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Spacecraft ADCS

Satellite Magnetic Torquer Attitude Control Simulator

A sizing tool for CubeSat-class (1U-12U) magnetic torquers (MTQ). Change altitude, inclination and coil specs to see the achievable magnetic moment, peak torque, time-to-target slew rate and coil power in real time. Useful for preliminary design of B-dot detumble and momentum dumping loops.

Parameters
Satellite mass
kg
Moment of inertia I_sat
kg·m²
Orbit altitude
km
Inclination
°
51.6° = ISS, 98° = sun-synchronous
Coil turns N
Coil area A
cm²
Coil current I
mA
Target slew rate ω_t
°/s
Angular rate to be reached by the slew
Results
—
Orbit B field (μT)
—
Magnetic moment m (A·m²)
—
Peak torque τ (μN·m)
—
Angular accel α (°/s²)
—
Time to target (s)
—
Coil power (W)
—
Satellite, coil and B-field vector

The satellite body (centre) carries a coil that produces a magnetic moment m. It interacts with the Earth magnetic field B (blue arrow) and produces a control torque τ=m×B (red arrow). The green ellipse is the orbit.

Peak torque τ vs altitude
Angular acceleration by CubeSat class
Theory & Key Formulas

$$\vec\tau = \vec m \times \vec B,\quad m = N\,I\,A,\quad \alpha = \tau/I_{sat}$$

Magnetic torquer fundamentals. m = magnetic moment [A·m²], N = coil turns, I = current [A], A = coil area [m²], B = geomagnetic vector [T], τ = torque [N·m], I_sat = spacecraft moment of inertia [kg·m²], α = angular acceleration [rad/s²].

$$B(h) \approx B_0 \left(\frac{R_E}{R_E+h}\right)^{3}\!\!\bigl[1+0.3\sin i\bigr]$$

Dipole approximation for B at altitude h and inclination i. R_E = 6371 km, B_0 ≈ 25 μT. Use the IGRF model for higher fidelity work.

Satellite Magnetic Torquer Attitude Control — B-dot, IGRF, CubeSat

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I've never heard of a "magnetic torquer". You can change a satellite's attitude with a magnet? There's no ground in space — where does the torque come from?
🎓
Good intuition. A magnetic torquer is basically "an electromagnet inside the satellite that pulls against the Earth's magnetic field." Even in LEO (a few hundred km altitude) there is still about 25–50 μT of Earth field around you, so if you run current through a coil onboard, you get a real mechanical torque from τ = m × B. No ground required. It is exactly the same physics that makes a compass needle point north, just rebranded as "rotate the whole spacecraft." No moving parts, so it lasts forever, and it is small and low-power — perfect for CubeSats.
🙋
OK but with the default values I get a peak torque of only 3.94 μN·m. That feels tiny. Does it actually do anything?
🎓
Right — micro-newton-metres is essentially nothing in everyday terms. But space has no friction, so small torques integrate. With the default 1U CubeSat (inertia 0.06 kg·m²) you reach a target slew of 0.5°/s in 133 seconds. That feels absurd on the ground but it is fine for a satellite whose orbital period is 94 minutes. The real challenge is the initial detumble: right after separation the satellite tumbles at 5–10°/s and bleeding that off can take 30 minutes to a few hours. Even so, there is no better small-package alternative, which is why almost every CubeSat carries an MTQ.
🙋
You mentioned "B-dot control" earlier. What is that? Attitude estimation sounds really hard.
🎓
B-dot is the simplest detumble law you can write — about five lines of code. You read the geomagnetic field B(t) with a magnetometer, take the time derivative dB/dt, and command the magnetic moment opposite to it: m = −k·dB/dt. The more the spacecraft tumbles, the larger dB/dt becomes, and the resulting m × B pulls angular momentum into the Earth's field. No attitude filter, no Kalman, no quaternion — perfect for a "we just separated, the world is dark, get me stable" safe mode that every CubeSat needs.
🙋
So can you do precise attitude control with just magnetic torquers? I've also heard of reaction wheels — why do you need both?
🎓
Great question. Pure magnetic control is "underactuated". From τ = m × B you can never produce torque about the axis parallel to B, so at any instant you cannot drive all three axes. Averaged over one orbit the direction of B sweeps around and three-axis motion is possible, but it is slow and not good for precision pointing. So the usual split is: reaction wheels for fast precise pointing, magnetic torquers for "momentum dumping" — bleeding off wheel angular momentum into the Earth field whenever the wheels saturate. Bradford Space MTQ-200, CubeSpace CubeTorquer, ISIS iMTQ are common commercial units; Planet Labs Doves operate exactly this way.
🙋
Is anything new happening in CubeSat magnetic-torquer practice?
🎓
One nice trend is "in-dispenser detumble". Traditionally B-dot starts after the satellite is ejected from the launcher; lately some Yaesu-style dispensers and SmallSat pods pre-condition the satellite magnetically before release. On the modelling side, newer IGRF coefficient sets improve on-orbit B prediction, and hybrid estimators that fuse the B-model with gyros and magnetometers are giving better attitude knowledge with the same hardware. The basic theory is sixty years old, but it is still actively evolving.

