Ada Audits the Safety Margins
Ada re-derives this chapter’s own numbers step by step, at full precision
ADA · CALCULATION AUDIT
Ada Audits the Safety Margins
Switching off a 100 mH relay coil carrying 80 mA in a microsecond looks harmless, yet the chapter’s own figures put the un-clamped flyback spike at 8000 V — enough to punch a transistor rated for 60 V. The chapter also sizes a 20 A relay for a 12.5 A heater and trips a watchdog when a logging delay stretches the 80 ms control loop past its 100 ms limit. This audit re-derives each of those margins and asks whether the numbers really support the rule that safety is a bounded chain, not a single part.
Companion to the chapter Actuator Safety and Protection — every number here comes from that chapter.
The safety story is physical: stored magnetic energy, timeout margins, relay current ratings, and RC time constants all need numbers. Use the chapter values already on the page and round only after the arithmetic is complete.
The chapter's values
Use only the chapter values above and below: a 100 mH relay coil, 80 mA coil current, 1 microsecond switch-off, 0.7 V diode clamp, 10 ms dissipation interval, an 80 ms control loop, 100 ms watchdog, 150 ms delayed iteration, a 12.5 A heater load, a 1.5x relay-rating rule, a 20 A relay, a 15 A fuse, and a 100 ohm + 100 nF snubber.
The worked checks
| Check | Arithmetic | Review meaning |
|---|---|---|
| Flyback spike without a clamp | 100 mH = 0.100 H; 80 mA = 0.080 A; 1 us = 0.000001 s; 0.100 x (0.080 / 0.000001) = 8000 V |
The stored field can force a transistor far past a 60 V rating if the design gives it no safe path. |
| Stored coil energy | 0.5 x 0.100 H x 0.080^2 A^2 = 0.00032 J = 0.32 mJ |
The energy is small, but it is concentrated at switch-off and must go somewhere controlled. |
| Diode dissipation check | 0.00032 J / 0.010 s = 0.032 W = 32 mW |
A 10 ms clamp interval turns the spike into a modest heat pulse instead of an uncontrolled voltage stress. |
| Watchdog timing margin | 100 ms - 80 ms = 20 ms; 150 ms - 100 ms = 50 ms late |
The normal loop has only a 20 ms margin; a 150 ms logging delay correctly trips the watchdog. |
| Relay current selection | 12.5 A x 1.5 = 18.75 A; 20 A - 18.75 A = 1.25 A |
The 20 A relay clears the stated minimum by 1.25 A, while the 15 A fuse remains below the relay rating. |
| Snubber time constant | 100 ohm x 100 nF = 100 x 0.000000100 F = 0.000010 s = 10 us |
The RC path acts on microsecond switching transients, not on slow actuator logic or software timeouts. |
Audit conclusion: the chapter's own values support the design rule: safety is not one component. It is a bounded chain of current ratings, stored-energy paths, timeout margins, isolation, and independent fallback behavior.
Every number above is taken from the chapter’s own examples and re-derived step by step.