by Steve Lewis *(Originally posted in March 2014)*:

When divers want to calculate, or in some cases are TOLD to calculate, the best nitrox and tri mixes for their dives, there are two major reasons for the task to be completed simply, and most importantly, accurately. If you guessed reason one is oxygen toxicity (the central nervous system kind), and number two is inert gas narcosis, you have earned a gold star.

Sometimes, less easy to answer is how to actually make sure the calculation process itself is simple and accurate, or as one of my instructor-trainers once explained, “That everyone colors within the lines.”

Having been a member of a team responsible for putting together diving textbooks – and being on the distribution list for feedback from students and instructors when new textbooks were launched – it strikes me as supremely important that any method used by rank and file divers (and that includes most of us) involve the least amount of high-school level mathematics.

Most of us have forgotten pre-calculus, our grasp of algebra has become shaky, and operating a scientific calculator to work out an exponential function requires a Google search and more than a couple of minutes of trial and error.

Because for many of us, math equals mystery, the less of it there is, the more likely we are to achieve the second goal of gas mixing: accurate calculations.

One of the old stand-bys in the world of scuba texts goes something like this: if it can be calculated with a table, use a table. Generally, tables result in a lower level of operator error. The closest thing we have to a table to tell us which gases are best for our dives are something called “Standard Gases.”

For those of us who have been diving for a while, our introduction to standard gases most probably were the “original” NOAA nitrox gases: EAN32 and EAN36. When nitrox was first introduced to the recreational diving community almost thirty years ago, these were what most dove: a 32 percent nitrox with a maximum operating depth of 40 metres/132 feet, and its 36 percent buddy, which was used to 34 metres/113 feet. (Both MOD’s calculated by the way for an oxygen partial pressure of 1.6 bar/ata.)

Of course, there’s more to using nitrox than being restricted to just two blends and it became very apparent to the folks writing the course guidelines at TDI that the concept of teaching students to “use the best mix for the dive” resulted in users who made the effort to work a little harder at it and had a better than average understanding of gas behaviors and gas mixing. Using a one-size-fits-all approach (or even a two-size-fits-all) may be fine for some users, and perhaps the majority of truly recreational divers, but it has limits that many “avid” divers find uncomfortable.

The limit of the standard gas approach also showed its face when it came time to teach students how to dive trimix (a blend of oxygen, helium and nitrogen). While standard blends of trimix do have advantages – familiarity with mixing, labeling and learning the decompression curve – they too may be a little too restrictive for all dives and all divers.

So, we are left with that question again: How do we make it simple (because we really do not have a table to work from)?

Let’s start with the calculations for the most complex gas – trimix – since learning the technique for it first, means we learn the technique for blending nitrox in the process; and let’s concentrate initially on narcosis!

There are several equations we can use to calculate the narcotic loading of a gas on a particular dive, the narcotic loading of a specific gas, and the best gas to use for a controlled narcotic loading to a specific depth. I never bother with them.

What we are looking for is an easier way that needs zero understanding of how to solve an equation. I mentioned before that a lot of folks dislike math of any type and I believe less algebra is better than a jam doughnut. So here is the simpler method originally shown to me by cave explorer Larry Green. I forget what he called it, probably something like the lazy-man method. I call it the Vacant Partial Pressure Method, but it is exactly what Larry showed me in 1995 and I’ve stolen it with apologies to him.

Anyone who has taken and remembers a basic nitrox course will be familiar with the concept of Acceptable Oxygen Partial Pressure. In a nut-shell, if we plan a dive with an acceptable oxygen partial pressure of 1.3 bar for our dive’s maximum depth, we can easily work out what the best mix is for a specific depth. With a couple of additional key strokes on our pocket calculator (or smart phone), we can also work out the oxygen dose of specific gas at any depth, or the maximum operating depth (MOD) of a specific gas.

Often, basic nitrox students leave their class with the idea that a partial pressure of 1.4 bar of oxygen (rather than the 1.6 bar suggested originally by NOAA for non-working dives) is the maximum acceptable level of oxygen for their dives. That’s a slight over-simplification but it works for most if not ALL single recreational dives.

In the world of simple math, we can refer to that 1.4 bar of oxygen as the acceptable oxygen depth. The actual depth in the water column can vary depending on the gas mix – 6 metres/20 feet for pure O2, 21/72 feet metres for 50 percent, etc. – but the oxygen depth is constant.

We can and should do a similar exercise for nitrogen! If we do, we can use the Vacant Partial Pressure Method to help manage gas toxicity, and that’s our present goal. However, how many bar is a maximum acceptable level of nitrogen for our dives?

There is not a hard and fast answer to that as far as I can tell. Read diving forum threads on deep air and you’ll understand why. More importantly, I am reluctant to tell you that X-point-Y bar will work because although your mate might be happy with that narcotic load, you may not.

But I can explain to you what works for a large number of folks, including me, when diving in cold (bottom of the Great Lakes cold) water.

At some point, a dive guru somewhere figured out that diving air to 30 metres/100 feet delivers an “acceptable” narcotic load. We can interpret this several ways, but the most popular is to figure that the nitrogen load at 30 metres is acceptable. Therefore, since nitrogen partial pressure at 30 metres or 100 feet is 3.16 bar (ambient pressure X gas percentage = 4 bar X 0.79 = 3.16 bar). An acceptable nitrogen depth is 3.16 bar (or ata).

