Sun and sky
Solar position from the NOAA / Spencer series: declination δ, equation of time, hour angle H = (TST/4) − 180°.
sin(el) = sinφ sinδ + cosφ cosδ cos H
cos H0 = cos 90.833° / (cosφ cosδ) − tanφ tanδ
The sky is the Preetham analytic model (Rayleigh and Mie scattering with turbidity T) plus a procedural cloud layer; the light colour is the sun transmitted through an air mass m = 1/(sin el + 0.506 (el+6.08)−1.64). That is why a low sun is gold: blue is scattered out along the long path.
Thermals and the convective boundary layer
S = 1361 · 0.72m0.678 · sin(el)
H = fH (1 − a) S / (ρ cp) [K m/s]
zi² = z0² + (2/γ) ∫ H dt (encroachment)
w∗ = ( g H zi / T )1/3
wcore(z,r) = 1.5 w∗ (z/zi)1/3 (1 − 1.1 z/zi) / 0.457 · exp(−r²/R²)
fH is the sensible-heat fraction (dry soil: high; wet crop: low), a = 0.2 the albedo, γ = 5 K/km the stability above the inversion. The vertical profile follows the Lenschow shape; the core factor 1.5, the radius R = 50 + 0.12 z (capped at 260 m) and the Gaussian cross-section are typical, illustrative values.
Stork as a glider
Typical values (flagged, check against literature): mass 3.5 kg, span 1.95 m, wing area 0.52 m² (aspect ratio 7.3), Oswald e = 0.85, profile drag CD0 = 0.022.
CD = CD0 + k CL², k = 1/(π e AR)
wsink = n v CD/CL, CL = n m g /(½ ρ v² S), n = 1/cosφ
(L/D)max = 1/(2√(CD0 k)), vbg = √( 2 m g /(ρ S) · √(k/CD0) )
r = v² / (g tanφ), climb = wcore e−r²/R² − wsink(v,φ)
Vxc = v c / (c + wsink(v)) (MacCready speed to fly, no wind)
Banking more shrinks the circle (better centring in a narrow core) but raises the load factor n and the sink rate: the model finds the best bank angle and airspeed numerically. A centring efficiency of 0.75 is applied to the average climb.
Chick heat balance and growth
m(t) = K / (1 + e−r (t − t0)), K = 3.3 kg, m(0) = 0.07 kg, t0 = 21 d
BMR = 3.79 m0.723 W, A = 0.1 m2/3 m²
Qloss = fexp U A (Tb − Ta), 1/U = d/kdown + 1/hc, hc = 4 + 6√u
The chick must produce Qloss minus absorbed sunlight; the ratio to BMR is compared with its metabolic ceiling (about 1.5x BMR in the first week, 3.5x later). A brooding parent covers most of the surface (fexp = 0.15) and shades it. Feeding: food = (2.5 BMR + 6.5 dm/dt) / (4.5 MJ/kg · 0.75), 150 g per visit, 14 h of foraging. All coefficients are typical, not measured on this nest.
Nest load on the pole
Mn+1 = 0.95 Mn + 25 kg (M1 = 30 kg)
Mbase = M g e + ½ ρ u² Cd A h, σ = 32 M / (π d³) + N/A
Safety factor against a characteristic bending strength of 24 MPa for pine (typical). The tip deflection is integrated numerically along the tapered pole and Euler buckling is checked for a cantilever (K = 2).
Independent numerical checks (live)
Hero models (white stork standing and soaring, stork chick, thatched hut) generated with Meshy.ai from text prompts, cleaned and decimated in Blender 5.2. The nest, pole, props and textures are procedural Blender bakes; the terrain, river, orchards and village scatter and its Progressive GPU lightmap come from Unity 6000.6; the live scene is Three.js r160. Not a wildlife-monitoring tool: all biology numbers are typical and flagged.