Thirds Question

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kkoski

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Recently, as an intro cave diver, I decided to practice calculating thirds with dissimilarly sized tanks. Confidently I made up a problem for myself:

Diver A is diving twin HP 100's filled to 3000 psi at the beginning of the dive. Diver B is diving twin HP 120's filled to 2800 psi at the beginning of the dive. What is the turn pressure of each diver?

Here's how I solved the problem:

First, I worked the problem for single tanks: the turn pressure for one single tank at 3000 psi will be the same as the turn pressure for two connected HP 100's at 3000 psi, which would be the same turn pressure for three connected HP 100's at 3000 psi, etc.

The dive should be turned when one diver has enough air in his tank to get both divers on the team out of the cave. The air Diver A requires to get out of the cave will be represented by A, likewise, the air Diver B requires to get out of the cave will be represented by B. We assume that Diver A requires the same air to get out of the cave as into the cave, so Diver A breathes A + A = 2A during the dive, likewise Diver B breathes 2B air during the dive. Each diver wants to reserve air for his buddy, presumably the amount the buddy breathed diving in, thus at the dive turn each diver should have A+B air in their tank, air for them (A or B) and air for their buddy (B or A). This quantity, which is in cubic feet, (A + B) tells the diver when to turn. The air in the divers tanks can be represented by:

Air in Diver A's tank= Diver A + ( Diver A + Diver B) = 2A + B (Equation 1)
Air in Diver B's tank = Diver B + (Diver A + Diver B) = 2B + A (Equation 2)

The quantity (A+B), in psi, is each divers turn pressure. This is what we want to find.

HP 100's have 35 psi/cf or 0.0286 cf/psi
HP 120's have 29 psi/cf or 0.0343 cf/psi

Diver A starts with 3000psi*0.0286cf/psi=(3000/0.0286)*(psi*cf/psi)=85.8cf
Diver B starts with 2800psi*0.0343cf/psi=(2800/0.0343)*(psi*cf/psi)=95.2cf

Plugging this in we get
85.8cf=2A+B (Equation 3)
95.2cf=2B+A (Equation 4)

From Equation 4:
A=95.2-2B (Equation 5)
Plugging Equation 5 into Equation 3:
85.8=2(95.2-2B)+B
85.8=190.4-4B+B
3B=190.4-85.8
B=34.8cf

From Equation 4:
A=95.2-2B
A=95.2-2(34.8)
A=25.4cf


The air remaining at thirds should be A+B or 25.4cf + 34.5cf = 59.9 cf

For Diver A this corresponds to 59.9cf*35psi/cf=2097psi
For Diver B this corresponds to 59.9cv*29psi/cf=1738psi


A quick check with the popular texts showed this was not the conventional way to calculate thirds. Thirds calculated conventionally would give Diver A's turn point as 2000 psi and Diver B's as 1921 psi.

Thirds calculated "my way" has Diver A turn the dive with a higher psi, while Diver B turns the dive with a lower psi. In real life, Diver A will be me, an air sipping lady, while Diver B is my beloved husband, an air gulping man's man. Since "my way" has the person with the higher SAC turn the dive at a lower psi this would work out nicely for us.

The question is (for those of you who were starting to wonder) do you think it is any less safe to dive thirds in the above manner, as compared to two divers starting with identical tanks filled to 3000 psi and each agreeing to turn the dive at 2000 psi?

-Katrina
katrina@koski.net
 
That third is for you as well as for your buddy. You are allowing a diver to go past the point where he can exit on his own if he has to isolate.

If a diver at maximum penetration, ie 1/3 consumed and 2/3 left, has a failure requiring isolation he has access to 1/2 of his 2/3, or 1/3. This leaves him with enough to exit on his own.

By your method, after isolating the diver with the greater SAC has less gas remaining than he used coming in because he calculated for his buddy with a lower SAC and not himself. He doesn't have enough to get out on his own now. The buddy would still have enough air for both, but why add extra risk for a few hundred psi?
 
I agree...why re-invite 1/3s? When you start changing the guidlines that's when trouble starts.

Also I don't know anything about the training you received for your intro cave cert, but I thought you were supposed to dive to 1/6s when you are intro level?
 
Wendy,

Why would you dive at 1/6th when intro? Surely this is changing the rules.

Is it because the intro diver is more likely to freak out than a non-intro diver and thus use more air? when does an intro diver become a non-intro - # of dives, more certification?

Thanks - Dave.
 
Hey,

According to the NSS-CDS, in intro level ave diving, you dive with a single tank and follow the rule of thirds. (www.cavediver.org).

You can use double tanks for intro level cave diving with the instructors permission and I was told that that is when you would dive using the 'rule of 1/6s'. I'm not sure of the reasoning behind this, maybe someone else on the board knows. If I had to take a guess I would have to say it would be like diving a single tank, even though they are diving doubles, so it keeps everyone at that training level at the same limitations. But some instructors do allow intro students diving doubles dive at thirds depending on the cave and the flow.

As for when is a cave diver no longer thought of as an intro cave diver, I would have to say once they move on to apprentice cave diver, full cave, or cave 2. Its not a number of dives thing, its a training thing, because there are limitations to the different levels of cave diving.
 
