Air–fuel ratio (AFR) is the mass ratio of
air to a solid, liquid, or gaseous
fuel
A fuel is any material that can be made to react with other substances so that it releases energy as thermal energy or to be used for work (physics), work. The concept was originally applied solely to those materials capable of releasing chem ...
present in a
combustion
Combustion, or burning, is a high-temperature exothermic redox chemical reaction between a fuel (the reductant) and an oxidant, usually atmospheric oxygen, that produces oxidized, often gaseous products, in a mixture termed as smoke. Combustion ...
process. The combustion may take place in a controlled manner such as in an
internal combustion engine
An internal combustion engine (ICE or IC engine) is a heat engine in which the combustion of a fuel occurs with an oxidizer (usually air) in a combustion chamber that is an integral part of the working fluid flow circuit. In an internal comb ...
or industrial furnace, or may result in an explosion (e.g., a
dust explosion). The air–fuel ratio determines whether a mixture is combustible at all, how much energy is being released, and how much unwanted pollutants are produced in the reaction. Typically a range of air to fuel ratios exists, outside of which ignition will not occur. These are known as the lower and upper explosive limits.
In an
internal combustion engine
An internal combustion engine (ICE or IC engine) is a heat engine in which the combustion of a fuel occurs with an oxidizer (usually air) in a combustion chamber that is an integral part of the working fluid flow circuit. In an internal comb ...
or industrial furnace, the air–fuel ratio is an important measure for anti-pollution and performance-tuning reasons. If exactly enough air is provided to completely burn all of the fuel (
stoichiometric combustion), the ratio is known as the stoichiometric mixture, often abbreviated to stoich. Ratios lower than stoichiometric (where the fuel is in excess) are considered "rich". Rich mixtures are less efficient, but may produce more power and burn cooler. Ratios higher than stoichiometric (where the air is in excess) are considered "lean". Lean mixtures are more efficient but may cause higher temperatures, which can lead to the formation of
nitrogen oxides. Some engines are designed with features to allow
lean-burn. For precise air–fuel ratio calculations, the
oxygen
Oxygen is a chemical element; it has chemical symbol, symbol O and atomic number 8. It is a member of the chalcogen group (periodic table), group in the periodic table, a highly reactivity (chemistry), reactive nonmetal (chemistry), non ...
content of combustion air should be specified because of different
air density
The density of air or atmospheric density, denoted '' ρ'', is the mass per unit volume of Earth's atmosphere at a given point and time. Air density, like air pressure, decreases with increasing altitude. It also changes with variations in atmosph ...
due to different altitude or intake air temperature, possible dilution by ambient
water vapor
Water vapor, water vapour, or aqueous vapor is the gaseous phase of Properties of water, water. It is one Phase (matter), state of water within the hydrosphere. Water vapor can be produced from the evaporation or boiling of liquid water or from th ...
, or enrichment by oxygen additions.
Air-fuel ratio meters
An air-fuel ratio meter monitors the air–fuel ratio of an
internal combustion engine
An internal combustion engine (ICE or IC engine) is a heat engine in which the combustion of a fuel occurs with an oxidizer (usually air) in a combustion chamber that is an integral part of the working fluid flow circuit. In an internal comb ...
. Also called air–fuel ratio gauge, air–fuel meter, or air–fuel gauge, it reads the voltage output of an
oxygen sensor, sometimes also called AFR sensor or lambda sensor.
The original narrow-band oxygen sensors became factory installed standard in the late 1970s and early 1980s. In recent years a newer and much more accurate wide-band sensor, though more expensive, has become available.
Most stand-alone narrow-band meters have 10
LEDs and some have more. Also common, narrow band meters in round housings with the standard mounting diameters, as other types of car 'gauges'. These usually have 10 or 20 LEDs. Analogue 'needle' style gauges are also available.
Internal combustion engines
In theory, a stoichiometric mixture has just enough air to completely burn the available fuel. In practice, this is never quite achieved, due primarily to the very short time available in an internal combustion engine for each combustion cycle.
Most of the combustion process is completed in approximately 2 milliseconds at an engine speed of (100 revolutions per second, or 10 milliseconds per revolution of the crankshaft. For a four-stroke engine this would mean 5 milliseconds for each piston stroke, and 20 milliseconds to complete one 720 degree
Otto cycle). This is the time that elapses from the spark plug firing until 90% of the fuel–air mix is combusted, typically some 80 degrees of crankshaft rotation later.
Catalytic converters are designed to work best when the
exhaust gases passing through them are the result of nearly perfect combustion.
