CFChristopher Farmer
Slew-time / dipole tradeoff
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Interactive · geomagnetic attitude control

Why magnetic control is stabilising but slow

The companion paper's central result in one chart. A magnetic actuator's torque is bounded by its dipole moment times the local field (τ = m×B). For a rest-to-rest slew of a large flexible platform, the time to turn scales as t = 2√(Iθ/mB). Set the platform and watch the required dipole for a fast slew rocket past anything ever flown — while an achievable dipole leaves you slewing for hours to days. That slowness is the paper's point: it matches magnetic actuation to slow tasks — detumbling, libration damping, biasing and momentum management — near a valid gravity-gradient equilibrium, which is itself conditional on principal-axis ordering and attitude. Slowness is not by itself proof of safety: the paper is explicit that low actuator bandwidth is not intrinsically safe for a flexible structure.

Illustrative screening relation. Bang-bang, single-axis, rigid-body slew under a bounded magnetic torque; the field is the deposited IGRF-14 orbit-mean. It bounds the rate question only — not pointing accuracy, flexible-mode coupling or three-axis control. Numbers are study values for a hypothetical platform.

Dipole required vs slew time

log–log · your platform is the gold curve
required dipole for a 90° slew ever-flown magnetorquer range your target slew time

Platform & orbit

10³ – 10⁶ kg (log)
slender-body inertia I = mL²/12
50 s – 30 days (log)
Provenance: slew bound t = 2√(Iθ/mB) from the companion paper; orbit-mean |B| at 51.6° inclination from the deposited IGRF-14 screen (geomagnetic_orbit_screen.csv). Reference check: a 1-km, 10⁵-kg platform, 90° in ~7 min → ~10¹⁰ A·m², reproducing the paper's figure. Flown-magnetorquer band ≈ 1–500 A·m² (illustrative). Not a controller design.