WHAT WE DID HERE

• All habitat geometries reengineered with modern materials.
• All steel cabling replaced with carbon fiber tendons.
• All skylights replaced with LED-lit floorspace.
• All mechanical hoop and deflection stress accounted for.
• All shielding set to reduce isotropic 25mSv/day to avg 5μSv/day.
• All decking is rated to hold 2500kg/m²

  HULL Mt  FLR km²  Hl kg/m²  Radi km  GEO  L:R     NOTES
  =======  =======  ========  =======  ===  ====  =========================
   0.0031   0.0003    11,000    0.015  Tor  1:5   Potocnik Wheel (1929)
   0.0169   0.0015    11,000    0.035  Tor  1:5   von Braun Station (1952)
        7        ½     6,126    0.250  Cyl  4:3   Kalpana One (2009)
        8        ½    15,410    0.256  Sph  2:1   O'Neill Island One (1976)
       11        1    11,025    0.892  Tor  1:5   ½mi² Stanford Torus (1974)

       10        4     2,580    0.279  Spi  5:9   1½mi² (2025)
       26        4     6,374    0.252  Cyl  10:1  1½mi² O'Neill Model 1 (1974)
       44        4    11,050    1.785  Tor  1:5   1½mi²
       62        4    15,427    0.707  Sph  2:1   1½mi²

       45        6     7,050    0.320  Cyl  10:1  1974 O'Neill Model 2 (1974)
      100        7    15,434    0.900  Sph  2:1   1976 O'Neill Island Two (1976)

       41       16     2,580    0.558  Spi  5:9   6mi² (2025)
      142       16     8,898    0.504  Cyl  10:1  6mi²
      178       16    11,101    3.569  Tor  1:5   6mi²
      247       16    15,454    1.414  Sph  2:1   6mi²

      165       64     2,581    1.116  Spi  5:9   25mi² (2025)
      717       64    11,203    7.138  Tor  1:5   25mi²
      892       64    13,945    1.010  Cyl  10:1  25mi² O'Neill Model 3 (1974)
      993       64    15,508    2.828  Sph  2:1   25mi²

      661      256     2,581    2.232  Spi  5:9   100mi² (2025)
    2,922      256    11,413    14.28  Tor  1:5   100mi²
    3,998      256    15,618    5.657  Sph  2:1   100mi²
    6,154      256    24,040    2.019  Cyl  10:1  100mi²

    8,044      512    15,710    8.000  Sph  2:1   Bernal Sphere (1929)
   23,054      643    35,850    3.200  Cyl  10:1  O'Neill Island Three (1976)

    2,644    1,024     2,582    4.463  Spi  5:9   400mi² (2025)
   12,138    1,024    11,854    28.55  Tor  1:5   400mi²
   16,223    1,024    15,843    11.31  Sph  2:1   400mi²
   45,292    1,024    44,231    4.038  Cyl  10:1  400mi²

   40,866    2,512    16,268    8.000  Cyl  25:4  Clarke - Rama (1973)
    57.1M   31,400     1.82M    5,000  Tor  1:5k  Banks Orbital (1987)
     332M    3.14M   105,667    1,000  Tor  1:2   Bishop Ring (1997)
    61.6B    13.3M     4.62M      461  Cyl  10:1  McKendree Cylinder (2000)

1. Got under 25Mt? Build tori; otherwise build spirals.
2. Got enough Mt for a 100mi² cylinder? Build 9 x 100mi² spirals instead.
3. Got enough Mt for a 400mi² cylinder? Build 17 x 400mi² spirals instead.

HULL MATH FOR ALL GEOMETRIES

CYLINDER

These are nation-scale habitats, proposed by Clarke [4] in 1973, and O'Neill [5] in 1974. Cylinder land area can reach millions of km². Heat removal is problematic, and one must minimize hills and hydrology to suppress tumbling. If you want a single habitat the size of Egypt, the cylinder is the only way to go.

• Shape: Soda can shape, L/R>1
• Range: Radius 450m<R<150km, high deflection cost for L/R>5.
• Floor area: 6.28LR
• Efficiency: 3500 + [3500/L + (L/R)⁴]R + R²/45 kg/m²
• Examples:
  • 1973 - Arthur C Clarke
  • 1974 - Gerard K O'Neill Island Three
  • 2000 - Tom McKendree
  • 2020 - Isaac Arthur McKendree lattice / Rungworld

SPHERE

Nation scale habitats, proposed even before the cylinder.
• Shape: Ball, Truncated cylinder, L/R=1
• Range: Radius 30m<R<10km
• Floor area: 8.0R² (flat projected are exceeding 0.3g)
• Efficiency: 15400 + 38R + R²/10 kg/m²
• Examples:
  • 1929 - John Bernal
  • 1974 - Gerard K O'Neill Island One

SPIRAL

These are city scale habitats, proposed by Barber [3] in 2025. The puck-like spiral geometry is self stabilizing, and has land area up to 1000km². The design rolls habitable land into a coil around the central axis, forming a wide river-valley, flowing on a multi-day journey through a variety of elevations and biomes. At radius 2250m (1.4mi) the valley is 1250m (¾mi) wide, 200km (125mi) long, with sky 75m (250ft) overhead. River circulation provides natural heat removal, a temperature-driven downhill breeze, and radiation shielding.

• Shape: coiled torus, ⅓<L/R<⅔. Default L=R/1.8
• Range: Radius 450m<R<4500m, sky R/30
• Floor area: 51.4R²
• Efficiency: 2580 + R/2 + R²/1900 kg/m² (effectively constant for R<20km)
• Examples: Tensegrity Spiral

TORUS

These are outpost scale habitats, in the classic spinning donut shape. The wheel like geometry is naturally stable, but requires large amounts of shielding.

• Shape: Donut shape, L/R<⅓
• Range: Radius 30m<R<10km, sky R/30
• Floor area: 6.28LR
• Efficiency: 11000 + 28R + R²/15 kg/m²
• Examples:
  • 1929 - Herman Potočnik R=15m
  • 1975 - Stanford Torus R=900m

RING

These are continent-scale habitats, first proposed by Niven [6] in 1970. Spinning structures at this scale exceed the tensile limits of even the strongest (100GPa) carbon nanotubes. All such "gigastrucure" habitat designs in science fiction assume miracle materials.

• Shape: Gigantic, open roofed torus open torus
• Range: Radius R>500km, sky open
• Floor area: 3,000,000+ km²
• Materials: impossible with known materials
• Examples:
  • 1970 - Larry Niven Ringworld R=150Mkm
  • 1987 - Iain Banks Culture R=2.2Mkm
  • 1997 - Forrest Bishop R=1000km
  • 2001 - Halo Array R=31000km

REFERENCES