engie
Posts: 5554
Joined: 7/9/2006
From: Jackson/Starkville, MS
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Ok...just got done with 1.5 hours with professor #1, WHEW...
It's really difficult to relate practically to a "formula" engineer which I now know this guy is. A "formula" engineer is a person that spends time/has understanding dealing in theoreticals. Their knowledge is "in the paper" so to speak. I'm more of a "mechanic" engineer in that my knowledge is almost strictly practical. Basically, we just go about determining the "answer" in different manners which makes conversation/relating very difficult.
Anyway, what I ended up with is as follows.
The first major problem with my theory is that "Heat" and "Temperature" are NOT the same thing. Heat is the inverse of work, while Temperature is actually used to find both heat and work, which leads me to the first couple of formulas.
Energy in = (heat - work)out
This is another way of defining efficiency. The output energy lost to heat is what causes inefficiency within the system. Thus, we see why heat is our enemy. For gasoline engines, about 35% efficiency can be expected. This means that for every $100 you put in your gas tank, only $35 is actually driving the vehicle. $65 is being lost to heat. Anyway... Moving on...
Work ~ P*V=N*R*Temp
P = pressure
v = volume
n = number of moles, or a constant related to molecular mass
R = universal gas constant for ideal gas
Temp = temperature
This is the ideal gas law, which is essentially what we assume we are dealing with here. In order to be "ideal", however, we must run at stoichiometric ratio(14.7:1), which is less than ideal for maximum horsepower. Thus, we will assume that we are running a constant A/F ratio at 12.5:1. It's important to note that the A/F ratio must be CONSTANT for the following statements to be accurate. If the A/F ratio is varying, it will change the pressure and volume in the cylinder, and the following assumptions can not be made.
Ok, now a major factor that we are neglecting is ambient(outside) temperature. The reason we can neglect it is because we are only trying to tune to perfection for "today". However, it's important to note that the timing will then be less than optimal when the temperature raises/goes down. That's just a problem for another day...
Ok, we know that spark "advance" is the technical term for the amount of time before TDC that the spark must fire in order to achieve maximum combustion pressure at TDC. The advance, measured in *, are the degrees that it takes the crankshaft to reach TDC after the spark is fired and the combustion process is began. This degree amount is directly proportional to the change in volume, deltaV, that the piston encounters between the time the spark is fired and it reaches TDC. OK. That leads me to my next formula...
deltaV/time is related to RPM, thus
RPM = c (deltaV/time)
C is an arbitrary constant that must be determined through analytical means...more later
time = the amount of time between when the spark fires and the combustion process reaches maximum pressure AT TDC...
deltav = the change in volume between when the spark fires and the combustion process reaches maximum pressure AT TDC
Ok, since we have clearly have a change in volume and time, depending on how much spark advance is required, they are the only variables. OK.
Well, we can analytically determine all of these factors at TDC, since it is essentially a constant and will be the same everytime. The problem lies in the variation within the advance...
DeltaV = V1 - V2 = N*R(temp1/p1 - temp2/p2)
This is derived using the equation for ideal gas that we determined earlier in the problem, and in trying to determine the change in volume...
Ok, combining the equations we determined earlier, this then becomes
Time = [C * N * R{(Temp1/P1) - (Temp2/P2)}] / RPM
Time = the amount of time it takes for the piston to reach top dead center from the time the spark is fired
C = same arbitrary constant we determined earlier that makes RPMs = the change in volume / time, instead of just being relational, this number makes them equal, and must be determined analytically
N = constant related to number of molecules in cylinder
R = universal gas constant
(temp1/p1) must be determined, and is the only variable in this equation other than the time, which is directly relational...
(temp2/p2) is a constant that we can discover analytically by knowing the temperature and pressure at TDC
RPM is obvious...
Using the above formula, we can solve for time in terms of the temperature and pressure at the point in time where the spark was fired until the piston reaches TDC...
This was as far as I got with him today. So, we know everything except your temperature and pressure when the spark actually fires, and the amount of time it takes it to go from that point up to TDC...
This time is a linear condition in relation to RPM. Thus for twice as many rpms, the spark must fire twice as early, assuming the same load. So, we only have to find the time in two separate conditions and we will know the time for all conditions.
Using this amount of time, your an algebra problem away from determining the true optimal advance. Knowing the Time that the piston travels between the Spark and TDC, and RPMs, you can then determine the distance that the piston travels in the given amount of time, and then you simply relate that motion back to circular motion to determine the actual advance...
Like I said...WHEW... Confused myself at least 10x in the process of writing this, so I don't really expect anyone to fully understand this just yet, but simply to have it as a reference in the future if they ever get the urge to determine any of this stuff. After a few days of thinking about it, I'm suspicious that this will become much more easy to understand...This formula should work on all possible engines....
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RE: wideband commander - 
Oh my, that's just Great right there!!! LOL!
...You sound like me John....Not a new baby , but I do have FOUR kids that are like a money Black Hole...and just last week...My 20 year old daughter tells me..she's pregnant....so I guess we will be having a new baby..... Grandpa at 40 years old...
