A theory is presented for the optimum shape of tension kites based on lifting-line theory combined with the requirement that the kite shape and tension be in equilibrium everywhere with the forces normal to it. The flying shape of the kite then emerges as part of the solution, along with the distribution of twist, which must be built into any particular kite to achieve the required loading. Results are presented first for a kite in ideal flow, when all the important parameters scale with the lift coefficient, and then for a kite of realistic shape and profile drag.
Nomenclature
A= reference area (e.g., top surface of the kite) b = kite span, or arc length of lifting line C D , C L , C T = force coefficients based on 1 2 ρ AU 2 D, L = aerodynamic drag and lift s = distance along kite from centerline T = tension in each of two kite lines t, φ = nondimensional measures of distance from centerline u, v, w = induced speeds v n = induced speed in the kite plane, normal to kite and to U x, y, z = coordinate axes α eff = effective angle of attack, α g − α i α g = total geometric angle of attack, α t + α k α i = induced angle of attack α k = incidence due to inclination ε of the kite plane α t = incidence due to twist, measured from zero-lift angle (s) = circulation of the kite at span s γ (s) = wake vortex sheet strength at span s ε = drag angle and flying angle of the kite θ(s) = slope of the kite in its own plane = aspect ratio, b 2 /A ρ, U = density and speed of incident flow