I have what some might think is an unhealthy interest in sewers. It's not really unhealthy, because, as I never tire of telling Mrs. R., I'm only interesting in theoretical sewerology, not the kind where I might actually visit a sewer (I tell her this whenever she wants me to do some plumbing repair in the house. I leave that to her. I prefer electricity. Truth to tell, I have actually taken a boat through the Paris sewers and visited a sewage treatment plant, but those were aberrations). I once edited a book that reprinted important papers and documents in 19th century sewer history. I ascribe my sewer fixation to their importance in the sanitary revolution of that century, which probably did more for public health than any medical advance.
Anyway. I've been thinking about manhole covers.
Originally sewers were visually inspected through small lamp-holes but these didn't allow getting in to do maintenance. So the bigger man-holes were cut in the large sewer pipes. Pipes big enough for manholes usually carried storm drainage as well as "domestic drainage" needed to be sized to carry the much larger volumes produced by rain events. Many of these systems move the drainage by gravity ("downhill"). The manholes allowed for venting.
Where is all this leading, you may wonder (besides the sewer)? One feature of round manhole covers is that unlike oval or square ones they cannot fall into the hole. I began to wonder what other shapes have that property and an obvious one (although not very practical for man holes) is an equilateral triangle. That raises the question of what are the characteristics of a plane figure that can't fall into a hole it just rests on. At first I thought that the circle might be the only convex such shape but then the triangle example occurred to me. Then I wondered about five pointed stars. Here the question is whether you could get them through the hole by tipping them a bit and levering them through that way. Then the two dimensional problem becomes three dimensional.
This is probably a well known problem that has been solved. Anyone know what the solution is?
This preoccupation is clearly the symptom of either someone with not enough work to do or too much work to do. I'll let you guess which category I fall into.
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Another advantage is that heavy, round discs can be rolled, unlike squares. The strength should be greater; a square ofthe same diameter should be heavier and weaker. In addition, the tunnel entrance should be stronger for being a cylinder.
Barry: Good point, the kind of thing I miss when my sewerology is theoretical.
Any Reuleaux triangle (or more generally, curve of constant width) has this property. An example of a non three sided shape with this property is the twenty pence coin. Reuleaux triangles can also be used to drill a square hole using only circular motion or function as a piston (in a Wankle rotary engine). In short, they are awesome.
'Cause knowledge is power:
http://en.wikipedia.org/wiki/Curve_of_constant_width
http://www.cut-the-knot.org/Curriculum/Geometry/CWStar.shtml
Actually, I think you're wrong about the equilateral triangle, but apparently a Reuleaux triangle would work:
http://en.wikipedia.org/wiki/Reuleaux_triangle
Dave, Andre: I knew there was an answer. Many thanks.
Interestingly they just recently finished the Combined Sewage Overflow mitigation project here in Rhode Island.
The Narragansett Bay Commission drilled two 2 mile long by 250' in circumference tunnels two hundred feet below the city of Providence. Now excess from storm runoff can be channeled into those tunnels to be processed later.
This result in less runoff into Narragansett Bay.
You hitteth upon it in two ways Revere as to why. The head shitologist at Memphis Light Gas and Water tells me that there are many reasons but mostly because of the two you mention. First is that it is totally round and cannot fall in whereas a square one with the clearances that are required to keep it from falling in could. The tolerances on a square one at the apex ends could over time wear and allow it to fall. His example on that is the storm drains on streets with their grates wear and collapse all the time and they have very tight clearances requiring a back hoe or bobcat to lift out for cleaning.
Second is the "pop up" factor. Whazzzat? The pop up factor is the elastic rebound of force applied to a steel iron lid. If you have never seen the backside of a manhole cover, except on the sidewalks they are generally counterweighted with steel ridges that are on the backside of the plate that extend downward at angles from the main plate. This allows for the dispersal of the weight to be countered by the weight on the other side of the plate as a high speed truck passes over it. This way it doesnt "pop up" from the inverse pressure rebound of the force applied from first one side, then the middle and then as the wheel leaves the plate. It basically absorbs the force applied to all quadrants of the plate all the same time. His example? Run over a piece of plywood in the road and even at an angle it responds to the force applied.
Amazing devices manhole covers. He said that the Romans designed the first feasible ones that were cast out of iron. Same thing applied when chariots ran over the little 2 foot wide ones.
He said he has to inspect a failing sewer in about a month and anyone who wants to tag along.........
You guys are working way too hard: Manhole covers are round because manholes are round.
As for the not falling in the hole bit, you could jigger that for non-round shapes by manipulating the width of the rim support; i.e. cover dimension vs. hole dimension.
So, what sort of manhole covers (we call 'em "access covers" here for gender nonspecificity) would the inhabitants of Flatland use?
