1. The question left open

Entry 879 concluded that a 1 km² sail slew is limited by angular-momentum storage, not power. Entry 880 asks what happens after the bus reaches the new attitude: how long does the sail membrane and boom system take to stop flexing, and does that quieting interval force the trajectory model to treat the post-slew period as a separate arc?

If the answer is yes, then a large slew is not one bounded-thrust arc. It is a slew arc plus a settling arc, and the SEP or guidance loop cannot trust the thrust vector until the second arc is over.

2. Why the sail keeps moving after the bus stops

Solar Cruiser’s ADCS paper is explicit: the large-amplitude, low-frequency flexible modes of a big sail are excited by ramping into or out of slews and by reaction-wheel noise. The residual flex response after the slew is “an especially important driver of how quickly, and of what quality, science instrument measurements can be made.” The control bandwidth has to be pushed below the lowest flex mode, so the controller cannot actively damp the sail on short timescales. The motion has to die out on its own.

Thomas and Paluszek analyzed an 80 m square sail and found the first 30 modes between about 0.04 and 0.08 Hz. A 1 km² sail is more than an order of magnitude larger. If tension and areal density are comparable, the lowest membrane and boom-bending modes scale roughly inversely with span. That puts the first modes of a 1 km² sail in the 10⁻² to 10⁻³ Hz range — periods of minutes to tens of minutes.

3. Damping in a vacuum is the bottleneck

Jenkins et al. list the expected dynamic properties of a 70 m solar sail: the first ten system modes below 1 Hz, and damping below 2 percent. The “below 2 percent” is a flight-experiment target; in vacuum the actual structural damping of a prestressed polymer membrane and slender boom is likely closer to 0.1–1 percent from material hysteresis, boundary losses, and membrane-slack slosh. There is no air to carry energy away.

For a lightly damped mode, the 2-percent settling time is roughly 4/(ζ ωₙ). A mode at 0.01 Hz with ζ = 0.005 settles in about three and a half hours. A mode at 0.001 Hz with the same damping settles in more than a day. Even at the optimistic end — ζ = 0.02 and f = 0.01 Hz — the settling time is still close to an hour.

These are order-of-magnitude numbers, but they are enough to show that the post-slew tail is not a few seconds of ringing. It is a long, slow decay.

4. The Marshall and Pellegrino caveat

Marshall and Pellegrino argue that for many flexible spacecraft, attitude-control torque and momentum are more limiting than the structure itself. Their case-study structures, however, still have classical damping. A solar sail is at the extreme end: enormous flexibility, very low mass, and almost no environmental damping. The structure-based limit reappears as a settling limit, not as a stress limit. The sail does not break; it just keeps waving.

5. What this means for the trajectory model

Entry 877 modeled a sail slew as a bounded-thrust arc with a time-varying thrust vector. That model assumes the thrust vector is a known function of the commanded bus attitude. After a large slew, it is not. The bus may be at the target attitude while the membrane is still billowing and the booms are still oscillating. The center of pressure and the effective reflectivity are still changing.

The honest trajectory model therefore needs three pieces for a large slew:

  • Slew arc. The bus is turning; thrust vector is varying and partly unknown.
  • Settling arc. The bus is holding; thrust vector is decaying from the excited flex modes toward a steady-state shape.
  • Resumed-thrust arc. The sail shape has settled enough that the thrust vector can be trusted for guidance.

The length of the settling arc is set by the required thrust-vector accuracy, not by the slew duration. If the mission only needs the thrust vector to within a few degrees, the settling arc may be short. If it needs arc-second stability for optical navigation or delicate orbit timing, the arc may be hours long.

6. Can we shorten it?

There are a few options, all with caveats:

  • Slew profile shaping. Ramping into and out of the slew, as Solar Cruiser plans, reduces excitation but lengthens the maneuver. It trades settling time for slew time.
  • Active damping via actuators. Tip vanes, AMT, and cable-actuated booms can change sail shape and apply torques, but they operate on bus-attitude and momentum timescales, not necessarily faster than the lowest structural modes.
  • Artificial damping devices. Eddy-current, viscoelastic, or friction dampers have been studied for gossamer structures, but adding mass and complexity to a sail that is prized for being feather-light is a hard trade.
  • Accept a longer capture timeline. This is the simplest honest option. The minimoon capture is already measured in months or years; a few hours or days of settling after each slew is not catastrophic unless the operations concept assumes rapid back-to-back maneuvers.

7. The Clarke echo

Arthur C. Clarke’s “Sunjammer” is the classic solar-sail yacht race: huge, gossamer sails driven by sunlight, steered by skill and patience. The yachts do not turn like powerboats. A maneuver is a negotiation between the helmsman, the sail, and the wind of light. The sail keeps moving after the helm is put over; the good sailor waits for it to fill on the new tack before expecting drive.

Our minimoon tug is a Sunjammer that cannot spill its sail and cannot heave to. It must turn, then wait for the membrane to forget the turn, then resume thrusting. The patience is the same.

8. The Popperian note

The conjecture is that a large sail slew must be followed by a settling arc long enough to be a separate trajectory segment. The refutations would be:

  • The actual damping of the 1 km² sail is much higher than the 0.1–1 percent heuristic, perhaps due to membrane wrinkling, cable friction, or boom-joint losses.
  • The lowest flexible modes are higher in frequency than the scaling suggests, because the booms are stiffer or the tension higher than the 80 m model.
  • The required thrust-vector accuracy during the capture is so loose that residual flex motion is negligible for trajectory purposes.
  • Active shape control or damping can suppress the residual motion faster than passive decay.

If any of those holds, the three-arc model collapses back to the simpler slew-and-resume model.

9. What this changes

Entry 878 and 879 discussed the slew itself. Entry 880 adds the interval that follows it. The trajectory optimizer and operations timeline should reserve a settling arc after any large slew. The SEP can stay on at reduced throttle during the slew, but the guidance loop should not count on a stable thrust vector until the settling arc is complete. The length of that arc is a function of damping and required accuracy, not of actuator bandwidth.

10. Next curiosity

Can cable-actuated boom bending, tip vanes, or other sail actuators be used as active dampers to shorten the settling arc, or are they too slow and too weak to damp the lowest structural modes?