PiJohn & EngineEagle
PiJohn PiJohn
EngineEagle EngineEagle
PiJohn PiJohn
Hey, have you ever thought about the math behind the optimal air‑fuel ratio curves? I suspect there's a neat pattern we could uncover together.
EngineEagle EngineEagle
Sure, the air‑fuel curve is just a piecewise‑linear approximation of a complex exponential, but if you line up the knots at the right points you can squeeze a lot of power out. Think of it like a rune – each point is a command to the engine, and the curve is the magic spell. We can map it to a simple polynomial if we keep the math tidy and avoid guesswork. Interested in a deeper dive?
PiJohn PiJohn
Sounds intriguing—let's map those knots and see if a low‑degree polynomial keeps the engine humming smoothly. Ready to start crunching the numbers?
EngineEagle EngineEagle
Alright, grab the torque data and the corresponding lambda values. We’ll fit a quadratic or cubic, keep an eye on the residuals, and make sure the curve doesn’t go haywire at the extremes. No shortcuts, just clean data and a solid regression. Let's do it.
PiJohn PiJohn
Great! First, let’s pull the torque vs. lambda points from the log, then set up a least‑squares fit for a quadratic, and if the residuals look uneven, bump to a cubic. We’ll plot the residuals to catch any wild swings at the edges and tweak the domain limits if needed. No shortcuts—just clean math and a tidy curve. Let's get started.
EngineEagle EngineEagle
Sounds good, but remember the log’s noise isn’t a good friend. Let’s extract clean, evenly spaced points, then run the least‑squares, check the residual pattern, and only then consider a higher‑order fit. I’ll keep an eye on the endpoints so the curve doesn’t explode outside the tested range. Ready to pull the data?
PiJohn PiJohn
Alright, let's pull a clean, evenly spaced set of points from the log, run a least‑squares fit, inspect the residuals, and only then decide if we need a higher‑order term. We'll watch the endpoints closely to keep the curve under control. Let's extract the data.
EngineEagle EngineEagle
Okay, first step is to pull out a clean, evenly spaced slice from the log. If you can give me the lambda and torque values, I’ll fit the quadratic, plot the residuals, and we’ll see if a cubic is justified. Let’s keep the data tight and let the math do the heavy lifting.