Gordon, ... You gonna just GIVE that kind of writing talent away??
Nice job. If so, how 'bout writing another version for the 170 News? All our members would surely enjoy it.
Just to give consideration to a few things:
Anything which creates additional drag will generally lengthen a takeoff.
This includes flaps extended prior to actual flight, elevator not streamlined (as in trying to prematurely lift the tail) prior to flying speed, etc.
By starting out with the tail feathers faired (i.e., with the elevator in nuetral position) and with the flaps retracted, and then accelerating to flying speed and "popping" the flaps to a takeoff setting, (while using prior experience to also provide exactly the right amount of up elevator simultaneously with the flap deployment) ... then in theory at least... the shortest takeoff roll will be achieved. The airplane accelerated without the drag penalty of deployed flaps....until the exact moment of flight when the takeoff flaps were suddently "set" by "popping" them... And the airplane also didn't suffer the additional induced drag of a downward elevator placed in such a position by a pilot anxious to get the tail up prematurely. (In other words, if the airplane began the takeoff roll with the elevator faired nuetral...then the tail came up as it was ready to come up of it's own accord...which happens to be a signal to the pilot that the airplane is approaching flying speed anyway.)
If a pilot then simply appies a small back-pressure (actually a relaxing of backpressure since the elevator no longer needs to be held nuetral) to
prevent the tail from further rising....then the airplane will not waste additional forward motion building unnecessary additional speed prior to lift-off.
The problem then exists in simply determining that exact moment when...with flaps deployed...the airplane will leave the ground. That's the moment the flaps would need to be "popped".
Practice, practice, practice.
Of course, that's a lot of "technique" and practice. And such experimentation is rarely if ever accurately documented. Most of us are not likely to be that exact or that proficient. Not even Cessna's test pilots were good enough or proficient enough to warrant promoting such techniques. They were certainly loathe to document any such techniques sufficiently to endorse them. And they had the benefit of experience, perfect, light-weight airplanes, and accurate documentation.
For the majority of us, it's probably best to do just what the book recommends. Set the flaps prior to takeoff. Release the brakes after power is set. Allow the tail to rise of it's own accord to a tail-low takeoff position... and let the airplane do what it was documented to do.
Just read the documentation so you'll know what it's gonna do before-hand.
I recall (when I was much younger, renting someone else's airplane) going into the shortest strips I could find, just for the thrill of getting back out of there. (The old Almeda-Genoa airport's southwest-bound runway comes to mind, as well as the old southbound grass strip at the old in-town Bay City, neither of which still exist.) I'm pretty certain that tree leaves left chlorophyll on the lower wing surfaces on some of those takeoffs that gave me such pleasure.
Now that I'm older, fatter, and own the airplane I fly,... I'm a lot less willing to give myself such challenges.
I suspect the undocumented performance of tundra grass and down-hill slope in the bush country remains conjecture to the rest of us. These airplanes, operated in such conditions, become the unique tool of the experienced bush-pilot in such situations. There's a reason they're successful at what they do. The rest of the wannabes either have their epithets on gravestones... or enjoy the tales of those bushpilots that do it regularly, ...while snug and safe by our fireplaces.
