
Sailing Hydrofoils and the Fold Catastrophe - ColinWright
http://www.penzba.co.uk/Catastrophe/
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VBprogrammer
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.

~~~
VLM
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.

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tlarkworthy
Seems a bit of a leap to tag that with catastrophe theory? Surely that's just
hysteresis, and that's found everywhere.

~~~
ColinWright
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.

~~~
tlarkworthy
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).

~~~
ColinWright
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.

------
eli_gottlieb
And now I really want to try sailing a hydrofoil just to experience the "pop".

~~~
pcl
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.

~~~
junto
Having sailed a 420 competitively, I can confirm that standing out on the
trapeze wire whilst on the plane is indeed "a very cool feeling". :-)

For real hydroplaning dinghies you could try a Int. Moth:
<http://www.youtube.com/watch?v=gK60RZDtnT8>