FAQ

For a coil-type magnetic torquer the magnetic moment is m = N·I·A, where N is the number of turns, I the current (A) and A the effective area of one loop (m²). A typical 1U CubeSat unit uses N=400 turns, A=80 cm² = 8e-3 m², I=50 mA giving m ≈ 0.16 A·m². This tool takes cm² and mA, converts to A·m², then evaluates the peak torque τ = m × B.
The Earth field is modelled as an internal dipole so |B| drops as 1/r³ with altitude. In LEO (200–1000 km) the magnitude is roughly 20–50 μT — about 50 μT at the surface and ~25 μT at 500 km. The field is also larger over the poles and weaker near the equator, which this tool captures with a sin(inclination) correction. The standard reference for real designs is the IGRF (International Geomagnetic Reference Field) model.
No. Because τ = m × B, no torque can be produced about the axis parallel to B, so instantaneously the system is underactuated. Pure magnetic control can only drive three axes on average over an orbit, which is too slow for high-bandwidth pointing. In practice CubeSats combine magnetic torquers with reaction wheels: the wheels handle precise pointing and the torquers dump accumulated wheel momentum (momentum dumping).
B-dot is the simplest detumble law: command magnetic moment m = −k·dB/dt, opposite to the measured field rate. Angular momentum flows out of the spacecraft into the Earth field. It needs only a magnetometer and the torquers — no attitude estimator — so virtually every CubeSat uses B-dot as a safe mode immediately after launch separation.

Real-world applications

Commercial CubeSat fleets (Planet Labs Doves): Planet Labs operates hundreds of 3U Dove satellites; each uses a magnetic-torquer + reaction-wheel combination to hold nadir pointing. Post-separation detumble is B-dot, imaging is on wheels, and long-term momentum dumping uses the torquers again. Coil specs of a few hundred turns × tens of cm² × 50–100 mA are typical and match the defaults in this tool.

Science missions (ICESat-2, CYGNSS): NASA's ICESat-2 ice-altimeter and the eight-satellite CYGNSS hurricane constellation both rely on magnetic torquers for momentum dumping. For small science spacecraft that demand precise pointing, "reaction wheels + magnetic torquers" has become the de facto standard. Polar and mid-inclination orbits give the magnetic field a healthy sweep, so the torquers stay effective.

Commercial ADCS units (Bradford Space, ISIS, CubeSpace): Off-the-shelf magnetorquers are sold for 1U–12U platforms — Bradford Space MTQ-200, CubeSpace CubeTorquer, ISIS iMTQ, Honeywell ACS-Series. Typical specs: 0.1–1.0 A·m² magnetic moment, 30–200 g mass, 0.1–2 W power. Buying COTS and bolting it in lets new entrants stand up an ADCS quickly, which is why startup smallsat builders love them.

CAE modelling of the magnetic environment: Magnetic-torquer design is normally finished off in MATLAB/Simulink or Basilisk, with the IGRF model generating B(t) along the orbit and a six-DOF rigid-body model integrating attitude. A closed-form tool like this one is used to size the coil early; orbit-averaged response and nonlinear coupling are then refined numerically.

Common misconceptions

The most common misconception is "magnetic torquers can do full three-axis precise pointing on their own". From τ = m × B no torque exists about the axis parallel to B, so instantaneous three-axis control is impossible (underactuated). Over the 90-minute orbit the field direction sweeps and motion in three axes is possible, but the response time is minutes to hours. For sub-second pointing (Earth observation imaging, optical comms, space telescopes) you must add reaction wheels or CMGs. Designs that claim precise pointing from torquers alone are a red flag.

Next, do not assume B is constant everywhere. This tool uses the simple B(h)=B₀·(R_E/(R_E+h))³·[1+0.3·sin i]; the real field varies with longitude, latitude, time-of-day and solar / magnetic storm activity. Over the South Atlantic Anomaly (SAA) the field weakens and torquer authority can halve, while during magnetic storms B spikes and unwanted torques appear. Accurate design implements IGRF-13/14 along the predicted orbit to produce B(t) time series.

Finally, the pitfall of "coil resistance is the only power loss". This tool just computes P = R·I², but the real torquer driver includes a PWM stage, filtering and over-current protection, all adding 0.1–0.3 W. The torquer's own field also disturbs the magnetometer, Hall sensors and reaction-wheel bearings inside the spacecraft, which forces a drive / sense duty management scheme (typically 50% on / 50% off). Always evaluate "average power" and "peak magnetic moment" separately.

How to Use

  1. Enter satellite mass (1–12 kg for CubeSat) and moment of inertia (0.001–0.1 kg·m²) using sliders or numerical input.
  2. Set orbital altitude (300–2000 km LEO) and inclination (0–98°) to compute ambient magnetic field strength using IGRF model.
  3. Adjust coil parameters (dipole moment, number of turns, wire gauge) to generate peak torque; simulator returns angular acceleration, slew time to target attitude, and coil power dissipation.

Worked Example

A 3U CubeSat (mass 4 kg, Iz = 0.008 kg·m²) at 500 km polar orbit (inclination 98°) experiences B-field ≈ 28 μT. With a magnetic torquer coil producing m = 1.2 A·m², peak torque τ = 33.6 μN·m. Angular acceleration α = 4.2 °/s². To rotate 90° (π/2 rad), time ≈ 38 seconds. Coil dissipates 0.35 W at 2 A current through 0.18 Ω resistance.

Practical Notes

  1. Geomagnetic field varies 20–60 μT in LEO; equatorial orbits (low inclination) experience weaker, less variable B. High-inclination (polar) passes offer stronger control authority near poles.
  2. For nadir-pointing CubeSats, align coil axis perpendicular to desired torque vector; simultaneous three-axis control requires orthogonal MTQ triad (X, Y, Z coils).
  3. Power scales as I²R; doubling current quadruples dissipation. Balance slew rate (τ/I_z) against thermal budget; typical 3U MTQ draws 0.2–0.8 W in eclipse periods.