

Ask HN for comments: Popular math article: Sailing Hydrofoils - RiderOfGiraffes
http://www.penzba.co.uk/Catastrophe/

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frig
If the article's really about catastrophe theory I'd better-motivate the
catastrophe reference; dropping it in at the last second is pretty much a wtf
moment for a reader not forewarned.

Motivate it in the abstract as like (but rephrased to match whatever style +
diction constraints you're operating under):

Informally, a catastrophe means bad stuff happens all of a sudden; in the area
of mathematics known as 'Catastrophe Theory' we have a more formal definition,
but the same intuition applies, with a slight caveat we will come to
momentarily.

Consider a car driving on an icy road. One minute it's handling smoothly, but
then all of a sudden it starts drifting on the ice; the driver attempts to
reacquire control but without success. The car spins out of control and lodges
into a snowbank (thankfully everyone inside unhurt).

Our intuition says this is a catastrophe (perhaps a small catastrophe, but a
catastrophe nonetheless): one minute everything was as normal, but then
something terrible happened.

A catastrophe theorist would agree -- a catastrophe _did_ just occur -- but
here the caveat comes into play: a mathematician's catastrophe _isn't_ the
horrible crash into the snowbank. Instead, the mathematician's catastrophe is
the loss-of-control, as in the moment during which the car transitioned from
still-steerable to uncontrollably-drifting.

Catastrophe theory is, loosely speaking, the attempt to characterize and
understand the fine structure of transitions between different states-of-
operation (like the transition from steerable to drifting).

Thankfully not all "catastrophes" are catastrophes in the casual sense of the
word. To provide a sense of the flavor of catastrophe I've prepared a much
happier example of "catastrophe" involving racing boats (no crashes, I
promise!) and as a bonus you'll also learn quite a bit about what makes boats
fast or slow.

...then in the conclusion reiterate that the transition between the planing
mode and the "normal" mode is the catastrophe (it's the road, not the
destination, that matters).

===

Be careful with the use of "we".

It's good b/c it makes it friendly + inclusive but it makes things very
jarring when of a sudden you drop to a 3rd person neutral point of view (eg:
"Our truck is now a sports car." is more coherent with your overall turn than
"The truck is now a sports car.").

===

Then the idea of planing arose. When planing a boat is no longer displacing
water, it's skipping over the top. Some of its "lift" comes from the dynamic
force of the water hitting the bottom of the hull, and so less water has to be
forced out of the way. Less pushing, less bow wave, more speed.

...is clunky. You introduce the concept (planing) before you define it. When
in the next sentence you do define "planing" you do so indirectly: does
"planing" _mean_ "a planing boat is skipping over the top of the water,
instead of sitting amidst the water" or is "planing" some as-yet unspecified
thing that has as a side effect the property that when a boat is planing it's
skipping over the water?

Not enough time to try rewriting this for you but consider defining-and-
motivating planing first -- "If we could get out of the water somehow we could
go faster" (but more accurate and better-phrased) -- and then introducing the
term "planing" second (We can, and call this "planing", but again better-
phrased).

===

But let's ask the reverse (actually "converse") question. For a given amount
of drag, how fast are we going?

->

Let's ask the converse:

If we have this much drag, how fast are we going?

~~~
RiderOfGiraffes
Great thoughts - thanks. I don't agree with them all, but you've given me to
think, and I'll adopt most of them.

I hope others provide their opinions too.

------
RiderOfGiraffes
I'm writing this article, and while there are a few things left to do I
thought I'd float it here (if you'll pardon the pun) to ask what you think is
missing. What more do you want to see? What details should be added or
expanded?

Hacker News wasn't my initial target audience, but I've realised that it's a
good target audience that won't hesitate to tell you when you've got something
wrong.

------
jacquesm
Thanks, I've never seen such a clear explanation of why a displacement hulls
length in sail boats is a large factor in the theoretical top speed of the
boat.

edit: ok, I've read the whole thing now, maybe there is a way to tie this in
with hysteresis for contrast ?

~~~
JimmyL
Same here - I raced boats for years and knew that waterline legth was
proportional to speed, but never why.

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Radix
Is this related to your post from several months ago? I've been wondering what
you would end up putting together, and watching for it.

<http://news.ycombinator.com/item?id=672067>

~~~
RiderOfGiraffes
It's related, yes, but I'm building a body of popular articles that can then
sit on top of deeper explanations.

Short answer: yes. Longer answer: there's a long way to go.

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tome
Great diagrams! How did you draw them? Tablet?

~~~
RiderOfGiraffes
By hand on an old Nokia 770 internet tablet.

