I wonder if it would have survived into the modern era, like many [0] of the compression-arch Roman bridges have. I imagine engineering history could have gone very differently, with such a crazy artifact standing as a proof-of-concept, inciting even bolder ideas. (What's the da Vinci version of steampunk called?)
Apparently there's a lot of other attempts (beside OP's) to build scaled versions of this bridge. (The article mentions a steel footpath bridge in Norway). Here's one I think is particularly interesting: a reasonably faithful replica at the 100-meter scale, built of pykrete [1] (sawdust-reinforced water-ice composite).
Not even that, really. He predates the pendulum by just about a century (and I mean Galileo's discovery of its regularity, not Huygens' employment of it). Sure, there was verge-and-foliot in limited number in cathedrals and monasteries, but common clockwork - Nuremberg eggs and that sort of thing - came along shortly after Leonardo went away. Sundials and water clocks were the order of the day in Leonardo's time.
>> I wonder if it would have survived into the modern era
No. The roman bridges, the ones still up, lasted so long because they were ridiculously overbuilt. The romans lacked a full understanding and so made everything far stronger than we now know is necessary. Even with a millennia of weathering and erosion they still have more than enough strength to remain standing. Da Vinci's bridge design is more efficient and uses less material. It spreads a similar load on a lesser amount of material. If using the same materials as the romans (stone) it would not last the centuries because it would have less reserve strength to lose to weathering.
Meanwhile, here in the USA, all we hear about is how our bridges are falling apart after 50 years and that we need to spend trillions to bring them and other stuff like that up to speed. Maybe we should have ridiculously overbuilt our bridges and roads so that they will last 2000 years. I know. Crazy ideas.
There’s no free lunch. An overbuilt bridge the magnitude of a modern suspension bridge may well take 50 years to build. The romans weren’t building them that big and the projects that were that big took generations.
Yeah, but I'm not talking about bridges like the Golden Gate or Brooklyn Bridges. Those bridges will never be in danger of falling down, because bridges like that are constantly repaired and maintained.
The bridges that I am talking about, and that most are talking about, are the shorter bridges. The ones that are 20 or 30 or 50 feet long - just the regular small bridges - there are thousands and thousands of them, all ready to fall down. Just looked it up, I was not even close - there are not thousands and thousands, there are more than 617,000 bridges across the United States. https://infrastructurereportcard.org/cat-item/bridges/
>No. The roman bridges, the ones still up, lasted so long because they were ridiculously overbuilt.
That seems like counterproductive for defense as destroying bridges were/is a common military strategy. Even the famous Trajan's Bridge (the longest arch bridge of that period) was supposedly destroyed to prevent barbarian invasions[1].
May be it was enough that the superstructure was purposefully weak to destroy it on demand and the substructure, foundation was overbuilt as you mentioned.
Even if it would have lasted, which I doubt, I also doubt it would have successfully inspired much, and certainly not any time before real engineering came about as a consequence of understanding physics and thus having a theory guiding and supporting work, rather than a cookbook of rules. (Like, the surviving ancient marvels notwithstanding, you can really only go so far in structures without an understanding of beam theory, stresses, even the square-cube law which wasn't articulated until Galileo.) When the architects and builders of the past (I think it's a stretch to call them engineers) veered too far from established practice, things tended to frequently collapse. A Roman example: https://en.wikipedia.org/wiki/Insula_(building)
I'm a bit shocked that in 2021, students rely on physically building the bridge and simulating earthquakes with moving platforms. This feels like dummy engineering.
I would have expected a mechanical engineer to actually be able to prove or disprove the feasibility through math, and create a CAD model on which to apply forces simulating earthquakes, heatwaves, etc.
On contrary, I am actually delighted to see the hands-on approach. Pure math is vulnerable to missed preconditions/unknown unknowns, with potentially catastrophic ramifications when it's carelessly applied to real building. You must know in advance what you're going to prove.
> Pure math is vulnerable to missed preconditions/unknown unknowns, with potentially catastrophic ramifications
Interestingly I see the opposite. I expect the replica to be full of dangerous approximations: scaled weight of the stones not realistic, friction of the material not taken into consideration, earthquake ground vibrations not properly emulated by just shaking plates, etc
I take issue with the term "pure math" here. Engineering simulation is strictly the realm of applied math, a dark art of floating point calculations, finite element analysis, idealized material properties, etc. Pure math demands much more rigor, and gets exact answers, but the methods available cannot handle the complexity of a bridge in this lifetime.
Why spend a lot of money making an error prone program when you can have reality simulate it for you?
This is a problem I had at my last job, actually. We'd spend a lot of time on simulation that was kind of accurate but still need to do a fair bit of rapid prototyping to make up for simulation deficiencies afterwards.
For simple stuff like a prototype jig to hold equipment mockups can be faster to make out of rough cut materials instead of spending 2 weeks making everything fit in a CAD program.
