Kai Lawson wrote: |
Peter,
I thank you very much for your explanation. Mathematics and geometry were never my strong suit, and having some of the basic steps for various situations laid out helps my understanding quite a bit. I will try this the next time I work on a sword. I think the concept is very interesting, and have watched with a mix of confusion and interest as this thread unfolds. Are there combinations of geometric layouts that indicate or can be used to locate ranges for handling points, like pivot points or estimates about balance or vibrational nodes, if thickness (and thus mass) measurements are known? Some of those would be harder to calculate, but I wonder if there could be geometric solutions that could be used to combine both the dimensionality and some of the gross handling characteristics? |
This method for design is no short cut for dynamic properties of a sword. Balance and position of pivot points and vibration nodes are determined largely by distribution of mass ands that is mostly decided by variations in thickness and cross section.
You cannot once for all decide thickness or distal taper in a sword by a geometric layout. Volume cannot be scaled the same way as outline. A small change in dimension would then have disproportionate result in mass.
Once you have decided for a design you then work out how thick the blade shall be and the volume of the pommel.
Or you keep this in the back of your mind as you work, adjusting for the effects of proportion and dimension as you work.
Either way, mass and balance are separate things from the proportions of the sword.
The only way proportion has a direct impact on handling is the ration between blade and hilt. This *will* have an effect on handling and position of nodes and to some extent pivot points. But this is not enough to give you the complete solution.