Kite Flight - 2D Force Balance

A tethered kite settles where lift, drag, weight and the string pull cancel; wind shear and gusts move that balance.

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The science

The wind blows horizontally at speed U. The kite is a flat plate at angle of attack alpha, giving dynamic pressure q = 1/2 rho U^2 S, lift L = q CL (vertical) and drag D = q CD (downwind) with the flat-plate fits CL = 1.1 sin 2alpha and CD = 0.05 + 1.28 sin^2 alpha.

Static equilibrium: the horizontal tether force equals the drag, H = D, and the vertical force at the kite is V = L - m g, so the tether leaves the kite at tan(theta) = (L - m g)/D with tension T = sqrt(D^2 + V^2). A heavy string hangs as a parabola with constant horizontal tension; the program solves its arc length numerically so the kite height follows from the string length. Wind shear follows the power law U(z) = U10 (z/10)^0.143.

Simplifications: a rigid flat plate with no induced drag or pitch dynamics, parabolic instead of catenary string, quasi-static response with a first-order lag to gusts. The best glide angle satisfies tan^2 alpha = CD0/(CD0 + CDN).

What to try
  • Press Light breeze: a big light kite still lifts; then try Heavy kite.
  • Use Stalled: lift falls and drag rises, so the kite sits low and pulls hard.
  • Toggle wind shear off to see how much altitude comes from the stronger wind aloft.
Lift and drag coefficients against angle of attack
Equilibrium altitude against wind speed
Tether tension against wind speed