How much air does a 777-300ER's pressure cabin hold?

I've been wondering how much air a 777-300ER's pressurised cabin holds, but, while most of its specifications are fairly easy to find, the amount of air it contains is not.

Does anyone know what volume of air is held by the pressure cabin of an empty 777-300ER?

• You need a fuselage station drawing diagram where you can get the distance between the pressure hull's front and rear bulkheads, along with the fuse barrel diameter, and from there it's a simple volume calculation. I didn't have much luck, but you might get lucky googling it after some hunting around. Jan 16 '19 at 22:31
• As most things in life, this can probably be approximated fairly well through appropriate use of integrals over solids of revolution. sketch the 777 from the side as a straight tube with two pyramids at both ends (you can taper using another function if you want to be very diligent). Then, revolve this shape around its long axis and compute the volume integral. Now, intersect the volume with a plane from the top and bottom, simulating the cargo compartment as well as the area above the pressure vessel, and subtract that volume. Voila!
– 0xdd
Jan 16 '19 at 23:15
• Cargo compartments are generally pressurized so the volume should be included. Jan 16 '19 at 23:51
• @Jules The cargo hold is pressurized. The flat cabin floor would have to be extremely heavy to be strong enough to be a pressure bulkhead. Jan 18 '19 at 14:59

I once read it's about 1 metric ton (1000 kg) of air for a large widebody.

Here's a ballpark calculation to verify this.

The 777's cabin altitude is 2430 meter (8000 ft) when it's cruising at max altitude.

Wolfram Alpha tells us that a cubic meter of air weighs 0.96 kg at that pressure.

DimensionInfo shows that the 300ER is 73.9 m long and 5.86 m wide.

For simplicity, consider the 777 to be a perfect hollow cylinder. The volume of the cylinder is:

$$\pi \cdot \left(\frac{5.86}{2}\right) ^ 2 \cdot 73.9 = 1993\: m^3$$

So that's about 1900 kg of air for the cylinder. You have to subtract a large amount for the air lost to non-pressurized volume, tapering of the cylinder, non-circularity of the fuselage, and volume not occupied by air (structures, furniture, insulation, wiring, luggage, passengers).

I'd guess it's somewhere between 1000 and 1500 kg.

Whether people are on board or not has very little influence. People float or sink in water depending on having air in the lungs or not. So the density of a human is around that of water: 1000 kg per cubic meter. [In other words: you could fit 10 people weighing 100 kg in a cubic meter if you pressed them hard enough]. So the density of air is a thousand times lower than that of the passengers. Three hundred people - weighing 30000 kg combined - displace less than 30 kg of air.

• Huh. That's surprisingly small! Jan 18 '19 at 3:43
• The volume of a cylinder is pi x radius^2 x length, not pi x diameter x length! So it's more like 2000 m^3. Jan 18 '19 at 9:33
• @Bianfable Of course you're right, thanks. I've fixed it. Jan 18 '19 at 9:46
• This can't be right. You're claiming that between 50 and 75% of the hull is non-pressurized and I can't believe that's even close. It sounds to me like you've just fudged your calculations to agree with the value you remembered. Jan 18 '19 at 15:02
• @DavidRicherby He is not claiming 25% (not 75) to 50% of the hull is unpressurized: as explained in the second to last paragraph, you have to subtract all otherwise occupied volume. Also, "about 1 metric ton" is perfectly consistent with 2 tons depending on your definition of "about". Jan 18 '19 at 15:08