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        riddles >> medium >> Medium: Manholes
        
(Message started by: Mixster on Jul 25th, 2002, 2:47am)
Title: Medium: Manholes
Post by Mixster on Jul 25th, 2002, 2:47am
Manhole covers are built round so that they cannot be turned on the diagonal and fit down the hole they're covering.  I'm guessing this happened once or twice and somebody got pissed after getting brained by one of these.  ;)

-Mixster
Title: Re: Medium: Manholes
Post by Nicodemus on Jul 25th, 2002, 6:12pm
Mixster, I think you've named the correct answer. However, I once asked someone this question and they gave a different, though valid, answer:

Manhole covers are very heavy. If they're round, you can roll them from place to place. Creative! :)

- Nicodemus
Title: Re: Medium: Manholes
Post by greg on Jul 25th, 2002, 7:08pm
Maybe they are round so they are more space-efficient? Doubtful, considering the price of steel, though.
Title: Re: Medium: Manholes
Post by Ion Rush on Jul 27th, 2002, 5:06am
when tiling (not the roof type, the under ground water drainage type) was first invented, it used clay tiles that were half cylinders placed on eachother, and then lined up with other cylinders.  This allowed water to seep in and flow away.  Large sewer systems were expansions of this type of system.  Also, when you want good water flow and desire to not have chuncks getting stuck, you would not want a square pipe (it would work fine if there was a large volume of water, but with little water, it would spread out and not flow well, flow slowly, zig zag across the floor, etc etc, a curved bottom collects the water, and even with just alittle bit flowing, you have a small deepish channel (like 3 inches wide 1 inch deep at deepest) rather than spread out (like 36 inches wide-the width of the square pipe- and less than a 10th of an inch deep)

so being that your horizontal subterranian pipe system is going to be round, why spend extra equipment and resources making special square pipes for going up into the street? Being that the shaft going upward is round, the most efficient shape for capping it would also be round
Title: Re: Medium: Manholes
Post by kenny on Jul 30th, 2002, 12:02pm
There are lots of answers to this, but I think the most common one is what Mixster said: so that the cover can't fall in the hole.

We all understand that a circle has the property that, if a circular manhole has a small lip inside it, and the cover is the same size as the hole above the lip, then it's impossible for the cover to fit all the way in the hole, past the lip.

A square, for example, does not have this property.

Question: Are there any other convex shapes, aside from circles, that have the same property, that the cover couldn't be rotated to fit past even an infinitesimal lip?

I think that's a more interesting puzzle.

-- Ken
Title: Re: Medium: Manholes
Post by anshil on Jul 30th, 2002, 1:27pm
An equilateral triangle ?
Title: Re: Medium: Manholes
Post by Nicodemus on Jul 30th, 2002, 6:43pm

Quote:
An equilateral triangle?


I don't think that works. Picture an equilateral triangle, one point (T) to 12 o'clock. Drop a line from T to the middle of the base edge. Let that be S (for short).

If we were to rotate the equilateral triangle 90 degrees out of plane around line S, the planar shadow of the triangle would be equivalent to S (plus some thickness). For any small thickness relative to the triangle, we can rotate S about 15 degrees around T, shift it away from T, and drop it through the triangle.

Sorry I don't have a way to diagram rather than describe this. :P


I would contend that the circle is the only (planar) shape which fits the bill. The criteria (as far as I can tell) are that the shape have the same maximum width when measured at an angle; if there were two different angles where the maximum width were different, then the shape could be manipulated such that the lesser width orientation passes through the greater width orientation.

If we allow convex shapes then we introduce a whole category of possibilities (which make no sense for manholes), such as two tangentially connected circles or a donut (ring). But it seems that, even for convex shapes, they only work when built from circles.
Title: Re: Medium: Manholes
Post by jkemp on Jul 30th, 2002, 8:05pm
Manholes are round for the same reason that ceiling access panels are square. We don't want manholes falling down the hole, but we do want to be able to remove a ceiling access panel without breaking the ceiling.

There is one other shape other than a circle that will not fall through diagonally. Such a shape must have a constant diameter. I don't know the name for the shape, but I saw it pictured once as an "alternative" for the wheel: it is a kind of triangular shape but with rounded corners. Any line drawn through the centre has the same length, so its diameter is constant; it would not fall down its hole diagonally.
Title: Re: Medium: Manholes
Post by Ryan on Jul 30th, 2002, 9:25pm
An equilateral triangle works because there is no possible way to make a line traverse the inside of the triangle that is of greater length than the sides.  No matter how you turn it, it will have a point that is equal to the length of one side.

