#fort galfridian math

[marquis-de-all-the-knives]

#UR NOT A TUMBLR TROGLODYTE I CHNAGED THE REBLOG BC I M DUMB I PULLED OUT MY DYNAMICS NOTS IM GONNA FIGURE THIS OUT#how did you avoid the differential equations🥺#what the fuck🥺🥺🥺🥺#okay i literally pulled out my dynamics text book and shit and did my research#fort galfridian whoever she is is fucking weird but like#okay ASSUMING the tube sun is DENSE ENOUGH that the cylinders rotate around it to simulate gravity#or wait do the cylinders rotate themselves?#because it depends what your center of rotation is#if it’s the sun!!!!#then yes congrats you have gravity#the thing is that each cylinder is a different distance from the tube sun#they’d all rotate at increasing velocities proportional to the increase in distance from the tube sun#so to keep THEM ALL going at gravity#each outer layer would get faster (think like how planets do the same thing as they’re further from our sun)#but their orbits (in this case the diameter of the cylinder) are longer as well#they could just let gravity decrease the further out you get from the tube sun#okay like but the sun is only 12.5 miles away from them?????? how do they not die?????#okay back to the main point#I THINK??????#if the next layer is moving at a velocity that allows them to also keep gravity constant#you would not notice the difference because typically as you get further from the center of rotation (ASSUMING ITS THE TUBE SUN???)#then you’d just get floaty#but if the next layer is still going fast enough to have gravity (that 9.81 m^2/s we know and love) then the only scary part i could see#is the transtion from one layer to another#im not sure what that’d look like though and it could be avoided by just having a 0 gravity transtion room between layers#well actually no the transition wouldnt be scary because you’re also rotating and so you’re frame of reference is not stationary#so tl;dr#each layer goes fast as FUCK and since you’re in one layer going fast as FUCK you won’t actually notice the change too much between layers#if the other layers don’t spin tho???#DO NOT STICK YOUR HAND OUT OMG SAY GOODBYE TO YOUR HAND YOU’RE RIGHT

okie i’m gonna move this into its own post @crychanwastaken​ and i’ll tag #fort galfridian math for anyone who’s lost interest at this point. and first of all i want to salute you for digging out old textbooks for this discussion. like, bravo, that is AWESOME.

(i did not avoid differential equations — i avoided the one class that was exclusively about differential equations and would’ve gone way more in depth than a standard calc class. ANYWAY—)

okie so @thedreadvampy​’s original post covered this but it was hidden under a readmore so here’s the basic idea:

two suns! one real, one fake. (fluorescent, according to the canon. the canon = High Noon over Camelot, an album by The Mechanisms.) nothing on the station is big enough to provide significant gravity, so everything is coming from the rotation. so yeah, you are absolutely right about the “gravity” varying with distance! by my calculations, if the innermost layer is radius 12.5 miles and the outermost 15 miles, you’ll only be going from 1 gee to about 1.2 gee. I have... no frame of reference for how wacky that would feel. but like, imagine suddenly gaining an extra 20% of your body weight. i feel like you’d at least NOTICE.

i did not even think of concentrically rotating cylinders for consistent gravity! i don’t have any impression that that was intended by the source material, as characters seem to navigate between the layers pretty much on foot and unrestricted. but it’s a fun idea to play with!

a summary of what we know about the station from canon: https://marquis-de-all-the-knives.tumblr.com/post/624472261126193152/all-references-to-the-structure-workings-orbit and also some extra context from the band artist here: https://thedreadvampy.tumblr.com/post/624542261472002048/a-round-boy-the-pylons-hold-up-the-sun-which-is and an illustration of the outside of the station here: https://twitter.com/windhounded/status/1286777579396108289 (by one of the bandmates)

I took a slight liberty in the diagram above by putting Fort Galfridian's axis of rotation perpendicular to the plane of its orbit. The tarot card art makes it look like the axis points along the radius of revolution, but I think it would get more even heating this way so that's how I've been imagining it.

[marquis-de-all-the-knives]

My brain isn’t done with Fort Galfridian yet, sorry. I got curious about stuff like how fast it would have to be rotating and how much the artificial gravity would vary between levels. Obviously we don’t have any solid numbers from the canon, but @thedreadvampy provided some conjectures in this post which I’ll be going off of for the sake of speculation. Specifically, we’ll assume the station has a diameter of 25 miles at its innermost level (i.e. Camelot-level).

If we want to have Earth-like gravity (9.8 m/s^2) at that level, what circular velocity do we need? I looked up the formula for centripetal acceleration in terms of velocity, which is actually nice and simple:

Don’t, uh... maybe don’t stick your hand out the window.

