Rebuilding Science in a Magic World

[Vol.5] Ch.37 Trigonometry



I took five days getting another few goblins trained on how to use the rest of the lead furnaces before spending another month and some change working on the zinc furnace.  Considering everything else was built in this area, I decided to go ahead and build the zinc processing area here too.

For Zinc refining, there are a few steps.  First, we take the zinc oxide we made by roasting the sphalerite, and crush it.  Then, we mix the crushed zinc oxide with charcoal.  Then, we heat that mixture to a decently high temperature, though the temperature is still quite a bit below the melting point of iron, so it's not that difficult.  The mixture then reduces the zinc oxide down to carbon monoxide and zinc metal vapors, both of which would be incredibly toxic to inhale.  So, the furnace needs to have a channeled air supply, which goes through a cooling chamber where the zinc metal can condense and reform into a metal. 

In Konkur's design, the remaining carbon monoxide is just left to go to atmosphere, but I didn't feel that comfortable with the safety of that, so I put a small second furnace in line at the end.  I'm sure that quite a bit of it burns before it actually reaches the second furnace, but I'd rather not have any accidents, and considering carbon monoxide is flammable, it wouldn't just be a poisoning concern.

That said, after getting the zinc process finished, spring was just about over, so I took a few days once again to train some goblins on the process before moving the crystal back to the coastal bathhouse.  The sea wall is slowly making progress in this valley now as well, but it'll probably take a bit longer than the first wall.  The coast here is a bit wider, and I expect that the new artificial tide pool they've been digging out over here will actually be completed before this sea wall, which means they'd need a new source of stone for construction, which will slow construction further.


At the end of spring, I took another two months finishing growing the new crystal for the auction later this year.  Given my growing concern with our total crystal supply, I only grew the large crystal, and didn't mess with increasing any more intermediates.  I still have a few of the 4 foot crystals, which should be enough to last us through the current crystal deposits for production. 

Since I had to spend a lot of idle time in the crystal growing lab, I took to refining more lightstone while I waited, something I used to do quite a bit while I worked in the lab.  We've taken to using metal for a lot of different things, due to differences in properties, but lightstone still has quite a few desirable properties so I find uses for it here and there.  If we had more uses for it, I'd consider finishing the vibration stack separator project, so we could produce more lightstone through mechanical labor, but for most construction, just about any stone from the island works fine, so there aren't that many projects that use it anymore.

In the off hours, while everyone else was asleep on the mountain, I spent most of my time reaching the remaining crystal deposits that I could find with tectonic sense, but I did check on the ore deposit that the miners have been working on.  It's quite deep, and I can tell from the rocks and the existing mine shafts that most of the deposit is already depleted, and that the quality of ore they're producing now is already below what I would have considered worth their time previously.  I've been busy with my own projects though, so I haven't really had time to give them new orders.

If I include the gypsum and quartz, then they've extracted hundreds of thousands of tons of useful material from this deposit.  Though as the quality of ores has declined, we're only getting fractional yields of useful output, but it's still a significant achievement for a few years worth of work.

I decided to shut this mine down now though.  The yields would only get worse from here, and as the yields get worse, we waste more and more fuel in the refining process.  Our current fuel supply isn't unlimited, we only have so much island that we can cut trees down on to make charcoal, so I'd rather be building up fuel stockpiles in preparation for higher quality ores than using that limited fuel in this manner.

With that in mind, I've decided to knock out two birds with one stone moving forward by creating a new source of stone for construction, and a new mineral exploration tunnel into the mountain.  Based on Konkur's notes, ore deposits are more likely to be found in deeper portions of volcanos like this, and closer to where water would have had an easier time interacting with the volcano.  Deeper stone in the volcano can be found in two ways though, one is by digging downward, but the second is by digging inward.

What I'm planning is to have the mining crew start digging a large tunnel straight through the mountain.  The entrance to the tunnel will be not far from the city walls, which means it'll only be about a hundred feet above sea level.  Initially, it'll be like the mining tunnels on the mountain, wide enough to run a cart through, with a little extra wiggle room.  Ultimately, I'd like that tunnel to run through the entire length of the island, to the far beach.  Then, down the road, the tunnel can be expanded and widened, which should cut travel time from one side of the island to the other down to less than a day.

