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Cantilevered card bridge

Don't breathe
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This is a house-of-cards style challenge in which the objective is not to build the highest tower but the one with the largest unsupported span. In principle it's possible to simply stack playing cards face up/ down to produce an arbitrarily large overhang. i.e. the top card can be laterally displaced from the bottom card by some distance less than or equal to infinity [insert lengthscale here]. Although the profile of an optimised stack can be derived mathematically, micron-scale manual precision will be required when placing the cards. Pre-fabricated construction aids such as formers and scaffolding are allowed to help erect the tower but these supporting structures must be removed prior to measuring the final unsupported span. A realistic overhang of three card lengths should be do-able with around 2000 playing cards, giving a tower approximately 500mm tall. Not suitable for outdoors.
EnochLives, Aug 05 2014

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       Name changed as suggested [bigsleep], despite it not actually bridging anything.
EnochLives, Aug 05 2014
  

       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.   

       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.   

       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.   

       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.
MaxwellBuchanan, Aug 05 2014
  

       “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.   

       [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.   

       Also your prism design would not be stable because the inner cards wouldn't be shorter than the outer ones.
pocmloc, Aug 05 2014
  

       //buttresses// Hmm. I think the rules should allow any surrounding structure which is not under or over the unsupported span.   

       //shorter// Good point (and well visualised). Is tactical card-bending allowed?
MaxwellBuchanan, Aug 05 2014
  

       I bid 4ft of diamonds
Ling, Aug 06 2014
  

       Also a arch would not be cantilevered, which would seem to break the implied rules of the title.
pocmloc, Aug 06 2014
  

       Only as long as the word "cantilevered" remains.
MaxwellBuchanan, Aug 06 2014
  

       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.
hippo, Aug 06 2014
  

       I assumed that bending, folding, cutting, tearing, glueing, reinforcing with steel girders etc. would not be permitted.
pocmloc, Aug 06 2014
  

       // I assumed that bending, folding, cutting, tearing, glueing, reinforcing with steel girders etc. would not be permitted. //   

       Correct. Deconstructing the cards into their constituent elements to form carbon nanotube suspension cables is also forbidden.
EnochLives, Aug 06 2014
  

       //buttresses//   

       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.   

       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.
EnochLives, Aug 06 2014
  

       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.   

       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.
MaxwellBuchanan, Aug 06 2014
  

       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.   

       1 card: 0.5
10 cards: 1.46
100 cards: 2.59
1000 cards: 3.74
etc.
sninctown, Aug 06 2014
  

       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.   

       //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.   

       //"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.   

       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.
EnochLives, Aug 07 2014
  

       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!
neutrinos_shadow, Aug 07 2014
  

       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.
pocmloc, Aug 07 2014
  

       I can't believe it's not buttressed...   

       Who would down-vote this? Fess up y' tarot-phobic fish-carcass slinger blighter!   

       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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