Calculating EAD and END for Nitrox and Trimix

Hello! Welcome back to your course on the theory of technical scuba diving.

Introduction

In our last lesson, we explored Henry's Law, which explains how inert gases like nitrogen dissolve into your body's tissues under pressure. This process, known as "on-gassing," is the root cause of decompression sickness if not managed correctly.

However, decompression is only one part of the story. The nitrogen absorbed by your body also has a narcotic effect, impairing judgment and coordination, a phenomenon often compared to alcohol intoxication. As you plan dives beyond standard recreational limits, managing both the decompression burden and the narcotic effect of your breathing gas is paramount.

This lesson introduces two fundamental tools for this purpose: Equivalent Air Depth (EAD) and Equivalent Narcotic Depth (END). These concepts allow you to quantify and control the physiological impact of the gas you breathe.

Lesson 4: Managing Inert Gas Effects

Learning Outcome: By the end of this lesson, you will be able to calculate Equivalent Air Depth (EAD) and Equivalent Narcotic Depth (END) for nitrox and trimix mixtures.

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1. Equivalent Air Depth (EAD) for Nitrox

When you dive with Enriched Air Nitrox (nitrox), you are breathing a mix with more oxygen and less nitrogen than air. Since nitrogen is the primary driver of decompression obligation for air and nitrox dives, reducing its percentage allows you to stay at a given depth longer.

EAD is a way to quantify this benefit. It answers the question: "Breathing this nitrox mix at my current depth, what depth would I have to be at if I were breathing air to have the same amount of nitrogen dissolving into my tissues?"

The answer will always be a depth shallower than your actual depth. This allows you to use standard air-based dive tables or computer algorithms to safely manage your decompression.

To see how this works in practice, let's start with a video that walks through the concept and the calculation.

The EAD Formula

As the video demonstrated, the EAD formula calculates the depth that has the same partial pressure of nitrogen ($P_{N_2}$) as your dive on nitrox.

The formula is:

• Imperial (feet): $\text{EAD}=\left[(\text{Depth}+33)\times \frac{F_{N_2}}{0.79}\right]-33$
• Metric (metres): $\text{EAD}=\left[(\text{Depth}+10)\times \frac{F_{N_2}}{0.79}\right]-10$

Where:

• Depth is your actual depth in feet or metres.
• $F_{N_2}$ is the fraction of nitrogen in your breathing gas (e.g., for 32% nitrox, $F_{N_2}$ is 0.68).
• 0.79 is the fraction of nitrogen in air.

Let's work through an example using metric units.

Example: You are diving to 30 metres using EAN32 (32% O₂, 68% N₂).

1. Identify the variables:

   • Depth = 30 m
   • $F_{N_2}$ = 0.68

2. Apply the formula:
   $\text{EAD}=\left[(30+10)\times \frac{0.68}{0.79}\right]-10$
   $\text{EAD}=\left[40\times 0.86\right]-10$
   $\text{EAD}=34.4-10$
   $\text{EAD}=24.4\text{ metres}$

Result: Diving at 30 metres on EAN32 gives you a decompression obligation equivalent to diving on air at only 24.4 metres. This translates to a longer no-decompression limit and less nitrogen absorbed.

If you're interested in the mathematical derivation of this formula from the gas laws we've already covered, the following resource provides a concise explanation.

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2. Equivalent Narcotic Depth (END) for Trimix

As dives get deeper (typically beyond 40 metres), nitrogen narcosis becomes a significant and unavoidable risk on air or nitrox. To manage this, technical divers add a third gas, helium, to the mix, creating trimix.

Helium is physiologically inert and, for practical purposes within sport diving limits, is considered non-narcotic. By replacing a portion of the nitrogen with helium, we can reduce the narcotic effect of the gas mix at depth.

Equivalent Narcotic Depth (END) is the concept we use to manage this. It answers the question: "Breathing this trimix at my current depth, what depth would I have to be at if I were breathing air to experience the same level of narcosis?"

The goal in trimix planning is to choose a gas mix that keeps the END at a manageable level (e.g., 30 metres or less), regardless of the actual depth.

