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I need help finalizing the plans for my WonderSaga. I need someone who actually understands calculus. Does such a person exist? If so, will you please help me?


May. 21st, 2009 02:28 pm (UTC)
That's what I thought.
Based on the info you've given, the distance from N-N would be directly related to how big the donut hole is.
Once you decide how big it is, I'd be happy to figure out the circumference of the torus.
If you're trying to figure out the distance on land to traverse the station, then I would also want to know how deep the soil would be relative to the 3 mile diameter.
May. 21st, 2009 02:35 pm (UTC)
Thanks! kiwiria has been very helpful up above, too. I suppose I could use some advice. I'm not sure how big the center should be.

The hub, so to speak, would probably do fine with a half-a-mile diameter. There would need to be some space for the shafts (also very large - like huge freight elevators). But would the center need to be as 'thick' as the torus to work as I want? Most likely, because I have the elevators (well, they call them nodes) coming out at different places - some dead center in one segment, some against one side wall or another in others. If that's the case, I guess the center hub might also need a three mile diameter, which I could put to use but it seems a bit excessive.
May. 21st, 2009 02:51 pm (UTC)
I'd actually recommend a larger donut hole, as the centrifugal force would increase with the inner radius, so that the station could spin slower for the same gravitational effect.
If you went with a 3 mile diameter center and an average of 1 mile high (hehehe) soil, you'd be looking at a distance of 22 miles to go from a starting point all around the station and return to the same point.
May. 21st, 2009 02:54 pm (UTC)
I'd still recommend a bigger donut hole if you want it to be "realistic". I can probably figure out what the rotational speed would be to simulate earth's gravity. :)

Oh man, am I ever a geek.
May. 21st, 2009 02:56 pm (UTC)
See, this I know nothing about :D I just know how to crunch the numbers ;)
May. 21st, 2009 03:12 pm (UTC)
Sweet, thank you so much! I suppose I'll go with 3 mile center, then, but is that just the hole itself or the hub that it's rotating around?

That gives a different length than kiwiria's figuring - 3 ; 56.5 ; 7.6 (Diameter of Centre;Length;Segments [all lengths in miles]). Is that because of the soil depth?

If you can figure out the rotational speed, that would be so awesome. You would not be a geek, but a hero. I've been so far working on the very simplified assumption that one rotation/min = 1 g.
May. 21st, 2009 03:20 pm (UTC)
I was including the hub in the hole.
Kiwiria and I are using different formulas. Mine's right, as I'm infallible.

I'm off to work now, so I won't be able to work on it for a bit, but i'll get back to you on the rotational speed thing. Where did you come up with your 1g per turn per minute?
May. 21st, 2009 03:27 pm (UTC)
Okay, thanks! That gives me a bit of wiggle room with the size of the hub then.

I really appreciate your help! Coddle me at your own leisure. I'll have to include you guys in the dedication when I become breakout famous. Or you can have a character in your honor, if you like.

I'm not sure where I got the rotation thing. I'd done a lot of reading last year just before nano, and I saw that somewhere during the course of that. I don't know what size a colony they were suggesting it for, though. I did, but I can't remember and don't have all my old bookmarks on this computer.

Incidentally, it seems I just stopped getting lj notifications. Ha!
May. 24th, 2009 10:13 pm (UTC)
I'd love to have a character in my honour. :)

I did some (very) brief research about rotational speed to gravity ratios and it looked more complicated than would be practical. I may see if there is an easier way to figure it out, but don't hold your breath.
May. 25th, 2009 09:07 pm (UTC)
Bummer. Oh well, thanks anyway!
May. 21st, 2009 03:22 pm (UTC)
Hm, I'm thinking I may have to go with a soil depth of 1.5 miles after all. Having the main farmland be two miles below the light source might be a bit too much.