An aluminium 80, the most common rental cylinder in the world, does not hold 80 cubic feet of gas. Filled to its rated pressure it gives you about 77. This is not a manufacturing tolerance or a dodgy fill; it is baked into the name, and it is one of several ways the numbers we use for cylinders quietly disagree with each other. A diver in Florida asks for an "AL80", a diver in Cairo asks for an "11 litre", and they walk away with the same cylinder. One number describes the gas inside, the other describes the bottle, and neither is quite what most people think it is. None of this is contested physics. It is just vocabulary that grew up in two measurement systems and never reconciled, so let us reconcile it.
Two ways to measure a cylinder
There are two honest things you can measure about a cylinder, and they answer different questions. The first is how big the bottle is: the volume of the empty space inside it. You measure it by filling the cylinder with water, because water will not compress, so the water that goes in is exactly the internal volume. That is why it is called the water capacity, often stamped on the cylinder shoulder as "WC", and it is the figure the metric world puts on the label.[1 ] An "11 litre" cylinder has eleven litres of space inside it, full stop, whether it is empty, full, or sitting on the bench.
The second thing you can measure is how much breathing gas the full cylinder will give you: the volume that gas occupies once you let it out and it expands back to surface pressure. That is the free-gas capacity, quoted in cubic feet, and it is the figure the US world puts on the label.[1 ,2 ] An "AL80" is named for delivering about eighty cubic feet of gas. The two numbers describe the same physical cylinder, but one is talking about the bottle and the other about the gas, and the gas number depends on how hard you pumped it in. That pressure is the cylinder's working pressure (or service pressure), the figure that tells you how full "full" is.
Same bottle, two stickers. The US quotes the gas it holds; the metric world quotes the bottle itself. Neither is wrong, but they are measuring different things.
The maths, which is just Boyle's law
Turning the bottle into the gas figure is one line of arithmetic. Squeeze a gas into a smaller space and its pressure rises in proportion, so the volume of gas you can stuff into a cylinder is just the bottle's internal volume multiplied by how many times over surface pressure you have pumped it. Fill an eleven litre cylinder to two hundred bar, roughly two hundred times atmospheric pressure, and you have crammed in about two hundred bottles' worth of gas, which is a couple of thousand litres once it expands back out.
free gas (ideal) = water volume × ( fill pressure ÷ atmospheric pressure )
An AL80: 11.1 L × (207 bar ÷ 1.013) = 2268 L = 80.1 cu ft, the same ~80 cu ft you get in imperial from a 0.392 cu ft water volume: 0.392 × 3000 psi ÷ 14.7.[3 ]
Metric divers usually skip the division and just multiply litres by bar, calling that eleven litre, two hundred bar cylinder "2200 litres". It is a fine shortcut, but it quietly rounds atmospheric pressure from 1.013 bar up to a round 1 bar, which overstates the answer by about 1.3%.[3 ] That same 1.3% rounding turns up again later, against a different yardstick. For now the headline is that the sum is simple, and it is built on Boyle's law: halve the space, double the pressure. At the pressures a recreational cylinder sees, this is all you need, and it is accurate to within a percent or two.
Why the name is a small lie
Boyle's law describes an ideal gas, an imaginary one whose molecules take up no room and ignore each other. Real gas molecules do neither, and once you pack them in tightly enough the difference starts to show. The bookkeeping device for it is the compressibility factor, written Z: the ratio of how much space a real gas actually takes up to what the ideal law predicts. For an ideal gas Z is exactly one. For real air at high pressure Z creeps above one, because the molecules are now crowded closely enough to push back on each other, which is a fancy way of saying air gets harder to compress the more you have already compressed it.[5 ] So you fit less in than the simple sum promised, and the real capacity is the ideal figure divided by Z.[3 ,6 ]
real capacity = ideal capacity ÷ Z
For air at a 207 bar fill and the 70 °F US chart temperature, Dive Kit's NIST tables give Z = 1.034, so the AL80's 80.1 ideal cubic feet become 80.1 ÷ 1.034 = 77.5 — landing on Luxfer's published 77.4.[4 ,9 ]
That is where the missing gas in your AL80 went. The cylinder is named eighty for the ideal figure, but real air at three thousand psi packs down about three percent worse, so you get seventy-seven and a bit. Move the controls below to see it for any cylinder: pick a size and pressure, or one of the presets, and watch the ideal figure and the real one pull apart.
On the ideal gas law this cylinder reads 80.1 cu ft. Real air at 207 bar is a little less compressible than ideal, so it actually holds about 77.5 cu ft, around 3.3% less.
