Wednesday, April 4, 2012

Why Are Manhole Covers Round?

One of the things they (or I guess "we" at this point, since I routinely fail to mention this at science-outreach events) never tell you about science is that most of it is waiting around.  A good percentage of my work time is spent waiting for processes to finish, waiting for vacuum systems to pump down, and waiting for machines to stabilize.  To make matters even more boring, most of that waiting happens in a clean room, where I'm wearing a bunny suit and forbidden from bringing in outside objects; it's not like I'm going to spend that time catching up on paperwork or reading a book.  The point I was gradually getting to: the other morning I was waiting for something science-y or other to happen and  killing time by repeatedly clicking the "random" button on theoatmeal.com.  While doing so, I ran across this:


(this is where you take a break and go read the hard-to-embed comic)


I realize that this is sort of missing the point, but the manholes question bugged the crap out of me for a solid day afterward.  The best answer I could come up with was "because the pipes they cap off are also round," but that's the worst kind of kick-the-can answer and just begs the question "well then why are the pipes round genius?"  So that's less than helpful.  All I accomplished from trying to come up with a better answer was getting the Teenage Mutant Ninja Turtles cartoon theme stuck in my head, so I decided to go to the Wikipedia.

Apparently this is an actual, somewhat famous question Microsoft likes to ask at interviews.  So for probably the 20th time today (and it's only a bit after noon), I'm extremely grateful to have a job despite quite clearly not deserving one.  Anyway, the reason Microsoft likes it so much is that there are a lot of good answers, and apparently which one you pick gives some unique insight into your personality (all my answer tells you is "MIT's Ph.D program has really gone downhill," so SUCK IT MICROSOFT).

Japanese manhole cover, which looks exactly how I'd expect it to.

The most important reason for having round sewer caps involves spatial geometry, so as someone who once got tagged "possibly learning disabled" in high school math I really never had a prayer here.  Basically, there's no orientation of a round sewer cap that can make it fall through a round hole of the same size.  A square/rectangular sewer cap, on the other hand, can easily be dropped down its corresponding hole if the angle is right. As an abortive childhood adventure inspired by either Goonies or Ninja Turtles taught me, sewer caps weigh like a quarter-ton; I can respect that dudes working underground, waist-deep in human excrement, probably have enough problems without the threat of one falling on their head.

The fact that sewer caps are so heavy also leads to a few other good reasons for them being round: they'll fit on the sewer in any orientation (no need to rotate to the correct angle), and they can be easily moved around via rolling.  Similarly, if there's a sewer cap in the road that's not correctly seated, it's a lot less likely to shred your car tires if it's got a round, vs. a sharply-cornered, edge sticking out.


Perhaps somewhat more practically, circular tunnels are both easier to dig and more stable than any other shape, so if you don't want your sewer system to collapse they're an excellent choice.  And finally, there's simple economics to consider: there's only a couple of companies that make sewer caps, and they all make exclusively round ones for all of the above reasons.  If you want any other shape, it's going to cost significantly more to have it custom-made.

You do occasionally see square sewer/utility hatches, usually in places that are a) not in a road, and b) leading down to electrical conduits, storm drains, or other things that don't run very deep.  The rugged individualists of Nashua, NH apparently use triangular sewer caps because LIVE FREE OR DIE or something.  I really hope their libertarian utopia is willing to make an exception and give sewer workers some decent health insurance. (addendum: there's no way a triangular cap can fall through a hole of the same size either.  See earlier comments on spatial geometry)

FREEDOM!!!!


So that's about six different, very good reasons for making sewer caps round, none of which I was able to come up with on my own.  That's disappointing, but I'm heartened by the fact that judging by such bestselling products as the Zune and Windows Phone 7, the question doesn't seem to be working out all that well for talent-screening at Microsoft.  Still, now you can go get a job there if you want, assuming they're dense enough to not change their interview questions after they turn up on both Wikipedia and random webcomics.  They'll probably ask you something like "why do we have a 120V/60Hz AC power grid" now, in which case you're welcome and you can repay me by doing something about the idiotic User Access Control in Windows.

7 comments:

  1. I like this, because of sharing the different types of manhole covers,but I would like to extend the description on manhole cover
    regards,
    Joshua.

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  2. Yes! Another classic interview question, pretty interesting since it creates a lot of discussion around it. This page is good too:

    Why are manhole covers round?

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  3. "(addendum: there's no way a triangular cap can fall through a hole of the same size either. See earlier comments on spatial geometry)"

    Point of order! This is, in fact, incorrect. A triangle such as the one shown can indeed be oriented to fall down through its own hole. The only triangle that will not is a "Reuleaux triangle", a specific variety of Reuleaux polygon (also known as curves of constant width), which is one where the sides are not straight but are in fact arcs centered on the vertex from the opposite side of the polygon (fun fact: Reuleaux polygons need an odd number of sides to work). You can find examples of several Reuleaux polygons on numerous British coins in the last decade or so, and an example of a Reuleaux triangle in particular being used for a manhole cover can be found here: http://www.maa.org/community/columns/maa-found-math/maa-found-math-2008-week-21

    You can find more discussion of Reuleaux polygons, with specific relation to manhole covers, here: http://mathtourist.blogspot.com/2010/08/manhole-cover-geometry.html and while there be sure to note the 12-sided manhole cover near the US Capitol building that they also mention.

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  4. It genuinely scares me sometimes that I managed to get an advanced degree and still have such staggeringly bad intuition about geometry.

    After playing with it on paper for a bit you're absolutely correct, thanks for pointing it out. The extra tidbit about Reuleaux polygons is interesting too. Someone should tell Nashua, NH that there's a relatively easy way to reduce their sewer worker body count.

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  5. Not really surprising; geometry, statistical puzzles (Monty Hall problem?) and most optical illusions, are very counter-intuitive subjects. We never evolved in an environment that needed those skills, so our brains aren't very well equipped to handle them.

    If you really want to have fun with Reuleaux polygons, consider the following: the circular manhole covers can also be considered a special case where the number of sides is expanded to infinity. Therefore, it simultaneously has one solid "side" (when considered as a regular geometric shape) and infinite "sides" (when considered as a Reuleaux polygon)! Of course, the circular nature also appears when you take regular polygons to the same infinite limit, as anybody who remembers reading* "Flatland" will remember, but for the Reuleaux theme it's still a nice point.

    And now, go write some new entries! I like this blog; don't let it languish...

    * Flatland is in the public domain. Go read it again. http://www.gutenberg.org/ebooks/201

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  6. Thanks! Always nice to hear feedback that isn't about my MSPaint illustrations being upside down.

    I'm trying to write some new entries but I've been low on free time since having a kid a few months back. Now that I think about it, "How do babies go to the bathroom so much that it violates the law of mass conservation?" might not be a bad entry...

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    ReplyDelete