Possibly apocryphal story of submarine failing at launch...

June 20, 2024 11:42 PM

I have long treasured an anecdote about an early submarine that when launched, proved unusable, because the hull was not perfectly circular. While its width had been measured repeatedly during construction, constant width is not the same as cirularity. However I can't remember the source...

... and diligent searching has turned up a maths text where I can't access the chapter indicated in the search excerpt, and a blog post from Mark Dominus, also clearly at "factoid" level. And another page noting that constant width curves are why submarine hulls must be built using a circular form to test for roundness.

My question is therefore: did this ever actually happen in early submarine construction? Or is it just a hypothetical confected for teaching about curves of constant width? And if the latter, is there a known first use of this story?

posted by i_am_joe's_spleen to Science & Nature (7 answers total)

I first read about curves of constant width in one of Martin Gardner's columns in Scientific American .

Could have been anytime in the 60s or 70s. The anecdote about the subs was definitely in the article and was presented as historical fact.
posted by jamjam at 2:16 AM on June 21 [1 favorite]

Response by poster: I feel like I read that same article in the 70s (or a later anthology). This is the Dominus blog post I mentioned, which has no source.
posted by i_am_joe's_spleen at 2:28 AM on June 21 [1 favorite]

I'm doing a simple GScholar search, and I suspect there will be something formal on this (but I'm on a phone and can't open pdfs);

submarine instability hull "earliest" roundness

this has better results:
submarine instability hull history circular roundness

interesting question as my grandather was a WW1 submarine architect/construction overseer, and designed many torpedos, as well as the first magnetic sea mine - for the British
posted by unearthed at 3:08 AM on June 21

I don't have a source, but I can throw in an additional search term that might be worth trying.

If it was a British article discussing curves of constant width, and was from 1969 or later, then I doubt the author would have been able to resist mentioning that the 50 pence coin is also such a shape, specifically a Reuleaux heptagon. This was an important property, so that a non-circular design could work with conventional coin slot mechanisms. The same is true of the five-sided 20p coin, but that didn't appear until 1982.
posted by automatronic at 7:17 AM on June 21 [1 favorite]

Here’s what Gardner had to say about subs in his article about curves of constant width:

Is the circle the only closed curve of constant width? Most people would say yes, thus providing a sterling example of how far one’s mathematical intuition can go astray. Actually there is an infinity of such curves. Any one of them can be the cross section of a roller that will roll a platform as smoothly as a circular cylinder! The failure to recognize such curves can have and has had disastrous consequences in industry. To give one example, it might be thought that the cylindrical hull of a half-built submarine could be tested for circularity by just measuring maximum widths in all directions. As will soon be made clear, such a hull can be monstrously lopsided and still pass such a test. It is precisely for this reason that the circularity of a submarine hull is always tested by applying curved templates.

No obvious reference to a source for this appears in the bibliography.

The book is The colossal book of mathematics : classic puzzles, paradoxes, and problems : number theory, algebra, geometry, probability, topology, game theory, infinity, and other topics of recreational mathematics , which also doesn’t specify which issue the original essay appeared in.
posted by jamjam at 1:47 PM on June 21

Here is a similar story dealing with the roundness/circularity of pieces of the space shuttle booster tanks - and which Richard Feynman believed could be a contributing factor to the leaks in the booster O-rings that finally led to the destruction of Challenger. This one seems to have decent documentation. Brief summary (from that link):

The total amount of squashing is only a fraction of an inch, but when you put the rocket sections back together, a small gap is enough to let hot gases through: the O-rings are only a quarter of an inch thick, and compressed only two-hundredths of an inch!

He then describes the procedure used to ensure the roundness of tanks, which was to check that the diameter was consistent at different angles around the tank - but then notes that this does not guarantee roundness, an arbitrary shape can have the same diameter at multiple different points, and there are even non-circular shapes that have a consistent diameter at every point.

Having tank sections slightly out-of-round may have contributed to the O-ring failure, and the method they used to ensure roundness was not theoretically sound, as it relied on an incorrect assumption that a circle is the only shape with a fixed diameter at all points.

See also p. 8-9 here.
posted by flug at 3:56 PM on June 21 [2 favorites]

US Submarines did NOT adopt circular hulls until USS Albacore (AGSS-569), which was commissioned in 1953. Previous submarines are really submersibles, a surface ship capable of underwater travel. AGSS-569 used a teardrop-hull. It is the first US sub to have a non-boat-shaped hull, and the first submarine that's faster underwater than surface travel.
posted by kschang at 5:26 PM on June 21 [4 favorites]