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Regrettably, that is not the problem at all.
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Look, I don't want to piss people off or alienate them.
That post does not show an issue at all. He is comparing apples and oranges by using the FTH on a standard day with the performance on a non-standard day.
FTH at 5000 meter is the FTH at pressure altitude or a STANDARD DAY.
What I mean by that is on a 95 F day, at 29.45inHg, and a 67 F dew point spread, when you are at 5000 Meters True altitude the airplane is at 6992 Meters Density altitude.
In otherwords, when you are standing at sea level on that day, it is the exact same as being at almost 1000 meters in the air on a standard day.