An interesting fact is that Concorde had a similar inversion in its drag curve where as it slowed down the amount of drag increased meaning you had to throttle up to maintain the same speed.
In Concorde's case this was caused by the massive delta wing which created huge vortices at high angles of attack which allowed it to fly at reasonably low speeds (high compared to normal airliners but manageable) while having suitably low drag to fly at 2.5 times the speed of sound.
Almost all aircraft have a "slow flight mode" (google for it) like that at a high angle of attack. I'd say all, but its probably only 99.9% and someone would bring up the X-3 perhaps confusing its pitch-roll coupling with slow flight or something weird like that.
The stall angle of attack usually is not coincident with peak lift to drag ratio. In fact I'm not even sure you can FAA certify an airframe where peak L/D AoA is ever at stall AoA at any airspeed, they'd probably totally freak out about spin susceptibility, or at least I certainly would. So you have an engine failure and automatically by training go into best AoA flight mode, with that design any turning or even a little wind gust or whatever would probably mean a possibly unrecoverable spin, which would kinda suck. I mean I think you could theoretically design a wing airfoil that way, and physically build it, but you'd get flamed pretty severely about it. I think this would also make takeoffs and landings overly unstable/exciting. Airframes traditionally have pretty cruddy maneuverability/performance at stall AoAs although you could probably fix that (lots of exotic jet fighters do pretty well under those flight conditions, then again they aren't "most planes"...)
Also you're going to get pilots and CFIs all wound up, by trying to talk about using throttle to control speed, at least theoretically to reduce pilot induced oscillations you'll formally be told that AoA should be used to control airspeed and throttle should be used to control rate of climb (aka altitude, in the calculus integrated sense). A smooth experienced pilot makes it very hard visually to tell exactly which control input at which time is having what effect, but at least in theory this is what you'll be trained at least for major flight maneuvers, in practice very small scale triming / autopilot is usually the other way around as you describe, or so it seems. And those "in between" adjustments make a formal definition kinda complicated, or meaningless.
Piloting is a very hands on experience, so its like trying to teach someone gymnastics by writing articles.
Yes, I need to expand that bit. The individual craft simply displays hysteresis, but the point here is that hysteresis is what you get if your system is a slice through a fold (or other) catastrophe. By looking at the parametrized systems you get the fold emerging, even though each one individually is "just" a system with (or without) hysteresis.
Understanding hysteresis as a part of a larger topological structure is a rather deep insight, and one that I've struggled to convey completely.
So thanks for your comment, it's helped me think again about how this should be expanded and enhanced to make that point clearer.
Hmmm. Is there really a fold though? If you added velocity and position above the water into the mix then the state transition is unique and smooth. The fold appears because important quantities are not plotted and resolved elsewhere.
The only real discontinuity is the when the hull touches the water.
Maybe I don't really know the definition of a catastrophe. To me a PID controllor exhibiting ringing would look "folded" in position space (smooth in position/velocity space).
If you plot "Steady State Driving Force" against "Steady Speed" then for any given craft there is a curve. This curve the changes from simple quadratic(ish) through to the version discussed for the hydrofoil. We can think of this as adding every more efficient and effective foils to a more-or-less standard craft.
Now in the space "Foil Size" x "Driving Force" we plot "Resultant Speed" and we get a classic folded manifold, including the singularity.
So yes, there really is a fold.
Physics tells us that if you include lots and lots of things in your phase space then all the transitions are "smooth." Even here, when the craft touches the water and decelerates dramatically, almost "catastrophically", the transition (when considered in sufficient detail) is smooth. We can plot keel height above water, and as that gets to -1 mm then the deceleration is increasing smoothly, etc. However, dealing with this on a macro level, it's more useful to consider the dynamics as being a fold catastrophe.
Oh I think I understand better now. Something flips and moves the attractor for the system. Like an elastic band snapping, but with boats. Thanks for your reply
You can feel this in any boat that can plane (e.g., a small sailboat like a Laser or 420, or a small powerboat like a Zodiac or a Boston whaler). Once you get up on a plane in a power boat, you can cut the power back considerably (maybe 10% less throttle in practice) without losing any speed. When racing a small sailboat, this becomes an important tactic when heading downwind -- do whatever it takes to get on a plane, and then be careful to stay there. It's a very cool feeling.
A simple display of converting from displacement mode to planing mode is being a waterskier. An enormous force trying to pull your arms out of their sockets while neck deep in the water while going like 2 knots, then once you are standing on the skis on the water its not uncomfortable anymore.
In Concorde's case this was caused by the massive delta wing which created huge vortices at high angles of attack which allowed it to fly at reasonably low speeds (high compared to normal airliners but manageable) while having suitably low drag to fly at 2.5 times the speed of sound.