IC engine performance and combustion basics

Why it matters

Engine test beds, emission calibration and gensets all come down to a handful of numbers: brake power, mean effective pressure, specific fuel consumption and the efficiencies linking them. A mechatronics engineer working on engine control units, dynamometers or hybrid powertrains reads these numbers daily. Combustion basics — air–fuel ratio, knock, ignition delay — explain why the controller does what it does with spark timing, injection timing and boost.

Key ideas

Power terms.

• Indicated power (IP): power developed by the gas on the pistons, from the indicator (p–V) diagram.
• Brake power (BP): power at the crankshaft, measured with a dynamometer from torque and speed.
• Friction power (FP) = IP − BP: bearing and piston-ring friction, valve train, pumping losses and accessories. Found by a Morse test (multi-cylinder engines), a Willan's line (fuel-rate plot extrapolated to zero load, CI engines), motoring, or IP − BP.

Mean effective pressure. Indicated MEP is the constant pressure that, acting over each power stroke, gives IP; brake MEP (bmep) gives BP. bmep is the best size-independent measure of how hard an engine works: about 8–12 bar for naturally aspirated SI engines and 15–25 bar for turbocharged diesels.

Efficiencies.

• Mechanical η_m = BP/IP (typically 0.75–0.90 at full load, falling at part load because friction stays roughly constant).
• Brake thermal η_bth = BP / (ṁ_f × CV); indicated thermal η_ith = IP / (ṁ_f × CV); η_bth = η_m × η_ith.
• Relative (efficiency) ratio = η_ith / η_air-standard.
• Volumetric η_v = actual air inducted ÷ air that would fill the swept volume at ambient (or intake) density. It governs the maximum power of a naturally aspirated engine; turbo- or supercharging raises it above 1.

Specific fuel consumption. bsfc = ṁ_f / BP, in kg/kWh or g/kWh; it is inversely proportional to η_bth. Typical: SI ≈ 250–300 g/kWh, CI ≈ 190–230 g/kWh.

Heat balance. Fuel energy goes to brake power, cooling water, exhaust gas, and unaccounted losses (radiation, friction heat). A typical petrol engine: about 25–30 % BP, 30 % coolant, 30–35 % exhaust.

Combustion basics.

• Stoichiometric air–fuel ratio: the exact air needed for complete combustion. About 14.7:1 for petrol and 14.5:1 for diesel by mass. Equivalence ratio φ = (F/A)_actual / (F/A)_stoich; φ > 1 is rich, φ < 1 is lean.
• SI combustion: spark → ignition lag (flame kernel) → turbulent flame propagation → afterburning. Timing is set so peak pressure occurs about 10–15° after TDC (MBT timing).
• SI knock: auto-ignition of the unburnt end gas ahead of the flame, producing pressure waves and the "pinging" sound. Promoted by high compression ratio, advanced spark, high intake temperature and low-octane fuel. Resisted by high octane number, retarded spark and a compact chamber. Do not confuse with pre-ignition, ignition by a hot spot before the spark.
• CI combustion: fuel injected into hot compressed air → ignition delay → rapid (premixed) combustion → controlled (diffusion) combustion → after-burning. Diesel knock comes from too long a delay: fuel accumulates, then burns all at once. It is reduced by a high cetane number, higher compression ratio and higher intake temperature — the opposite of SI knock remedies.
• Exhaust emissions: CO and HC from rich or incomplete combustion; NOx from high peak temperatures; soot (PM) from rich zones in diesel sprays. A three-way catalyst needs φ ≈ 1, which is why closed-loop lambda control exists.

Formulas

BP = 2π N T / 60 — W; N in rpm, T (torque) in N·m. IP = p_mi L A n K — W; p_mi: indicated MEP (Pa), L: stroke (m), A: piston area (m²), n: power strokes per second per cylinder (N/60 for two-stroke, N/120 for four-stroke), K: number of cylinders. The same form with bmep gives BP. FP = IP − BP η_m = BP / IP η_bth = BP / (ṁ_f CV) — ṁ_f in kg/s, CV: calorific value (kJ/kg), BP in kW. bsfc = ṁ_f / BP — kg/kWh when ṁ_f is in kg/h and BP in kW. η_bth = 3600 / (bsfc × CV) — bsfc in kg/kWh, CV in kJ/kg. η_v = ṁ_a / (ρ_a V_s n_i) — ṁ_a: air mass flow (kg/s), ρ_a: ambient air density (kg/m³), V_s: total swept volume (m³), n_i: intake strokes per second (N/120 for a four-stroke engine). V_s = (π/4) D² L K — total swept volume (m³), D: bore (m). IP (Morse test) = K × BP_all − Σ BP_(cylinder i cut) φ = (F/A)_actual / (F/A)_stoich

Worked examples

Example 1 (standard, engine test). A four-cylinder four-stroke petrol engine (bore 80 mm, stroke 90 mm) gives 120 N·m at 3000 rpm and uses 9 kg/h of petrol (CV = 44 000 kJ/kg) and 140 kg/h of air (ambient density 1.18 kg/m³). Find BP, bmep, bsfc, η_bth, η_v and the air–fuel ratio.

1. BP = 2π N T / 60 = 2π × 3000 × 120/60 = 37 699 W = 37.70 kW.
2. V_s = (π/4) D² L K = 0.7854 × 0.08² × 0.09 × 4 = 1.8096 × 10⁻³ m³.
3. Cycles per second = N/120 = 25. bmep = BP/(V_s × 25) = 37 699/(1.8096 × 10⁻³ × 25) = 833 300 Pa = 8.33 bar.
4. bsfc = ṁ_f / BP = 9/37.70 = 0.2387 kg/kWh.
5. η_bth = 3600/(bsfc × CV) = 3600/(0.2387 × 44 000) = 0.343.
6. Swept-volume air rate = 1.8096 × 10⁻³ × 25 = 0.04524 m³/s; actual = (140/3600)/1.18 = 0.03296 m³/s; η_v = 0.03296/0.04524 = 0.729.
7. A/F = 140/9 = 15.6 (slightly lean of stoichiometric 14.7).

BP ≈ 37.7 kW, bmep ≈ 8.33 bar, bsfc ≈ 0.239 kg/kWh, η_bth ≈ 34.3 %, η_v ≈ 72.9 %, A/F ≈ 15.6

Example 2 (GATE level, Morse test). A four-cylinder engine gives 30 kW with all cylinders firing at constant speed. With cylinders 1, 2, 3 and 4 cut out in turn (speed restored each time), BP is 21.2, 21.0, 21.4 and 21.6 kW. Find IP and η_m.

1. IP of cylinder i = BP_all − BP_(i cut): 8.8, 9.0, 8.6 and 8.4 kW.
2. IP = K × BP_all − Σ BP_cut = 4 × 30 − (21.2 + 21.0 + 21.4 + 21.6) = 120 − 85.2 = 34.8 kW.
3. η_m = BP / IP = 30/34.8 = 0.862; FP = 4.8 kW.

IP = 34.8 kW, η_m ≈ 86.2 %

Example 3 (stoichiometric A/F of octane). C₈H₁₈ + 12.5 (O₂ + 3.76 N₂) → 8 CO₂ + 9 H₂O + 47 N₂.

1. Air per kmol fuel = 12.5 × 4.76 = 59.5 kmol × 28.97 kg/kmol = 1723.7 kg.
2. Fuel = 8 × 12.011 + 18 × 1.008 = 114.2 kg.
3. A/F = 1723.7/114.2 = 15.1.

(A/F)_stoich ≈ 15.1 (commercial petrol, a blend, is about 14.7)

Common mistakes

• Using N instead of N/2 power strokes for a four-stroke engine in IP = p_m L A n K.
• Mixing kW and W, or kg/h and kg/s, in bsfc and η_bth.
• Calling knock "premature combustion". SI knock is auto-ignition of the end gas after the spark; pre-ignition is a separate problem.
• Applying SI knock remedies (lower r, lower intake temperature) to diesel knock, which needs the opposite.
• Using air–fuel ratio by volume (moles) when the question means by mass.
• Ignoring that mechanical efficiency drops sharply at part load.

For GATE ME

Questions are usually short numericals: BP from torque and speed, IP and bmep from cylinder geometry, η_m, η_bth, bsfc, η_v, Morse test, and stoichiometric air–fuel ratios from a fuel formula. Conceptual questions test knock in SI and CI engines, octane and cetane numbers, and the effect of operating variables. Practise one compact test-data problem that chains all of these, keeping units explicit.

Quick check

1. An engine delivers 50 N·m at 3600 rpm. What is its brake power?
2. IP = 40 kW, FP = 6 kW. Find η_m.
3. bsfc = 0.25 kg/kWh and CV = 42 000 kJ/kg. Find η_bth.
4. Does a higher cetane number increase or decrease diesel knock?
5. How many power strokes per minute does one cylinder of a four-stroke engine make at 3000 rpm?

Answers: 1. 2π × 3600 × 50/60 ≈ 18.85 kW. 2. BP = 34 kW, η_m = 34/40 = 85 %. 3. 3600/(0.25 × 42 000) ≈ 34.3 %. 4. Decrease (shorter ignition delay). 5. 1500.