Fourteen point seven

Fourteen point seven to one. It is the most quoted number in engine work and the least explained. Most people who can recite it could not tell you what it is a ratio of, and almost nobody can tell you why it is that number rather than some other one.

It is not a target because it makes the most power. It is a target because it is the ratio at which every molecule of fuel finds exactly enough oxygen to burn, with none of either left over — and because a catalytic converter can only do both of its jobs when the exhaust arrives at that ratio.

Both halves of that sentence need proving, so let us prove them.

First: it is a mass ratio, and the numbers are bigger than they look

14.7 kilograms of air per kilogram of fuel. Mass, not volume — because what has to meet what is a mass of oxygen and a mass of fuel, and volumes of gas change with temperature and pressure while masses do not.

Petrol density: 0.745 kg/L, so one litre is 0.745 kg of fuel

Air required: 0.745 × 14.7 = 11.0 kg of air

Air density at 20 °C and sea level: 1.20 kg/m³

Volume: 11.0 ÷ 1.20 = 9.1 m³

Nine cubic metres. A small bedroom full of air, drawn in and pushed out again, per litre of fuel. When people say an engine is an air pump that happens to burn something, this is the scale they mean — the fuel system is a trickle and the air system is a firehose, and that asymmetry decides almost every tuning question you will ever meet.

Second: where the number comes from

Petrol is not one compound, so start with one that is. Iso-octane, C₈H₁₈, is the reference fuel that defines 100 on the octane scale, and its complete combustion balances cleanly.

C₈H₁₈ + 12.5 O₂ → 8 CO₂ + 9 H₂O

Check it balances — C: 8 = 8. H: 18 = 18. O: 25 = 16 + 9. Good.

Molar mass of C₈H₁₈ = (8 × 12.011) + (18 × 1.008) = 114.23 g/mol

Mass of O₂ needed = 12.5 × 31.998 = 400.0 g per mole of fuel

Oxygen per kg of fuel = 400.0 ÷ 114.23 = 3.50 kg

Air is 23.14% oxygen by mass, so air per kg of fuel:

3.50 ÷ 0.2314 = 15.1 kg

15.1:1, not 14.7. That is not an error — it is the honest answer for iso-octane, and it is the first clue that 14.7 is a figure for a nominal petrol rather than a constant of nature.

Pump petrol is a blend of a few hundred hydrocarbons with rather less hydrogen per carbon than iso-octane. Represent it per carbon atom as CH₁.₉₅ and the arithmetic lands where the trade says it does.

CH₁.₉₅ + 1.4875 O₂ → CO₂ + 0.975 H₂O

Molar mass = 12.011 + (1.95 × 1.008) = 13.98 g/mol

Mass of O₂ = 1.4875 × 31.998 = 47.60 g

Oxygen per kg of fuel = 47.60 ÷ 13.98 = 3.41 kg

Air per kg of fuel = 3.41 ÷ 0.2314 = 14.7 kg

So 14.7:1 is a real derived number, and it is also a slightly soft one. Change the fuel's hydrogen-to-carbon ratio and it moves; textbooks using a C₈H₁₅ surrogate get 14.6. Add an oxygenate and it moves a long way.

Ethanol: C₂H₅OH + 3 O₂ → 2 CO₂ + 3 H₂O

Molar mass = 46.07 g/mol; O₂ mass = 3 × 31.998 = 96.0 g

Oxygen per kg = 96.0 ÷ 46.07 = 2.08 kg; air per kg = 2.08 ÷ 0.2314 = 9.0 kg

Ethanol is therefore 9.0:1 — it brings its own oxygen atom to the reaction.

E10, blended 10% by volume, is 10.5% ethanol by mass:

(0.105 × 9.0) + (0.895 × 14.7) = 14.1:1

E85 is 85.7% ethanol by mass:

(0.857 × 9.0) + (0.143 × 14.7) = 9.8:1

This is why the trade stopped quoting raw ratios and started quoting lambda. λ is the actual air–fuel ratio divided by the stoichiometric one for whatever is in the tank, so λ = 1 means "exactly enough" on petrol, on E10, on E85 and on diesel alike. A scan tool reading λ = 0.95 tells you something true about the combustion. A scan tool reading 14.0:1 tells you nothing until you know what the car is drinking.

