Walter,
I was worried that my responses were a bit verbose. You have eased my mind ;).
> ** 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.
Interesting, I suppose if you take the assumption that the engine is completely stopped, precisely at TDC and no vibrations or other forces exist to move the crank, then there would be no work accomplished. However, if any momentum is left over from the compression stroke, then the crank would continue to rotate, the piston would travel down the cylinder, the combustion gasses would expand, the engine would run and the maximum possible output would be achieved.
Contrary to your assertion, you would not have infinite ICP because the fuel does not contain infinite energy. However, the cylinder would experience the maximum possible ICP for the given fuel, which is good from the standpoint of efficiency. I will concede that with current materials and compression ratios, the engine would have a difficult time handling the temperature and pressure, but that is a separate issue.
**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.
You seem to be under the impression that a theta PP of zero will somehow cause the crank to stop at TDC. Consider the situation when pull starting you stubborn chain saw. One good pull gets several complete turns of the crank shaft even if it doesn't fire. In this 'real world' example, theta PP is just barely BTDC (the result of heat transfer and leakage). Yet the engine continues to turn and none of the bad things you have described comes to pass. Mr. Newton is still right about his second law. You just seem to have forgotten how to apply it properly.
**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.
I agree and I would suggest you re-analize your model of crank-rod geometry. If the mechanical energy absorbed by the piston is not equal to the mechanical energy absorbed by the crank (less friction, leakage, etc.), then you still have it wrong.
**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.
Actually, as I have stated previously, the timing is set to optimize power or to protect the engine. There is nothing magical about 16dATDC. It just happens that for the engine speed and configuration you generaly work with, best power falls in this neighborhood. Change the speed, the fuel or the engine and this value will change as well.
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.
For a particular engine at a fixed speed, temperature and cranking pressure, I agree completely.
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.
I think I have pretty well demonstrated my points and I don't want to devolve into pointless debate here on the list. If you still don't understand the fundamentals, contact me off line and I will be happy to help you with the concepts.
Happy new year,
Rob