Equivalence Ratio (EQ) Discussion

[Keith@HPTuners]

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.

[DSteck]

So in the VCM Editor, for example (a GM file)... Can we leave all of the Open Loop modifiers in phi but make PE display in lambda?

E40 ECMs report EQ ratio in the scanner as phi. E38/E67/E92 report it as lambda. What will the VCM Scanner default to, and how will it know that the E40 reports it differently from the later hardware? I currently use some very specific math to run calculations based on commanded lambda, commanded stoich, and actual lambda. For E40, I have to invert the commanded EQ ratio parameter for the math to work. Will this update alleviate that issue and allow the same calcs to work for all the hardware?

[Keith@HPTuners]

In VCM Editor, you should be able to do that.

I think what we will do is leave the the default SAE EQ ratio as lambda, but add an additional SAE EQ ratio that reports in phi, for the oddball GM PCM's.

In VCM Scanner, on the channels display, when you click Vehicle Defaults, it will chose the correct EQ parameter for your vehicle.

With this scanner change, when you use the EQ Ratio (Commanded) and EQ Ratio (Actual) sensors for your equations (which the built in math parameters will do), everything should "just work", and you can then chose your output unit of lambda or phi.

This is the theory, the implementation is to follow.

[LSxpwrdZ]

Dummied down I basically did this in the past versions by creating VCM Scanner.cfg files for each platform I tune so the commanded EQ was correct for calculating commanded lambda. It's nice to see you guys implementing these calculations in the background to free up some custom pid space.

[Keith@HPTuners]

So in the VCM Editor, for example (a GM file)... Can we leave all of the Open Loop modifiers in phi but make PE display in lambda?

E40 ECMs report EQ ratio in the scanner as phi. E38/E67/E92 report it as lambda. What will the VCM Scanner default to, and how will it know that the E40 reports it differently from the later hardware? I currently use some very specific math to run calculations based on commanded lambda, commanded stoich, and actual lambda. For E40, I have to invert the commanded EQ ratio parameter for the math to work. Will this update alleviate that issue and allow the same calcs to work for all the hardware?

E40 will report the correct EQ ratio unit in tomorrows beta.

If you know of any other controllers that report EQ Ratio Commanded (SAE) as phi and not lambda, let me know and we can fix it.

[1slowbusa]

Maybe this is a stupid question but I cannot seem to find an answer anywhere. Maybe one of you guys can answer this for me. I'm still a little confused on how to get the correct EQ Ratio when the fuel stoich is anything other than the ones mentioned by Keith above. Lets say the stoich is 13.7.

You always read to get PE EQ Ratio, you take the stoich of the fuel you are using divided by the desired AFR at WOT. Example 14.63/12.8=1.142.

But if I change the EQ Ratio with the new fuel 13.7/12.8=1.07. Now i know this is not correct because lambda is inverse of eq ratio and 1/1.142=.875 which is what I want at WOT on a NA tune. But I got the 1.142 by 14.63/12.8 not 13.7/12.8.

So, for example, if I wanted to change my EQ Ratio for PE to 13.0 AFR, would I use the 14.63/13.0=1.125 or would I use the actual fuel stoich (13.7) I am using as stoich in the tune 13.7/13=1.05.

Another example would be running a dry nitrous kit. If say I wanted to command 11.5 with this fuel, would I use 14.63/11.5=1.272 or would I use the stoich of the new fuel 13.7/11.5=1.191?

So basically, when tuning with different fuels, will I take the actual stoich of the fuel located in the the tune and find the EQ Ratio for PE or will I always use 14.63. 14.63 was the stock value in my tune.

Thanks in advance.

[Jggregory99]

To my knowledge, at least on my vehicles, I change the stoich in the editor to reflect the stoich of my available or most used fuel. Example being... Here in NY everything is bet 5-10% Ethanol, which changes stoich. So in the Fuel>General>Stoich I change the value to 14.08.. The stoich of E10.. and calculate desired AFR based on that stoich value. This has always worked for me...As far as PE... I always go 15% of stoich... So my PE EQ Ratio is always 1.15.. Giving a commanded AFR of 12.24.. Because if you apply this same principal to E85... Stoich is 9.0..With a PE set at 1.15... Commanded is 7.82... So like I said... I set stoich to the fuel I use..

[schpenxel]

1. This is why AFR sucks. Use lambda. That's all that really matters. Another way of thinking about PE EQ ratio is how much EXTRA fuel do you want? 10%? 15%? Doesn't matter what the stoich value is. The point is you're injecting an extra 15% or whatever value you're using.

2. All widebands read in lambda, multiply x 14.7 (NO MATTER WHAT FUEL YOU ARE RUNNING) and spit out a number. If you're running E85, and at stoich, lambda=1, a wideband will show an AFR of 14.7. Clearly this isn't correct but this can cause issues if you're trying to tune in AFR and have stoich sent to one value in the tune and your wideband still reporting 14.7 for lambda=1.

3. You're overthinking it and this is why everyone should use lambda and not AFR. Forget about E10, E50, Ewhatever. What PE EQ ratio would you use if you were running pure gasoline? Use that.

[Jggregory99]

1. This is why AFR sucks. Use lambda. That's all that really matters. Another way of thinking about PE EQ ratio is how much EXTRA fuel do you want? 10%? 15%? Doesn't matter what the stoich value is. The point is you're injecting an extra 15% or whatever value you're using.