Free gas referenced to 1 atm (the dive-industry standard). Z values are approximate, from reference compressibility data.
The gap is not fixed; it grows with pressure. Down low it is nothing, which is why nobody worried about it for years: below about 140 bar, real air and the ideal-gas calculation agree to well within a percent, and you can do the easy maths with a clear conscience.[3 ] Push past that and the two diverge, slowly at first and then faster, so the cylinders that lose the most to compressibility are the high-pressure ones.
At low pressure the two lines sit on top of each other; ideal-gas maths is fine there. The gap only opens up as you pump harder, which is why a high-pressure steel cylinder loses more to compressibility than a low-pressure one, and trimix (with helium) more still.
The names do not even agree with themselves
If every cylinder were simply named for its ideal figure, you could at least correct them all the same way. They are not. The naming grew up piecemeal, and three common cylinders show three different habits.
| Cylinder | Water vol | Pressure | Ideal | Real (air) | Named for |
|---|---|---|---|---|---|
| AL80 | 11.1 L | 207 bar | 80.1 cu ft | ~77.4 cu ft | its ideal figure |
| HP100 | 12.9 L | 237 bar | 106.6 cu ft | ~101 cu ft | its real figure |
| LP85 | 13.0 L | 182 bar | 82.5 cu ft | ~81 cu ft | neither |
The AL80 is named for its ideal eighty and really holds about seventy-seven.[4 ] The high-pressure HP100 is named for its real capacity, near a hundred, even though its ideal figure is nearer a hundred and seven.[3 ] And the low-pressure LP85 is named for neither: the eighty-five came from an early US importer's optimistic maths on a Faber low-pressure cylinder, and it really holds about eighty-one (its maker's sheet says 82.9, reckoned against a slightly more generous reference).[2 ,7 ] So the number on the sticker might be the ideal capacity, the real capacity, or a number someone liked the look of, and there is no way to tell which from the name alone. The only figures that never lie are the two stamped into the metal: the water capacity and the working pressure. Everything else is a story told about them.
Higher pressure, and helium
Two things widen the gap between the label and reality. The first is pressure, which we have met: a three-hundred-bar steel cylinder loses around a tenth of its ideal figure to compressibility, where a modest recreational fill loses almost nothing.[5 ] The second is helium. Swap some of the nitrogen in your mix for helium, as technical divers do to cut narcosis (the dulling, drink-like haze of breathing nitrogen deep) and gas density on deep dives, and the compressibility penalty grows, because helium is even less inclined to pack down tightly than nitrogen is. The rule of thumb the trade uses is that the shortfall runs around five to ten percent for air and sport nitrox (oxygen-enriched air), and can reach ten to twenty percent for helium-rich trimix at high pressure.[3 ]
This is the case where the ideal-gas calculation stops being a harmless simplification. On a deep trimix dive your whole plan rests on the gas you are carrying, and a planner still using Boyle's law can hand you a cylinder that reads full and is short by a fifth of what you pencilled in. It is also a dangerous error, and an invisible one: an oxygen analyser checks your oxygen fraction but cannot see a helium shortfall at all. This is the reason Dive Kit's gas tools and its cylinder figures moved off the ideal gas law and onto a real-gas model, working each component's compressibility from reference data and combining them for the actual mix, so the free gas it quotes is the gas the cylinder really gives you.
Telling your dive planner which cylinder you have
All of this names a quiet trap in software: which of these numbers should an app ask you for? A metric diver thinks in water volume, so a litres box reads naturally. An imperial diver thinks in the nickname, and if an app asks for "volume in cubic feet" the only honest answer is 0.39, a number no US diver has ever said out loud. What they type instead is 80, and the app silently stores a cylinder nine times too big. A sharp-eyed ScubaBoard diver caught Dive Kit doing exactly this: his AL80 bailout proudly reported 668 cubic feet remaining, which would be quite the tank.
The fix, shipped in Dive Kit 2.8.4, is to ask each diver in their own sizing language. Metric units ask for the water volume, as before. Imperial units now ask for the capacity and the working pressure together, the way the tank is actually described, and the app inverts its real-gas model to find the water volume it actually needs, showing the derived figure under the fields so nothing is hidden.
