Rebuilding Science in a Magic World

Things were quite hectic for the semester, as I frantically worked to get the equations nailed down so that I could begin the process of planning out the power plants. I ended up utilizing quite a few students over the course of the semester in order to handle all the math. We did end up getting an empirical equation derived, but considering the way we had developed it, I was a bit worried that we had perhaps overfit our data. As such, we took a few weeks doing proof positive tests for layouts that were nothing like the initial testing layouts.

The equation held well enough, though there was more error the more absurd the layout was. In either case, before I could even start on designing the individual generators, I'd have to settle on the layout. The way the equations ended up being developed, it's a summation of the effect each crystal has on its neighbors based on distance. Thankfully, the drain on mana seems to function independent of how effective the individual crystal is, so there isn't any recursion.

The unfortunate part is that the number of individual factors that have to be calculated goes up with the square of the number of crystals, as each crystal's individual efficiency and output is directly tied to both its size and the proximity, size, and number of other crystals. While some of those values are reciprocal and symmetries can reduce the total number of calculations, it still explodes exponentially based on the number of total crystals.

The good news is that beyond certain values, as anticipated, adding more crystals adds little output, so there is an upper limit on what is useful. We also noticed a pattern in the efficiency and total output of crystals in the center of formations thanks to our testing. It shouldn't be much of a surprise, but when crystals are surrounded by other crystals, their output is pretty much directly tied to the area that isn't closer to another crystal. The theory is that it's only really gathering new mana coming in from above, as mana from other sides flowing along a mana gradient would already be used up.

Now, that is only really true when the size of a formation is infinite, as some mana leaks passed other crystals in the formation to get inward. If it didn't, then our equations would have been much easier to solve. However, it did give me insight into more efficient layouts for power plants to allow effective use of mana.

These layouts also had to go through an extreme number of calculations to verify values, so I was again reliant on students to help me process all the necessary calculations. After the printing press, it may be worth pursuing a calculator utilizing the vacuum tubes I developed for radio, though that would end up being a decently long endeavor. A mechanical calculator wouldn't be out of the question either, though it would be far less efficient.

The reason I had to determine a layout first was because I need to settle on something that ensures the most number of engines have the same power output, minimizing the number that I have to design and have parts for. Since sets of engines will be linked to central shafts to drive generators, they need to all perform at a similar level, just like cylinders in a car engine. Ultimately, after a lot of design work and calculations, the layout I settled upon was a triangle with a central bullseye inside it.

Each side of the triangle will consist of eight engines that utilize the smaller of the two sizes of fluorite crystals in a line hooked into a generator. The generators will sit at a vertex, and there is a gap set up between each side. Then, in the center, six larger engines drive a central shaft for a larger generator. There might be a more effective layout, but this one allows me to only need two sizes of engines, and each time I have the calculations redone, it takes time to verify everything.

If the math is correct though, each facility should produce about twenty-five megawatts of power. I had hoped we'd be able to do more, but as our math shows, building bigger doesn't increase that power by much compared to the amount of infrastructure needed, and it barely increases the distance that the power plant affects, instead, the closer areas are disproportionately more drained of mana, which has increased negative effects on individuals working there and nearby plant and animal life. The engine on our ships is about half that power output around our island, and significantly less when in open water. The central part of the power plant actually produces about the same amount from a similar amount of crystal material.

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What that means, ultimately, is that the spacing between the power plants based upon the existing tunnel layout is far more than necessary. There are nearly 200 such tunnels spaced around the island however, which means we don't really have a shortage of available work. That would represent nearly 5 Gigawatts of potential power that could be redirected from unused sections of the island, with the upper limit of the total available power being between 10x and 100x that amount dependent upon how much negative impact we're willing to accept to the environment.

This has the potential to reduce the amount of fuel we need for our ever increasing smelting operations, which has required more and more area be dedicated to growing forests to replenish the amount being cut down. Though large scale smelting efforts using arc furnaces require incredibly large amounts of electricity, on the scale of tens to hundreds of Megawatt-hours, that could easily become a reality after some time. The grid does need to be balanced however, as you can't actually just waste electricity, demand and supply have to be matched. Having facilities like this to form a baseline load would go a long way to actually making the grid more stable, as long as they operate overnight and always have a smelter going.

This brings me to a different point on the matter, but we'll actually need to establish the idea of a central grid controller and telephone systems. We've actually pretty much handled the idea of a telephone network already, since we've designed radio. The circuits we use for modulating radio waves can easily be changed to send that signal through a wire to a receiver instead. The reason this is important is to convey, in advance, any major disruption that could require power facilities to turn on or shut down.

The semester was frantic, and I ended up not really focusing on the students in my classes as much as I feel like I should have. I was given a directive though, and I'm only one of a number of ministers in the Kemboran government. Since the other ministers are also providing me with a number of liberties related to the academy, it'd be quite bad if I shirked those responsibilities. We'll see if I can make up for lost time next semester. I'm technically not done with development yet, since I still need to design the peripheral parts of the electrical grid, but at least that has a longer timeline to completion, and I've already done a lot of the difficult design work to integrate those portions.

The summer break was filled again with a lot of meetings. As they've continued mining deeper under Kembora, the dwarves have found larger deposits, and ones of different types that will need to be analyzed. These have all been found below sea level, which I suppose shouldn't be a surprise. The chemistry of rock formation is drastically different when it happens constantly exposed to sea water, after all.

I purposefully designed the power plants to require as little work from a construction team as possible as well, minimizing the amount of effort necessary to build them. The mainland has finally started to calm down enough that we're considering running the railroad this winter, and might begin selling fluorite powered machines again. Given the scale that power production is intended to be built at, we're also considering increasing the fluorite production levels. I've left it up to the other ministers to pursue that matter as they see fit.

Within the academy, there are 13 upcoming graduates that are being eyed up by different departments to hire on as faculty, and I have 4 students I'm eying to hire to work separately on other things. I mentioned previously that I wanted to hire both of the Karnosk brothers, though the older one is the only one graduating right now. One of the students I want to hire is a demon who has been quite helpful in handling a lot of the mathematics calculations. While I wouldn't say he's skilled enough to teach anything more advanced than what we already teach, I do believe he'll be valuable to either assist me directly, or to check over other students research work to verify their math.

The other two I'm looking to hire are dwarves. The first dwarf, while not actually that innovative or skilled himself has functioned as the head of the self-propelled wagon club since he's been here. With the prospect of selling automobiles on the horizon, I think hiring him to start working on that project will actually provide me with better leverage to hire others from the club later. If I establish a link directly between the club and a manufacturing system, we can establish a pipeline for graduates that seems like a natural course for them to follow.

The other dwarf has been fairly skilled at geology and has been working with Konkur quite a bit. Since we're currently in need of someone to actively start analyzing the new geology we're uncovering under Kembora, he seemed like a good fit. While Konkur is still far more experienced, he is also much busier. Having someone who can filter things down to only the pertinent questions that are necessary and provide us with the information we need to capitalize on these new finds is what we need. During this next semester, I'm going to begin pursuing each to see if I can convince them to work for us.