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Calculus?

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?

Comments

kiwiria
May. 21st, 2009 01:52 pm (UTC)
I love calculus :D

Edit: Ah, I see you already got somebody to help :)

Edited at 2009-05-21 01:52 pm (UTC)
ahavah
May. 21st, 2009 01:54 pm (UTC)
Hopefully! But feel free to weigh in if you like. :) Thanks for offering!
kiwiria
May. 21st, 2009 02:05 pm (UTC)
Let's see... you know the diameter of the "small" circle (inside the tube), and want to know the diameter of the "large" circle (across the spaceship), is that correct?

As far as I understand the formula you linked to, the diameter of the "large" circle can really be as big as you want it to, as the size of the torus has no bearing on the size of the tube. Of course the torus has to have a diameter of a minimum of 6 miles, or there won't be room for the 3-mile tube (which would give you a length of just under 19 miles from N-N), but you can expand it to anything beyond that if you need.

Is the torus divided into 8 equal segments? If so, they'd be 2.35miles each.

Hope this helped and I didn't misunderstand you completely :)

Edited for a geekier icon ;)

Edited at 2009-05-21 02:06 pm (UTC)
ahavah
May. 21st, 2009 02:15 pm (UTC)
Waa ha! I hope you did understand me completely, because I needed the milage!

I'm not sure if I personally needed the diameter of the bigger circle. I just wanted to know how long around it would be. I was thinking that if the diameter was three miles, the segments might be longer.

Does my explanation for mc_questionmark down below change anything? I do need to have a bit of a larger space in the 'hole' of the torus. That might make it longer, if the length can be variable.

Thank you so, so much!
kiwiria
May. 21st, 2009 02:27 pm (UTC)
That does change it somewhat. The millage I gave was for the bare minimum - i.e. no space in the center at all. You can increase the milage basically as much as you want - depending on how big a hole you want in the center.

Here are some example numbers - you can see if any of these fit you.

Diameter of Centre;Length;Segments (all lengths in miles)
3 ; 56.5 ; 7.6
4 ; 62.8 ; 7.9
5 ; 69.1 ; 8.6
6 ; 75.4 ; 9.4

etc. :) If you want to go even larger the general formula is:
r ; (r+6)*2/pi ; answer from before/8
mc_questionmark
May. 21st, 2009 02:35 pm (UTC)
Keep in mind that the depth of soil would alter this somewhat.
The correct formula would be 2r*pi, with r being the distance from the centre to the soil level.
ahavah
May. 21st, 2009 02:39 pm (UTC)
Oh yeah, I forgot to mention the soil depth. I'm still wavering on that (at first my torus was only a mile and a half, but we decided to double it). I'm thinking 'sea level' has a depth of at least one mile, possibly one and a half. I want some segments to be mountainous regions, with the highest mountain being about a mile above sea level. I'd have to have mega lights up top to keep things growing, though, so I don't want the mountain tops too burnt out or the valleys too cold. So 1-1.5 miles?

Sorry I haven't been clear straight off the bat. Math is so beyond me, I didn't even know what info you'd need. >
ahavah
May. 21st, 2009 02:42 pm (UTC)
Even the formula is beyond me. But your assistance is definitely helping me understand it a bit better! I addressed Mark's soil-depth issue below. I'd be interested in having both of you guys' input on that and the 'hole' diameter.
kiwiria
May. 21st, 2009 02:53 pm (UTC)
I'd probably have the 'hole' diameter no bigger than 3 miles - perhaps even just 1 or 2. I think any larger than that and your torus would get too unstable and the artificial gravity not strong enough... but that's space physics and I know absolutely nothing about that ;)

I'm not sure how the soil-depth would affect the length of the tube though... I assume the 3 miles are from "bare edge to bare edge" - disregarding the soil? If so, the numbers wouldn't change. But that may be because I don't know enough about it.

Anyway, the numbers for a 1 or 2 mile hole would be:
1 ; 44 ; 5.5
2 ; 50.2 ; 6.3
ahavah
May. 21st, 2009 03:19 pm (UTC)
I really appreciate all your help!

I'm not sure about the soil depth thing, but perhaps bisecting the length through the middle would mean less length around than if following the far edge?
kiwiria
May. 21st, 2009 03:25 pm (UTC)
Ah! Yes, that it would. My numbers were based on following the far edge.

If you have a 3 mile diameter hole and an average of 1m soil depth, that'd give you 44 miles N-N.
(no subject) - ahavah - May. 21st, 2009 03:31 pm (UTC) - Expand
(no subject) - kiwiria - May. 21st, 2009 03:42 pm (UTC) - Expand
(no subject) - ahavah - May. 24th, 2009 02:19 am (UTC) - Expand
(no subject) - kiwiria - May. 24th, 2009 09:19 am (UTC) - Expand
(no subject) - ahavah - May. 24th, 2009 09:20 am (UTC) - Expand
(no subject) - kiwiria - May. 24th, 2009 09:23 am (UTC) - Expand
(no subject) - ahavah - May. 24th, 2009 09:24 am (UTC) - Expand
(no subject) - kiwiria - May. 24th, 2009 09:26 am (UTC) - Expand
(no subject) - ahavah - May. 24th, 2009 09:27 am (UTC) - Expand
(no subject) - kiwiria - May. 24th, 2009 09:29 am (UTC) - Expand
mc_questionmark
May. 21st, 2009 02:54 pm (UTC)
I love your icon, kiwiria.
kiwiria
May. 21st, 2009 02:55 pm (UTC)
Thanks! It made me laugh, so I knew I had to have it.
ahavah
May. 24th, 2009 09:28 am (UTC)
Hey, look at that. Your very first suggestion was what it ended up being anyway.
kiwiria
May. 24th, 2009 09:29 am (UTC)
Cool! :-)