Hi all,
hardrockminer mentioned the Ideal Gas Law - PV/T = C. This is correct - the air/fuel mix is close enough to an ideal gas.
You also mentioned Boyle’s Law - P1*V1 = P2*V2.
And while both of these formula are correct, neither of them really apply in this case. And that's because when compressing a gas, it heats up. Boyle’s Law only applies for a set amount of air molecules (which we have) and a constant temperature (which we don't). And while the Ideal Gas Law does apply, we don't know the temperature. So when increasing compression, we can't simply change PV/T = C, since we don't know what T is changing to.
For cylinder compression, the best method to calculate the final pressure and temperature is assuming adiabatic compression. This assumes that no gas or heat enters or exits the system, and the only work that enters or leaves the system is that of the compression. So instead of the standard ideal gas law that uses temperature (PV/T = C) we use the polytropic process formula - PV^n = C, where n is about 1.4 for air in an adiabatic process.
We know the staring pressure and volume, so our constant is:
P1V1^n = C = 100,000 Pascals x (0.0001 m^3)^1.4 = 0.2512
Now that we know our constant, we can use P2V2^n = C to calculate our final pressure:
0.2512 = P2V2^n = P2 x (0.00001 m^3)^1.4
=> P2 = 0.2512/( (0.00001 m^3)^1.4) = 2511886Pa
That's 25.2Bar or 364 psi.
Of course, you'll never see that kind of number on a real engine. The polytropic process formula assumes that no air or temperature leaves the system - you will get some air escaping through rings and valves, and you will get a small amount of heat leaving the system (though only a very small amount for a fast compression like you will see in an engine).
More importantly - at speed, the starting pressure is lower as the cylinder acts as a vacuum to suck in the air, and even at 10:1 the valves don't open close exactly at bottom dead centre. So your starting pressure is lower, your compression ratio isn't truly 10:1.
Does removing volume from the combustion chamber have a linear effect on measured pressure? Is there any reliable relationship between measured volume and measured pressure?
Does that mean that every cylinder, no matter its volume or design, will have the same volume ratio and pressure ratio? I am pretty sure that this is not the case, as changing the cam profile will change the pressure readings. Is there a dependable relationship between the two?
The bottom line is that the relationship between volume and pressure is *not* linear. It would only be linear if the temperature did not change, which is not the case. For a given compression ratio the final temperature can be calculated regardless of cylinder design - but as you mentioned, changing the cam profile will change the pressure readings. That's because the cam profile will change the valves, and will effectively change the compression ratio.
There is no dependable relationship, as there are too many moving variables. The shape and size of the valves change the starting pressure, and the design of the cam changes the effective compression ratio. Throw in the heat and pressure from combustion, and everything changes again.