There are a few problems that they're likely to run into with the tunnel, though.  The first issue is water.  Other tunnels have run into aquifers throughout the island, and I fully expect that to be an issue with this tunnel too.  So, the tunnel will be dug with a gentle upward slope until it's near the middle of the island.  A channel will need to be dug for the water to collect and run out from the tunnel.

The second problem is that at some point, we'll have to do quite a bit of detailed work to figure out our exact position, then dig in from the other side to finish the tunnel, though that'll be years from now.  While the mining team digs the small scouting tunnel, looking for ore deposits, a construction team can eventually begin expanding the tunnel when they need a new source of stone after the second tide pool is completed.  This could result in some logistical issues if an ore deposit overlaps with the construction team's planned work, but hopefully those instances would be separated by enough time that they never intersect.  If they do, then the construction teams can always resort to expanding the dam's reservoir for stone like they used to.

Before they start any construction though, I want to make a bunch of tools for them, to reduce construction error as much as possible, so that when the time comes to join the eventual two tunnels, it can be done relatively easily.  With that in mind, I'll probably need to take quite a few days to make everything.


While I worked on their new tools, I gave the mining team a vacation.  As I thought about the various things I needed, I realized it was going to take a while to prepare everything for them and that I needed to do a lot of math before they could start working, and they deserved a reward for excavating the previous deposit to completion.  There were a handful of tools I needed.  First, I need tools to find the midpoint of the tunnel we plan on digging, then I'll need tools for the mining team to use for digging the tunnel with precision.

For finding the midpoint, I could use a rope of known length, a water level, a plumb bob, and a protractor.  Of course, saying I could do so, and the practice of doing so was quite different.  I had two ropes of 100 feet, with a loop that fit on a stake tied on either end.  The stakes also have measurements on them, so I could tell how high the rope stands above the ground.  Then, I'd drive a stake into the side of the road, note it's height, and then, 100 feet away, I'd put the stake somewhere on the opposite side of the road, drive it in, and mark the height, then drive the third stake, mark it's height, and then use the plumb bob and protractor to measure it's rising angle, and the protractor again at the middle angle.

After taking those notes, I had to go back, unloop the rope from the first stake, and move the whole thing to the next 100 feet.  In doing so, I could do trigonometry to make a geometric measurement for the midpoint between two sides of the island along the road.  I left the marked stake in the ground where I had driven it, and made a marking on it to indicate which number the stake was, in case I needed to return to it later.

Ultimately, going 100 feet at a time meant it would take about fifty-two measurements to travel a mile.  I became quite discouraged as I worked due to the pace I moved at.  If I had needed to sleep, it would have been even worse, but thanks to my ability to work while half asleep, I traveled and measured the length of our road around the island in thirty-six days.  The total number of measurements I took was 1,864, meaning the road runs a little over thirty five miles, not factoring in that I alternated sides of the road with each measurement to avoid any plant life interacting with the rope.  I decided then that if I need to do something like this in the future, I'm hiring and training someone else to do it.

I then had to actually calculate everything, which was just as tedious.  I'd have to work using one triangle at a time to get the rise and run of a segment, and put those into a new column with their marked points each.  Then, with that new information, I could calculate the height differential between any two stakes, which ultimately let me know that my starting stake and ending stake were about 35 feet different in height from each other, with the far beach's road being lower.

Then, using the projected length of run for each rope, and the angle that was formed between the two ropes, I could calculate a hypotenuse between them, along with the new angle between the hypotenuse and the next segment.  Ultimately, the calculations were complicated enough that I couldn't do them while half asleep, so all the math ended up taking another twenty days, but I had the central line length calculated.  The distance between the two points that I wanted to start digging the tunnel at was a whopping 17.63 miles.  I made sure to replace the smaller stakes at the two points with larger stone markers, so that my work wouldn't be wasted.

There is still a lot of work to do before any digging can be done, but winter is about a month away, so I need to finalize everything for the auction before I continue work on this project.  The mining team has been on vacation for more than enough time already now, so I'm going to have them assist in excavating the artificial tide pool area until I'm ready for them to start on the tunnel.


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