Minimum T/O & LDG Pressure Altitude
 

As per the thread title, I understand the reason for having a maximum pressure altitude, but fail to know the reasoning behind a minimum.

One would assume that the great performance from a having a lower pressure altitude would be better.

Is it due to the greater tire pressure differential at lower pressure altitudes?

What the certification testing that was done. There is a reasonable assumption that -500’ MSL is good enough and lower PA is unlikely, so it wasn’t tested and, not being tested, means it’s a limit.

200 psi tire pressure is about 13.6 atmospheres (differential)

so .1 atmosphere change or less does not change the differential that much thus is not a problem.

..which of course does not account for, say, Bar Yehuda Airport, -1240 feet MSL (Dead Sea region of Israel).

It's not a limitation for a dude in a 172, who can take off at any pressure altitude he darn well wants to try. (I won't bore you with the war stories)

But for flights that legally require TO calculations involving PA, if the charts, graphs and databases have a floor of -500 feet, simply for reasons of "why bother going lower?", then those pilots are limited to what they can calculate for.

It is sort of the flip side of the temperature ceilings that prevent some planes flying out of PHX on hot days. I'm sure they could successfully take off even at 52°C - but the charts don't go that high, so they can't do the legally-required calculations for that temperature, so they are grounded: 52°C (or -505 feet PA) lie in the "Here be dragons" regions.

Wouldn't there be lower tire pressure differential at lower pressure altitudes? Though lower differential seems more likely to cause a problem than higher. (And if you filled the tires at a low pressure altitude to a fixed PSIG, there'd be at a higher differential when the aircraft returned to given altitude.)

Of course, as Wiedehopf pointed out, none of these differences are very big.

And if there are commercial or Part 25 certified planes operated out of LLMZ, they can get data for it. Of course there are exceptions, bu5 most data stops at -500’P.A.

There's a consideration of combustion chamber pressure at T/O. A ~30:1 pressure ratio from P1 means very high pressures.

The airframer needs to certify the operating envelop - and that includes below Sea Level pressure altitude performance. In most cases it's just paperwork, but sometimes you do run into issues - for example a FADEC that only has power setting defined to -500 ft. (you'd be amazed at some of the unintended consequences you can get when you exceed the table limits).
At entry into service, the 747-8F was certified to -1000 ft. - which everyone figured was adequate. Then Europe was hit with a very cold weather system and the pressure altitude at some airports dropped down to about -1,200 ft. The 747-8Fs were effectively AOG! There was some serious scrambling at Boeing to certify updated performance limits to -2000 ft.

Hence that old adage .. if you want to be innovative out there in the field ... be innovative in a very conservative manner ... just in case it bites you on the tail.

Meh, not really. Combustion chamber pressure at takeoff from Bar Yehuda would be about 3% higher than at sea level.