One Threshold, One Physical State: A Fleet-Wide Stability Law for Drone and eVTOL Battery Packs

Electric vertical takeoff and landing aircraft impose a load their battery cannot refuse. The takeoff pulse must be delivered on demand, at full power, with people on board. The question that matters is not how much capacity a pack has left, but whether it can still absorb the load it is about to be asked to carry, and how long that will remain true. This paper applies a single stability law, Theta = I / R, to that question. I is the imposed load, taken as the takeoff current draw. R is the pack's capacity to absorb that load, measured as the reciprocal of its internal resistance. Both quantities are already present in any flight log. The instrument requires no additional sensor, no model training, no fitting, and no per-cell calibration. Run on the CMU eVTOL Battery Dataset, 22 real Sony-Murata VTC-6 cells cycled to failure on a real eVTOL mission profile, a single fleet-wide threshold Theta = 1.08 detected 9 of the 9 cells that reached end of life, with zero misses, at a median of 53 days of advance warning (range 8 to 73 days). The three cells that ended the test in the healthiest condition never alarmed at all. The central result is not the lead time. It is the consistency. Across every cell that alarmed, the alarm fired at a mean battery health of 87.2 percent with a standard deviation of 1.5 percent. Those cells were operated very differently from one another: ambient temperatures of 20, 30, and 35 degrees Celsius; cruise segments from 400 to 1000 seconds; different discharge powers, charge currents, and charge cutoff voltages; observed lives ranging from a few hundred cycles to well over two thousand. One threshold caught all of them at the same physical point in their decline. That is the distinction this paper argues for. A model learns a dataset and reproduces its statistics. A law reads a state, and reads it the same way regardless of how the system arrived there. The evidence presented here is that Theta = I / R behaves as the latter. An initial version of the detector, using the raw per-cycle resistance step, failed: it was noise-sensitive, produced seven spurious alarms, and missed one true end-of-life cell. That failure and its correction are reported in full, alongside all other limits. Paper 12 in a continuing series.