Secrets of the sticks

New software, soon to be released as a free download, promises to help bow makers measure historical examples and adapt their own methods accordingly. Nelly Poidevin explains how it works

Equipment set up to measure the stiffness of the bow stick, as shown in Figure 3

For some time now, I have been using a new kind of tool in my workshop. Part of it is visible near the workbench, but most of it is housed in my computer. It arose from a collaborative project called PAFI (Plateforme d’Aide à la Facture Instrumentale, or ‘platform to support instrument making‘) and is basically a system to measure the thicknesses of the bow stick, its camber and the stiffness of the wood. Each of these is something over which the bow maker has control (stiffness coming partly from the choice of wood). With this system I can record the data for every historical bow that comes into my workshop, and use it to guide my choices when making my own models.

First of all, I take a succession of thickness measurements along the length of the stick: the vertical and the horizontal diameters. They appear as a curve on a graph (figure 1) which shows all the peculiarities of the thicknesses across the length. Then I take a backlit photo of the untightened bow, and use the PAFI software to record the camber measurement, taken from the centre line of the stick. The camber is represented by a curve on another graph, where the longitudinal and vertical axes have different scales. Figure 2 shows the difference in camber of three bows, by Peccatte, Lafleur and Pajeot, allowing us to see clearly the evolution of the bow curve (see Paolo Sarri’s article in the last issue).

FIGURE 1 Graph comparing the thicknesses of bows by Peccatte (red) and Pajeot (green)

Finally I measure the stiffness of the stick. Two methods are possible: the ‘static’ method consists of measuring the deflection, i.e. the vertical displacement of the stick at a single point, under the effect of a weight applied at this point (figure 3a). The ‘dynamic’ method is based on measuring the vibration of the stick when loaded by a known mass. The frequency at which the assembly oscillates when subjected to a slight impulse is linked to the stiffness of the stick at the location of the mass (figure 3b).

FIGURE 2 Graph showing the variations in camber of sticks by Peccatte (blue), Pajeot (yellow) and Lafleur (red)

ALL IMAGES COURTESY NELLY POIDEVIN

FIGURE 3 Two different methods of measuring the stiffness of a bow stick

The stiffness of a stick depends both on the rigidity of the material, and on its geometry – namely the length, the shape of the cross-section (round or octagonal), and the thicknesses. Since the stiffness and geometry of the stick are both known, the PAFI software can calculate the intrinsic rigidity of the wood (known as Young’s modulus). The more resistance the material has to deformation, the higher its Young’s modulus. When it comes to making a new bow, the system can also be used to assess the elasticity of a raw stick before planing it.

The PAFI system offers very practical possibilities for archiving objective bow characteristics.

I now have, in condensed form, information on many historical bows that I have been able to measure in museums because the procedure is fast and noninvasive. The representation of thicknesses and camber makes it possible to compare bows by displaying several curves simultaneously. It has also broadened my understanding of the bow’s historical development. Having access to the mechanical qualities of the woods used by historical bow makers is an utterly new opportunity. In addition, it is possible to compare the stiffness of bows of different lengths, or made from different materials, which often happens when dealing with bows made for early music performance. A simple deflection-measuring device does not enable that; it only allows identical models to be compared.

Of course, I also extract and archive this type of information on my own bows. I characterise the woods, track the production process, and adapt it to each type of wood. The system also helps me when it comes to adjusting the camber of my bows. Not only does it allow me to check if a bow has lost its original camber, but another feature helps me estimate the optimum amount of camber to give my sticks. It does this by calculating the hair tension, which can be estimated from a photo of the tightened bow (figure 4).

FIGURE 4 Graph showing the camber of a bow made after a 1657 Gabbiani painting, when at rest (unbroken line) and under tension (dotted line)

The process uses a mathematical model to simulate the deformation of the stick as a function of hair tension. On top of that, the software has a very practical feature when making copies of bows: it simulates the changes in geometry that you need to apply when you want to reproduce a bow with a different wood from the model. It calculates the diameters to be applied, considering the Young’s modulus and the density of the two woods, to obtain either the same stiffness or the same weight.

THIS SYSTEM HAS BROADENED MY UNDERSTANDING OF THE BOW’S HISTORICAL DEVELOPMENT

The PAFI software is the result of research work carried out in the Acoustics Laboratory of Le Mans Université (LAUM). It will soon be made available as a free download from the ITEMM institute’s site (https://itemm.fr). The equipment is light, and can be made easily at home: it consists of a deflection frame made of aluminium bars, 3D-printed supports and a backlit screen. Tutorials will be put online for the manufacture of this material. Training on the use of the software will be proposed in practical sessions, beginning in May 2021. PAFI remains an interactive project, and as far as possible it will be enriched with new features suggested by users. With this collective tool, we hope that the PAFI system will become a great resource for exchanging information on bows.