Hummm very interesting
pete nicely done. Data don't lie.
I could be wrong but this is why small 320's and 360's done run LOP very well, the spread in peak's v ff.
ACT I, what I see, normally WOT the fwd cylinder #1 an #2 run leaner than the back two, where the left one #4 is the most rich.
Act II, you close the butterfly a little and change the fuel distribution and almost reverse it front to back and lower the overall FF. (OK makes total sense since the butter fly angles fuel fwd and you have cut overall fuel.)
ACT III, carb heat has an overall leaning effect and seems to have balance the fwd cylinders left/right - #2/#1 peaks. I think this is partially random. I assume you have a Van's FAB. Unlike the carb heat airbox on a Cessna or Piper the flap or valve in not right under the throat of the carb, so carb heat has little effect other than lower MAP and increase air temp, which apparently reduces overall FF due to lower power (restricted airflow and lower density air). There is a technique C-182 guys do with the Carbed Continental that involves cracking the carb heat open to balance the peaks. I do not think this works as well or at all with our air box.
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Theory: Because ALL the fuel originates out the mouth of the carb and than into sump plenum and 4 runners. After that its kind of hit miss where the fuel goes, #1, #2, #3 or #4. Now each cylinder is asking "FEED ME". There may be differences in the cylinders them self or the runners to each cylinders. However a good start is have a balanced feed to the 4 runners.
If you can divert or direct the air flow into one of the four runners you can manipulate the air/fuel balance. You could cut and modify the sump but that has some down side and may be bad news, so what about the air box?
The air flow into the carb mouth can be manipulate with something in the air box. This should have down stream affect on the flow of air/fuel mixture in one of 4 corners of the sump plenum?
Clearly the carb butter fly does a great job with fwd and aft bias. Now we need left right balance that does not use carb heat, which is very inefficient on the RV FAB. (It gives overall loss of power.)
Solution: Some little shape like a vane or cone in the bottom center of the air box that you can manipulate. Once the shape or shapes of the flow divider'(s) and/or guide'(s) are determined they are fixed. Doing this creates different airflow into the mouth of the carb, which in theory changes the output of the carb, favoring or starving one or the another cylinder as needed. Call it an AIR FLOW TRIM VANE or GUIDE.
You could make it fixed and change it between flights to experiment with the shapes in side the air box that balances the flow. The final balance may be good while still WOT and no carb heat! Anything in the base of the air box to divert more or less air into one of those 4 corners may be key to "trimming the air flow".
Cons: The big down side is anything in the induction that can or could come apart and get into the engine is bad, that is why I did not like the magnetic alt air door van offered with the FAB360. (Now he changed to a manual cable operated valve which is better but I don't need or think is needed for VFR ops.)
Summary: I think this has some merit. Clearly the Cessna C-182 airbox carb heat valve does fuel balancing as claimed by those operators. It's a big "seesaw" valve right under the carb. May be a little valve seesaw cable operation valve in the bottom air box may be a solution but at greater complication.
Experiment: My first shape would be a cone that slopes up from the bottom of the air box near the edge of the air filter to the center of the carb. It would be symetric at first and 360 degrees around. Offsetting the center of the cone (left/right/fwd/aft) relative to the carbs center, would smooth and bias the air flow. The result would be to enrichen or lean one or more cylinder as needed.
(click pic below)