Ask HN for comments: Popular math article: Sailing Hydrofoils

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).

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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.").

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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).

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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?

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.

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 ?

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

Great diagrams! How did you draw them? Tablet?