Then the same forum caught the sequel, and it is a beautiful piece of detective work. A diver saw a metric 11 litre, 200 bar cylinder rendered in imperial as "76 cu ft at 2901 psi" and tried to verify it. Working backwards from the only convention US specs ever use, gas at one standard atmosphere, the compressibility factor implied by those numbers came out between 1.004 and 1.014, and no real gas at 200 bar behaves like that. He had not found a physics bug. He had detected, to three decimal places, that the app was quoting its cubic feet against 1 bar while he was reading them against 1 atm: our true Z of 1.023, divided by the 1.01325 between the two yardsticks, is exactly the 1.009 his arithmetic implied. Dive Kit 2.8.5 retired that last private yardstick. Capacity is now computed precisely the way the charts print it, real gas at 1 atm and 70 °F, so typing Luxfer's 77.4 at 3000 psi lands on the measured 11.1 litre water volume exactly, a steel HP100 reads the hundred it is named for, and the figure in the app is the figure on the sheet. Either way the number you typed is the number every screen reads back, and an impossible cylinder can no longer hide behind a unit conversion.
A word on temperature
One last reason a "full" cylinder might not be: heat. Pumping gas in quickly warms it, and a warm gas pushes harder, so a cylinder filled fast can read full while it is still hot and then lose pressure as it cools to water temperature. Nothing leaked; the gas just shrank back. The rough figure is around five to six psi for every degree Fahrenheit, so a cylinder topped to two hundred and thirty bar in a warm compressor room can settle nearer two hundred and ten once it has sat in ten-degree water for an hour.[8 ] It is the same gas law running backwards, and it is why a careful fill is a slow one, and why the pressure you see on the boat can sit a little under what the shop's gauge promised.
Knowing what a cylinder really holds is only half of any gas plan: it is the supply. The other half is demand, how fast you breathe that gas down once you are at depth, which is your surface breathing rate multiplied by the ambient pressure and the time, and which has its own tangle of names worth sorting out separately. Put the two together and you can answer the only question that matters underwater: is what I am carrying enough. The first step is just refusing to take the number on the sticker at face value.
参考文献
- 1. Diving cylinder. Wikipedia. "The internal volume… can be measured easily by filling the cylinder with fresh water. This has resulted in the alternative term ‘water capacity’, abbreviated as WC". The US "cylinder capacity… is a measure of the volume of gas that can be released from the full cylinder at atmospheric pressure." en.wikipedia.org/wiki/Diving_cylinder.
- 2. How to Select a Scuba Tank. Dive Gear Express. "Several tanks actually hold much LESS air than the size used to describe them… the ‘standard’ aluminum 80 (AL80) truly holds only about 77 ft³ of air and the steel ‘low pressure 85’ truly holds only about 81 ft³." divegearexpress.com.
- 3. Calculating Scuba Cylinder Capacities. Dive Gear Express / N2 Diving. Ideal capacity = water volume × service pressure / 14.696 psi; True ≈ Ideal / Z; the metric "litres × bar" shortcut "makes the ideal capacity overstated by 1.3%"; Z factors "prepared using the NIST REFPROP database… version 10". divegearexpress.com.
- 4. Luxfer / XS Scuba Aluminum Cylinder Specifications (rev 19A). LAL80: Service Pressure 3000 psi / 207 bar, True Capacity 77.4 cu ft, Water Volume 11.1 litres. Luxfer spec sheet (PDF).
- 5. Compressibility factor. Wikipedia. "Z = pV/nRT… For an ideal gas the compressibility factor is by definition 1." Air at 300 K: Z = 1.0326 at 200 bar, 1.1089 at 300 bar. en.wikipedia.org/wiki/Compressibility_factor.
- 6. When Real Gas Corrections Matter. The Theoretical Diver, 2 November 2017. Air "exhibits Z > 1 at high pressures, meaning cylinders hold less free gas than ideal gas law predictions suggest." thetheoreticaldiver.org.
- 7. Worthington Steel Cylinder Specifications. XS Scuba. LP85 (BS85): Water Volume 13.0 litres, Service Pressure 2400+ psi / 166+ bar, True Capacity 82.9 cu ft at 2640 psi (the 10% over-fill). Worthington spec sheet (PDF).
- 8. Gas Laws for Divers (Boyle, Charles, Gay-Lussac). NOAA Diving Center training slides. Rule of thumb: a steel cylinder's pressure changes about 5 psi per °F, an aluminium one about 6 psi per °F. NOAA (PDF).
- 9. NIST Chemistry WebBook, Thermophysical Properties of Fluid Systems. The reference equations of state behind the compressibility tables Dive Kit uses (Span et al. for N₂, Schmidt & Wagner for O₂, Ortiz-Vega et al. for He), tabulated as Z = P/(ρRT) from molar density. webbook.nist.gov/chemistry/fluid.