h a l f b a k e r yA few slices short of a loaf.
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Name changed as suggested [bigsleep], despite it not actually
bridging anything. |
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I don't think the structure you refer to is very
interesting - the length of cantilever is limited
only by the number of cards you have and how
precisely you can place them. |
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But the idea of a competition for maximum
unsupported span is a good one, assuming that
entrants have free choice as to the design. It
should also be limited to the standard deck of 54
cards. |
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In theory (and only in theory) the widest span
would be almost 54 cards wide - an shallow arch
consisting of cards placed end-to-end (like a
normal stone arch, but with the stones being
incredibly thin top to bottom). However, this
structure would be at best meta-stable. |
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You might be able to do something similar, but
only a little less than 18 cards wide, by building an
arch in which each segment ("stone") consisted of
three playing cards in the form of a triangular
prism (axis running along the arch). Alternate
triangular segments would be rotated 180°
relative to eachother, providing a reasonably
stable structure. I think this could actually be
done. |
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“Bridge” suggests a span touching the table at each end; my initial impression was that we were looking for an “overhang” supported at one end only. |
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[MB] a shallow arch needs to push outwards at the ends - what do the rules say about the nature of the table surface or the use of weighted blocks as buttresses? I am guessing they are not allowed. |
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Also your prism design would not be stable because the inner cards wouldn't be shorter than the outer ones. |
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//buttresses// Hmm. I think the rules should allow
any surrounding structure which is not under or over
the unsupported span. |
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//shorter// Good point (and well visualised). Is
tactical card-bending
allowed? |
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Also a arch would not be cantilevered, which would seem to break the implied rules of the title. |
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Only as long as the word "cantilevered" remains. |
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A much stronger 'building block' could be made by making a short tear halfway down the left and right side of a normal playing card, rolling the card into a tube and slotting these tears into each other. Then, these cylinders can be joined end-to-end to form a 'pipe', slightly less than 54 playing cards long. |
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I assumed that bending, folding, cutting, tearing, glueing, reinforcing with steel girders etc. would not be permitted. |
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// I assumed that bending, folding, cutting, tearing, glueing, reinforcing with steel girders etc. would not be permitted. // |
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Correct. Deconstructing the cards into their constituent elements to form carbon nanotube suspension cables is also forbidden. |
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This is crucial. If buttresses are banned then that implies that the bridge carries no axial load or bending moment at mid-span. If this is the case then the bridge is effectively two non-interacting cantilevered "overhangs" (as was the intent of the original idea) joined back-to-back which seems somewhat redundant. |
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I can see that a cantilever has limited design potential and will only ever acheive moderate spans (with finite resources), but buttresses feel like cheating. I'm undecided which I would rather see, but I suspect "bridge of cards" is baked. |
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OK, no buttresses it is. However, you would also
need to specify the surface on which the thing is
constructed - friction against a rough surface can
provide a lot of buttrefication. |
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So, a defined surface, and no folding, cutting or
sticking. You'd have an issue over the definition of
"folding". For instance, putting a slight bow in a card
gives it vastly more regidity at right angles to the
bow. |
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What's the formula for span vs. number of cards
(perfectly) stacked? If the n-th card added to the
base of the stack adds 1/(2*n) card lengths to the
span, then you can span an infinite distance with
an infinite stack of cards, but the stack will be
much taller than it is wide. |
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1 card: 0.5
10 cards: 1.46
100 cards: 2.59
1000 cards: 3.74
etc. |
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As you say [sninctown] the offset between successive cards is 1/(kn), where n is the number of cards and k is a kind of stability factor which must be >=2 for positive stability. I concur with your calculations. Part of the challenge would be deciding on the optimum value of k, thereby trading stability for height. |
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//surface// Something dead flat and stable. A 4" thick steel precision measurement table (the kind used for CMM measurements) springs to mind. Every home should have one. To deter people from roughening the surface to gain a frictional advantage the first card could be stuck to the table and then all cards have to be placed above that. |
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//"folding"// One solution to this might be that all cards have to succesfully pass through an automated card shuffler after dismantling the build. You could think of it as a post-race drugs test for playing cards. |
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I think that if contestants stick rigidly to this set of rules we can pretty much guarantee that no fun will be had by all. |
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I think a smooth working surface would be too detrimental to progress. Something more like a pool table would be better - flat and rigid enough, but the fabric covering would allow card edges to "grip", facilitating construction (or perhaps more sand-paper-like?). But not external butresses or other supports, just cards. I like it! |
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Not having a pack of cards in the house, I experimented with 10 CD cases. I found that a genuinely cantilevered structure, ie. 1 case on the first level, 2 on the 2nd, with a counterweight on top etc. it was much easier to build a quick overhang than using a single exponential overhang. My guess is that the single stack has a final result higher, but the more symmetrical cantilever is more tolerant. So I think if there were also a time limit (perhaps 1 minute) the game might become more fun as well as encouraging alternative designs, trading theoretical maximum against ease and speed of construction. |
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I can't believe it's not buttressed... |
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Who would down-vote this? Fess up y' tarot-phobic fish-carcass slinger blighter! |
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There should be unlimited classes but based on exact multiples of fifty two.
Adding weights to the center of the span after construction could also be a variable. Not the longest span of cards, but the strongest span would win. The same arch might even win in both categories, but it would all depend on the keystone. |
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