Why a heavy bird can hang in the air. An albatross has a very long, narrow wing (aspect ratio AR = b^2/S, here about 15.5). Its lift and drag follow L = 1/2 rho V^2 S C_L and D = 1/2 rho V^2 S C_D with the parabolic drag polar C_D = C_D0 + C_L^2/(pi e AR). Gliding in still air it descends at the angle tan g = C_D/C_L, so the lift-to-drag ratio is L/D = C_L/C_D. Best glide: C_L = sqrt(C_D0 pi e AR) and (L/D)max = 0.5 sqrt(pi e AR / C_D0); minimum sink at C_L = sqrt(3 C_D0 pi e AR) (here limited by stall, C_L,max). The sink rate is w_s = V / (L/D).
Slope soaring over waves. Wind blowing over a wave must rise on the windward face. For small waves of height H = 2a, wavelength L, k = 2 pi/L, the linear potential-flow solution has the stream function psi = U (z - a e^{-kz} sin kx), giving a vertical wind w = U a k e^{-kz} cos kx and a horizontal perturbation u = U (1 + a k e^{-kz} sin kx). The updraft fades exponentially with height. A bird that holds station over the windward slope climbs until U a k e^{-kz} = w_s(V = U), i.e. at z = ln(U a k / w_s) / k; if the peak updraft U a k is below the sink rate it cannot stay up.
How the simulator works. The bird is a point mass in the vertical plane (no turns, no flapping) integrated with 4th-order Runge-Kutta at 200 Hz. Lift is perpendicular to the wind relative to the bird, drag opposes it; the bird chooses its lift coefficient from the airspeed it wants (C_L = 2 m g / (rho S V^2), limited by stall). In station-keeping mode a simple controller adjusts the speed so the bird stays over the best updraft. The sea height is a sin kx; touching it within 0.4 m counts as a splashdown.
What is simplified. Real swell is not a single sine, wind is turbulent and sheared (the effect behind dynamic soaring, a different lab), waves move and the air feels them through a coupled boundary layer, and the linear theory needs small steepness ka (about under 0.3); wave height is capped at one eighth of the wavelength. The bird has no banking, no wing flexing aerodynamics and no flapping. Bird numbers (mass 9 kg, span 3.1 m, wing area 0.62 m2, C_D0 = 0.020, e = 0.8, C_L,max = 1.4) are rounded typical values chosen to give a best glide ratio near 22, in line with published values of roughly 20 for this species; they are not measurements of a single bird and should be spot-checked against literature before being quoted.
Checks on this page. (1) The simulator is flown at six airspeeds and compared with the closed-form polar; (2) the best glide ratio is found by scanning airspeeds in the simulator and compared with the formula; (3) the wind field is incompressible by finite differences; (4) the flow follows the sea surface (kinematic condition); (5) the station-keeping height from the simulation equals the logarithmic formula within a few percent.