Ada Audits the Motor Load Numbers

Ada re-derives this chapter’s own numbers step by step, at full precision

ADA · CALCULATION AUDIT

Ada Audits the Motor Load Numbers

A 6 V gearmotor that draws 180 mA free-running pulls 600 mA under load and 1.8 A at stall, yet the example driver is rated only 700 mA — about 2.57 times below the stall case. Its loaded running power is already 3.6 W, and a 2.0 A spike is normal for 80 ms but signals a jam if it lasts 2 s, exposing the driver to 25 times the startup charge. This audit re-derives each figure and asks whether a driver sized to the tidy running point is a safety argument, or whether startup and blocked-load behavior must be sized on their own.

Companion to the chapter DC Motors — every number here comes from that chapter.

— current, power, and fault timing, ~4 minutes

The mathematics checks the electrical budget; the physics reminder is that current changes as the motor starts, loads, stalls, and generates back-EMF. A driver sized only for the usual running point is not a safety argument.

The chapter’s values

Use only the chapter values above: a 6 V gearmotor, 180 mA no-load current, 600 mA loaded running current, 1.8 A stall current, a 700 mA driver example, a 70% PWM command, and the 2.0 A current spike at 80 ms versus 2 s.

power = voltage x current; average_voltage = duty x supply; charge = current x time

The worked checks

Check	Arithmetic	Review meaning
Running power	6 V x 0.600 A = 3.6 W	The loaded motor is already a multi-watt power path, not a GPIO load.
No-load versus loaded current	0.600 A / 0.180 A = 3.33	The real mechanism draws about 3.3 times the bench no-load current.
Stall versus driver rating	1.8 A / 0.700 A = 2.57	A 700 mA driver is about 2.6 times below the stall case, so the fault path must be explicit.
PWM average voltage	0.70 x 6 V = 4.2 V	The command matches the chapter's average-voltage example, but it still does not prove shaft speed.
Startup spike charge	2.0 A x 0.080 s = 0.16 A*s	A short spike can be normal if supply sag, thermal stress, and restart behavior are bounded.
Jam exposure	2.0 A x 2 s = 4.0 A*s; 4.0 / 0.16 = 25	The two-second jam exposes the driver and supply to 25 times the startup charge.

Audit conclusion: the chapter's own numbers support the review rule: size for startup and blocked-load behavior, not just the running current, and pair PWM commands with current, speed, limit, airflow, pressure, or timeout evidence.

Every number above is taken from the chapter’s own examples and re-derived step by step.