Minimum Sound Shell for an Allowable Trunk Strength Loss
The inverse of the trunk-decay-strength tile: the minimum radial sound-wood shell thickness for a maximum acceptable strength loss, t = (D/2) x (1 - (loss/100)^(1/3)). A 24-in trunk held to a 29.6% loss needs a 4.0-in shell (t/R 0.33, just above the Mattheck 0.30 trigger). Because loss goes as the CUBE of the hollow ratio, the minimum shell is small - a thin shell still holds most of the strength. Flags a shell below the Mattheck t/R 0.30 concern. An open cavity is far weaker; a screen, not a load rating.
Formula and source
min_shell t = (D/2) x (1 - (loss/100)^(1/3)); the inverse of loss_pct = ((D - 2t)/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, solved for the shell thickness.
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