Overlook of an SI Car Engine

Thermodynamic cycles can be divided into two general categories: power cycles, which produce a net power output, and refrigeration and heat pump cycles, which consume a net power input. The thermodynamic power cycles can be categorized as gas cycles and vapor cycles. In gas cycles, the working fluid remains in the gas phase throughout the entire cycle. In vapor cycles, the working fluid exits as vapor phase during one part of the cycle and as liquid phase during another part of the cycle. Internal combustion engines and gas turbines undergo gas power cycle.

Internal combustion engines, which are commonly used in automobiles, have two principal types: spark-ignition (SI) engines and compression-ignition (CI) engines. This section will introduce the spark-ignition (SI) engines and the ideal cycle for spark-ignition engines - Otto Cycle.

    Internal Combustion Engine Terminology

Nomenclature for Reciprocating Engines


Internal combustion engines are reciprocating engines, which basically are piston-cylinder devices. The sketch of a reciprocating engine is shown on the left. The sketch is labeled with some special terms.

  • The piston is said to be at the top dead center (TDC) when it has moved to a position where the cylinder volume is minimum. This volume is called a clearance volume.
  • The piston is said to be at the bottom dead center (BDC) when it has moved to a position where the cylinder volume is maximum.
  • The volume swept out by the piston when it moves from TDC to BDC is called the displacement volume.
  • The distance from TDC to BDC is called stroke.
  • The bore of the cylinder is its diameter.

Definition of MEP

Two other terms frequently used in conjunction with reciprocating engines are compression ratio (r) and mean effective pressure (MEP). The compression ratio is defined as the ratio of the maximum volume formed in the cylinder to the minimum volume (clearance volume).

      r = Vmax/Vmin

The mean effective pressure is a fictitious pressure. It is defined as the pressure that would act on the piston during the entire power stroke, to produce the same amount of net work as that would be produced during the actual cycle.

      Wnet = MEP Displacement volume


      MEP = Wnet /(VBDC - VTDC)

    Four-stroke Combustion Cycle

Four-stroke Compression Cycle
for SI Engine


In a spark-ignition (SI) engine, a mixture of fuel and air is ignited by a spark plug. Spark-ignition engines are suited for use in automobiles since they are relatively light and lower in cost. Most cars currently use what is called a four-stroke combustion cycle to convert gasoline into motion. The four strokes are:

  • Intake stroke
  • Compression stroke
  • Combustion stroke (power stroke)
  • Exhaust stroke

The piston is connected to the crank shaft by a connecting rod. When the engine goes through its cycle:

  • The piston starts at the top, the intake valve opens, and the piston moves down to let the engine take in a cylinder-full of air and gasoline. This is the intake stroke.
  • The piston moves back up to compress this fuel/air mixture. Compression makes the explosion more powerful. This is the compression stroke.
  • When the piston reaches the top of its stroke (TDC), the spark plug emits a spark to ignite the gasoline. The gasoline in the cylinder explodes, driving the piston down. This is the combustion stroke.
  • Once the piston hits the bottom of its stroke (BDC), the exhaust valve opens and the exhaust leaves the cylinder to go out through the tail pipe.This is the exhaust stroke.

Then the engine is ready for the next cycle, so it intakes another charge of air and gas.

    Air-standard Assumption

Internal combustion engine operates on an open cycle since its working fluid is thrown out of the engine at some point instead of being returned to its initial state. That means the working fluid does not undergo a complete thermodynamic cycle. A detailed study of the performance of an actual gas power cycle is rather complex and accurate modeling of internal combustion engines normally involves computer simulation. To conduct elementary thermodynamic analyses of internal combustion engines, considerable simplification is required. To simplify the analysis, air-standard assumptions are made:

  • Gas and air mixture are modeled as air and an ideal gas, which continuously circulates in a closed cycle. Thus, there are no intake and exhaust processes.
  • All the processes making up the cycle are internally reversible.
  • The combustion process is replaced by a heat-addition process from an external source.
  • The exhaust process is replaced by a heat-rejection process and the gas returns to its initial state.

In addition, if specific heats are assumed constants at their ambient temperature, this assumption is called a cold air-standard assumption.

    Ideal Otto Cycle - Ideal Cycle for Spark-ignition Engines

Isentropic Compression (1-2)

Constant Volume Heat Addition (2-3)

Isentropic Expansion (3-4)

Constant Volume Heat Rejection (4-1)


The Otto cycle is the ideal cycle for spark-ignition engines, in honor of Nikolaus Otto, who invented it in 1867. In ideal Otto cycles, air-standard assumption is used. The ideal Otto cycle consists of four internal reversible processes:

  • 1-2 Isentropic compression
  • 2-3 Constant volume heat addition
  • 3-4 Isentropic expansion
  • 4-1 Constant volume heat rejection

The Otto cycle is executed in a closed system and the working fluid is air according to the air-standard assumption. Also, changes in kinetic and potential energies are negligible. No heat transfer is involved in the two isentropic processes. The energy balances for these two processes are:

      -w12 = u2 - u1

      -w34 = u4 - u3

w12 is negative since work is needed to compress the air in the cylinder and w34 is positive since air does work to the surroundings during its expansion.

In the constant volume heat addition and heat rejection process, no work interaction is involved since no volume change occurs. The energy balances for these two processes are:

      q23 = u3 - u2

      q41 = u1 - u4

q23 is positive since heat is added to the air and q41 is negative since heat is rejected to the surroundings.

The thermal efficiency for an ideal Otto cycle is 

      ηth, Otto = wnet/qin

According to the analysis above, the net work output is

      wnet = w34 + w12 = q23 + q41

      qin = q23

      ηth, Otto = 1+ q41/q23


Under the cold air-standard assumption, the thermal efficiency of the ideal Otto cycle is


Process 1-2 and process 3-4 are isentropic. Thus,


Since v2 = v3 and v4 = v1,



Relation between Thermal Efficiency
and Compression Ratio with k = 1.4


Considering all the relations above, the thermal efficiency becomes,


where r is the compression ratio and k is the specific heat ratio.

The expression of thermal efficiency under cold air-standard assumption is only a function of the compression ratio. Thus, a higher r can generate a higher thermal efficiency. But when higher r is used, the temperature of the air-fuel mixture may rise above the auto ignition temperature of the fuel during the compression process, and will cause an early and rapid burn before the spark ignition. This early and rapid burn produces an audible noise, which is called engine knock. Engine knock in spark-ignition engine cannot be tolerated since it hurts performance and can cause engine damage. Thus there is an upper limit of compression ratio for spark-ignition engines.