The situation on the mainland with property destruction has slowed down a bit, but is still an ongoing issue. The graduation of the first group of students at the end of last semester was fairly straightforward, and the dwarven studies department seems to have managed to hire on the graduate they had their eyes on. Next year's graduating class will likely have a much larger impact when they return to the mainland, given their relatively larger number.

Most of the railway on the mainland connecting Korsask to the trade city is complete, but we're not yet going to operate any trains. We're going to wait a little longer for the situation to calm down more. Train engines aren't cheap to make, and the risk of a boiler explosion causing serious harm if someone tried to sabotage it is quite high. Such an incident would potentially re-ignite the panic that has been slowly decreasing.

I hired a handful of interns over this winter break that have been helping me with a lot of the necessary data collection that I need for sizing power plants. While I've been gathering data so that I can size individual generators based on ambient mana data, there was still the question of how many individual mana engines can operate in a fixed location, and how they impact each other. To collect data on that, I designed various configurations to have fluorite crystals placed in, along with dozens of manascopes placed in places around the fluorite crystals.

The idea was to first measure the mana with no crystals, then install one, then two, then more crystals, and remeasure the mana levels over the course of 48 hours to determine how crystals affect each other and the environment. By using heat fluorite and bimetal thermometers, we can also measure the effectiveness of each individual crystal. The idea was that by having all this information, I could create an empirical model that could be used for sizing a power plant without having to estimate it. For good measure ambient temperature, wind speed, and wind direction were also recorded alongside the approximate time that each measurement happened.

I sort of underestimated just how much data we'd be collecting, and how long it would take to process it. We collected data over the full two month period of the break, save for a few sets of days intermittently, meaning we ran a total of 25 experiments. With thousands of pieces of data per experiment, it became apparent that I had my work cut out for me mathematically. There are four main equations that I'm interesting in deriving, the first being a distance to mana level equation where the central area of crystals is treated as a single black box. While this might be initially daunting, as the value that black box has for mana consumption is actually dependent on the properties of each individual crystal inside it, there is a different approximator that can be used.

There were mana scopes placed close to the central crystal area. Those mana levels could be compared to the initial mana levels before any crystals were present to act as a stand in value for the black box. The second equation relates the output of each individual crystal with the number of and distance to other nearby crystals. This equation could take multiple forms, so I expect it will be quite tricky to actually pin down. I'll probably have to try to employ some students to actually do the data comparison work for various equations that I set up, just to get all the data cross checked. I'm hoping that polynomials will be enough to handle the resting steady state data.

The third equation will relate the first and second equation, relating the central manascope values to the number and configuration of fluorite crystals. One could then substitute both equations together to create an overarching equation, but it would likely be very difficult to actually handle, when in most instances you would be more interested in the two parts separately, unless you have some minimizing function you want to run on both parts together.

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The final equation is a derived equation from the second equation, which looks at the total power output from the whole facility. I've known for some time that adding more fluorite increases total power, likely to a leveling off point, but it makes each addition less effective than the last. These all have to be evaluated against wind speed as well, since I've long since established that some amount of mana is carried in the air, which means that higher winds result in a faster replenishment of depleted mana. It also changes the shape of the mana depleted area, with upwind seeing almost no depletion, and downwind having a significantly larger influenced area.

Overall, there is a lot of work that needs to be done with this before I can start on the final design for the generators. I need to be able to determine exactly how much heat each individual fluorite crystal plate will produce to appropriately size the generators, which requires me knowing how many of them will be in an area. I have about 5 months to do all that work, which will be cutting it pretty close. The good news is that once I actually have all my equations, it shouldn't take me that long to design out everything. Then it'll be up to Zeb to build cookie cutter power plants all over the place on Kembora.

About halfway through the semester I'd gotten one of the four equations pretty well nailed down. I feel like we aren't that far from the other three either. Initial data checking for simple polynomials for describing the performance of individual fluorite crystals wasn't giving great results. That said, the equations we're checking now are showing promising results. They factor in some lumped variables that approximate how far from the 'outside' of the crystal formation the individual crystal is, and have multiple constants in portions of the equation that rely on both that, the number of crystals, and an average calculation for crystal distance.

For simplicity of design, we only tested crystal layouts that would be useful for a power plant, which generally meant grid patterns. I don't intend to have each individual engine have it's own generator attached. Each stirling engine will act as a single stroke on a larger crankshaft that drives a larger coil to reduce complexity and maintenance demands Though there may still be more than one generator per power plant, there should be less generators than engines.

I also got word that a pretty large fluorite deposit was found on a lower floor in the mine, so we're no longer worried about running out of fluorite any time soon. That doesn't change anything for me though, as mainland demand is still not there. I've been so busy working on this project that I feel like I'm being a bit neglectful of some of the students that I had previously said I wanted to form closer relationships with, like the dwarven brothers.

That doesn't apply to everyone though, as I've had Zentoo assisting me with a lot of the fluorite work for the power plant project. Even if he doesn't end up doing fluorite research, he'll at least be quite useful for assisting in projects like this in the future that utilize fluorite. If he can end up being able to handle even half the work I've had to do for projects like this, then he'll be incredibly useful.

Not that the other students who helped weren't also useful though. I've had a lot of students doing basic arithmetic with the assistance of lookup tables for multiplication and exponentials. This has sped things up drastically, as I'm able to simply provide them with certain data, and have them plug the values in, and then compare the result to the measured values to see if the equation is good or not. Though that is a far cry from being able to make the equations themselves, they do help.

I've also made my mind up that after I finish the design work for this, we need a printing press. I had to have scribes make dozens of copies of multiplication tables, which takes a lot of time and effort. When we have modern paper, not having a way to quickly use it is quite the waste. Even if those tables are now done and could be used, they're still confined to staying in the academy. Further, because they're hand copied, not only can mistakes be made between tables, but they're somewhat limited in their scope. Having fifty thousand items in a table just isn't feasible to be hand copied. Plus, there would probably be considerable value in being able to print a large number of documents for propaganda. The printing press was quite revolutionary in that regard.

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