Calculating Air Consumption

Many people are often put off by the maths involved when calculating air consumption in diving. This article is designed to explain how air consumption can be calculated in easy to follow steps. There are also some exercises to test your knowledge (with answers).

DISCLAIMER: The author and Stafford Sub Aqua Club are not liable for any damages or losses that may occur, as a result of relying on the information contained within this article.

For easy navigation, the article is split up into sections, please use the links below to select the information you wish to view. The end of each section includes details of related exercises.

Units

Unfortunately, we're going to be dealing with lots of different measurements and this means that there are lots of different units. For brevity, we tend to abbreviate the units of measurement. The table below summarises the units we will need:

Measurement	Units	Abbreviation
Pressure	bars	bar
Depth	metres	m
Volume	litres	L
Time	minutes	min
Breathing Rate	litres per minute	L/min
Ascent Rate	metres per minute	m/min

Table of measurements, units and abbreviations

Don't worry if you forget a unit or abbreviation, you can always refer to this table.

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Pressure

As we dive below the surface of the water, the pressure increases. If we are at sea level, we say that the air pressure is 1 atmosphere. This is actually equivalent to 1.01325bar, but for our purposes 1bar is near enough. For every 10m depth, the pressure increases by 1bar, therefore the pressure can be calculated using this straightforward equation:

So for example, if you were diving to a depth of 17m the calculation would be:

You may be wondering why I started off by telling you how to calculate the pressure underwater, when you wanted to know how to calculate air consumption? Well, I'll get to that shortly... Before you calculate air consumption, you'll need to calculate the pressure.

Question 1 in the exercises is about calculating pressures.

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Boyle's Law

Now it's time for a little science... You may remember from your high school physics lessons, learning about Boyle's Law? Don't worry if you can't, it says:

"For a fixed amount of an ideal gas, kept at a fixed temperature, pressure and volume are inversely proportional." https://en.wikipedia.org/wiki/Boyle's_law

So what does this mean? Basically, as the pressure increases, the volume of gas decreases and vice-versa. If you were to take a balloon underwater, the following would happen, when you reached 10m depth, the volume inside the balloon would have halved, because the pressure is double. At 20m depth, the volume inside the balloon would be a third. The diagram below shows this and also highlights an important point, about expansion of air on ascent.

Balloons at Depth Image — Balloons at Depth

So why is this so important? Well, as you descend, your regulator delivers air to your mouth and lungs at ambient pressure (the pressure of the surroundings). The reason is, you would struggle to breathe if it didn't. Therefore, you are breathing twice the amount of air at 10m, compared to the amount of air that you would be breathing at the surface.

This is one of the reasons why you can't take a hose down with you and use it as a long snorkel. Technical divers, that use air supplied from the surface, have their air delivered at pressure (i.e. higher than 1bar).

The balloons on the right hand side of the diagram also demonstrate why you should never hold your breath during an ascent. If you did, as you ascended, the air inside your body would expand and this could result in a burst lung.

Questions 2 - 4 in the exercises is about Boyle's Law.

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Air Consumption

At the surface, the average breathing rate is 25L/min. It's easy to see how you would calculate how much air you'd breathe in say 15 minutes, just multiply the two numbers:

Assuming a square dive profile* (i.e. you go to your maximum depth straight away and remain at that depth for the duration of the dive), your air consumption can be calculated as shown:

Really, this equation is the same as the first, except that pressure is now included. The pressure is used in the first equation, but as we take it to be 1bar on the surface, the result is the same if we'd left it out.

So, for example, if I dived to a depth of 13m for a duration of 30mins and my breathing rate on the surface was 25L/min, I would calculate my air consumption as follows:

* In reality, you'd never dive a square profile, because you'd need to clear your ears on the way down. You must also allow for a safety stop or the required decompression stops on ascent, with maximum ascent rates of 15m/min to 6m, then 6m/min to the surface and a maximum descent rate of 30m/min. By calculating your air consumption as a square profile, you are building in a safety factor, meaning your consumption should be less, assuming your breathing rate doesn't ever exceed 25L/min.

