Re: [Phys-L] Cabin pressure

[John Denker <jsd@av8n.com>]

On 7/2/22 3:47 AM, Antti Savinainen via Phys-l wrote:

> "The air pressure at 10 km is much smaller than on the ground. The pressure
> difference between the cabin and outside is decreased by having a decreased
> cabin pressure, something like we have at 3 km. If this were not done, the
> airplane structure should be more sturdy to sustain the force due to
> pressure difference."
>
> Is the explanation correct? I don't know much about aeroplane design, but
> the explanations involves a valid physical idea.

The concept is correct.

1) The concept is called "cabin pressure altitude". For
 purposes of pressurization (and for some other purposes)
 pressure is measured not in terms of force per unit area,
 but rather in terms of height in the standard atmosphere.
 Beware that high pressure altitude (feet) corresponds
 to low pressure (PSI) and vice versa.

2a) Part of the reason for having a cabin pressure that
 is not too high (cabin pressure altitude not too low)
 is to reduce stress on the airframe.

2b) Another part is energy aka fuel aka money: At high
 altitude, it takes a lot of energy to pump air from
 outside to inside. This energy is not recovered when
 old air is dumped overboard to make room for new
 fresh air.

 Incoming air is produced by "air cycle machines" which
 regulate pressure, temperature, and humidity. This
 involves a bunch of interesting thermodynamics and
 mechanics:
   https://en.wikipedia.org/wiki/Air_cycle_machine

 This requires so much energy that one of early items
 on the engine-start checklist is to make sure the
 air cycle machine is turned off. Otherwise you'll
 never get the engine started.

3) Airliners are designed and built so that they
 can maintain a cabin pressure altitude of 8000
 feet (2.4 km). This is covered by FAR 25.841(a):
  https://www.ecfr.gov/current/title-14/chapter-I/subchapter-C/part-25/subpart-D/subject-group-ECFRc61d71ee0787390/section-25.841

 Oddly enough, the operating requirements allow the
 cabin pressure altitude to be as high as 10,000 feet
 (3 km). The rules (FAR 121.329) are complicated:
    https://www.ecfr.gov/current/title-14/chapter-I/subchapter-G/part-121/subpart-K/section-121.329

 Above 10,000 feet they assume 10% of the passengers
 will need supplemental oxygen. That's a nightmare
 since you don't know which 10% that will be.

 People who reside in Bogotá are acclimated to the
 altitude and are perfectly comfortable at altitudes
 well above 10,000 feet.

4) Dan M. mentioned that the number of "cycles" i.e.
 pressurization/depressurization cycles is a limiting
 factor, having to do with accumulated metal fatigue.
 Strictly speaking that's true, but in practice for
 modern designs the limit is so high that typical
 airplanes never get anywhere near the limit. Some
 exceptions can be found in Hawaii, where there are
 a tremendous number of short flights.
   https://www.flightradar24.com/blog/nothing-but-a-number-aircraft-age-explained/

 The first jet airliner, the de Havilland DH.106
 Comet, had issues with this.
   https://en.wikipedia.org/wiki/De_Havilland_Comet

5) For some purposes e.g. medevac flights it is nice
 to increase the cabin pressure, although this may
 require cruising at a low altitude, so as to not
 overstress the airframe, i.e. to not exceed the
 allowed cabin pressure differential.

6) Things get interesting on descent, in the same
 way that getting into a parking place is trickier
 than getting out. You dial the destination field
 altitude into the cockpit control. Then the system
 interpolates between cruising altitude and field
 altitude, so that there is zero differential when
 you arrive, without any sudden changes.

7) As Anthony L. hinted, sometimes the main door is
 wider than the doorway, so it cannot be blown open
 by internal pressure. It's also true that it opens
 outwards, but you have to first move it inwards,
 then rotate it, then move it out through the hole.
 Boeing likes this design:
    https://www.youtube.com/watch?v=tO2wkubIsGc

 OTOH for some other aircraft e.g. Airbus, the door
 is not wider than the doorway. It opens outward in
 the prosaic way.
   https://www.youtube.com/watch?v=1rOI-4oGj7c

 Typical emergency exit windows are both taller
 and wider than the frame they're in. Nowadays the
 instructions say to pull the window inwards and
 set it on the seats. You could throw it out the
 hole, but that would require a complex rotation,
 and in an emergency some people are not clever
 enough to figure that out.

 So this is an interesting ill-posed question.
 The answer is underdetermined.
    https://www.av8n.com/physics/ill-posed.htm

8) In case of a failure of the pressurization system,
 it may be desirable to descend to an altitude where
 there is no need for pressurization or supplemental
 oxygen. This can be done in about 3 minutes, at a
 vertical speed of 8000 feet per minute. That is to
 say, the vertical component of velocity is 91 MPH.
 That involves dissipating energy at an astounding
 rate. Airliners are designed to have not much drag,
 so you really have to work at it to produce that
 much drag.

9) There is such a thing as high altitude pulmonary
 edema which is very very serious. However, usually
 it takes a couple of days at altitude for this to
 set in.
   https://www.ncbi.nlm.nih.gov/books/NBK430819/

 Short-term exposure to high altitudes usually just
 results in sleepiness, impaired vision, and impaired
 judgment.