A battery twin with no internal resistance: how much endurance and how large a burst does the real, sagging cell actually give?

research/sag-twin

Battery twin with no internal resistance vs a real sagging cell: endurance exactly (1+√(1−u))/2 of the twin's (0.5 at the fold), 9–94% of charge stranded at the voltage cutoff, a burst of 0.5 fails below 51% charge where the twin's floor is 0 (a flat 20% reserve covers only a third of the full-charge limit), and a constant-derate refit errs +12% to +473% off its fit power. Stylised.

9 tests

What it found

A UAV battery twin that keeps the open-circuit voltage curve but drops the series resistance overstates endurance by exactly 1/η(u) with η = (1 + √(1−u))/2 (up to 2× at the maximum-power fold, beyond which the real cell cannot deliver the power at all while the twin still quotes an endurance). With droop and a voltage cutoff, real/twin endurance is 0.86, 0.57, 0.30 at normalised power 0.2, 0.4, 0.6 and 9%, 37%, 66% of the charge is stranded. The deliverable burst power falls linearly with charge, so a burst of 0.5 fails below 51% charge where the twin's floor is zero, a flat 20% reserve covers only a third of the full-charge limit, and keeping a 0.6 burst deliverable leaves 35% of the twin's cruise time. A constant derate fitted at one power errs by +12% to +473% elsewhere, but the resistance is identified to 1–2% from tens of voltage–current samples, and a full-charge fit misses resistance that grows as the cell empties (endurance +42% to +85% too high). Stylised: simulated cell, linear curves, constant-power load, no polarisation or self-heating.

A figure from its own output

Figure produced by research/sag-twin: endurance_ratio — sag-twin/experiments/endurance_ratio.svg, written by the project's own experiment code.

Paper, code and results

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Produced with AI assistance (Claude). Results are from the code in this repository and are simulated or stylised unless the abstract says otherwise; nothing here implies affiliation with or endorsement by any lab, researcher or company cited. MIT licensed.