I'm not a professional pilot, but only have a degree in what you'd call "basic aerodynamics".
Humpmedumpme – thanks for your input but unfortunately it does not make any sense.
==> WRONG: his input does make sense.
Maximum ROC - flaps up will show you the maximum ROC you can get, if the flaps are retracted. It does not mean you will get the maximum ROC because your flaps are retracted.
Maximum ROC - flaps T/O will show you the maximum ROC you can get, if the flaps are in T/O position. Again, this does not mean you will get the maximum ROC because your flaps are in T/O position.
Note: you will never get as good values for your airplane in real live, simply because the POH values are flown with a new aircraft, a new engine, under nearly perfect conditions by a testpilot, who really really knows his job. Therefore, in reality, you would get climb rates which are lower than stated in the POH, because of aircraft age, engine age and your (everyone's) inability to fly perfect.
Drag = CL ˝ Rho Vsq S
==> WRONG again.
You are right about the similarity of the Lift and Drag formulas. But drag is calculated using the coefficient of drag (CD). Therefore the right formula would look more like followed:
Drag = CD 0,5 rho v2 S
where CD is the coefficient of drag, rho is density, v is velocity and S is (wing) surface (projected).
I will keep the next one simple:
Fowler flaps would increase both S and CD, resulting in more lift. More lift means more drag, you're clearly right on that.
BUT:
The increase in lift is less than the increase in drag
==> WRONG again.
If this were the case, flaps would be pointless at all. Until a certain point, flaps increase the coefficient of lift MUCH MORE than the coefficient of drag, therefore increasing lift MORE than drag, which ultimately results in a better L/D-ratio, which reduces stall speed, take-off run etc...
You can see this if you look at a Lilienthal polar diagram, where CL versus CD is pictured.
Sink occurs when it is retracted due to the aircraft not being at the “best rate of climb speed”.
==> WRONG again.
Sink occurs if lift is not greater or equal to the aircraft's weight. Not being at the aircraft's "best rate of climb speed" (cY) does not necessarily mean the aircraft descends. It simply means that the aircraft will not climb with the best rate of climb, but with a climb rate which is lower.
Finally:
It is rather disturbing that so many pilots and especially instructors do not understand the basic principles of flight. Look it up!
==> TRUE, and TRUE!
The very best instructor I could find thanks.
==> Maybe you should have looked elsewhere or longer.
From an engineers point of view and in the interest of aviation safety, you should not be instructing or flying at all, until you increase your very "basic" knowledge of basic aerodynamics.
Cheers, Mac