1/3s and Dissimilar Tank Volumes

[xiSkiGuy]

So from my Cavern and Basic Cave classes I feel like I understand how to match thirds with dissimilar tank volumes. For example:

Diver A has LP-85s with 3400psi
Diver B has E8-130s with 3500psi

To prevent the team from penetrating beyond a point where Diver A's gas supply could get both divers back to open water if Diver B lost all his gas, we limit Diver B's third to match the volume of the third of the smaller tanks:

LP-85s: 170cf / 2640psi x 100 = 6.4 cf per 100psi.
We round 3400psi down to 3300 and divide by 3 to get thirds = 1100psi
In LP-85s 1100psi = 70.4 cf (6.4 x 11)

So we now limit Diver B's penetration volume to 70.4cf:

E8-130s: 260cf / 3442psi x 100 = 7.5 cf per 100psi
70.4 / 7.5 x 100 = 938psi.
So rounding down we limit Diver B's penetration to 900psi.
3500 - 900 = 2600psi turn pressure.
Now each diver has enough gas to exit the cave on a third and has a a big enough third in reserve for their buddy (or themselves if the had to isolate and exit alone).

It all makes sense to me, but I have been wondering: Can you do it another way that gives Diver B (who has a higher SAC rate) more penetration volume and is as safe as if both divers had the same size tanks?

Does it work to have Diver A keep a reserve that is equivalent to Diver B's third?

Using the same example: Diver B's penetration volume is 1100psi. In E8-130s 1100psi is 82.5 cf (7.5 x 11). So Diver B needs 82.5cf to exit the cave if he loses all his gas right as he turns on thirds.

So what if Diver A finds his turn pressure by reserving 82.5cf and halving the remaining supply:


82.5cf / 6.4cf = 12.89cf x 100psi = 1289psi.
Call it 1300psi.
3400psi - 1300psi = 2100psi.
2100psi / 2 = 1050psi (round down to 1000psi).
3400 - 1000 = 2400psi turn pressure.

This gives Diver A 154.5cf to exit the cave. This allows 82.5cf for his buddy and 72cf for himself. He used 64cf getting to thirds.

Diver B uses thirds and has 180cf to exit the cave. This allows 82.5cf for him and 97.5cf for his buddy.

Both divers have enough volume at two thirds to get themselves and their buddy out. Both have enough to isolate and exit alone on one tank.

Am I missing something that make this unsafe?

Before anyone comments, this academic exercise assumes the dive is a cave where thirds are appropriate (into highflow). And yes, currently I only have a Basic Cave cert, so I limit my all my cave dives 1/6 of doubles.

 

[karstdvr]

I am not going to comment on your math,but I would add one variable to your plan. 1/3rds is a bare minimum,that is assuming nothing compromises your exit such as a silt out or restriction,nobody gets excited and SAC rate elevates,and anything else Murphy will throw at you. Sheck used to comment that 1/3rds was overly liberal and wouldn't guarantee an exit 100% of the time. So just as a decompression software has a conservatism factor,why kind of conservatism does one want to build into these situations

 

[xiSkiGuy]

1/3rds is a bare minimum,that is assuming nothing compromises your exit such as a silt out or restriction,nobody gets excited and SAC rate elevates,and anything else Murphy will throw at you. Sheck used to comment that 1/3rds was overly liberal and wouldn't guarantee an exit 100% of the time. So just as a decompression software has a conservatism factor,why kind of conservatism does one want to build into these situations

Definitely a good point to keep in mind. That is what I was trying to account for when I qualified the situation with: "this academic exercise assumes the dive is a cave where thirds are appropriate (into highflow)." But your point is also: Why remove some of the conservatism involved with the traditional calculation? Got it.

 

[karstdvr]

Nothing wrong with your suppositions. Before 1/3rds we had 1/2 +200,until somebody came along with something better.

 

[Scuba_Steve]

Not sure exactly what you're saying since thirds as above is calculated and will work irrelevant of SAC rate.

If I see what you've done correctly, Diver A first turn pressure is 2300psi, in the second example it is 2400psi which is more or less a result of where in the calcs, you're rounding off (the 100psi difference). When you see how little cf it is on top of that, I don't see a reason to further complicate because I couldn't tell a 6cf difference on my rather inaccurate gauge.

Maybe I'm not seeing what you're asking, but that's how I see it.

 

[xiSkiGuy]

Not sure exactly what you're saying since thirds as above is calculated and will work irrelevant of SAC rate.

If I see what you've done correctly, Diver A first turn pressure is 2300psi, in the second example it is 2400psi which is more or less a result of where in the calcs, you're rounding off (the 100psi difference). When you see how little cf it is on top of that, I don't see a reason to further complicate because I couldn't tell a 6cf difference on my rather inaccurate gauge.

Maybe I'm not seeing what you're asking, but that's how I see it.

It is Diver B who benefits from my math. He has the higher SAC rate and gets to use 1100psi (>82.5cf) penetration volume as opposed to 900psi (<70.4cf). He'll probably still be the one who turns the dive.

 

[Scuba_Steve]

I see your math, and I know it's just academic for you. 1/3rd's is way too balsy for me anyway you wanna slice it.

 

[in_cavediver]

It is Diver B who benefits from my math. He has the higher SAC rate and gets to use 1100psi (>82.5cf) penetration volume as opposed to 900psi (<70.4cf). He'll probably still be the one who turns the dive.

Well remember the idea behinds thirds. You want to make sure that at the furthest penetration, each diver will have enough gas to get him and his buddy out. The second, and often overlooked part, is it has to be simple to implement and understand. I know of a couple different ways to do this. My preffered method is the traditional match by volume with is nice for me. I have 8cf/100psi, my wife has 6cf/100psi. Simple math, I can do it on the fly and it works. The other methods using tables or complex formula are simply to complex for me to want to use. (screwing it up could really make it a bad day)

I mean really, if you don't like the thirds you get, carry a stage!