HHmmnnnn . . .
Dead space. It too is filled with the CFM flow. We call that "clearance > >
You create some of the more fun questions here Grant!
A few people seemed to have touched on the answer, but no one seems to have made it clear. Let me try.
The problem lies with the dead space at the top of the cylinder. You can't calculate the CFM unless you also have an good measure of the effective volume of that dead space (and I have no clue what is typical).
The problem Grant, is what Pete says here. Not all the air in the stroke actually gets pushed out into the tank. The worst case is that none of it gets pushed out. But even with the normal case, not all of the air which was in the stroke volume, will get pushed out.
The calculations that Pete posted yesterday I believe were invalid because they seemed to be based on the assumption that CFM was a measure of compressed volume (which is a good guess - but just not true).
Lets do an example with simple numbers. Lets say we have a stroke volume of 90 cubic inches, and 10 cubic inches of dead space (not trying to be realistic here). This means that the 100 ci of the cylinder gets compressed down to 10 ci at TDC. So the pressure will go from 15 PSI, to
150 PSI in this compressor. That means that the max it can do is 150 PSI. At 150 PSI, no air will go into the tank per the exmaple Pete gave.At 140 PSI of tank pressure, the air won't start to flow until the cylinder pressure reaches 140 PSI. 140/15 is 9.3e so that's a 1 to 9.3 compression ratio we need. But because the piston must compress both the stroke volume AND the dead space volume, we need more than 1:9.3e of stroke compression. We need enough piston movement to create a 1:9.3e compression on that 110 ci of air before air will start to flow to the tank. The cylinder volume needs to be reduced from 110 to 110/9.33 or 11.79 ci before air flows. From that point, the stroke is only 1.79 ci away from TDC. So as it pumps the air out, the pressure effectively stays at 140 PSI, but only 1.79 ci of air gets pumped out. The rest stays in the dead space and doesn't go into the tank.
1.79 ci of air at 140 PSI, is the same as 1.79 * 9.33 = 16.7 ci of air at 15 PSI.So where the stroke of this example was 100 ci per stroke, the air moved per stroke was only 16.7 ci when the pressure reached 140 PSI. So the efficiency of the compressor drops as the pressure rises. And it's all because of the dead space at the top of the cylinder. The larger the dead space, the faster the CFM numbers drop as tank pressure goes up.
Now I assume for air compressors, they attempt to minimize that dead space. But with a reed valve popping open, there must be some "blow back" as air in the reed valve area pushes back into the cylinder as the piston starts to fall and the valve closes. Or in other words, the area created by the opening of the valve, adds a little to the dead space.
At the same time, I wonder if too little dead space might be a safety concern? The compressor can only take so much pressure before blowing up or breaking a connecting rod, and one simple sure way to limit the max pressure is by intentionally including a little dead space. Like the numbers I used above the system was limited to 150 PSI. Maybe for a 120 PSI compressor they might limit the pressure to 200 PSI by adding a little dead space for safety reasons? They way, even if the pressure cutoff switch malfunctioned, the pressure could not go above 200 PSI even with the motor constantly running?
None the less, the only problem with Grant's numbers that I can see, is that he didn't include the effect of the dead space at the top of the cylinder. With the tank pressure at 0, his calculation should be close to correct. But as the tank pressure rises, the CFM numbers will drop. Without knowing the effective volume of the dead space, you won't be able to calculate how much the CFM drops.
But since he has a number for the CFM, we should be able to calculate the dead space.