Rob:

For starters, let's confirm some common understanding of some definitions:
1) ICP - internal cylinder pressure.
2) thetaPP - the angle in degrees from TDC of the crank when the peak pressure of the combustion event is realized. Theta is negative before TDC and positive after TDC. For example, timing is set at negative thetas and the peak pressure is realized a positive thetas. TDC = thetaPP zero
3) Peak pressure - the point at which the combustion chamber is under the highest pressure from the burning charge and/or compression. This is at the point where one half of the charge has been burned (according to the accepted, authoritative engineering texts).

In response:

**Consider a perfect ottocycle engine with perfect fuel. Mechanically the engine can survive whatever pressure the fuel can generate and the fuel burns infinitely fast. In this perfect world, with no cylinder leakage and no heat transfer, the cylinder pressure at any theta after ignition on the power stroke is always the same, no matter where ignition takes place.**

I'll agree with you. That doesn't exist. <vbg> I have no data on or knowledge of that engine, so whatever you say is unarguable.

** If the fuel is ignited at TDC, then the entire charge is combusted at TDC and Theta PP is also at TDC. Now, the piston sees the maximum possible pressure force at every inch of downward travel. Energy is force times distance so this has to extract the most shaft power from the fuel charge.**

There's one BIG problem with that statement. If that case were to exist, NO WORK would be accomplished. You would have an infinite ICP with a thetaPP of Zero and NO piston movement at all. The engine would not run. This is what happens in pre-ignition to destroy the engine--the thetaPP approaches TDC until the increasing ICPs exceed the strength of the combustion chamber and it fails.
 
**If we ignite the fuel prior to TDC, then theta PP still occurrs at TDC. We still see the same energy extracted from the fuel charge as we did at TDC, however we now have to do additional work on the compression side due to the higher presure of the precombusted fuel. Thus the net shaft power of the engine is reduced.**

Nope, NO work would be done if the thetaPP is at TDC. The conrod angle is zero and the piston will not go down--the head will come off! In your mythical engine above, there will be a BIG explosion, NO piston movement and it will get HOT--unless Sir Isaac Newton was wrong about the Second Law.
 
**Next, consider the condition where ignition and theta PP are delayed until ATDC. During the period of crank rotation between TDC and ignition the piston is driven with only compression pressure. As this pressure, and the resulting piston force, is much lower than the combustion pressure would have been, less energy is imparted to the piston over this distance and shaft power is reduced accordingly.**

There seems to be a misunderstanding of the effects of mechanical advantage of crank-conrod geometry. Either I do not understand your premise , or you're missing something very basic.
 
**To extract the most energy from the combusted fuel during the power stroke, theta PP should still be at TDC. Unfortunately, nearly all of the fuel would have to be burned BTDC and the addtional compression pressure would absorb substantially more energy on the compression stroke, greatly reducing the net shaft power. Accordingly, ignition is timed to provide for a minimal amount of combustion BTDC to mimimize the compression stroke power requirement and a minimal theta PP to maximize power stroke power. The faster the engine turns, the bigger the compromise.**

With all due respect, no. The timing is set to optimize the thetaPP at as close to 16dATDC as possible, not as close to TDC as possible. In fixed timing applications the timing is a compromise to result in a thetaPP that is closer to TDC at takeoff than optimal and further form TDC during cruise. The solution to this is being able to move the timing on the fly so the thetaPP is always occurring at the optimal crank angle of 16dATDC.... (according to Taylor and Heywood, two of the acknowledged experts). For example, if the thetaPP is 10 and all you do is alter the timing so it moves to 16, HP output will go UP. If the ThetaPP is 20 and you move the timing to make the thetaPP move to 16, HP will go up. That's not just theory, it's measurable. It's one of the biggest reasons to have moveable timing. There are three ways I know of to do that. 1) measure many parameters and calculate the estimated thetaPP, 2) estimate the timing needed, or 3) MEASURE the thetaPP and adjust accordingly. #1 is what the auto industry and TCM's FADEC are attempting to do. (requires a lot of sensors and data crunching.) #2 offers some very engaging advantages over mags, but isn't confirmable as optimal to an outside observer. #3 is not yet commercially available, but appears to be the holy grail--simply, directly measure that which you need to know and adjust accordingly. Easier said than done.

** Consequently, it should be clear that there is no universal value for optimal theta PP or even the ratio of burned to unburned fuel at theta PP. These values change for different engines as well as different speeds on the same engine.**

Taylor and Heywood disagree with that. They are two of the most respected, authoritative combustion technology text authors out there.
 
Walter