Tensions in expanded dugout and cracking threshold

Derivation of tension formula

As one can see from the formula on the drawing, tension T grows proportionally to thickness of sample walls h and in reverse proportion to initial radius of the log R. So the bigger a log, and the thinner it was hollowed, the easier it expands. The member (1-1/k) approaches unity when the expansion rate k tends to infinity, i.e. when a sample becomes completely flat.

Flat planks made of log halves approx. 30cm in diameter and 12mm thick walls cracked a lot when drying after expanding, so the tensions must be considered beyond the threshold in this case:

T = (12/150)*(1 - 1/∞) = 0.08 ( beyond threshold);

Bottom piece made of 45cm log with ~14mm walls was expanded to approx. 65cm final radius, and cracks were few:

T = (14/225)*(1 - 1/(650/225) ) = ~0.038 (below threshold);

So we can assume the threshold tension to be approx. 0.04 for pine wood and for this particular technique.