There's another shape that works, although it is very unconventional.  Take 3 equal size half circles and connect them diameter to diameter such that they enclose an equilateral triangle shaped space.  
Title: Re: Medium: Manholes
Post by jkemp on Jul 30th, 2002, 9:27pm
No, an equilateral triangle (indeed, any triangle) can be turned and dropped down the hole. Not down the middle of the hole, obviously, but near one side.
Title: Re: Medium: Manholes
Post by Ryan on Jul 31st, 2002, 2:06pm
Ah, I see it now.
You're right.
Title: Re: Medium: Manholes
Post by Yossarian on Aug 5th, 2002, 7:19am
Actually there is an infinite number of so-called equal width
shapes. An example is Releaux shapes.
So, the answer is : the circle is the most well-known
shape of equal width.
Title: Re: Medium: Manholes
Post by anshil on Aug 5th, 2002, 9:40am
But the circle is the only one having one central rotation centrum, or? I mean the 3 half circles figure, you can't hang it up in the middle and rotate it on a plane without the hangup point going up and down. (altough the distance top-plane is constant)
Title: Re: Medium: Manholes
Post by Capt.Bushido on Aug 5th, 2002, 1:02pm
Actually, I think I've heard an ENTIRELY different answer than
any given here, once before:

Why are manholes round?

Because manhole covers are round.

And vice versa, of course.   ;D
Title: Re: Medium: Manholes
Post by jeremiahsmith on Aug 5th, 2002, 1:17pm
One of the reasons that circles are chosen over equilateral triangles is that you don't have to orient a circle in any particular way to get it in the hole. :)
Title: Re: Medium: Manholes
Post by Jonathan_the_Red on Aug 5th, 2002, 1:37pm
Yep. There are many good answers to the question of "why are manhole covers round"... perhaps the best general-purpose answer is "because that's the best shape."
Title: Re: Medium: Manholes
Post by Yossarian on Aug 6th, 2002, 3:25am
> There are many good answers to the question of "why are
> manhole covers round"... perhaps the best general-purpose
> answer is "because that's the best shape."

If it's the best shape, then why not ALL manholes
are round ? ;-)
Title: Re: Medium: Manholes
Post by Kozo Morimoto on Aug 6th, 2002, 4:45pm
According to a civil engineer friend who actually designs the damn things, the dropping theory is pretty cool, but the main reason is probably to do with the same reason why portholes on ships are round - to distribute the load stress evenly and avoid stress points.  When you have heavy loads (ie trucks and buses on roads driving over manholes constantly) having 'pointy' shapes would reduce the life of the manholes and increase maintenance requirements.  If the dropping thing is correct, why don't they just attach the covers with cables/hinges or make them slide across rather than be able to completely remove them?
Title: Re: Medium: Manholes
Post by jkemp on Aug 6th, 2002, 5:21pm
I like the load-spreading answer. I still think the "not falling down the hole" answer is the best one, since it is a simple design with a simple reason. No need for hinges, cables or slides which would degrade over time and make the cover harder to open.
Title: Re: Medium: Manholes
Post by LMD on Aug 11th, 2002, 1:21pm
Well, technically, for any shape of manhole cover, you can make it impossible to fall through the manhole.   Just make the cover hell of larger than the hole.  ;D

Round shape is just more effecient.
Title: Re: Medium: Manholes
Post by KamBha on Oct 8th, 2002, 6:30pm
Hi I am new to this board but this problem has me intrigued.  

I had another answer (Sorry if it has already been mentioned).  No, if I understand my manholes, to open a manhole you need a key that you stick into the cover then you lever open.  Now, if you have a shape with corner then there will be a place where you cannot lever the manhole. (ie the corners)
Title: Re: Medium: Manholes
Post by James Fingas on Oct 9th, 2002, 6:46am
I think they lever them open by sticking a pick-axe into one of those small square holes, then using the pick-axe as the handle. You could still do this on any shape of manhole cover.
Title: Re: Medium: Manholes
Post by The_Beast on Nov 23rd, 2002, 10:30am
Perhaps it is because the human body is more round that square.  Having a square manhole cover with lines tangent to the a circle inside the sqaure, would require more material.  Multiply this wasted space by the millions of manholes, and you save $$$.
Title: Re: Medium: Manholes
Post by jon_G on Dec 3rd, 2002, 5:25pm
I had to use a crow bar to open one before. My first guess was structural integredy then how it would be easier to fit in being a human and all. ;)
Title: Re: Medium: Manholes
Post by Samdog on Dec 18th, 2002, 5:00am
This really isn't an answer but rather just something that hasn't been brought up: manhole covers are not 2-dimensional. It seems for practical purposes they ought to be as thin as possible while maintaining structural integrity, but the fact is they must have some depth and could have a significant depth.