Questions 5 & 6 in the exercises is about calculating air consumption.

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Rule of Thirds

When diving, you should follow something called the 'Rule of Thirds'. When planning a dive, you should return with a third of the air that you entered the water with. This means that the first third can be used for the first half of the dive, the second third for the second half of the dive and the final third is a reserve, in case your buddy gets into difficulty and needs to use your spare during the ascent.

Therefore, when calculating your air consumption, you need to divide your answer by 2 and multiply by 3:

For the previous air consumption example:

An alternative way of calculating this, is to multiply your air consumption by 1.5.

Question 7 in the exercises is about calculating air required.

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Air Available

So now you know how to calculate how much air you are going to breathe on a dive, but you still don't know how much air you have to start with. The amount of air in your cylinder can be calculated as:

A cylinder can usually be charged to a maximum of 232bar or 300bar, but in reality, you're likely to get an air fill that's less than this, for example 200bar. This is because, as air is compressed, it gets hotter. Likewise, as air is decompressed, it gets colder. The hotter a gas becomes; the more volume it takes up (Charles' Law). When the cylinder is first disconnected from the compressor, the gauge may read 230bar, but as the cylinder cools, the volume will decrease slightly.

So for example, a 12L cylinder charged to a pressure of 210bar, the capacity is:

Question 8 in the exercises is about calculating air available.

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Putting it all Together

So, using the two examples above, would you have enough air for the dive?

The answer is no. The amount of air required is greater than the amount of air that you have in your cylinder. It must be the opposite way around, otherwise you could run out of air:

Therefore, you have a number of options. You could:

get more air put into your cylinder to the maximum working pressure, e.g. 232bar (for most cylinders)
use a bigger cylinder (for example, 15L)
dive to a shallower depth
dive for a shorter amount of time

The first two options, are measures that could be taken to increase the amount of air you'll be carrying and the last two options, are measures that could be taken to decrease the amount of air that you'd use.

In reality, your breathing rate is likely to be less than 25L/min, so can you get a more accurate result? By calculating your average breathing rate, you can use this instead of 25L/min. This is done by taking your total air consumption on a dive, dividing it by the average pressure, then dividing the result by the time you were underwater. In practice, this is fairly complex because it requires you to plot your dive profile and calculate the average depth during the dive. Many dive logbook software packages, that are able to plot your dive profile, will also be able to calculate your average air consumption, based on the amount of air you entered and left the water with.

This guide should have helped to demystify the task of calculating air consumption for a dive.

REMEMBER TO: 'Plan the dive and dive the plan', allowing for worst case scenarios.

Questions 9 & 10 in the exercises is about putting it all together.

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Exercises

Below are some exercises that are designed to test your knowledge of calculating air consumption. Start with question 1 and work your way through, as they build on each other. It's advisable to write your working out down too, as this will help you, if you get stuck. If you still can't answer a question, look back through the article and see if you can work out how to answer it by using the examples. The questions are all based on the examples given above. Remember, all numerical answers will need a unit (refer to the table of measurements and units above). When you have answered all of the questions, check your answers below.

