Part 3: Refining & Developing
In the previous parts (one and two) we outlined the problem and found the optimal options to choose in the general case, where we assign the same conditions to each beam because only considering one set of variables and dimensions is a lot easier than considering every set for each beam in the design! We found the best material to make all the beams is "Pine" and the optimal cross-section is one of the two hollow ones. However, the hollow cylinder has fewer variables, so we chose that one to work with. The next step is about how to lower the cost whilst also reducing the bridge's mass.
This is where things become a bit more of an art... Without needing to demonstrate it explicitly I hope it is uncontroversial to state that generally as the radius of a beam's cylinder increases its strength will also increase. Of course, in a real-world scenario we would very quickly run into issues like the beam being unable to support its own weight. However, the model being used on the back-end of the codefest is heavily simplified and does not think about these limitations. In other words, we can make the beams arbitrarily large and thin!
Except, actually we can't. There are some restrictions in place to prevent excessively non-physical solutions, but with a bit of tweaking and playing around with the numbers through trial and error it is possible to skirt very close to these limits and create a design that is both cheap and strong.
The quick and dirty design I created to take advantage of these limitations is as follows.
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Suggested geometry
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Cylindrical beams
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Pine
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inner radius = 5.15 m
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outer radius = 5.1503555 m
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cost = $992
We did it! A <$1000 design with minimal effort and just a bit of fiddling around with trial and error. However, as is hopefully clear, this method has huge room for improvement and I can't wait to see how people tackle the problem differently to me.
Doing better
To get this cheap design you could say I cheated a bit. I did, after all, abuse the physics engine just a teeny tiny bit. In my defense I originally created the solution in an hour during one of the codefests to demonstrate how plausible it is to get a sub $1000 answer without trying that hard. However, I am certain that with a more rigorous and thorough approach, greater, more physical, solutions could be developed. In particular I didn't touch the geometry at all and I know that the suggested design has a lot of unnecessary material in it, since it was deliberately designed to only do two things:
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Work. Aka be a viable solution
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Look like a bridge.
Efficiency was not a requirement and these suggested designs were very much created "by-eye". You could definitely do better. I can not wait to see the innovations people come up with. Perhaps a bridge path that hugs the rock boundaries would work better, perhaps a more judicious use of materials and cross-sections would be enough. That's the sort of answer I'm hoping to see when we run events like this one.
###Check-in Have you ended up here with no idea what's being discussed? This is the final article in a three-part series. You should probably read the previous installments in this series. You can find them here: