Pressurized Airplanes and Temperatures

This is one of those things from high school physics I feel right at the edge of my understanding.

So a pressurized aircraft is flying at some great altitude. The temperature outside is scary-cold but the cabin interior is nice and warm. Despite this, the coolers (air conditioners) are going full blast to keep the cabin temperature down.

I seem to recall it has something to do with pressure. All I know is that when I spray the Cheez Whiz, the can gets cold. Little help?

Please type slowly as I feel quite stupid about this.

The phenomenon is called adiabatic heating/cooling, where “adiabiatic” means no heat transfer. The heating and cooling is caused by mechanical work being done to compress the air (or mechanical work being done by the expanding air). The energy added/removed is manifested as a change in temperature. This is why diesel engines work: the piston compressed the air, it heats up hot enough so that when you inject fuel, it ignites.

If you’ve ever used a hand pump to inflate a bicycle tire, you may have noticed it can get pretty warm, especially right at the tire valve stem. Same thing: you’re compressing the air, doing mechanical work to make that happen, and the result is that the air heats up.

So imagine a plane cruising at 37,000 feet. At that altitude, ambient pressure is about 3.14 psi, temperature -63F. The cabin is kept at a “pressure altitude” of about 5000 feet - that is, the pressure is kept the same as you would feel if you were on the ground in Denver, about 12.26 psi.

When you take air at 3.14 psi and compress it to 12.26 psi, it heats up. A lot. The equation is thus:

T[sub]2[/sub]/T[sub]1[/sub] = (P[sub]2[/sub]/P[sub]1[/sub])sup/1.4[/sup]

Make sure your temperatures are on an absolute-zero scale, so T[sub]1[/sub] is actually 396 Rankine, instead of -63F. Anyway, solve for T[sub]2[/sub] and you end up with 584 Rankine, which is equal to 125 degrees Fahrenheit. That’s pretty damn hot, so yeah, you have to cool that air off before you dump it in the cabin.

So if it gets colder when I let the Chez Whiz out (by decompressing the gas) it gets warmer when I put the Chez Whiz (or the air) in?

That is straight forward.

But do they actually run air conditioners during flight? I’d think there is enough heat loss through the fuselage skin that they’d need a heater, if anything.

From the Wikipedia article on cabin pressurization:

Depending on which airport you’re at and what time of year, you’ll need some kind of air conditioner while the aircraft is on the ground. The system is actually surprisingly complicated to allow tight control over cabin pressure/temperature/humidity despite widely varying outdoor conditions and engine operating points (the engines are the source of the compressed air).

ETA: Slightly too slow; Machine Elf beat me to it.

Airline pilot …

This is a decent explanation I wrote awhile ago.

In summary, the engines compress air to presssures of many atmospheres and temps of hundreds of degrees C. Most of this air is then combined with with fuel & burned to create thrust to drive the aircraft. Some of that air (upstream of the burners) is diverted to the “air conditioners” to supply the cabin. Those units take that hot high pressure air as input and cool it and depressurize it to human-compatible pressures & temps, then inject it into the cabin to keep the people alive.

So at altitude the air we’re pumping in is very much heated & pressure-increased compared to outside ambient, but at the same time has gone through a lot of cooling and pressure reduction through the enviromental control system before it gets to you.

The current standard design of aircraft environmental control systems uses a device called an air cycle machine to manage the pressure & temperature stepdown. No freon or compressor / evaporator is used.

It seems paradoxical to try to cool a cabin on the ground by starting with 500 degree C air, but it works. And it’s mechanically simple and relatively lightweight, two major measures of merit for aircraft designers.

Paul, the actual physics behind all this is the Ideal Gas Law

In crude summary it says that given a chunk of gas, pressure and temperature are connected. if you add temperature you automatically get more pressure. And if you reduce pressure, you automaticaly get less temperature. Mother’s Nature’s books remain balanced because you get a corresponding change in volume the other way.

So the air cycle machines exploit that physics to make the hot high pressure air expand and lose pressure, thereby creating lower temps as well. Along with a couple stages of heat exchangers (air/air radiators) to carry away some of the heat energy, the net effect is convert air at very high pressure & very hot temps into air at slightly-higher-than-room pressure and more-or-less-room temperature.

And once you’re dropping the temp all the way from 500C down to around 25C, whether you want a little heat at 30C or a little cool at 15C doesn’t much matter.

Is it possible that through some mechanical failure of the cooling system the cabin temperature could get hot enough to kill off the people on board? I’ll be flying again soon, and I need something else to worry about.

Probably not. Machine Elf’s prediction of 125 F assumes no energy was lost from the ambient air (which is unlikely) and while that temperature is certainly unpleasant, it would take a long time to kill you.

To deal with this (more or less impossible) problem, it would be easy to reduce cabin pressure.

The other thing is that each passenger is emitting about as much heat as a 60-watt light bulb, which is a significant heat load right there.

**Paul **- Here is a good diagram of a single-stage air cycle machine with some explanation of the various steps the air goes through. It’s from the training material for a small turboprop aircraft. The same overall concept applies to ACMs on bigger fancier aircraft.

xoferew - That particular worry is not realistic. But …

There are other ways for excessively hot air to get loose where it doesn’t belong, with potentially dangerous consequences.

The remedy is to turn it off from the most upstream air valve which is installed right outside the engine itself. And if that valve’s stuck open, we can shut down the engine, thereby stopping the production of the hot air. Now we’ve got a different dilemma, but flying with one engine off is not a big deal.

If you want to worry about something, worry about the car next to you on the freeway driving to or from the airport. it’s driven by an amatuer, is designed with little or no redundancy in critical systems, and if its maintained at all, that’s also done to pretty low standards. But above all, it’s driven by an amatuer. And it can kill you in a fraction of a second, far quicker than you can react even if you’re Dale Earnhardt’s kid.

Now *that *scares the bejeezus out of me every time I drive to work.

And yet the safety of auto and airline transport seem to be comparable. Googling produces lots of varying data, but it seems that figures around 1.3 to 1.5 fatalities per 100 million passenger-miles are about right for both.

It’s also worth noting that auto accidents attributable to poor maintenance apparently are a modest percentage of the total, and that the single item most involved here appears to be tire condition.

Not according to Wikipedia. Air travel is significantly safer than road travel. And it becomes even safer if you only consider scheduled air service (i.e., planes that are not being flow by “amateurs”).

Further Googling suggests you’re right. They are not too far apart in deaths/hour, but airlines are considerably better in deaths/passenger mile.

Thank you all, I think I got it.

On our aircraft there are three places that might get hot. The bleed air itself might be too hot in which case it is shut off, the aircon pack might get hot in which case it is shut off, or the aircon duct temp downstream of the aircon might get hot in which case the aircon controls are automatically set to cold, if that doesn’t fix it the pack can be turned off. The worst possible outcome would be no airconditioning which means no pressurisation so a descent to a safe altitude that doesn’t require pressurisation would be made. Flying at the lower altitude means you burn more fuel and fly slower but in the planning stage of a flight you must ensure you have enough fuel to enable you to suffer a depressurisation at the most critical point of the flight and continue to an alternate aerodrome. In other words, it’s not a failure case you need to worry about.

BTW, the cabin can be ventilated with ambient air in the case of a pressurisation failure.

What if the airplane were on a tread-THUNK

Got 'im!!

Nonchalantly slips blackjack back into pocket and walks away whistling.

La de da de da, nothing to see here folks …