2.1 Four-Stroke Petrol Engine Operation, Thermodynamics & Cylinder Configuration

2.1 Four-Stroke Petrol Engine Operation, Thermodynamics & Cylinder Configuration

Automotive light vehicle technicians must possess a thorough mechanical and thermodynamic understanding of internal combustion fundamentals. The spark-ignition petrol engine operates on the four-stroke Otto cycle, first commercialized by Nikolaus Otto in 1876. Translating reciprocating linear motion into continuous rotational torque requires precise synchronization of gas exchange, valve timing, fuel delivery, and high-voltage ignition.

[!NOTE] Core Engine Kinematics & Geometric Definitions

• Top Dead Center (TDC): The uppermost position of piston travel within the cylinder bore, representing the point of minimum cylinder volume ($V_c$, clearance volume).
• Bottom Dead Center (BDC): The lowermost position of piston travel, representing the point of maximum cylinder volume ($V_t = V_d + V_c$).
• Bore ($d$): The internal diameter of the finished cylinder bore, expressed in millimeters (mm) or inches (in).
• Stroke ($s$): The linear distance traveled by the piston between TDC and BDC, equal to twice the crankshaft throw radius ($s = 2 \times r_{crank}$).
• 720° Cycle Relationship: Because each stroke corresponds to 180° of crankshaft rotation, completing all four strokes requires $4 \times 180^\circ = 720^\circ$ of crankshaft rotation (two full crankshaft revolutions) for every single rotation of the camshaft ($360^\circ$), establishing a strict 2:1 rotational gear ratio.

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The Four-Stroke Otto Cycle: Step-by-Step Breakdown

   INTAKE STROKE       COMPRESSION STROKE      POWER STROKE        EXHAUST STROKE
   (0° to 180°)          (180° to 360°)       (360° to 540°)       (540° to 720°)

    Intake Exhaust        Intake Exhaust       Intake Exhaust       Intake Exhaust
     OPEN   CLOSED        CLOSED  CLOSED       CLOSED  CLOSED       CLOSED   OPEN
      |       |             |       |            |       |            |       |
      v       |             |       |            |       |            |       ^
   +-------------+       +-------------+      +-------------+      +-------------+
   |    (Air/    |       |   (Charge   |      |   (SPARK)   |      |  (Exhaust   |
   |    Fuel)    |       |  Compressed)|      |  Combustion |      |    Gases    |
   |      |      |       |      ^      |      |      |      |      |      ^      |
   |      v      |       |      |      |      |      v      |      |      |      |
   |   [PISTON]  |       |   [PISTON]  |      |   [PISTON]  |      |   [PISTON]  |
   |      |      |       |      |      |      |      |      |      |      |      |
   |      v      |       |      ^      |      |      v      |      |      ^      |
   +-------------+       +-------------+      +-------------+
       Downward               Upward              Downward              Upward
      Motion (BDC)          Motion (TDC)        Motion (BDC)          Motion (TDC)

1. The Intake Stroke (Crankshaft 0° to 180°)

• Kinematic Action: The piston moves downward from TDC to BDC.
• Valve Status: The intake valve opens slightly before TDC (typically 5°–15° BTDC) and remains open past BDC (typically 35°–50° ABDC); the exhaust valve is closed.
• Thermodynamic Behavior: As the piston descends, the volume inside the cylinder expands rapidly. This volumetric expansion causes cylinder pressure to drop below atmospheric pressure ($101.3\text{ kPa}$ or $14.7\text{ psi}$ at sea level), creating a partial vacuum (atmospheric depression) ranging from $-40\text{ kPa}$ to $-70\text{ kPa}$ (12 to 21 in-Hg manifold vacuum in port-injected engines at idle/part throttle). Atmospheric pressure pushes the ambient air charge through the throttle body, intake runner, and open intake valve into the low-pressure cylinder.
• Intake Valve Closing (IVC) Dynamics: Closing the intake valve after BDC appears counterintuitive, but it takes advantage of incoming air column inertia (ram effect). At high engine RPM, the incoming column of air possesses substantial kinetic energy; leaving the valve open after BDC allows this air momentum to continue packing into the cylinder even as the piston begins its initial upward rise, maximizing volumetric efficiency.

2. The Compression Stroke (Crankshaft 180° to 360°)

• Kinematic Action: The piston travels upward from BDC to TDC.
• Valve Status: Both intake and exhaust valves are firmly seated and hermetically sealed.
• Thermodynamic Behavior: As the trapped air-fuel mixture is compressed into the combustion chamber clearance volume ($V_c$), mechanical work is converted into internal thermal energy (adiabatic compression). Dynamic compression raises in-cylinder pressure to $10–15\text{ bar}$ ($145–220\text{ psi}$) and mixture temperature to $350^\circ\text{C}–450^\circ\text{C}$. This rapid temperature rise vaporizes liquid fuel droplets into a homogeneous combustible gas, preparing the molecules for rapid chemical oxidation.

