Wheels and tori

The classic von Braun / 2001 / Stanford Torus form: a rim habitat connected to a hub by spokes, or a self-supporting ring.

Key results

Strengths

• Inherently stable. It spins about its maximum-inertia axis, and damps itself if fluids or flexing transfer momentum Paul451, 2023-11-08.
• One continuous floor at one g. "Everyone on one floor", easy circulation, no elevators Coastal Ron, 2024-07-30.
• Self-similar modules. A torus is a repeating row of identical modules that can be mass-produced on Earth and berthed end to end in orbit. mikelepage argues this lowers assembly cost more than the barbell's geometric saving mikelepage, 2024-07-23; mikelepage, 2023-03-09.
• Suits active magnetic shielding. Toroidal superconducting cables project a field outward and null it inside mikelepage, 2023-06-01. See radiation shielding.
• Grows by widening. A wheel can be widened with more rings or bands, or built as a baton → cross → full ring Coastal Ron, 2023-03-07; Coastal Ron, 2015-09-13; Paul451, 2022-10-30.

Weaknesses

• Poor area/volume ratio. A thin torus has far more surface per unit volume than spheres of the same volume, which is costly when shielding is thick Twark_Main, 2022-11-09; Twark_Main, 2022-10-30.
• Minovitch's 1991 torus (r/R = 0.02) holds 8000 m³ against 63,000 m³ in its central columns: "a baton with a great marketing department" Twark_Main, 2022-12-17.
• For a given habitable volume, John Fornaro's large ring uses about 2.7× the shielding of a compact bola Twark_Main, 2024-07-05.
• When shielding matters, prefer large r/R tori Twark_Main, 2023-06-17.
• Cannot be shrunk. The minimum 1 g torus (2 m minor radius, 4 rpm) is ~3100 m³ Twark_Main, 2022-10-30.
• Linear circulation. A long thin corridor is a poor layout, like an office building stretched into a tunnel Twark_Main, 2024-07-31. A single-path ring loses safety if one module is blocked Coastal Ron, 2025-04-09.
• Floppy noodle. Docked modules alone do not make a rigid ring; a stabilizing structure is needed Twark_Main, 2024-07-29.

Structure

• Self-supporting torus limit. Using only the spare longitudinal wall tension of a pressurized torus, at 100–200 kg/m³ interior density, the maximum major radius is only ~50–100 m before shielding Twark_Main, 2022-11-13.
• Spokes vs a tensile drum. A flat isotropic tensile sheet (a drum head) saves half the mass of spokes Twark_Main, 2022-11-13. Spoke-suspended stations put spokes in simple tension, but spoke mass likely exceeds that of an equivalent circumferential beam lamontagne, 2022-10-13.
• Rim as bicycle wheel or suspension bridge: cables joined at the centre, modules on the "road" Coastal Ron, 2014-02-18; Coastal Ron, 2015-02-14.
• Module orientation.
• Tangential modules (perpendicular to the radius) give uniform g TakeOff, 2015-03-30.
• Modules parallel to the spin axis let the ring close without curved modules mikelepage, 2024-07-23.
• Coastal Ron's modules run perpendicular to the curve, giving 30 m straight sightlines Coastal Ron, 2024-01-29.
• Straight segments tilt the gravity vector up to 22° (8 segments) omegahacker, 2025-01-10.

Variants

• Fixed outer ring with a spun inner ring on maglev. jongoff's favourite: non-rotating exterior for arrays, radiators and docking anywhere; modular; any µG:AG ratio jongoff, 2023-12-29.
• Two counter-rotating rings (L = 0). See angular momentum and Shevek23 rings.
• Folding and self-deploying tori:
• NASA Langley's 1960s hexagon (SP-4308 ch. 9).
• The Exodus DeTA.
• mikelepage's folded 8-module torus (45.5 m radius from a 13 m fairing, 1 g at 4.5 rpm) mikelepage, 2016-01-08.
• Wheel of sideways modules (London-Eye-like) (darkenfast).
• Spiral habitat growing outward, with older "uptown" sections at lower g Asteroza, 2023-03-09.

