DALTON'S DIAMOND
Dalton’s Law, or the Law of Partial Pressures, states that the total pressure exerted by a mixture of gases is equal to the sum of the partial pressures of the gases in the mixture.
So what does that mean and what does it have to do with scuba diving? Well as to what it means, that is pretty simple... It means that all the different pressures of different gases in a mix will add up to the total pressure. Duh, right? But what does that have to do with diving? Dalton's law allows us to calculate what percentages of gas we are breathing at what depth. Through that was can determine how narcotic or dangerous a certain gas mix will be at a given depth. We can also figure out what the best gas to breathe will be. All of this can be calculated by using Dalton's Diamond.
Dalton's diamond has three variables.
- Pg which stands for Pressure Gradient, or Partial Pressure.
- % which is the percentage of gas you are working with - this must be represented in decimal form though!
- ATA which is the depth in atmospheres.
Don't remember how to get atmospheres? No worries... it is just your depth + 10, then divided by 10 if you're using metric, or your depth + 33, then divided by 33 if you're using imperial.
Now that we know what everything stands for, how do we use the formula? It is a basic T formula. T formula's rely on you having two pieces of information, and looking to find a third. To get the third you either divide or multiply the two numbers you do have, depending on where they fall in the formula. You divide down, and multiply across. So if you have your Partial Pressure and your Atmospheres, you would divide the Partial Pressure by the Atmospheres. If you have the Percentage of Gas and the Atmospheres, you multiply them to get the Partial Pressure, and so on.
So we know what everything stands for, and we know how to use the formula. But that still doesn't tell us how it pertains to diving. Well there are two main ways we use this formula. We use it to calculate; Maximum Operation Depth, and Best Mix. We can also use it to tell if we can use a pre-mixed tank for our planned dive, as well as the narcotic level of a mix. Narcotic level is a bit advanced, so we'll talk about that in a later post.
MOD (Maximum Operating Depth)
Every time we use a Nitrox tank, we should be calculating the Maximum Operating Depth. As the name suggests, it is the deepest depth we can safely dive that mix. To get this value, we already know two things, the Percent of the oxygen in the mix we want to use, as well as the maximum safe Partial Pressure of oxygen (1.4, as learned in the Nitrox course, which you would have needed to have taken to get a Nitrox tank). With those two pieces of information we can plug them into our formula to get our MOD.
For example, we have a tank of 29% Nitrox. The 29% refers to the amount of oxygen. Now, as states above we need to convert that to a decimal. To convert to a decimal, we just move the decimal point to the left two places, so 29% = .29 . Now we simply put our values into the formula where they belong, and we can see all we need to do is divide 1.4 by .29 . Now this gives us a pretty small number of 4.8. Remember this is the Atmospheres. To convert from Atmospheres we must take that number, and subtract one (for the atmosphere of pressure we are under right now) then multiply it by ten for metric, or 33 for imperial, which gives us 38 m / 125 ft. So 38 m / 125 ft is the maximum depth we can safely dive 29% Nitrox. Simple stuff right?
Best Mix
As the name suggests, Best Mix is the best mix of oxygen for the depth that we plan on going to. We use it when we already know how deep we want to dive, and we want to optimise the effect of oxygen / Nitrox. Once again, we already have two pieces of information; our depth and the maximum safe Partial Pressure of oxygen.
In this example, say our reef is at 25 m / 82.5 ft . We need to convert that to Atmospheres. For metric, we will add 10, to give us 35, then divide by 10 to give us 3.5 ATA. For imperial we will add 33, to give us 115.5, then divide by 33 to once again give us 3.5 ATA. Now once again we just plug into our formula, 1.4 divide by 3.5, which gives us .4 . To convert .4 to a percent we move the decimal point right two places, making this 40%. So for a dive to 25 m we would want 40% Nitrox. Once again, fairly easy so far.
Using this formula we can also tell if a pre-mixed tank will work for our planned dive. To do this we just multiply our depth (in Atmospheres) by our percent of oxygen (in decimal form) to give us the Partial Pressure oxygen would be at at that depth. Since we know 1.4 is the maximum oxygen we want to expose ourselves to if the number is higher than 1.4 we know it is unsafe to dive, if it is lower we know it is ok. Most people however will just calculate the MOD for their mix to tell if it will allow them to go to their planned depth.
As we get into higher levels of diving and diving with more mixed gases we still use this formula, but we may switch from working with oxygen to other gases. That will all be covered in another mixed gas planning post.