3) In addition to what S starfish said, diving independent double tanks takes a bit of self-discipline. The 'right' way is to keep switching back and forth every 500 psi so you breathe both down evenly. Easy to do, just isolate your tanks. Tried it, forget it.
Not quite. The important thing to consider in managing independent doubles is to ensure you have enough left in either thank to turn the dive and get back to your exit point or first deco stop if you lose the contents of the other tank.
It is not as hard as it sounds. If for example you have 3000 psi in each tank, you'd use 1000 psi (1/3rd) out of the first tank, switch to the second tank, and use 2000 psi (2/3rds) out of the second tank, then switch back to the first tank to use the second 1000 psi out of it (1/3rd). Once you reach 1000 psi in the first tank you should be at your exit point or first deco stop with 1000 psi (1/3rd) left in each tank.
This ensures that at your maximum point of pentration you have used 1/3rd of the contents of each tank and have 2/3rds remaining in each tank - enough to get you back out on one tank. or you and your buddy back out with each of you using one tank. It also means you only make 2 switches during the dive - a lot simpler than switching every 500 psi - and the difference in contents is close enough that you do not end up with trim issues.
If thirds are not conservative enough, you adjust accordingly with the same ratio - X psi out of the first tank, 2X psi out of the second tank, and finally X psi out of the first tank with the rest of the contents of each tank in reserve. Obviously you need an SPG on each first stage.
Manifolded doubles are not always an option in some destinations and neither is shipping your doubles, so it is worth knowing how to dive independent doubles. Side mounts are also becoming popular and they are in essence independent doubles.
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I agree that diving doubles means nothing if you are not willing to turn the dive if you have a failure. If you have a failure you no longer have a fully redundant system and if you are in conditions where doubles and that level fo redundancy are requires, the dive is over.
That said, if an instructor also had a pony and was in an open water situation, it is not necessarily a sin to continue the dive with one post shut down. He would have at least as much redundancy as any of the single tank students and in an OW situation would not need any more. The doubles with one post shut down become essentially one big single tank and the pony with its additional second stage is still available if the need arises to share air.
The real issue is not having an SPG and from a standards perspective that should have been reason enough to call the dive. But to be fair, and to step back from the armchair/keyboard quarterbacking of the issue, it depends on the situation. If the 2nd dive is shallow and you know from the results of the first dive that you are in the water with hoover students some of whom will be bingo on air long before you are, a case could be made that it was not an unsafe thing to do as he also had a pony in reserve.
The alternative here would have been to scrub the dive, get out of the water and make all the OW students come back some other day to finish. A inconvenience and additional expense for all involved so I can understand (if not agree with) the instructor's motivation to do a cost benefit analysis and decide to continue the dive.
The thing I still do not have a complete handle on is his configuration -normally the dry suit gets run off one post and the wing gets run off the other, or alternatively a separate inflation bottle is used for the dry suit - but this is not the same as a pony as it has no second stage and if there was no pony, the dive should not have continued.
Bouyancy wise, given that it is dive 2 and he is on the last half of the doubles with half the original swing weight from the gas, it's possible to do the dive with just the drysuit unless he is excessively over weighted.
I short, without more information its hard to determine whether is was truly unsafe as oppsed to something that violates the standard requiring an SPG.
More importantly, from the student perspective, now is as good a time as any to understand that you, not the instructor or DM, is ultimately the person responsible for determining if a given dive is within your comfort zone. If the instructor's decision to continue was not something you were comfortable with, you should have spoken up and if the instructor still persisted you should have gotten out.