Passive Magnetic Attitude Control (PMAC) Sizer
Size permanent bar magnets and soft-magnetic hysteresis rods for PocketQube alignment and despin time.
DETERMINISTIC PHYSICS & DATA METHODOLOGY
How This Calculator Works
Source modules: lib/physics/magnetics.ts
Sizes a passive magnetic attitude control (PMAC) assembly consisting of a permanent AlNiCo/NdFeB alignment dipole and orthogonal soft-magnetic hysteresis rods/ribbons (HyMu-80 / amorphous FeBSi), computing restoring torque, hysteresis dead-band, and rotational despin time.
Governing Equations & Physical Model
τ_rest = m · B · sin θEvaluated at θ = 10° pointing offset in a representative 42 µT high-latitude LEO geomagnetic field.
W_v = (8/3) · H_c · B_s, t_despin = (2π · I_t · ω₀) / (k_w · W_v · V_rod)Integrates kinetic energy removal from initial tip-off rate ω₀ = 15 °/s with orientation efficiency k_w = 0.5.
θ_db = arcsin(min(1, H_c / H_⊥))Evaluated against H_⊥ = 18.5 A/m (~23.2 µT equatorial field).
Inputs, Parameters & Units
| Parameter | Unit | Physical definition |
|---|---|---|
| m | A·m² | Permanent bar magnet dipole moment. |
| V_rod, H_c, B_s | mm³, A/m, T | Total soft-magnetic damper volume, coercivity, and saturation flux density. |
| I_t | kg·m² | Spacecraft transverse principal moment of inertia. |
Assumptions & Validity Limits
- Assumes slender damper aspect ratio (p ≫ 50) and sufficient lateral separation from the permanent magnet so stray field H_∥ < H_sat (avoiding rod pinning; see peakRodFieldAm in lib/physics/magnetics.ts).
- Uses idealized (8/3)·H_c·B_s loop area rather than Rayleigh minor-loop scaling near zero rate.
Worked Default Reference Case
For I_t = 1.1×10⁻⁴ kg·m², a 45 mm³ HyMu-80-class rod set damps a 15 °/s tip-off rate in 0.93 hours with a ±3.7° coercive dead-band and 5.83×10⁻⁷ N·m restoring torque at 10°.
- Despin time (from 15 °/s)
- 0.93 h
- Coercive dead-band
- ±3.7°
- Restoring torque (at 10°)
- 5.83×10⁻⁷ N·m
- Transverse inertia I_t
- 1.1×10⁻⁴ kg·m²