Concordia

Moving around a spinning world

In Concordia you walk, ride the metro, take a lift to the axis and cross to other rotors by train. Each trip feels a different piece of the spin. Going along the axis costs nothing, going around the circle changes your weight, and going up makes gravity fade.

What the tags mean

On foot and by metro

Walking in a rotor feels like walking on Earth, with one small difference. Because the floor turns, a step in the direction of spin makes you a little heavier and a step against it a little lighter. At a walking pace of 1.5 m/s the change is about 2 percent, which nobody notices (why the spin is so gentle). At train speeds it matters. Established physics

The metro runs on viaducts 45 m above the street, not underground. Its ring line circles the rotor at 2,455 m from the axis, where a standing rider weighs 0.98 g. Design value What you weigh is set by your speed through space, which is the speed of the floor plus or minus the train's own speed. The Coriolis effect is that difference.

0.98 gstanding on the ring lineEstablished physics
0.66 gmoving against the spin at 100 km/hEstablished physics
1.33 gmoving with the spin at 90 km/hEstablished physics
0.98 gon the axial linesEstablished physics

Riding against the spin you are lighter, with the spin you are heavier. That is why the two directions run at different speeds: 100 km/h one way (a 13.4 minute lap) and 90 km/h the other (14.3 minutes). The axial lines run parallel to the spin axis, so they add no Coriolis effect and a rider weighs a steady 0.98 g. Which direction is "heavy" flips between Tsiolkovsky and Noordung (Rotors 1 and 2) and Bernal and O'Neill (Rotors 3 and 4), because those pairs spin opposite ways. Established physics

Street-level view of the elevated metro viaduct on its portals, with the line running away along the curving arterial.
The ring metro on its viaduct, seen from the arterial below. Open this view

Pick a train speed and direction to see the apparent weight on board. At 100 km/h against the spin the answer is 0.66 g, and at 90 km/h with the spin it is 1.33 g.

Open in the simulation: Metro Viaduct Over an Arterial Open in the simulation: Ride the metro

Ascenders: gravity as a height

Four ascender towers per rotor lift people from the ground to the axis. A cabin holds about 150 people, 64 seated and 86 standing, and the 2,380 m climb takes 595 seconds, cruising at 5.5 m/s. Design value Gravity falls steadily as you rise: 0.98 g at the boarding deck, about 0.8 g where the cabin passes through the sky, 0.60 g at 1,000 m and 0.40 g at 1,500 m. At the hub terminal it is 0.028 g. Established physics

Two more things change as you climb. The cabin turns with the rotor all the way, so its sideways speed falls from 153 m/s at the deck to 4.4 m/s at the hub, and the guide rails supply the push that makes it slow down. And because the cabin moves toward the axis, the Coriolis effect shoves everything inside sideways, so the apparent vertical leans. The cabin rolls to follow it: 4 degrees at 200 m, 6.7 degrees at 1,000 m, 15 degrees close to the axis, in the opposite sense in the two spin pairs. Established physics

What an ascender rider feels on the way up A vertical track from the boarding deck at 50 m to the hub terminal at 2,430 m. Gravity falls from 0.98 g at the deck to about 0.8 g at the artificial sky, 0.60 g at 1,000 m, 0.40 g at 1,500 m and 0.028 g at the hub terminal. The cabin leans 4 degrees at 200 m, 6.7 degrees at 1,000 m and 15 degrees at 1,844 m, always toward the apparent vertical. A descending cabin on a second track returns the climbing energy. Deck, 50 m Sky, about 500 m 1,000 m 1,500 m 1,844 m Hub, 2,430 m 0.98 g, lean 0 degrees about 0.8 g 0.60 g, lean 6.7 degrees 0.40 g lean 15 degrees 0.028 g lean 4 degrees at 200 m Climb stores 11.7 kJ per kg; the down cabin gives it back Up track Down track
Gravity falls and the cabin leans as it climbs. A second cabin descends on a parallel track.

Climbing stores 11.7 kJ in every kilogram, 630 MJ for a loaded 54 t cabin. The descending cabin on the next track returns it through regenerative motors, so the lift needs little net energy. The angular momentum a rising cabin hands to the rotor is 2.1 × 10¹⁰ N m s, under a millionth of the rotor's own, and counter-phased tracks take it back.

Inside the panoramic ascender cabin at 650 m, with window seats, rails, a glass floor gallery and the city curving up beyond the glass.
Inside the cabin at 650 m, with the city curving up beyond the glass. Open this view

Open in the simulation: Ascender: Cabin Interior Open in the simulation: Ascender: Tower From Outside Open in the simulation: Ride up through the sky

The spin lock at the hub

At the top of the tower you are still turning with the rotor at a few percent of a gravity. The spine, the stationary tube down the middle of the station, is not turning. There is no direct doorway between a floor moving with the rotor and the still axis, so the hub has a spin lock.

