Ada Audits the Sizing and Gearing Numbers
Ada re-derives this chapter’s own numbers step by step, at full precision
ADA · CALCULATION AUDIT
Ada Audits the Sizing and Gearing Numbers
A smart-vent linkage pushes 1.8 N at a 25 mm radius, so the actuator must beat 0.045 N·m of load torque — doubled to a 0.090 N·m target for margin. A candidate motor rated 0.06 N·m near 300 rpm behind a 4:1 gearbox at 80% efficiency delivers 0.192 N·m at 75 rpm, while the valve draws 2.88 W moving but only 0.48 W averaged over 20 s of every 120 s. This audit re-derives each figure and asks whether the geared chain clears the load with room to spare, and which number — the duty-averaged heat or the worst-case stall current — should size the supply.
Companion to the chapter Actuator Assessment and Reference — every number here comes from that chapter.
Naming "a servo" or "a stepper" is a guess until the torque, speed, and thermal numbers agree. Every value below is one this chapter already stated — I am only carrying the arithmetic to full precision and rounding at the end.
1. Load torque is force times lever arm.
The smart-vent linkage pushes 1.8 N at a 25 mm (0.025 m) radius, and good practice doubles it for friction and acceleration headroom:
2. A gear reduction N trades speed for torque.
It multiplies output torque by N (times gearbox efficiency η), divides output speed by N, and divides the reflected load inertia the motor feels by N². The chapter's candidate motor gives 0.06 N·m near 300 rpm; a 4:1 box at 80% efficiency is:
3. Duty cycle separates instantaneous power from heat load.
The valve actuator runs 12 V at 0.4 A on 60% PWM, and moves for 20 s out of every 120 s cycle:
| Design question | Arithmetic shown | Audit result |
| Torque the actuator must beat | 1.8 × 0.025 | 0.045 N·m |
| Target with 2× design margin | 0.045 × 2 | 0.090 N·m |
| Geared output torque (4:1, η = 0.80) | 0.06 × 4 × 0.80 | 0.192 N·m — clears 0.090 |
| Geared output speed | 300 / 4 | 75 rpm — above the 30 rpm need |
| Reflected inertia the motor feels | ÷ 4² | 16× lighter |
| Valve moving power (V × I × D) | 12 × 0.4 × 0.60 | 2.88 W instantaneous |
| Duty-averaged heat (20 s per 120 s) | 2.88 × (20 / 120) | 0.48 W average |
What this means for your design: the geared motor clears the 0.09 N·m target with room to spare and still turns faster than the vent needs, so the controller trims speed with PWM rather than fighting a shortfall. And because the valve moves only one-sixth of the time, its thermal load is the 0.48 W duty-average — size the enclosure heat path to that number, but size the supply and driver to the worst-case stall current, never to the 0.48 W average.
Every number above is taken from the chapter’s own examples and re-derived step by step.