ADCS sizing
ADCS Sizing Calculator
What fights your satellite's attitude — and how much actuator do you need to win? Size the disturbance torques, then the wheels and magnetorquers that beat them.
// First-order Attitude Determination & Control System (ADCS) model. four LEO disturbance torques — gravity-gradient, aerodynamic, solar-radiation-pressure, magnetic — plus reaction-wheel + magnetorquer sizing. SMAD Ch. 11 / Wertz. trade study, not flight-grade attitude simulation.
This calculator estimates the four classical low-Earth-orbit (LEO) disturbance torques — gravity-gradient, aerodynamic, solar radiation pressure, and magnetic (Space Mission Analysis and Design (SMAD) ch. 11; Wertz) — then does the actuator sizing that answers them: reaction wheel sizing for momentum storage (the worst-case torque accumulated over one orbit) and slew torque, plus the magnetorquer dipole needed to desaturate the wheels against the geomagnetic field. It is a first-order trade study for a preliminary design, from a 3U CubeSat to a several-hundred-kilogram microsat — flight work needs a six-degree-of-freedom attitude simulation.
How this model works & what it omits
Every satellite in low Earth orbit (LEO) is constantly nudged off-attitude by its environment. The Attitude Determination & Control System (ADCS) exists to resist those nudges and to point the spacecraft where the mission needs it. Sizing an ADCS starts with one question: how strong are the disturbance torques, and which one dominates? That answer sets the reaction-wheel and magnetorquer hardware.
This tool estimates the four classical environmental disturbance torques (SMAD Ch. 11, Wertz):
- Gravity-gradient — an asymmetric inertia tensor in Earth's 1/r² field feels a restoring torque T = 1.5 n² |I_max − I_min|, worst case at 45° off local-vertical.
- Aerodynamic — residual atmospheric drag on the projected area, applied through the centre-of-pressure / centre-of-mass (CP–CM) offset: T = ½ ρ C_d A v² · d. Dominant below ~500 km.
- Solar radiation pressure (SRP) — photon momentum flux (~4.5×10⁻⁶ N/m²) on the projected area, scaled by (1 + reflectivity), through the CP–CM offset. Dominant at high altitude where the air thins out.
- Magnetic — the spacecraft's residual magnetic dipole crossed with the local geomagnetic field: T = D × B. A clean magnetic build keeps this small.
The four torques routinely span several orders of magnitude, which is why the breakdown is drawn as a log-scaled bar chart — the dominant source is the one that actually drives the design. The worst-case total torque, accumulated over one orbital period, sets the reaction-wheel momentum storage (H = T · P). The slew requirement is sized separately: a rest-to-rest bang-bang maneuver (accelerate for the first half, decelerate for the second) needs wheel torque T = I · α with α = 4θ / t². Finally, the magnetorquer dipole needed to desaturate the wheels against the field is D = T / B.
What this tool does not capture: thruster sizing, sensor selection and pointing-knowledge budgets, flexible-mode and fuel-slosh coupling, eclipse-cycle thermal-snap torques, the full time-varying geomagnetic field (a single worst-case polar value is used), per-axis wheel allocation, or control-law stability margins. The spacecraft is modelled as a uniform rectangular box. Treat the output as a preliminary trade study — flight design needs a six-degree-of-freedom attitude simulation.
// pick a spacecraft class, then dial mass / geometry / orbit / slew.
Spacecraft
// modelled as a uniform rectangular box for inertia + projected area.
Orbit & maneuver
// circular orbit; rest-to-rest bang-bang slew.
Surface & magnetics
// drives the aerodynamic, SRP, and magnetic disturbance torques.
ADCS sizing
// orbit period 94.6 min · I = [0.050, 0.126, 0.156] kg·m²
Magnetic
Dominant disturbance
5.23e-6 N·m
Total disturbance torque
0.030 N·m·s
Wheel momentum storage
9.05e-5 N·m
Slew wheel torque
1.00 °/s
Peak slew rate
0.11 A·m²
Magnetorquer dipole
0.156 kg·m²
Max moment of inertia
94.6 min
Orbital period
// environmental disturbance-torque breakdown — log-scaled bars
// bars are logarithmic — each minor step is a factor of ~10. exact N·m values shown at right.
// shareable URL encodes every input. no backend.
// ai-generated breakdown of what these numbers mean — with diagrams.
Common questions
How do you size a reaction wheel for a CubeSat?
Reaction wheel sizing comes down to two independent requirements. Momentum storage: the worst-case disturbance torque accumulated over one orbital period, H = T · P. Slew torque: a rest-to-rest bang-bang maneuver needs T = I · α with α = 4θ / t². For the 3U CubeSat preset (4 kg, 500 km, a 20° slew in 120 s) that gives ~0.014 N·m·s of storage and ~4×10⁻⁶ N·m of slew torque — pick a wheel that clears the larger of each with margin. (The tool sizes one worst-case wheel; per-axis allocation is among the listed omissions.)
Which disturbance torque dominates in LEO?
It depends on altitude and on the build — which is why the tool draws the breakdown on a log scale. Aerodynamic torque grows below ~500 km and with the centre-of-pressure / centre-of-mass (CP–CM) offset; gravity-gradient grows with inertia asymmetry; solar radiation pressure takes over at high altitude; magnetic torque scales directly with the spacecraft's residual dipole. In the 3U preset, the modest 0.05 A·m² residual dipole is the largest single contributor — well over an order of magnitude above gravity-gradient — which is why magnetic cleanliness is one of the cheapest attitude-budget wins on a small spacecraft.
Why do reaction wheels saturate, and what desaturates them?
A wheel absorbs disturbance momentum by spinning faster. A secular torque — one that pushes the same way orbit after orbit — winds the wheel up until it reaches maximum speed and can absorb no more: saturation. The stored momentum must then be dumped through an external torque. This tool sizes the magnetorquer dipole D = T / B that can continuously shed the worst-case accumulation against the local geomagnetic field — ~0.05 A·m² for the 3U preset. Thruster-based desaturation is outside this model.
How much torque does a slew maneuver need?
The bang-bang profile — accelerate for the first half, decelerate for the second — needs T = I · 4θ / t². The t² in the denominator is the design lever: halving the slew time quadruples the wheel torque. The 3U preset's leisurely 20° in 120 s asks for only ~4×10⁻⁶ N·m; load the Earth-observation microsat preset (45° in 30 s on a 250 kg body) to watch agility, not disturbance rejection, become the wheel-torque driver.
References
- // Wertz, J. R., Everett, D. F., Puschell, J. J. (2011). Space Mission Engineering: The New SMAD, ch. 11 (Spacecraft Subsystems — ADCS).
- // Wertz, J. R., ed. (1978). Spacecraft Attitude Determination and Control. Kluwer / Reidel.
- // Larson, W. J., Wertz, J. R., eds. (1999). Space Mission Analysis and Design, 3rd ed., ch. 11 — disturbance-torque equations 11-11 through 11-15.
- // Sidi, M. J. (1997). Spacecraft Dynamics and Control: A Practical Engineering Approach. Cambridge University Press.
- // US Standard Atmosphere 1976 / SMAD Table 8-3 — mean atmospheric density vs. altitude.
