Open-Cavity Trunk Strength Loss (Smiley & Fraedrich)

an open face (wound, seam, fire scar) makes the ring a broken tube, far weaker than a closed hollow. loss = (hollow_d^3 + R x (D^3 - hollow_d^3)) / D^3 x 100, where R is the opening arc / circumference (Smiley & Fraedrich 1992). Collapses to Wagener at R = 0; validated against the paper's example (4-in stem 70% hollow, 2-in opening -> 45%). A 24-in trunk with a 3-in wall and an 8-in opening loses 48% vs the 42% a closed hollow shows. A screen, not a load rating.

hollow_d = D - 2t; R = min(1, opening_width / (pi x D)); closed_loss = (hollow_d^3 / D^3) x 100; open_loss = (hollow_d^3 + R x (D^3 - hollow_d^3)) / D^3 x 100.

Smiley & Fraedrich (1992) open-cavity strength-loss formula, by name.

The Smiley & Fraedrich open-cavity relation is published arboriculture research (ISA Arboriculture & Urban Forestry); a qualified arborist governs the assessment.

Estimate. AHJ and licensed professional govern.

Field names used by the API: diameter_in, shell_thick_in, opening_width_in, closed_loss_pct, open_loss_pct, opening_penalty_pct

• Opening ratio R = opening arc / circumference; the opening adds R of the remaining sound wood (D^3 - hollow_d^3) to the lossSmiley & Fraedrich 1992
• Collapses to Wagener at R = 0 (closed hollow) the formula equals the Wagener (hollow_d/D)^3 lossSmiley & Fraedrich 1992