Cost reference points

• mikelepage's mock-up: 24 modules from a Starship-lander-style bay → a 103 m diameter ring under 2500 t, 3 rpm, 0.5 g, 2% head-to-foot difference mikelepage, 2022-10-15.
• Coastal Ron's 100 m Mars-g wheel: at least 200 Starship launches Coastal Ron, 2023-06-02.

Open questions

• Does the modular-assembly advantage of a torus outweigh the barbell's area/volume advantage in LEO, where shielding is thin? (A central open debate from 2023 to 2024.)
• How wide can a torus be before its "fat wheel" dynamics need active control?

Related pages

• Dumbbell/barbell · Comparison · Hoop stress · Stanford Torus and O'Neill

Sources

Forum posts

• Coastal Ron, 2014-02-18 (reply #44): Cable-spoked wheel like bicycle wheel. Post.
• Coastal Ron, 2015-02-14 (reply #275): Suspension bridge curled into circle. Post.
• TakeOff, 2015-03-30 (reply #547): Orient modules tangentially. Post. Attachments: orientation of rotating sections2.png, orientation of rotating sections.png.
• Coastal Ron, 2015-09-13 (reply #633): Bands added to widen station. Post.
• mikelepage, 2016-01-08 (reply #782): Folding torus of 8 modules. Post.
• lamontagne, 2022-10-13 (reply #2049): Spokes vs circumferential beam; hoop equations. Post.
• mikelepage, 2022-10-15 (reply #2104, 3 likes): 24-module 103 m ring <2500 t (3 likes). Post.
• Twark_Main, 2022-10-30 (reply #2257): Torus inefficient vs spheres. Post. Attachments: solid_black_line_is_the_one_to_look_at.jpeg.
• Twark_Main, 2022-10-30 (reply #2258): Minimum torus 3100 m³. Post.
• Paul451, 2022-10-30 (reply #2260): Barbell → cross → torus. Post.
• Twark_Main, 2022-11-09 (reply #2334): Torus remolded to spheres: area ratio vs r/R. Post. Attachments: B72423F3-4BCA-4446-877C-1AF379384BDC.jpeg.
• Twark_Main, 2022-11-13 (reply #2377): Self-supporting torus limit 50–100 m. Post.
• Twark_Main, 2022-11-13 (reply #2378): Tensile drum sheet saves half vs spokes. Post.
• Twark_Main, 2022-12-17 (reply #2660): Minovitch torus = baton with great marketing. Post. Attachments: torus_volume_to_area_vs_barbell_by_radius_fraction.jpg.
• Coastal Ron, 2023-03-07 (reply #3527): Widen the wheel; modular Mars-g station. Post.
• Asteroza, 2023-03-09 (reply #3531): Spiral habitat growth. Post.
• mikelepage, 2023-03-09 (reply #3537): Modularity and mass-manufacturing overwhelm geometry differences. Post.
• mikelepage, 2023-06-01 (reply #3763, 1 like): Torus + magnetic shielding may beat sphere + passive (1 like). Post. Attachments: Torus vs Sphere Major Radii.png, Torus vs Sphere Surface Area Ratio.png.
• Coastal Ron, 2023-06-02 (reply #3766): Mars-g station ~200 Starship flights. Post.
• Twark_Main, 2023-06-17 (reply #3887): Prefer large r/R tori. Post.
• Paul451, 2023-11-08 (reply #4335, 1 like): Torus passively stable. Post.
• jongoff, 2023-12-29 (reply #4381): jongoff: fixed outer ring + maglev spun ring. Post.
• Coastal Ron, 2024-01-29 (reply #4432): Modules perpendicular to curve; 30 m sightlines. Post.
• Twark_Main, 2024-07-05 (reply #4646): Torus ~2.7× shielding vs bola. Post.
• mikelepage, 2024-07-23 (reply #4656): Torus assembly by berthing identical modules; LEO Mars-g design. Post.
• Twark_Main, 2024-07-29 (reply #4664): Docked modules = floppy noodle. Post.
• Coastal Ron, 2024-07-30 (reply #4667): Torus: everyone on one floor. Post.
• Twark_Main, 2024-07-31 (reply #4675): Long thin linear layout. Post.
• omegahacker, 2025-01-10 (reply #4811): Straight segments tilt gravity vector. Post.
• Coastal Ron, 2025-04-09 (reply #4841): Single pathway safety issue. Post.