[Fun Maths]Centrifuge Fun

[Eagle]

Well like any good Orbiteer, I like to play around with centrifuges. I highly recommend SpinCalc: http://www.artificial-gravity.com/sw/SpinCalc/SpinCalc.htm

Aesthetically I prefer 2001 Discovery type centrifuges. I'll share a design that I'm working on now that I think is pretty neat. So my crew section is a 34m sphere (big I know, but its a deep space ship). So I add in a 8 wide centrifuge with floors at radii of 16, 13.8, 11.6, 10.4, and 7.2 meters. I could elaborate but the design has a 2 m wide circular walkway on every floor. Fun things like moving the walkway can allow for larger 6m deep rooms or smaller 4 and 2m on either side.

I can spin it at a leisurely 1.4 rpm and get a useful .016 -> .035g (moon is .020g). Now that's pretty nice to live at, the Coriolis shouldn't get you too sick.

Now if you want to exercise things get interesting. You would think (or at least I did at first) that running on the lowest floor would be the best exercise. Walking ~2m/s (3:20 400m) with the wheel gives little change of .059g at the bottom floor but a much higher .132g at 7.2 m. Running at a healthy pace of 5 m/s (1:20 400m) you get a good .34g at the lowest level and .56g on the top floor. So you actually can get more gravity running in a smaller centrifuge.

Now running in a smaller centrifuge isn't the same as running on a planet or ringworld. Your upper body will feel like its being hunched forward as your legs must rotate your body backwards to keep oriented with the floor. It might feel a bit like running up a hill (Yay more exercise!). You might actually be able to get significantly faster because of lower gravity and get exercise similar to that you could get in a full g.

The hunching feeling combined with the exaggerated Coriolis effect from your increased speed might disorient you a bit. Then again, we all know otherwise fit people who throw up after a run on Earth.

Other fun things to consider is moving the wrong way in the centrifuge (not so useful for exercising). At the highest floor its moving at 1 m/s, you could go that speed and float as the centrifuge rotates around you. Walking at 2 m/s gives you the same gravity as if you were standing still (subtract 2*floorspeed from your tangential velocity for calculating effective gravity). The lowest floor is only moving about 2.4 m/s, an easy enough walk.

Anyways the purpose of this thread/post is to get people thinking about excitingly fun artificial gravity. Ask questions, post inanities, or share some fun calculations, theoretical examples and other whatnot.

 

[tori]

I always liked the idea of running against the rotation to counter the artificial gravity, flying about and having fun, and then having to "land" back on the floor, which would be going at around 10 km/h (in your setup), breaking a bunch of bones, and having a cool story to tell later.

 

[eveningsky339]

Interesting, I wonder if this calculator can accurately make measurements for an entire spacecraft that spins (head over tail tomahawk style, like Orion). I find that idea much more appealing than your run-of-the-mill centrifuge. :thumbup:

 

[T.Neo]

Interesting, I wonder if this calculator can accurately make measurements for an entire spacecraft that spins (head over tail tomahawk style, like Orion).

It shouldn't have a problem with that, AFAIK.

Essentially physics-wise, a head-over-head spacecraft is identical to a centrifuge.

With a head-over-head spacecraft, you gain the advantage of having no moving parts to sustain artificial gravity.

 

[vejiita]

Reminds me of the Discovery in 2010 They had to use the ladder from the center of the ship and go "down" to the hatch situated in the front of the ship

I wonder if one could re-produce this in Orbiter with UMMU...

 

[tori]

With a head-over-head spacecraft, you gain the advantage of having no moving parts to sustain artificial gravity.

You can do that with an Y-axis spinner too, just roll.

I think the main advantage is that you get much larger radius and the possibility of having a gravity vector aimed down your thrust vector (i.e. no need to strap gear down when firing main, as you'd have to do with a side-rolling centrifuge).

With the larger radius you get all the advantages like multiple floors with almost the same gravity.

 

[Andy44]

I think the main advantage is that you get much larger radius and the possibility of having a gravity vector aimed down your thrust vector (i.e. no need to strap gear down when firing main, as you'd have to do with a side-rolling centrifuge).

With most tumbling designs such as Orion, the crew section is on the opposite end from the radioactive propulsion end, so when thrusting the gravity is "down" but when tumbling you stand on the ceiling.

 

[Eagle]

Because I like you guys here are some goodies. I've got 3 images for you.

The first is a 4 part cutaway of the centrifuge floor plan. Black lines denote walls, the little red H denotes a connecting hallway between the sets of ladders (I forgot to add a second one above it). The inner 3 have a different circular hallway location from the lower 2 so the upper floors will have smaller rooms on both sides and the lower floors will have wide rooms on one side of the hallway. (my rationale is that rooms lower in the centrifuge are more valuable and likely to be communal while higher rooms can be used for bunks and activities that are made easy with only minimal gravity like hygiene activities.

The second picture just gives you an idea of how the centrifuge fits in the crew section. Not pictured is a counter spinning wheel just aft of the fuge to negate those pesky gyro problems.

