A Simplified Tether Drag Model with Belly and Drag Spiral for AWE

A kite flying a circle on a tether pulls the tether through the air and pays for part of its drag. The usual rule puts one quarter of the full tether drag on the kite, which holds for a straight tether. A real tether bows out into a belly under centrifugal force, and its drag makes it lag the kite as a spiral. This note solves the steady equations of such a whirling tether, without gravity and wind, as a series in the belly number Kl and the drag slope ν, with exact rational coefficients to order 12. It also gives Padé approximants beyond the series’ radius of convergence. Main results: The drag at the kite to first order: the belly raises it and the spiral lowers it. The spiral number S = ν²T/(μv²), the ratio of the two effects, in which the corrections read most simply. The radial force a straight-tether model must lump at the kite, and the value of S where it changes sign. For flyable cases, how far the quarter rule is off, and the size of the effects left out: gravity and crosswind. The model has no gravity and no wind. The equations are classical for circularly towed cables, and the paper cites the earlier work. The exact series was computed with samara, a computer algebra system written by the author. AI assistance was used to draft text, run computations and review; the author takes responsibility for the content. The record contains the paper (PDF). This is a preprint and has not been peer reviewed.