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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 02:15 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!
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
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.
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. >
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.
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
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?
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.
May. 21st, 2009 03:31 pm (UTC)
Hm, Mark says that would give 22 miles N-N. I'm so torn! You all are far ahead of me, so I'll let you guys battle it out. I have come to think that 1 mile depth may not be enough, and maybe I should go with 1.5 after all.
May. 21st, 2009 03:42 pm (UTC)
Mark's right. I forgot to divide by 2 since I was using diameter rather than radius. Unfortunately, that goes for all of my numbers :( Embarrassing!
May. 24th, 2009 02:19 am (UTC)
I haven't heard back from Mark about this. Could you help? If I were to change the soil depth to 1.5 miles, would it change the overall length of the torus? (From 22 miles to something else?) Thanks!
May. 24th, 2009 09:19 am (UTC)
Yes, it would. If the soil depth was an average of 1.5 rather than 1 mile, and keep the 3mile diameter hole, you'd get a length of 18.8 miles N-N.
May. 24th, 2009 09:20 am (UTC)
Woo hoo! Thank you SO much! :) *muah*

I think I'm near ready to buckle down and start writing this thing.
(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
May. 21st, 2009 02:54 pm (UTC)
I love your icon, kiwiria.
May. 21st, 2009 02:55 pm (UTC)
Thanks! It made me laugh, so I knew I had to have it.