Optimizing Nitrox Blends for Depth

Hello! Welcome to your next lesson in the "Technical Dive Planning and Gas Management" module.

In our previous lesson, we established that for deep dives, both air and standard nitrox mixes become dangerously dense, increasing the work of breathing and the risk of CO2 retention. The solution, we noted, is to add low-density helium to our breathing gas.

Today, we will learn exactly how to do that. This lesson focuses on designing the ideal breathing gas for a specific dive. We'll move from the why of using trimix to the how of calculating it.

By the end of this 60-minute lesson, you will be able to calculate the 'best mix' for a given depth based on target Equivalent Narcotic Depth (END) and oxygen partial pressure limits. This is one of the most fundamental skills in technical dive planning.

1. The 'Best Mix' Philosophy

When planning a technical dive, we are trying to solve an optimization problem. We want a gas that is safe to breathe at our target depth, but we also want to manage the narcotic effects of nitrogen. The "best mix" is the blend of oxygen, nitrogen, and helium that achieves this balance.

To calculate it, we must first define our safety limits:

1. Maximum Partial Pressure of Oxygen (PPO2): This is our limit for avoiding central nervous system (CNS) oxygen toxicity. For the deep, or "bottom," portion of a dive, this is typically set between 1.2 and 1.4 ata.
2. Target Equivalent Narcotic Depth (END): This is the maximum level of narcosis we are willing to accept. We express this as an equivalent depth on air. A conservative and common target for technical dives is an END of 30 meters (100 feet) or less.

With these two values—our target PPO2 and target END—we can calculate the ideal percentage of each gas in our mix for any given depth.

The process involves three steps:

1. Determine the oxygen percentage to satisfy our PPO2 limit.
2. Determine the nitrogen percentage to satisfy our END limit.
3. Fill the remainder with helium.

Let's work through each step.

2. Step 1: Calculate the Oxygen Percentage

The first step is to ensure our gas doesn't become toxic at depth. The fraction of oxygen (FO2) in our mix is determined by our chosen PPO2 limit and the absolute pressure at our maximum depth.

The logic is a direct application of Dalton's Law. The formula is:

$\text{Fraction of Oxygen (FO2)}=\frac{\text{Target PPO2 (ata)}}{\text{Absolute Pressure at Depth (ata)}}$

This calculation is identical to finding the "best mix" for a nitrox dive. The following video explains this concept clearly.

Worked Example (Part 1)

Let's plan a dive to 60 meters.

• Target Depth: 60 meters = 7 ata (6 bar of water + 1 bar of atmosphere)
• Target PPO2: 1.4 ata

Using the formula:
$\text{FO2}=\frac{1.4\text{ ata}}{7\text{ ata}}=0.20$

Our mix should contain 20% oxygen.

3. Step 2: Calculate the Nitrogen Percentage

Now that we have our oxygen percentage, we need to determine how much nitrogen we can have in the mix without exceeding our narcosis limit. This is where the Equivalent Narcotic Depth (END) comes in.

First, let's formally define END.

As the article shows, the formula for END (in meters), when treating O2 and N2 as equally narcotic, is:

$\text{END}=(\text{Depth}+10)\times (\text{FO2}+\text{FN2})-10$

To find our best mix, we need to work backward. We know our desired END, Depth, and FO2, so we can rearrange the formula to solve for the fraction of nitrogen (FN2):

First, solve for the total fraction of narcotic gases (FO2 + FN2):
$\text{FO2}+\text{FN2}=\frac{\text{END}+10}{\text{Depth}+10}$

Then, isolate FN2:
$\text{FN2}=\left(\frac{\text{END}+10}{\text{Depth}+10}\right)-\text{FO2}$

Worked Example (Part 2)

Continuing our plan for a dive to 60 meters, with a target END of 30 meters.

• Target Depth: 60 meters
• Target END: 30 meters
• FO2 (from Step 1): 0.20

Using the formula:
$\text{FN2}=\left(\frac{30+10}{60+10}\right)-0.20$
$\text{FN2}=\left(\frac{40}{70}\right)-0.20$
$\text{FN2}=0.571-0.20=0.371$

Our mix should contain approximately 37% nitrogen.

4. Step 3: The Remainder is Helium

This is the easiest step. The portion of the gas that isn't oxygen or nitrogen must be helium.

$\text{Fraction of Helium (FHe)}=1-\text{FO2}-\text{FN2}$

Worked Example (Part 3)

• FO2: 0.20 (20%)
• FN2: 0.37 (37%)

$\text{FHe}=1-0.20-0.37=0.43$

Our mix should contain 43% helium.

Putting it all together: The "best mix" for a 60-meter dive with a target PPO2 of 1.4 and an END of 30 meters is Trimix 20/43 (20% O2, 43% He, 37% N2).

The following video provides a great real-world demonstration of this exact process.

An Alternative View: The Vacant Partial Pressure Method

Another way to think about this is by considering the partial pressures of each gas at the target depth. This "Vacant Partial Pressure Method" can be more intuitive for some.

This method reinforces that no matter how you approach the calculation, you are simply allocating the total absolute pressure at depth among the three gases according to your safety limits.

Practice Problem

Now it's your turn. You are planning a dive to 50 meters. Your personal limits are a target PPO2 of 1.3 ata and a target END of 25 meters.

Calculate your best mix.

Click here for the step-by-step solution

Parameters:

• Target Depth: 50 meters = 6 ata
• Target PPO2: 1.3 ata
• Target END: 25 meters

Step 1: Calculate FO2
$\text{FO2}=\frac{\text{Target PPO2}}{\text{Pressure}}=\frac{1.3\text{ ata}}{6\text{ ata}}=0.216$
Let's round this to 22% Oxygen.

Step 2: Calculate FN2
$\text{FN2}=\left(\frac{\text{END}+10}{\text{Depth}+10}\right)-\text{FO2}$
$\text{FN2}=\left(\frac{25+10}{50+10}\right)-0.22$
$\text{FN2}=\left(\frac{35}{60}\right)-0.22$
$\text{FN2}=0.583-0.22=0.363$
Let's round this to 36% Nitrogen.

Step 3: Calculate FHe
$\text{FHe}=1-\text{FO2}-\text{FN2}$
$\text{FHe}=1-0.22-0.36=0.42$
This gives us 42% Helium.

Result: Your best mix is Trimix 22/42 (22% O2, 42% He, 36% N2). This is a common normoxic trimix blend.

Conclusion

In this lesson, we've translated the abstract safety requirements of technical diving into a concrete, three-step calculation for designing a custom breathing gas.

Key Takeaways:

• The "best mix" for a dive is a trimix blend that balances the risks of oxygen toxicity and inert gas narcosis.
• The calculation requires you to first define your personal limits: a target PPO2 and a target END.
• Step 1: Calculate the required oxygen fraction (FO2) based on your target PPO2 and depth.
• Step 2: Calculate the required nitrogen fraction (FN2) based on your target END, depth, and the FO2 you just found.
• Step 3: The remaining fraction is helium (FHe).

Preview of the Next Lesson:

Planning your bottom gas is only part of the puzzle. To return to the surface safely and efficiently, you need to switch to different gas mixtures during your ascent. In our next lesson, we will focus on how to calculate optimal decompression gas mixes based on depth and oxygen exposure constraints.