The flat-landers would have to put up with a vulgar assymetrical shape, like an oblong with squares or oblongs cut out of two of its corners on one side, and so thin as almost to be a line. The cutout corners would allow the shape-hole to sit across a break in the floor line without falling into it or being capable of lateral displacement.
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Round covers will not fall through the hole. A square or other shaped cover can fall down if placed incorrectly. It's just that simple.
I just wanted to mention that I L-O-V-E this post and its comments.
I'm just trying to picture an overweight city worker lugging fifty feet of hose and various tools down a star shaped hole. Even a triangle would have a lot of wasted area in the corners.
Brian Hayes from American Scientist has started an interesting Flickr group on this and similar topics, http://flickr.com/groups/industriosphere/
mpb: Holy Smokes. Those Japanese manhole covers are unbelievable.
Yes, the President is convening a meeting in the morning. It is of national importance to make sure manhole covers do not fall in. We may not be able to get Iraq right and satisfy everyone, but this we should be able to get this one together. Yes, Rumsfelld and Halliburton will be attending. Cheney is out hunting.....
MRK,
Our politics may not be congruent, but your sense of humor works for me.
It seems to me that, in addition to the reasons already offered, that a round cover has the advantage that you can't put it back over the hole "wrong". Those covers are heavy, and workers don't have to worry about maneuvering a circle to get the corners lined up right -- however it gets put back in, it fits.
Good point Rev. People have also already mentioned the Reuleaux triangle, and in general any Reuleaux polygon with an odd number of sides would work.
I would also note that round covers are easier to manufacture than square ones or ones of more complex shape. And it's the shape that most closely approximates the cross sectional shape of the (possibly circumrotund) human body.
Dave is right: there were experiments (mostly in France) with alternative shapes, but while judged aesthetically pleasing by the Academie Merde Traitement Francais, there were problems with what translates into 'fat bloke hang up' when sewerage workers who had overdone the pastis, charcouterie and croissants tried to get into the sewers. Postmodernists are still arguing that all shapes are of equal value, and the Europeal Union committee report on personhole standardisation is expected sometime in 2010.
I have a nice book of manhole cover designs titled, with pleasing forthrightness, "Manhole Covers."
The Criterion DVD of The Third Man includes contemporaneous archival footage of the sewers of Vienna (which has a ring of multiple triangular covers). Fascinating stuff.
"we call 'em "access covers" here for gender nonspecificity"
the "man" in manhole is an abbreviation of maintenance, and therefore there is no gender implied in the term. political correctness can be carried too far.
(1) "What can you do with chocolate covered manhole covers?" -- short story by Larry Niven.
(2) Brother of gradschool rommate of mine made cash by stealing manhole covers and making them into coffeetables.
(3) I first described "the coffeetable book of coffeetables" in 1973, but agree that Kramer on Seinfeld show extended my result usefully with fold-out coffetable legs from the book.
(4) "Womanhole" starts as politically correct, but veers quickly into objectification, and reference to Courtney Love.
(5) Multidimensional manhole covers: in 3-D sphere is best, but Reuleaux polyhedra make nice aspherical ball bearings between two flat surfaces; in 4-D hypersphere is best, but Reuleaux polytopes make nice ahyperspherical ball bearings...
The Reuleaux triangle will also work as the slot for a tamper-resistant screw which can't be removed by wedging a flat screwdriver blade into it.
I saw it described in one of Henry Petroski's books a few years ago, but I diddn't know what that shape was called until now.
Rose George visits the London sewers - short, easy, good read. Published in the London Review of Books, May 2006.
href=http://www.rosegeorge.com/frameworks/generic/public_users/morearticles…
(can't get linking to work in any way)
She didn't bother her head about the manholes.
The shape of the manhole cover is a great example of a artefact that was designed to fulfill a few functions only yet free of dire constraints, as it basically only had to be easy to produce, handle, and had to admit entry and exit for humans, as a flat 'stopper' in a plane, with no other functions. There was a choice of shapes (see above), the best was obvious.
The ideal shape for a fridge is a sphere. (Efficiency.) But that didn't fit into kitchens, as rooms built by humans tend to be rectangular or square. Just one example.
copying link does not work..
http://www.rosegeorge.com/frameworks/generic/public_users/articles.asp
and go to In the London sewers. Ouf!
See page 191 of David Feldman's When Do Fish Sleep? for a scholarly exposition on this topic.
Years ago I sold real estate in Ponsonby,Auckland, a popularly known homosexual area,and had strident feminists demanding to inspect "person-holes".WHHAAH? Being, as I am, a person with an altogether unnecessary imagination,the first request was fodder for my fevered immagination.I was poised for requests to examine "wimmin-holes" but was spared that experience.
Wonderful thread, even though I'm late.
I intuited R-frency triangle for this problem as a kid, as having a constant diameter. But I didn't know the name, and also did not know then that I could make fun of frenchy pronunciation. That revelation came after working with a Frenchman.
i have been wondering this myself for school. I don't think they will acept this site though