Minimum Sound Shell for an Allowable Trunk Strength Loss
The minimum radial sound-wood shell thickness for a maximum acceptable strength loss.
Example
You enter
- Trunk diameter outside bark (in) 24
- Allowable strength loss (%) 29.6
You get
- Minimum sound-shell thickness 4
- Min t over r 0.333
Details, formula, and sources
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.
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.
The Wagener cube-law loss and the Mattheck t/R rule are published arboricultural results; a qualified arborist and a TRAQ assessment govern.
Estimate. AHJ and licensed professional govern.
Field names used by the API: diameter_in, allow_loss_pct, min_shell_in, min_t_over_r
- Closed hollow the loss estimate assumes a central closed hollow; an open cavity (slot) is far weakerWagener 1963
- Concern trigger t/R < 0.30 (sound shell below 30% of the radius) flags escalation to a full TRAQ assessmentMattheck & Breloer