Concordia
Looking along the momentum control bay past the reaction ring machines in their vacuum housings toward the rotor 4 end wall.

Why doesn't the whole station spin?

Four rotors turn at the heart of Concordia, but the station as a whole does not. The rotors spin in opposite pairs so their angular momentum cancels, and the station stays pointed where it is pointed.

What the tags mean

Predict

Suppose all four city rotors spun the same way. How hard would each end of the station have to push to turn it 1 degree a day?

  1. About 4 thousand newtons
  2. About 400 thousand newtons
  3. About 4 million newtons
Show the answer

About 4 million newtons at each end, continuously: 4.1 MN with the industrial rotor, Ehricke, and the rings already working against it. The station as built needs at most 4.5 kN. The difference is a factor of about a thousand.

Observe

Open the momentum overlay on the whole station. Tsiolkovsky and Noordung carry one sign, Bernal and O'Neill the other, and the net is zero.

Open in the simulation: Exterior Hero: Complete Habitat

The whole station with the momentum overlay: minus 50 percent for the first two rotors, plus 50 percent for the second two, net zero.
The station with the momentum overlay: rotors one and two against three and four, the industrial rotor, and a net of zero. Open this view

Explain

A spinning rotor is a gyroscope. Push on it to turn it and it pushes back at a right angle. Each rotor holds 1.17 × 10¹⁷ N·m·s of angular momentum, so four spinning the same way would hold 4.7 × 10¹⁷ and resist every turn. Established physics

Concordia avoids that by pairing. Tsiolkovsky and Noordung turn one way and Bernal and O'Neill the other, so the habitation rotors sum to zero. The industrial rotor turns against rotor four and holds about 4 percent of the total. Momentum rings trim whatever is left, to within 0.1 percent. Design value The pairs spin against each other at the spine, so the spine, hull and ports sit still between them.

That is the answer to the title. The rotors do spin, once every 100 seconds. The station frame does not, and it can turn on a few kilonewtons of electric thrust. Momentum is traded between rotors and rings, not thrown away, so turning costs electricity and not propellant.

Go deeper: The thrust arithmetic

Turning a body with angular momentum L at rate W takes a torque L × W. A couple across the 21 km hull supplies it.

W = 1° / day = 2.02 × 10⁻⁷ rad/s
all four one way (net 4.28 × 10¹⁷ N·m·s):
torque = 4.28 × 10¹⁷ × 2.02 × 10⁻⁷ = 8.6 × 10¹⁰ N·m
force at each end = 8.6 × 10¹⁰ / 21,000 m = 4.1 MN
as built (inside the 0.1 percent band): 4.5 kN

Counter-rotation has the full ledger, including the rings.

Change a parameter

Press All four spin one way in the ledger and read the thrust. Then press Concordia as built and watch it fall to a few kilonewtons.

A ledger of angular momentum for the four rotors, the industrial rotor and the rings. As built the net is zero; with all four rotors spinning one way the thrust to turn the station is 4.1 MN at each end.

  • 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.