Bozon lets not play this Book thing, if you have ever been in cruise in a plane with highspeed flaps, and you blow one notch, you will climb. I was not trying to get academical, I was giving a broad explanation, of flaps. I have the FAR, and the AIM setting at my desk, I did not feel the need to break them out and write a chapter. I was trying to Keep it simple. Everything I wrote was correct, I did not see the need to get in depth into the subject, I doubt that there are many folks studying for the Private pilots License, or the Commercial license.
BnZ if you look at the POH for the P-210, Smith Aerostar, the MU-2, they call for 1 notch of flaps on take off. Infact the reason that airliners lower flaps on takeoff is to increase lift, they change the profile of the wing, making the chord bigger, greating more lift, they raise them as they climb out they raise them because at a certin time it becomes a hindrance, because a thinner wing is a faster wing.
Again I was not trying to quote from a book or get seriously in depth, I was being very broad. I didnt think that most people care about the flight school aspect of flaps. Again to increase the rate of decent without an increase in airspeed by inducing drag in most types of flying.