no again. Sry. But you are in inviscid and incompressible.
Those eq are valid only bellow Mach 0.3. Btw 0.3 and O.6, this can do a nice guess-estimate if you had a coeff. Above 0.6, you can't rely on this way for calculating perfs.
Remind that 0.X is the LOCAL maxima of speed.
Thx however for the details you pushed here.
REM: If you had used your calculation to estimate the time of accel from Stall speed to 200mph, I won't have said anything (if you have added a coef in 2Pi*Alpha). Or the cruise speed (WWII).
~S
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