It's the "Unknown Unknowns" that bite you. Via simulations and calculations you can be fairly sure that everything you've thought of will be fine, but there may be things you haven't thought of, and they may prove fatal to the design.
In a later comment you say:
> "I expect the replica to be full of dangerous approximations: scaled weight of the stones not realistic, friction of the material not taken into consideration, earthquake ground vibrations not properly emulated by just shaking plates, etc"
How do you know that your model accurately represents the earthquake ground vibrations? How do you know that your model accurately represents the friction? Compressibility and friability of the materials? The scaled weight of the stones?
How many times have you written a large and complex program, only to find that there are real world cases you haven't considered?
I'm sure they did the computer modelling, but personally, I'm happy to see people building real-world versions to verify their (software and mathematical) models.
> Via simulations and calculations you can be fairly sure that everything you've thought of will be fine, but there may be things you haven't thought of, and they may prove fatal to the design.
I don't deny that, the theorical approach will surely not be 100% accurate. Still, I expect that I would give me thousands of time more confidence than a 3D printed replica.
> How do you know that your model accurately represents the earthquake ground vibrations?
Because I expect the earthquake simulations in architecture CAD software to be made by physicists that spent time carefully modeling the realistic and complex set of forces that a structure would feel during an earthquake.
> How do you know that your model accurately represents the friction?
Again, because architecture CAD software are specifically crafted for that purpose, and can theorically simulate the friction and adherence of various materials much more realistically than a mockup 3D printed replica.
You say that architecture CAD programs simulate things better than physical models with a lot of confidence, but I am not sure why.
One way to think of this is that the physical world is a vastly superior computer. We cannot make a fluid simulation that runs as precisely as an actual river, for example. Tribological models have to make tons of approximations since friction is insanely complicated - but the physical universe manages to calculate the real friction effect basically instantly!
the initial team of "modern" structural engineers were convinced - after mathematical analysis and computers simulations - that the bridge could not possibly be re-built exactly as it was.
Then we contacted to verify the calculations an "old" structural engineer that believed that if something has been built and resisted (before the bombing) some 400 years, it can be built and is resistant enough.
It came out that due to some limitations of the software used at the time, and to some approximations in the design of the computer model, the resistance (and influence) of the lead fixed steel pins (that were - for the time of building - a technical marvel) was greatly underestimated, as well as the effect of the steel strips.
See here for some details on how the bridge was built:
We're all speculating here, of course, but I would expect it to be rather difficult to simulate both the static properties of the finished bridged and the dynamics of putting it together, which is obviously an important part of the process (see the keystone anecdote).
Arches are tricky. The undergraduate way to model arch bridges is as three hinged structures - free to rotate at both ends and with a virtual "pin" in the middle, in order to make the math tractable.
That's the kind of approximation that goes into mathematical models.
You can take one fast look at the design and see where the biggest problem is going to be: the lateral (spreading) forces against the ends of the bridge will require some clever anchor or ground lock of sorts, otherwise the ends will just shove apart and the middle will collapse.
Notice in the modern model, they have the ends not only anchored, but actually blocked within boundaries that prevent spreading.
Other bridges have used a similar design, but they had much more of a vertical component. Then the forces at the ground were more perpendicular to the earth plane, so gravity and mass of the stones (and friction of the stones against the earth) could better prevent separation.
To be fair, even modern arch style bridges have the same concerns. For example, overhead arch bridges get around it by using ties between the ends running underneath the actual bridge itself to prevent the ends from separating. The Hernando de Soto bridge used this type of design and was recently closed for a few months because one of the ties had started to fail.
33 comments
[ 3.1 ms ] story [ 77.8 ms ] thread[0] https://en.wikipedia.org/wiki/List_of_Roman_bridges
Apparently there's a lot of other attempts (beside OP's) to build scaled versions of this bridge. (The article mentions a steel footpath bridge in Norway). Here's one I think is particularly interesting: a reasonably faithful replica at the 100-meter scale, built of pykrete [1] (sawdust-reinforced water-ice composite).
https://www.cursor.tue.nl/en/news/2015/april/tue-team-to-bui...
https://www.youtube.com/c/BridgeInIce/videos
[1] https://en.wikipedia.org/wiki/Pykrete
I can't find a good post-mortem article, but it looks like it collapsed during construction and was abandoned. (?)
Clockpunk.
No. The roman bridges, the ones still up, lasted so long because they were ridiculously overbuilt. The romans lacked a full understanding and so made everything far stronger than we now know is necessary. Even with a millennia of weathering and erosion they still have more than enough strength to remain standing. Da Vinci's bridge design is more efficient and uses less material. It spreads a similar load on a lesser amount of material. If using the same materials as the romans (stone) it would not last the centuries because it would have less reserve strength to lose to weathering.
