# Two Plus Two Equals Purple

Seeing as how it has been such a math-centric week with people barking numbers at you nonstop from the TV I thought I’d spend some time helping folks ease out of it with less stressful, more personally interesting math. How much you breathe. Not just how much you breath, but knowing, within just a few psi/bar how much you have breathed so that when you look down at your gauge it is simply confirming information that you already have. This stuff holds true at any level of diving. And while breathing should be interesting enough in and of itself, what I wanted to talk about might also save you, personally, a bit of money. That is, if you’ve ever considered air-integration. It is important to note, first and foremost, that I am not at all mathematically-minded. In a 1/2 dozen tries I never made it through trigonometry and up to calculus in school; something about logarithms turns off my brain. I’ve heard it said that people who are comfortable with math also have a deeper capacity both to appreciate and to play music. Well… I have never been able to play an instrument and I listen primarily to punk. So. Yeah. Almost certainly BECAUSE math is such a difficult, foreign language to me I find the numbers and formulas I’m going to touch on here as useful and cozy as I do. Because, for the large part, you only need to do a little bit of math once, write it down, and then never pay any of it much mind again. You might (though I have no idea why you might) remember that a few months ago I changed my primary pressure gauges over to metric as bit of professional development and personal training. Now, months later, I am 100% committed to never going back. This has nothing to do with whether metric is better or easier (though it is). This, too, is more because I am not terribly mathematically clever and I have discovered an eccentricity that makes my gas consumption rates extraordinarily easy to calculate. I breathe 1 bar per minute. 30 minute dive = 30 bar consumed. 70 bar available as usable gas = 70 minutes it is time to turn the dive. It doesn’t get easier than one-to-one. Now this only works given a certain set of parameters that happen to be the near-norm for me personally. And we’ll circle back to that. This preamble was meant to be a way of saying: Don’t be scared of math. I am going to speak in both imperial and metric, but do feel free to just ignore whichever system you don’t think in if there are too many numbers on the screen and you need to suppress the urge to jump up screaming like that kid in Real Genius. Let’s start easy. With how much gas is in a tank. AL80s, being far and away the most commonly dived tank on the planet, are as good a place to start as any.

**BASELINES**
You know why an AL80 is called an 80? Because AL77.4 is too much of a mouthful to say. But that’s actually how much gas is in there. At the rated pressure of 3000psi an AL80 has 77.4 cubic feet of gas in it.
In metric tank it’s simply an 11L tank because that’s how much water you’d fill it with if you took the valve off. I can’t stress this enough: do not take the valve off your tank and fill it with water. There are far more appropriate vessels you can bring to the gym that would fit better in the SpinCycle cupholders.
77.4cf per 3000 psi.
Let’s take the first step of our voyage by figuring out how many cubic feet are in a single psi.
77.4/3000 = .025/1
So for any single psi that’s .025 cf. Which is a pointless number for a variety of reasons. First and foremost among them: no pressure gauge on any regulator anywhere on planet Earth is calibrated to that level of accuracy.
Which is why I always tired very quickly of folks with spiffy AI computers who tried to explain that they had 1738psi. I don’t care; just tell me 17 and get back to looking at your nudibranchs.
You know what is an interesting number, though? Move that decimal point over two places and you get: 2.5cf/100psi.
So for every 100psi in an AL80 you’ve got 2.5cf.
Metric switch:
An 11L tank at 1ATA/BAR (or, sitting there with the valve removed) contains 11 litres of gas. Put the valve back on and pressurise it to 2ATA/BAR and you’ve got 22 litres of gas. 3 bar = 33 litres. If you've used 50 bar you've breathed 550 litres, and so on until you’ve got 210 bar, which is full, containing 2310 litres. And that’s the end of that.
For our imperial friends, now you’ve got the baseline of a single AL80: 2.5.
If we apply this to, say, my favourite tanks back in the dear, dim past when I was a wreck diver, HP120s: 120cf (fill capacity) divided by 3600 (fill pressure) you wind up with .033. Move the decimal, and you get 3.3cf/100psi. Go ahead and do this to find the baseline of whatever your favourite tanks happen to be.
If you happen to use doubles just multiply that baseline by two. In any case here’s a handy chart for you:

If you are a single tank 80s diver, just remember the number 2.5 OK, great. We have a number. Yeay us! What the hell do we do with it?

**SAC RATES**

This is, obviously, far more highly variable. Do you know yours? Well why the hell not? Oh… you’re one of those divers that looks down at their pressure gauge occasionally and is perpetually surprised at the information displayed? Well, you dig, that’s exactly what I set out to try to help you remedy with all this. Maybe you vaguely remember something about it being mentioned in your AOW or Deep Diver class but haven’t paid it any mind since? The way I’ve always seen it taught (and you shouldn’t hear criticism or an eyeroll in that statement, the method works just fine): 1) Find a constant depth. 33 feet works great. 2) Mark your starting pressure and a stopwatch. 3) Float there for 5 minutes doing nothing. 4) Mark your ending pressure. 5) Repeat the pressure records for 5 minutes of light exercise and again swimming hard. 6) Reverse engineer (using the baseline we worked out above) how many cubic feet you’ve breathed in each of those 5 minute blocks. 7) Divide everything by 5 (because you were doing a thing for 5 minutes). 8) Divide everything by 2 (to counter the 2ATA you’ve been doing all this). 9) Now you’ve got your SAC (Surface Air Consumption) rate in cf/minute. Now you can multiply this by whatever depth (in ATA) your dive plan averages out to and you’ve got your RMV (Respiratory Minute Volume). In metric just turn step 6 into, “Multiply bar by tank volume and you’ve got how many litres you’ve used.” Rather dry. And it’s 15-20 minutes of dicking around on a quarry platform or whatever. But it’s a useful number. It’ll change over time. And depending on level of comfort that day or whatever. But you’ve got a good working platform. There are other methods of finding and periodically updating what you know your SAC rate to be. I don’t care. I’m not your dad, I’m not going to tell you exactly which one to do. Just do something to find out a ballpark. For most people a light-work SAC hovers around .5-.75cf or 15-20 litres per minute. But there’s always that one 80lbs woman on the boat who has been diving for 50 years and comes back with more gas than she left. Fuck that jerk. So… fantastic. Now we have another number. So what? So what? So let’s integrate the two.

**BREATHING INTERVALS**
For argument’s sake let’s say we now know that our SAC rate is.75cf/minute. And we’re breathing a single AL80 with its baseline of 2.5cf/100psi.
With this information let’s fill in another little chart with our RMVs at different depths:

I threw in a multiplication of 5, too. Why? Do you really want to check your pressure gauge every minute? Wouldn’t it be way nicer and more practical to break your dive up into 5 minute intervals? But don’t worry. You don’t need to remember these numbers. That’s the good news. The bad news is that there is still one more bit of math. Let’s translate those cubic footages back to psi. Our baseline was 2.5cf/100 psi. I don’t know how to do the new math, so we’re going to cross-multiply like god intended. So divide each of the below numbers by that baseline and then multiply by 100. (I am also going to eliminate the 1ATA row. Because who cares?

Now we can just tidy up a bit, remove the information that serves no practical function on the dive, so you’re left with something to write in your wetnotes.

There.

This little chart is our end-goal.

Four little numbers that are calculated to you, personally. So that when you’re doing a dive that’s been mostly around the reef at 60 feet give or take, 15 minutes into the dive you can think to yourself, “I should have used around 1200-1300psi.” And when you glance at your pressure gauge you are simply confirming what you already knew to be true. 420 psi per 5 minute interval. 15 minutes is 3 5 minute intervals. 420x3= 1260. Or you can simply go even further, if you’re a mathematical dunce like me, by rounding (within reason). Call the interval 400. Remember what I said about pressure gauge accuracy? The idea is not absolute precision. The idea is to not be surprised by critical life support information or just fly blind until the needle points to the red area which tells you it was time to ascend several minutes ago. If you started with a full tank, were at 100 feet for 5 minutes and then came up to 30 feet for the last 25 minutes, you should already know that you have about 900psi left in your tank and it’s time to head back to the boat. (600psi for the interval at 100 feet + 300x5 for the intervals at 30 feet all subtracted from 3000psi starting pressure.)

**BREATHING INTERVALS MADE EASY**
For those of you who have been enduring imperial and gritting your teeth with the absurdity of it, here’s a metric example.
Let’s say a diver has a SAC rate of 10-12 litres per minute and is using double 11L tanks and we’ll go all the way back to the beginning.

That was fun, right? Know what’s even more fun? You didn’t have to do it. Joke’s on the imperial people. We get to skip several steps. You know how many liters you breath per minute, and you know how many litres are in your tank(s), all you’ve got to do is divide by the later and then multiply by 5. Double 11L tanks is 22L.

And prettied up for this particular diver to be written in a wetnotes:

This particular diver, by the way, is me. My most usual configuration these days is AL80s. And diving in shallow Mexican caves, my average depth tends to be around 30’/10M. So the only numbers I really have to remember, quite conveniently and as I said a jillion words ago, is one-to-one. “I’m 40 minutes into the dive? Wow, I’ve used 45 bar instead of 40… I’m off my game today.”

**WHY BOTHER**
I suggested at the start of this adventure that going through all the trouble of sitting down one day and going through these calculations for you personally, plugging in your breathing rate and your favourite tanks, could save you money.
Do you really need to spend the extra hundred bucks on a transmitter? That adds a couple of negligible, but still-extent failure points? That gives you an excess of information beyond what the calibration is really capable of? That reacts slower than a mechanical gauge? That is rendered useless anywhere near a shipwreck due to all the iron in the water?
And, most of all, should just be there to confirm what you already know at any given point on the dive?
That’s really the most important point. Whether you like the transmitter because it’s neat and just absolutely have to have one or if good old brass-and-glass is more your style. Know how much you’re breathing.
Do the math for yourself. All you need in the end is a little chart with 4 numbers on it. Write it out so you don’t even have to remember it during the dismal times between dive vacations.
If something I’ve tried to explain above has been confusing to you (which is obviously well inside the scope of possibility), feel free to drop me an email or a PM and I’ll do my best to work it out with you. If you want copies of any of the charts I’d be happy to send them to you, but, frankly, now that you know the math I’d encourage you to just build them yourself to firm up the relationships between the numbers in your head.
Put in the work up front, from the safety of your own desk when you should be paying attention to your Zoom meeting. It's just one more way to make diving, what's really important, that much safer, easier, and more enjoyable.