Calculate the pressure at the following depths, assuming a pressure on the surface of 1bar.
1. 1m
2. 5m
3. 13.2m
4. 20m
What does Bolye's Law state?
If a balloon is inflated with 2L of air, what will the resulting volume be at the following depths? Remember to look at the diagram to see the multiplying factor for some of the answers.
1. Inflated on the surface
  1. 5m
  2. 10m
  3. 15m
  4. 20m
2. Inflated underwater at 20m
  1. 15m
  2. 10m
  3. 5m
  4. 0m
Why is it essential to breathe out when making an ascent?
Assuming a square dive profile, calculate your air consumption, given the following pressures and dive times, assume a breathing rate of 25L/min.
1. Pressure of 1.3bar
  1. 10mins
  2. 12mins
  3. 15mins
  4. 30mins
2. Pressure of 2bar
  1. 5mins
  2. 14mins
  3. 22mins
  4. 30mins
3. Pressure of 2.7bar
  1. 7mins
  2. 15mins
  3. 24mins
  4. 32mins
Assuming a square dive profile, calculate your air consumption, given the following depths and dive times, assume a breathing rate of 25L/min.
1. On the surface (0m)
  1. 12mins
  2. 15mins
  3. 20mins
  4. 43mins
2. Depth of 7m
  1. 4mins
  2. 11mins
  3. 20mins
  4. 35mins
3. Depth of 18.6m
  1. 6mins
  2. 13mins
  3. 27mins
  4. 30mins
Using the 'Rule of Thirds' calculate how much air is required, given the following air consumptions:
1. 1000L
2. 1300L
3. 1785L
4. 2000L
Calculate the air available in a cylinder, given the following gauge readings. You may ignore any temperature differences.
1. 10L Cylinder
  1. 100bar
  2. 120bar
  3. 200bar
  4. 230bar
2. 12L Cylinder
  1. 120bar
  2. 150bar
  3. 200bar
  4. 220bar
3. 15L Cylinder
  1. 80bar
  2. 130bar
  3. 180bar
  4. 230bar
Remembering to take into account the 'Rule of Thirds', calculate how much air you would require to safely complete the following dives, assuming a square dive profile and breathing rate of 25L/m:
1. 7m for 40mins
2. 13m for 27mins
3. 16m for 25mins
4. 20m for 21mins
Remembering to take into account the 'Rule of Thirds', calculate how much air you would require to safely complete the following dives, assuming a square dive profile and breathing rate of 25L/m, hence deduce if you have enough air.
1. 15m for 30mins with a 15L Cylinder at 200bar
2. 17m for 28mins with a 12L Cylinder at 220bar

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Answers

Below are the answers to the exercises. If you get stuck, please look back at the article before looking at the answers. All questions are based on examples given in the article.

Details

Pressure Calculations
1. 1.1bar
2. 1.5bar
3. 2.32bar
4. 3bar
"For a fixed amount of an ideal gas, kept at a fixed temperature, pressure and volume are inversely proportional." – As pressure increases, volume decreases and vice-versa.
Balloon Volume Calculations
1. Inflated on the surface
  1. 1.33L
  2. 1L
  3. 0.8L
  4. 0.67L
2. Inflated underwater at 20m
  1. 2.4L
  2. 3L
  3. 4L
  4. 6L
Breathing out whilst making an ascent is essential to ensure that the expanding air inside you can escape. Holding your breath during an ascent is dangerous and can lead to a burst lung.
Air Consumption Calculations – Pressure Given
1. 1.3bar
  1. 325L
  2. 390L
  3. 487.5L
  4. 975L
2. 2bar
  1. 250L
  2. 700L
  3. 1100L
  4. 1500L
3. 2.7bar
  1. 472.5L
  2. 1012.5L
  3. 1620L
  4. 2160L
Air Consumption Calculations – Depth Given
1. 0m
  1. 300L
  2. 375L
  3. 500L
  4. 1075L
2. 7m
  1. 170L
  2. 467.5L
  3. 850L
  4. 1487.5L
3. 18.6m
  1. 429L
  2. 929.5L
  3. 1930.5L
  4. 2145L
Rule of Thirds Calculations
1. 1500L
2. 1950L
3. 2677.5L
4. 3000L
Air Available Calculations
1. 10L Cylinder
  1. 1000L
  2. 1200L
  3. 2000L
  4. 2300L
2. 12L Cylinder
  1. 1440L
  2. 1800L
  3. 2400L
  4. 2640L
3. 15L Cylinder
  1. 1200L
  2. 1950L
  3. 2700L
  4. 3450L
Air Required Calculations
1. 2550L
2. 2328.75L
3. 2437.5L
4. 2362.5L
Full Calculations
1. Available = 3000L, Required = 2812.5L – Yes
2. Available = 2640L, Required = 2835L – No

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