This is a real Euler–Bernoulli beam solver, not a phenomenological curve. The active, just-printed span is an uncured cantilever carrying its own weight as a uniformly distributed load w = ρAg (N/m), from the current material's density ρ and the spar's actual cross-section area A (hollow tube, wall thickness = 20% of radius). Its tip deflection and root bending moment follow the textbook cantilever-under-self-weight solution:
w = ρ·A·g
δ_tip = w·L⁴ / (8·E·I)
M_root = w·L² / 2
σ_root = M_root·r_outer / I
E is the material's real Young's modulus and I = π/4·(r_o⁴ − r_i⁴) is the tube's moment of inertia — both plugged in live as you switch material or drag the spar radius, so stiffness responds instantly and correctly. Once a temporary scaffold strut bridges a span, that span stops behaving like a cantilever (fixed one end, free the other) and becomes a simply-supported beam between two supports — a much stiffer configuration, using the standard formula δ(x) = w·x·(L³ − 2Lx² + x³) / (24·E·I), with the well-known 5wL⁴/384EI mid-span peak.
- Structural status — compares root stress on the active cantilever span to the material's real yield strength: RIGID below 30%, STRESSED above 30%, CRITICAL above 65%, COLLAPSED at 100% (the print halts — reset to retry with a stiffer material, thicker spar, or scaffolding).
- Microgravity — w = 0, so deflection and stress are exactly zero at any length: the physical reason a robotic printer in orbit needs no scaffolding at all.
- Lunar gravity (1.62 m/s²) sits between the two — a span that would collapse on Earth may only sag or stay rigid on the Moon, letting you compare all three regimes directly.
This differs from a generic static point-load beam calculator: the load here is the structure's own weight, growing in real time as the print head advances, and a scaffold strut genuinely re-derives which beam formula governs each span.