a 3ft square manhole cover that is 1.5ft deep could never fall through a 3ft square manhole (with the normal, required lip that prevents circular manholes from falling) because the smallest cross-sectional side of the cover would be 1.5ft by 3ft.
Title: Re: Medium: Manholes
Post by Lightboxes on Sep 24th, 2003, 6:38pm
What about this shape?   Won't it stop from falling within itself?
Or even regular polygons that have an odd number of vertices like a pentagon?
Title: Re: Medium: Manholes
Post by towr on Sep 24th, 2003, 11:41pm

on 09/24/03 at 18:38:49, Lightboxes wrote:
What about this shape?   Won't it stop from falling within itself?
Or even regular polygons that have an odd number of vertices like a pentagon?
No, because they are shorter in one direction than another. In this case point to point is longer than point to base (well, the base of the enclosing pentagon), so you can just drop it in that way.
Title: Re: Medium: Manholes
Post by saurabh_007 on Aug 5th, 2004, 3:28am
After all its a hole it has to be round ......all holes are round
Title: Re: Medium: Manholes
Post by BNC on Aug 5th, 2004, 6:43am

on 08/05/04 at 03:28:36, saurabh_007 wrote:
After all its a hole it has to be round ......all holes are round



Not really...
From MW:


Quote:
Main Entry: 1hole
Pronunciation: 'hOl
Function: noun
Etymology: Middle English, from Old English hol (from neuter of hol, adjective, hollow) & holh; akin to Old High German hol, adjective, hollow and perhaps to Old English helan to conceal -- more at HELL
1 a : an opening through something : PERFORATION <have a hole in my coat> b : an area where something is missing : GAP: as (1) : a serious discrepancy : FLAW, WEAKNESS <there are holes in your logic> (2) : an opening in a defensive formation; especially : the area of a baseball field between the positions of shortstop and third baseman (3) : a defect in a crystal (as of a semiconductor) that is due to an electron's having left its normal position in one of the crystal bonds and that is equivalent in many respects to a positively charged particle
2 : a hollowed-out place: as a : a cave, pit, or well in the ground b : BURROW c : an unusually deep place in a body of water
3 : a wretched or dreary place
4 a : a shallow cylindrical hole in the putting green of a golf course into which the ball is played b : a part of the golf course from tee to putting green <just beginning play on the third hole>; also : the play on such a hole as a unit of scoring <won the hole by two strokes>
5 a : an awkward position or circumstance : FIX <got the rebels out of a hole at the battle -- Kenneth Roberts> b : a position of owing or losing money <$10 million in the hole> <raising money to get out of the hole>
- in the hole 1 : having a score below zero 2 : at a disadvantage


Nowhere does it mention the roundness of the hole...
Title: Re: Medium: Manholes
Post by justine on Oct 4th, 2004, 10:54am
so.. after all this discussion, has anyone thought of why MS manholes are square?
Title: Re: Medium: Manholes
Post by Grimbal on Oct 5th, 2004, 3:57pm
Because apples are round.
Title: Re: Medium: Manholes
Post by John_Gaughan on Oct 5th, 2004, 9:28pm
And GNUs are... nevermind :)
Title: Re: Medium: Manholes
Post by Karthik on Apr 1st, 2005, 11:37pm
Is it possible that the round shape could be because it might help in some kind of closing mechanism. In other words, most bottles have around cap. The bottle and the cap are threaded and hence closing the bottle securely only involves rotating the cap from outside. It seems tough to develop a simple closing mechanism for square objects.
Title: Re: Medium: Manholes
Post by Icarus on Apr 3rd, 2005, 12:38pm
No - manholes lids are slightly larger than the manhole itself, and rest on an indented lip. There is no latching mechanism. The only thing that keeps them in place is the indention (which stops them from sliding to the side) and gravity.
Title: Re: Medium: Manholes
Post by Sir Col on Apr 3rd, 2005, 3:30pm
I think that the family of superellipses with equal axes (a=b) demonstrate quite nicely why the circle is a unique solution for negligible thickness covers:
http://mathworld.wolfram.com/Superellipse.html

If you imagine a circumscribed square performing a full rotation. With the exception of the circle, for which the diameter remains constant, the square will grow and shrink as it rotates and so it will have different minimums and maximums. Hence for some lateral orientation it will slot through.

However, depending on the thickness of the manhole cover I would argue that for n~=2, there are other non-circular covers that will not fall through.


An interesting and challenging question would be...

Given the thickness of the cover is t, find the interval, p<=n<=q, for which the cover will not fall through.
Title: Re: Medium: Manholes
Post by towr on Apr 4th, 2005, 1:14am

on 04/03/05 at 15:30:52, Sir Col wrote:
I think that the family of superellipses with equal axes (a=b) demonstrate quite nicely why the circle is a unique solution for negligible thickness covers:
http://mathworld.wolfram.com/Superellipse.html
Wouldn't any shape that has a fixed width for any orientation work?
And aren't there infinitely many of those. For example the Reuleaux Triangle (http://mathworld.wolfram.com/ReuleauxTriangle.html)
Title: Re: Medium: Manholes
Post by Sir Col on Apr 4th, 2005, 10:33am
You're absolutely right, towr!

