Some basic guidelines:

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DIMENSIONS:

The choice of dimensions also responds to some logic. If we want something that’s feasible (in less than the next millenium!), physically and financially, it has to be as small as possible. However, it can’t be so small that it will have to be spun at undecent speeds to generate an earth-like gravity! It also has to be large enough to hold a sufficient number of clients to be commercially interesting.

The pulling strength (or centrifugal force) generated within a rotating structure, is proportional to the radius of the structure: the longer the radius, the stronger the force. It is also proportional to the square of the rotational period: the faster the rotation, the greater and greater the force! (see The Physics of Artificial Gravity)

For example, a room turning every 15 seconds at the end of a 40-meter-long rod will be subject to a 0,8 G of artificial gravity, or eight tenth the earth’s gravity. To get a gravity equal to that of earth, you need to accelerate the rotation to 12,65 seconds, or stretch the rod to 56 meters.

Here are some examples of artificial gravity values for various radii and rotational periods:

    Rotation period            
   

10 sec

15 sec

28 sec

30 sec

1 min

63 sec

5 min

1 hour

Radius

25 m

1,01 G

0,45 G

0,13 G

0,11 G

0,03 G

0,03 G

0,00 G

0,00 G

 

56 m

2,25 G

1,00 G

0,29 G

0,25 G

0,06 G

0,06 G

0,00 G

0,00 G

 

200 m

8,04 G

3,57 G

1,03 G

0,89 G

0,22 G

0,20 G

0,01 G

0,00 G

 

223 m

8,97 G

3,98 G

1,14 G

1,00 G

0,25 G

0,23 G

0,01 G

0,00 G

 

895 m

35,98 G

15,99 G

4,59 G

4,00 G

1,00 G

0,91 G

0,04 G

0,00 G

 

1 km

40,20 G

17,87 G

5,13 G

4,47 G

1,12 G

1,01 G

0,04 G

0,00 G

 

22,4 km

900,53 G

400,23 G

114,86 G

100,06 G

25,01 G

22,69 G

1,00 G

0,01 G

 

3 230 km

129852 G

57712 G

16562 G

14428 G

3607 G

3271 G

144 G

1,00 G

(Wanna try out some other values ? Get this EXCEL Worksheet and have fun !)

My favourite is the 40-meter and 14,2 seconds combination: such a building could host around 100 paying clients. Of course, I’d love to think of a 1-km-wide spatial hyper-city that rotates in no more than 1 minute, but it’s unlikely that mankind can achieve such an endevour in the near future. Meanwhile, a 40-meter radius seems not too small, not too large, and while the 14,2-second rotation is probably a bit fast, there are chances we can get by with it. And the 20% less gravity will make it just interesting : who would complain about weighting a few kilos less ?

 

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