Predict, then run

An engine is running at 14.7:1. You richen it to about 12.5:1 and hold everything else the same. What happens to the power it makes?

It falls — there is not enough air to burn that much fuel

Nothing changes — 14.7 is the ratio that burns everything

It rises a few per cent

It rises by a third or more

Commit

You learn more from being wrong on purpose than right by accident.

So if 14.7 is not the best mixture, why sit there?

Because of what is bolted to the exhaust.

A three-way catalyst is asked to do two chemically opposite jobs at the same time. It must oxidise carbon monoxide and unburnt hydrocarbons, which needs spare oxygen. And it must reduce oxides of nitrogen, stripping oxygen back off them, which needs the opposite.

Those two requirements only overlap in a very narrow band, roughly one per cent either side of λ = 1. Run lean and NOx conversion collapses because the reducing job has no chance. Run rich and CO and hydrocarbon conversion collapses because the oxidising job has no oxygen. There is no mixture at which you can have power and both conversions, so a road car sits at λ = 1 nearly all the time and gives up the few per cent of power that richer running would have bought.

The window is so tight that the engine cannot simply aim at it and hold still. It dithers — the ECU deliberately swings the mixture slightly rich and slightly lean around λ = 1 about once a second. The catalyst's washcoat stores oxygen on the lean swings and releases it on the rich ones, which widens the useful window from something almost unholdable to something a control loop can actually live in.

That is also why a healthy pre-catalyst lambda sensor signal oscillates. A flat one is not a stable engine. It is a dead sensor.

The two mixtures that are not 14.7

Best power: λ ≈ 0.85 to 0.90, about 12.5 to 13.2:1.

Two mechanisms, and the first is the important one. The cylinder is limited by the mass of air it managed to swallow — volumetric efficiency is the real ceiling on an engine's output, and fuel is easy where air is hard. At exactly stoichiometric, mixing is imperfect enough that a fraction of the oxygen never meets fuel in the time available. Give it a surplus of fuel and essentially none of the air goes unused. Second, petrol has to evaporate to burn, and evaporating takes heat out of the incoming charge. A cooler charge is denser, so a little more of it fits, and it is further from the temperature at which the end gas self-ignites into knock.

Best economy: λ ≈ 1.05 to 1.10, about 15.4 to 16.2:1.

With excess air the combustion products are diluted with nitrogen and oxygen that took no part, peak temperatures fall, and less of the energy leaks into the cylinder walls. At part throttle it also means the throttle plate opens further for the same fuel, which cuts the pumping work the engine does dragging air past it.

Cold start, which looks like an exception and is not

A cold engine is given a far richer mixture — several times richer than stoichiometric for the first firing cycles, tapering as it warms. The usual explanation is that cold engines "need more fuel", which explains nothing.

The mechanism is that only vapour burns. Injected petrol sprayed at a cold port wall and a cold cylinder does not all evaporate; a good deal of it lands as a liquid film and stays there. So the mixture in the vapour phase — the only part that can find a flame — is far leaner than the mass ratio you metered. Inject enough that the vapour fraction alone reaches something ignitable, and the surplus liquid comes along for the ride.

It is why cold starts produce most of a trip's hydrocarbon emissions, why the catalyst is placed close to the head so it lights off quickly, and why short trips are harder on an engine and its oil than long ones.

Where this goes next

Once the engine is warm and in closed loop, the lambda sensor is telling the ECU how close it landed, and the ECU's correction is recorded as a fuel trim. That number is one of the most informative things on a scan tool, because it is not a measurement of a component — it is a measurement of the disagreement between what the engine thought it was breathing and what it actually breathed.

A long-term trim of +20% at idle that falls to +5% at 2500 rpm is a vacuum leak, and the reason is arithmetic: a leak of fixed size is a large fraction of a small airflow and a small fraction of a large one. The same trim sitting at +20% everywhere is a fuel delivery problem, because that one scales with demand.

By the time you have followed the chain from 14.7 through the lambda sensor to a fuel trim to a leak, a P0171 has stopped being a code you look up. It is a conclusion you arrived at.