ADCS Sizing Calculator

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.

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.