Air Fuel Ratios and Stoichiometry

Burning fuels is a chemical reaction, and has to abide by a number of rules. Petrol is a Hydrocarbon, which is made of Hydrogen and Carbon. Other additives in the petrol also add more elements, but for the purpose of this article, we'll just look at the hydrocarbons. Air is a mixture of gasses, mostly Nitrogen which is quite unreactive under normal conditions, and there is also about 21% Oxygen. The Oxygen reacts with the hydrocarbons when burnt to produce Carbon Monoxide (CO), Carbon Dioxide (CO2) and Water (H2O). Under the temperatures and pressures involved, Nitrogen also forms some oxides, collectively referred to as NOX.
Depending on the temperatures, and ratios of air to fuel, different products will be made, and also there will be different power outputs for each mix.

  • Petrol     14.7:1
  • Diesel     14.6:1
  • Methanol 6.4:1
  • Ethanol   9:1
  • LPG        15.5:1

Those are the Air to Fuel ratios for the most common fuels, by mass, known as the Stoichiometric Ratio. The Ratios do not tell the full picture though. They are the perfect ratios for a well mixed air and fuel vapour. In an engine, the mixing takes place very quickly and a perfect mix is impossible. Introductions like Swirl flaps or Disturbed Air Admittance valves agitate the air going in to mix the air and fuel better, but still, a perfect mix can't be attained.

Inside the cylinder will be a cloud of vapour, with some patches richer in fuel, and others leaner. The fuel can be accurately controlled, so the limiting factor in a Normally Aspirated petrol engine is the amount of air. To achieve the best power, all of the air has to be used as efficiently as possible, so the mixture will be enrichened by adding more fuel. The AFR for maximum power is usually between 12-13:1, depending on how well mixed the vapour was beforehand.
The extra fuel increases the likelihood of the free oxygen being closer to a fuel molecule for the reaction. Some fuel will be wasted as there is an excess in the cylinder, but it helps ensure all of the air is used to it's full effect.
Likewise, running lean is better for economy. Where economy is concerned, you are looking to use all of the fuel injected by having an excess of air. Free oxygen taken into the cylinder will be wasted but the priority for an economic tune is to avoid wasting fuel.
Lean running will increase the temperatures of the combustion, and will also make more of the Nitrogen in the air oxidise into Nitrogen Oxides (NO and NO2, Nitrous Oxide is N20 and a different kettle of fish). The excess heat if unchecked can cause engine and Catalytic Converter damage, and the NOX is an undesirable air pollutant.

This chart shows the resultant gasses from burning petrol at different AFRs. Rich mixtures are cooler but you can see the increased Hydrocarbon emissions as the excess fuel is unused. Nitrogen oxides are low from the cooler temps, but Carbon Monoxide is far higher with the lack of free oxygen to convert the CO to CO2.
Lean mixtures around 16:1 AFR produce the best economy, but the extra heat oxidises the Nitrogen in the air increasing air pollution, but with low CO levels. Leaning the mixture further past this point creates lean misfires with the mixture failing to completely combust, lowering temperatures (and therefore NOx levels). The Hydrocarbon (HC) levels start to rise as unburnt fuel exits the exhaust and power drops off.
The Stoichiometric ratio of 14.7:1 can be seen on the chart which provides a good compromise between power, economy and emissions, and this is the target for closed loop operation which will be covered in the next section.

Lambda sensors, Monitoring, and Catalysts

The Stoichiometric ratio mentioned for different fuels above has the simple name Lambda and is denoted by the Greek symbol λ. Figures lower than λ=1 are rich, and higher lambdas are lean.
To calculate the λ, simply divide the actual AFR by the Stoichiometric AFR.
The AFR of an engine can be measured by a Lambda Sensor in the exhaust gasses. Also known as an Oxygen Sensor, the Lambda sensor comes in 2 varieties, Narrowband and Wideband.

Narrowband Lambda Sensors

The Narrowband sensors can only measure the presence of oxygen in the exhaust, so can only correctly show if the system in lean, with excess oxygen passing through the exhaust. Once the system is rich, there is little or no free oxygen left, so exactly how rich can't be determined. The Narrowband lambda sensor produces a voltage of approximately 0.8v+ when rich, quickly dropping to 0.2v or lower when lean by using a Nernst Cell.
To maintain the correct AFR, the ECU will alter the air fuel mix slightly in each direction and makes sure the changes flip the output voltage between rich and lean.
When working correctly, the measured signal from the lambda sensor flicks between 0.8v and 0.2v at a steady rate from the mixture alterations, but the response time is too slow for engine speeds over 3-4k rpms. Above these speeds, the ECU works in open loop which is a default rich condition, and these may be subject to the long term fuel trims available in OBD2 ECUs, when the ECU has measured a factor to correct the AFR.

These sensors also require an operating temperature of approx. 300°C to function effectively, so an electric heater is fitted to get them to operating temperature quicker, or they are often fitted close to the cylinder head in the exhaust manifold where the exhaust gasses are hotter.

Wideband Lambda Sensors

A Wideband Lambda sensor can measure the exact AFR over a wider range, unlike they Narrowband which can just tell which side of Stoich the gasses are.
A Wideband Lambda sensor consists of a Pump Cell, a Nernst Cell (regular Narrowband sensor) and Reference chamber. The exhaust gasses enter the Pump cell of the sensor, and the sensor pumps Oxygen via diffusion into the exhaust gasses if it is rich, or away from the gasses towards the reference cell if it is lean. The current flow needed to maintain the sampled gasses will either be positive or negative depending on the gasses being rich or lean.
The Current flow is proportional to the amount of Oxygen present. If it is at λ1, there is no current flow. The current, either positive or negative is then converted into a Voltage signal that the ECU can read which will tell it how far on each side it is away from Lambda=1.

The Wideband Lambda reacts far faster than Narrowband sensor, and is usable at all RPM ranges, and is also highly accurate. It does however require even greater temperatures to function, at about 600°C.

The final piece of kit in the exhaust system is the Catalytic Converter. This forces a reaction onto the remaining exhaust gasses to reduce the pollution. The majority of Cats used today are Three Way Catalytic Converters.
The three functions are firstly to break the Nitrogen Oxides (NOx) into Nitrogen (N2) and Oxygen (O2). The Oxygen is used to Oxidise the Carbon Monoxide (CO) into Carbon Dioxide CO2, and finally Oxidise the remaining excess Hydrocarbons into CO2 and H20 (water).
As with Lambda Sensors, Catalysts need to be at a high temperature to operate, and are often kept as close to the manifold as possible. OBD2 introduced secondary Lambda sensors after the Catalyst to monitor it's performance. Care should be taken when measuring post-cat AFRs as the lambda values will show a slight reduction is O2 levels from the oxidation of the exhaust gasses. This reduction is the evidence the ECU requires to confirm the Catalyst is working effectively.