Combustion in SI engines: knock and octane number

Why it matters

Knock is the limit that stops a petrol engine from simply using a higher compression ratio or more boost to gain efficiency and power. Every SI engine design decision, from compression ratio and chamber shape to spark timing, turbo boost and the fuel grade on the pump, is bounded by knock. Knowing what knock is, what promotes it and how octane number measures a fuel's resistance to it is basic to engine design, calibration and fuel specification.

Key ideas

Normal SI combustion. The spark ignites a small kernel; after an ignition lag (a preparation phase of a few crank degrees with little pressure rise) a turbulent flame front propagates across the chamber, compressing and heating the unburned charge ahead of it; finally there is a short after-burning phase near the walls. Peak pressure ideally occurs about 10–15° after TDC.

Knock (detonation). The unburned mixture ahead of the flame is called the end gas. As the flame advances, the end gas is compressed by the expanding burned gas and heated by compression and radiation. If the end gas reaches its auto-ignition conditions and its chemical ignition delay runs out before the flame front arrives, it ignites spontaneously and almost at once throughout its volume. The resulting very rapid local pressure rise sets up pressure waves that reverberate across the chamber, producing the metallic pinging sound and high heat transfer to the piston crown and head.

• Knock happens after the spark, in the end gas. It is a race: knock if the end-gas ignition delay is shorter than the time the flame needs to reach it.
• Pre-ignition is different: the charge is ignited before the spark by a hot spot (glowing deposit, overheated spark plug electrode or exhaust valve). Pre-ignition advances combustion, raises temperatures and can lead to heavy knock; knock can in turn create hot spots, so the two can feed each other.
• Effects of knock: power loss, local overheating, piston crown erosion and ring-land cracking, bearing loading, noise, and higher heat loss through broken-up thermal boundary layers.

Factors affecting knock. Anything that raises end-gas temperature or density, lengthens the time before the flame arrives, or uses a fuel with a short ignition delay increases knock:

• Temperature and density factors: higher compression ratio, higher intake temperature and pressure (boost), higher load (more charge per cycle), advanced spark timing, poor cooling and hot spots all increase knock.
• Time factors: larger bore and longer flame travel, spark plug far from the end gas and low turbulence increase knock. Higher engine speed reduces knock, because turbulence and flame speed rise roughly with speed, shortening the flame-travel time; central plugs, two plugs and compact chambers also reduce it.
• Composition factors: the knock tendency is highest near stoichiometric to slightly rich mixtures; very lean or very rich mixtures knock less. EGR and water dilution reduce knock. Fuel structure matters most: straight-chain paraffins knock readily; branched paraffins, aromatics and alcohols resist knock.

Note the contrast with CI engines (next topic): the factors that reduce SI knock (low compression temperature, fuel that resists auto-ignition) are the ones that cause CI knock.

Octane number. The antiknock quality of a petrol is rated in a standard single-cylinder variable-compression CFR engine against blends of two reference fuels: iso-octane (2,2,4-trimethylpentane, ON = 100) and n-heptane (ON = 0). The octane number of a test fuel is the percentage by volume of iso-octane in the iso-octane/n-heptane blend that gives the same knock intensity under the same conditions.

• Research Octane Number (RON) – mild conditions: 600 rev/min, intake air at about 52 °C, fixed spark timing.
• Motor Octane Number (MON) – severe conditions: 900 rev/min, mixture heated to about 149 °C, speed-dependent spark advance. MON is lower than RON for real fuels.
• Sensitivity = RON − MON: how much a fuel's knock resistance drops under severe conditions (typically 8–12 for market petrol).
• Indian pump petrol is sold on RON (for example RON 91 regular and higher grades); in North America the pump figure is the anti-knock index (RON + MON)/2. Always check which number a question uses.
• Fuels better than iso-octane are rated by a performance number (PN) using iso-octane plus additive; it is linked to ON by an empirical relation.

Raising octane. Refinery processes (reforming, alkylation, isomerisation) produce branched and aromatic components. Blending components such as ethanol (E20 in India), MTBE/ETBE and aromatics raise octane; tetraethyl lead was once used but is banned because it poisons catalysts and is toxic.

Knock control in modern engines. A piezoelectric knock sensor on the block picks up the characteristic vibration frequency; the ECU retards spark timing on the knocking cylinder, then advances it gradually again. This lets the engine run close to the knock limit with any fuel grade, at some cost in efficiency when spark is retarded. Turbocharged engines also use intercooling, direct injection (charge cooling by fuel evaporation), cooled EGR and enrichment at high load.

Formulas

ON = percentage by volume of iso-octane in the matching reference blend

• Dimensionless; valid from 0 to 100.

S = RON − MON

• S = fuel sensitivity (dimensionless).

AKI = (RON + MON) / 2

• Anti-knock index (dimensionless), the pump octane number used in North America; not the same as RON.

