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Topic: Medium: Manholes (Read 13664 times) |
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Lightboxes
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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?
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towr
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Re: Medium: Manholes
« Reply #26 on: Sep 24th, 2003, 11:41pm » |
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on Sep 24th, 2003, 6:38pm, 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? |
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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.
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| « Last Edit: Sep 24th, 2003, 11:43pm by towr » |
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saurabh_007
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After all its a hole it has to be round ......all holes are round
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BNC
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Re: Medium: Manholes
« Reply #28 on: Aug 5th, 2004, 6:43am » |
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on Aug 5th, 2004, 3:28am, saurabh_007 wrote:| After all its a hole it has to be round ......all holes are round |
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Not really...
From MW:
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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
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Nowhere does it mention the roundness of the hole...
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justine
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so.. after all this discussion, has anyone thought of why MS manholes are square?
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Grimbal
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Re: Medium: Manholes
« Reply #30 on: Oct 5th, 2004, 3:57pm » |
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Because apples are round.
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John_Gaughan
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Re: Medium: Manholes
« Reply #31 on: Oct 5th, 2004, 9:28pm » |
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And GNUs are... nevermind 
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Karthik
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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.
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Icarus
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Re: Medium: Manholes
« Reply #33 on: Apr 3rd, 2005, 12:38pm » |
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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.
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Sir Col
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Re: Medium: Manholes
« Reply #34 on: Apr 3rd, 2005, 3:30pm » |
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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.
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towr
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Re: Medium: Manholes
« Reply #35 on: Apr 4th, 2005, 1:14am » |
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on Apr 3rd, 2005, 3:30pm, Sir Col wrote: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
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| « Last Edit: Apr 4th, 2005, 1:16am by towr » |
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Sir Col
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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?
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| « Last Edit: Apr 4th, 2005, 10:35am by Sir Col » |
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towr
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Re: Medium: Manholes
« Reply #37 on: Apr 4th, 2005, 10:58am » |
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on Apr 4th, 2005, 10:33am, Sir Col wrote:Question...
Why must the polygon have an odd number of vertices? |
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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..
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Sjoerd Job Postmus
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Re: Medium: Manholes
« Reply #38 on: Apr 4th, 2005, 11:02am » |
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on Apr 4th, 2005, 10:33am, Sir Col wrote:Question...
Why must the polygon have an odd number of vertices? |
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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
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Icarus
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Re: Medium: Manholes
« Reply #39 on: Apr 4th, 2005, 5:20pm » |
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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.
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raprap
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Re: Medium: Manholes
« Reply #41 on: Jul 16th, 2005, 4:17am » |
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 I 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
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Jonathan Cohen
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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.
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sov
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Re: Medium: Manholes
« Reply #43 on: Nov 3rd, 2006, 5:56pm » |
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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.
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towr
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Re: Medium: Manholes
« Reply #44 on: Nov 5th, 2006, 7:04am » |
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on Nov 3rd, 2006, 5:56pm, sov wrote:| Round covers cannot even accidentally fall into a round hole that is smaller than the cover, but any other shaped covers can. |
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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)
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Edward_E
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Re: Medium: Manholes
« Reply #45 on: Nov 17th, 2012, 12:04pm » |
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You can fit a circle manhole cover into its cavity in any orietation. Other shapes, not so much.
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