The Relation Between Lambda and AFR

• Posted on: 10/01/2019
• By: Author

Lambda and AFR are two paths to the same purpose, a well-tuned engine with a unique combustion. An engine doesn’t know the difference between AFR and Lambda.

They are both indicators of an engine's combustion mixture. However, AFR is dependent on the type of fuel being used, while lambda is not.

AIR FUEL RATIO (AFR)

Air-fuel ratio is the ratio between the mass of air and mass fuel used by the engine when running. Thermal engines use fuel and oxygen (from air) to produce energy through combustion. To guarantee the combustion process, certain quantities of fuel and air need to be supplied in the combustion chamber. A complete combustion takes place when all the fuel is burned, in the exhaust gas there will be no quantities of unburned fuel. The ideal AFR, for a complete combustion, is called stoichiometric air-fuel ratio or ''stoich''.

When you are tuning the engine according to AFR you should know the ''stoich'' value of the fuel your engine uses and aim for that value for the ideal results. When the air-fuel ratio is higher than the stoichiometric ratio, the air-fuel mixture is declared lean. When the air-fuel ratio is lower than the stoichiometric ratio, the air-fuel mixture is called rich. Below we can see the stoichiometric air-fuel ratio for several fossil fuels.

AFR Analogies
FUELChemical FormulaAFR
Methanol CH3OH 6.47:1
Ethanol C2H5OH 9:1
Butanol C4H9OH 11.2:1
Diesel C12H23 14.5:1
Gasoline C8H18 14.7:1
Propane C3H8 15.67:1
Methane CH4 17.19:1
Hydrogen H2 34.3:1

For example, in order to burn completely 1 kg of Gasoline, we need 14.7 kg of air and to burn 1 kg of diesel fuel, we need 14.5 kg of air.

LAMDA

Lambda, which is a Greek letter demonstrated by the symbol λ, represents all fuels' stoichiometric value as 1.00.

In reality, internal combustion engines do not work exactly with ideal AFR, but with values close to it. Therefore we’ll have an ideal and an actual air-fuel AFR. The ratio between the actual air-fuel ratio and the ideal/stoichiometric air-fuel ratio is called lambda (λ).

λ=AFRactual/AFRideal

For example, the ideal air-fuel ratio for a gasoline engine is 14.7:1. If the actual/real AFR is 13.5, the equivalence factor lambda will be:

λ=13.514.7=0.92

Depending on the value of lambda , the engine is working under lean, stoichiometric or rich air-fuel mixture.

λ ValueAir-Fuel mixture typeDescription
λ<1.00 Rich There is not enough air to burn completely the amount of fuel; after combustion there is unburnt fuel in the exhaust gasses
λ =1.00 Stoichiometric (ideal) The mass of air is exact for a complete combustion of the fuel; after combustion there is no excess oxygen in the exhaust and no unburnt fuel
λ>1.00 Lean There is more oxygen than required to burn completely the amount of fuel; after combustion there is excess oxygen in the exhaust gasses

Lamda is calculated by a wideband sensor which compares the oxygen left in the exhaust to the sensor’s reference pump cell which is referencing stoich. This is why free air calibration is paramount to correct sensor operation.

Because the sensor reads oxygen content, it is impartial to the fuel type being used. If the engine is burning fuel at its specific stoichiometric ratio, all of the oxygen is consumed during combustion. When the sensor detects this stoichiometric condition (no oxygen in the exhaust flow), the lambda gauge will display 1.