Diving a single 80 I always figure Rock Bottom as 10 times depth +300. e.g. at 100 feet its 10X100 +300 = 1300 That works great for a multi level dive. Leave 100 feet at 1300 psi, leave 60 feet at 900 psi etc. I ran the exact numbers long ago using a SAC rate of 0.6 . Has the great advantage of simplicity.
I like Ian's idea the best, because I can't remember a lot of numbers but I wanted to validate it myself. So I made the calculation assuming:
1. 30 secs to swap reg
2. total SAC of 2 cu ft/min for the two of us. My ave California SAC is 0.75 and I peak at 1.3 so 2 is about right
3. 3 min safety stop
4. forget the deep stop
5. tank reserve of 300 psi. If necessary it can be breathed down to almost zero at surface.
6. ascent rate of 30 ft/min. The ideal ascent rate according to my Galileo Sol manual is faster than that below 60 ft and a little slower at shallower depths. For example at 128 ft the ideal ascent rate is 56 ft/min. So on the average 30 is conservative.
at a depth of D:
1. swap reg 0.5* 2 * (D/33+1) cu ft
2. ascent to surface (D/30) *2 * (D/2/33+1) cu ft where D/2 is average depth
3. safety stop 3*2* (13/33+1) = 8.7 cu ft
sum those up to get the RB in cu ft and to get PSI multiply by (nominal tank pressure)/(tank vol) = 3442/80, 3442/100, and 3000/77.4 for HP80, HP100, and al80 respectively.
so I did this on a spreadsheet and plotted the numbers vs depth. as you can see from above the formula is of the form aD^2 + bD + c in other words it's a parabola,
but the section from 0 to 100 ft or so can nicely be fitted by a line as Ian noted and 10*depth in feet is not that bad an approximation for the slope of the line fitting the parabola.
My only correction is that his base of 300 slightly underestimates the RB as calculated above. Here is the RB in PSI for the three tanks according to the assumptions above:
HP80 600+ 10*depth(in feet)
al80 500+ 10*depth
HP100 400+ 10*depth
For each tank you only have to remember one number, the constant of the line, the slope of 10 psi/ft being the same for the three tanks.
at 100 ft with al80 this gives a RB of 1500 psi in agreement with Aquaregia. At 66ft 1160 psi, and at 33ft 830 psi, compared to his 1000 and 600 psi.
Adam