🧲 Magnetorquer Sizing & Momentum Dumping

Available torque · dump time & required dipole · B-dot detumble estimate

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Torquer & Field

Dumping & Detumble

Results

Field B used
– µT
Available torque
– N·m
Dump time for h
– min
Dipole to dump in time
– A·m²
Detumble time
–
–
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📖 How to use

  1. Set the altitude and pick the field case — dump planning uses the orbit average; guaranteed-authority checks use the equatorial minimum.设置高度并选磁场工况——卸载规划用轨道平均值，保底能力校核用赤道最小值。
  2. The available torque m·B·η must comfortably exceed the secular disturbance for wheel desaturation to keep up.可用力矩 m·B·η 需明显大于长期干扰力矩，卸载才能跟得上积累。
  3. Check the dump time against your dump window, or read the required dipole directly; magnetorquers only torque perpendicular to B — hence the geometry efficiency.对照卸载窗口检查卸载时间，或直接读所需磁矩；磁力矩器只能产生垂直于 B 的力矩——即几何效率的来源。
  4. The detumble estimate (I·ω₀ / average torque) sizes the commissioning phase; B-dot control approaches this bound within a factor ~2.消旋估计（I·ω₀ / 平均力矩）用于入轨初期设计；B-dot 控制实际耗时约为该下限的 2 倍以内。

Magnetorquer relations

Torque: T = m·B·η, where B ranges from M/r³ at the equator to 2M/r³ over the poles (M = 7.96×10¹⁵ T·m³) and η accounts for the average angle to the field.

Momentum dumping: t = h/T; required dipole m = h/(B·η·t).

Detumble: the momentum to remove is I·ω₀, so t ≈ I·ω₀/(m·B·η) — a lower bound that B-dot control approaches.

Magnetic control cannot torque about the local field direction; full 3-axis authority needs the field direction to rotate over the orbit (fastest in high-inclination LEO, weak in GEO).

All computation runs locally in your browser.

磁力矩器关系式

力矩: T = m·B·η，B 从赤道 M/r³ 到极区 2M/r³（M = 7.96×10¹⁵ T·m³），η 计入与磁场的平均夹角。

动量卸载: t = h/T；所需磁矩 m = h/(B·η·t)。

消旋: 需卸除的角动量为 I·ω₀，故 t ≈ I·ω₀/(m·B·η)——B-dot 控制接近该下限。

磁控无法绕当地磁场方向产生力矩；三轴完整控制依赖磁场方向随轨道旋转（高倾角 LEO 最快，GEO 很弱）。

全部计算在你的浏览器本地完成。