Calculating Tank Size for Onboard Air? (1 Viewer)

[96TrailSurfer]

Perhaps of our ubiquitous rain, I got tired of hooking up my Viair 400P directly to the battery and decided to go with onboard air with ARB CKMA12. What I am trying to figure out now is the the size of the air tank required so I can fill all four tires in a minimum time. Either the tank will hold enough air to fill all of the tires, or as it gets depleted it will be topped up quickly enough by the compressor.

It has been way too many years since my university days, so I am having trouble with calculations.

Here my specs:

- tire size: currently 33" (285/75R16), but I want this to work for 35" (315/75R16)
- required fill pressure: from 10 to 15 PSI
- max compressor pressure: 100 psi (although it seems that it's possible to get it to 180 psi by overriding a safety valve)

By my calculations, a 33" tire is supposed to have around 118 L volume. Where I got stumped is how to use this information to figure out volume of air at the needed pressures, and the required tank size.

Any help? If you know how to figure this out, would appreciate if you could at least briefly set out the formula you used.

TIA

 

[GeologistFelix]

Most people don't set their onboard air up like this because it takes a gigantic tank, but let's do the math real quick.

V_Tank = V_Total - V_Tires
V_Tires = 118 L / Tire * 4 Tires = 472 L
P_Initial = 20
P_Final = 35
P_Tank = 100 PSI

Time to do some algebra!

(100 PSI * V_Tank) + (20 PSI * V_Tires) = (35 PSI * V_Tank) + (35 PSI * V_Tires)
(100 PSI * V_Tank) - (35 PSI * V_Tank) = (35 PSI * V_Tires) - (20 PSI * V_Tires)
65 PSI * V_Tank = 15 PSI * V_Tires
V_Tank = 15/65 * V_Tires
V_Tank = 109 L

So, you're looking at a 29 gallon tank if you want to air all four tires up from 20 to 35 (would be slightly different but similar for other start/end values) without the compressor having to kick on. Since it doesn't fill each one up instantly, because it's not a garden hose sized air line and tire stem, the pump will be able to keep up somewhat. I think a 20 gallon tank would probably air the tires up as fast as a 29 gallon one.

That said, you'd better hope the tank is full when you need it, because it's going to take around 8-10 minutes to fill the tank back up (10-12 if it's a 30 gallon tank instead of 20).