Dude, your math is flawed. Where does 1700 PSI for diver B come into play? least cubic feet divided by three, subtract answer from beginning gas supply of both divers, 1/3's

And DLARBALE, one possible reason for intro divers diving 1/6's is that penetration is limited. This is a way to introduce cave in smaller pieces to build students up to the level of Full Cave. That's why they call it intro and apprentice.

It's like a Discover cave diving course.

On a side note, singles don't belong in overhead. Intro is taught in singles, which sets a poor example from the beginning. On this level, Gooey is superior to the other training agencies.
 
1/6th on doubles when only Intro certified. That is ok though, because you can easily run out of manline before you hit 1/6ths in some cave systems. For instance, on double steel 104's pumped to 3500psi, I was able to make it to the end of the Peanut Line in peacock, 1800 feet, and back and still had 2300 in my tanks.
 
The question is (for those of you who were starting to wonder) do you think it is any less safe to dive thirds in the above manner, as compared to two divers starting with identical tanks filled to 3000 psi and each agreeing to turn the dive at 2000 psi?

Katrina, once again, over-engineering comes to mind. :wink: You seem to be making it more difficult than it needs to be.

Start out by getting the baseline for the tanks you are using.

(Cubic feet/rated pressure) x 100 = Baseline for single tank
(Cubic feet/rated pressure) x 200 = Baseline for doubles

Your HP100's have a baseline of 5.7. You have 5.7 cubic feet per 100 PSI.

Say you are diving the HP100's with a starting pressure of 3600psi, and Jeff is using LP95's with a starting pressure of 3300psi. You have approx 205CuFt, Jeff has approx 237CuFt. Obviously, when you see the volume of gas, you know that yours is limiting. Your turn pressure is 2400psi, which means that you can use approx 68Cuft on the inbound leg. Take that 68 and divide it by 7.2(the baseline for double 95's), and you come up with 9.44(944psi). Round it to 900, and subtract that from Jeff's starting pressure.

Your turn pressure is 2400psi, Jeff's is 2400psi. You have the same turn pressure(although I didn't plan this little equation to work out that way - DOH!), but different remaining volumes. You have enough to get yourself out of the cave if you have to isolate, or both of you out of the cave otherwise. Jeff has enough to get himself out if he has to isolate, and more than enough to get you both out.

Mike
 
There is a way to calculate turn pres using the sac of both divers. I didn't look very close but I don't think you did it. It is very pretty math wise but relying on sac isn't a good idea IMO. You need to calculate this in your head or on your slate after your in the water and your tanks cool. Your going to limit each diver to one third of the smallest supply (volume). The smaller supply you just calc as normal. Round down to something divisable by three (this is a third) then subtract that presure from the starting presure. Now, what volume does that represent? Subtract that volume from the larger supply, figure the presure at that volume and that is turn. Just like in the NSS or NACD texts. I would guess they do it the same in the GUE text but I havn't seen it. To make calculations on the fly easier I figure cubic feet/100 psi for each tank size ahead of time.
 
Munin: Thank you, you're right, there would not be enough air left for self rescue. I totally overlooked that. Your answer-- "this is unsafe because..." was just what I was hoping for. What if you started with 2A+B air in the smaller tanks, and 3B air in the larger, and turned at (A+B) and (2B) respectivly? It's really a theoretical question at this point, because I don't think the turn pressure will differ enough from traditional thirds to make it worthwile.

Wendy: Yes, as an intro cave diver you are suppose to use 1/3rd of a single tank or 1/6th of doubles. However, you are not forbidden from practicing calculations of 1/3rds with doubles, which was what I was doing. I swear, I didn't even get wet! The exact calculation I posted was to find thirds for differntly sized single tanks, so I was even technically within the guidelines.

Also, as an intro cave diver I was planning on practicing with doubles in open water (I dove single tanks in my intro class). Since there are not many caves where I live my buddy and I were going to treat the open water dives as "cave dives" and use the dives to practice with reels, s-drills, thirds, bubble checks, etc.

Why reinvent thirds? I was practicing calculations for my upcoming full cave class, and I wanted to see if I could do the calculation with out looking at the book. The way I did the calculation made sense to me, at the time, but Munin pointed out the error in the method. I'm not going to accept something just because it's taught to me. I understand our rules (TGADL) come from accident analysis and we've learned from other's fatal mistakes. I respect that. But I'm still going to independently think about every method I choose to adopt in diving. If everyone blindly accepted NSS-CDS/NACD training there wouldn't be a GUE, would there?:)

Mike: Sorry you had to see more of my over-engineering. I can't help it, it's my nature:(

MikeFerrara: I didn't use SAC's. I totally agree that simplier is better for in water calculations.

GUE does do it the same way, except they also have a pretty cool "Battlefield" method (read: in water), where they use a "GUE Factor", which is ((tank size)/(rated pressure))*100 ps), rounded to the nearest whole number. For LP 121's (2640 psi) the GUE Factor is 9, for HP 80's (3500 psi) it's 5 (both GUE Factors are for doubles). You take the GUE factor * psi/100 to get the volume in the tanks. Since you are multiplying a two digit number by a GUE factor of 5,6,7,8,or 9 it's easy (easier) to do in your head. You do thirds, and then divide by the GUE factor to go back to psi. (If anyone can't live without knowing exact details, email me).

Thank you to all who replied.
 
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