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 shielding set to reduce 25mSv/day to avg 5μSv/day.

BEST GEOMETRY SCALING TABLE

   * 900m+ radius is under 1.0rpm. Human comfort zone.
   * 900m-3500m radius ideal for rim-to-rim transport between habitats.
   * For total mass we assume 2000kg/m2 payload.
   * For context, historical examples included in GREY.

  TOTAL Mt   HULL Mt  FLR km2  HULL/FLR  RADIUS m   GEOMETRY  NOTES
  ========  ========  =======  ========  ========  =========  =======
        1         1         ¼      3839       450      Torus  🌏 
        6         4         1      4303       900      Torus  🌕
       83        63        10      6300      2840      Torus  
       88         7        41       167       900     Spiral  15mi2 🌏⟺🟠
       92        51        20      2473      1600     Sphere  1974 O'Neill 1&2
      284        24       130       182      1600     Spiral  50mi2 🌏⟺🟠
      559        50       254       195      2250     Spiral  100mi2 🪐🌕 
     1140       110       515       214      3200     Spiral  200mi2 🪐🌕
     2281       245      1018       240      4500     Spiral  400mi2 max
     2480      1451       515      2818      3200   Cylinder  1974 O'Neill 3a
     3993      2969       512      5799      8000     Sphere  1929 Bernal
     5583      3547      1018      3484      4500   Cylinder  1974 O'Neill 3b
    17894     12682      2606      4866      7200   Cylinder  1000mi2 ✨ 
    41724     31670      5027      6300     10000   Cylinder  1973 Clarke/Rama
   104000     84000     10000      8400     14000   Cylinder
       3M        2M    100000     25000     45000   Cylinder
      75M       75M        1M     75000    150000   Cylinder  max
    2500M     2500M       10M    250000    460000   Cylinder  2000 McKendree

RECOMMENDATIONS

  * Build one 450m torus in low Earth orbit. 🌏
  * Build one 900m torus around the Moon. 🌕
  * Place two 900m or 1600m spirals in Aldrin-cycler orbit between Earth and Mars. 🌏⟺🟠
  * Send four 2250m or 3200m spirals from L4/5 to orbit Titan. 🪐🟠
  * Build more spirals in equatorial rings around Dione/Rhea/Titan/Iapetus. 🪐🌕🌕🟠🌔
  * Send 7200m mega-cylinders (or multiple spirals) from L4/5 to other destinatons. ✨

MATH FOR ALL GEOMETRIES

TORUS - donut shape 
  Measures:    Radius 30m<R<10km, width R/5, sky R/30
  Floor area:  1.24R2
  Hoop area:   2.5R2 (carbon tendons)
  Hoop carbon: 0.5R kg/m2
  Side area:   0.2R2 (structural spokes)
  Side carbon: R/7 kg/m2
  Shielding:   1550 kg/m2 = 1500kg h2o + 50kg envelope
               (envelope = liner+shell+ablative+foil)
  Bulk mass:   R2 (1.279 R + 4185)
               = (1550)(2.7R2)+(R/2)(2.5R2)+(R/7)(0.2R2) 
  Efficiency:  3375 + 1.031R kg/m2
  Examples:    1929 - Herman Potočnik R=15m
               1975 - Stanford Torus R=900m

SPHERE - ball shape
  Measures:    Radius 30m<R<10km
  Bulk hull:   12.5R2 (spherical area)
  Bulk area:   9.9R2 ("flat" surveyor area)
  Floor area:  8.0R2 (flat exceeding 0.3g)
  Hoop area:   8.0R2
  Hoop carbon: 0.42R kg/m2
  Shielding:   1050 kg/m2 = 1000kg h2o + 50kg envelope
  Bulk mass:   R2 (4.158 R + 13125)
               = (1050)(12.5R2)+(0.42R)(9.9R2)
  Efficiency:  1641 + 0.5198R kg/m2
  Examples:    1929 - John Bernal R=8km
               1974 - Gerard K O'Neill Island One R=1.6km

CYLINDER - soda can shape
  Measures:    Radius 450m<R<150km, length 8R
  Floor area:  50.27R2
  Bulk hull:   56.55R2
  Hoop area:   50.27R2
  Hoop carbon: R/2 kg/m2
  Side area:   6.283R2
  Side carbon: R/10 kg/m2
  Shielding:   1050 kg/m2 = 1000kg h2o + 50kg envelope
  Bulk mass:   25.7 R2 (R + 2300)
               = (1050)(56.55R2)+(R/2)(50.27R2)+(R/10)(6.28R2)
  Efficiency:  1180 + 0.512R kg/m2
  Examples:    1973 - Arthur C Clarke R=10km
               1974 - Gerard K O'Neill Island Three R=3.2km,4.5km
               2000 - Tom McKendree R=460km
               2020 - Isaac Arthur McKendree lattice / Rungworld

SPIRAL - coiled ribbon or jelly roll shape
  Measures:    Radius 450m<R<4500m, sky R/30, river valley width R/1.8
  Floor area:  50.27R2
               = ( πR2(1-0.32)/(R/30) + 2πR0.75 )(R/1.8)
  Hoop area:   7.767R2
  Hoop carbon: R/60 kg/m2 - Tensegrity geometry dramatically distributes the load.
  Side area:   5.84R2
               = 2π(R2 - (0.3R-R/30)2)
  Side carbon: R/60 kg/m2
  Slope area:  47.6R2
               = ( πR2(1-0.32)/(R/30) )(R/1.8)
  Slope carbon: R/60 kg/m2
  Shielding:   550 kg/m2 = 500kg h2o + 50kg envelope
               NOTE: 80% of floor space in radiation shadow of decks above and below.
  Bulk mass:   1.020 R2 (R + 7336)
               = (550+R/60)(7.767R2)+(R/60)(47.6R2)+(550+R/60)(5.84R2)
  Efficiency:  149 + 0.0203R kg/m2
  Examples:    Timothy Barber

RING
  Measures:    Radius R>1000km, 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


BIBLIOGRAPHY