A perfectly stoichiometric mixture burns very hot and can damage engine components if the engine is placed under high load at this fuel–air mixture. Due to the high temperatures at this mixture, the detonation of the fuel-air mix while approaching or shortly after maximum cylinder pressure is possible under high load (referred to as
knocking or pinging), specifically a "pre-detonation" event in the context of a spark-ignition engine model. Such detonation can cause serious engine damage as the uncontrolled burning of the fuel-air mix can create very high pressures in the cylinder. As a consequence, stoichiometric mixtures are only used under light to low-moderate load conditions. For acceleration and high-load conditions, a richer mixture (lower air–fuel ratio) is used to produce cooler combustion products (thereby utilizing
evaporative cooling
An evaporative cooler (also known as evaporative air conditioner, swamp cooler, swamp box, desert cooler and wet air cooler) is a device that cools air through the evaporation of water. Evaporative cooling differs from other air conditioning sy ...
), and so avoid overheating of the
cylinder head, and thus prevent detonation.
Engine management systems
The
stoichiometric mixture for a gasoline engine is the ideal ratio of air to fuel that burns all fuel with no excess air. For
gasoline
Gasoline ( North American English) or petrol ( Commonwealth English) is a petrochemical product characterized as a transparent, yellowish, and flammable liquid normally used as a fuel for spark-ignited internal combustion engines. When for ...
fuel, the stoichiometric air–fuel mixture is about 14.7:1 i.e. for every one gram of fuel, 14.7 grams of air are required. For pure
octane fuel, the oxidation reaction is:
:25 O
2 + 2 C
8H
18 → 16 CO
2 + 18 H
2O + energy
Any mixture greater than 14.7:1 is considered a
lean mixture; any less than 14.7:1 is a
rich mixture – given perfect (ideal) "test" fuel (gasoline consisting of solely ''n''-
heptane and
iso-octane). In reality, most fuels consist of a combination of heptane, octane, a handful of other
alkanes, plus additives including detergents, and possibly oxygenators such as MTBE (
methyl ''tert''-butyl ether) or
ethanol
Ethanol (also called ethyl alcohol, grain alcohol, drinking alcohol, or simply alcohol) is an organic compound with the chemical formula . It is an Alcohol (chemistry), alcohol, with its formula also written as , or EtOH, where Et is the ps ...
/
methanol
Methanol (also called methyl alcohol and wood spirit, amongst other names) is an organic chemical compound and the simplest aliphatic Alcohol (chemistry), alcohol, with the chemical formula (a methyl group linked to a hydroxyl group, often ab ...
. These compounds all alter the stoichiometric ratio, with most of the additives pushing the ratio downward (oxygenators bring extra oxygen to the combustion event in liquid form that is released at the time of combustions; for
MTBE
Methyl ''tert''-butyl ether (MTBE), also known as ''tert''-butyl methyl ether, is an organic compound with a structural formula (CH3)3COCH3. MTBE is a volatile, flammable, and colorless liquid that is sparingly soluble in water. Primarily used as ...
-laden fuel, a stoichiometric ratio can be as low as 14.1:1). Vehicles that use an
oxygen sensor or other feedback loops to control fuel to air ratio (lambda control), compensate automatically for this change in the fuel's stoichiometric rate by measuring the exhaust gas composition and controlling fuel volume. Vehicles without such controls (such as most motorcycles until recently, and cars predating the mid-1980s) may have difficulties running certain fuel blends (especially winter fuels used in some areas) and may require different
carburetor
A carburetor (also spelled carburettor or carburetter)
is a device used by a gasoline internal combustion engine to control and mix air and fuel entering the engine. The primary method of adding fuel to the intake air is through the Ventu ...
jets (or otherwise have the fueling ratios altered) to compensate. Vehicles that use
oxygen sensors can monitor the air–fuel ratio with an
air–fuel ratio meter.
Other types of engines
In the typical air to natural gas combustion burner, a double-cross limit strategy is employed to ensure ratio control. (This method was used in World War II). The strategy involves adding the opposite flow feedback into the limiting control of the respective gas (air or fuel). This assures ratio control within an acceptable margin.
Other terms used
There are other terms commonly used when discussing the mixture of air and fuel in internal combustion engines.
Mixture
Mixture is the predominant word that appears in training texts, operation manuals, and maintenance manuals in the aviation world.
Air-fuel ratio is the ratio between the ''mass'' of air and the mass of fuel in the air-fuel mix at any given moment. The mass is the mass of all constituents that compose the air or fuel, whether they take part in the combustion or not. For example, a calculation of the mass of natural gas as fuel — which often contains
carbon dioxide
Carbon dioxide is a chemical compound with the chemical formula . It is made up of molecules that each have one carbon atom covalent bond, covalently double bonded to two oxygen atoms. It is found in a gas state at room temperature and at norma ...
