Calculating Balance Point Shift

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.

Thanks Elizabeth!!!!


3 thoughts on “Calculating Balance Point Shift

  1. Thanks for posting this. I think I’ll spend some time trying to figure out a way to measure a bow more accurately. I think, realistically without lasers, I can eyeball a straightedge to (maybe) 1/4 mm, more realistically, .5 mm. This is enough for neck centering, etc. To do this consistently for bows, we need a permanent setup jig: a peg(s) (to brace bow head, give a standard starting place to measure) aligned and affixed referenced to a measuring straightedge; say, a setup which you could pop the bow in and out while adjusting, which would give consistent repeatable measuring results better than merely a tape measure.

  2. Hi Eric,

    I’ve been putting together a spreadsheet to guide my carving and use of garnish. I stumbled on your site when I was doing general searches on the subject.

    Before music and bow making, I came from an aviation background and it’s informed my thoughts here.

    I was hoping I could paste in an excerpt from the FAA’s Weight & Balance Handbook but apparently it was too graphic rich and I couldn’t manage it. I’ll just paraphrase instead.

    You were asking how to establish a balance point on a stick that’s wobbling around too much to position a fulcrum in place. Actually it’s done with aircraft all the time. It’s a pretty critical measurement. A badly balanced bow may give a musician a bad day. A badly balanced aircraft may give you your last day.

    To establish the weight and balance (point) of the empty plane, it’s towed or jacked onto scales. A plumb line is used to assure it’s level. There’s one scale for each wheel. Each scale is a known distance from a datum line (may be the firewall in a small plane, may be a point actually in front of the plane where the original flight test probes were located in a larger one…doesn’t matter as long as you use consistent placement). The weight measured at each scale is multiplied times it’s distance from the datum (arm) and the result is a moment. The three moments are totaled and divided by the the sum of the weights and the result is the total CG in relation to the datum.

    In theory you could do the same with a bow using two scales (or one scale and a block the same height as the scale making two separate measurements). In my spreadsheet I’m using the throat as the datum because it’s a fixed point on any bow. Later I convert it in terms of inches from the frog or end of the stick. But let’s set the datum at the front edge of the ferrule so your CG will be as we usually think of it. Say for a cello stick, if you measured the ferrule at maybe 60 gm and the head at 20 gm. The ferrule is at zero mm so it’s moment is 60 x 0 = 0. The throat is about 565 mm in front of the ferrule. it’s moment would be 565 x 20 = 11300. Total moment divided by total mass is 11300 / 80 = 141.25 mm or about 5.5″ in front of the frog.

    The tricky thing would be making sure the head and ferrule were perfectly level (playing cards as shims under the scales?). Practically, you’d probably end up with the same error as the finger method because you’d likely never get the setup perfectly level every time, but it’s fun to think about as a mind experiment.

    Not in the workshop now but I’ll try it when I get back Thanks for the blog.

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