Heavy-elastica boundary value problem, solved live in your
browser by RK4 shooting. Nothing is precomputed.
Fabric
0.220
60 mm
Live solution
Λ = ρgL³/B
—
chord droop
—
tip deflection
—
At the 41.5° condition
overhang L
—
bending length c = L/2
—
G = W·c³
—
B (exact)
—
theta'' = -L (1-u) cos(theta)
theta(0) = 0, theta'(1) = 0
L = rho_A g L^3 / B
Λ* = 8.006
ASTM implies exactly 8 (from c = L/2, G = W·c³).
Our first-principles solution agrees to 0.08%,
mesh-converged over 501→4001 nodes. The standard is confirmed,
and so is the solver.