Wideband O2 calibration

According to the manufacturer, the operating range of the NGK AFX is an AFR of 9.0 to 16.0 (0 to 5V linear).

So based on the manufacturer, the transfer function should be:

AFR = Vactual/((Vmax-Vmin)/(AFRmax - AFRmin)) + AFRmin

AFR = V/.714 + 9

To start with, I plugged in a transfer function that I found in the HPTuners forum posted by DStreck.  Sadly, without re-reading the post that I got it from, I do not know how he derived this value...I'll have to dig that up

V/0.709 + 9.068

The more that I think about this, since I am using AFR % error to do all tuning, it would make a lot of sense to calibrate my wideband to match the narrow band O2 sensors on the car since they're designed to be extremely accurate at stoich.  Currently, I have followed the manufacturer's directions and calibrated the wideband against open air, which should be accurate, but wouldnt it make more sense to have the calibration be relative to the car itself since the sensors present on the car will dictate the fueling correction when the car is in closed loop?

The manufacturer also assumes that Stoich is 14.57AFR.  Stoich is 1Lambda regardless of fuel type, and the sensor really reads deviation from Stoich, so wouldn't the display show 14.57 if you were running a different fuel at stoich, even though its true stoich AFR value is significantly different?  If this is the case, then converting from registered and commanded AFR to registered and commanded Stoich, would be a much simpler way to look at the %error without having to worry about differences in fuel octane, fuel type, etc.

For a lambda calculation, the manufacturer says that the unit operates between .62 and 1.10 lambda
Lambda = Vactual/((Vmax-Vmin)/(LambdaMax - LambdaMin)) + LambdaMin
Lambda = V/10.4167 + .62

...i'll add more to this post when i get time