How much usable air in an air compressor?

Question

I'm trying to figure out how long a small 3 Gallon compressor tank will last in between the compressor kicking on and off. I know the tank volume, and cut-in/cut-out PSI, and my approximate SCF usage per minute. So can I just calculate the SCF of the tank at the cut-in and cut-out pressure, and then subtract them to get "usable SCF"?

The cut-in/cut-out pressure are the tank pressure before the regulator, which will step the pressure down 40-100 PSI. But converting to SCF should accommodate for this, right?

I'm using SCF = ACF * (tank pressure + 14.7) / 14.7 (in cubic feet and PSI units), where ACF is the actual tank volume.

Then the "usable air" = SCF_cutout - SCF_cutin?

EDIT: Concrete example:
Tank: 3 Gallons = 0.4 cubic feet (ACF)
Compressor Cut-out: 150 PSI
Compressor Cut-in: 120 PSI

Tank SCF @ 150 PSI: 4.5 cubic feet
Tank SCF @ 120 PSI: 3.7 cubic feet
"Usable SCF" = 4.5 - 3.7 = 0.8 cubic feet <-- is this correct?

RE: regulator pressure, it will be between 20-80 PSI - but the conversion to SCF should account for that, no?

Long story short, if I'm using 2.0 SCF/minute constantly, with only 0.8 SCF available in the tank between compressor cycles, then the compressor will always be on, which is bad, right?

[all this is ignoring temperature for simplicity, which I acknowledge is unrealistic]

Answer 1

You should just measure the usage time through real world experimentation. This will give you the quickest and most accurate information at your real world set of conditions.

Empirical measurement methods will factor in all the variables of the system that may not be considered in a simple theoretical mathematical model. In fact the empirical method would be used repeatedly to verify any mathematical model while all the unaccounted variables are factored into the model.

If you do not currently have the air compressor unit on hand to do the empirical test you should consider one of:

1. See if you can borrow a similar compressor from a friend or colleague. It may be even easier to take your attachment gear with you to their shop or garage to do the test since for a test on a 3 gallon tank it will not take a long time at all.
2. Rent a unit from a rental yard for a half day. Schedule it so you can use it when you can also plan to use it for a regular task.
3. Take your gear with you to the orange colored BigBox store....many have rental sections....and explain that you are looking to purchase a unit from the store and ask them if they would help you run the empirical test right there in the store.