The following video explains the rationale for using trimix and how the concept of END is applied in planning a deep dive.

The END Formula

You might be surprised to learn that the formula for END is identical to the one for EAD. This is because both are based on the physiological effects of nitrogen. The only difference is the intent: EAD is for managing decompression, while END is for managing narcosis.

• Imperial (feet): $\text{END}=\left[(\text{Depth}+33)\times \frac{F_{N_2}}{0.79}\right]-33$
• Metric (metres): $\text{END}=\left[(\text{Depth}+10)\times \frac{F_{N_2}}{0.79}\right]-10$

Example: You are diving to 60 metres using Trimix 20/40 (20% O₂, 40% He).

1. Identify the variables:

   • Depth = 60 m
   • First, find the fraction of nitrogen ($F_{N_2}$). Since the gases must sum to 100%, $F_{N_2}=1.0-F_{O_2}-F_{He}$.
   • $F_{N_2}=1.0-0.20-0.40=0.40$

2. Apply the formula:
   $\text{END}=\left[(60+10)\times \frac{0.40}{0.79}\right]-10$
   $\text{END}=\left[70\times 0.506\right]-10$
   $\text{END}=35.4-10$
   $\text{END}=25.4\text{ metres}$

Result: Even though you are at 60 metres, the narcotic effect you experience is equivalent to being on air at a much safer depth of about 25 metres. This demonstrates the power of trimix in maintaining mental clarity on deep dives.

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3. Practice and Key Distinctions

Let's solidify your understanding with a couple of practice problems.

Problem 1 (EAD): You are planning a dive to 120 feet using EAN36 (36% O₂, 64% N₂). What is your Equivalent Air Depth?

Click to see the solution

• Identify variables: Depth = 120 ft, $F_{N_2}$ = 0.64
• Formula: $\text{EAD}=\left[(120+33)\times \frac{0.64}{0.79}\right]-33$
• Calculation: $\text{EAD}=\left[153\times 0.81\right]-33=123.9-33=90.9\text{ feet}$
• Your decompression is calculated as if you were on a 91-foot dive.

Problem 2 (END): You are diving to 70 metres on Trimix 18/45 (18% O₂, 45% He). What is your Equivalent Narcotic Depth?

Click to see the solution

• Identify variables: Depth = 70 m, $F_{N_2}=1.0-0.18-0.45=0.37$
• Formula: $\text{END}=\left[(70+10)\times \frac{0.37}{0.79}\right]-10$
• Calculation: $\text{END}=\left[80\times 0.468\right]-10=37.4-10=27.4\text{ metres}$
• At 70 metres, your narcosis level is equivalent to a 27-metre dive on air.

It's important to be precise about these terms:

Concept	Purpose	Applicable Gas	Inert Gas(es) Considered
EAD	Decompression Planning	Nitrox	Nitrogen
END	Narcosis Management	Nitrox, Trimix	Nitrogen

For nitrox, EAD and END are numerically identical because nitrogen is the only inert gas affecting both narcosis and decompression. For trimix, the END calculation tells you about narcosis, but calculating the decompression obligation is more complex because helium and nitrogen have different solubility and diffusion properties (a topic for a future lesson). Modern decompression algorithms handle these two gases separately.

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Conclusion

In this lesson, we've translated the physical principles of gas laws into practical tools for dive planning. You now understand how to quantify and manage the effects of inert gases on your body.

Key Takeaways:

• Equivalent Air Depth (EAD) is used with nitrox to find an equivalent, shallower depth on air tables for decompression planning.
• Equivalent Narcotic Depth (END) is used with nitrox and trimix to calculate the narcotic load of a breathing gas, ensuring it stays within acceptable limits.
• Both calculations use the same formula, which is based on the fraction of nitrogen ($F_{N_2}$) in the breathing mix.
• By adding helium to create trimix, divers can dramatically lower the END, enabling clear thinking at depths where air would be dangerously intoxicating.

Next Lesson Preview:
Having covered the physiological effects of breathing gases under pressure, we will turn our attention to their physical behavior. In the next lesson, we will explore the thermodynamic principles governing gas expansion and compression, which have critical implications for everything from filling cylinders to the performance of your regulators.