[Magic] Using Shape Earth and Earth to Stone in construction

[Michael Thayne]

Originally Posted by Anaraxes

If you fuse all the stones, you don't necessarily get a true arch. You get a shape that could be described as post-and-lintel with a semicircle chopped out of the center bottom of the lintel. I'm not an engineer, but it's not obvious to me that an homogeneous block with a semicircular cutout is stronger than the full post-and-lintel (itself weak compared to an arch).

The point of the arch is converting the downward stress into stress along the perimeter of the arch, and thus making it compressive around the arch span rather than tensile at the bottom edge of the lintel. Qualitatively speaking, the wedge shapes of the arch stones (or the stones + their mortar) gradually change the downward stress into more transverse compression, starting with trying to drive the keystone down into the rest of the arch, the driving of which wedge becomes a stress forcing the two blocks to either side apart horizontally, and so on around the boundary of the arch. For another comparison, there's a shape called a "jack" arch, which isn't curved at all, but rather a horizontal series of wedge-shaped blocks or bricks slanted outward at the tops, with those wedges filling a flat horizontal shape, identical in outline to a lintel. If it were only the bottom edge of the shape that mattered and not the internal connections, then a jack arch wouldn't be any stronger than a lintel, but merely decorative at best, but structurally not worth the bother.

If the crystals in solid stone could do that redirection of the downward force on their own, then it seems post-and-lintel would have been a fine solution to start with -- though cutting out the middle reduces the load the lintel itself contributes, it also weakens the lintel by making in thinner where the most stress is. Maybe removing part the stone makes the forces go sideways just because they no longer have a choice (other than to go down "into the air" and break the stone). But maybe it's the more macroscopic geometry of those "voussior" wedges that make the real difference, rather than the crystalline structure of the minerals in the stone or molecular bonds, or just the curved outline of the span over the doorway.

I don't suppose anyone out there just happens to be a civil engineer or architect?

I thought about this. But I don't think this can be right, because caves can have natural vaults/domes, and AFAICT large caves can be as wide as artificial ones made with voussoir wedges. GURPS Underground Adventures has a nice diagram of how domed/vaulted caves can form, basically by caving in up to the point of the natural arch. I'm not sure where jack arches fit in, but according to one source I found online, a rule of thumb is that jack arches can only span about six feet, which makes me think maybe their entire advantage over lintels is that the wedges of the jack arch can be moved into place one at a time. The reason people don't create arches by cutting semicircles out of lintels is that most lintels aren't thick enough for this in their vertical dimension.

However, suppose Shape Earth can't fuse stone together, but can do dovetail joints. Could an earth mage who doesn't realize the value of voussior wedges end up creating a wide ceiling by doing something like this? Basically you solve the problem of lintels not being thick enough by joining them together as you might in woodworking, then carving out that semicircular arch. Of course if you want a room with vertical walls, as opposed to being all dome (or vault), you'd need additional support for the lintels during construction.

[Anaraxes]

Originally Posted by Michael Thayne

I don't think this can be right, because caves can have natural vaults/domes

True. But then why wouldn't corbels be just as good as a true voussior arch, as long as they have the same shape on the bottom edge? ("Intrados" -- if nothing else, the question has been good for my vocabulary. So thanks :)) Perhaps the natural domes get by the same way the false arches do -- sufficiently thick walls, even if they're not as efficient as the true arches.

Originally Posted by Michael Thayne

Could an earth mage who doesn't realize the value of voussior wedges end up creating a wide ceiling by doing something like this?

Most people (or such is my impression) subscribe to the notion that mages can only create useful, functional, or beautiful items with their magic as well as they could create such a thing by mundane means. That is, they need the appropriate skills for art or crafting or engineering whatever material they're Shaping and whatever item they're trying to make, and are limited by their TL knowledge in what they even know to try. They can't just create anything their player can imagine (like the pseudo-medieval mage Shaping Metal into a 9mm handgun), or automatically succeed in a flawless creation just because "it's magic". If they do have such skills, though, mages have a huge advantage in time and effort and precision to do the work.

(Anthony pointed out applications for Find Weakness. Measurement is also very handy for construction and crafting. I'd like to reward the would-be mage-engineers for their additional investment in relevant knowledge. Magic's already too good at preempting skills as it is; the more you can keep them relevant to the mages, the better.)

[Anthony]

Originally Posted by Anaraxes

The point of the arch is converting the downward stress into stress along the perimeter of the arch

The point of the true arch is that it uses angled bricks that avoid a particular failure mode of flat bricks. The problem with a corbeled arch is that flat blocks can slide against one another; absent that, it also converts downward stress into stress along the perimeter.

[Michael Thayne]

Originally Posted by Anaraxes

Most people (or such is my impression) subscribe to the notion that mages can only create useful, functional, or beautiful items with their magic as well as they could create such a thing by mundane means.

I mostly agree, but if the only reason you can't do something by mundane means is something like "that would require the stone to become temporarily ductile", I think you should be able to do the thing with Shape Earth. E.g. if you can make a metal chain, you can probably make a stone chain with Shape Earth, even if you don't have the skill to chisel a stone chain. I'd apply the same reasoning to stone dovetail joints.

[Anaraxes]

Originally Posted by Michael Thayne

E.g. if you can make a metal chain, you can probably make a stone chain with Shape Earth

I agree. You could use Blacksmithing skill with Shape Stone, in this case. The skill's not there for the physical ability (even if it's DX-based), but the knowledge of the objects and how they're constructed. (I'd also let you use Sculpting with Stone Shape to make a very attractive stone chain :))

That stone chain might not work so well given that stone lacks the properties of metal, though (say, tensile strength in this case). Once you drop the Shape spell, the material's back to normal. The mundane skills probably give you some insight into those potential pitfalls as well. For instance, those arches from another thread may not stand up well if they aren't naturally sound, dirt and soil have their natural angle of repose, and so on.

[Astromancer]

In a conventional Fantasy setting (which is generally TL3 or less) Shape Earth and Earth to Stone are going to be used in building projects. The roads will be vastly better. Canals will be commonplace. City fortifications will be far more extensive. Bridges (the lack of which was a major economic issue) will be everywhere.

The economy will quickly improve.

[dcarson]

Yes on bridges. A mage with Shape Stone and a reasonable diving sklll can do work on bridge foundations that would take weeks with cofferdams and pumping water out in seconds. That would be a major change.

[Astromancer]

Originally Posted by dcarson

Yes on bridges. A mage with Shape Stone and a reasonable diving sklll can do work on bridge foundations that would take weeks with cofferdams and pumping water out in seconds. That would be a major change.

Plus building small bridges on smaller roads. A good firm bridge on a back road becomes a pragmatic reality. With Earth to Stone added cities get paved streets and functional gutters.

[dcarson]

They make precast concrete arches so having separate pieces does not seem needed.