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Castleland dragon flight - 2D side view

Change the angle of attack and the wing, and watch the speed and path angle settle to the steady glide. Green = lift, orange = drag, white = weight. They balance in a steady glide.

Independent checks

Each row compares the simulation with a separate closed form or a finer numerical calculation.

The science

Forces. Lift L = ½ ρ v2 S CL and drag D = ½ ρ v2 S CD act perpendicular and parallel to the flight path; weight is m g.

Wing model. CL rises linearly with angle of attack, with lift slope 2π AR/(AR + 2) per radian for a finite wing, until a stall angle near 14 degrees after which lift falls and drag climbs. Drag is CD = CD0 + CL2/(π e AR).

Steady glide. With the nose angle fixed, L, D and W balance when tan γ = CD/CL and v = sqrt(2 m g cosγ / (ρ S CL)). The best glide ratio is ½ sqrt(π e AR / CD0) at CL = sqrt(CD0 π e AR). The moving dragon integrates m dv/dt = -D - m g sinγ and m v dγ/dt = L - m g cosγ, so it also shows the slow speed oscillation (phugoid) before settling.

Simplifications. A fantasy creature treated as a point mass with a wing of the given area; no flapping, no thrust, no pitching dynamics, uniform air. The same lift-and-drag idea drives the 3D sandbox; the numbers here are for explanation, not for designing aircraft.