And as you suggested, infinitely many do exist; one can be generated from any regular polygon with an odd number of vertices: draw a circle centred at each vertex and with a radius equal to the longest diagonal in the polygon. The curved edges closest to the polygon form such a shape.

Below is an example of one generated from a 5-gon.


Question...

Why must the polygon have an odd number of vertices?
Title: Re: Medium: Manholes
Post by towr on Apr 4th, 2005, 10:58am

on 04/04/05 at 10:33:27, Sir Col wrote:
Question...

Why must the polygon have an odd number of vertices?
Otherwise there is no opposing edge, just an opposing vertex. And you can't draw a curve between one opposing vertex, on the other hand you can between the vertices of an opposing edge..
Title: Re: Medium: Manholes
Post by Sjoerd Job Postmus on Apr 4th, 2005, 11:02am

on 04/04/05 at 10:33:27, Sir Col wrote:
Question...

Why must the polygon have an odd number of vertices?

It seems that r is the distance between the two fartest points in the polygon. For an even polygon, given point a, and opposite (or fartest) point b, there is only one point b. So when drawing the circle, you'd get a full circle, instead of an semi-circle.

For an odd regular polygon, there'd be two points b(and c) with the same distance from a. You get a triangle with one short side, and two other sides with the same length. (or, in the case of a 3-polygon, 3 sides as long. This's a special case).

Hope I explained it good enough
Title: Re: Medium: Manholes
Post by Icarus on Apr 4th, 2005, 5:20pm
Actually, you can generate a curve of constant width having almost any (convex?) curve for one side. I don't remember all the details and am too lazy to go look it up now, but it goes something like this. Take an open curve (probably it has to be convex, but I don't recall). We want to close the curve to form a curve of constant width. Set the width r to be the distance between the two endpoints, and "draw disks" of radius r about each of the points of the curve, taking their union. The boundary of this set should (with appropriate but fairly loose conditions on the initial curve) contain the two endpoints of the original curve. Use the segment of the boundary between these two points and going in the opposite direction from the original curve to close the original curve and form a curve of constant width.
Title: Re: Medium: Manholes
Post by Mjags on Jul 12th, 2005, 8:57pm
yea the real answer is what mixster said see http://www.improvedconstructionmethods.com/why_are_manholes_round.htm
Title: Re: Medium: Manholes
Post by raprap on Jul 16th, 2005, 4:17am
:DI had a boss who would ask this question of interviewees.  Actually he'd ask them to give three reasons that manholes were round, and the falling in the hole answer was one of them.  The other two?

My answers were that round rolls and it's a way to maximize the clearance in the hole while minimizing the surface area (simple optimization.)

I learned a fourth reason when a masonry structure engineer showed me that a round hole provides no vertices, and stress tends to collect at vertices.  

He also showed me an Engineering sewerage handbook where square manholes were described---note most square manholes incorporate a hinge in the cover to prevent the dropping in the manhole problem.      

Rap  
Title: Re: Medium: Manholes
Post by Jonathan Cohen on Nov 22nd, 2005, 2:30pm
Another reason for the rounded nature of manhole covers could be that if u have a square and a circle of equal circumference/perimeter the circle will have the greater area.

Imagine a square of side 10units (perimeter 40units) it has an area of 100units^2. A circle of circumference 40units (radius 20/pi) has an area of just over 127units.

Therefore when u need to send someone down the manhole a circle gives them the biggest area to work in.
Title: Re: Medium: Manholes
Post by sov on Nov 3rd, 2006, 5:56pm
They are round to keep the manhole covers from falling into the hole onto anyone.  Manhole covers are heavy and difficult to move around and can easily kill the biggest of men.  Round covers cannot even accidentally fall into a round hole that is smaller than the cover, but any other shaped covers can.  If I'm not mistaken this was a lesson learned by done degree of trial and error.

I also think that round covers would be stronger and be able to handle heavier weight than any other shape because with round the pressure on the cover and connecting rim is more evenly distributed that with other shaped covers.
Title: Re: Medium: Manholes
Post by towr on Nov 5th, 2006, 7:04am

on 11/03/06 at 17:56:42, sov wrote:
Round covers cannot even accidentally fall into a round hole that is smaller than the cover, but any other shaped covers can.
Untrue, there are infinitely many shapes that can't fall in. Sir Col gave an example a few posts up.
And of course, you could hinge the manhole cover, so it can't fall in and can even be opened more easily (an example of which was shown in another thread)
Title: Re: Medium: Manholes
Post by Edward_E on Nov 17th, 2012, 12:04pm
You can fit a circle manhole cover into its cavity in any orietation.  Other shapes, not so much.


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