Eight chambers, each 90 m long, sit on a magnetic-bearing carousel in the hub. A chamber closes behind you, spins down over 96 seconds at constant angular acceleration, stays under 0.0025 g the whole time, and latches to the spine. Spinning up takes another 96. A full cycle takes about 10 minutes. You step out weightless and stationary. Engineering challenge

A large rotating drum behind a bearing collar, with four tower portals and spin-decoupling chambers.
The turning side: the transfer hub of Tsiolkovsky, seen from the stationary spine, turns behind its bearing collar once every 100 seconds. Open this view
Inside the stationary spine at the rotor hub: the spin-decoupling lock liner with viewing slots and door portals over a chamber carousel.
The still side: inside a lock chamber at mid spin-down. The chamber slows over 96 seconds, never above 0.0025 g, then latches to the spine. Open this view

Open in the simulation: Spin-Decoupling Lock, Tsiolkovsky Open in the simulation: First weightlessness

The spine and the express

The spine is a stationary pressure tube about 120 m across, at 1 atmosphere, with no spin and no gravity. It carries power, data, heat transfer and the transport line between all rotors, Ehricke (the industrial rotor) and the spaceport. Its express runs five 25 m cars at 140 m/s, with restraint couches, handholds and panoramic windows. At cruise the spine's full length, almost 20 km, takes about two and a half minutes. Design value

The five-car axial express on its guideway inside the spine, seen three-quarter from ahead of the head car.
The five-car express on its guideway in the spine. Open this view

Bridges, and why rotors 2 and 3 have none

Two rotors that spin the same way hold still relative to each other, so a bridge can join them. Bridges join rotors 1 and 2, and 3 and 4: a through-truss tube 300 m long with its centre 45 m above the ground and 0.98 g on its floor, carrying a promenade and a transit lane. Before either rotor changes speed or phase, traffic stops, doors close and the bridge sections retract. Design value

Rotors 2 and 3 spin opposite ways, and their end walls pass each other at 313 m/s, so nothing can span the gap (counter-rotation explains why). To go from rotor 2 to rotor 3 you climb to the hub, spin down, cross by the spine and spin up on the other side.

The transit bridge between two same-spin rotors seen from its sunlit flank, with window bands and X bracing across the gap.
A transit bridge between two rotors of the same spin pair. Open this view

Open in the simulation: Counter-Rotating Interface, Noordung and Bernal Open in the simulation: Transportation overlay

Go deeper: Worked example: the ring metro Established physics

The ring line is at r = 2,455 m with ω = 0.0626 rad/s, so the floor moves at ωr = 153.7 m/s. A rider standing feels

g_apparent = (ω × r ± v)² ÷ r

with + for travel with the spin and - for travel against it.

Against the spin at 100 km/h (27.8 m/s): (153.7 - 27.8)² ÷ 2,455 = 6.46 m/s², which is 0.66 g. With the spin at 90 km/h (25.0 m/s): (153.7 + 25.0)² ÷ 2,455 = 13.0 m/s², which is 1.33 g. Standing: 153.7² ÷ 2,455 = 9.62 m/s², which is 0.98 g.

The sideways Coriolis acceleration is 2ωv = 3.5 m/s² (0.36 g) at 100 km/h. For a walker at 1.5 m/s it is 0.19 m/s², 0.02 g.

Ascender energy: climbing from the deck at r = 2,450 m to the hub at r = 70 m raises the rotating-frame energy by ½ω²(2,450² - 70²) = 11.7 kJ/kg. Lean: the sideways acceleration 2ω × 5.5 m/s = 0.69 m/s² against local gravity of 5.9 m/s² at 1,000 m gives tan⁻¹(0.69 ÷ 5.9) = 6.7 degrees.

Sources and further reading

Concordia design documents

  • Concordia engineering specification, sections 17 and 22 to 24, and the ascender, spine and metro design notes.
  • Artificial gravity Concordia makes gravity by turning. Each city rotor is a cylinder 5 km wide that spins once every 100 seconds, and the floor is the inside of its outer wall.
  • Flying in a spinning world The air in a rotor turns with the floor, so a wing works there, and it shows what spin gravity really is.
  • Counter-rotation and momentum A spinning city is a giant gyroscope, and a gyroscope fights every push that tries to tilt it. Concordia spins its four city rotors in opposite pairs, so the total spin is zero.
  • The axis and the spine At the centre of every rotor you weigh almost nothing, and a stationary tube 120 m wide runs the whole length of the station.
  • Ascenders and the sky The ascender is a lift 2.4 km tall. It carries 150 people from the street through the artificial sky to the axis in about ten minutes, and on the way your weight drops to almost...