Damn Pressure

[RTC'83]

I am learning how to calculate PA and DA by hand, and need help. Here is what I am working with:

Airport MSL 588'
Temp 22C
Altimeter 30.22 in Hg
Airport Density Altitude 1291

PA=[(29.92-30.22)*1000]+588
PA=288

DA=PA+[120(OAT-ISA Temp)]
DA=288+[120*(22-15)]
DA=1128

Why does my DA not the same as the Airport reported DA?
What I have learned is that my plane will perform as if it was 288 ft when I am actually at 588 because of PA, so what does DA affect?

All input is appreciated it.

[drseti]

It is DA, not PA, that determines how your airplane will perform. In your example, because of a combination of higher than standard barometric pressure and higher than standard temperature, your plane's performance is equal to what it would be at 1128 feet on a standard day. PA is merely what your altimeter would read on the ground if you dialed standard pressure (29.92) into your Kollsman window. It corrects for atmospheric pressure, which is the first step in computing DA, but to get DA you must also correct for temperature (and in this case, the higher than standard temperature dominates the calculation, raising your DA well above field elevation, and thus degrading aircraft performance).

[drseti]

Actually, I just calculated DA as 1165, which is between your solution and the reported DA. I suspect either rounding error, or truncation error in the constants used in your equation. But, don't get too hung up on the exact numbers. After all, you only knew temperature to two digits, so when you calculate an answer to four digits, the last two are meaningless. In other words, rounding down to two significant figures, 1165, 1291, and 1228 all equal the same thing: about 1200. (Don't expect any difference within plus or minus 100 feet to mean anything.)