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During one of your worked examples on the Motec M1 Andre mentions aborting a run if he see's and AFR that is either too rich or too lean. What kinds of numbers are we talking about and what kinds of time frames do these numbers need to persist for before we consider the condition transient.
Usually if I go around 3-5% (lean) away from my target I will abort the run and make a change or around 10% to rich.
If it is a quick transition of around 250rpm then not so bad, but if it is a trend (going leaner) then I will stop.
It can be a little tricky with high powered individual throttle NA motors as they do transition through rich and lean spots which can be hard to eliminate.
It's really very dependent on the engine, the fuel, and the specific power level you're producing.
For example on pump gas on a stock N/A engine it's going to be reasonably hard (but not impossible) to damage it from a lean mixture. As Chris mentioned, a 3-5% tolerance is going to be ok in this instance. For a maximum effort turbo engine I might drop this down a little to maybe 2-3%. If I'm tuning a maximum effort engine on methanol I'll be pretty fast to abort as soon as the lambda deviates from my target.
There's no real danger with being too rich other than the fact you may possibly end up with the plugs fouled. Either way though you're going to need to remove some fuel so if I see the lambda move maybe 10% richer than target I would probably choose to abort and fix the fuelling.