3. The Power / Expansion Stroke (Crankshaft 360° to 540°)

• Kinematic Action: The piston is driven downward from TDC to BDC by high-pressure expanding combustion gases. This is the only stroke in the cycle that produces net positive mechanical work.
• Valve Status: Both intake and exhaust valves remain tightly closed.
• Combustion & Ignition Timing: The spark plug discharges prior to TDC (typically 10°–15° BTDC at curb idle, advancing to 30°–42° BTDC under high-speed cruise). Petrol combustion is a controlled deflagration rather than an instantaneous detonation; the flame front propagates outward from the spark plug electrodes at approximately $20–30\text{ m/s}$. Initiating ignition BTDC gives the flame front sufficient time to consume the air-fuel mixture so that peak cylinder pressure (typically 40 to 60 bar / 600 to 900 psi) is reached precisely at 10° to 15° After Top Dead Center (ATDC). This specific crankshaft angle provides the connecting rod and crankshaft throw journal with optimum mechanical leverage to generate maximum turning torque.

4. The Exhaust Stroke (Crankshaft 540° to 720°)

• Kinematic Action: The piston travels upward from BDC to TDC.
• Valve Status: The exhaust valve opens well before BDC (typically 40°–55° BBDC) and closes slightly after TDC (typically 5°–15° ATDC); the intake valve remains closed until near TDC.
• Blowdown & Scavenging Dynamics: Opening the exhaust valve before BDC initiates the blowdown phase. Although the power stroke is ending, in-cylinder pressure at 50° BBDC remains at $3–5\text{ bar}$ ($45–75\text{ psi}$). This residual pressure allows high-temperature exhaust gases to begin rushing out into the exhaust manifold under their own pressure differential before the piston reaches BDC. As the piston rounds BDC and ascends to TDC, it mechanically sweeps the remaining burnt combustion products out through the open exhaust port, clearing the cylinder for the next incoming charge.

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Valve Overlap and Inertia Scavenging

Valve overlap is the brief angular duration—measured in crankshaft degrees—around TDC during which the intake valve has begun opening while the exhaust valve has not yet fully closed.

                 TDC (Overlap Period)
                   \   /
  Intake Opens      \ /      Exhaust Closes
  (e.g., 10° BTDC)   X       (e.g., 10° ATDC)
                    / \
                   /   \
         Exhaust Stroke  Intake Stroke

Physics of Inertia Scavenging

As the high-velocity column of exhaust gas accelerates down the exhaust runner and manifold header, it develops significant kinetic mass and inertia. When the piston reaches TDC, this exiting exhaust gas column creates a localized low-pressure depression (suction wave) directly behind the exhaust valve head. Because the intake valve is already cracked open during overlap, this depression pulls the fresh intake charge into the cylinder before the piston even begins descending, while simultaneously drawing out the last traces of burnt exhaust gas trapped in the clearance volume.

• High-RPM Benefit: Greatly enhances volumetric efficiency, increases engine power output, and cools the exhaust valve head.
• Low-RPM / Idle Penalty: At curb idle, low exhaust gas velocity prevents effective inertia scavenging. Instead, the intake manifold vacuum can draw exhaust gases backward into the intake runner (reversion), causing combustion instability, rough idling, and elevated unburnt hydrocarbon ($HC$) emissions. Variable Valve Timing (VVT) resolves this compromise by retarding the intake cam or advancing the exhaust cam at idle to minimize overlap, and increasing overlap under mid-range cruising loads.

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Mathematical Formulas & Worked Calculations

Automotive technicians must calculate engine displacement, compression ratios, and thermal efficiency when performing engine overhauls, cylinder boring, or performance reconditioning.

1. Cylinder Swept Volume ($V_d$)

The swept volume (displacement) of a single cylinder represents the volume displaced by the piston crown moving between BDC and TDC:

$V_d = \frac{\pi}{4} \times d^2 \times s$

Where:

• $V_d$ = Cylinder swept volume (cubic centimeters, $\text{cc}$ or $\text{cm}^3$)
• $d$ = Cylinder bore diameter (centimeters, $\text{cm}$)
• $s$ = Piston stroke length (centimeters, $\text{cm}$)

2. Total Engine Displacement ($V_{total}$)

$V_{total} = V_d \times N$ Where $N$ equals the total number of engine cylinders.

