Rob, Terry, what is the correct interpretation of that “700 g per unit-length”? Is the breaking strain expressed thus, or simply as a weight applied to ANY length of the thread? I’m still hiding behind being a physics/maths dunce, and yes, I have looked at the basic formula Terry’s friend set out… but I’m not clear how he gets to 700g per cm… Put another way, if your thread breaks when you hang a 700g weight on it, what is the tension per cm (or any other unit of length? Surely it is the same regardless of the length?
If my befuddled noddle is getting anywhere with this, if the tension in one full circumference-length of thread (2piR) applied T/R inwards radial force, the figure derived from that calculation would be the total radial pressure applied by that circuit of thread around the circumference, not the point pressure? So Terry’s 4.4k would be distributed evenly around one thread-line. If I’m right and we stick to the Professor’s 1cm radius and a tension of 700g, any given 1/10th of a mm of wood under the thread would be receiving inwards pressure of 44g? (Mathematicians HELP!)
(EDIT: Duh, no.
Obviously, if the radial pressure per cm is 700g, then per mm it will be 70g and per 0.1mm it will be 7g??? I got distracted by Terry’s gross figure and divided the wrong thing! Or will it? - This is where I’m confused by the “unit length” bit…)
Even if I’m way off with this, I still don’t think we have a full and accurately applicable model in discussion regarding thread pressure… even if that is the/an agent of tenon bore perturbation.
(I agree with George here that using the thread’s breaking strain is way over the top, BTW, no matter how you apply the tension while winding.)
Another thought on the middle part of lapping-trough angle… The trough is the thinnest part of the wood and thus the most susceptible to any disruptive influences - de-and re-hydration, thread pressure, shrinkage from of-its-nature wood cellular structural changes with aging, etc. The ends of the trough usually have shoulders of slightly thicker wood which will act as supports to the parts of the trough adjacent to them, and the body-end of any tenon is further supported by the still thicker wall of the main part of the joint. Therefore, the central area of the trough is the least re-inforced/weakest. It might just be that in some instances - particular pieces of wood - it just does this “by itself” because of its particular structures and the shape the maker cut it to, maybe “helped” by usage factors like moisture… It also occurs to me that this problem seems to be commonest and most severe in upper-body upper-tenons - the ones with the largest diameter and therefore with reduced cylindrical structural strength - I believe I’m right in thinking that a smaller diameter tube will be stronger (against compression or shrinkage) than a larger one with the same wall-thickness?