2. All widebands read in lambda, multiply x 14.7 (NO MATTER WHAT FUEL YOU ARE RUNNING) and spit out a number. If you're running E85, and at stoich, lambda=1, a wideband will show an AFR of 14.7. Clearly this isn't correct but this can cause issues if you're trying to tune in AFR and have stoich sent to one value in the tune and your wideband still reporting 14.7 for lambda=1.

3. You're overthinking it and this is why everyone should use lambda and not AFR. Forget about E10, E50, Ewhatever. What PE EQ ratio would you use if you were running pure gasoline? Use that.

I agree with you Carson, and not trying to step on toes...Lambda IS much easier, I was just trying to clarify 1slow's issue about changing the Stoich value itself and which one should be used to calculate PE EQ Ratios. I personally, because that is how I was taught, change the stoich in the tune to reflect the predominate fuel being used regardless of whether I am using Lambda or AFR. If I am using Lambda, on E10 with a PE EQ Ratio of 1.15, my EQ should read .85 in Lambda, if I was using AFR I would expect to see an AFR value of 12.24 as that is 15% enrichment with a stoich of 14.08 on E10. Either one gives me my desired 15% enrichment. My particular WB allows me to set the AFR reading to whatever stoich I choose it to be, E10, E20, E85, 100%Eth, Meth, Diesel, etc... All I need to know is the Stoich of a fuel and use the WB software to set that value as the reported stoich.. Like I said, not trying to rile or step on toes... This is just how I was taught... So it is what I do...

[1slowbusa]

1. This is why AFR sucks. Use lambda. That's all that really matters. Another way of thinking about PE EQ ratio is how much EXTRA fuel do you want? 10%? 15%? Doesn't matter what the stoich value is. The point is you're injecting an extra 15% or whatever value you're using.

2. All widebands read in lambda, multiply x 14.7 (NO MATTER WHAT FUEL YOU ARE RUNNING) and spit out a number. If you're running E85, and at stoich, lambda=1, a wideband will show an AFR of 14.7. Clearly this isn't correct but this can cause issues if you're trying to tune in AFR and have stoich sent to one value in the tune and your wideband still reporting 14.7 for lambda=1.

3. You're overthinking it and this is why everyone should use lambda and not AFR. Forget about E10, E50, Ewhatever. What PE EQ ratio would you use if you were running pure gasoline? Use that.

Thanks guys for the reply.

Basically what schpenxel said makes sense and he made it simple. This clears things up. Thanks again.

[StopGap]

1. This is why AFR sucks. Use lambda. That's all that really matters. Another way of thinking about PE EQ ratio is how much EXTRA fuel do you want? 10%? 15%? Doesn't matter what the stoich value is. The point is you're injecting an extra 15% or whatever value you're using.

2. All widebands read in lambda, multiply x 14.7 (NO MATTER WHAT FUEL YOU ARE RUNNING) and spit out a number. If you're running E85, and at stoich, lambda=1, a wideband will show an AFR of 14.7. Clearly this isn't correct but this can cause issues if you're trying to tune in AFR and have stoich sent to one value in the tune and your wideband still reporting 14.7 for lambda=1.

3. You're overthinking it and this is why everyone should use lambda and not AFR. Forget about E10, E50, Ewhatever. What PE EQ ratio would you use if you were running pure gasoline? Use that.

So, I am using an LC-2 WB and it is on the dropdown list when setting up my channel tables in the scanner. I have the WB setup to read/record AFR which was there in the list. Still learning all of the nuances of the tools, but is there a dropdown option to choose lambda for the LC-2 or do I need to write a formula to convert it? Thanks!

[schpenxel]

It's under equivalence ratio, then pick LC-2. They call it that instead of Lambda for whatever reason

[07GTS]

what i do is loop the WB input from pin 1 to pin 2 also then i setup the WB for Lambda and AFR

[schpenxel]

Not a bad idea

If you're in lambda/EQ ratio then you can also change the "units" pretty much anywhere to display "AFR" based on a bunch of different common stoich values also.

That's partially why I tell everyone to setup their WB's in lambda. Worst case you can right click on it and change the units to display in AFR if you prefer.

[07GTS]

yea found lambda good to learn from the start which keeps it easier with a scaled tune and E85 no extra maths just works as is any way u have it scaled

[schpenxel]

Yup! I still have to convert back and forth every now and then but for the most part AFR doesn't even make sense to me anymore, I've used lambda for too long

[StopGap]

I might try to do that. Right now I set up my LC-2 AFR on pin 3 (grnd pin5). I could use pin 4 to loop lambda. The reason I chose to use pins 3/5 is that I can easily unplug the 3 pin connector from my dashlogic and plug directly into the MPVI using positions 3/4/5 w/o having to physically rewire the connections every time I want to datalog.

So if I set up another channel analog PID, on input 4, select LC-2 Equiv ratio loop from pin 1 to pin 2 on the dashlogic conn, then I should be able to read/record both AFR and Lambda at the same time? I'm guessing maybe in dashlogic too if I write a formula for Lambda off PID 2.

[schpenxel]

There's really no need to bother with double connecting it in either place. Just set the formulas up in lambda and you can make it display / function as AFR if you want.

[schpenxel]

I'll post some pictures later, covered up at work for at least a few hours.

[07GTS]

yep looped it will log both inputs so u can change them to read what ever u want, was good at the start to mainly use lambda but also have look at AFR just to get use to it, but like mentioned after a while u just get use to lambda and don't even take notice of AFR, also when setting to the WB i use the pin 1 as lambda and loop to pin 2 and set to read 0-5 volts so then u get a better look at what volts are what lambda and how far out it is when setting up the volts offset ect