The bridges that I am talking about, and that most are talking about, are the shorter bridges. The ones that are 20 or 30 or 50 feet long - just the regular small bridges - there are thousands and thousands of them, all ready to fall down. Just looked it up, I was not even close - there are not thousands and thousands, there are more than 617,000 bridges across the United States. https://infrastructurereportcard.org/cat-item/bridges/
That seems like counterproductive for defense as destroying bridges were/is a common military strategy. Even the famous Trajan's Bridge (the longest arch bridge of that period) was supposedly destroyed to prevent barbarian invasions[1].
May be it was enough that the superstructure was purposefully weak to destroy it on demand and the substructure, foundation was overbuilt as you mentioned.
[1] https://en.wikipedia.org/wiki/Trajan's_Bridge#Destruction_an...
Even if it would have lasted, which I doubt, I also doubt it would have successfully inspired much, and certainly not any time before real engineering came about as a consequence of understanding physics and thus having a theory guiding and supporting work, rather than a cookbook of rules. (Like, the surviving ancient marvels notwithstanding, you can really only go so far in structures without an understanding of beam theory, stresses, even the square-cube law which wasn't articulated until Galileo.) When the architects and builders of the past (I think it's a stretch to call them engineers) veered too far from established practice, things tended to frequently collapse. A Roman example: https://en.wikipedia.org/wiki/Insula_(building)
I would have expected a mechanical engineer to actually be able to prove or disprove the feasibility through math, and create a CAD model on which to apply forces simulating earthquakes, heatwaves, etc.
I agree, engineering is art + science, impossible to iron everything out theoretically.
Interestingly I see the opposite. I expect the replica to be full of dangerous approximations: scaled weight of the stones not realistic, friction of the material not taken into consideration, earthquake ground vibrations not properly emulated by just shaking plates, etc
This is a problem I had at my last job, actually. We'd spend a lot of time on simulation that was kind of accurate but still need to do a fair bit of rapid prototyping to make up for simulation deficiencies afterwards.
For simple stuff like a prototype jig to hold equipment mockups can be faster to make out of rough cut materials instead of spending 2 weeks making everything fit in a CAD program.
I would think that could commonly be done without any university.
Making the actual physical model could be considered a better use of MIT resources while they are there.
I still remember some of the shake table stuff I did 30 years back.
> Both of these factors are tested through analytical means and a 3D physical model supported by moveable abutments
http://congress.cimne.com/formandforce2019/admin/files/filea...
In a later comment you say:
> "I expect the replica to be full of dangerous approximations: scaled weight of the stones not realistic, friction of the material not taken into consideration, earthquake ground vibrations not properly emulated by just shaking plates, etc"
How do you know that your model accurately represents the earthquake ground vibrations? How do you know that your model accurately represents the friction? Compressibility and friability of the materials? The scaled weight of the stones?
How many times have you written a large and complex program, only to find that there are real world cases you haven't considered?
I'm sure they did the computer modelling, but personally, I'm happy to see people building real-world versions to verify their (software and mathematical) models.
I don't deny that, the theorical approach will surely not be 100% accurate. Still, I expect that I would give me thousands of time more confidence than a 3D printed replica.
> How do you know that your model accurately represents the earthquake ground vibrations?
Because I expect the earthquake simulations in architecture CAD software to be made by physicists that spent time carefully modeling the realistic and complex set of forces that a structure would feel during an earthquake.
> How do you know that your model accurately represents the friction?
Again, because architecture CAD software are specifically crafted for that purpose, and can theorically simulate the friction and adherence of various materials much more realistically than a mockup 3D printed replica.
One way to think of this is that the physical world is a vastly superior computer. We cannot make a fluid simulation that runs as precisely as an actual river, for example. Tribological models have to make tons of approximations since friction is insanely complicated - but the physical universe manages to calculate the real friction effect basically instantly!
https://en.wikipedia.org/wiki/Stari_Most
the initial team of "modern" structural engineers were convinced - after mathematical analysis and computers simulations - that the bridge could not possibly be re-built exactly as it was.
Then we contacted to verify the calculations an "old" structural engineer that believed that if something has been built and resisted (before the bombing) some 400 years, it can be built and is resistant enough.
It came out that due to some limitations of the software used at the time, and to some approximations in the design of the computer model, the resistance (and influence) of the lead fixed steel pins (that were - for the time of building - a technical marvel) was greatly underestimated, as well as the effect of the steel strips.
See here for some details on how the bridge was built:
https://www.litosonline.com/en/article/old-bridge-mostar-rec...
It also once again makes me consider the idea that da Vinci was a time travelling physicist having the time of his life.
Notice in the modern model, they have the ends not only anchored, but actually blocked within boundaries that prevent spreading.
Other bridges have used a similar design, but they had much more of a vertical component. Then the forces at the ground were more perpendicular to the earth plane, so gravity and mass of the stones (and friction of the stones against the earth) could better prevent separation.
https://no.wikipedia.org/wiki/Da_Vinci-broen