ON = 100 + (PN − 100) / 3

• Empirical link between octane number and performance number for fuels better than iso-octane; PN dimensionless. Treat it as a textbook correlation.

t_f = L / S_f

• t_f = time for the flame to cross the chamber (s); L = flame travel distance (m); S_f = mean turbulent flame speed (m/s). Knock is expected if the end-gas ignition delay τ is shorter than t_f.

θ = 6 × N × t

• θ = crank angle swept (degrees); N = speed (rev/min); t = time (s).

η_Otto = 1 − 1 / r^(γ−1)

• r = compression ratio; γ = ratio of specific heats (1.4 for air-standard). Shows the efficiency benefit that a higher-octane fuel unlocks by permitting a higher r.

Worked examples

Example 1 (standard): rating a fuel. In the CFR engine a petrol matches a blend of 91% iso-octane and 9% n-heptane under research conditions and a blend of 82% iso-octane and 18% n-heptane under motor conditions. Find RON, MON, sensitivity and AKI.

1. By definition ON equals the iso-octane percentage of the matching blend: RON = 91, MON = 82.
2. Sensitivity: S = RON − MON = 91 − 82 = 9.
3. Anti-knock index: AKI = (RON + MON) / 2 = (91 + 82) / 2 = 86.5.

Answer: RON = 91, MON = 82, S = 9, AKI = 86.5.

Example 2 (GATE level): what a higher-octane fuel is worth. Switching to a higher-octane fuel allows the compression ratio of an SI engine to be raised from 9 to 10.5 without knock. Using the air-standard Otto cycle (γ = 1.4), find the new efficiency and the percentage reduction in fuel consumption for the same work output.

1. η = 1 − 1 / r^(γ−1). At r = 9: 9^0.4 = 2.408, η₁ = 1 − 1/2.408 = 0.5848.
2. At r = 10.5: 10.5^0.4 = 2.561, η₂ = 1 − 1/2.561 = 0.6096.
3. Fuel for the same work is proportional to 1/η: reduction = 1 − η₁/η₂ = 1 − 0.5848/0.6096 = 0.0407.

Answer: η rises from 58.5% to 61.0%; fuel consumption falls by about 4.1% (the real-engine gain is smaller but of the same order).

Example 3 (GATE level): the knock race. In an SI engine the flame must travel 70 mm from the plug to the end gas. The end-gas ignition delay under the operating conditions is 3.0 ms. (a) Will the engine knock if the mean flame speed is 20 m/s? (b) At a higher engine speed of 3000 rev/min the flame speed rises to 25 m/s; check again and find the crank angle of flame travel.

1. (a) t_f = L / S_f = 0.070 / 20 = 3.5 × 10⁻³ s = 3.5 ms. Since τ = 3.0 ms < 3.5 ms, the end gas auto-ignites first: knock.
2. (b) t_f = 0.070 / 25 = 2.8 ms < 3.0 ms: the flame consumes the end gas first, no knock.
3. Crank angle: θ = 6 × N × t = 6 × 3000 × 2.8 × 10⁻³ = 50.4°.

Answer: (a) knocks; (b) does not knock, flame travel ≈ 50° of crank rotation. This is why higher speed (more turbulence) reduces SI knock.

Common mistakes

• Calling knock "premature ignition". Knock is auto-ignition of the end gas after the spark; pre-ignition is ignition before the spark by a hot spot.
• Saying higher engine speed increases SI knock. It reduces it (more turbulence, faster flame); it is CI knock that is tied to the delay period.
• Confusing RON with the North American pump number (RON + MON)/2, or assuming MON is higher than RON.
• Treating octane number as an energy measure. A high-octane fuel does not contain more energy; it only allows a higher compression ratio or more spark advance.
• Mixing up the reference fuels: iso-octane is 100, n-heptane is 0 for octane rating; for cetane rating the references are different.

For GATE ME

Questions are mostly conceptual: the mechanism of knock, the difference between knock and pre-ignition, which operating changes increase or decrease SI knock (and how this is opposite for CI knock), and definitions of octane number, RON, MON and sensitivity. Short numericals ask for ON from a reference blend, the AKI or sensitivity, and the efficiency gain from a higher compression ratio via the Otto cycle. Practise the factor table until you can answer each "increase or decrease?" item without hesitation.

Quick check

1. Where in the chamber does knock originate?
2. A fuel matches a blend of 95% iso-octane and 5% n-heptane. What is its octane number?
3. Does increasing engine speed increase or decrease knock in an SI engine?
4. A fuel has RON 95 and MON 85. What is its sensitivity?
5. Which way should spark timing be moved when the knock sensor detects knock?

Answers: 1. In the end gas, the unburned charge farthest from the spark plug; 2. 95; 3. Decrease; 4. 10; 5. Retarded.