Airplanes and Air

When commercial airplanes ascend to 35000 ft, their cabin must be pressurized with air so the passengers do not pass out and die to a lack of oxygen. My question is, how much air (by weight) must be added to the cabin to keep it at atmospheric temperature? For my sake, lets use a Boeing 747 as our plane. No need to provide an exact answer, ballpark answers work well too.

I seem to remember 1 ton (2000lbs) of air needs to be added, but I’m not quite sure on that.

Why “add” any air at all. If the plane is airtight then it should retain its pressure at altitude. I think that it is more an issue of replacing stale air with new air. I think they don’t even bother with replacing all the air that they vent, since plane are typically presurized to 5,000 ft or so.

I’ll bet you can get a factual answer to this in GQ.

[ /Moderating ]

I’m only familiar with the Dash 8 pressurisation system, but the principles are the same for any aircraft.

Aircraft cabin pressurisation systems work by having a pressure vessel (the cabin), an inflow of air, and a metered outflow of air.

In current systems the inflow of air is excess air from the engine. “Bleed air”, as it is called, is taken from one or more of the compressor stages of a turbine engine (both props and jet.) It is then ducted to the air conditioning pack and in to the cabin and cockpit.

The “metered outflow” of air is the key to the system. By letting a measured amount of air out of the cabin and in to the atmosphere, a particular cabin pressure can be maintained. Due to structural restrictions, the cabin is pressurised to an equivelant of 8,000 feet. Low enough to keep you awake and healthy.

Normally the outflow is controlled by a computer but it is possible to control the pressure manually in case of a computer failure.

The pressure at 8000’ is approximately 753 mb or 22.2 inches of mercury. The pressure at 35,000’ is 238 mb or 7.04 inches. So I guess you’d have to add approximately 2 times the cabin volume to get to the required pressure.

According to this website, a B747-100 (rather outdated model now days) cabin has a volume of 516m[sup]3[/sup]. To make things more difficult, it is not just the cabin that gets pressurised, the cockpit (obviously) and at least part of the baggage and cargo area is also part of the pressure vessel.

Sorry, didn’t see that you wanted the answer in weight. If we go with 516m[sup]3[/sup] for a B747 cabin. 1 litre of air at sea level weighs 1.3g. So at an altitude of 35,000’ 1 litre would weight about 0.3g. The 516m[sup]3[/sup] cabin will then weight 154.8kg. To get the pressure down to the equivelant of 8,000’ you need to add roughly twice that amount of air. So you are adding about 310kg of air.

If we can get someone to give a more accurate volume for the entire pressurised part of a B747 hull then you’ll get a better answer.

You don’t actually have to add “extra” air to have the cabin pressurised - just don’t let the air that was already in it on the ground escape while you ascend to 35000 ft!

However, this is oversimplifying. As DanBlather says, some of the air that was in the plane is allowed to escape as you ascend, causing the cabin pressure to fall to the equivalent of up to an 8000 ft altitude. Also, during the flight, air is allowed to escape and is replenished with pressurised air from the engine compressors, maintaining the same pressure but replacing the oxygen consumed by the passengers and removing the carbon dioxide exhaled by them.

If you read the Facts and trivia about the 747, it does indeed declare that “when pressurised, the Boeing 747 holds about a ton of air”. This doesn’t mean that an extra ton of air has been added however - in fact it implies that the 747 holds more than a ton of air when it’s sitting on the ground with its doors open.

Your question can be answered, in terms of how much more air there is in the plane when it is pressurised compared to how much there would be at 35000 ft. For an exact answer we need to know the pressurised volume of a 747, which isn’t easy to find out - for one thing, there are so many variants. But for a ballpark figure:

747-400 - passenger cabin volume is 876 cubic meters, and the cargo volume is another 150 cubic meters.

First, sitting on the ground:

The mass of a cubic meter of air at atmospheric pressure is 1.22 kg, so that implies that a 747-400 contains about 1300 kg of air, sitting on the ground with its doors open, with the air at 15 deg C.

Then you need to know the density of the comfortably warm, slightly moist air in the pressurised cabin, and the density of the very cold, dry, thin air outside it at 35000 ft.

There’s quite a few variables there, which I don’t propose to play with. For a ballpark figure we can use the pressures and assume that air behaves like an ideal gas, i.e. halving the pressure halves the density. I’m going to neglect temperature completely.

At ground level, the pressure is 760mm of Hg, and the density is 1.22 kg
At 8000ft, the pressure is 565mm of Hg, implying a density of 0.9 kg /m[sup]3[/sup]
At 35000ft, the pressure is 179mm of Hg implying a density of 0.3 kg /m[sup]3[/sup].

So the mass of air in the 747-400 pressurised to 8000 ft is about 920kg, and the mass of air in a 747-400 that has suffered a complete blowout at 35000 ft is about 308 kg. So I make the “extra” air to be in the 600kg region - closer to half a ton than a ton.

And on preview, I see that working with about half the pressurised volume I was, 1920s Style Death Ray comes up with about half my answer, which is good!

Missed out the source for the pressures:

They are not airtight. If you leave the bleed air turned off, the aircraft won’t pressurise.

Not to mention expansion.