There are easy formulas which you are probably aware of for this. You can print out cheat sheets which can be easily laminated and put in your wet notes to do the math on a boat for a double check or an instabuddy.
No need for cheat sheets, tank factors are pretty simple in both concept and execution.
For example, if you are diving double 95s you just need to know the capacity at a given service pressure. A 95 holds 95.1 cu ft at 2640 psi.
Divide the capacity by the service pressure and take it times 100 and you get the tank factor: (95.1/2640)(100)=3.6.
Since you are diving doubles, you double the tak factor: 3.6x2= 7.2
What that means is that each 100 psi = 7.2 cu ft.
An X8-130 holds 130 cu ft at 3442 psi and if you do the math you get a tank factor of 7.5 for double 130s. You'll notice it is very close to the tank factor of double LP 95s as their internal volumes are very similar. In fact you can use the tank factor to see what doiuble LP95s willhold if cave filled to 3600 psi. 36x7.2= 259 cu ft.
An X7-100 on the other hand holds 100 cu ft at 3442 psi and double 100s have a tank factor of 5.8, which is a significant difference.
In technical diving, your reserve gas is also in essence your buddys reserve gas, so you alwyas want to ensure you have enough gas in any set of tanks to get anyone on the team out. That's what is meant by gas matching.
Lets say you are diving with 130s and your buddy has 100s and they are all filled to 3500 psi. 1/3rd of your gas supply is considered the minimum reserve so you use a third going in ,a third exiting and athird in reserve. SAC rate is not the big concern, what is the big concern is the concern is that you both turn on the same volume of gas and with different tanks, that third is different. Normally you take the first pressure divisible by 3and divide it by three to get your "third" . In this case 3300/3=1100 per third for both the 100s and 130s.
However, 5.8x11= 63.8 cu ft while 7.5x11=82.5. This creates a problem as if the diver with larger tanks used 80 cu ft of this third going in and then had a problem and lost all his gas,, the 63 cu ft the diver with the smaller tanks has in reserve will not be enough to get the other diver out of the cave.
So you take take the smallet third on the team (63.8 cu ft) and divide it by your own tank factor to get the number of Ppsi for yopur third. 63.8/7.5=8.5, or 850 psi. So rather than turning at 2400 psi (3500-1100=2400) you will turn at 2650 psi (3500-850=2650).
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In the real world, to keep the math simpler, it works like this.
1. The diver with the small tanks notes he has 3500 psi in his 100s, figures out he will use 1100 psi per third and takes this times 6 (rounds up 5.8) and decides he has a 66 cu ft third. (Or if he is a bit better with numbers, will take 5.8x1000 = 58, then add 5.8 cu ft (the left over 100x5.8) to get 63.8).
But we'll assume he is math challenged and call it 66 cu ft as the 2.2 cu ft difference will probably get lost in the noise of gauge error anyway, and in this case you are already discounting 1/3rd of 200 psi from the third calculation by using a start pressure of 3300 rather than 3500, creating a 1 cu ft pad. (But in the real world, again the diver with 100's will quickly memorize his thirds at common fill pressures.)
2. The diver with 130s also notes he has 3500 psi, rounds down to 3300 and normally would have an 1100 psi third, turning at 2400 psi. But he knows the other diver has smaller tanks, and upon figuring/learning the size of that third, takes the 66 cu ft and divides it by 8. Being a little math impaired himself, he knows 8x8=64 (800psi) and that 64 is close to 66 (and more conservative) so he will turn after using 800 psi (at 2700 psi).
As long as the person with the big tanks rounds up on the tank factor he uses to figure his turn pressure, any rounding errors tend to come out in the wash. In this case, the diver with 100s really has 64 cu ft thirds and after all the rounding, the diver with the big tanks is turning only 50 psi on the conservative side of his actual 2650 turn pressure - and that 50 psi difference is more precise than the accuracy of his SPG.
So...you can keep the math simple and figure in your head in the water just before you ascend.
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To add another wrinkle, lets say the guy with the 130s got a bad fill or already did a dive and only has 2200 psi 22x7.5= 165 (or round down to 7 and get 154). Either one is less than the 200 cu ft the guy with the doubel 100s has, so you will turn on the volume of tanks with the least gas in them - in this case the underfilled 130's.
He starts wth 2100 psi and estimates 700 psi thirds. He is conservative and takes it times 7 to get 49 cu ft, or knows that the leftover .5x7=3.5 more cu ft and adds it in to get 52 cu ft.
The guy with the 100s takes that 52 and divides by his tank factor of 5.8 (and rounds up to 6 to be conservative) to figure that 6x8=48 (800 psi) and 6x9=54 (900 psi) and dedcides to split the difference with an 850 psi third. 3500-850 means he will turn at 2650 psi rather than 2400 psi to ensure his reserve matches his buddy's reserve.
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It is pretty easy if you do a little practice at home to get comfortable with how to set up the equations in your head. Do the math first, then do it in your head rounding and using using digit tank factors in either one or two steps to see how it works. If you are still struggling, Mark Vlahos here on the board has an excel spread sheet with tank factors and turn pressures for most tanks in a matrix format.
