ALTITUDE ENGINEERING LAB

Simulations

Explore how a small wheel changes the way a CanSat turns.

Reaction-wheel attitude control

Single-axis yaw · open-loop model

Set a rotation and a time. Compare the requested manoeuvre with what your motor and flywheel can actually achieve.

Flywheel 40 gRemaining CanSat 300 g

Remaining mass includes everything else; this is not a verified system budget.

Advanced settings Geometry, speed and disturbance limits

Apply a linear motor torque–speed envelope

The default motor limit is available output torque at the operating point. With the optional envelope enabled, it becomes the zero-speed torque intercept and falls linearly to zero at the specified no-load speed. This is an assumed motor curve, not a measured rating.

Peak wheel speed ideal required · relative to body

—RPM

Required motor torque ideal manoeuvre

—mN·m

Peak body angular velocity actual simulated

—°/s

Minimum feasible duration undisturbed rest-to-rest profile

—s

Yaw response

Solid: actual motion · dashed: selected request when limited

Angular acceleration

Positive acceleration in the first half; braking in the second. Dashed boundaries show the motor torque limit.

Inspect time 0.00 sHover, tap, or use the time slider to compare every visible trajectory.

Calculating…

This model estimates idealised single-axis yaw response. Actual descent performance depends on parachute dynamics, external torques, motor characteristics, sensor feedback and actuator saturation.

Model assumptions and equations

The total mass includes the rotor. Body inertia is I_b = (M − m_w)k_b², and wheel inertia is I_w = f m_wr_w². A thin rim uses f = 1; a uniform disc uses f = 0.5. Increasing radius changes inertia with its square, but geometry, balance and containment still need verification.

The ideal request uses two equal, opposite torque phases, with required torque 4I_bθ/T². Positive body yaw uses negative motor torque in the first half. Wheel speed is relative to the body; its inertial speed also includes body rotation. With no external torque, (I_b + I_w)ω_b + I_wω_w,rel stays zero.

Operating limits constrain the actual response. Constant disturbance torque acts in the positive yaw direction when positive, continues after the command ends, and can leave residual rotation. The controller is an open-loop torque schedule; it does not correct attitude errors using feedback. The minimum duration describes an undisturbed rest-to-rest manoeuvre under the configured actuator model.

The body radius of gyration is a lumped estimate, not a CAD-derived inertia tensor. The model omits pitch, roll, suspension restoring moments, wheel-axis offset, bearing friction and structural flexibility. Wheel RPM alone cannot determine performance, and a motor's maximum RPM does not establish its torque capability. The RPM setting is an analysis limit and does not certify rotor safety.

Read the model and validation notes · Python reference calculations