Here's the general ship plan to get your bearings. Note that the non-centrifuge decks could possibly use either thrust acceleration or a tumbling method like Orion.

 

[JamesG]

The problem with a spherical rotating structure is that it minimizes the useable area with the highest centrifugal loading, the "equatorial" (for lack of a better term) band, which is the whole purpose of the structure.

I suppose if you used the "wasted" space as storage or for machinery, or left the entire thing open as a kind of arborium or habitat module (which would be interesting to see how a tree would grow as the taller it got, the less gravity there was). But a plain ol' torus is still the most efficient "artifical gravity" configuration.

 

[T.Neo]

But a plain ol' torus is still the most efficient "artifical gravity" configuration.

AFAIK, a flat-paneled "torus" would be better from a construction point of view, but less so from a pressure point of view.

 

[JamesG]

A "flat panel torus" is a skinny cylinder, not a torus.

 

[T.Neo]

A "flat panel torus" is a skinny cylinder, not a torus.

It has a hole through the middle, thus it is a torus.

 

[JamesG]

"a ring-shaped surface generated by rotating a circle around an axis that does not intersect the circle"

http://www.google.com/search?hl=en&...&oi=glossary_definition&ct=title&ved=0CAoQkAE

 

[T.Neo]

"a ring-shaped surface generated by rotating a circle around an axis that does not intersect the circle"

Yes yes.

I don't mean torus in the geometry sense, I mean it in the "this describes this sorta-fine, so I'll use it" sense.

But it is not fitting of the description of "cylinder", either.

Either way, it is a means of achieving a similar effect using a simpler shape.

Example:
The first MMU stands within a representitive square centrifuge (coloured in red). He is allowed the same amount of floorspace as the width of the square cross section of the rotating section.

The second MMU stands within a representitive circular centrifuge (coloured in blue). He is allowed only a small amount of floorspace within the circular cross section of the rotating section.

The third MMU stands within a representitive circular centrifuge (coloured in blue), with an internal floor coloured in red. He is allowed the same amount of floorspace as the width of the rotating section, at the cost of half the height of the circular cross section through the rotating section.

Hull thickness, internal structures, storage areas and alternate floor layouts are not taken into account. But it is a clear demonstration of the geometry of various layouts.

 

[JamesG]

The rectangular structure is not practical with our current material science. It would need to be ridiculously massive to maintain its integrity at 1 atmosphere and under centrifugal loading.

You would design your diameter to allow an effective "floor" to be placed on the lower deck and an upper deck.

 

[Eagle]

The rectangular structure is not practical with our current material science. It would need to be ridiculously massive to maintain its integrity at 1 atmosphere and under centrifugal loading.

You would design your diameter to allow an effective "floor" to be placed on the lower deck and an upper deck.

Well it depends how you build it. 14.5 psi isn't terribly dangerous, and you don't necessarily need to keep the sea level pressure. Also note you can go down to near 5 psi if you use an oxygen only environment.

 

[T.Neo]

The rectangular structure is not practical with our current material science. It would need to be ridiculously massive to maintain its integrity at 1 atmosphere and under centrifugal loading.

I somehow doubt that. Flat panels should easily be able to resist the centripetal acceleration (after all, look at the large number of steel structures in the world today that are actually made of quite weak steel).

I suppose bracings or triangulated crossbars would add to the structural integrity.

As for pressure, as Eagle has said sea level-pressure is not *that* dangerous. And if all else fails, the extra mass can be used as radiation shielding- which you need anyway.

You would design your diameter to allow an effective "floor" to be placed on the lower deck and an upper deck.

...Which will cause you to have a larger diameter. And probably more mass, anyway. For a larger amount of wasted space.

 

[Andy44]

So split the difference. Build it with a flattened oval profile. This allows a curved pressure vessel for integrity, and a wider inside for a deck or two.

The "wasted" space is actually useful for things like plumbing and ducting and power cables, as well as under-floor storage space.

 

[Eagle]

One of the reasons why I like the Discovery's layout is that the centrifuge is completely within the pressure hull. No rotating seals, The centrifuge decks only need to support the weight of themselves and the loads from (possibly moving) objects inside itself.

Air pressure needs to be accounted for somewhere, and if the pressure hull is the centrifuge walls, the spinning will reduce its bowing out at the sides and your load bearing structure that keeps people from falling through the floors already might already have enough strength to keep the air in.

And for the OMG MATERIALS SCIENCE NOT GOOD ENOUGH!!! worries consider 2 real things, an astronaut's spacesuit and a cloth cot (trampoline if you don't get it). Spacesuits manage to keep the astronaut breaking, and it is possible to support somebody's full weight using metal tubing and cloth. For a working floor something that flexes less would be nice (like metal or composite panels). How is it that people can walk around pressurized airplanes without falling through the floors...

 

[JamesG]

Go talk to a structural or A/S engineer. They would probably be more interested than I in spelling out all of the technical reasons of "why things are the way they are".