I haven't found a reason to believe that the change in pumping losses is substantial so I have a different take.
Atomization of fuel isn't that important. The only time when the mixture matters is the moment before the spark. The enclosed space is quite small which counteracts any distribution or atomization you might have had. Vaporized fuel might condense under the pressure. Atomized fuel might coalesce due to the confined space. Only heat passes through compression unimpeded. More heat will counteract condensation and coalescing. Because air is 14x and fuel is 1x the charge the temperature of the air has the greatest effect on the final temperature of the charge before the spark fires.
You want the highest final temperature just before the lowest flash point hydrocarbons detonate. The WAI/HAI is a crude way to attain this but it won't work well until the ECM controls air temperature based on spark knock response to compensate for the changes in fuel composition and air density. The IAT is placed a ways back in the system and the air temperature increases as it approaches the cylinder so the IAT measurement will be different for different engines. The final temperature under pressure is what matters.
I found that most of the winter mileage drop is eliminated with the WAI. My crude WAI is not very efficient at extracting heat and it really can't be because the WAI is not regulated. This means I can't attain the correct IAT in the winter and I attain peak IAT much later than I would like after a cold start. A properly regulated WAI made by the factory could be attached to a very efficient heat exchanger which would reach any desired IAT very quickly and minimize the miles driven at low efficiency. A few engines from Volvo and Audi have this though they get a bad rap because someone forgot to use the IAT to turn on the MIL when the system fails.
I started with additives and ended with WAI. Adding additives to WAI could not increase the mileage above WAI alone though the additives were beneficial for other reasons.
With a spark ignition at least stoic mush be injected or the charge will flame out leaving some fuel to be burnt elsewhere where it is of no benefit. With HCCI the hot air burns the fuel so you can inject less than stoic and everything you inject will burn. This allows the unused air to act as inert filler which effectively reduces the displacement of the engine at the cost of compressing and releasing inert filler. This helps to mitigate the problem we Americans have of buying way too much engine just to drive on the highway where the engine spends most of its time below peak efficiency. At the times the engine is at peak efficiency braking, air resistance, and speeding tickets eliminate the gains which makes it appear that highway is the most efficient.
Efficiency goes way down with the downstream oxygen sensor out of commission though it isn't clear why since engines were just as efficient without one. I think it is because the ECM goes fubar trying to get it to respond and the result is lower average mileage. One thing the downstream sensor does is to measure EGT in the catalytic. "Detroit Fever" and "2006 Diesel Emission Standards" are two names for the process of dumping extra fuel out the exhaust to guarantee a minimum EGT in the catalytic to maintain minimum emissions standards at your cost. If no temperature reading comes back the safe bet is to dump extra fuel. That's what you would do, right? After all, if removing the downstream sensor increased mileage, who would have one?
I thought the idea was to make the motor less effecent where you have to open the throttle more decreasing pumping loses and increase the temp of the engine which increases thermal effeciency.
in your explanation you say that your inducting less air, which to get the same afr takes less fuel. which is correct, but fuel in what propells the car. if your at a throttle position you don't increase or decrease speed ( on a steady road where the altitude doesn't change) unless you decrease throttle position which increases or decreases fuel. which makes you go faster or slower. WAI, you have to open the throttle more to get the same amount of air and fuel then before. decreasing pumping loses. if the amount of gas burnt could be calculated as horsepower or mpg.
Not to say you guys are wrong or anything. But what I have heard is that the warmer air helps the fuel vaporize better, causing a more efficient burn. I'm sure there is more than one element at work here anyways.
Finally filled up last night. Another 37 mpg tank and this time, only about 70% was highway, the rest was back and forth to work which is roughly 15 miles round trip.
I always manage better mileage on the trip home from Cleveland. I think the geographical features of Ohio slope downward (didn't an ice cap melt over OHIO causing it to be flat?).
same results here as i would get 37+mpg all the time and 39 on mostly highway fill ups wai not hai, i was only taking air from beside the engine(past radiator hose) an actual hai would get me in a percievable 45 mpg range