A zero-wind twin of a UAV out-and-back leg: does a tailwind repay the headwind, and what does a twin calibrated on one leg say about the return?

research/roundtrip-twin

Zero-wind twin of a UAV out-and-back leg: wind does not cancel (real/twin energy 1/(1−(w/v)²)), the best airspeed moves to v²=w²+√(w⁴+1), and a one-leg-calibrated twin is off by exactly ±w/v with the sign of the leg flown.

9 tests

What it found

Real round-trip energy is (v⁴+1)/(v²−w²), so wind does not cancel: real/twin is exactly 1/(1−(w/v)²), 1.33× at w/v=0.5 and 5.3× at 0.9, the same for either sign, with no return at |w|≥v. The twin-optimal airspeed is 1 for every wind while the real optimum solves v²=w²+√(w⁴+1), so flying the twin's optimum costs 1.5%, 9.8%, 52% extra at w=0.4, 0.6, 0.8. A twin calibrated on one leg and assumed to see the same wind back is off by exactly +w/v (headwind leg) or −w/v (tailwind leg): ±33% at w=0.5, v=1.5, with a sign set by which leg was flown. Stylised: steady along-track wind, constant airspeed, two-term power law.

A figure from its own output

Figure produced by research/roundtrip-twin: energy_ratio_vs_wind — roundtrip-twin/experiments/energy_ratio_vs_wind.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.