The definition of AFR (air-fuel ratio) is the mass of air inducted divided by the mass of fuel consumed. The AFR for different operating points (engine speed and load) can be quite different. Accurately measuring an engine's air consumption is inconvenient because a large surge tank is required to damp individual cylinder pulsations.
Inferring AFR from the chemical composition of the exhaust gas has been a tempting and fruitful avenue to pursue. The technique dates back to the late 1870s and was initially used for flue gas analysis in boilers.
Something called the Orsat apparatus (after its inventor, Louis Orsat) was employed to determine the relative content of oxygen, carbon dioxide, carbon monoxide, hydrogen, and sulfur dioxide in the exhaust gas. The remainder was assumed to be nitrogen. Today we do this with a multi-gas EGA (exhaust gas analyzer).
But wouldn't it be nice if we could determine AFR in real-time via an inexpensive electrochemical gadget that we could stick into the exhaust stream? Yes, yes it would!
When considering the usefulness of measurements produced by wideband oxygen sensors (WBO2), it's important to understand how a wideband system arrives at an AFR number.
The wideband sensor is just a narrowband sensor, called the “reference cell”, with the addition of a “pump cell.”
Like all narrowband sensors, the reference cell operates in a “switching” mode. Its output switches from about 1 volt for slightly rich mixtures, to about 0 volts for slightly lean mixtures. The difference between slightly rich and slightly lean is very narrow — tighter than between 0.02% excess fuel and 0.02% excess air.
For any given exhaust gas composition, the controller attempts to provide the right amount of current to the pump cell to just get the reference cell perfectly balanced at stoichiometric. The amplitude (and polarity) of the current it takes to do this is used to infer the composition of the exhaust gas.
If the exhaust gas is stoichiometric, the pump current needed to balance the reference cell is zero.
If the exhaust gas is lean (excess oxygen), the pump current needed to balance the reference cell is positive.
If the exhaust gas is rich (excess hydrocarbons), the pump current needed to balance the reference cell is negative.
Note that the pump current is not linear with AFR.
The controller measures the current that it must drive into the pump cell to “neutralize” the exhaust gas. This current is then linearized, and finally an answer is provided.
But what happens when both oxygen and hydrocarbons are present? This is an important question because there is always oxygen in the exhaust gas. Even for very rich mixtures, the exhaust gas is about 1% oxygen.
So the AFR value reported is based on neutralizing an exhaust gas that has an unknown (and varying based on operating conditions) quantity of oxygen present. Unfortunately, this is what happens when two things are combined and measured with only a single result being reported.
It's a bit like saying, “I have a 125cc cylinder.” Well, is that 52×58, 54×54, or 56×50? Inquiring minds need to know.
The high-performance community is used to seeing mixture ratios expressed with numbers like 14.7 AFR. I think this presentation has become popular because the numbers are easy to remember. It also makes it easy to see that we need a relatively large mass of air to completely burn a relatively small mass of fuel.
Air-Fuel ratio and Fuel-Air ratio are just reciprocals of one another. In the first case, you divide the mass of the air by the mass of the fuel. In the second case, it is the mass of the fuel divided by the mass of the air.
Historically, the technical literature rarely used air-fuel ratio, preferring to state the reciprocal relationship instead. This produces numbers like 0.068 (stoichiometric for gasoline). There is good reason to do this. For one thing, when performing thermodynamic calculations, a unit mass of air is often assumed (1 pound in the English system of units). Knowing the fuel-air ratio (say 0.068), it is a simple matter to multiply that number by the heating value of the fuel used (say 20,400 Btu per pound for gasoline) and come up with the amount of energy released (1387 Btus). I have also read that F/A ratio is preferred because (for a given operating condition) the mass of air inducted is fixed. Thus, fuel is the controlled variable, and it is more appropriate to state the amount of fuel we are providing for that fixed mass of air, rather than the other way around.
More recently, in the technical literature, you will see “equivalence ratio” used (the symbol being the Greek letter capital Phi Φ). The equivalence ratio is defined as the “actual fuel-air ratio delivered” divided by the “stoichiometric fuel-air ratio” for a given fuel. So an equivalence ratio of 1.0 means stoichiometric. Mixtures leaner than stoichiometric have Phi smaller than 1.0. Mixtures richer than stoichiometric have phi larger than 1.0.
The reciprocal of Phi is lambda (lowercase λ). This is just the “stoichiometric fuel-air ratio” for a given fuel divided by the “actual fuel-air ratio delivered”. Similarly, a lambda of 1.0 means stoichiometric. Mixtures leaner than stoichiometric have lambda larger than 1.0. Mixtures richer than stoichiometric have lambda smaller than 1.0.
Lambda is popular in the high-performance community because of the availability of inexpensive wideband sensors. The sensor itself does not know anything about the composition of the mixture — all it knows is that it sees leftover oxygen (lean) or leftover hydrocarbons (rich) or nothing (stoichiometric) in the exhaust gases. The AFR values it reports are often just hard-coded equivalences for “typical” gasoline.
Below is an example comparison table for what is typically considered gasoline.
But as I've mentioned elsewhere, gasoline is a chemical soup made up of many compounds. Thus, the stoichiometric burning ratio varies according to the composition of the gasoline and will depend on the proportions of the specific hydrocarbons present in the fuel. If you know the average ratio of hydrogen atoms to carbon atoms in a fuel (and any oxygen present), it is possible to compute the AFR for stoichiometric combustion.
Gasoline is sometimes approximated as iso-octane (2,2,4-Trimethylpentane to a chemist, and C8H18 for our purposes) which has a stoichiometric AFR of 15.1 : 1.
Whereas the stoichiometric AFR for a typical US pump gasoline (E10) may be more like 14.4 : 1.