(nah, I’m just kidding, there’s no air out there to actually create a ~1000-mph drag wind, so totally feel free to stick your hand out the window. You MIGHT however burn to a crisp due to lack of radiation shielding. You ALSO probably just punched a hole in the atmosphere containment system, so have fun with that!)

Anyway. Given that circular velocity = circumference / period, we can also get from this that the station takes about 4.74 minutes to complete one rotation, which I think is kinda nifty to know even though no one inside is probably aware of it. The Saxons might know, since they have viewports. I think a great way to give yourself vertigo is to look out a window and see the stars hurtling past once every five minutes.

Once we know the period, we can calculate the circular velocity at any distance from the center. Note that yes, the velocity does vary! Someone very close to the core / tube sun (TUBE SUN!) only describes a small circle in those 4.74 minutes, whereas someone on the outer hull describes a circle with a circumference somewhere north of 75 miles in those 4.74 minutes, so one of those people is traveling much more quickly. 

And guess what else varies with radius? Centripetal acceleration! I wrote a little Python script to calculate a bunch of values. Here’s the gravity you would feel at various distances from the core (1gee = earth gravity):

mile 0 (center) -  0 GEE mile 12.5 (Camelot) -  1 GEE mile 13 -  1.04 GEE mile 14 -  1.12 GEE mile 15 -  1.2 GEE mile 16 -  1.28 GEE mile 17 -  1.36 GEE mile 18 -  1.44 GEE mile 19 -  1.52 GEE

The further out you go, the heavier you feel. It’s not clear to me how thick the layers of the station are, but even just a one-mile-thick shell would provide a huge amount of space with not too much variation in gravity. I’m also not sure what the limits of human tolerance are for extended high-gee living. I imagine that 1.5 gees would be pretty drastic, so if the station goes out that far, those levels were most likely built for maintenance functions rather than habitation. (Not that that’s stopping the Saxons, of course.)

Anyway, that’s all I have for now, but I hope this was as fun for you as it was for me! LMK if you spot any errors, or want to see some of the equations I handwaved, or if you have more fun facts to add!

[marquis-de-all-the-knives]

hm I’m trying to get my head around what the artificial gravity situation means for hanging objects e.g. for instance let’s say just as a thought oh Brian

[marquis-de-all-the-knives]

Hi! I was reading your Fort Galfridian posts (thank you for the math btw!) and I was wondering, sorry if it's a dumb question, wouldn't there have been a way to use Avalon as the station sun? Why build an artificial one? and on the subject of space cylinders and suns, Queen of Candesce (the second book in the Virga series) is a novel that explores both, that series has some interesting worldbuilding.

Glad you enjoyed the math! The genuine answer to your question is “I have no idea”. All I know about the station is what we get in the album and what thedreadvampy has discussed about drawing the art for it. All I know about space stations is what I learned from Wikipedia and a couple of novels. That said, I don’t find it terribly hard to picture a ring-shaped station with a transparent skin that would let starlight in, or with a mirror system to bring starlight to the interior. But since we have a cylinder and a tube sun, if you’d like my speculation, this is it:

Possible reason 1: The station needs to be fully enclosed. (Well, it does—it has to maintain air pressure.) More specifically, it has to be fully enclosed in steel (or aluminum or something else better, but there is a lot of steel mentioned in the album). The station is so big, and the outer hull’s integrity so important, you don’t want to make too many compromises with large amounts of glass. So if most of your shell is just Going to be opaque, mirrors may actually be more work than an artificial sun.

Possible reason 2 (crackpot): What if... the station was not intended to always orbit around a star. “Holder of the Grail” makes mention of a solar sail, and if we assume that wasn’t just for the sake of a rhyme, well, solar sails to my knowledge are mostly intended as way to accelerate to a fraction of lightspeed over the course of a very long interstellar journey. Interstellar journey => no sunlight => tube sun.

Possible reason 3 (the best one): It’s funny. (And it justifies nobody having any clue what Galahad’s vision was about.)

Thanks for the tip about Queen of Candesce! This whole Tube Sun affair has made me want to learn a lot more about speculative space habitats, so I will have to check those out!

[marquis-de-all-the-knives]

ohhhhh gotcha. my sympathies

My brain isn’t done with Fort Galfridian yet, sorry. I got curious about stuff like how fast it would have to be rotating and how much the artificial gravity would vary between levels. Obviously we don’t have any solid numbers from the canon, but @thedreadvampy provided some conjectures in this post which I’ll be going off of for the sake of speculation. Specifically, we’ll assume the station has a diameter of 25 miles at its innermost level (i.e. Camelot-level).

If we want to have Earth-like gravity (9.8 m/s^2) at that level, what circular velocity do we need? I looked up the formula for centripetal acceleration in terms of velocity, which is actually nice and simple:

Don’t, uh… maybe don’t stick your hand out the window.

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