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I wrote this post as an answer to a question in one of the threads, and while composing I thought that it might we worth a separate thread. I'd love this thread to focus on the scientific and proven types of things, and I'll try to update it as I progress. I hope this thread will once become a home not only for theoretical stuff, but also for FJ-applied practice. Please feel free to post your thoughts here.

I highly recommend reading this book for anyone interested in modern ECUs: Designing and Tuning High-Performance Fuel Injection Systems: Greg Banish: 8601406610408: Amazon.com: Books

Please excuse my quick disclaimer first though
1. What follows is my current understanding of the engine physics. I have a lot to learn.
2. In no way do I mean to look or sound like a smarta$$. There surely are folks here that knew all this and then some. I just find all this extremely interesting, and I wrote this for anyone, who's interested in how modern engines work.

Okay, enough with the intro.

Overall there's a lot of factors that influence engine torque, but I don't want to dive into the mechanics. Let's say we have a basic naturally aspirated engine that has certain mechanical parameters, such as displacement, CR, bore to stroke ratio, combustion chamber shape etc etc. Let’s also assume that this engine operates within designed ECT (Engine coolant temp) it’s neither cold nor overheated, everything is in decent condition. For a common internal combustion engine torque is a function of cylinder pressure. From the ECU/engine control POV this engine basically has several controllable factors that influence cylinder pressure and therefore produced torque:
  • Volumetric efficiency (VE)
  • Air/fuel ratio (AFR)
  • Spark advance (SA)
Volumetric Efficiency is defined as

the ratio of air volume drawn into the cylinder to the cylinder's swept volume. More specifically, volumetric efficiency is a ratio (or percentage) of the mass of air and fuel that is trapped by the cylinder during induction divided by the mass that would occupy the displaced volume if the air density in the cylinder were equal to the ambient air density.
, thank you, wikipedia.

For the NA engine VE can rarely exceed 100%. While this can happen due to intake and exhaust resonance, creating conditions for better cylinder fill, it’s not important for us now.

The ECU controls VE via the throttle plate and camshaft(-s) angles (we’re omitting a lot of complications, but that will do for us now). The less the throttle opens - the less VE we have. Here’s what’s important – for each engine speed there is a VE that would produce maximum torque possible, defined as optimum airflow.

The AFR is essentially air mass to fuel mass ratio. The airflow is measured by the MAF sensor, converted to mass with an account for IAT (and again a lot more factors, but...). The fuel mass for gasoline is set in the ECU, so the ECU can scale the injector pulsewidth accordingly, as injector parameters are also set in the ECU. Most of the time the ECU wants the engine to run in closed loop mode and on stochiometry AFR as this is the balance point between ecology, performance and fuel consumption. Toyota sets its stoich to 14.60. I believe the exact scientific number for iso-octane is 14.68, though pump gas is different. Naturally the engine can't always run at stoich as while being a balance point, this AFR is not ideal for acceleration/deceleration conditions, high engine speeds, heating, etc. so there is a lot of additives, most known among which are Power Enrichment, Cold Engine Enrichment and Component Overtemp Protection Enrichment. Honestly AFR deserves its own article, so I’ll stop here.

Foe each engine speed and load combination there also is an AFR that would produce maximum torque, somewhere around 12.5-12.6. It may not be desirable though, due to heat or detonation concerns.

The Spark Advance is where it gets really interesting. Torque is produced by the gas pressure on the piston, developed as a result of burning fuel. It does not develop instantly, instead it builds up as combustion takes place until it reaches it’s peak and then it starts to decrease, as the piston is moving away from TDC. Ideally, we want this pressure peak to happen somewhere around 12 deg ATDC.

This means that there always is a point in time when igniting the mixture makes best torque. This is called Maximum Brake Torque Spark, or MBT spark. In general it works like this:
  • MBT increases as engine speed increases
  • MBT decreases as VE increases
It’s important that for any given engine there is an MBT spark table, and it is “physical”, meaning that it’s the result of factory calibration on the engine dyno.

Moving away from MBT to either side means losing torque. However engines do not run at MBT spark all the time, mostly because knock (and several other factors too, but we’ll skip them now). For heavier loads knock starts to happen long before we are at MBT, so a compromise is necessary. There’s some ground to gain by running the engine richer, but only so much.

Now that we have described the three torque factors, let’s move on to torque management.

All modern engines have electronic accelerator pedal, which is translated into Driver Demand, or, to put it simply - how much torque is requested by the driver. The driver here is merely one of the requesters, alongside with A/C, transmission, ESP (VSC) etc. So the ECU balances these requests and produces a solution, translating it to certain commands to the controlled outputs: throttle plate motor, injector pulsewidth and spark system.

We can put it like this:

Produced TQ = TQ(VE) + TQ(AFR) + TQ(SA)

Here’s where the spark efficiency shows up. If we want to up the VE, we open up the throttle more, letting more air into the engine and add more more fuel to keep the AFR stoich. Works as we increase Produced TQ, but mileage suffers. If we want to have more torque by using best-power AFR we have to move it from stoich to rich (which is normally totally not controlled by the driver), but then emissions and mileage suffer. We can run our spark as close to MBT as we want, only keeping an eye for knock, and that would be free.

This is why running good octane gas is important. Better gas > Less knock > Higher SA > More TQ(SA) > More Produced TQ.

So what if we manage to increase the TQ(SA) but we actually don’t need more Produced TQ? Well, we can decrease TQ(VE) at the very least, close that throttle more, use less fuel. All from just increasing the spark efficiency. No magic, just physics. That is why a properly tuned street engine has both better power and better mileage – it’s simply more efficient.
 
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