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 isotropic 25mSv/day to avg 5μSv/day.
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 900m torus in Lunar orbit. 🌕
* Build four 2250m spirals in Lunar orbit. 🌕
* Build four 2250m spirals at Lunar L4/L5. 🌕
* Send all L4/L5 spirals to Titan. 🪐🟠
* Build more 2250m spirals around Dione/Rhea/Titan/Iapetus. 🪐🌕🌕🟠🌔
* At that point you now have a diversified backup for much of Earth's biosphere.
* Eventually expand to Uranus, and Neptune.
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
REFERENCES
- Potočnik, H. 1929. Das Problem der Befahrung des Weltraums - der Raketen-Motor. Berlin: Richard Carl Schmidt & Co. [First concept of a rotating wheel/torus habitat; radius 15 m]
- Johnson, R & Holbrow, C (Eds). 1975. Space Settlements: A Design Study. NASA SP-413. Washington, DC: NASA. [Stanford Torus design, radius 900 m]
- Bernal, JD. 1929. The World, the Flesh and the Devil. London: Kegan Paul. [Introduced "Bernal Sphere," radius 8 km]
- O'Neill, GK. 1974. The Colonization of Space. Physics Today, 27(9), 32-40. [Island One/Two designs, sphere variant, radius 1.6 km]
- Clarke, AC. 1973. Rendezvous with Rama. London: Gollancz. [Depicted a 10 km-class rotating cylinder habitat]
- O'Neill, GK. 1974. The Colonization of Space. Physics Today, 27(9), 32-40. [Island Three design, radius 3.2-4.5 km]
- McKendree, T. 2000. Optimal Large Space Structures for Settlement. Presented at the NASA/SSI Space Manufacturing Conference. [Proposed 460 km "McKendree Cylinder"]
- Arthur, I. 2020. Science & Futurism with Isaac Arthur. [Video series: McKendree lattice / Rungworld concepts]
- Barber, TP. 2025. Tensegrity Spiral Space Habitat. 2AI Labs. [Introduced the spiral/Archimedean "coiled ribbon" geometry]
- Niven, L. 1970. Ringworld. New York: Ballantine Books. [Fictional megastructure, radius 150 million km]
- Banks, IM. 1987. Consider Phlebas. London: Macmillan. [Culture Orbitals, radius 2.2 million km]
- Bishop, F. 1997. Ringworld Engineering. Nanotechnology Magazine (early online essays). [Speculative 1000 km rings]
- Bungie Studios. 2001. Halo: Combat Evolved. Microsoft Game Studios. [Halo Array, radius 31,000 km]
Dr. Timothy P. Barber / 2AI © 21 AUG 2025
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