(),
nitrogen
Nitrogen is a chemical element; it has Symbol (chemistry), symbol N and atomic number 7. Nitrogen is a Nonmetal (chemistry), nonmetal and the lightest member of pnictogen, group 15 of the periodic table, often called the Pnictogen, pnictogens. ...
(), and various
alkanes — includes the mass of the carbon dioxide, nitrogen and all alkanes in determining the value of ''m''
fuel.
For pure
octane the stoichiometric mixture is approximately 15.1:1, or ''λ'' of 1.00 exactly.
In naturally aspirated engines powered by octane, maximum power is frequently reached at AFRs ranging from 12.5 to 13.3:1 or ''λ'' of 0.850 to 0.901.
The air-fuel ratio of 12:1 is considered as the maximum output ratio, whereas the air-fuel ratio of 16:1 is considered as the maximum fuel economy ratio.
Fuel–air ratio (FAR)
Fuel–air ratio is commonly used in the
gas turbine
A gas turbine or gas turbine engine is a type of Internal combustion engine#Continuous combustion, continuous flow internal combustion engine. The main parts common to all gas turbine engines form the power-producing part (known as the gas gene ...
industry as well as in government studies of
internal combustion engine
An internal combustion engine (ICE or IC engine) is a heat engine in which the combustion of a fuel occurs with an oxidizer (usually air) in a combustion chamber that is an integral part of the working fluid flow circuit. In an internal comb ...
, and refers to the ratio of fuel to the air.
:
Air–fuel equivalence ratio (''λ'')
Air–fuel equivalence ratio, ''λ'' (lambda), is the ratio of actual AFR to stoichiometry for a given mixture. ''λ'' = 1.0 is at stoichiometry, rich mixtures ''λ'' < 1.0, and lean mixtures ''λ'' > 1.0.
There is a direct relationship between ''λ'' and AFR. To calculate AFR from a given ''λ'', multiply the measured ''λ'' by the stoichiometric AFR for that fuel. Alternatively, to recover ''λ'' from an AFR, divide AFR by the stoichiometric AFR for that fuel. This last equation is often used as the definition of ''λ'':
:
Because the composition of common fuels varies seasonally, and because many modern vehicles can handle different fuels when tuning, it makes more sense to talk about ''λ'' values rather than AFR.
Most practical AFR devices actually measure the amount of residual oxygen (for lean mixes) or unburnt hydrocarbons (for rich mixtures) in the exhaust gas.
Fuel–air equivalence ratio (''Φ'')
The fuel–air equivalence ratio, ''Φ'' (phi), of a system is defined as the ratio of the fuel-to-oxidizer ratio to the stoichiometric fuel-to-oxidizer ratio. Mathematically,
:
where ''m'' represents the mass, ''n'' represents a number of moles, subscript st stands for stoichiometric conditions.
The advantage of using equivalence ratio over fuel–oxidizer ratio is that it takes into account (and is therefore independent of) both mass and molar values for the fuel and the oxidizer. Consider, for example, a mixture of one mole of
ethane
Ethane ( , ) is a naturally occurring Organic compound, organic chemical compound with chemical formula . At standard temperature and pressure, ethane is a colorless, odorless gas. Like many hydrocarbons, ethane is List of purification methods ...
() and one mole of
oxygen
Oxygen is a chemical element; it has chemical symbol, symbol O and atomic number 8. It is a member of the chalcogen group (periodic table), group in the periodic table, a highly reactivity (chemistry), reactive nonmetal (chemistry), non ...
(). The fuel–oxidizer ratio of this mixture based on the mass of fuel and air is
:
and the fuel-oxidizer ratio of this mixture based on the number of moles of fuel and air is
:
Clearly the two values are not equal. To compare it with the equivalence ratio, we need to determine the fuel–oxidizer ratio of ethane and oxygen mixture. For this we need to consider the stoichiometric reaction of ethane and oxygen,
:C
2H
6 + O
2 → 2 CO
2 + 3 H
2O
This gives
:
:
Thus we can determine the equivalence ratio of the given mixture as
:
or, equivalently, as
:
Another advantage of using the equivalence ratio is that ratios greater than one always mean there is more fuel in the fuel–oxidizer mixture than required for complete combustion (stoichiometric reaction), irrespective of the fuel and oxidizer being used—while ratios less than one represent a deficiency of fuel or equivalently excess oxidizer in the mixture. This is not the case if one uses fuel–oxidizer ratio, which takes different values for different mixtures.
The fuel–air equivalence ratio is related to the air–fuel equivalence ratio (defined previously) as follows:
:
Mixture fraction
The relative amounts of oxygen enrichment and fuel dilution can be quantified by the
mixture fraction, Z, defined as
: