Rebuilding Science in a Magic World

I spent nine days getting the 12-inch fluorite growth chamber designed and built.  I decided to slow down the descent rate even more, to compensate for the larger size.  I had the 8-inch crystal descend over 3 days.  I expect material probably deposits at a fixed rate based on the available surface area, meaning that the growth rate is probably approximately linear from the surfaces.  So a 50% increase in height would correspond to a 50% longer growth time.  Just in case it's a bit slower, I'm going to have the crystal descend over the course of 5 days, equating to a 66% longer growth time.

A 12-inch crystal's volume is about 3.5 times the volume of an 8-inch crystal, so I'm hoping that having a fifth of the natural mana down here will be enough to prevent issues.  I've installed another nine of the mana heat sinks in the air lines, but haven't noticed that much of a change in the total mana available down here.  I also need to find a few goblins who I feel will make good operators down here for monitoring the crystal growth process.  It's fairly hands off, but you do need to make sure that the charcoal pellets don't get jammed in the dispenser, and refill the hopper if it gets low, or else the whole process ends up a failure.

While I was able to get some goblins to help me and learn the ropes, the resultant crystal was still very hot and difficult to handle, though it was successful.  While we waited for it to grow, I made some new pedal operated crystal cutting saws down here, with a catchment to get the extra fluorite dust that was cut away.

At least cutting the crystal down makes it easier to handle, since it's producing less heat.  I started to wonder about the exact application and effects geometry had on the crystals.  While regular shapes, like a rectangular prism and a regular octahedron, seemed to only be affected by volume, was that actually the case for all shapes?  Did I mess up by cutting the heat sink mesh into the plate on the stirling engine providing air down here?

That seemed easy enough to test using this new crystal.  First, I cut the large central plate, about 8.5 inches to a side, and 1.5 inches thick.  Interestingly, that plate has more total volume than the 8-inch crystal has in total.  I know that cones are weird when it comes to calculating volume, but it's still wild to think that such a small vertical cross-section has such a large amount of the volume for this object.

Next, I cut pairs of 1 in thick plates out of the remaining two equal square pyramids left over from each half.  For one of those plates, I cut a grid through half the thickness, and for the other, I left it untouched.

I crafted two buckets of equal size on the surface, and filled them with water, and then submerged each plate at the same time.  Each of these plates was an average of 6-inches to a side, making them comparable in size to the plates in the stirling engine on the surface, which I knew that plate could boil water.

The uncut plate boiled slightly faster.  I repeated the test a few times, and the results were pretty definitive.  There was about a 15% difference in the time between the uncut bucket and the cut bucket.  My working hypothesis is that it for any crystal that is a convex polyhedron, volume is the primary factor, for but a concave polyhedron, there is some amount of loss based on how isolated portions are.  In the grid pattern, for example, the bottom is a solid plate a half inch thick, and the top is, for the purposes of this discussion, comprised of about 16 smaller plates. 

Now, why that only results in 15% slower boiling time is beyond me. For good measure, I tried cutting it even further, so only a sliver of material was left connecting each section of the grid, and it performed even worse.  I cut the uncut grid into individual pieces the same size as the grided plate, and this new pairing performed almost identical, with a slight edge going to the still connected grid.

I could do all sorts of studies on how different shapes are affected, but for now, I'll work with the knowledge that making a shape concave is probably resulting in lost efficiency.  In the future, I could also try making multiple shapes of identical volume, and conduct similar tests to try to determine if all convex solids are actually the same or not.  Previous tests with my initial crystal samples seem to indicate yes, or at least that the differences are negligible, but surely there exists a transitional point, where an extra thin and long rod of the crystal would either under or overperform for it's volume as compared to an octahedron of the same volume.

To conduct such a study would require multiple grown crystals, so that I could carve shapes out that are large enough to do a water boiling test like the one I just did.

As I let the goblins run the new fluorite growth chamber, I noticed that we weren't reducing the mana in the basement, even after adding in more mana heat sinks.  I was intrigued, so I started testing various things to determine the cause.  My first hint was that the stairwell, with it's stagnant air and connection to the raw fluorite storage, had less mana than the fluorite growth room.  The second hint was something that I noticed before with the submerged mana crystals.  While the mana seemed to flow downriver, it also did affect upriver some degree.

So, I decided to move a few of the heat sinks from the inlet to the outlet.  Sure enough, within about an hour, there was significantly less mana in the room than there was previously.  I still think that we'll need a few more heat sinks installed on both sides to reduce it as much as possible, but we're already at about 1/15th of the surface's regen values.

When the next crystal was ready, while still warm, it was at least cool enough that it could be held in your hands without causing pain without needing heat resistance.  Since I don't yet know exactly what purpose I'm going to employ these particular crystals, I'm going to have the goblins making them keep them stored away.  I've made a small area in a corner of the room, where the crystals can be stashed, at least until I come up with a use for them.

For the time being, I'm going to have them keep making the 12-inch crystals while I start designing the even larger growth chamber.  The good news is that despite only mining once a month, the mine still outpaces our current fluorite consumption, due to how slowly these crystals grow.  To everyone, including the dwarves, this just seems like novel applications of natural materials, no different than burning wood to make a fire.  To me though, this is magic, and I'm combining it with technology I already know.  The mana crystals, while grown with technology, were a sort of low tech, direct to body thing.  These heat crystals are real magitech.  A magical component that can drive technology.

I settled on making the large fluorite growth container 36 inches for the crystal height.  Meaning it'd have 3 times the height of our current 12 inch crystal.  Since the vat needs to lower away from the heat source, I dug into the floor about two feet to make everything fit nicely while still making operation easy.  Since the 12 inch crystal grows over 5 days, I decided to go with 18 days of growth for this crystal.

Building everything took ten days, and while I was eager to start, I was a little worried that the ambient mana might be a little too high still, so while I waited for more of the mana filters to be built, I decided I should start building the area where Tiberius will eventually work, if he chooses to pursue this research path.

While we have quite a lot of cut quartz, I don't think we'd be able to make a massive room for it, so I've settled on two fairly small rooms, with double doored hallways connecting them.  The first room will be eight feet long by six feet wide, and six feet tall, with a small two foot by two foot alcove on one side where I'll install a small crystal grower like the ones in the main lab area.  This particular crystal grower will be much smaller than all the others, and is planned to only grow a 4-inch crystal over the course of two days.

The double doored hallways are also quite narrow, only 2.5 feet wide, and 4 feet long, with a sliding door on either side.  These are meant to help prevent air mixing between chambers if used correctly.  That way, a small amount of heat producing fluorite can be installed in each area, and should passively consume most of the mana in the area, reducing the odds of an accident occurring.  The final room will be a small test chamber, six feet on all sides, making it a cube.  Ultimately, I'll probably need to add various functions to that chamber, but I'll wait until those requests come in before I actually work on them.