A twin without ground effect: where does a landing altitude loop go wrong?

research/groundeffect-twin

Rotorcraft altitude twin without ground effect vs real thrust gain 1/(1−(R/4z)²): hover sits 18 mm high at one rotor radius (twin: 0), and a delayed loop with 28% twin headroom goes unstable at 0.54 rotor radii. Stylised.

12 tests

What it found

With the constant-power ground-effect multiplier G(z) = 1/(1−(R/4z)²) a gravity-feedforward altitude hold sits above its target by 2.7, 17.7 and 30.2 mm at 3, 1 and 0.6 rotor radii (twin: 0), 0.9% to 50% of the height. A sampled loop with one-sample delay that the twin gives 27.6% gain headroom at every height loses it as the vehicle descends: the real margin is 1.19 at one radius and reaches the stability boundary at 0.54 radii, confirmed by a nonlinear simulation; the undelayed thrust-gradient stiffness matters, since scaling the gain alone misses the instability. Negligible above about two radii. Stylised: point mass, closed-form ground-effect model, no rotor lag.

A figure from its own output

Figure produced by research/groundeffect-twin: gain_margin — groundeffect-twin/experiments/gain_margin.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.