Kite in the wind - 2D side view

Forces on a tethered kite

The wind pushes on the sail with dynamic pressure q = ½ ρ U². Lift is perpendicular to the wind, L = q A C_L(α), and drag is along it, D = q A C_D(α). Gravity adds the weight W = m g. The line is the only other force, so a steady kite sits where the three forces cancel: horizontally T cosθ = D, vertically T sinθ = L - W. Dividing gives the line elevation tanθ = (L - W) / D and the tension T = √(D² + (L - W)²).

Why a kite needs a minimum wind

The kite can only climb when L > W, which sets U_min = √(2 m g / (ρ A C_L)). Because force grows with U², a modest increase in wind raises the tension a lot while the line elevation is limited by the lift-to-drag ratio.

Flat-plate coefficients

The sail is modelled as a flat plate: C_L = 1.1 sin 2α and C_D = 0.08 + 1.9 sin²α. Beyond about 45° the lift falls and the drag keeps rising, which is the stalled kite that dives.

Honest simplifications: the line is straight, weightless and has no drag (a real long line sags and adds drag, lowering the angle); the kite is a point with a fixed angle of attack set by the bridle; the coefficients are textbook flat-plate fits, not a measured kite; the wind is uniform with height (a real boundary layer is faster aloft). Gusts here move the kite through the same quasi-static balance.

• Raise the wind from 2 to 14 m/s and watch the line elevation and tension; below the red U min line the kite cannot rise.
• Make the kite heavier: the minimum flying wind grows with the square root of the mass.
• Push the angle of attack past 40 degrees: lift drops and drag soars (stall).
• Turn up the gust strength and see the tension swing roughly twice as fast as the wind.