How can I calculate the running time of my compressor knowing the CFM rate of the compressor motor, tool, and tank size?

So, I actually have a real world application for the things my calc teacher tried to shove into my head, unfortunately it's been ten years since I took the class, and it all leaked out.

That being said, I'd like the calculate the duty cycle of my compressor. I have all sorts of numbers that I think I can use to figure it out, I just don't know how.

Also, I'm assuming a spherical compressor.

• Tank Volume - 26 Gallons
• Motor Output - 4.1 SCFM @ 90 PSI
• Motor cuts on when pressure is 90 PSI
• Motor cuts off when pressure is 150 PSI
• Tool Consumption - 2.3 CFM @ 90 PSI
• The air to tool outlet is regulated to 90 PSI

I believe that I can just say "2.3 over 4.1 is ~56%" and know that my compressor will run about half the time I'm using the tool, but I'd be curious to know the math to work out how long it will run to get from 90 PSI back up to 150 PSI and how long it will take to drain from 150 PSI back to 90 PSI.

1 Answer

After some research, I think I've found the solution, and it doesn't involve calculus!

Using boyles law (P₁V₁ = P₂V₂), I can calculate that at 150 psi, my 26 gallon compressor equates to a virtual 43.3 gallon tank at 90 PSI. (150 * 26 / 90 = 43.3).

My Compressor will kick back on when it reaches 90 psi, and that will be when I have brought the size of my virtual tank back down to 26 psi (the actual size of the compressor), so I will have used 17.3 Gallons of air. (43.3 - 26 = 17.3)

Since my compressor output is regulated to 90 psi, and the tool I'm using uses 2.3 CFM at 90 psi, I know that my virtual tank is loosing 2.3 CFM. If I convert the 17.3 gallons of air I have used to cubic feet, I get ~2.312674 cubic feet of air.

Since I will use ~2.3 f³ of air between the 150 PSI and 90 PSI, and my tool consumes that in 1 minute, my compressor will cycle on for slightly more than one minute. Since the tool uses slightly more than half the amount of air that is compressed while the compressor is off, then I can assume that the compressor will cycle off for slightly less than one minute.