3. Compression Ratio ($CR$)

The static compression ratio compares the total cylinder volume when the piston is at BDC ($V_t$) to the clearance volume remaining when the piston is at TDC ($V_c$):

$CR = \frac{V_d + V_c}{V_c} = \frac{V_d}{V_c} + 1$

To find clearance volume when swept volume and compression ratio are known: $V_c = \frac{V_d}{CR - 1}$

Worked Example: 4-Cylinder Passenger Vehicle Engine

• Given Specifications:

  • Cylinder bore ($d$) = $82.5\text{ mm} = 8.25\text{ cm}$
  • Piston stroke ($s$) = $92.8\text{ mm} = 9.28\text{ cm}$
  • Number of cylinders ($N$) = $4$
  • Combustion chamber clearance volume ($V_c$) = $49.63\text{ cc}$

• Step 1: Calculate single-cylinder swept volume ($V_d$): $V_d = \frac{\pi}{4} \times (8.25)^2 \times 9.28 = 0.785398 \times 68.0625 \times 9.28 = 496.06\text{ cc} \approx 496.1\text{ cc}$

• Step 2: Calculate total engine displacement ($V_{total}$): $V_{total} = 496.06\text{ cc} \times 4 = 1,984.24\text{ cc} \approx 1.984\text{ Liters (marketed as a 2.0L engine)}$

• Step 3: Calculate the static compression ratio ($CR$): $CR = \frac{496.06\text{ cc} + 49.63\text{ cc}}{49.63\text{ cc}} = \frac{545.69\text{ cc}}{49.63\text{ cc}} = 10.995:1 \approx 11.0:1$

4. Theoretical Otto Cycle Thermal Efficiency ($\eta_{th}$)

Thermal efficiency dictates how effectively an engine converts the chemical heat energy of fuel into mechanical crankshaft work:

$\eta_{th} = 1 - \frac{1}{CR^{\gamma - 1}}$

Where $\gamma$ (gamma) is the ratio of specific heats for air ($\approx 1.4$). For an engine with a $10.0:1$ compression ratio: $\eta_{th} = 1 - \frac{1}{10.0^{1.4 - 1}} = 1 - \frac{1}{10.0^{0.4}} = 1 - \frac{1}{2.512} = 1 - 0.398 = 0.602 \quad (60.2\%\text{ theoretical})$

In real-world light vehicles, actual brake thermal efficiency ranges between 30% and 36%. The remaining energy is lost through:

• Exhaust gas enthalpy heat rejection (~30%–35%)
• Engine cooling system heat transfer (~25%–30%)
• Internal mechanical friction and pumping losses (~5%–8%)

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Cylinder Configurations, Firing Intervals & Engine Balance

Light vehicle engines are configured in several distinct geometric layouts depending on vehicle packaging, center-of-gravity targets, and NVH (Noise, Vibration, and Harshness) requirements.

Firing Orders and Crankshaft Throw Spacing

Crankshaft throws are spaced radially to evenly divide the 720° cycle among the cylinders ($720^\circ / N$):

1. Inline-4 Engines ($180^\circ$ intervals): Firing order 1-3-4-2 (most common) or 1-2-4-3. Cylinders 1 and 4 reach TDC together, while cylinders 2 and 3 are at BDC. Because connecting rods swing through an angle, pistons accelerate faster through the top half of their stroke than through the bottom half. This creates a secondary harmonic vibration occurring at twice engine speed ($2\times\text{RPM}$). In engines larger than $2.0\text{L}$, manufacturers incorporate twin counter-rotating balance shafts driven at twice engine speed to cancel this secondary shake.
2. Inline-6 Engines ($120^\circ$ intervals): Firing order 1-5-3-6-2-4. The 120° crank throws create mirror-image symmetry across the center main bearing, resulting in perfect primary and secondary natural mechanical balance without balance shafts.
3. V6 Engines ($120^\circ$ intervals): Firing order typically 1-4-2-5-3-6 or 1-2-3-4-5-6. In a 60° bank V6, six discrete crankpins produce natural 120° firing. In a 90° bank V6, standard crank throws would cause an uneven firing sequence alternating between 90° and 150°. To achieve smooth 120° even firing, crankshaft manufacturers incorporate splayed or split crankpins, machining a 30° offset into each rod journal pair.
4. V8 Engines ($90^\circ$ intervals): Cross-plane crankshaft firing order 1-8-4-3-6-5-7-2 (GM/Chrysler) or 1-5-4-8-6-3-7-2 (Ford). The cross-plane layout features four crankpins oriented at 90° to one another in two perpendicular planes, requiring substantial counterweights to yield exceptional low-vibration operation at the expense of rotating assembly inertia.

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Four-Stroke Events, Crank Angles & Valve Positions