Am I right in think that a turbo charged aircraft would reach 2000 feet faster than a non turbocharged aircraft because
the turbocharged engine is simulating sea level pressure all the way up to 2000 feet so no power is lost
whereas the non turbocharged aircraft would be losing power while climbing to 2000 feet
Your theory is right.
However, ASSUMING you bolt a turbo
normaliser (i.e. no increase in the max engine power) onto a plane, then climbing from 0 to
2000ft I doubt you would see any difference. Any half decent plane (of the kind which might have a turbo option) will climb at +1000fpm or so, minimum, so 2000ft comes up pretty fast.
If you said 15000ft then there is a significant difference - probably 1/2 the time.
Also the turbo normalised plane will have a ceiling of ~ 25000ft whereas the same but non-turbo one will have a ceiling of about 19-20000ft.
Actually, the power output of a normally aspirated engine will initially increase during climb from sea level. This is because the back pressure on the exhaust side decreases, and that effect overcompensates the power loss due to decreasing air density.
Do you have a reference, with some data, showing a power increase between a given IAS at sea level and the same IAS at some higher level?
The back pressure drop does improve matters but nowhere near enough to compensate for the MP drop. If it made that much difference, nobody would need a turbo