How much battery should a UAV carry when its twin has a constant wind?

What it found

A leg flown at airspeed v against a headwind that is uniform across flights costs P(v)/(v−w) in energy per distance; a constant-wind twin has no spread. Its cruise speed is nearly right (1.100 vs the real optimum 1.123, regret 0.10%), but its energy claim is low by exactly artanh(x)/x with x = a/(v−μ) (3.5% here), and a battery sized to that claim runs out in 50% of real flights (42% with a 5% margin). A 5% depletion target needs a 39% margin and 1% needs 44%, in closed form, and the real-optimal speed trims only 39.2% to 37.6%. The speed error itself grows to 6.4% of the optimum at wind half-width 0.6, and the twin speed meets a stalling wind (infinite energy) once the half-width exceeds v−μ = 0.80. Refitting the twin to n = 50 logged winds beats the constant-wind speed in 97% of fits. Stylised: one leg, constant airspeed, wind fixed within a flight, chosen parameters, no gusts or turn-back.

A figure from its own output

Paper, code and results

• README and method
• White paper
• Experiments and results
• Code
• Tests

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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.