Wow - I can't believe the controversy this has started. Everyone is making this far more difficult than it needs to be. Assuming a safe ascent rate to the safety stop depth, there are only two possible scenarios:
1. - any time we are under water we are taking on excess nitrogen that our body can't process. If this is true as some have asserted, then a safety stop would do more harm than good. Let's refer to the amount of nitrogen one has in their body, after the dive (regardless of depth), as "x". If, at safety stop depth, the body is still taking on excess nitrogen at the rate of "y" per minute, with "y", by definition, being a positive number, after a 3 minute safety stop the amount of nitrogen in the body would be x+3y, which any day of the week is greater than "x". After a 5 minute safety stop the amount of nitrogen in the body would be x+5y. Therefore, after completing a safety stop the amount of nitrogen in the body is greater than before the safety stop.
-or-
2. - that the body can efficiently handle and expell nitrogen up to a certain depth. Lets call this depth "d", since the actual depth is not only open to controversy in this forum but will, in fact, differ from diver to diver. Once someone goes below "d" depth, they take on excess nitrogen at a rate which their body is incapable of expelling it. When they get back to "d" depth, they have a certain amount of nitrogen built up. Once again let's call that amount "x". Once they rise to above "d" depth the body is now processing and expelling gas faster than they are taking it on. Let's call this rate "y". It is also agreed that at "d" depth one will expell gas slower than at d-1, and at a depth of d-1 the body will process it slower yet than at d-4 or d-10 (those are minus signs, not dashes). Therefore, the rate at which someone can offgas can be expressed as y=(rate of nitrogen expulsion at current depth - rate of nitrogen intake at current depth). This means that at any time one is above "d" depth, they are offgassing. It also dictates that any safety stop must be above "d" depth and must be for a length of time that compensates for the "y" factor in the equation above.
I think that TSandM was the one who put forth the notion that there is a curve, and that as depth decreases the ascent should be slowed. This means that nitrogen is more capable of being offgassed at shallower depths (i.e. comes out of solution quicker) but that the body's ability to expell it is either constant or that it is on a curve as well, but less of a curve, requiring more time to process it. It doesn't matter which of these is true, or in fact if either is true. My assertions do not rely on this at all. All that my assertions rely on is the fact that at some depth the body begins to process nitrogen faster than it is taking it in. And, as long as that is true, and assuming that a "safe" ascent rate was maintained, then as long as the safety stop is above "d" depth, and as long as the time is adjusted for said depth, and as long as the remainder of the ascent is at a "safe" ascent rate, then the requisite offgassing will be achieved.
However, if the "curved" model above is true, it would establish that the ideal thing to do would be to gradually ascend at a very slow rate, lets call it "r" rate, beginning at "d" depth. Ideally "r" rate would be the ascent rate at which the body's ability to offgas matches the nitrogens ability to be processed (the rate at which it comes out of solution). In other words, the ascent rate should allow for the value of "y" in the above equation to be a positive number, and would allow for both "y" and "x" to be zero at the surface. And, if these two rates are not equal, then numerous safety stops of shorter duration and greater frequency would be a better alternative. Now, while this is a more "accurate" solution, I agree that the difference between the method I put forth and the 15 ft safety stop may be scientifically insignificant.
Not advanced nitrogen/solution theory, just plain old basic algebra.
And, taking into account what I put forth above, that means that when at the safety stop, while in slightly pitching waters in the open ocean with 7 other divers in my group, each clinging to the ascent line with the person at the top at 12 feet and me at the bottom at 20 feet, in order for me to avoid the bends I don't need to wrestle my way through the other divers to 15 feet in some underwater wrestle-royale James Bond style, I just have to extend my stop by "y", and maybe even add another little one at 10 ft.
So tell me again - if basic algebra proves it is right, how am I wrong?
There is only one way - if just about everyone that has posted is wrong, and that may be the case. Maybe the laymans understanding is a bit flawed. But even in this eventuality, my math may be wrong, but the theory is still right.
The one thing that would prove this all wrong is if the body is perfectly capable of handling the amount of nitrogen than it is taking on at any depth, but it is unable to process it because it is in solution. That would then promote the theory that one must ascend, let the nitrogen come out of solution, process and expell it, and then ascend again to repeat the process. However, while that may prove my math wrong, it still proves my theory right.
Anyone who has been on a deep dive (and I haven't, but I have heard about it and even seen pictures - thats how I roll) knows that if you descend, blow up a balloon, and then ascend, the balloon will explode. So lets say that we try an experiment to see how to inflict the least amount of stress on the balloon while bringing it up. Do you think that the best method would be to ascend "x" feet (to a safety stop), let it expand (nitrogen come out of solution), and then stop (safety stop), let a little air out (wait to offgas), and then ascend again? Or would it be to make an ascention of constant speed while letting air out at the rate needed to keep the balloon at a constant circumference?