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This answer proclaims one way to mitigate barotrauma:

reduce the rates of your descents, which will give your ears a chance to equalize. ATC, however, expects you to descend at between 500 and 1,500FPM, unless you are given "AT PILOTS DISCRETION."

Correct me if I don't write this mathematically correctly, but what's $\dfrac{d(barotrauma)}{d(FPM)}$: the first derivative of barotrauma with respect to FPM?

E.g. how much less painful is 500 compared to 1 500 FPM?

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    $\begingroup$ Your question may be objectively unanswerable since susceptibility varies between individuals, and even for the same individual on different days. Personally, I've never experienced anything more than slight discomfort on any flight, commercial or private. Probably about all you can say is that a slower descent allows more time for pressure to equalise and thus less chance of pain. $\endgroup$ – CatchAsCatchCan Oct 20 '19 at 10:25
  • $\begingroup$ Did you really mean "E.g. how less painful is 500 compared to 1 500 FPM?", or did you mean "how MUCH less painful is 500 compared to 1 500 FPM? $\endgroup$ – quiet flyer Oct 20 '19 at 17:12
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It's purely subjective, but I can tell you from personal experience descending in unpressurized airplanes that a 500 fpm descent is WAY less painful than a 1500 fpm descent if you have something like a blocked sinus passage. The blockage is usually not 100%, so the pressure rate of change has a huge effect on the pressure differential that is allowed to build up in your head as pressure equalizes, but just not fast enough.

Your head and sinus cavities (or inner ear) are effectively turned into a human Vertical Speed Indicator (which simply measures the rate of air pressure equalization between an aneroid chamber and ambient static through a restrictor, like your blocked sinus), but instead of a VSI pointer on the dial, you have the pain receptors in your skull. Like the VSI, a 1500 fpm descent will crank your pain receptor dial quite a bit higher than a 500 fpm one will if you have a sinus infection.

The important thing to point out however, is the typical airline passenger never experiences anything more than 500fpm in normal operations, because pressurization control schedules limit the rate of change in cabin pressure to that value. In any jet you are normally descending anywhere from 1-3000 fpm on an arrival, and even on final on a normal glideslope at, say 130kt, you are descending somewhere around 750 fpm.

It's only in unpressurized airplanes do you generally try to limit climbs and descents to 500 fpm when passengers are on board.

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I can tell you I was once in a situation where I was caught by severe sinus pain while descending in a light plane that I could not eliminate with the Valsalva maneuver. By climbing immediately I could eliminate the pain with the Valsalva maneuver and then apply the Valsalva maneuver during another descent, with minimal discomfort. Unfortunately I can't recall the descent rate used in either the first or second attempt.

In most cases, if the pilot (or passenger) "keeps up with" the situation by applying the Valsalva maneuver immediately at the first sign of the slightest discomfort (or perhaps even as a precaution before experiencing discomfort), s/he will be able to comfortably tolerate a much higher descent rate, than if s/he does not. Once a severe pressure imbalance develops, the Valsalva maneuver may not be always work.

So the answer to your question is going to depend on how alert the pilot or passenger is to the first sign of developing discomfort, and whether or not they know what to do about it.

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