First, some reference materials: https://en.wikipedia.org/wiki/Air%E2%80%93fuel_ratio
Basically, I see a lot of posts discussing EQ Ratio as being equal to 1/Lambda. That statement is only correct for Fuel/Air EQ ratio. Not Air/Fuel EQ Ratio.
Basically, you have these non-EQ measurements:
Air/Fuel Ratio (AFR)
- = mass of air / mass of fuel
- = 1 / FAR
Fuel/Air Ratio (FAR)
- = mass of fuel / mass of air
- = 1 / AFR
Neither of these measurements take into account the stoichiometric burn value for the fuel though. That is, neither factor in how many moles of air to how many moles of fuel will result in a perfect burn.
That is where Equivalence Ratio comes into play.
There are two EQ ratio formats, one for each ratio described above:
Air/Fuel EQ Ratio
- = AFR / AFR (stoich)
- = FAR (stoich) / FAR
- less than 1 is rich, 1 is stoich, greater than 1 is lean
- Measured in units of Lambda (λ)
Fuel/Air EQ Ratio
- = FAR / FAR (stoich)
- = AFR (stoich) / AFR
- less than 1 is lean, 1 is stoich, greater than 1 is rich
- Measured in units of Phi (ϕ)
When describing fuel modifiers, F/A EQ ratio is easy to understand because, increasing the # increases the fuel delivery. An F/A EQ Ratio of 1.2 = 20% more fuel over stoich.
When we use wideband meters, they report in Air/Fuel EQ Ratio.
Wait, what? Widebands report values in Lambda.
Air/Fuel EQ Ratio is the term for the function, who's unit result is Lambda (λ).
Fuel/Air EQ Ratio is the term for a function, who's unit result is Phi (ϕ).
These two EQ ratio formats are each others inverses:
Air/Fuel EQ Ratio = Lambda = 1 / Phi
Fuel/Air EQ Ratio = Phi = 1 / Lambda
Knowing the TYPE of EQ ratio is critical to interpreting the numeric value. When you know the type of EQ ratio, you can convert to/from the inverse EQ Ratio, as well as to an air/fuel ratio (as long as you know the stoich value of the fuel).
So, to clear things up moving forward, I've added a unit of measure called Mixture Ratio. In it I've defined the following units:
Lambda (standard unit)
Phi
Air/Fuel Ratio (6.4 Stoich) - Methanol
Air/Fuel Ratio (9.0 Stoich) - Ethanol"
Air/Fuel Ratio (14.6 Stoich) - Diesel
Air/Fuel Ratio (14.7 Stoich) - Gasoline
Air/Fuel Ratio (15.5 Stoich) - LPG
Air/Fuel Ratio (17.2 Stoich) - CNG
What this means is, if your input is an EQ Ratio (or lambda...), you will be able to convert it to the inverse EQ Ratio, or any AFR value providing the fuels stoich value is one of the above listed.
Wow, that's great, but what if my input is AFR?
Well, that's where it gets tricky. Let's say your input is reported by some sensor as AFR. The only way to convert it to an EQ Ratio (lambda/phi), is if you also provide the stoich value used to generate the AFR value. This is not practical within our software. What that means is, if your input is AFR, you're stuck with that number, and you must know what your actual stoich AFR is (per your sensor or parameter) to actually understand what your AFR value means.
This is why using Air/Fuel EQ Ratio (Lambda), or Fuel/Air EQ Ratio (Phi) is better. The value of 1 will always be stoich, so you will always know if you are richer or leaner from stoich, and how far from stoich you are.
Ok, so what about that pesky Commanded EQ Ratio (SAE) parameter?
Here's where it gets really messed up. Per the SAE Document that manufacturers use to implement their protocols, SAE defined the parameter as Fuel/Air EQ Ratio, but used the unit of Lambda (instead of phi). They mixed up the equation and units. As a result, some OEM's use the actual Fuel/Air EQ Ratio formula (reporting phi), while others report Air/Fuel EQ Ratio (reporting lambda).
VCM Scanner:
Moving forward, in the next few days EQ Ratio parameters in VCM Scanner (both vehicle generated, and aux input generated), will report using the quantity of Mixture Ratio, allowing you to convert between lambda and phi, as well as to target air/fuel ratios.
VCM Editor:
Over the next few months, we will be also converting any EQ table/axis to the Mixture Ratio quantity, again allowing you to convert between lambda and phi.
If you have any questions/comments, please add them. I know a bit about this but am no expert.
I do plan to document this in our next version of help files as well.