Next, we add the oxygen depth to the nitrogen depth (1.4 + 3.16) and arrive at 4.46 bar. This is the total pressure, ambient pressure, depth (all three are the same thing) that is “acceptable” according to our simple math guidelines. Any deeper and we have a vacant partial pressure.

The metric unit divers have already worked out that 4.46 bar is the ambient pressure at 34.6 metres. The Americans in the audience need a calculator to arrive at 114 feet: the ambient pressure at 114 feet is also 4.46 bar or ata.

Ergo, if we plan to dive deeper than 34.6 metres or 114 feet you have a choice, break the “acceptable partial pressure” rule or fill the gap – any vacant partial pressure – with something else.

### SIMPLE CALCULATIONS ACHIEVED

Here’s how simple the calculations work. Say we wanted to dive to 45 metres/150 feet. The ambient pressure down there is 5.5 bar.

Our first step is to find how much vacant partial pressure there would be if we want to maintain our acceptable limits of nitrogen and oxygen loading. This is pretty simple to work out: subtract 4.46 bar (our combined oxygen and nitrogen depths) from the 5.5 ambient pressure/depth at 45 metres or 150 feet. The result: 5.5 – 4.46 = 1.04 bar. This means that we have to add another gas – and helium is the only workable solution – to fill that gap.

Since the outcome of running down to our local dive shop and asking for a gas mix capable of delivering 1.4 bar of oxygen, 1.04 bar of helium, and 3.16 bar of nitrogen is likely to be hit or miss, we have one step left. We need to turn common fractions into percentages, which are an altogether different species of fraction, and which is a process that’s simpler than it sounds.

To do this for our example and all future calculations, the numerator (the integer above the line) will be the partial pressure of the gas whose percentage we want to find, and the denominator (the integer below the line) represents the ambient pressure. In our example above, the conversion to find the percentage of oxygen will be 1.4/5.5 = 25. Thus, the oxygen percentage we’re looking to get in our mix is 25 percent. Now for the helium, which is 1.04/5.5 = 19 percent (or close to it). The remainder will be nitrogen. (Convention is that we typically do not bother to write the nitrogen percentage on a request for mixed gas.)

In the real world, I believe most mix divers faced with these results would actually ask for a 25/20. If the dive were to be one of many in a series of multi-day exposures, the percentage of oxygen would likely be dropped a couple of points to help allay 24-hour CNS levels, and the helium might be bumped up for cold, working dives.

Whatever the final decision on one’s mix might be, vacant partial pressure calculations are simple and fast. The combined oxygen and nitrogen pressures remain constant and the remainder has to be helium.

Nitrox of course is even simpler: the same technique with one less gas.

For example, a dive to 26 metres/85 feet subjects a diver (you and me) to an ambient pressure of 3.6 bar/ata. If we want to dive with a maximum oxygen partial pressure of 1.4 bar the process of finding the “right” blend of nitrox simply requires us to divide 1.4 by 3.6, which equals 38.8, and that is the blend of nitrox (the percentage of oxygen) that would work for our dive! If we wanted less oxygen partial pressure for some reason on the same dive – let’s say 1.2 bar for instance – we’d simply divide 1.2 by 3.6 and the result would be an EAN33.3.

Thanks for the article. It is very helpful as a quick and easy way to calculate best mix for trimix diving.

That being said, I think you made a simple addition error early on in your example… When you add the acceptable PPO2 level (1.4) to the acceptable PPN2 level (3.16), you arrive at 4.46. Shouldn’t this be 4.56? Of course, this changes the results through the rest of the equation, but the process appears to be sound.

Thanks again!

Wonderful read. It’s a great peak into the world of trimix. Generally speaking, due to resources I am a self taught individual. I should have gotten advanced certifications, but generally was not that motivated to, I know lazy ass, like I said I was fortunate to have the resources that I had.

Any rate I was never particularly interested in deco diving, but I have recently began to used nitrox. Naturally boning up on the physiology and calculation tables… at least to me one is just learning an alternate to the regular air tables… and besides knowing about the different physiology affects… the understanding of reasons why it can be toxic… a nitrox class is just a repeat of open water class but with a fork in the road leading to different tables. Dont get me wrong, I wish I took the coarse back then, now its practically double even triple the price, oh well..

While interesting I do not fathom of actually doing such technical diving, when I have a plethora of coral and wrecks in 20ft to 120ft range, although there are a few bad awesome wrecks in the deeper 140-160ft range I would not mind eventually doing (actually getting to using my computer(s) to there full potential I paid for), gotta go get me some twin steel tanks now…

But now after a break of watching the industry I have started to research again, one particular topic that peeked my interest was the advancement of closed circuit re-breathers. Of particular humor is the marketing of one particular manufacturer, that their CCR is fully automated, and particularly marketed for the recreational diver that has a pocket of cash to burn (not me!). Now while the advancement of the gear leaves me drooling, I am well aware of the particularities of such CCR equipment (particularly the soda lime canister as it relates to its use in anesthesia equipment). While all of those options and configuration decisions leaves my head spinning (You have to understand I like to over think things from a learning stand point) I would rather prefer to keep things simple. But I am intrigued about the silent side of the underworld. Really looking forward one day to check out a CCR demo dive perhaps one of these days.

Anyways again thanks for sharing!

PS, I am beginning to loath more and more having grown up with imperial units of measure.