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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

( 50 comments — Leave a comment )
maiabee8
May. 21st, 2009 12:36 pm (UTC)
I *heart* calc! I never got much past calculus of three variables in college due to time constraints but I would be happy to help in any way I can.
ahavah
May. 21st, 2009 12:44 pm (UTC)
squee!
Oh, thank you so, so much! Calc is beyond me. In fact, I'm hoping that's even the right field...I seem to remember sine & cosine from precal, which I barely passed with a D. :/

So I'm not sure how much you know about my WonderSaga, but it's set in a torus-shaped spaceship. Nifty equations for figuring out torus parameters can be found here. I don't understand them! I know that I want the width of the ship (or the width of the torus tube) to be three miles.

What I can't figure out is how long the tube would be. My torus is basically divided into eight segments (directional segments, like N-NE, NE-E, etc.). I need to know how long each segment would be, and how many miles around the whole thing would be from N to N again.

Do you think you could help? I would be in your debt!
maiabee8
May. 21st, 2009 12:49 pm (UTC)
Re: squee!
Ok - I can definitely help. First, when you say 'width' do you mean inside the tube or the diameter of the circle that tube makes in its taus shape?
Re: squee! - ahavah - May. 21st, 2009 01:05 pm (UTC) - Expand
Re: squee! - maiabee8 - May. 21st, 2009 07:18 pm (UTC) - Expand
Re: squee! - ahavah - May. 21st, 2009 07:24 pm (UTC) - Expand
Re: squee! - maiabee8 - May. 21st, 2009 08:21 pm (UTC) - Expand
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!
(no subject) - kiwiria - May. 21st, 2009 02:27 pm (UTC) - Expand
(no subject) - mc_questionmark - May. 21st, 2009 02:35 pm (UTC) - Expand
(no subject) - ahavah - May. 21st, 2009 02:39 pm (UTC) - Expand
(no subject) - ahavah - May. 21st, 2009 02:42 pm (UTC) - Expand
(no subject) - kiwiria - May. 21st, 2009 02:53 pm (UTC) - Expand
(no subject) - ahavah - May. 21st, 2009 03:19 pm (UTC) - Expand
(no subject) - kiwiria - May. 21st, 2009 03:25 pm (UTC) - Expand
(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
(no subject) - mc_questionmark - May. 21st, 2009 02:54 pm (UTC) - Expand
(no subject) - kiwiria - May. 21st, 2009 02:55 pm (UTC) - Expand
(no subject) - ahavah - May. 24th, 2009 09:28 am (UTC) - Expand
(no subject) - kiwiria - May. 24th, 2009 09:29 am (UTC) - Expand
mc_questionmark
May. 21st, 2009 02:01 pm (UTC)
If I understand your question correctly, more information is required to give you an answer.
If I were to cut out a disc-shaped sliver of the torus, it would have a diameter of 3 miles, right?
If this is the case, then there are multiple answers possible, depending on the curvature of the ship.
I guess what we really need to know is how much open space you want in the middle.
If there is no space in the middle, it would look something like this:
http://www.fractal.org/Bewustzijns-Besturings-Model/Sacred-Geometry_files/torus_top_view.gif

If there is space in the middle, like the image in the link you provided, then it's a different result. Both of these toruses could have a cross-sectional diameter of three miles, but would obviously be dramatically different in their size.
ahavah
May. 21st, 2009 02:09 pm (UTC)
If I were to cut out a disc-shaped sliver of the torus, it would have a diameter of 3 miles, right?

I believe that's right. If you look at this pic, I'm talking about the diameter of the smaller, red circle.

I do need to have space in the middle. Not sure how much, but considerably more than both of those pictures, I think. The ship is a torus, because it will provide artificial gravity by rotating around a fixed center. I don't think it needs to be too awfully big, but there will be an area in the middle where the generators that keep it rotating go, and a bit of space for storage & null-g recreation. There will be kind of 'spokes' coming off it to the torus proper, and these lead to elevators that come down into each section of the torus.

I hope that makes a bit of sense. I really appreciate the help!
mc_questionmark
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.
(no subject) - ahavah - May. 21st, 2009 02:35 pm (UTC) - Expand
(no subject) - mc_questionmark - May. 21st, 2009 02:51 pm (UTC) - Expand
(no subject) - mc_questionmark - May. 21st, 2009 02:54 pm (UTC) - Expand
(no subject) - kiwiria - May. 21st, 2009 02:56 pm (UTC) - Expand
(no subject) - ahavah - May. 21st, 2009 03:12 pm (UTC) - Expand
(no subject) - mc_questionmark - May. 21st, 2009 03:20 pm (UTC) - Expand
(no subject) - ahavah - May. 21st, 2009 03:27 pm (UTC) - Expand
(no subject) - mc_questionmark - May. 24th, 2009 10:13 pm (UTC) - Expand
(no subject) - ahavah - May. 25th, 2009 09:07 pm (UTC) - Expand
(no subject) - ahavah - May. 21st, 2009 03:22 pm (UTC) - Expand
merenda
May. 21st, 2009 03:22 pm (UTC)
I failed Calc II twice in college back in the 80's. So do you want me to help? :) :) :)
ahavah
May. 21st, 2009 03:28 pm (UTC)
I never even made it to Calc I. I appreciate the offer, but I think the infallible MC? has it covered for me. :)
merenda
May. 21st, 2009 03:35 pm (UTC)
oh, I was joking. You don't want me anywhere NEAR calculus! :)
peaonix
May. 21st, 2009 03:30 pm (UTC)
I don't know what's going on here, but I DO know that I want to read your writing ;) Let us in!!!
ahavah
May. 21st, 2009 03:35 pm (UTC)
Aw, thank you so much! I've added you to my NaNo filter, which is where I worked on this last year. I've recently scrapped and redesigned my entire idea, so this ship is quite different from the original. I've been trying to map that out and populate it, so I'm not actually at the real writing point yet. I think I will be soon! I have been working on my character bios. I believe you loaned me your name? I haven't done yours yet, but I've been thinking about it.
( 50 comments — Leave a comment )

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