500 ft/min for a 2-valve head and push-rod
gear would be reasonable for a 200 bhp passenger automobile engine. See Table 13-1, Taylor (Reference 2, Vol. 1), for mean piston speeds used in US practice.
Friction and Power to Drive Auxiliaries
The difference between the internal power produced in the cylinder (ihp) and that measured at the crankshaft (bhp) is accounted for by these factors: power to overcome friction in pistons, bearings, cams and other moving parts and power to drive auxiliaries such as oil, water and power steering pumps (fhp). We express this difference by the following equation:
Or, in terms of mean effective pressure:
13For preliminary design, fmep can be estimated from Figure 6 (taken from Taylor), which is reprinted
11 Reference 2., Vol.2. 12 Id., p 385. 13 Id., Vol. 2, p 382.
Figure 6: Curves for Estimating Friction mep of 4 Cycle Engines
1. Select a compression ratio and air-fuel ratio for reasonable efficiency; and a fuel with an
appropriate octane rating. Estimate volumetric and combustion efficiencies.
2. Perform a hot air-standard analysis of the cycle and find net work (Btu/lb), specific displacement 3/lb), imep, isfc and thermal efficiency. (ft
3. Adjust imep to reflect changes from the ideal hot air standard cycle. Actual imep is about 75% of 14ideal (Otto cycle) imep.
4. Select an appropriate mean piston speed.
5. Estimate friction mep (fmep) from Figure 6.
6. Calculate brake mean effective pressure (bmep).
7. Calculate total required piston area.
Where: U = mean piston speed; S = stroke (in), N = engine speed p
Or, expressing the equation with units attached:
Where: η = volumetric efficiency; PS = Power stroke, n = rev/cycle ν
8. Divide the total piston area, A, by the number of cylinders to get area per cylinder; then calculate p
the bore. Multiply bore by 1.20 and by the number of cylinders to get the approximate engine 15length.
9. Stroke. To keep engine height to a minimum, select a relatively small S/B ratio, say, 0.8. Then
calculate the stroke and engine speed.
10. Calculate brake thermal efficiency and brake specific fuel consumption.
11. Estimate engine weight. SI truck and bus engines weigh in the range 1.36-2.93 lb per cubic inch 16of displacement. Automobile engines probably approach the lower of these figures.
14 Reference 1., p 83. 15 Reference 2, v.2, p.387. 16 Id, p. 387.