Hollow / Decayed Trunk Strength Loss
A tree-risk screen for a standing tree with internal decay: the Wagener strength loss (hollow_d^3 / D^3) x 100 from a central hollow, plus the Mattheck t/R ratio and the t/R < 0.30 concern flag. The cube law keeps loss small until the hollow is large -- a trunk can be two-thirds hollow and keep most of its strength. An open cavity is far weaker.
Formula and source
hollow_d = D - 2t; loss_pct = (hollow_d^3 / D^3) x 100; t_over_R = t / (D / 2); concern when t/R < 0.30.
Hollow-trunk strength-loss screen (Wagener 1963; Smiley & Fraedrich 1992; Mattheck & Breloer t/R; ISA TRAQ), by name.
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