Note: This post was written by Elizabeth Freeland, a local physicist, professor, and amateur violinist, as a result of a number of conversations we had in the shop concerning bows, tip material, and balance points. In an earlier post about silver head plates, I pointed out that balance points changed only very sightly despite the addition of heavier tip material at the head of the bow. Elizabeth thought it would be interesting to come up with some math to calculate exactly how much the balance point would shift on a violin bow given the addition of a given amount of weight to the head.
Follow up: Elizabeth’s last point concerning the actual method of measuring balance on a bow is interesting. While testing and exploring her equations, we realized that balancing the bow on one’s finger was rather too crude to be scientifically accurate. I clamped a piece of 2mm thick wood in a vice and attempted to balance bows on this thin strip, but it proved to be almost impossible to get the stick to balance smoothly. I’m sure an inventive bow-maker out there has created some kind of clever bow balancing contraption – if so, please share!
Even if one uses something thinner than a finger, but thicker than 2mm, like say, a pencil, and uses a ruler, we believe that the error rate in reading the balance point will still be in the +/- 2mm range. Seeing as this is about how much the balance point was seen to move with the addition of a heavier silver headplate, one has to wonder if such small balance shift really matters to the majority of players. The truth is that most bow makers and repair folks are making somewhat approximate changes when working on balance issues with bows due to their standard practices, so arguing over a 2.5mm balance shift seems silly.
Do I believe that some players can sense such a small shift? Without a doubt, yes, but it will only matter to a minority from a functional perspective. Remember, one can always add more weight to the end of the bow to equalize the stick if a player has a problem with the extra tip weight, but if we as bow-makers want to work at such a level of detail, we need to develop more scientifically accurate measuring methods.